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‘¬ E topo+



‘Each point is a world in itself.’ Leibniz, on the Monad, mind of space-time.

‘Space is motion relative to a frame of reference.‘ Einstein on the Non-Euclidean point of space-time.



 Mathematical and Logic Languages.  Geometry: Non-Euclidean Postulates.

1st Postulate: Points with Parts: The 3 Fractal Topologies of Super-organisms.

5th Postulate: i-logic Points of View.

2nd Postulate: Waves of Energy and Information.

4th Postulate: Self-similarity.

3rd Postulate: Planes of Existence.  Organic, Social Classes.



1. The fractal point, Non-Euclidean, logic geometry
2. Duality
3. trinity
4. Superorganisms.

Abstract IN THIS POST, complementary to the one on I-logic, dedicated to the inner structure of languages as mirror of a ternary, ∆§t Universe and its logic properties and the way they create reality, we shall introduce the most formal ‘perception’ of those 5 Ðimotions, that provided by Non-Euclidean geometry… 

The method of Gst derives all what exists including languages, as mirrors of reality from the realization that all  is a by-product of the 5 Ðimotions of space-time, themselves, ‘degrees of grey’, of the two ‘extreme’ purest forms of Space – absolute stillness or languages of pure form, ‘residing’ into an emerging ‘wholeness’ or upper scale, ¡+1, of the fifth dimension – and time (absolute motion or entropy, dissolution of the being into an scattered, ¡-1 lower scale or 4th dimension).

So space, form, yin and time, entropy, yang, combine into the 3 intermediate states, we perceive in a single plane, often as adjacent topologies of a superorganism:

  • Limbs and fields of locomotion (ordered entropy with no scattering or dissolution, akin to energy).
  • Heads and particles of informative perception (form with motion, as it allows the being through its language to move and interact with its world).
  • Reproductive bodies of information and energy that combine and iterate both.

So we shall redefine the main branches of mathematics, starting by its most important, geometry and topology with 5 Postulates that relate to those 5 Ðimotions and will be the basis on the future for a more vital model of mathematical thought as mirror of reality. To that aim we redefine the 5 most important elements, axioms and postulates of Euclid in correspondence with those 5 Ðimotions, taking into account the ‘cyclical nature’ of reality that either after completing a ‘world cycle of five Ðimotions’.

1Ð-5Ð: So the first-fifth postulate defines a point as a mind of perception, akin to the first Ðimotion of being – to perceive; and the fifth-first postulate that defines a point as a world in itself, a superorganism with its inner parts are the same. We just might consider that the point has evolved and grown to emerge from its minimal ¡-1 state in the first postulate – points with inner breath; into a full super organism, ¡º, living in the ¡+1 world, in the fifth postulate studied here.

 2Ð: And it has done so through a process of locomotions and changes of waves and forces of communication with other points that define the second postulate – lines with inner breath…

3Ð: And then it has formed planes, defined as social networks that correspond to the third Dimotion of energy and reproduction, becoming a super organism.

4Ð: According to the fourth postulate of congruence, which defines its relationships with other beings, based in his ‘angle of parallelism’, such as similar beings evolve socially together in groups, complementary ‘left-handed female/right-handed male’ beings come together in couples, and beings which are not equal neither complementary enter either in relationships of entropic perpendicularity, or ignore themselves if their worlds are ‘disconnected’. So the fourth postulate gives us the ‘¡logic rules’ of engagement between forms and particles.

And so we establish an immediate relationship between the fundamental concepts of geometry, the point, the line, the plane, and its congruence or dissimilarity, its relative parallelism and perpendicularity, and the 5 Dimotions of existence, the point is the mind that perceives first, the first Ðimotion; the line is the point in motion, in cycloid patterns, or two points communicating with smaller ¡-1 parts, as in the Fermion<Boson>Fermion relationship of forces; the plane has ‘holes’, it is a network of reproduced points socially connected into the 3 different species of networks that make a super organism (informative, reproductive and entropic, digestive, moving networks), and all this is ¡logically established according to the relative dissimilarity or perpendicularity between the beings (4th entropic Ðimotion) or social parallelism that evolves the point into a superorganism, a new whole (5th Ðimotion).

But as we have seen, the process of cyclical repetition of the 5 Dimotions of space-time, from the point to the wave to the network according to congruence or dissimilarity that will bring an entropic dissolution or a social evolution of the system into a new plane of existence is profoundly embedded in the duality of ¡logic systems that either devolve perpendicularly or evolve socially in parallel waves. 

Thus we can also treat those 5 Postulates in terms of the ‘growth’ of complexity in its logic points of view, from the ‘Aristotelian’ fractal point, the self-centered monist being, which merely absorbs as a black hole of information, the energy and forms around it within its language; to a more objective dualist view of reality, as the point becomes complementary of a second point, communicating and exchanging energy and information with it, to the social network with its complex organic logic, to the planes of existence with its relative infinity of points merged through ‘social love’ into a whole.

So a logic view of those postulates will move from the selfish mind into the complementary couple, into the ternary super organism of 3 networks to the relative infinite world of multiple points of view in which the being co-exists. And so we talk also in the second part of the growth of logic ‘stages’ in the awareness of the point that perceives, on the existence of other points and societies and worlds outside of it.

In that sense, aware that for some reason, someone is reading this post on this hardly ever seen, never commented web, according to the laws of information that improve the message in each cycle of feed-back communication I have cleaned it up a little bit.

l§, July, 2018



‘Gods are unmovable, the primary cause which moves the energy of its vital space’. ‘We are all Gods.’ Aristotle on the mind.

All systems have a mind, a concept closely related to that of a head-particle-linguistic class, or informative Tiƒ point of view of a super organism, as minds are the points of maximal communication of a certain ‘space-time organic system’, and so most likely the mind is in the Tiƒ particle-head-linguistic class of the society. The mind is by essence selfish, subjective, with perspective, distorting with his will of actions the Universe, to make it converge into its inner mirror, dying and or reducing its total information in the process of obtention by the mind of an image of an outer self, with deception as the tool to camouflage its inherited weakness and obtain a token of energy and form of each other part of the Universe. As the mind constructs its consciousness of being a knot of thought=language=perception, it crashes into itself – making it grow is stiffen its surroundings till all is silence, quietness, mind-view, 0-sum, void.

Minds order as linguistic gods a territory around themselves, its fractal body and entropic world. As such they are the linguistic Aristotelian, final unmoved singularity Gods of reality. In the graph we see them ordering with different languages, different scales of reality which will reflect in a larger whole, the linguistic image they hold.


selection of languages

In the graph, the Universe in all its ecosystems selects the species who speaks better languages. Till recently we thought the word, our human language was supreme, and indeed in our ecosystems of history prophets and politicians ruled, but mathematics turned out to be a better language and finally in this blog we shall show you how the enhanced forms of logic, I-logic and mathematics non-e mathematics are the best language mirrors as they encode fully the true properties of space and time, form and motion the fabric of reality. So we shall improve the laws of those languages.

In other words, languages are selected by its efficiency to mirror the spacetime scales and other minds of the Universe, and for that mathematics has been the most fruitful, likely language of atoms and particles of matter.
So how we can upgrade mathematics to the pentagonal logic of the Universe and its organic scalar §paœ?
The answer is the non-Æ postulates of vital mathematics studied in this post and subsists.



The foundations of mathematics as an experimental stience, which was clearly proved by Godel and Lobacjevsky and sponsored by Einstein, and its grammatical structure as a ternary form that mirrors the laws of GST and its Generator of Space-Time beings IS the key new stience in which all other GST scales rest, as logic time and mathematical topological space are the best mirrors of the ultimate substances there are, in most ‘minds’ of the Universe. Indeed, it all seems to indicate that the ‘founding scale of reality’, the ∆±3 galaxy atom and its ‘mind-singularity’, is primarily a mathematical, logic structure and so the mathematical, logic languages seem to give us the maximal information on the Universe of timespace.

How humans ignored all these ‘evident’ truths is as usual a problem of ego, which made humans think that ‘only God and man spoke mathematics’, and even that ‘humans create/imagine mathematics’ and so they were the ‘chosen species’ (axiomatic method), and many other ‘mind-biased’, human anthropomorphic perspectives which culminated in the dismissal in the XIX c. of the fundamental elements of logic mathematics, the point of simultaneous space and the number of sequential time. 

Instead humans decided in a curious paradoxical inverse fashion to that of Physics that the elements origin of mathematics were NOT experimental space-points and time-sequence numbers – the minimal units of reality – but the ‘modern’, more complex categories (sets, groups and its combination in category theory) of reality. Why is that? 

Essentially because the mind is synoptic, a mapping of reality as a whole. And so because egotist humans thought their mind ‘imagined points, congruence and planes’ (Hillbert), they ‘created the philosophical foundations of mathematics’ from the roof of the mind down, as ‘God would had it’. But when studying physical systems, despite Bohr’s attempts to ‘invent particles and waves’, the madness of egotist humans stop in the experimental fact that ‘atoms’ do exist! So they accepted the inverse analytic concept that the smallest parts are the origin o the whole. Thus alas, we have physicists’ idealism, who think all is created from the bottom down, vs. the mathematical idealism of all coming from the whole ‘category, set, group’ structure. All of it, without even acknowledging the cultural influence of German idealism, the true origin of the cantorian ‘set paradise’, Hilbert’s axiomatic method, Bohr’s interpretation of the observer creating the ‘moon’, nazism, communism and the Berlin olympic games, II world war and the holocaust among other things.

Yes, I feel sanguine today, fed up of the egotist theory of reality… Instead we are going back to the basics. The point is the fundamental unit of reality in space, and as it evolves sequentially in time, and grow in ‘scales of size’, it becomes the number, the fundamental unit of time. And those are the foundations of experimental mathematics – merely that we need to upgrade them according to our discoveries on the cyclical nature of time and the fractal nature of space, defining ‘points with breath’, and ‘social numbers’ to fully understand them.

Non-Euclidean Space

The formalism of ∆-planes: Non-Euclidean definitions.

In the graph, the 5 postulates of Non-Euclidean geometry define a point with parts, a line as a wave and a plane as an organic network of points:

The 2nd postulate explains the interaction between two points connected by a wave of communication or ‘line’; the 3rd postulate explains the type of interactions between 2 points according to their relative equality, which will bring them together into a social network or dissimilarity, which will make them not interact or enter into a Darwinian relationship in which a point absorbs the energy of the other.

Self-similarity is required to start an organic process of eusocial evolution; or else systems that do not understand their information use each other as energy, in Darwinian hunting processes or ignore their paths.

The 4th postulate defines the creation of networks made of systems of points across multiple scales of space-time. It defines spaces as networks of points, interconnected by flows of energy and information: All in the Universe are thus complementary systems made of networks of non-Euclidean points. Finally the 5th postulate that explains the processes of absorption of waves of energy and information that the point gauges to act-react with the Universe.

It is then the social evolution of points into numbers and structures – groups, sets and categories (not the bottom but the top element of the evolution of points and numbers), what mimics the creation processes of Nature, where identical beings, points of ‘one dimension’ (as seen externally, but with three internal dimensions), evolve socially first into lines-waves (2D, as waves have volume, thickness, made of points with volume), then into topological networks (planes), and finally recreate a larger ‘fractal point on the ∆+1 scale’.  So the postulates of vital mathematics explain in a synoptic mental way how points evolve socially through scales of dimensions, to become first waves, then planes and social numbers which create a final Non-E ‘fifth postulate’ of a larger whole point through which infinite parallel flows of energy and information can cross:

The new 5 postulates of a Non-Euclidean, fractal geometry of Multiple Spaces and Times are:

1st Postulate: ‘A fractal point is a world with an inner content of information that creates its 3 internal, topologic, organic dimensions and a content of energy that traces its external motions=time arrows’

2nd Postulate: ‘A line is a wave of fractal points.’

3rd Postulate: ‘2 fractal points are self-similar when their external, spatial perimeter or their inner information is equal. Similar points form organic networks by sharing their energy and information. Dissimilar points ab=use each other in Darwinian relationships’

4th Postulate: ‘A plane is a network that joins points through waves of energy and information.’

5th Postulate: ‘Non-Euclidean points perceive energy and information: A fractal point has inner apertures to the world, through which multiple waves of energy and information can cross.’

The first postulate defines a point with form and energy. Points are not ‘points with no breath’ (Euclid), an abstract definition that created the simplified concept of a space-time continuum but ‘fractal points’, which grow in size when we come closer to them. And so stars are points in the sky that become huge as we come closer to them. And a microscope discovers an entire world in the minimal size of a cell. Einstein offered a partial solution to this conundrum considering that from our scale of size, those Non-E points seem to curve the information of the universe that fluxed on it. But Leibniz had given a better answer: ‘the smallest point is a world in itself’. This is the meaning of a fractal point, whose internal parts respond to the 3 topologies of a 4-dimensional Universe: a hyperbolic, informative system; an energetic, planar or spherical membrane and a cyclical, toroid region with reproductive organs. And we shall find those 3 topological regions in all points-species of the Universe.

Non-Euclidean points are the souls, Atmans, Monads of the Game of Existence, the knots with a living will, which they display in their action, exi. Leibniz failed to realize they would communicate. Buddhist with the concept of Atmans are closer: knots of relationships with other i-points. Such multiple, perceptive Universe merely extends the nature of being human, a self-perceptive point always feeding, perceiving, reproducing and socializing, which is also what life does, to all the entities of the Universe.

All is life. All shows the will of life. All keeps reproducing self-similar points of view, points of order. A point is any entity of the Universe. In a more detailed analysis those parts turn out to be self-similar in geometrical terms in all of them, defined by the three canonical topologies of a four-dimensional Universe, which describe an informative, hyperbolic region or ‘head’, a toroid, ‘reproductive body’ and lineal or planar energetic limbs and membranes, common to all the points of the Universe. Thus, we define time cycles, forms with motion, its multiple knots of time cycles and networks with a new geometry of space-time, Non-Euclidean geometry, born of the completion of the work of Einstein in physics and Riemann, Lobachevski in the field of mathematics. Since now all points have form and motion, they have breath; and since now all lines have form and motion they are waves; and since now all planes are networks, they are discontinuous planes. Thus, the new formalism of space-time redefines also the geometry of the Universe in dynamic, discontinuous terms:

Networks are made of relative points with form and motion, which can be defined as time cycles – trajectories traced by an entity in search of energy, information, reproduction or social interaction. Those time cycles enclose a surface of vital space or energy and so they define a certain space-time. Any entity will however trace many cycles in search of its organic motions to feed, gauge, reproduce and evolve socially into bigger networks. So each entity will be a knot of multiple time cycles.

Those knots of time cycles become fractal Non-Euclidean points. The basic unit of the new paradigm is thus mathematical – the point – but a very special point, a fractal point which grows in detail and information the closer we come to it, till it becomes, as Leibniz put it, a world in itself with internal complementary networks=organs of energy and information (fields and particles in physics; limbs, body and head in biology).

In the formalism of Systems sciences we call them Non-Euclidean points, since they are points through which infinite flows of energy (parallels) and information can cross. We also represent them with the symbol ‘i’, which is the next vowel to the A-ristotelian, E-uclidean paradigm, the symbol of information and a visual image of the 2 components of the point, the informative, cyclical part, o, and the lineal, energetic one, |, which we call the body and head of a biological Point; or the field and particle of a physical point (Principle of Complementarity).

The universe is made of networks of such i-points, and each network is what we call a world or discontinuous space-time, st, unit of a bigger fractal network, a new st-point in itself. So a network of particles becomes an atom, which becomes an st-point of a molecule and so on till creating the Universe.

Even humans can be studied as Non-E points, in which each head is indeed a spherical point that communicates energy and information with other humans, forming social networks.

The anthropomorphic reader might think that humans are different from the rest of points of the Universe, but it is a fact that all points obey in their actions and communicative flows within a network the same laws: humans and electrons behave the same when they move through slits or in herds; the geometries of social groups are also the same; and the ultimate purpose of those points, to feed on energy and information, whatever kind, is also the same in all networks of the Universe.

Thus the laws of networks become the social, organic, reproductive why of all beings of the Universe: the Universe reproduces information and organize forms socially into networks. From magnetic and electric fields, made of magnetic and electric constants that mix and reproduce a light wave to fundamental particles, quarks and electrons that absorb energy and reproduce new quarks and electrons, to energetic males and informative females that reproduce together, all in the Universe can be described with the formalism of networks, connects the why with how and when of the 3rd paradigm of metric measure that has analyzed those networks, its motions and forms in detail. Why those i-points with an ego-driven will that desires selfishly more energy and information and self-reproduction collaborate in herds, becoming parts of a whole has to do with the complexity by which the arrow of social evolution impose systems to its parts. Parts become enslaved by their dependency to the higher energy and information provided by networks.

5D isomorphisms show a Universe made of multiple scales of broken, intertwined ‘spacetime’ membranes. Thus, its formalism must combine geometric equations and causal, logic, sequential time laws.

So we need to upgrade our simplex space language (continuous single space defined by Euclidean geometry) and time causality (Aristotelian one-dimensional causality from past to future, A->B) to explain multiple spatial scales and 3 time dimensions, past-energy and future-information combined into complementary, present beings. I baptized this new mathematic-logic formalism, ‘i-logic geometry’ that completes the 5 Postulates of Non-Euclidean Geometry.

What mathematicians did was rather a runaway path. Because once geometers realized that multiple lines can cross a point, they could not use any longer the Euclidean definitions.

Now points, lines, planes and equality could no longer hold under the definitions of Euclid (points, lines and planes with no breadth), they remained undefined, when Hilbert, the father of modern mathematics affirmed ‘I imagine lines, points, planes…’.

Instead the proper solution was to redefine them in terms of their ‘inner parts’ as fractal points that grew in size when we observed them with a more detailed ‘hyperbolic geometrical view’, as that unveiled by non-E mathematics. So we ‘create new postulates of geometry’ by defining its essential elements, points, lines, planes and the laws of congruence (similarity) between them, as well as re-interpreting the concept of a Non-Euclidean point crossed by infinite parallels (5th postulate) in terms of a mind that absorbs flows of energy and information: O-mind x ∞ time cycles = Spacetime mapping.

So T.œ redefines points, planes and line-waves and their relative laws of equality (also called congruence) and continuity (which no longer holds), to refound mathematics on the basis of a far more realist view of its laws as ‘experimental laws’ that reflect the geometry of the 5th dimension and the complex casualty of a world with multiple time motions. And consider that those points with volume form social ‘numbers’, whose laws are therefore related to the laws of the 5th dimension that brings parts into social wholes.

Knots of Time cycles: the fundamental particle.

Once we have studied the minimal units of the Universe, the action of space-time, we shall define the main structural, architectonical element of reality, the knots of time cycles, existential points, œ, which perform those actions of existence, site of will and perception of the Universe – whose simplest definitions in philosophy are the monad of Leibniz, the mind of Descartes, the God of Aristotle, and in mathematics, a Non-Euclidean point, the unit of Einstein’s gravitational laws.

Systems are knots of time cycles of exchanges of energy and information with its space and time parts, Œ, which allow them to survive in the Universe.

Thus the first ‘stable structure of reality’, is a knot of time cycle which swiftly goes webbing around the paths of its exchanges of energy and information, ∆±exi, actions, its survival strategies, trying to maximise its existence, Max. ExI, in a state of perpetual balance, E=I…

This dance of being and not being is performed by each Œ, knot-function of existence, defined both as an infinitesimal point from its upper perspective and an an absolute whole from its lower plane, since all knots of times space cycles web their existences through several of such plane

The zero-points: monads that order the Sentient Universe.

This first example of the complexity of the Universe, which many scientists, mostly physicists, have shunned off, obscuring a deeper knowledge of reality, hopefully prepares you to persevere in the understanding of the complex ambivalence of the Universe, simplified by the human mind, whose equation in the metric of the 5th dimension – one of the infinite varieties of Tƒ x Sp = ST – we can now explain:

tO (infinitesimal zero-point or mind) x ∞ Sp (Universe perceived) = RI (constant mapping of reality)

What a mind does is rather simple. The Universe out there has infinite time cycles that carry the in/form/ation of the Universe in the frequency and form of its cyclical motions. This is an ∞, which we cannot store inside us.

So we simplify all those motions into ‘forms’ perceived as extensions of space, Sp.

On the other hand the mind is a Tƒ, spherical system, with 2 different spheres: an external membrane with sensorial detectors, which ‘shrinks’ into a relative smaller point, the eye and then the brain, which transforms Sp, the infinite cycles made into spatial forms, and keeps shrinking them to an infinitesimal mapping of reality, a still image, very much as the way a camera reduces reality to a virtual shallow image in 2 dimensions.

And this can be done because of a property of spherical forms, called the Poincare Conjecture: you can  shrink  a topological sphere (any closed membrane, a skin, a planetary surface, is a sphere), as much as you want without deforming its information.  So we find infinite minds in the Universe, ‘monads’ in Leibniz’s terms, which as he said ‘are points, which store a world in it selves’.

So we could also define the Universe as an infinity of ‘Universes’, fractal minds perceiving reality from those zero points. What all those fractal minds do? Time cycles? Why. Because they keep perceiving and gauging information through them, and they keep absorbing ‘energy’ to move, and they keep reproducing their time cycles in parallel forms of space-time, and they keep evolving with other points into larger systems of points, topological networks, which have organic nature.

Now, we have described you the Universe internally, in its ultimate cause. This actually had to come at the very end of this post. But i just rewrote it ‘again’. I do rewrite many times these posts, as i am fully aware nobody reads them (-; Yet also because the universe is a simple mandala, an iteration of infinite minds, ∏Tƒ, which are knots and networks of time cycles, perceiving, ∑Sp, infinite motions in space, and doing actually the same. So we can rewrite our generator as: ∞ ∑Sp x ∏Tƒ=i.

And this will represent, infinite bodies/waves in motion, which carry heads/particles of information that move and perceive across the Universe, from small particle-points, to large black holes, from bacteria to living beings.

You see, the richness of the ‘Fractal Generator’ of the Universe, and the importance to be able to see the multiplicity of it all? Its varieties? In that regard, a Taoist would be probably more prepared to understand the 5th dimension, despite its mathematical rigor, when he said: ‘the function of existence is not the perceived reality, but the game of yin=form and yang=motion, which combine creating its 10 thousand beings’.

This function of existence is then another way to express the Generator equation:  e x i = ST. Here we could say that the combination of ‘energies’, vital spaces with motions, e, multiplied by informations, ‘forms’, e x i , create a ‘constant space-time being’, ST.

Non-Euclidean Points and bidimensional network-planes. The new mathematical formalism.

When Einstein said that Leibniz was right but we had to reconstruct the building of western science he showed an understanding of the difficulties to recast the Universe on the new light of multiple times and multiple energy quanta. But he did not have the tools to do so. In that sense it was necessary to evolve  further mathematical concepts to fully grasp the underlying structure of that world of infinite time cycles and space quanta. As 3 new concepts were required:

The concept of a fractal, which is a geometry that repeats in different scales of space, with similar forms. It implied that reality was broken in ‘wholes’ made of smaller ‘parts’ that were similar to those wholes. Mandelbrot discovered them in 1973. And since the model of relational space-time needed fractals, it could not be found before.

The completion of Non-Euclidean Geometry, which Einstein used to describe the Universe of multiple clocks of time. In Non-Euclidean geometry, points have ‘breath’, that is, they can hold infinite parallels that cross them. This miraculous contradiction (a point without breath can only fit logically a single line), made Einstein curve the lines to fit them, but still they do not fit (curved or not the lines are still many and the point without breath only fits one).

I solved the impasse that made Einstein conceive the concept of space-time curvature, when I combined it with Mandelbrot’s fractal concept. Since now a particle-point, a star-point, a cell-point, any entity which can be called a ‘point’, could be considered a fractal that grew in size when we came closer to it and enlarged it at scale. And as it grew, you could fit many parallels, as it acquired volume. Thus the logic contradiction of Einstein’s work was now solved.

I did then developed the 4 remaining Non-Euclidean Postulates, defining a point with breath or fractal point. A line as a wave of points with volume (since now points with volume formed waves instead of lines). Then a plane as a bidimensional membrane with thickness, made of networks of points. And suddenly the Universe became much more real in its mathematical description. As all was made of planes of space-time: ‘networks of points with volumes’ which seen in detail were actually, cyclical forms with rotational motion, time cycles, made of smaller, cyclical clocks with motion, new time cycles, again organized in networks, which were made of smaller… Suddenly an astoundingly beautiful architecture appeared, a reality where the words of Leibniz acquired its full meaning: ‘each point is a world in itself’.

 The nature of mathematics and logic.

The first concepts and ideas of mankind tend to be simple, intuitive and truth. The forest is clear and the details of the trees do not hide the whole. So the oldest philosophy of the Universe, that of the Chinese agricultural Neolithic about a world made of yin=information and yang=energy, which combined to recreate the infinite ‘waves of existences’ (Ch’ang), is still the most accurate philosophy of reality, now forgotten with the arrival of so many scientific details that the overview of the forest is lost.

The same happens with the understanding of time, which all earlier civilizations considered cyclical and causal, synonymous of change; and so they study all different types of change, establishing repetitive rhythms of change and causal relationships, creating the science of Logic (Aristotle).

The Greeks also defined mathematics as the language of space and so Geometry became the foundational science of mathematics; and it remained so till the XVII century, to the point that Al-Jorizim, the founder of modern mathematics (Algebra and Algorithms are words derived from his names and books, translated by Middle Age Spanish mathematicians and then spread during the renaissance to Europe), proved all its quadratic theorems with geometrical methods.

Mathematics is defined in encyclopaedias as the science of sequential numbers (algebra) and static space (geometry). Till the XIX century, the science of sequential numbers or ‘mathematics of time’ used only Aristotelian Causality with its single time arrow to order them. On the other hand, the ‘mathematics of space’ considered only a lineal, continuum space defined by Euclid. Both sciences were fusioned by Descartes (analytic geometry) with his Cartesian Plane; and we can thereafter talk of mathematics of spacetime, albeit in its simplest conception: a single, static space, and a lineal, unicausal time.

It would be latter in the XIX and XX centuries (with the exception of the insights of Leibniz), thanks to the work of Frege, Boole, Riemann, Einstein, Poincare, Cantor, Bourbaki, Mandelbrot and Computers, which this work advances a step further, when Space and Time – hence Logic and Geometry – were first mixed, but without a full formalism that made possible to extract all the laws of spacetime and grasp in depth the meaning of those languages, due to the limits of the Cartesian single space-time plane.

A theory of multiple spaces-times thus has to refound the key concepts of mathematics, the plane, which now is a multiple plane in which each point creates its own frame of reference, interacting with other points and planes through exchanges of energy=motion and form that re-establishes the balances between their distances and topographies; and the number is now a network of self-similar points that have at least a formal bidimensionality. Mathematics includes several sciencces in one: the science of numbers can be stretched to consider the science of networks as each number is a point of a network with a geometrical form.

Numbers and geometry are thus essential sides of the same coin. On the other hand geometry is mainly topology, related to causal transformations of a complementary networks of energy and form, whose ‘numerical’ cells go through growths and extinctions through life, described with differential equations. Those equations thus can be reduced to cases of the generator equation, Se<=>Ti, which in this manner resumes all other differential equations. And indeed, when we use equations to explain repetitive events of nature we are normally mapping out an exchange or transformation of energy into information, which in a generic way is represented by the exi function.

Thus topological networks, differential equations that map out the life/death cycle of an event with its growth and diminutions of energy and information, exchanges of energy and form between networks and membranes and causal chains that repeat those events till creating very complex systems, are the key mathematical operations of 2 sciences, logic and mathematics, in which the most general laws of networks are written. Those Mathematics of multiple space-times have illustrious precedents:

In the XIX and XX century mathematicians developed theories of multiple spaces and defined spaces with motion (Klein), and spaces as networks of self-similar points (Riemann) but maintained 4 of the 5 postulates of Euclid, the single Cartesian spacetime continuum and a single causal arrow of lineal time in its theory of numbers.

Thus a theory of multiple space-time arrows requires the evolution of the science of space (geometry), completing the 5 postulates of Non-Euclidean Geometry and also the evolution of the science of temporal, sequential numbers, expanding its laws of causality. This was partially done with the use of the Complex Plane, since real numbers roughly correspond to the properties of continuous energy and complex numbers to the property of discontinuous, informative time. But its dual nature as an expression of the different properties of space and time has never been fully understood even if Physicists use the Complex plane in modern physics.

In that regard there are two possible representations in a plane of complex, informative numbers:

– They could be placed in the inverse, negative side of the graph of Cartesian coordinates as the arrow of information – to better represent the duality of energy and form (I<=>E). Then many results obtained with complex numbers become intuitive, as it is the case of the metric of Special relativity, where the time factor has a negative side – c2t2 meaning indeed that time-information contract space and ‘rests’ to the positive arrow of Einstein’s equations.

– Or they can be placed, as it is customary in the perpendicular Y dimension. Since a dimension of a mathematical plane becomes a sequential order of numbers, then the Complex plane becomes a bidimensional mathematical representation of the 2 simplex arrows of time, energy and form; while a 3D complex plane represents 3 time arrows where exi=z represents the reproductive arrow.

Finally a fractal, multiple space-time built with a series of complex planes (a task started by Riemann with his description of polynomials as a series of planes of space, stacked one after another), is the appropriate form of defining the 4th arrow of time.

From a philosophical perspective the study of multiple sequential time (algebra of Multiple Spaces-Times) and multiple, fractal spaces (5 non-E postulates) improves the accuracy of mathematics as an image of the reality of multiple space-times and explains its ultimate meaning, as the science of space (geometry) and time (numbers): Space is mathematical, geometrical; time is logical, sequential, numerical and the conjunction of both is organic; reason why complexity and system sciences, who observe the Universe from an organic perspective are the sciences of sciences.

We cannot treat all the aspects of complex mathematics in this introduction. We shall therefore focus on. its 2 key elements: the geometry of numbers with form and its postulates that describe how the 4 arrows or wills of time construct networks of fractal points and the algebra of the generator equation, which describes that geometrical construction from an analytical, numerical, differential perspective.

Recap: Geometry is the language of spatial form; Logic is the language of time events. The algebra of the generator equation of space-time cycles and the non-Euclidean geometry of fractal points fusions both creating a model of multiple, sequential dimensions of numbers and multiple planes of space closer to a description of reality and its organic systems.

This is done by resolving the 5 non-Euclidean postulates of Geometry, which describe knots of time arrows as points, and by observing the self-similarity of mathematical equations, which describe groups of knots of time arrows as numbers and the equations of Multiple Spaces-Times derived of the Generator equation of the Universe or Principle of conservation of energy and information. Thus, the 4th paradigm upgrades the postulates of Non-Euclidean Geometry and the foundation of Logic to include the causal relationships between time arrows and explain better a universe of multiple spaces and a logic to of Multiple Time cycles and arrows of time cycles.

In all those systems planes are made with cellular points, Riemannian spheres with volume that form lines, which are waves between points that exchange ‘Dimotions’ and information and planes, which are organs of self-similar points that process ‘Dimotions’ or information in parallel networks.

Thus the 5 Postulates of Non-E Geometry vitalize the Universe as a series of networks of ‘Dimotions’ and information of self-similar cellular points. Since the line and the plane acquire volume and become self-similar to the commonest forms of the Universe, the wave and the network of points with a 3-D volume.

This simple fact explains one of the most important discoveries of modern physics, the Holographic principle, according to which information might be bidimensional, as in the screen of a computer or the page of a book. Now bidimensionality no longer becomes ‘magic’ since the 3rd dimension is the relative size of the ‘fractal point-particle’. Thus bidimensional sheets of information do have a minimal 3rd Dimension; the inner content of the point, which in a relative universe of infinite sizes seems to us a particle-point without volume, as we don’t see either the volume of a sheet of paper or a pixel.

All in the Universe are thus complementary systems made of networks. Now this might sound absurd to the anthropomorphic reader that thinks humans are different from the rest of points of the Universe, but it is a fact that those points obey in their åctions and communicative flows within a network the same isomorphisms: humans and electrons behave the same when they move through slits or in herds, the geometries of social groups are also the same and the ultimate purpose of those points, to feed on ‘Dimotions’ and information, whatever kind, is also the same in all networks of the Universe. And so that group of isomorphisms of networks becomes a primary why for all beings of the Universe.

A fact the leads us to the final element needed to understand the why of the Universe: ‘non-Euclidean points’ organize networks that become points of a higher scale, which reproduce and organize new networks; and so the Universe keep growing in fractal scales, from particles that organize networks and become atoms that organize networks and become molecules that organize networks and become cells, that become organisms, that become planetary societies and planets and stars form gravitational networks that become galaxies, organized by dark matter into Universal networks.

Because all entities have motion reproduction is merely the repetition of a motion with form. Because each entity has 4 time arrows, all of them trace multiple trajectories in search of those arrows, hence they realize multiple time cycles.

For example, a human feeds on ‘DImotions’ and information with body and head, reproduces through multiple social cycles and evolves into societies. Our åctions are more complex but essentially the same of those of any particle.

So the unit of reality is a space-time cycle, and many of them create a knot of time cycles or entity of reality, which will be reproduced by repeating those formal cycles with motion in other region of space-time; and many of those knots of time cycles, which are self-similar, since they are born from the reproduction of a first form, come together with self-similar beings into networks. Some of those networks are spatially extended with a lot of motion (fields in physics, bodies in biology) and some are very tight, formal, with a lot of in/form/ation, (particles and heads or nuclei in physical and biological jargons). Both types of networks together then create a complementary organism, which is fitter to handle both ‘DImotions’ and form; hence it survives better, it ‘exists’.

Today scientists of measure scorn philosophical and logical analysis of causality in time because it cannot be easily put in numbers. But numbers are only one of the languages of information in the Universe, and many of its properties of bio-logic nature are better described with logic words. In that regard, we can now fusion philosophy and science answering the fundamental question, ‘why we exist’; since once we realize that we are ‘made of time cycles’, knots of time cycles and networks of knots of time cycles, an intelligent, informative, eternal universe of motions and wills of existence makes the dogmas of deism and mechanism, childish myths.

‘What is existence’ cannot be revealed from the simplex point of view of a mechanical world, which cannot explain the fact that we are made of motions with form that leave a trace on space but are essentially åctions in time that have a social finality – to create more complex networks, chaining knots of åctions into systems. This social will of every point and entity of the Universe is completely at odds with a mechanist, fixed, solid, senseless, dumb Universe. Motion in Time and social evolution are concepts that require the capacity to gauge information and interact with other self-similar points to create those organic networks. Further on, dual networks tend to evolve and reproduce new points through exchanges of ‘Dimotions’ and information.

The result is the creation of 3rd network/system: the reproductive network. And so most systems of the Universe are organic, ternary systems made of points (which can be anything from atoms to cells to human heads) organized in 3 networks. We exist as organic networks, to sense flows of ‘Dimotions’ and gauge information. Existence justifies itself.

Those Non-Euclidean points crossed by infinite parallels are able to gauge information, which implies a perceptive, intelligent Universe in all its fractal, self-similar scales of reality – a world in which even the smallest atoms can act-react to the environment, ‘apperceiving’ light and gravitational forces. Aristotle and Leibniz, the 2 foremost predecessors of the 4th paradigm of biological whys distinguished conscious perception from vegetative and mechanical perception.

It means perception has degrees of complexity. So the simplex particles of the Universe act-react in a mechanical way; yet they still gauge information, reason why quantum physicists called their theories gauge theories, and they still have 2 complementary networks of ‘Dimotions’ and information, reason why quantum physics is based in such complementary principle.

Yet this intelligent, active, temporal, informative Universe can be described with the formalism of logic and mathematics because its fundamental unit – a spacetime cycle – can be explained with ‘feedback’ equations, used in system sciences to explain the back and forth interaction between two poles or elements of an equation. SeTƒ where Se is a component of spatial ‘DImotions’, a motion element, body or field and Tƒ is a cycle of time that carries information, particle or head, becomes the syntactic, logic, minimal unit of reality.

These simple first elements of reality – points with volume that exchange ‘—motions’ and information, creating waves of Dimotions’ with form (no longer lines – 2nd postulate), according to a set of isomorphisms based in their self-similarity, (no longer equality – 3rd postulate), that makes them evolve into different topological networks (no longer planes – 4th postulate) – make mathematics an organic language able to describe the logic of creation of all systems of the Universe made of infinite fractal, organic networks intersecting and creating when we put them together under those isomorphisms and topological restrictions, the puzzle of reality that the simpler, 3rd paradigm called the space-time continuum and becomes now a General System of Multiple, Fractal Spaces with vital ‘DImotions’ and Time cycles with information, the two substances of which all beings are made.

And so with those 3 scales of ‘existence’: time cycles, knots of time cycles and networks of knots of time cycles (Non-E Points) we can explain all the ‘åctions’ and systems of reality made of those cycles, knots and networks; and describe a complex Universe that exists ‘in time’ more than in fixed space, since it has always motion; it is also dynamic, made of cyclical, feed-back equations whose causal relationships, forms and trajectories are the essence and purpose of existence.

We thus consider a more complex analysis of time arrows, beyond the duality of ‘Dimotions’ and information, which combine creating a reproductive arrow, Sp X Tƒ, and further on socialize, ∑Sp X Tƒ, creating networks. And so the universe has also an organic will: to create networks of self-reproductive points of ‘—motions’ and information.

Yet the most astounding property of those points is to be points of view, points with will, which perform åctions with the purpose mechanical or not, but probably felt in all scales as the inner freedom of the point, of obtaining ‘Dimotions’, information reproduction and social evolution. The 4 wills or whys of the Universe are indeed embedded in the postulates of i-logic geometry. The point to exist has to be complementary, to feed and gauge ‘DImotions’ and information and to last beyond its wearing it has to form part of bigger social networks or reproduce itself to last beyond death.

This simple program self-selects those species that reproduce and evolve socially even if that contradicts the primary individual arrows of the point. Thus the engine of the contradictions of behavior of points is that tug of war between the Galilean paradox of all points which gauge bigger his nose than Andromeda but need to hunt in herds and control the forms of the Universe with self-similar minds, joined in networks, this eternal duality of freedom vs. order, individual ego vs. collective spirit.

Tƒ exist is to act with motion and form, trying to achieve the ‘arrows of time’ or will of the Universe – feeding your ‘DImotions’ network, absorbing information for your informative network, reproduce your system and in doing so, starting an external process of social evolution with self-similar entities to yourself.

Those processes can be described with mathematics but we have to accept an intelligent, perceptive, fractal, self-similar Universe of infinite points of view gauging reality in a mechanical, vegetative or conscious way to explain why it happens. Their mathematical description stems from the duality between geometric form and logical function (hilomorphism).

Thus, the postulates of fractal i-logic geometry define also the basic arrows= cycles/dimensions of the Universe: the 1st and 5th postulate define a point as a system whose inner parts are able to transform and emit ‘DImotions’ and information, Sp>Tƒ<Sp; the 2nd postulate defines an Sp X Tƒ wave of communication that reproduces ‘DImotions’ and form between 2 fractal points; the 4th postulate defines the social evolution of a herd that creates a fractal plane – a network with dark spaces; and the 5th postulate explains a point mapping reality, as it absorbs ‘Dimotions’ and transforms it into information through its small apertures to the Universe. Since even a minimal quark, as Einstein affirms, should be crossed by a relative ∞ number of strong forces.

It is the organic will of all systems that search for those 4 arrows what makes the quark to exist as a knot of such flows of time arrows: a physical particle traces energetic cycles described by the principal quantum number; shapes the form of its trajectory, a fact explained by the secondary quantum number; iterates along the 3 coordinates in similar shapes, an act described by the magnetic number, and gauges information to evolve in social groups, a fact described by its spin number. And those 4 numbers define it as a Non-Euclidean quantum knot of complementary ‘DImotions’ and information with a 4D will of time. And as it happens they express the 4 arrows of time: Sp->Principal number; I-> secondary number; Re-> spin number; 4-> social evolution: magnetic number.

Further on, we can reduce all those topologies of social numbers and networks to the canonical 3 topologies of a 4-dimensional Universe, proving that those 3 topologies have the properties of ‘Dimotions’, information and reproductive events.

And so we talk of 4 ‘arrows of time’ or dimensions of change that create the future: energetic and informative systems and events, which reproduce a wealth of self-similar beings that organize themselves into social networks, creating bigger wholes – new scales of reality. And this simple game of complementary beings that in favorable conditions reproduce self-similar beings, self-organized into bigger social networks becomes the why of all realities. Even the simplest particles, quarks of maximal information and electrons of maximal spatial extension and motion ‘decouple’, reproduce, when absorbing ‘Dimotions’ into self-similar forms, and associate in complementary networks called atoms, made with a central informative mass of quarks and an energetic, electromagnetic, wider body of electrons.

The 3rd paradigm of metric measure is not at ease with such ‘dynamic, spiritual concepts’, even if they can be described with the same mathematical formalisms as the previous example of the quantum numbers show. Those apprehensions however are dogmas, which stem from anthropomorphic beliefs.

Fact is that even the simplest complementary systems (quarks and electrons) interact together and if they can absorb more ‘Dimotions’=motion they are able to repeat=reproduce the cycles of its system. And so we talk of a 3rd reproductive system: from quarks and electrons, the fundamental particles of the Universe that decouple in new particles when they absorb new ‘Dimotions’ to living organisms, the fact that all is motion with form makes easy to reproduce those formal motions in an organic way. Thus the new concept of a world made of formal motions brings about also a more complex philosophy of reality – organicism. Organicism and its mathematical units, fractal points, that gather into social networks called topological spaces substitute the restricted concepts of Euclidean points, continuous spacetimes and mechanism, explaining why all those time cycles exist, guided by 4 time arrows: ‘Dimotions’ feeding, information gauging, reproduction and social evolution.

Those 4 categories are the so-called drives of living beings, the quantum numbers of particles, the 4 dimensions of our light space (electric-informative height, reproductive magnetic width, energetic length and social colors). Thus, there is a ‘Universal Plan’ with an existential finality: to create organic systems, departing from ‘DImotions’ bites and information bits evolved 1st into social networks, then into complementary systems and finally into organic systems, news points of a bigger fractal whole: particles become atoms that become molecules that become cells, organisms, planets, galaxies and Universes. It is the 4th organic why that completes the adventure of science and this work explores in all its consequences.

Reality can be resumed in 2 words: networks, whose flows of exchange of ‘Dimotions’ and form creates the patterns and events of reality and organicism, the philosophy of reality based on them. Organicism means reality and all its fractal parts are made of vital spaces (bodies and forces) and time cycles (informations). We do not exist in an abstract background of time and space but we are made of time cycles and lineal spaces, cyclical and lineal strings if we were to use the restricted jargon of physics, a specific case of the wider jargon of general systems, which evolve socially to create the complex systems of each science.

Those wider, more complex definitions of time and space will substitute and absorb according to the Principle of Correspondence that makes each paradigm a particular case of the new, wider view, the limited concepts of a single space-time continuum and a mechanist description of the Universe, proper of the age of metric measure, which the pioneers of systems sciences and complexity have wrestled with throughout the XX century.

Recap. A Universe made of motions in time, extending through multiple scales of relative space, requires evolving the human languages of space (Euclidean geometry) and time (Aristotelian logic), used to describe the simpler space-time continuum of classic science. This task started by the pioneers of modern science (Riemann, Darwin, Planck and Einstein) must be completed before we can study the properties of physical and biological entities with the new tools of Non-Euclidean mathematics, which describe a world of multiple, relative space-time networks made of points as Complementary entities with energetic and informative system or ‘Points of view’ and the new tools of Non-Aristotelian logic, which describe the creation of the future by multiple causes – all the points of view or agents that create a certain network space.

The universe is a game of creation and destruction of networks of fractal knots of time cycles=st-points.

The minimal unit of the universe is a Non-Euclidean point/number, which classic mathematics defines as void of inner form and organic properties, to simplify the networks of numbers and point-like entities of the Universe for its geometric study. In reality though, points have breath; that is, they are real entities with ‘Dimotions’ and information parts, and so we have to upgrade Euclidean definitions of points, planes, lines and equality with the new tools of Fractal and Non-Euclidean mathematics to make the language of geometry closer to reality.

What mathematicians did was rather a runaway path. Because once geometers realized that multiple lines can cross a point, they could not use any longer the Euclidean definitions.

Now points, lines, planes and equality could no longer hold under the definitions of Euclid (points, lines and planes with no breadth), they remained undefined, when Hilbert, the father of modern mathematics affirmed ‘I imagine lines, points, planes…’.

Instead the proper solution was to redefine them in terms of their ‘inner parts’ as fractal points that grew in size when we observed them with a more detailed ‘hyperbolic geometrical view’, as that unveiled by non-E mathematics. So we ‘create new postulates of geometry’ by defining its essential elements, points, lines, planes and the laws of congruence (similarity) between them, as well as re-interpreting the concept of a Non-Euclidean point crossed by infinite parallels (5th postulate) in terms of a mind that absorbs flows of energy and information: O-mind x ∞ time cycles = ∏ime§paœ mapping.

So T.œ redefines points, planes and line-waves and their relative laws of equality (also called congruence) and continuity (which no longer holds), to refound mathematics on the basis of a far more realist view of its laws as ‘experimental laws’ that reflect the geometry of the 5th dimension and the complex casualty of a world with multiple time motions. And consider that those points with volume form social ‘numbers’, whose laws are therefore related to the laws of the 5th dimension that brings parts into social wholes.


    The 5 Postulates of Non-Euclidean, i-logic Geometry.

You are getting accustomed ‘you’ of course in the future, as i doubt anyone has ever read so far, to the 3±i method, that is the 5D³ method. All is five, five motions, five dimensions, five ages, so five will be the postulates of geometry refurbished from euclidean axioms, definitions and postulates to ‘build’ up as the Universe does, its dimensions from points into lines, lines into planes, planes into scales which become then again, points of the next scale.

And that is what we need, 5 postulates, the first for the fractal point, the second for the wave-line (as point has volume so lines are waves of cycloid form), the third for the similarity NOT congruence THAT DEFINE organically and topologically the i-logic of association according to similarity of points into lines, wave, networks and planes, which is the fourth postulate, as all continuous PLANES do have in detail holes (galilean paradox on scaling: continuous simple description of discontinuous networks – not CONTINUITY forget Dedekind cuts, IS not REAL)

And thus one we have the network, we have the super organism that mixes 3 plane-networks. And we have A NEW POINT-WORLD, which is focused in the mind – the fifth postulate.

According to the Correspondence Principle a new scientific Theory has to include all previous ones. So happens with Multiple Timespace Theory, which includes as specific cases all other simpler geometries of space-times, by completing the 5 Non-Euclidean postulates of geometry and adding the concept of a fractal point developed in XX C. fractal geometry. The result is a geometry that includes all other geometries; since the incomplete non-Euclidean geometry discovered in the XIX c. (5th postulate: a point can include many parallels) already included the previous Euclidean postulates based in points through which only one parallel can be traced. Those new postulates describe with more accuracy all type of space-times belonging to all kind of sciences, from the physical space/time of atoms (described by quantum Physics) to that of galaxies (which Einstein described in his General Theory, using the 5th Non-E postulate); from the organic space/time of cells and species to the historic space-times of nations.

Thus, according to the Correspondence Principle, we establish a hierarchy of completeness among all those geometries that stretches from the simplest Euclidean Postulates to the i-logic geometry of fractal space-time, which includes all others as particular cases; and it is in itself a partial image of the total information about space-time we call reality – always bigger than any ‘linguistic’ image we made of it with the languages of the mind that reduce the total information of reality to fit it in the brain:

Euclidean Mathematics (Light- Space)> Classic Non-Euclidean geometry> (Gravitational Plane) > Fractal space-times (all scales) > Total Reality 2

We consider Euclidean geometry, the natural geometry of a single, continuous space-time, made by the ‘eye’ only perception of light-space and its 3 perpendicular dimensions (height/electric field, width/ magnetic field, and length/c-speed). But that space is not all the spaces of reality. It misses at least a second fractal scale, gravitational scale and all the complex, vital spaces of organisms of information and matter. In Non-Euclidean mathematics, the new unit of ‘fractal space-time’ is the 3-dimensional Fractal Point of view, whose main property is to have in/form/ation – an inner content, which in a Universe made of multiple scales of size, we perceive as we come closer to the point and observe it in detail. Those fractal points with volume are described by the 5 Postulates of Non-Euclidean Geometry, which adapt to fractal, discontinuous space and cyclical time, the classic 5 Euclidean postulates.

The first postulate explains a fractal point, as a point with parts. In a more detailed analysis those parts turn out to be self-similar in geometrical terms, in all systems, due to the specific lineal vs. cyclical, concave vs. convex geometries of energy and information and its ‘planar combinations’. In its more complex versions those geometries are defined by the three canonical topologies of a four-dimensional Universe, which describe the informative ‘head’, reproductive ‘body’ and energetic limbs and membranes of all the superorganisms of the Universe. The 2nd, the interaction between two points connected by a wave of communication or ‘line’, the 3rd, the type of ‘biological’ interactions between 2 points according to their relative equality, and finally the 4th, the complex structure of a system of points across multiple organic space-time planes, such as those who create a human being.

Thus, the more evolved Fractal, i-logic Geometry of space/times includes all previous geometries as simplified cases of the more complex structure of the Universe in multiple scales. We call it a fractal, i-logic Geometry because some postulates can be interpreted in geometric terms, as the definition of the essential elements of any geometry of space/time (the point, 1st postulate; the line, 2nd postulate and the plane, 4th postulates) and some in logic terms, as the description of the different causal chain of events that can happen when st-points enter in communication -3rd, 5th and 4th postulates:

Further on, according to the duality between geometric form and logical function, those postulates of fractal i-logic geometry define also the basic arrows= cycles/dimensions of the Universe: the 1st and 5th postulate define a point as a system whose inner parts are able to transform and emit energy and information, e>i<e; the 2nd postulate defines an exi wave of communication that reproduces energy and form between 2 fractal points; and the 4th postulate defines the social evolution of a herd that creates a fractal plane, a network with dark spaces; and the 5th postulate explains a point in its iterative actions as it absorbs energy and transforms it into information through its small apertures to the Universe. Since even a minimal quark of mass, as Einstein affirms should be crossed by ∞ parallels.

The importance of the ‘linguistic laws’ of i-logic geometry resides in the fact that all systems of the Universe follow in space the laws of geometry and in time, the laws of logic, so the enhanced linguistic mind of science obtained with those laws can be used, as this author has done in multiple works to resolve long-standing questions in all sciences, which can further be ordered in a pyramid of increasing information and diminishing energy: Physics studies the simplest forms with maximal energies. But if we consider the 2nd arrow of ‘creation’ of reality, that of form, of information, the summits of science are biology, which studies the most complex forms of information (life) and Sociology/Religion, which goes a step further into the analysis on how the arrow of eusocial love creates Human Societies according to the Organic laws of the Universe (eastern religions).

To be able to consider biologic behavior (social evolution) and ‘mental perception’ (informative gauging), as factors dependant on geometrical qualities is an astounding break-through for science, which will be developed in its details in this work, to show an enormous number of experimental proofs. Indeed, fractal, i-logic Geometry achieves a long-sought goal, which Plato, Spinoza and Leibniz tried to realize, but failed, with the use of simpler Euclidean geometry: to unify the logic and mathematical principles of the Universe. Since the 3rd and 5th Non-Euclidean postulates are logic, the 1st and 2nd are geometric and the 4th, the nature of a topological plane or network of non-E points is both logic and geometrical, as it defines the fundamental logic-geometric structure of the Universe: the superorganism.

The logical and mathematical conclusions we shall arrive in this chapter are the same we achieved in the previous one with a more descriptive, less formal analysis: the Universe’s final goal is to create ‘topological, organic planes, super-organisms’ – the 4th, more complex ‘geometrical postulate/form of reality’ – departing from simpler forms, points and cycles. We shall try to get to that conclusion step by step, first by describing the geometrical postulates, then by fusioning them with fractal mathematics and finally by studying the most fascinating of all of them, the 3rd postulate, which proves that behavior among the points of the Universe is based in the degree of equality or self-similarity between their inner form that determines if those forms communicate symbiotically or destroy each other, thus defining the duality of eusocial evolution as a group of a number of self-similar beings or destructive extinction.

Some, first-hand consequences of those postulates are:

– 1st Postulate: We correct Euclidean geometry, increasing and relativizing the dimensions of a point that fits inner energy and information. Since all points have either 1 motion, a time dimension, when we consider them from the perspective of the upper st+1 Plane for which they are in the limit of invisibility (what quantum scientists call a point-particle) but still has a motion or ‘function’ in that upper ecosystem, st+1 in which it exists; and 3 dimensions/networks/functions when we consider them from the inner perspective of the point. This is the case even in the smallest planes of theoretical strings, made of points with parts, with volume – since we require 3x3s+1t theoretical inner dimensions to describe them – a paradox that can only be resolved if we consider the to be ‘strings’ of fractal points with inner, fractal dimensions.

– 2nd postulate: When we observe a one-dimensional line as a form with inner parts it becomes then a 4-dimensional wave made of cyclical points with motion. Hence in quantum theory we say that any particle in motion has associated a wave. Thus the 2nd postulate resolves the wave/particle duality, as all lines are now waves traced by a point with inner volume. Further on, since all lines have volume, they carry information and so all forces can in fact act both as a source of energy and as a language of information – as physical experiments prove. Since when we observe a ray of light in detail it becomes a 4-dimensional wave with electric height and magnetic width, often exchanging flows of energy and information in action-reaction processes of communication between bigger points.

3rd Postulate: Equality is no longer only external, shown in the spatial perimeter of any geometrical form (3rd Euclidean Postulate) but also internal and further on it is never absolute but relative, since we cannot perceive the entire inner form of a point – hence the strategies of behavior such as camouflage. Forms are self-similar to each other, which defines different relationships between organic points, according to their degree of self-similarity. The 3rd postulate is thus the key to explain the behavior of particles as the degree of self-similarity increases the degree of communication between beings. Some of the most common behaviors and ‘events derived from this postulate are:

1) Reproductive functions in case of maximal self-similarity or complementarity in energy and form;  ei->Sei or Max E x min. I (male)= Min. e x Max I (female).

2) Social evolution, when points share a common language of information, i=i -> 2i.

3) Darwinian devolution when forms are so different that cannot understand each other’s information and feed into each other: i ¹ i. In such cases if those 2 entities meet they will start a process of ‘struggle for existence’, trying to absorb each other’s energy (when E=E) or simply will not communicate (when E¹E, since then there is neither a common information to evolve socially nor a common energy to feed on). Yet because any point absorbs only a relative quantity of information from reality, self-similarity is relative and it can be faked for purposes of hunting, allowing biological games, such as camouflage and capture, or sociological memes that invent racial differences, allowing the exploitation of a group by another.

The geometric complexity of the 3rd Postulate is caused by the topological forms created by any event that entangles Multiple Spaces-Times. Since it describes the paths and forms of dual systems, which connect points: Self-similarity implies parallel motions in herds; since equal entities will maintain a parallel distance to allow informative communication without interfering with the reproductive body of each point. Darwinian behavior implies perpendicular confrontations, to penetrate and absorb the energy of the other point. Finally, absolute, inner and outer self-similarity brings bosonic states, which happen more often to simpler species like quarks and particles that can form a bosonic condensate as they do in black holes, where the proximity of the points is maximized. And indeed, the same phenomenon between cells with the same inner information /DNA originates the ‘collapse’ of waves into tighter organisms.

The 3rd Non-Euclidean postulate is implicit in the work of Lobachevski and Riemann who defined spaces with the properties of self-similarity (Riemann’s homogeneity), which determines its closeness (Lobachevski’s adjacency).

4th postulate: Now because a plane has an inner volume – that of its points – it is a cellular, organic topography, a network of self-similar points. And because networks of points of energy and information are complementary, often we find systems with 2 complementary networks that form ever more complex geometries – based in the geometrical dualities of lineal energy and cyclical information – with the results we observe in nature: the creation of an enormous number of complementary systems which are, as we shall see latter, all of them self-similar in its geometries and functions. Thus, the types of Non-Euclidean planes of space-time range from the simplest Euclidean planes to the more complex organisms with a volume given by the relative point/beings that form its space-time networks.

Thus, a plane becomes a real topography made of points with volume, extended as a cellular surface. We can observe its surface as a bidimensional membrane of information (for example your skin, or the screen of a computer made of pixels, or the sheet of this work). Or we can consider the 3-dimensional inner structure of its points and then it becomes a network with inner motions, as those points will form a lattice in which they communicate lineal flows of energy and information that maintain the lattice pegged. Often 2 topological planes of energy and form combine to create a 4-dimensional organism. Such is the most common structure of the Universe, a 4-dimensional World, which is a Universe in itself, made of self-similar cells or networks of points that constantly exchanges energy and information within the ecosystem in which it exists.

5th postulate: It defines points as informative knots or linguistic eyes – minds of information that absorb a flux of forces used by the point to perceive a relative world. A non-Euclidean point corresponds then to our concept of a relative mind that gauges the information reality with a certain force, similar to the concept of a monad in Leibniz relativistic space-time. In words of Einstein: a point of space is a fixed frame of reference.

Thus, Non-Euclidean mathematics fuses the logic and geometry of the fractal Universe, greatly improving our understanding of Reality even in terms of mechanist measure. Since mathematical solutions to problems with several points of view are impossible to find in continuous space (i.e. 3-body problem in gravitation), given the fact that a network of infinite points of view is local and relative and each point is a focal knot that acts from its perspective. Thus, the absolute truth of a system is the sum of all its points of view, which influence each other. Yet even if we cannot calculate precisely with mathematics, systems with more than 2 bodies, since those systems are organic, hierarchical, made of networks with attractor points, fractal structures and self-similar paths, the new mathematics of attractors, fractals, scales and Non-Euclidean systems, refine greatly our analysis. In essence, indeed, we observe that ‘networks’ integrate parts/points into wholes, which then ‘act’ as a single point. So in the complex models of i-logic geometry we can tackle many problems by defining sets of points as ‘wholes’ of a ‘higher space-time’.

But the most rewarding consequence of the new language of the mind is the ‘deep’ understanding of the meaning of many experimental facts about the species of the Universe till now merely explained as hows.

For example, the previous principle of local measure, where each point is a relative center of the Universe, is called in relativity the diffeomorphic principle, which now becomes explained as a partial case of the wider law we called the ‘Galilean paradox’; the duality particle of information/wave of energy becomes a specific case of the application to physics of the duality of energy and information found in all systems and so on.

The expansion of the laws of quantum theory (complementarity principle) and Relativity (relativity of scale, local measure, etc.) to other sciences and the organic principles of the 3rd and 4th postulate to physical particles is therefore the consequence of those postulates. Yet it requires the understanding of the new, i-logic, organic laws of the Universe and its networks, because E-mathematics has clear limits to extract all the information of the Universe, given the fact that it syntax includes a priori errors and simplifying postulates (single space-time continuum of points without parts, etc.).

Thus, when the event described is complex, performed by a great number of points/variables you enter into non-lineal systems, which require topological descriptions (chaotic attractors, fractal non-differentiable equations and Non-Euclidean mathematics), and the i-logic laws of organic networks and systems – a better syntax in which to fit experimental evidence, especially in phenomena of informative nature (since only formless energy is continuous and resembles the models built with a single arrow of energy and a single plane of space-time). So while classic physical systems calculate accurately the energetic, continuous properties of the Universe an overview on how multiple points of view emerge into wholes requires organic laws. Of course, this search of whys also applies to the understanding of mathematics. For example, the previous postulates resolve the long-standing question of what is the nature of the 3rd and 5th postulates that seemed redundant (as the 5th describes also properties of a point like the first does, and the 3rd seem to describe a non-geometrical property). They are no longer redundant, but they are more concerned with causal logic and time than spatial geometry in its purest forms (points, lines and planes.)

There is also self-similarity between the fractal postulates of i-logic geometry (since the 5th is geometrically self-similar to the 1st, as both are concerned with points) and the 4 dimensional time paths/arrows of the universe. This is not casual since all languages of space-times depict in self-similar ways the 4D Universe. Thus if the 1st and 5th postulates define a gauging point of information as the fundamental unit of the Universe, the 2nd postulate defines a line or flow of communication of energy and information between 2 points, which reproduces part of the information of the ‘generator’ point across a surface of space; the 3rd postulate defines those points, which are not similar as energetic substances that will be absorbed by the points. Yet if those points are self-similar they will gather through the arrow of eusocial love, creating according to the 4th postulate a network of space/time, a new organic plane of existence. So the 4 arrows of space-time are explained by the 4 postulates of i-logic geometry.

Recap. The study of the geometric paths of Time Arrows with the tools of mathematics, explains the whys of mathematical laws:  Geometry and topology acquire now its ‘why’: topology explains in detail the 3 canonical parts of all Points of view, while the i-logic postulates of geometry explain the universal structures that those points of view create.

In organic terms, the 5 postulates of fractal Geometry describe how points become parts of social webs, which self-organize fractal planes made of networks of points, which emerge as cellular units of a higher fractal space-time or new superorganism… Thus, according to the Principles of Correspondence and Relativity, proper of physical reality, those different geometries are relative descriptions of the same fundamental structure of the Universe: the point with parts and its more complex social forms, lines and planes. The fractal generator of the Universe is a logic equation that represents the main interactions between the arrows of time. Yet all languages mirror that logic equation in its syntax, since all minds gauge and represent the cycles of the Universe with languages of perception.




Topological Spaces. The why of geometrical forms.

Reality is made of fractal points, which are knots of Time Arrows, able to perform energetic, informative and reproductive functions. As complex as one of those points-entities might be when observed in detail, any fractal point is made of 3 regions whose geometry responds to the topological forms of a 4-DimensionalUniverse, the convex plane, the torus and the sphere.

The Universe comes down to two bidimensional elements, energy and information, and its 4-dimensional combinations. Thus all entities can be described as wholes made of 3 internal parts whose geometrical properties maximize their energetic, informative and reproductive functions:

– Max Ti: an inner, dual center, corresponding to convex topologies (left), made with 2 cyclical forms. It is the dominant informative topology of any fractal organism, described by Belgrami in the XIX c. as a conical form with ‘height’, with negative curvature.

– <=>: A middle, reproductive zone, described by Klein as a disk of quanta in cyclical motion that communicate energy and information between the inner and outer zones.

– Max. E: An outer membrane of energy, described by Riemann’s spherical geometry.

When we see fractal points far away we describe them as points with breath, with the tools of Euclidean geometry since the ‘inner space’ shrinks to a point and so the ‘bulk’ or curvature of space-time shrinks to a plane. Yet, when we come closer to them, they grow into points with volume. The volume of those Fractal, Non-Euclidean points can thereafter be studied with the 3 types of canonical, Non-Euclidean geometries or topologies of a 4-Dimensional Universe – the Universe we live in. Those 3 topologies make up the 3 regions of the point, which correspond each one to the 3 essential arrows/functions of any species: the external, energetic membrane; the central, informative brain and its reproductive combination, exi.

It follows that the first part we observe in a point is the external membrane, which without detail seems to have a continuous, energetic appearance. But on close view, we observe most external membranes store and/or absorb information (Holographic principle) due to its fractal geometry. This can be generalized to any membrane which shows a ‘bidimensional surface’ that acquires more form, more ‘fractal steps’ when we come closer to it. Thus, the Holographic principle, which physicists know in the restricted field of black hole theory but can’t explain why exists, is both explained and extended to any bidimensional membrane of information. We find bidimensional, warped, fractal membranes that store information not only in black holes, but also in the development of organic senses, departing from the exoderm (external membrane of the fetus), in the seminal cells that reproduce life, formed as an outgrowth on the body surface (genital systems) or in the complex forms pegged to the surface/skin of the Mandelbrot and Julia sets, the best known mathematical fractals.

This external, energetic membrane has the topology of continuous surfaces called the Riemann sphere, which is the external surface of any point – the skin and limbs and any of its multiple self-similar entities, some of which are drawn at the bottom of the graphic. In any system of the Universe, the membrane acts as the energetic, external surface of the informative, point through which the point absorbs energy from the external Universe, to process it into information.

–  The toroid, which is the body or reproductive region (seen as a cyclical path of space-time), which fills up the space-time between the nuclei and the external membrane. It is the zone where the reproductive organs of the system exist, and where the information of the system is born.

–  Energy and information systems have inverse properties: energy is expansive, external, more extended, and information is implosive and smaller. Thus we find the informative head or system either on top of the reproductive body, with a spherical and smaller size or in the center, and its topologies will correspond to those of maximal form; the so-called hyperbolic topology. In the upper graph, it is the double ring, or convex, hyperbolic surface, with maximal form, or informative center of any entity of the Universe, the point in which the fractal reproduction of information reaches its zenith. It is the same form than the toroid but reproduced into a higher content of information, by doubling the initial form.

– Finally between both topologies of energy and information, the point will have a middle region of exchange of energy and form, made of cycles that go back and forth between those regions, which correspond to the 3rd canonical topology. It is the torus, plane or Klein disk – a curved region of energy & information quanta, with cyclical motions, confined by 2 limits, an external, spherical membrane of max. energy and an internal informative nucleus. It must be noticed that according to Klein, the topologist that studied better this type of surface, the toroid is NOT really a fixed form of space, but we must consider those cycles’ motions and add the parameter of speed. Thus Klein introduces the Paradox of Galileo to describe the Non-Euclidean geometries of the Universe as we have done in this book. Cycles are mere static perceptions of motions and we must always consider distances as space-time distances. So we say: London is at 4 minutes distance because we consider distance and speed together. This is ultimately the meaning of time in physics, a measure of the speed of motion as a way to gauge space-distances: v=s/t.

In the graph, we observe several non-Euclidean points created by those 3 canonical topologies that can adopt multiple forms by deformation, but suffice to construct all the shapes of our Universe. Indeed, a topology is deformable. So an external membrane, which corresponds to the topology of a sphere, can become any shape, as long as it is not torn up, to enclose a reproductive and informative zone. So your skin is in topology a sphere, which encloses the complex forms of your reproductive organs. Those organs are Klein cycles of great complexity that exchange energy and information. Since those 3 topologies suffice to describe any 4-Dimensional form, it follows that the Universe is merely a puzzle of energetic, informative and reproductive parts, associated in ‘numbers’, groups and all kind of entities as those shown in the previous graph, from different sciences, which are created with those 3 topologies.

The 5 Non-Euclidean postulates and 3 topologies common to all species prove that all fractal points are complementary, made of regions that process spatial energy and regions that gauge temporal information, both of which exchange motion and form in cycles mediated by its intermediate, dynamic, reproductive ‘body’ region. This is what Lobachevski, Riemann and Klein discovered when they invented Non-Euclidean Geometries in the XIX c.: Euclidean space is a simplification of a moving space, made of points with volume that constantly trace cycles.

In a 4-D Universe there are only 3 topologies of space, which actually display the properties of energy, information or a combination of both, the 3 canonical topologies structure the inner geometry and functions of the organs of any species, proving the homology of all space-time fields in the Universe. In the graph, an animal, an embryo, an electromagnetic flow, a galaxy, a proton, a seed, a planet, a cell and a boson display the 3 topological zones of a fractal point, each of them performing 1 of the 3 functions/arrows of space-time.

Topology describes the internal parts of Non-Euclidean points when we come closer to the ‘fractal point’ and see its formal parts in detail, as we do in the last graph, with several systems of Nature made of those 3 topological regions that correspond to the 3 main arrows of time of each of those systems:

Information x Energy = Reproduction

Time arrows are performed within each space/time point by one of the 3 topological regions, which explain causal processes of transformation of energy unto information as topological transformations. While the 4th arrow of social evolution, which requires more than a point, is described by the 2nd and 4th postulates of lines and planes. Thus Topology confirms a fundamental tenant of Multiple Spaces-Times, the 4-dimensionality of the ‘Holographic Universe’ made of bidimensional energy and information, which combine its properties to create the ‘visible’, bulky regions between the informative center and energetic membrane of those points.

Each of the 3 elements of fractal points displays the properties of one of the 3 Time Arrows: the center has height, it accumulates information and it is small. The external membrane is larger, continuous and protects the system. The intermediate zone reproduces the information given by the center with the energy absorbed by the membrane creating new energetic and informative bites and bits, which latter migrate towards the other 2 zones.

– Informative particles accumulate in the inner region as units of the central brain. Or, if they are seeds, they migrate to the surface of energy where they become fractal systems of information, senses in organisms, informative human beings in the Earth-crust, ovules in mothers. And once detached, they start a fractal, reproductive, palingenetic process.

– Energetic particles migrate to the membrane, becoming parts of a discontinuous protective shield. So in a cell we find mitochondria that produce energetic proteins and RNA for the surface membrane.

The internal, reproductive region happens also in all systems. In the human body the organs reproduce the cells needed for the blood network and the hormones and products used by the brain. In a galaxy, the intermediate region produces energetic stars and informative black holes, which migrate to the central region; in an ecosystem, the territory of the informative center, the predator, produces preys in which the predator feeds, bringing them to its central den.

Recap: The fundamental Particle of the Universe is neither physical nor spiritual but logic-mathematical: the fractal point described by the Laws of Non-Euclidean, fractal Geometry and topology, as an entity which becomes more complex when we come closer to it, till we can differentiate its 3 regions, corresponding to the 3 topologies of a 4-dimensional Universe: an energetic membrane, an informative center, and an exchange zone of bites of energy and bits of information between both.

4. Formalism of i-logic geometry. Causal Algebra.

The ternary structure of all points formed by the 3 topologies of a 4D Universe can be expressed with the symbols of the ‘Generator Equation of energy and form’:

– Max. Σ S: An external membrane or of max. extension, described by Riemann’s spherical geometry.

– <=>: A middle, reproductive plane or toroid, whose cyclical paths happen between the skin/boundary of a sphere and a central hole, described by Klein as a disk, made of quanta in cyclical movements that communicate energy and information between the inner and outer zones.

– Max. Ti. The inner, dual center – a convex hyperbolic, informative, central couple of disks, which display maximal form in minimal space, with a growing dimension of height that touches the poles of the sphere and channels the flows of energy and information of the system. It is the dominant informative topology of any fractal organism, described by Belgrami in the XIX c. as a conical form with height with negative curvature.

Since function is form, those 3 topologies are perfectly suited to perform the 3 temporal functions of any super-organism: energy feeding, reproduction and information.

So we can write with causal arrows the topology of each point and its 3 regions: ΣS < EXI> Ti.

The 3 non-Euclidean geometries structure the geometry and functions of the organs of any species, proving the homology of all space-time fields in the Universe. In the graph, an animal, an embryo, an electromagnetic flow, a galaxy, a proton, a seed, a planet, a cell and a boson display the 3 topological zones of a fractal point, each of them performing 1 of the 3 functions/arrows of space-time.

There is in that sense only a small correction to classic topology needed to fully understand the structure of organic systems with the 3 topologies of reality. In topology we distinguish two types of spaces called closed balls and opened balls. Open balls are spheres with a center ‘a’ and a maximal distance/radius, r (from a to its surface), defined by all the points x, such as x < r (therefore an open ball does not include the surface or perimeter r); and closed balls are spheres which include all points x≤ r.

In i-logic geometry, all organisms are both, closed and opened balls, depending on our perspective.

As closed balls they include the 3 regions, previously described which are, a, the hyperbolic center; r, the perimeter; and x, the points of the intermediate space.

The intermediate space is on the other hand, an open ball, which does not include the membrane, r, as it constantly exchanges energy and information with the external universe; but it does not include either a, the center, so it is also opened inwards, to the information system.

This is for example, the case of a black hole, which is wrongly understood in classic physics, since the black hole has 3 regions, a, the singularity, ∑ x, the quark-gluon soup of extreme density, whose cyclical mass vortex are the black hole in itself, and r, the event horizon, which is not the black hole per se, but the membrane of exchange of energy with our electromagnetic space the black hole warps and feeds on.

Recap: In a discontinuous Universe there are infinite fractal points, but all of them are composed of the same 3 ΣS, EXI, Ti zones; the external membrane, the intermediate region and the inner center.

Mathematical description of the 3 regions of a st-point

The complex analysis of those fractal points that move and have inner fractal parts, made of cycles, started in the XIX century. First Lobachevski, a Russian geometrician, defined Non-Euclidean points as curved forms, crossed by multiple lines, which give them spatial volume. Then Klein studied its cyclical movement and introduced the variable of time in their description. Finally Riemann generalized its nature, considering that all space-times were Non-Euclidean space-times with movement. For readers versed in mathematics, we shall reconsider the common properties of those 3 zones of any fractal point, according to its discoverers, which develop in abstract terms the organic properties we just described:

According to Lobachevski and Belgrami, space is curved since information curves the energy of any real space-time. So points move in curved, cyclical paths gathering energy and information for their inner ‘dimensional networks’.

– According to Klein Non-Euclidean space-times have motion. So their speeds measure distances; as physicists do in Cosmology with the distances of galaxies, which are proportional by a ‘Hubble constant’ to their speeds; or as people do in real life when we say that Brooklyn is at 5 minutes by train from Manhattan not at 2 miles.

– Riemann summoned up those findings and generalized them to all possible space-times. His work should be the guide to understand them philosophically. He also defined planes as networks of similar points and treated dimensions, as we do in this work, no longer as mere abstract definitions of extensions but as ‘properties of those points’. So points can have beyond its discontinuous borders an inner space-time with several networks/dimensions, one for each of its ‘energetic or informative properties’, as it happens with the points of physical reality. Yet a network of points that form a space with ‘common properties’ defines the dimensions of those points as ‘fractal dimensions’, limited by the extension of the energy or informative network (static point of view), which ‘puts together’ a complementary dual, organic being.

Those pioneers defined the 3 topologies of information, energy and reproduction of all st-points:

– Max. Information: The informative, fractal center, particle or brain of the point is the so-called Belgrami hemisphere, a space-time with a dimension of height that transforms energy into information, absorbed or emitted by the central singularity. It is a fractal, informative region similar to a black hole structure. Since it follows the ‘black hole paradox’ of all informative centers, displaying max. form in min. space. So according to the inverse properties of space and time, the center has max. Informative Time and minimal Energetic Space. Moreover any point which comes closer to it, suffers a mutation of its spatial coordinates into informative, height dimensions. This is the case of any particle coming to a black hole, whose space-dimensions become temporal/informative dimensions as it rises in height.

The center has more information because its geometry has at least 2 fractal disks, which channel and transform the energy absorbed through the surface into complex information. Regardless of the complexity of the entity, the structural function of the hyperbolic center as a system that process the information of the network remains. For example, in living systems, those disks might evolve its topology till becoming the relative energy center or ’heart’ of the blood network with 4 divisions; or evolve further its hyperbolic geometry till becoming the informative center or ‘brain’ of the system, attached to the informative network.

– Max. Space: An external, continuous membrane or Riemann’s sphere of maximal energy that acts as a relative infinite, unreachable distance. The membrane isolates the point as an island Universe, creating the discontinuity between the inner parts of the point and the outer universe. Since the internal cellular points are either jailed by the membrane’s structural density or destroyed by its energy when touching it. The membrane is the opposite form to the central, informative singularity, with max. spatial extension and continuity, hence with a minimal number of fractal, discreet elements: Max.ΣSe=Min.Ti.

Thus all Fractal points are ‘inner worlds’ whose membrane creates a discontinuity that defines an External Universe or outer world from where the point obtains its energy and information. However the membrane is also the zone through which the point emits its reproduced micro-forms of information, and so it displays ‘sensorial holes’ to relate the point to the external Universe. And those points, despite being discontinuous, will have in their external membrane several generic openings or ‘senses’ joined to the informative networks or ‘brains’ and energetic, ‘digestive networks’ of the organic system:

   – Max. +ΣSe: Amouth’ or opening that absorbs energy.

   -Max. –ΣSe: Cloacae’, through which the cyclical body expels its temporal energy.

Max.+Ti: Aneye’ through which the informative center receives external information.

Max.–Ti: Anantenna’ to emit information.

Those apertures vary in their number, location and size, depending on the form of the point. In the simplest spherical ‘seeds’ of most species, they are mostly situated in 3 regions:

 – Max. ΣS: The Equator of the system, through which the membrane absorbs energy.

 – ΣS=Ti: The Tropics where often the same opening emits and absorbs temporal energy.

– Max.Ti: The Poles or points of confluence between the membrane and its central informative region of height, which hits perpendicularly the membrane on those poles. North and South Poles orientate Anti-symmetrically, acting as 2 relative, negative and positive apertures, communicated by the height dimension of the singularity or Belgrami hemisphere. Thus the Positive Pole absorbs temporal energy that crosses through the central singularity where it is absorbed and ejected to the intermediate region where it is re-elaborated before its emission through the negative Pole.

– ΣS<=>Ti: The reproductive, central region, which combines Energy and Information:

In all fractal points there is an inner middle volume or intermediate territory, discovered by Klein, which combines the energy coming out of the external, spherical, topological membrane and the information provided by the convex, complex formal center.

According to Non-Euclidean mathematics this region is made of self-similar points that form groups, fractal herds of ‘points with parts’ in perpetual movement, that draw cycles of parallel lines, between the other 2 regions, as they gather the energy and information they need to survive. And they create space by cycling within the other 2 regions.

In many fractal points the informative and energetic centers establish 2 opposite flows of energy and information that become the negative/ positive poles. So often, the particles of the intermediate region cycle around the inner region tracing elliptical trajectories, focused by those 2 informative points. It is the case of any bipolar system, from binary stars, one dominant in energy and the other an informative neutron star or black hole; to bimolecular systems or n-p pairs in the nuclei of atoms. The same duality of 2 specialized centers controlling a common territory, or vital space happens in biology where most species have male-energetic and female-informative genders, ruling a common territory.

Such abstract conceptual space describes in fact the behaviour and form of many real, spatial herds. For example, a herd of animals in an ecosystem will move between their hunting and water fields (where they gather energy) and their breeding, inner region where they reproduce information, making cyclical trajectories between both regions. In this manner, they occupy a vital space, called a ‘territory’, which shows the properties of a Non-Euclidean Klein space. A fundamental property of the intermediate space is the fact that it is confined between the other 2 regions, which are never reached in the cyclical trajectories of the inner cells of the space. For example, in a cell, the molecules of the organism will not touch the protein membrane or the central DNA nuclei. Thus, the inner quanta are confined within the Klein’s disk by the 2 other regions, which have more energy and information and might destroy them and/or absorb their energy and information at will.

In abstract terms, mathematicians introduced in the XIX c. the concept of an infinite, relative distance measured no longer in terms of static space but in terms of time and movement, as the distance between the point and a region that cannot be reached. Thus Klein defines a relative infinity, as the region beyond the discontinuous membrane whose insurmountable borders the inner time-space quanta can’t cross, as a cell cannot go out of a body, an atom beyond C speed or 0 K temperature and a man beyond the Earth’s atmosphere. Thus, the informative center and external membrane become the 2 relative infinities or limits that the movements of the intermediate point cannot breach.

As in the myth of Achilles and the turtle, Achilles never arrives because every time he moves he crosses a smaller spatial distance. The same happens in a fractal space-time, when a point moves temporally towards its inner or outer space-time limit and finds an increasing resistance to its movement, till finally it is deviated into a cyclical trajectory around the outer, energetic membrane or the height dimension of the inner informative singularity or is destroyed. So the intermediate, fractal cells of the point circulate in parallel cycles always inside the interior of the sphere with contact zones of the type A (central, 2nd row of figures in the previous graph).

In a human organism, the blood system might seem infinite for the red cells that transport energy since they never reach the outer Universe. For that reason in the drawing, Klein interprets the intermediate region of the Non-Euclidean point as an infinite circle with an invisible, unreachable membrane, whose motion-distance is unreachable, hence infinite, equalling the ‘space-time distance’ between the intervals B1-B2 (long) and B2-B3 (short but difficult to cross), despite being B2-B3 increasingly shorter in space. Since the quanta take longer in each step and don’t reach the membrane. This is often due to an increase in the ‘density’ of the space, which despite having less distance has more ‘points’ in its network, such as the case of black holes or jails. When those inner points reach the membrane at point C they become destroyed or deviated.

Thus, the energetic membrane and informative center are the discontinuities that isolate the intermediate cellular quanta, creating a discontinuous ‘World’ within the point. Those discontinuities are called in Geometry a relative infinite, in Biology a membrane, in Sociology or Topology a national border, in fractal theory a co-dimension of a point. They are defined in physics by Lorenz Transformations that make c-the limit of energetic speed and 0 k the limit of temporal, formal stillness. Yet those physical limits are not the limits of an absolute Universe, but the limits of the fractal space-time membrane of light and its evolved electroweak beings, since the Universe has at least another bigger gravitational membrane, in which the smaller light-space exists; a fact with enormous repercussions for a proper description of the Cosmos, which extends beyond those limits. Since the gravitational scale should be faster than light-speed forces and cooler than 0 K masses.

Recap: Fractal points are organic points, whose topologies maximize the energetic, reproductive and informative cycles they perform. The details of those cycles are described by Non-Euclidean topologies.

Dimensions of the 3 regions: Holographic Universe.

In terms of dimensions the spherical membrane and inner informative singularity are bidimensional fields: The central singularity is a bidimensional surface of convex in/form/ation that curves the external spatial energy coming through the bidimensional membrane, creating together the 4-dimensional quanta of the intermediate region. For example, physical models of the inner nuclei of atoms made of informative quarks, define them as bidimensional, convex singularities. Black holes are said to store bidimensional information in its external membrane or black hole horizon. The computer screen or sheet of a book stores bidimensional information. The vacuum energy of the galaxy has a planar form, etc.

A 2nd consequence of the inner volume of points is a rational explanation of bidimensionality. Since now points have a minimal volume a bidimensional sheet of information has in fact a minimal height, but since reality is fractal and size is relative, from the ‘giant’ p.o.v. of our perception that depth of a sheet of paper or computer screen is a relative ‘zero’, yet makes bidimensionality ‘real’.

Recap: informative regions have more dimensions of form than energetic topologies, more extended in space.

Morphological change and informative dominance.

Natural organisms start as spherical seeds of information and then through morphogenesis differentiate in 3 functional regions that ensure the capacity of the system to process energy and information and reproduce itself, surviving in the Darwinian Universe.

As the species changes and evolves into more complex shapes those functional zones are kept. For example, the informative egg evolves into the energetic, lineal larva or young phase of most insects, by translating the inner, informative center to the dominant, forward head region and the external membrane to the ‘tail’, but both functions are preserved. Thus the inner informative regions migrate through the informative dimension of height to the dominant zone of the system. Yet the dominance of the informative center is not compromised:

 In all systems we find a core/brane that acts as the dominant region of the organism and display paradoxically less spatial extension than the other regions they rule. It is the smaller nucleus of cells, humans and galaxies generates its information (DNA, human brain/eye system, galactic black hole, CPU (central processing unit) in computers, etc.)

In a galaxy the halo of dark matter and the central black hole dominate and seem to feed and form the radiant matter of which we are made. In man, the informative brain, extended through the central spine and senses, dominate the reproductive body and guide it.

The 2nd region in importance is the ‘body’ or reproductive region, which absorbs energy from the limbs that become imprinted by the system’s information.

And finally the 3rd region of the system, which is easier to renew, due to its formal simplicity is the energetic region, the skin, limbs and membranes, which brings energy to the intermediate region to allow the reproduction of the information stored in the center or head of the system.

Given the ∞possible deformations of those 3 unique topologies of 4-D space-time, reality creates an enormous variety of species, from an original seed of spherical information that develops those 3 regions in morphologies that soon resemble energy lines, reproductive cycles and information centers.

Our energetic region extends in lineal limbs; reproductive cells group into organs, becoming the body; while the informative centers move to the height dimensional and multiply its cellular forms in the sensorial boundaries of the head.

All those processes studied by morphogenesis, can now be explained not only in its how but its why.

Recap: The 3 relative forms of energy (external membrane), information (dual ring) and reproduction (the cyclical paths that exchange energy and information between the external membrane and the inner convex form), can be found in any system of reality. In all those systems, the informative region dominates the bigger, simpler reproductive body.

The ternary structure of all Universal systems.

The 3 functional topologies of a Non-Euclidean point become the 3 regions of all Natural organisms:

Atoms have a central, informative mass of quarks, spatial, electronic membranes and fields of gravitational and electromagnetic forces exchanged between them. Those 3 topologies also describe the galactic structure: the central black hole is the hyperbolic, informative topology, the Halo of the galaxy is a Riemannian, spherical form, and the stars in the intermediate region, which feed the dark matter of black holes and reproduce the atoms of life, turn in cyclical, toroid paths around the central black hole.

Physical space-time is the simplest world where the most basic morphologies play that same process of transformation of external energy that converges and reproduces cycles, attracted by a Non-Euclidean point, charge or mass: E=Mc2.

Cells have lineal, external membranes of proteins, which are a deformation of a Riemann sphere, an informative nucleus and in between they are invaginated by all kind of e<=>i cycles that transfer energy and information from the outer world to the cell.

Finally, a human being has a reproductive body, lineal, energetic limbs and a cyclical head, with an informative, smaller brain, composed of two hemispheres, which are hyperbolic, convex, warped forms, corresponding to the informative dual ring of a Belgrami cone. The hyperbolic, highly warped brain is a double toroid, self-similar to the hyperbolic topology of informative cycles. And so the brain hosts more information in lesser space than the body, as a mirror of its functions. Man though, while responding to the same canonical topologies in his organs, is by far the most complex being of information known in the Universe. And so his topologies are immensely more complex than the simpler physical particles and its transformations just described.

Recap: All systems of the Universe are made with the 3 canonical regions of a non-e point, which perform the 3 arrows/functions of all existential beings. Galaxies show the topology of non-Euclidean point, with a complex informative black hole of maximal mass, an energetic membrane of dark matter, and an intermediate region of reproductive stars that create the atoms of the cosmos. Human beings have also 3 ternary regions, the cyclical, hyperbolic informative brain, the reproductive body and its organs that produce the energetic bites and informative bits of the organism and the lineal limbs that cause our motions.



Fractal points gauge information with infinite parallels.


The fact that all points interact with the external Universe is explained by the 5th postulate of Fractal Logic, which completes the 1st postulate.  The 5th postulate defines a point as a knot of communication of multiple flows of energy and form, which the point absorbs to obtain energy and information for its organic cycles of iteration.

Thus we introduce a new perspective in our study of a Non-Euclidean, fractal point of view: its capacity to gauge information and absorb energy, acting-reacting to the Universe. Since beyond those 3 internal regions the point feeds on an external world of relative forces, which provide the point with energy and information to map out reality and feed its body with motion. Thus, while energy and form will be different for each point according to the scale and form, all entities of the Universe will be able to absorb a relative number of ‘infinite parallels’ to create mental fractal mappings and keep on moving: light feeds particles, intergalactic gas feeds stars; plants feed animals that feed man; stars feed the black hole, and so on.

In science, mathematicians and physicists seek to describe reality as ‘made of mathematical entities’; while logicians try to explain reality as a series of causal events. But only when we use i-logic geometry we can mix both approaches, describing reality as a series of ‘mathematical points of view’, or entities that ‘gauge’ the geometry of the Universe, constantly mapping out the universe, to achieve a ‘selfish’ will, the desire of all entities to feed on energy, gauge information, reproduce and evolve socially. Those points of view are thus ‘mathematical minds’ because they gauge and somehow ‘perceive’ the geometry of the Universe, acting according to that geometry as they gauge and move with an ‘automatic’ behavior, trying to absorb energy for their body, information for their gauging mind, and combining both, to reproduce ‘self-similar points’. So we shall consider that the Universe is made of i-logic, fractal ‘points of view’, akin to the concept of souls and Atmans in western and eastern religions’, of ‘Non-Euclidean points of view’, ‘monads’ or ‘Spinoza’s geometrical entities’, in western philosophy of science and mathematics; of ‘gauging particles’ in physics, or ‘informative DNA nuclei’ in biology and perceptive heads in biology. The size and form of all those points varies but all of them are spherical knots of information with sensorial apertures to absorb and emit energy and information, from bosonic particles to sound waves or light signals.

Leibniz, the first philosopher of modern science, which considered points as the ‘fundamental particle’ of the Universe departed from the hypothesis that all what exists can be reduced to such points of view, he called Monads. Yet those monads could either share energy and information between themselves as they do on reality or become static, perfect non-communicative points. This easier choice – non-communicative points of view – was Mr. Leibniz’s error. Since the points of the universe are in perpetual communication as parts of networks of self-similar points, sharing flows of energy and information – waves of forces. The essence of any point of any relative space-time is precisely to be in constant communication with the Universe as a ‘knot’ of Time Arrows, which shares flows of energy and information with other points, creating the network-spaces of which reality is made. Points that communicate energy and information, that feed and gauge are real. What is the proper name for all those logic parts that exist, for all those points of space that perceive, gauge information, and act-react to it under a simple program of ‘survival’: grow and reproduce, exist, repeat yourself? We call them a Non-Euclidean point of view. And we affirm the Universe is made of such type of points of view.

Thus ‘mathematical, Non-Euclidean points of view’, whose ‘motions’ have a ‘will’ or ‘purpose’ – gauging information, feeding on energy and reproducing themselves’ – become the logic and geometric units that shape the networks of energy and information of reality, thanks to their capacity to communicate and share energy and form. Such type of points are more akin to the view of Eastern philosophers that consider the Universe made of ‘atmans’, which are knots of communication that anchor a certain entity to the world that surrounds them, which is only a part of the total Universe.

Since those mathematical points of view exist in many different fractal space-times or ‘scales of existence’ in which they gauge information with different languages and perceive different ‘worlds’ within their minds.

If you are a particle – an electron – you will see only light (energy) and darkness, and you will move to the light that feeds you, as we observe in electrons. If you are a human eye you will see all type of colors but red will be the color of energy that ‘feeds and attracts your eye (so you see bloody movies and like red meat). So there are an infinite number of types of organic points of view with different mental worlds, which gather into social networks that exist in different ‘planes of existence’ or ‘scale of reality’. Yet in all those systems the same game of ‘gauging’, ‘feeding’, ‘reproducing’ and evolving socially takes place.

We exist in a Universe, whose fundamental particle is not a material form, as simple science thinks, but points of time space, which mirror in their inner, i-logic, fractal topologies the information of their world, acting-reacting to the Universe. Thus only by mixing perception and motion, mathematics and organicism, we can define those points of existence, as the fundamental particles of reality and:

‘The Universe has a body and a soul called logos.’ Plato

So we describe a Universe with a geometrical how, the laws of Non-Euclidean points of views, the cycles they trace, the mathematical laws that describe those cycles; and a bio-logical, temporal why: the will to move, trying to fulfill the 6 arrows of time. It is the game that all P.O.Vs of all planes of existences, from atoms to human beings perform.

Those logic and mathematical laws of points of view are the metaphysical laws of the Universe – the only essential events/forms that repeat unchanged in all forms. And so, a proper description of the Universe should start with the laws of i-logic geometry; then apply them to the 2 simplest motions of reality, lineal forces and cyclical masses/charges; and then, once those ‘immortal laws’ are defined for any system of energy and information, science should use them to define the specific events of each scale of reality and its species, as we all play the same Game of Exi=stence.

Recap. A Universe made of motions in time, extending through multiple scales of relative space, requires evolving the human languages of space (Euclidean geometry) and time (Aristotelian logic), used to describe the simpler space-time continuum of classic science. This task started by the pioneers of modern science (Riemann, Darwin, Planck and Einstein) must be completed before we can study the properties of physical and biological entities with the new tools of Non-Euclidean mathematics, which describe a world of multiple, relative space-time networks made of points as Complementary entities with energetic and informative system or ‘Points of view’ and the new tools of Non-Aristotelian logic, which describe the creation of the future by multiple causes – all the points of view or agents that create a certain network space.

The equation of the mind.

The 5 i-logic postulates define the unit of reality as a fractal point that observed in detail is in itself a World, which contains within it all the mathematical topologies of the 4D cosmos. This can be deduced in a logic manner, through the equation of a mind/p.o.v., which can map out as a mirror the whole Universe we perceive in its infinitesimal mirror.

In the fractal Universe all systems of i-logic information gauge reality, transforming a force they absorb into a logic language, which mirrors the Universe. It is obvious that the essential particles, quarks, photons and electrons cannot have a wide mapping of reality unless the fractal scales of size are infinite (and then an atom might be the upper bound of a new scale – a nano-galaxy).

Yet even if reality has upper and lower limits of size and point-like particles are not fractal world but the limit of universal form, those simple particles still gauge information and store some type of logic, mathematical computer-like structure that allows them to behave as they do, organically. Since particles orientate their position in a herd of self-similar particles; they move towards light, its energy, when the electromagnetic field is in its neighborhood and they decouple=reproduce into new particles when they absorb more energy. All those properties are the minimal properties we ascribe to a fractal ‘point of view’ or ‘mind’ in a broad sense – a structure that gauges energy and information, creating smaller fractal mirrors of reality. Such structure has within itself a minimal amount of geometric paths and logic processes that allow it to form the forces it uses as energy and information source. We thus call such structure a mind. Since any point of the Universe becomes a focus of infinite parallel forces that flux into the point, creating a static image of reality in Complexity, we define a Mind, as an infinitesimal mirror-world that reflects the infinite Universe:

0 (Mind-cell) × ∞ (Universe) = Linguistic Wor(l)d

The equation of the mind, defined by the 1st and 5th postulates of illogic geometry, sets limits of truth in linguistic science, comparing the worlds created by any mind and the Universe at large, much bigger than any informative, mental, linguistic image we have of it.

It is however the why that explains why entropy doesn’t dominate the Universe; since now the increase of order and information in the Universe is mainly caused by those ‘perceptive points’ that gauge information.

Those points might or might not be conscious in a vegetative or reflexive way, depending on its complexity; but they are ‘aperceptive’ – an expression coined by Leibniz to express perception without consciousness. And so they have a will to order and perceive more information, not only a will to feed and increase their energy. And so there are two ‘wills’ of feeding and gauging common to all points, which we can measure objectively, externally by the fact that when energy appears, particle move towards energy (so electrons jump and feed on light) and when other particles appear they gauge their distances. We observe this property in all systems when they form a focus, which emerges as the point of maximal order in which the network of the system integrates its information. Then the system becomes more stable: A crystal grows faster when the network creates a central point. A hurricane can be destroyed when the central, still point where all the flows converge is disturbed. A life being becomes erratic in its motions when it becomes blind.

A galaxy acquires order when a black hole, which probably gauges gravitational information, appears in its center. The existence of an infinite number of such points is undeniable objectively and adds an enormous amount of order to the Universe, which mechanist science does not account for. Stillness to focus information into a pixeled map of the Universe, and the existence of a network that fluxes in that point through which ‘infinite parallels’ can cross, are the two conditions of formation of gauging points. Then we can establish the birth of a complementary network of energy and information, an exi=stential point: exi=k; where k represents a ‘mapping of reality’ in the informative language that the waves of communication of the point with the external universe have created. This means that the models of metric measure developed by mechanist science merely creates a ‘space-time world’ self-similar to the mind of man in our machines, which does not exhaust all the measures of the Universe and its possible mappings.

We cannot construct if we want to account for all the cycles of time, dark spaces and events of reality, a theory based only in a continuum, mechanical, light-space and its Euclidean coordinates of light-measure. The limits of that model have been reached, as the limits of precision of the Ptolemy’s model of astronomy were reached in the Renaissance.

Those limits of an Euclidean, continuum space-time were proved by Riemann, Poincare, Mandelbrot and this author, expanding and completing the Euclidean postulates. Einstein applied part of those new models and created Relativity Theory. This work applies the rest of those discoveries to create a model of Multiple Space-times, which includes the concept of absolute relativity, where measure – the gauging and mapping of the external universe by a non-Euclidean point, is relative to the observer and the rods of measure it uses.

Recap: All entities of the Universe gauge information and act-react to the external world. Thus we consider all entities to have a mind – an internal, linguistic mapping of reality made with those forces.

The human point of view: I = Eye + Wor(l)d

That all what you see is a construction of the mind is the main tenant of philosophy of knowledge, from Plato’s world of ideas to Descartes’ devil putting reality inside us, from Schopenhauer’s world ‘in the eye’ to Schrodinger’s cat.

We are an I=Eye+Wor(l)d, a mind of 2 languages, as the other languages of sensorial experience, touch, smell and taste are irrelevant. We can exist without them. We see and verbalize reality, converting ‘whatever is beyond’ in geometrical images with the eye and temporal chains with verbs of past, present and future.

At present, the I=Eye has been highly developed in science due to instruments, mechanisms made of metal, a better atom than our paltry 1-6-7-8, HCNO structures. So we have pictures of all kind of scales of reality, from the infinitesimal atom to the galaxy. Beyond those scales things become blurred. Yet curiously enough the parameters of atoms and galaxies in terms of energy and information are self-similar. Is this because each atom is a galaxy of a nano-universe, or because our Mind, who measures, gets an aberration of distance parallel in atoms and galaxies?

That the mind’s scalar and continuous distance from those 2 realities, might cause our perception to equalize forms of atoms and galaxies is a way of thought proper of our awareness that all what we see is information already ‘cooked’ by the mind, ‘deformed’ and ‘transmuted’ by the Maya of the senses. We are not seeing the real Universe. We are a geometrical and verbal mind, which applies geometric and causal categories to interpret reality. And so all what we can talk is about the 3 dimensions of our spatial perception and the 3 dimensions of time, past, present and future, explained by our verbs. Hence, the importance of evolving our mind languages to have a better mirror in the smaller scale of the brain, reflecting the entire Universe. But the linguistic Maya, the ‘a priori’ mind who perceives, the I=eye+wor(l)d will always be limiting our truths.

The 3 dimensions of space perceived mathematically and the 3 ages of time perceived verbally are thus the last components of reality, which reflect the paths and arrows of time deployed by each species of each scale:

– In time, we observe constantly forms being born, going through an energetic big-bang, growth, maturity and then a still, solid warped stage before death.

– In space, we see 3 topological regions that correspond to energetic, reproductive and informative functions.

The total Universe is the only entity that stores all the information about itself. We exist as a dialog between the image of the Universe of our eye and the verbal information we extract from it, our I.

Humanity lives in a light-space world which scientists measure with machines and artists with the linguistic mapping of our senses, created with our inner languages.

Scientists in that sense are creating a new EyeóMind, the mind of machines that also measure space and time:

Mechanical Eye <=> Digital Thought.

 Indeed, scientists are not discovering the absolute truth of reality but creating a more complex Linguistic World, a world of digital thoughts and images that future perceptive machines will use to control reality. And because that world of mathematical and instrumental perception has more information than the human IóWor(l)d, on the long term A.I. robots might extinguish us, as superior minds/bodies. Of course, scientists do not understand this because they think the machine is an extension of their ego.

Ultimately we exist within our mind and so our truth is a subjective, human truth developed with our languages. We do not see the external world of quantum fluctuations but what our light/electronic mind creates, extracting only a part of the total reality to map visually the Universe, reduced to a light-space world. Our ego, our consciousness is and eye <=> Wor(l)d, a fractal space/time dialog between our informative mind, the wor(l)d and our energetic space, the eye:

‘I think and see therefore I exi=st’

So we are indeed a fractal equation/function of existence:

The Human Mind:  E (Eye) <=> I (Wor(l)d).

Minds are focused, ‘Aristotelian Gods’, defined in his metaphysics as unmoved, intelligent brains around which energy flows and ‘bodies’ turn, as they move the mind. Stillness is indeed the nature of mind perception. Even if reality is a moving fractal soup, our eye is not out of focus because its virtual images are still, like the pictures of a film that stops in front of the camera. Both images, in the eye and the camera, only move and change when we blink our eyes or the camera closes its window, stopping our perception. Thus, perception is also a stop and go process that focuses a still image through the senses and then processes that information into a thought, while the eye-senses are blinking, closed and the reproductive body moves slightly the eye-mind. In the human case that stop and go, perceive and move rhythm lasts a second, our ‘dharma’ of relative present-existence in which we create a still, simultaneous mental image of the Universe. Each second our fractal, informative mind closes a mental, cyclical act of perception:

Cycles of temporal energy=>sensorial in-forma-tion =>Brain-clock of time.

Truth is given by the languages of the mind. A truth is a mental/linguistic mirror of information within the mind that reflects the external universe.

Thus, unlike the naïve realism sponsored by physicists, a fundamental thesis of Systems sciences is to consider there is much more information in the Universe than the one we can perceive. Since each mind needs to select its information. Because each mind has a limited quantity of vital space, it can store only a limited quantity of linguistic ‘information’ about the cycles performed by other entities in the Universe, and so it selects only those pieces of energy and information that give an accurate depiction of the world in which the entity finds its energy and information and other self-similar species to reproduce and evolve socially. The rest of the Universe thus becomes a relative dark space.

Since the Universe is a game of entities of energy and information, relative ‘points of view’ that search for more energy and information to reproduce themselves and survive as self-similar ‘logic forms’, that game of survival has imposed limits to the information we perceive, maximizing information that ensures the reproductive and social games, the ultimate will of the Universe that ensures the ‘durability’ of each point of view, which will only exist beyond its ‘caducity date’, if it is able to repeat its energy and information into a self-similar being that continues the game of existence, once the original form is broken.

The 5th postulate combined with the analysis of the internal parts of a point and the trajectories of the cycles that the flows of energy and information between points follow, defines not only philosophical questions like perception and the nature of fractal information, but the fundamental causal arrow of time of the Universe: Energy->Information.

Since the flows of forces absorbed by the point create the ‘reality’ we see by constructing an image which is not there – the world as an ‘idea’ (Schopenhauer); that is the world-mind, the I=Eye+ wor(l)d we perceive, different from that of other species that perceive with other forces and minds.

Recap: The human mind, and probably all other minds/systems of information use 2 basic language of perception, a geometrical language able to perceive space and a logic language, able to perceive time. Humans perceive space with visual images and time with logic words. We are an I=eye+wor(l)d. Yet other species should use other versions of those 2 geometric/spatial and logic /temporal languages. For example, the complexity of visual languages ranges from a simple light/dark, on/off switch in simple particles to the simple geometrical motions of particles, to the richness of visual perception in animal eyes. While the complexity of Logic chains of events ranges from simple Aristotelian chains, A->B, which define the simplest arrows of Time (feeding, where A is energy that becomes B, the food of the predator), performed by all entities, to complex social networks in which causality is multiple, as each informative ‘neuron’ of the network relates through its axons to all the other cells of the informative system.

 The linguistic method and the ternary principle.

Our world is the creation of a space-time mind. Our ego is an image of our exi=stential self-made of eye-spatial experiences and verbal temporal feelings. Within those restrictions truth will always be related to the languages of the mind. Thus a truth will be higher when our linguistic image of reality has better ‘syntax’ to parallel the exi=stential syntax of the Universe (the generator equation, EóI), with our 3 languages: logic, temporal words, geometrical, spatial mathematical and visual images, which are the 3 legs that put together create a scientific truth:

Scientific, linguistic truth= Experimental, visual data + Logic, temporal truth + geometric, spatial truth.

Yet beyond our scientific/mechanical and human/artistic senses, beyond our I=eye+word, based in light images there is an even wider world with more information, the gravitational, invisible world, which might be mapped out, gauged and measured by quarks and masses.

The relativity of all minds that only decode part of the total information of the entity creates a new method of knowledge, the informative or linguistic method, which validates the existence of all kind of languages and senses to give us a more complex, multiple image of reality that a single language cannot provide:

‘Only the organism or universe stores all the truth about itself. If we give to that absolute truth a probability 1, the highest probability of truth will be the maximal number of points of view over the organism, expressed with the maximal number of languages.’

 Since there are ‘multiple spaces-times and points of view’, the linguistic method states a higher probability of truth is achieved with several perspectives on a certain system – as each point of view will create a self-similar image of the Universe, and so by comparing all those self-similar images we can obtain a kaleidoscopic image of the whole. And so in the same way a circle is not drawn with a pencil but born of multiple flows of energy and information that converge on it, a truth is not only mathematical, but man has at least the spatial, visual language, the verbal, temporal language and its two synoptic equivalents, mathematics and logic; and it has 5 senses, which give us other points of view, despite the belief of physicists that ‘the language of God is mathematics’.

The linguistic method however validates the dictum of the Upanishads: ‘the languages of god are infinite’.

And so knowledge must follow a simple scheme:

-First we define a scale of depth on the analysis of the metric measures of the 3rd paradigm (what and when): monism, dualism and the ternary principle, the highest form of knowledge. Then we apply the ternary principle to the 3 symmetries of the Universe:

– The analysis in space of the 3±st topologies of the fractal point and its interactions that create the being in space.

-The analysis in time of the 3±st ages and sub-ages of the existence of the being.

-The analysis of the being in space-time as a system that co-exists in 3 st±1 scales of reality.

– And we try to do this from as many languages of perception, not only mathematics, as possible on the being.

Recap. The linguistic method that widens the metric paradigm starts considering not only the ‘what and when’ of metric measures, but also the knowledge provided by other languages; and then it analyzes it from 3 ternary perspectives:

– A spatial, topological analysis of the 3±st regions of the being and its relationships between them as a whole.

– A temporal analysis of the 3±st ages of the being and its transitions and sub-ages.

– A space-time, analysis of the st ±1 scales=planes of existence of the being and its relationships as a whole.

Only then we shall achieve a deep knowledge of the entity.

 Physical particles. Bosonic Minds.

In the physical realm, besides our electronic minds there are gravitational minds, black holes and masses, which Einstein defined as foci of gravitational space:

 ‘Space=Energy is motion relative to a simultaneous frame of reference=a mind’ A. Einstein

We added in italic the concepts of Multiple Spaces-Times equivalent to those used by Einstein, who understood space as a moving energy warped by a mass, a frame of reference that ‘measures’ space-time. Yet Einstein was an abstract physicist, philosophically shy, and so he did not considered how a ‘mass’ can measure – an informative, mental action.

We consider that a mass or any particle of the Universe can measure space-time because it can perceive a minimal quantity of the gravitational or light forces that make up the 2 physical membranes of reality. Some particles exist only in one of those membranes (point-particles like quarks who exist only in the gravitational world or light which exists only in light-space). Other complementary entities, such as atoms co-exist in both membranes. All of them should be able to make relative, different measures from their P.O.V.s, which will allow them to act-react in their world but will differ from the relative measures of humans or machines, we call reality.

‘Naïve realism’ affirms that for example, the distance between you and me is exactly 2 meters, because an electromagnetic signal or rod measures it as 2 meters. This is not truth. Reality goes beyond what we see and measure with machines: The distance of 2 meters happens to be in light measures or light space. But if we measure with feet as the Greeks did, 2 becomes 6. And if we do not measure in light-space the light we see, but in gravitational space, as Einstein proved it, the distance would be bigger, as light warps the more extended, non-Euclidean world of gravitation in which the membrane of light space-time we call reality floats. Thus, our light-world is a reduced version of the gravitational world: a simplified Euclidean surface, whose 3 coordinates, x, y and z are perpendicular and lineal as the 3 fields of light, the magnetic, electric and wave-field are.

We exist in a space-time membrane made of light, whose final structure is the 2.7 k basic light membrane emitted by gravitational black holes that becomes the background frame of reference of our light World, only a fractal membrane of the infinite Universe.

The Universe is more complex than our simplified, naïve sense of reality that thinks the space-time membrane of light that humans inhabit and see is all what there is to it. With the same reasoning, if we had not eyes to measure the light-universe, but merely noses to smell it as ants do, we would see even a more reduced world, as our pixel unit of reality would be a pheromonal atom. The mapping of reality by our mind would be shorter and so distances would be perceived as smaller, as fewer pixels would create our smelling mind.

How the process of gauging information takes place in the Universe? We can only hypothesize that perception is an inner quality of the motions of the Universe. In other words, a software image of reality, a fractal mirror made of forces is a whole, who perceives itself. So the electronic image of the Universe a human mind has ‘perceives in itself’; and as the image changes when we move the head, our ‘ego-self’ made of images and words seems to change.

So should happen in physical particles that focus the forces of the Universe. Yet if we observe externally the process, according to the 3 topologies of Non-Euclidean points we can describe objectively those events of absorption of energetic forces by cyclical particles (charges and masses) as topologic transformations of external, lineal forces of energy into cyclical motions. Those cyclical motions finally reach the hyperbolic center of the particle, a double ring or singularity of increasing height, which should perceive the ‘translation’ of the information carried by those forces. Then those forces are transformed again into flows of energy and expelled back to the Universe, as magnetic flows in atoms or gravitational dark energy in black holes.

In most particles, it all starts in a surface of energy that curves itself into cyclical motions, which become smaller, faster and reproduce into faster fractal cycles, till reaching the center. Yet those forces, will never reach as quantum physicists believe the central point of infinity; because the cycle will fractalize into new cycles moving upwards in the informative dimension of height (Belgrami semi-sphere depicted in the graph of the previous paragraph) till it becomes expelled upwards through the poles, as a thin line of forces. And so the center of a fractal point, where physics find infinity remain silent, still virtual images, the perceptive eye of the hurricane or the black hole:

A flow of forces converges toward the event horizon or external membrane of the point (the Schwarzschild radius of the black hole or the Bohr Radius of the atom). Beyond this membrane, the flow of forces starts a process of creative, formal warping, as it rotates at increasing speed and also increases its frequency (height dimension), in each cycle. Because a bidimensional vortex stores more information than a lineal frequency, as it adds a new dimension of form, those forces acquire information. So we observe a bidimensional, cyclical wave of high frequency/informative mass that accelerates toward the center, becoming a convex topology, which the equations of black holes show, as the dimension of space becomes a high temporal dimension. And finally the left-overs of the force – once a mirror-image is formed inside the hyperbolic center of the particle, called in topology a Belgrami cone – are shot up through the poles as a magnetic flow in charges or a flow of dark energy in masses, invisible to us, but observed in quasars. Those flows of magnetism or dark energy of maximal speed and minimal form, once again will start a cycle of information, warping again into light under c-speed. So galactic black holes emit dark energy that becomes a seminal flow of protonic matter, which might give birth to a new galaxy, as it is observed in the galaxy M83.

Recap: A dynamic analysis shows that most events of physics are transformations of lineal forces back and forth into cyclical motions (particles and charges), which can be described as topological transformation between hyperbolic and spherical or planar geometries.

The many worlds=minds interpretation of reality.

All fractal points are Galilean paradoxes that perceive and act with a will defined by their desire to survive, absorbing energy and information from their environment.

To that aim the mind creates a ‘subjective world image’ of reality tailored to achieve its arrows of time; while the rest of reality is a relative ‘dark space and dark matter’ of other cat alleys and networks we are not interested on. Thus we exist in a single fractal universe of infinite worlds, which are mirror-image of that single Universe.

The difference with the quantum interpretation of multiple Universes is clear: now the ‘quantum Universes’ co-exist as mental world in the same single reality.

Such paradox explains the self-centered behavior of all systems that fix reality into form. The mind sees stillness and hence death in all those forms in fixes in its brain and yet all has movement all has a life to it; all forces can be understood as languages when the proper codes are translated. Indeed, for all what we said it is also obvious that the intelligence of the Universe doesn’t speak a single language, understood by man, but all beings can perceive and remember information, stored in rhythmic patterns and linguistic codes. The resolution of those codes in different languages and scales is indeed the essence of knowledge. Each species has limited languages of perception, the most complex perceive more languages and forces. In the atomic world, quarks, the most complex particles perceive, ‘see’ we say in gauge theory, all the forces. They are the most complex particles, probable cells of the black hole. In our world, men are the most complex beings. Nevertheless, animals who understand only smelling, chemical codes and visual codes are also intelligent and so are electrons who do not perceive gravitation in the atomic word – we are in fact electronic minds as computers are. Languages can use any of those codes. Cephalopods developed both the first complex eyes and a pigmented skin, which changes and modulates emotional messages in a silent code understood by other squids. Insects use magnetic codes to guide swarms.

Recap. Reality is a game of mental worlds of information. But we need to translate those languages to reveal its intelligence to the dumb human being who speaks so few codes properly and thinks the rest of the intelligent Universe is mute.

15. The speeds of time: different mind rhythms.

The rhythms of existence are organic, vital. We do not see them in stones and plant, because rhythms vary its speed and men only consider vital rhythms those similar to theirs.

Each species has a different rhythm of perception and existence, a different language of knowledge and mind, a different speed of times or capacity to act-react in the Universe. The rhythms of rocks are slow. So are the rhythms of galaxies. Thus, we transform mathematically the different rhythms and speeds of times to see them alive. For example, when we see in fast motion the living cycles of plants that seem dead, in slow motion, they acquire living properties. It is again the Paradox of Galileo: we see many temporal cycles as fixed forms in space, as we see the moving Saturn rings as a fixed form, yet all is moving, cycling in an organic way.

Physicists don’t understand that their clocks of time are abstract inquisitions of the mind. Instead of a ‘moving cycle’, often a living ‘ time’, when they think of time they see a number in a graph. Yet even a watch measures the cycle of expansion of its inner spiral, made of metal that dilates, expanding space; even the sun measures a year-cycle as it swims on the gravitational flows of the galactic spiral, feeding on fractal, gravitational space. Clocks are brains that measure cycles of time. So today the clocks of science have evolved into cyclical computers that are truly ‘metal-brains’ of machines. Time is measured as information for biological, survival purposes. Since the ‘fastest brain-clocks’ of temporal information survive better. They see with more detail everything alive and act-react faster to the Universe. So our incapacity to see a living Universe is only a proof of our limited intelligence and memorial detail. Andre Guide affirmed, regarding a similar phenomenon, that ‘the more insensitive the white man is to the beauty of Africa, the more he despises and mistreats the black people’. So happens today with humanity at large with Nature.

 Recap. When we understand that there are many energies that feed space-time beings, many ways to inform brains, many speeds of perception and hence life; yet all are harmonic with each other, a deeper philosophical sense illuminates our mind: We are part of the same Universe and share the common properties of any of its infinite organic systems.

The harmonies of living points: Chip paradox.

A huge organic system of temporal energy like a planetary core crystal might form an image-thought each day; a plant thinks slowly, a fly sees faster, a rat beats its heart faster than we do. For example, spiral and elliptic galaxies are phases of a feeding cycle in which the spiral bar appears and disappears after collecting interstellar gas for the black hole every 1010 years. Scientists are now ‘putting together’ many similar dual forms that are phases of an organic, existential cycle. This is the new trend in Astrophysics: First neutrons and protons were considered 2 particles but now they are 2 phases of a nucleon E (proton) <->I (neutron) cycle, as nucleons absorb pions, transforming into each other so fast we can’t see it in detail. Last year we realized that the 3 neutrinos were part of the same particle, mutating its state. The same phenomenon happens when we see a human being externally: our skin appears as a fixed organism in space as its cellular cycles are perceived as a stable form.

Only anthropomorphism and the limits of perception make us differentiate those scales. Yet when we ‘enlarge’ the image of a non-AE point, for example, an insect, the detail of the information we observe grows and so the world of insects is as rich in meanings and forms as the macro-world in which we live. Since all waves carry the same amount of fractal information regardless of its spatial size, according to 2 simple, paradoxical laws: the law of the vortex for cyclical, implosive, attractive ‘particles’ (charges and masses), Vo x Ro=K, and the fractal law that defines transversal, explosive waves, E/v(t)=K. Both show that temporal energy increases when the masses or waves cycle becomes smaller.

All is alive yet with a different rhythm, a different beat. The beat of each temporal organism is an action-reaction cycle with a different clock, a different fractal rhythm and temporal speed. They are all around you. In a garden, the wings of a ‘hummingbird’ take energy from the air 200 times per second. It is a clock faster than the energy beat of your heart, 80 beats per second. The energy of the wind moves the leaves every 2 minutes. A gardener is a clock that waters plants a beat each day… Those action-reaction cycles are everywhere in the Universe. Some beings are faster in their active cycles like the hummingbird; some are slower like the plants and the galaxy. In most cases the bigger the species are, the longer they take in each of their active cycles: A galaxy turns around every 200 million years, the Earth every day, your eyes beat and absorb light-energy every second, the hummingbird’s heart beats 800 times every minute, the electron turns 30.000 cycles per second. Each organism, each region of the Universe, has a different speed of feeding and perception. People think that slow species are dead. But that is not true. They tend to be energy species that just have slow rhythms of information and live longer. While more informative, evolved species think faster and live shorter. Often the smaller the species the faster it can complete its cycles of information. So brains are small and chips evolve, becoming smaller as they become more powerful. Yet chips last a couple of years. And man, an informative species seems so self-destructive, so loving of information, the age, which precedes death, that we might be the shortest living animal on Earth.

The main law of existence is the balance between space and time, ExT=K. As we diminish in spatial size in the Universe, beings become faster in time, creating a balance according to which, smaller beings perceive and exist faster, being able to escape, slower Goliaths. Those regularities of the game of existence show a certain equalitarian justice in the Universe. Indeed, in each world-ecosystem the subjective existence of its organic systems is similar, despite their different size. So we can gather them in ‘families of species’ around a ‘constant of action’, K=T x E, which is the product of its speed of perception or frequency of perception of temporal information and its spatial extension. For example, it seems all mammals have the same metabolic existence: The rat lives less than an elephant but her heart beats faster. That faster perception speed also prevents small species to become extinct in the same ecosystem inhabited by bigger species, as they act-react faster and so they can escape top predators.

For example, according to the previous inverse law of mental speed a fly sees 10 times faster than human do, since flies are smaller, so they perform 10 visual fractal actions by each human blink. Yet because its brain’s fractal neuronal density is not very high, it is not a top predator as robotic insects might be in the future.

Curiously enough the oldest insects, ant queens and cockroaches, can live up to 7 years. Yet cockroaches react in 20 milliseconds and humans in 200. Which means that if they perceive time cycles 10 times faster than we do, subjectively they process 10 times more fractal actions of temporal energy, or ‘dharmas of existence’ (philosophical jargon). So they live the same subjectively life of 70 years… the same length of a human existential= generational cycle.

It follows that there are parallel worlds, one for each relative hierarchical space-time scale, based in different Constants of Existence. In physical worlds the most important of those constants are the Universal constants of force, which express the previous K= ExI balances in different abstract ways. For example in quantum theory H= ExI is always constant (Heisenberg Principle). But that constant of the microcosmic world is different from its equivalent constant, temperature, in the atomic world, which also shows a self-similar balance for gases: P(t)  xV(E)=nkT.

Other constants however are written not as TxS=K balanced, but as E/I or I/E processes of Darwinian evolution, which define instead of organic balances, processes of transformation of certain energy into for and vice versa. The most important of those constants in the 2 physical space/time planes are G and Q, which represent, as the Newtonian and Coulombian formula shows, T/E, Mass-Charge/Distance events, in which in words of Einstein, cyclical masses absorb and bend the energy of space. On the other hand, in the electromagnetic world light-space is absorbed and transformed, curved into electronic form. Yet since the density of information of the electromagnetic world is smaller than that of masses, given the fact that electrons are lighter and more extended in space than gravitational quarks, paradoxically the energy of its electromagnetic constant is much bigger.

Thus the relative transformations of gravitational and light spatial forces into masses and charges are also ruled by decametric harmonies, as those of the biological speed of action-reaction of flies and humans. All together we can consider a simple scheme of the main many-worlds of the Human Universe, according to their relative energy and information density. Indeed, According to the different forces of the Universe, each organic system has a different mind since it absorbs different temporal energies and so it creates different mental, linguistic ‘spaces/times’, relative virtual worlds, mirrors of the Universe.

The world of each being represents a quantity of spatial information with a size, form and number of dimensions that are relative to the spatial reach, form and dimensions of the informative, linguistic forces it uses to observe the Universe.

So while the Universal Syntax all minds use to create their virtual maps of the Universe is homologous in all beings, in as much as they reflect a single Universe, the details, quantity and quality of the information of those maps depends on each brain; since worlds are multiple, fractal, diffeomorphic. So, depending on which type of temporal force of energy each fractal being absorbs to create its mental map we can define different worlds or ecosystems in which a certain force is shared by multiple discontinuous Fractal points that interact only with the other points of the same ecosystem but now with parallel worlds. For example, masses are fractal nodes that inform and/or perceive gravitation, which we do not see. We are fractal knots of light perception. Ants have olfactory brains that perceive atoms. Different beings live in parallel discontinuous worlds within the same Universe.

Even an electron, the smallest form known to man, processes light information and jumps towards a moving photon, absorbing its energy to enhance its survival chances. Equally, black holes and quarks process gravitational information, locating themselves in the best position to absorb it as masses. While a chip uses digital information to guide a machine, etc. There are other spaces and ways of measuring time besides light and clocks, other possible virtual worlds and intelligences besides man. Since man is made of the same atomic material that the rest of the Universe, the capacity to communicate in this universe – the most clear prove of life – is not exclusive of human atoms but a property that takes place through different atoms and forces; including metallic atoms such as those of computers or gravitational forces used by celestial bodies. So men talk, chips digitalize, animals see, plants ‘smell’ and masses process gravitational information.

We classify those worlds, according to the volume of temporal energy their linguistic forces carry, in a scale of increasing st-complexity, ruled by the Black Hole paradox: The smallest and faster particles scan with more detail the Universe; so they carry more information and create bigger, faster mental worlds, inhabited by species with more TxS force. Accordingly we consider 4 basic worlds:

– Big, slow atomic quanta create animal olfactory minds that perceive small metric territories inhabited by small animals like ants.

– Smaller, faster electrons create electronic minds that perceive kilometric territories inhabited by bigger animals like human beings.

– Photons create bigger worlds of planetary size perceived by huge machines and chips (the brain of future robots) at global scale (Internet, satellites, etc.).

– Gravitational forces of reduced size create words of galactic size, which might be perceived by celestial bodies like Black Holes (minds of the galaxy).

So the Gravitational world is bigger than the light world, bigger than the electronic world, bigger than the molecular world because paradoxically gravitons are faster and smaller than photons, which are faster and smaller than electrons, which are faster and smaller than molecules. So a black hole can perceive an image ‘with more detail’, more ‘pixels’. And since gravitation is faster than light it should ‘change’ the fractal mind’s images it creates faster. On the opposite extreme, plants and olfactory animals perceive molecules, which create images ‘with huge pixels’ that offer little detail and change very slow. Thus we consider that every organic system in the Universe, which processes information and survives efficiently, is a focus of a dual force that carries temporal energy and helps him to act-react externally in a manner that seems to improve the survival of that entity.

Each bigger world and faster language increases the TxS force of its species, which become top predators. And indeed, the analysis of the theoretical speed of informative perception in black holes has shown that they are the fastest ‘computing minds’ of the Universe. So black holes can easily destroy a planet; huge machines kill animal life; human beings kill olfactory ants and insects kill plants. It means top predators are defined in terms of the power of their linguistic brains.

Reality is a game of Russian dolls in which each bigger Doll /World encloses the smaller one. The gravitational World encloses the light world, which encloses the electronic world, which is bigger than the atomic world of ants and so on.

Recap. Each species has a rhythm of times. Slow species are perceived as dead space by faster species. We think plants do not perceive because they are slow in their rhythms of Times. Yet they are alive, feel, and sense in a chemical manner, through their roots and leaves.

Mind dimensions. Holographic principle revis(it)ed.

We explained in the simplified lecture that introduced multiple space-time theory that the Universe is a holography of an informative bidimensional field and an energetic bidimensional field that created the 4 dimensions of reality.

This is the case of the simplest forms like light, which is merely a membrane with two perpendicular energetic and informative fields.

But complex ‘closed topological balls’ with 3 regions, a hyperbolic, informative center, an energetic planar spherical membrane and a Klein body of reproductive cycles has a more complex holographic principle and other ‘varieties’ of higher or lesser dimensionalities.

In those ‘complete’ st-points the central discontinuous zone of a fractal point is an informative region, which adds the dimensions of the energetic membrane and reproductive body to create a mapping of itself and the Universe (imprinted in the senses of the external membrane). And this gives birth to different dimensionalities according to which ecosystem we study but a simple law stays:

Hyperbolic dimensions=Body + membrane dimensions.

If the reader observes the graph in our lecture on topology (II, 4) of the 3 regions of a non-Euclidean point, it will observe that the central region of a st-point doubles its form, as the brain that maps out the rest of the Non-E point.

And so there is a hyperbolic region of pure information that doubles the topology of the membrane and body region. Since the hyperbolic center of higher form/information has by definition more dimensions than the energetic bidimensional membrane and the reproductive bidimensional toroid; since it holds the 4-dimensional holography of the Universe. It is the key law of dimensionality of Non-Euclidean structures; of which 2 variations are paramount:

Bidimensional-reproductive system + Bidimensional energetic membrane = 4-dimensional hyperbolic, informative mapping.

Bidimensional external membrane +3-dimensional cyclical volume:

5-dimensional hyperbolic nucleus.

 These simple laws of dimensionality balance the 3 regions of a Non-Euclidean topology and it is central to understand the workings of different minds, which in terms of information write as:

Information of hyperbolic ‘brain’= Information of Klein’s ‘body’ + Information Riemann membrane

In metaphysics, which searches for the logic and geometric laws, derived from the 5 Non-Euclidean postulates, from where the arrows and wills of the organic Universe are deduced; a mind is understood as a fractal image, reflection of an internal body and an external Universe, which connects both regions of the st-point. In a st-point the membrane is the first mapping of the Universe, and the intermediate body, the inner world that reproduces, feeds and maintains the system. A mind will constantly check both, the membrane and its sensorial image to which it is connected through a nervous/informative system and the inner body, to which is connected through a reproductive/energetic system. So a human brain is connected to the inner world through the blood system and the external world through the membrane senses. It has two images of reality and it combines them both, word feelings and eye-images, to act with 2 purposes: to maximize the informative perception of the external world and the inner, reproductive and energetic feelings and pleasures of the Internal world.

This complex explanation of the human being, explored in more detail in other works, is reduced to a minimal skeleton, maintaining the scheme of wills and purposes, when we study the simplest forms of the Universe. And it is the origin of the Maldacena Conjecture A,12 (a black hole, informative center of the galaxy has in 5 dimensions the same structure than a galactic mapping in 4 dimensions.)

Recap. The dimensions of the hyperbolic, informative center are the sum of the dimensions and information stored in the cycles of the reproductive body and the energetic membranes, whose senses map out the external Universe.



A line is a wave-like event which communicates 2 st-points through a herd of fractal micro-points- a lineal action, exi, of energy that carries a frequency of information in which a message is encoded. The language of information is highly invisible to points outside the network that emit those messages as a flow of micro-points, self-similar micro-replicas of the mother-point that travel in waves across the external Universe transferring energy and information.

In most events those flows balance one point with more energy, Ei, that each science defines with different slangs, (‘a white hole’, ‘energizer’, ‘past form’, ‘male’, ‘body’, ‘yang’, ‘moving field’, etc.); and an informative point, Ot, the smaller form (‘a black hole’, ‘codifier’, ‘future form’, ‘female’, ‘head’, ‘yin’, particle or ‘center of perception’, etc.) Both become united by a dual wave that transfers energy from Ei to the informative point of relative future, Ot, and information from the future point, Ot, to the relative past point, Ei, creating together a cycle of temporal energy. The description of those points and cycles, which are common to all beings of space-time, creates a fractal, i-logic geometry common to all sciences and Universal species.

Motion as reproduction of in-form-ation.

Because points are constantly gauging information and feeding on energy, the most common events of the Universe are the absorption of waves of energy and form and its communication between 2 points that share energy and form.

In the graph, we observe some basic acts of communication in which self-similar complementary species exchange energy and form in actions that bond them. Human sexual species communicate information and energy (social love) but also seminal particle that combine both reproducing a self-similar being (sexual love); fermions, big atomic particles, communicate bosons, smaller particles of forces. Humans communicate with machines through prices and salaries. Thus money is the force of communication that creates the actions of consumption and reproduction=work of machines by human beings. In all those events there will be however different they might seem, certain laws of i-logic geometry, which all systems will follow and will define the outcome of such encounters, according to the 3rd postulate of Non-Euclidean geometry that defines the relative equality between st-points. So certain events are ‘Darwinian’, when species are so different that cannot share information with a common language and so use each other as relative energy, or events of eusocial love if the points are self-similar.

The main element to take into account when 2 knots of time communicate is the nature of the information and energy they communicate. This process is described in the next equation, which is a causal chain deduced from the Generator equation of all events of energy and information E<=>I:

∑ est-1 (energy converging into the point)+∑Ist-2 (flows of information)->

EIst feeding and perception) -> ∑ est-1 x  ∑ist-2

The previous equation is a general law of all systems that process energy into information:

– The membrane will absorb through its mouth bits of energy of lesser form than itself, normally from a lower scale of relative space-time. So we feed on ‘meat’, extract the amino acids and molecular information we require to create our own flesh and expel a degraded mass of molecular atoms. Light imprints its form in the gravitational space-time of the lower scale; electrons feed on light photons, etc.

– Yet to perceive and map the world we need maximal detail achieved by absorbing ‘pixels’ of a force, whose micro-points are from at least 2 smaller scales than the point. So particles seem to communicate and perceive gravitation (entangled, faster than light effects of quantum physics) and we absorb the smallest pixels (light) and smell atoms.

– Finally to communicate we share entities, created with combinations of that primary energy and information, encoded within it. Yet the value and intensity of the communication and the bondage created will depend of the density of form and quality of energy we share. Thus the lowest scales of energy and form will not be used to communicate but will be expelled constantly as the left-overs of our constant feeding of energy and information.

For example, humans feed on meat and can share food, to create bondage, but will not share ‘waste’ or violent ‘energy’ without form, if they want to create bondage. Black holes absorb light and mass from the galaxy and seem to produce faster-than-light gravitational, dark energy of lesser form, belonging to the lower space-time scale of gravitation.

And yet because of the scalar, hierarchical structure of space-time, nothing is wasted, since for ‘lower’ entities waste might be energy to recreate simpler forms (flies that feed on waste, irregular galaxies born from the energy emitted by black holes, which evolves back into matter).

The reader must understand the importance of those scalar laws, ignored by standard science, stuck in the concept of an abstract, single space-time continuum. Since the Universe is ‘equalitarian’ in the same scale, but hierarchical when we study the relationships between cells and wholes, lower and upper scales of reality, and the paradoxes, contradictions and harmonies between the Points of view of those scales are essential to understand most events of reality.

Once the process of creation of a fractal wave information is defined, we can explain most actions and events of communication as processes that involve first the ‘fractal reproduction’ of a form which uses its micro-forms to pattern a message that will be shared with a self-similar form.

The st-point is not static but in constant communication with the external Universe, populated by other st-points that obtain energy and information also through acts of communication, which are dual events, defined in fractal Geometry by the 2nd postulate of communication. Since according to Newton, an action never goes unanswered: There would be a reaction often of the opposite sign. Thus to understand any event we have to wait for a reaction to complete a cycle. One-dimensional science often forgets this duality, considering ceteris paribus analysis of a single action. In the human social scale, individualism often forgets such duality when a nation attacks another nation, or when a group exploits another social group or an individual acts selfishly without expecting the proper reaction. Yet sooner or later the just, cruel, Darwinian Universe will react and balance the game.

Because the Universe is essentially dual, made of lineal energy and cyclical, dimensional form, this duality happens in almost all the events of reality. So points will emit micro-points, with a combination of energy and form. For example, if the original st-point has emitted a fractal action, dominant in energy, ΣS, it will receive an opposite reaction, often dominant in information, Ti, completing a cyclical action of temporal energy, ΣS<=>Ti.

In the same manner when a group of points emits a wave, it will receive an opposite wave from the receptor, creating a cellular, complex cycle.

Finally, if we combine 2 planes or networks of points, communicating waves of energy and information, for example, human cells communicating energy and information through the blood and nervous network of life beings, we obtain a complementary event or Organism.

The two main types of ‘forms’ any point emit are also, either a ‘seed ‘of information or a ‘ghost’ of space: Fractal entities can emit a self-similar microscopic cell, with maximal form and minimal energy/extension; or they might move or vibrate, emitting a ‘wave’, a vibration of its external whole with maximal energy and minimal form. It is the first of the multiple dual solutions, which any entity can choose, according to the dual arrows of energy and information of the Universe. Thus Duality becomes essential to classify the multiplicity and variety of events in the Universe, since it sets self-similar limits due to the existence of only 2 arrows/forms/ substances to play with. It means most events will be either dominant in energy, or information or a balanced combination of both.

In the ∞ Universe, actions and reactions that define those events will have different names according to the st-plane of existence in which they occur, but they will respond to self-similar existential laws.

Since sciences are accustomed to analytical, detailed studies that differentiate species, they do not search, as this synthetic work does, for the self-similar laws of all those communicative actions. Yet precisely the beauty of the fractal Universe is that both approaches are meaningful. Since self-similarity doesn’t mean equality: fractal scales create self-similar forms, which are never an exact replica of the original. Those variations across space/time scales differentiate species, which still compare in terms of the similar properties of all relative energies and forms that together shape a communicative action, according to 2 fundamental laws:

-The law of self-similarity, which states that any action will be a micro-form self-similar to the mother-cell, and:

-The law of balance, ΣSxTi=K, which implies that the product of the energy and time of the action is constant.

For example, if the point is a particle of the light-membrane, the communicative action will be a multiple of h, the smallest micro-form of energy and time of the electromagnetic world, ruled by the law of balance, e x t=h; if it is an atom, it will be a vibration with a temperature, T, which again will be ruled by the law of balance, in this case PV=nkT. And because we have ascended our plane of existence from spatial, lighter particles into atoms denser in form with less spatial speed, the action will be denser and reach lesser extension than a fractal h-action.

This will be the case also in biological actions of communication: if the mother-cell is a living being, it will emit an ovule of pure information that will merge with a seminal seed with higher energetic movement, or male seed. Both will be replicas of the fractal generator or mother.

Finally in the human social sphere, actions are often purely informative: certain thoughts act transforming our environment through the intermediate motions of machines that increase the energy and information of the human action. Those machines are themselves replicas of our energetic and informative functions. Yet unlike most actions of physical particles, machines have a peculiar structure. Their function/information is often simpler than that of man, so a car is simpler than the leg, whose energetic function substitutes, but larger in space, so the car moves faster. Those complex relationships between humans and machines, which enhance our energy and information when we consume them, can now be understood in the context of our search for more energy and information, creating a symbiotic species that we call in our complex analysis of history, an ‘animetal’: animal+metal.

Thus, all, including men, generate actions made of flows of energy that carry information, used to communicate with other points. So we widen the fractal unit of quantum physics, the action of temporal energy that communicates particles to define all type of actions-reactions in all space-time systems.

Thus the 2nd postulate of fractal geometry defines a line, no longer as an abstract form like Euclidean geometry does, but as a physical wave of self-similar, fractal micro-points that carry energy and information, as they move between 2 macroscopic points, with 2 possible functions, to communicate energetic forces or linguistic information.

2nd Postulate: A cycle of fractal space-time:

‘A wave of communication is a group of self-similar micro-points that move in parallel lines between 2 macro-points, transferring energy and information between them’.

In Non-E geometry a line with parts is not defined by a sequence of numeric intervals within a straight line, but by the communication of 2 poles of energy and information that establish a flow of particles in 2 opposite directions, creating a simultaneous, paradoxical wave. Such waves again can have different purposes. A wave dominant in information communicates symbiotic particles, creating an informative bondage/network; a wave dominant in energy might be an aggressive action between different species that fight for each other’s vital energy or territorial space; and a wave that balances the energy and information of both points meets in the center, creating a new self-similar, seminal particle, as when 2 electrons emit waves of densely packed photons, which merge in the middle and give birth to another wave.

When we generalize those concepts to n-points we can define a space as a network of Non-Euclidean points. Indeed, Riemann affirmed that a space is a network made of herds of points with similar ‘properties’. Planes of space are therefore networks of points. The self-similarity of their properties defines its density determined by the number of points and its proximity that grows with self-similarity. So similar points come together into a tighter, more continuous space; whereas the density of the space is proportional to the similarity of its points, till reaching ‘bosonic state’ of maximal density when points are equal.  And when a volume of spatial energy is very dense, it is very difficult to go through it, as it happens in the ultra-dense, small space of black holes.

Spatial extension and form/density/mass are inverse parameters, Max. E = Min. I. If we generalize that property to all scales, we can define different fractal spaces by its proportion of mass/density and energy /distance. This is done with ‘Universal constants’ that explain the proportions of energy and information of those spaces. For example, in physical scales, there are 4 fundamental space-times, the gravitational space-time between galaxies of max. energetic space and minimal formal density; the light space-time of our world, which carries information in the frequency of the wave; the electronic space-time of atoms with more formal density and lesser spatial speed and finally the quark-gluon liquid of atomic nuclei and probably black holes, with maximal density and minimal space. All of them are defined by Universal constants and equations that are either ratios between the energy and form of those space-times, or define the transformations of one space-time into the others. Einstein’s field equations would be the first case, defining the relationship between energy and mass in a gravitational space, while the fine constant of electromagnetism would define the transformation between light space and electronic space/ charge; and the gravitational constant between gravitational space-time and quark/mass. Where the relative densities of information and extension in space of those space-times are in balance, such as ΣSxTi=K. Thus electrons move slower than light but have more density.

All this said it is thus obvious that the fundamental unit defined by the 2nd postulate is no longer a point but an action, ex i= k between points, which becomes the 2nd fundamental ‘particle’ or ‘parameter’ of reality. We, points of time, create actions, exi, with a minimal quantity of form, moved by an energy force, creating lines, which therefore become actions of energy and time. And all what we do are actions. So we say often ‘I don’t have time or energy to do so’. Actions become thus the fundamental event of all points of view, in search of their arrows of time; it becomes the dynamic definition of a line, as we are all in constant motion, and so all point in motion can be perceived in slow camera as a ‘line of action’. And indeed, in physics an action is the fundamental unit of our light-space membrane, exi=h; and an action is the fundamental unit of biological behavior, which also defines the existential force of a being, exi=k, or the momentum, m(i) x V(e) = k of a physical being. An action is also the name given to the fundamental unit of economical organisms (companies). The Universe is thus a world of infinite points of view performing lineal actions in search of their arrows of time.

Recap: Non-Euclidean points constantly communicate energy and information with other self-similar points and the external Universe, by sharing flows of micro-points of a lower scale of space-time, which carry the energy and form of the particle into the external universe. The laws that define those acts of communication are hierarchical laws between planes of space-time and laws of balance between the energy and form of those ‘actions’ of communication, exi, which become the fundamental dynamic event of any scale of the Universe.

Ternary principle of creation.

A fundamental principle of Time Theory is the ternary principle: because all systems are designed with 3 purposes, to process energy and information or mix both in a balanced, reproductive, exi, action, we often find in all type of events a ternary choice, which will be specially relevant to understand the processes of ‘guided evolution’ that limit the number of possible creative species. For example, we can define human evolution as a constant differentiation of ape species into energetic, informative and reproductive ones; where the human lineage is that of species with maximal informative/head evolution, while the gorilla lineage is one of maximal energetic/body evolution and so on.

The 2nd postulate differentiates according to the ternary Principle 3 types of waves: A language that transfers only information, (Max. i); a force that transfers only energy (Max. E); and a wave that transfers both forms (ExT). All forces and languages are waves, since actions mix energy and temporal information; which will be perceived as languages when the absorber can decode that information. It is the receiver, which selects the wave as a force of energy or a language of information, defining how it will react to the emitter, according to its self-similarity that will allow him to understand its information. For example, plants absorb light as energy and animals decode it as information; but light is dual.

In algebraic terms, a function of existence is described with 2 parameters, X and Y that represent an informative subject and an energetic object, often complementary.

In biological terms, an organism is defined by a head of information, a relative future, more evolved form; and a body of energy, a relative, less evolved, past form. So we can consider also dual organisms as acts of communication between two poles, the reproductive body and the informative head, where the neck is the bridge that carries the bigger number of veins and nervous paths – the informative and energetic networks of cells that communicate body and mind.

Since the head directs and decides ‘the future’ of the entire system, informative poles are future poles. So a relative informative region is a future form and a relative energetic region is a past form. And both come together into a discontinuous, relative fractal, intermediate region or ‘present space-time’, in which they combine creating ‘reality’. That region is a present region because it is the most visible region of the Fractal point, limited by the future, informative region and the past, energetic membrane.

Those temporal distinctions and degree of visibility of the 3 topological regions of a point, now studied as two poles of communication are real; since the reproductive, present region, is always the most visible, given the bidimensionality of energy and information. For example, we do not see the black hole and dark halo that controls the galaxy but only the intermediate region of stars. In this manner the game of space-time existence that creates reality merges 2 poles dominant on spatial energy and temporal information into a new combined form, a relative present, fractal space-time:

Past=energy body xFuture informative head=Present organism

We explained before the 3 dimensions of time, past=energy, present=repetition and future=information, showing that most systems in the Universe live through those 3 dimensional ages, dying back into energy, as they dissolve its formal networks. Yet, while the Universe has very few elements/arrows to play with, its diversity comes from the possible variations and combinations of those arrows. And so, while we can write Past->Present->Future, as the natural causal arrow of the life cycle, there is also an equation of relative times, past x future = present, which defines the complementarity between reproductive bodies/fields and informative heads/particles and explains the present stability of systems which have both components or can switch between motion and formal states.

Further on, the use of the ternary principle, applied to the 3 languages of man (energetic geometry, temporal logic and exi, visual perception) will allow us to verify in a higher degree any statement, by considering at least the biological function/motion and geometrical, still form of the species we study, which have to be self-similar. For example in a galaxy, the black hole is the spherical center of information. And we can prove this according to the linguistic/ternary method in the space-time languages of man, the mathematical language of space, the bio-logic language of time and the visual language that merge both together. In algebra, Einstein equations prove that black holes transform its spatial parameters into temporal parameters. Hence they transform spatial energy into temporal information. In visual terms they curve space-time into height; hence they transform energy into information. If we consider its biological function, they absorb the energy of star-plants. So Black holes are sinks of gravitational information.

And gravitation is obviously the informative force of the Universe; since it is not dual but it shows only the arrow of in-form-ation, attracting and lumping masses and it is 1040 times less energetic than electromagnetism. So when we observe vitally, visually, in action, those black holes, they show the maximal amount of the 2 dimensions of temporal information: height and rotational rhythm; as they seem to turn at light speed and theoretically transform the plane of energy of the galaxy in a tube of infinite height. Thus all languages and experimental data prove the fact that a black hole is the informative brain of a galaxy that feeds on electromagnetic space towards the future. The extended, faster plane of rotating stars is the body or energy surface of the galaxy that feeds them. Apparently a human body and a galactic body should not have anything in common; but if we observe the morphology of both, it is clear that those morphologies respond to the generic morphology of information and energy, and so do their functions in time.

Recap. Events in the Universe are limited by the ternary principle. Actions of communication also obey the principle: There are energetic, informative or reproductive events, creating often complementary systems with an energetic pole or body and an informative pole or head, communicated by a dense network or neck that carries the actions. The 5 Postulates of non-Euclidean geometry are based in the definition of a fractal point as a point with inner parts, revealed when we come closer to the point. According to such definition, lines are waves of points and planes topological networks of points, communicated through flows of energy and form. While equality requires also equality in the inner form or information of the point, which prompts communication through waves of energy and information that build networks. Communication between points is now possible because points can fit infinite parallel/waves used to gauge the Universe and create an inner image of reality. Non-Euclidean fractal geometry thus improves our vision of the Universe closer to reality and allows the definition of organic systems and logic behavior in bases of geometrical form, a long-sought dream since the times of the Greek.





In the graph, a complex organism can be written with the algebra of Multiple Spaces-Times as a chain of points joined by energy/information flows between several ‘planes of existence’.

The 4th Postulate: networks and chains of existence.

Exact topological graphs however are only important when we study simplex, physical, homogenous planes where the diffeomorphic dimensions of energy/form/reproduction correspond to the 3 dimensions of Euclidean space.

Because of the flexibility of networks can adopt open and closed, motion and formal geometries in most cases, such as the graph we have to consider more than the basic O-cyclical i-nformative and |-energetic forms, shown in the graph, with symbols of i-logic, the causality of the events, which allow us to apply the same laws to all disciplines. For example in Economics Ricardo points out to the logic of increasing communication between points when he explains the advantages of free trade of different products between nations (nails from England and Porto from Portugal).

The same ruled applied to points of view means that ‘complementary points’ of energy and information that can exchange energy on one side for information on the other side are beneficial for both points of view. This explains the abundance of dual, complementary, fractal structures in which 2 networks, one of energy and the other of information entangle together, as in your body (nervous and blood system) or in the Universe (light and gravitational networks).

We have now the tools and understanding of the structure of mathematics to tackle in the rest of this work on the Languages of spacetime the ‘big question’ about reality that those languages enlighten: how can we describe better, the construction of the super-organisms of knots of time, which extend through ‘several planes’ of existence, and underlie the ‘structure of reality’.

All this belongs to the most complex and fundamental postulate of i-logic geometry, the 4th postulate, coupled with the understanding of the ‘causal, multiple logic of time arrows’ that structure several planes of existence, displaced not only in space but also in time, into a single organism.

The Universe is a fractal of planes of space-time’, which constantly appear, grow and dissolve in infinite events of existence. How Multiple Spaces-Times become chained and connected, building from simplex particles super-organisms – those planes of existence of reality that structure the Universe? The answer is the 4th postulate that defines the creation of networks of points, called planes.

Each st- point is a knot of times that becomes chained in a dynamic relationship with other points of time through its arrows of energy, information, reproduction and social evolution. In this manner points form ‘chains’ of existence, which become either ‘Darwinian relationships’, when one of the 2 points of communication is ab=used as energy of the other one with ‘more existential force/momentum’ or a stable, complementary relationship if both points are symbiotic, as energy and information or parallel, self-similar, forming a herd – a network of equal points that act together as a whole.

In Geometrical terms, the Universe starts with simplex st-points that communicate flows of energy and information, creating lines and geometrical groups. And the rules of those geometrical events of creation are defined by the 1st and 5th postulate that explains the parts of the point and its apertures to the external universe from where it communicates flows of energy and information; by the 2nd and the 3rd postulate which define in geometrical and behavioral terms the relationships and lines of communication between two points, according to their degree of equality. So the 1st/5th postulate, which defines geometrically and logically a point and the 2nd/3rd postulates, which defines how they communicate, establish the conditions that will determine the type of topologies or network/spaces that the system creates. Those organic topologies is what we call planes of exi=stence, explained by the 4th postulate of i-logic geometry. Since a plane is a group of points coming together as a relative space, which will be ‘more dense’ according to their degree of self-similarity (Riemann’s masterful definition of any space made of Non-E points).

Thus, if the first & fifth postulates are related to the perception of information and energy by a point, with its inner body/head parts; and the 2nd and 3rd postulate are related to the arrow of reproduction between complementary energy/form, male/female, yang/yin beings, the 4th postulate explains the details and possibilities of social creation of arrows of time; facts which establish a clear mathematical relationship between the arrows of time and the postulates of geometry in which all mathematical laws are based.

 Creation of Planes of Space=networks of points.


The Universe constructs super-organisms, building Planes, which are networks/herds of non-Euclidean points, step by step, according to the geometrical and biological laws, described in the 3 first postulates of Non-Euclidean geometry: The graph breaks a standard knot of time in its 3 planes. The point is an entity that constantly searches information with its head and energy with its body, creating symbiotic and Darwinian events with other knots of time, through 3 time arrows/dimensions between 3 planes of existence, the plane of the point, i, a lower plane of relative energy, st-1, and an upper plane of relative information, st+1.

In the graph we show the point as a complex i±1 plane, interacting with that plane or ecosystem (geometrical/ biological jargon) through those 3 arrows, which are its 3 dimensions of existence or ‘vital coordinates’ that create the motions of information and energy of those points. Because the frequency and speed of those arrows/exchanges of energy and information with the ecosystem vary, we also talk in complex Time Algebra of 3 relative speeds, Vs, Vt and Vts, which correspond to the arrows of spatial energy, temporal information and reproduction of the point, (for which often the point will chain itself with a relative complementary being), normally represented in the x(se), Y(ti) and z(st) coordinates.

Further on, those 3 ‘actions’, ‘arrows’ or ‘motions’ of time produce in the spacetime around the point different dynamic transformation:

– I<E: Energetic arrows produce an expansion of the spacetime around the point as in a big-bang or process of death.

– E>I: Informative actions produce an implosion, as energy becomes warped, informing the point.

– EI=ei: Finally reproductive actions tend to maintain the space-time around the point stable as they combine the arrows of energy and information, creating a self-similar point in a parallel region of space-time.

And we use the geometric/algebraic symbols of implosion of information, >, explosion of energy <, and parallel creation, =, to signify events belonging to one of the 3 arrows/dimensions of the point.

Thus, those 3 dimensions/arrows of time define the self-similar will and actions of most entities of the Universe, despite their apparent, different morphology and degree of complexity.

The interaction of those individual points of view, constantly throwing its ‘subjective arrows of time’, capturing energy and information from the universe, is the game we all play, and in doing so we establish relationships with other self-similar points of view, creating herds, ‘parallel planes’ of points of view or Darwinian relationships between relative energy victims and top predators, which we represent as events  between two different planes of simpler and more complex forms: Est-1->Ist, where E refers to the energetic function of the victim, belonging to a plane (st-1) of less complexity than I, the predator belonging to an upper plane of more information, I.

All those relationships are reflected in the drawing in which we see complex chains of time arrows between points of view, which forms an organic system. In each plane of existence or scale of the Universe such chains will represent a specific species that curiously enough show homological properties with other species of other scales existence. The previous graph could be, for example, a complex molecule. Such molecule represented here with ‘Time Algebra’ could also be represented as classic chemistry does with ‘lines’ of forces and ‘spheres of information’ that will show the geometrical topologies of those points.

Organic systems of points in different scales of reality.


When we visualize the world in terms of points of existence and flows of communication of energy and information we can see the dynamic creation of networks of points of time in any scale of reality. A human group is like a cellular body communicated through verbal codes of information (words) and systems of energy (light/spatial location, light-based food, such as plants and animals). Human groups are social networks of increasing degrees of complexity that grow in a decametric scale from individuals to families, clans, tribes, villages, cities, nations, civilizations and the speciesC. The graph shows a group of human beings, whose cyclical points of view or heads, are maintained in a parallel, relatively equal plane of existence to share information through flows of words communicated through the air medium/space and share energy coming from a relative ‘lower’ plane of existence, the table. Arguably those configurations are not different from the ones established in atomic networks or herds of sky gulls moving towards the lower plane of seafood as they maintain their parallel distance based in the sounds and motions of the air. Moreover human beings will always try to maintain such geometric configurations between their Non-Euclidean points =heads (not between their bodies, which are blind tails of energy for those points/heads that store the will of times): Observe humans relating to each other with motions and words emitted by their heads that are always kept in a relative parallel plane of existence with other human planes.

Reality is a game of points that gauge information and form lines, by sharing energy and information with other forms of view. Those lines, e x i become then networks of self-similar points, planes of existence, of which the most sophisticated is a complementary, social organism: exI +Ei, made with a head/particle dominant in information and a body/field dominant in energy.

When many points=cellular elements communicate they create more complex simultaneous presents by self-repeating in growing scales those ‘simplex’ patterns. And finally, through those multiple events they transcend, emerging as a new Plane of Existence. Such systems explain the structure of all kind of planes, including the simplex physical planes. So recently fractal theorists have proved with a theory called ‘causal triangulation’ that Time Arrows can form causal triangles whose connections grow by iteration till reproduce the 4-dimensional Universe of Relativity. Thus, when we generalize the 2nd and 3rd postulates to n-points in communication we create a finite, organic ‘plane of existence’, either a simple network (such as a Crystal or a sea of water) or a dual network, a ‘complementary organism’, with 2 exi networks.

The subjective will of ∞ points of view, acting selfishly come together creating a complex, eusocial reality. Order dominates the chaos of infinite selfish points of view, building a single reality, for biological reasons: The survival of points is better achieved, when acting together. So they become stronger than individuals; hence they win in the struggle for existence, defining in the process an arrow of social evolution that creates with herds of points, fractal, social planes and cellular super-organisms. So points first associate in couples that share flows of energy and information, creating waves = lines with volume, whose shape in space and duration of time is defined by the 2nd and 3rd postulate of relative equality (self-similarity). And finally they create complex organic topologies of existence of a relative number of infinite points of view.

When we add on all postulates – the structure of each point (1/5th postulates), the types of connections and waves between them (2, 3rd Postulates), and the causal, i->e->r->s chains of the Universe – we can explain creation, since the number of combinations of e and i is obviously limited; and so are the number of events, of reality. Thus we can know the outcome of each and every possible event or combination of the 3 wills=arrows of time of each point, (energy, information and reproduction), according to the 3rd postulate.

Thousands of pages and mappings of the laws of existential geometry, applied to each specific species and scale of existence of the Universe, prove that reality is quite deterministic, in as much as points constantly behave in the same manner, absorbing energy and information and trying to emit it with the purposes of reproducing or playing a social role in a higher plane of existence.

Of all those possible events, the commonest chain of existential events departs from a point of view that gauges information, in order to absorb energy, till it can reproduce its fractal form, ExI, till creating a social mass of points, ∑Exi that become a stable network, st, a vital, topological space: ∑Exi = st.

The Universe creates constantly ‘feedback equations of existence’, the ultimate essence of all realities.

Recap. Self-similarity determines the different ways in which Non-E points relate to each other, either associating together or fighting for survival, trying to absorb the energy of other points when they don’t understand each other or building social planes when they can create informative networks. As a result, and when those relationships are generalized to n->∞ points we obtain different organic planes of social points.

Dark spaces: the rest of the Universe.


Points of view are a mixed topology of membranes with open balls that have a dark space they can’t see.

Topological planes are dynamic, geometric networks of st-points=numbers, constantly moving and communicating through flows of energy and information. Yet those networks rarely form a continuous tight space:  space-time planes are filled with holes in which other networks might co-exist, or where flows of unknown, dark energy and information cross.

Thus, the creation and destruction of networks of self-similar points of view – the generation of complementary organisms – is all what we see; but there is also all what we don’t see, as most information and flows of communication between p.o.v.s, which are not similar to us, remains invisible.

Such dark space will be the surface of reality that a st-point with limited apertures to the Universe cannot perceive (an energetic mouth, an informative eye and a reproductive jet).

The degree of ‘dark space’ a point does not perceive depends of the complexity and apertures of the point. If we consider the simplest bidimensional point, a pi-vortex made of 3 standard units that form its outer membrane, it will have π-3=0’14 apertures to the Universe. And it will have a total dark space of 0’14/π=96% of circular reality, which the point doesn’t see through its apertures. That quantity is curiously the same quantity of dark, gravitational space and matter we do not perceive as beings belonging to the membrane of light-space.

So all planes are quantic networks of social points/cycles put together by n-flows of temporal energy, which have ‘dark spaces’ within the holes of the network:

‘A plane is a network of n st-points joined by flows of energy and information’.

The existence of dark spaces and planes which are discontinuous networks is essential to build up a Universe of multiple worlds, webbed into a relative infinite number of parallel planes that intersect, communicate through bridges between the network-planes and allow the existence of complex complementary organisms in which a relative wider, simpler energetic network is controlled by a denser, smaller, informative one, intertwined through those dark spaces.

Thus without dark spaces a complex reality of complementary beings is not possible. In the Universe the membrane of dark matter are the points of a network of flows of dark, gravitational energy over which the electromagnetic membrane warps itself, absorbing that energy and forming light-waves and more complex, evolved light particles.

In a human being, the blood network surrounds and warps around the digestive network from where it obtains its energy; and the nervous, informative network surrounds and intersects the blood network from where it obtains its energy. It is thus precisely the fact that planes are networks of points and dark spaces fill most of the network what allows the interaction between complex planes that form organic systems. A human being is in fact made of 10 of such subsystems totally warped together in exchanges of energy and information that permits our existence.

All this is the essence of a reality constructed with multiple planes of space-time that biologists recognize as networks of cells’ but physicists, stuck in the paradigm of metric measure of a single, continuous space-time still fail to recognize.

Recap. Points perceive through apertures only a part of the Universe. We could theorize that all what we see is merely the light-space membrane that floats in a much wider gravitational Universe.

The continuous and discontinuous reality.

The human aberration of perception is the true barrier modern science has to accept those living cycles. And so we define according to the Fractal Principle, 3 phenomena that create that aberration of perception: the limited scales of space we perceive, which prevent us from seeing in detail small or far away beings; the relative speed of human, cyclical time we use to observe reality that prevent us from perceiving very fast or very slow beings as living beings. Finally, our incapacity to translate other languages, as information is smaller and quantized. Therefore, we perceive better bodies and energy than minds and brains. This creates the ‘energetic aberration of naïve realism’ that makes scientists think all is ‘energy’ and information is secondary. Since informative messages, which are ‘faster’ and ‘smaller’ than energy forms are the most difficult to perceive.

We don’t see pheromones and so biologists thought for centuries ants acted as individuals when in fact they act as part of a whole super-organism, the anthill. We did not perceive the informative, chemical languages that cross ‘the synapse’ between neurons for so long, that most scientists thought that the entire brain was a cell to be able to work together until Cajal saw those discontinuities. Yet today biologists are decoding new languages of information: they found that monkeys learn to use money, rats sing songs, flies calculate. So the real barrier to understand the intelligent Universe is ideological, anthropomorphic mechanism. Only when science accepts organicism, it will start to understand the whys and wills of reality instead of merely gathering data. To perceive that organicism it only has to ‘translate’ different speeds of time to the ‘real speed’ at which any species exist.

Let us consider one of those dualities in more detail: the continuous and discontinuous reality, ruled by a simple law that relates two different scales of existence.

`The mean distance in space-time between 2 relative cells, st-1, of a fractal superorganism, i, equals the distance between its relative molecular systems, st-2, in time and space.’

The law of fractal jumps structures hierarchical organic systems through social planes, Est, of different i-nformation, among which the fractal jumps take place:

So beings seem continuous because their discontinuity is minimal, only a ‘cellular’ distance, both in space (so between axons, a simple chemical molecule overcomes the jump) and time (so chemical information, the next simpler language of life, jumps and translates the electronic message through hormonal discharges). Again between molecules the most habitual distance is that of an atom of 10-10 m.; and between atoms in its solid, informative state, the usual distance is a valence electron, its lower formal level. While between electron orbits the quantum jump is a photon with a constant of space-time, h, which is omnipresent in all the electronic cycles. In the same way a biological, fractal jump that reproduces a foetus implies the minimal fractal jump in space as the child is born contiguously to its mother.

Though st-points are discontinuous they have 3 apertures through which energy and information flow. Those apertures are fractal, small holes where only st-1 particles might flow. Hence the st- point communicates quanta from its lower, past scale of existence. All communication acts are fractal jumps both in time and space that can either communicate energy or information between similar particles or particles from st±2 planes of existence according to hierarchical, illogic laws:

‘2 particles on the same space-time plane transfer information and energy in both directions.

A st-1 space-time plane transfers energy to the st- plane from which it receives information.

A st-2 space-time plane transfers temporal energy, without receiving anything on exchange.’

Though the existential laws of i-logic might seem strange to the scholar accustomed to operate in abstract, they do apply to reality and reach enough detail to connect them with experimental events. The strength of a communication or bondage between knots of time is the essence of what the 3rd postulate measures. And such bondage is maximal in complementary forms, couples, and then in parallel forms, brothers. It is all about bondages creating strong knots of time due to the symbiosis of the arrows of existence of two forms. Forms share and the frequency increases the speed of the cycle of sharing. All action requires a reaction. Newton in fact defines the principle of cyclical inertia, which the 2nd and 3rd postulate clarifies further.

Those laws are based in the hierarchical structure of the Universe that creates organisms with 3 discontinuous ‘social classes’. So only particles from the first plane enter into just action-reaction processes – while flows of energy and information between 2 different, st and st-1 planes are asymmetric as the upper classes receive energy and give only information. But we said that Fractal jumps are contiguous, so how in the 3rd case might exist a flow between st-2 and st planes, separated by 2 scales? Obviously because the st-1 space-time field dies, exploding into st-2 particles that feed as energy or information the st form. Thus the 3rd case describes the extinction of a victim that the predator absorbs after destroying its cellular parts. For example you feed on the amino acids of the animal you eat, after destroying its cells into its micro-particles.

The previous ternary events, which can be formalized with the symbols of Fractal logic, are essential to describe and explain all kind of mysterious phenomenon in physical and biological space-times. Let us consider some examples:

– Borders between the 2 planes of physical space-time, the plane of gravitational masses and electromagnetic charges, are black holes that emit dark, expansive, gravitational energy. Still 96% of the gravitational world is invisible to us, including the discontinuous inner dimensions of masses, quarks and black holes.

– The 1st case between equal forms writes: ExI<ei=ie>IxE. It explains the 2nd law of Newton, the law of action reaction, according to which, exi, the fractal action of Ei over Ie, is equal in value to ‘ixe’, the action of Ie over Ei.

– Yet what Newton missed was the fact that ‘actions’ and ‘reactions’ are equal in Exi force but not always equal in substance. It is the 2nd case that explains relationships between 2 different planes of existence: Often an action is informative and its reaction is energetic and vice versa, so they compensate each other, cancelling the past and future into a present. It is the principle of conservation of energy and information: Energy becomes transformed into information and vice versa, E<=>I. Fractal physics explain the 2nd case with a mysterious principle that not even Physicists fully understand: ‘time and space are non-commutative’. That is I->E is not E->I, I>E is an energy transformation and E>I is an informative flow. And they are not the same. So in quantum physics and Fractal theory the order of the parameters of an action matters.

Recap. Energy flows towards the informative, future form and energy towards the past, establishing a hierarchy between information and energy, the 2 simplex arrows of the Universe. Both together create hierarchical organisms, distributed through several planes of existence in chiral, hierarchical 3 class-structures, in the dominant dimension of height and information. Only a present space, repetition of the same form in extended surfaces is democratic, equalitarian, creating a mass of undifferentiated quanta without much height dimension.

Organic networks as planes of existence.

The 4th postulate of Non-Euclidean-geometry explains how to create a plane as a network of ‘simultaneous, present, self-similar beings’ created by the multi-causal flows of energy and information between all those self-similar points that merge together into the organism. Since the fundamental mathematical property of those points-beings is its social nature. Indeed, a number – the social unit of algebra – is a social set. While a plane – the social unit of geometry – is a social herd. Thus, the fact that all beings have mathematical properties means they associate in herds and organisms, represented by sets of numbers and topographic 4-D planes, which are networks made of fractal points with a certain content of spatial energy and information. A plane is a network of points – reason why we can relate geometry and numbers. If we return to a previous example, a ‘point’ is the minimal unit or number ‘1’.

Thus, a number is a ‘class or set of self-similar beings’ simplified as ‘points’ (so we say 3 not 3 pears or 3 humans). Mathematics in that sense, in its simplest elements represent the rules of engagement of ‘herds of points of view’, since ‘each number’ has certain geometrical properties, so 1 is indeed a point, 2 define a wave of communication, 3 form the simplest plane, and those 3 fundamental numbers have only a variation (you can only draw a figure to connect them). So the ultimate answer which explains the enormous application of mathematics to describe the behavior of any ‘group’ is precisely the existence of ‘Laws’ which independently of the type of entity of energy and information we describe, apply to all points of view, to all entities and scales of reality and to all herds just because they are herds=waves and they are systems of energy and information. Those general laws that apply to all beings by the mere fact of being made of ‘spatial energy’, a substance with geometrical/ mathematical properties and being part of a group or ‘number’ whose social properties are defined by the possible relationships between couples, triads, foursomes and tetrarkys are the laws we are most interested in.

The most important universal numbers are the decametric scales since 10 is the ultimate constant of the Universe, the perfect network, the most common number of ‘points’ that create a fractal network, 3×3+st. It is the tetrarkys already understood by Pythagoras, who considered it the perfect number: 3 elements dedicated to the arrows of energy, information and reproduction in 3 opposite directions and a 10th element, first of the next scale, communicating them, protected in its center: A perfect topology to play the game of existence. Since Numbers are geometries that create networks of Non-Euclidean points. And so they can be classified by their efficiency as forms of Nature.

In that sense, reality is more like a carpet in which several nets web together into a tighter configuration or rather like a cat alley, which we do not notice in our own web of relationships but creates an entire different ecosystem, or the duality of the web of microscopic insects and macroscopic mammals that co-exist in two different scales of reality. Because networks tend to create ‘parallel’ bidimensional webs, in a 4 dimensional Universe with a 3rd dimension of height and one of motion that constantly displaces those networks, many networks can co-exist and interrelate together, creating the complex ecosystems of reality. Moreover if we consider that 96% of dark space to be standard the quantity of parallel and intersecting networks/planes of existence that can co-exist together is enormous – at least 25 networks, each occupying a 4% of reality can fit in the 100% of spacetime of reality.

Each super-organism is a world in itself, created by the confluence of 2 or 3 space-time networks of energy, information and in more complex systems, reproduction, where each network accomplishes one of the 3 arrows of time of the organism. Yet the energetic, informative and reproductive network, which extend the point in 3 relative space-times, whose topologies correspond to the spherical, hyperbolic and toroidal topologies of any st-point, become a unit of a new scale of existence of increasing complexity. And so we talk also of 3 scales of size in more super-organisms: the ‘molecular’, organic and social scales. Finally the whole system will evolve, living through 3 ages of increasing informative warping…

For example, the humans system is made of 3 main systems, the energetic, digestive system; the reproductive, blood system; and the nervous system. The 3 systems are fractal, cellular networks in perpetual motions, which intersect in certain regions of exchange of energy and information. So the blood and energy system intersect in the lungs in which they exchange energy with the blood system and the blood, reproductive and nervous informative system, intersect in muscles, in which perpendicular nerves exchange information with the muscles. And the 3 systems form the physiological systems that define life and its 3 arrows of energy, information and reproduction, each of them attached to a given number of cells. So if we were to take the p.o.v. of the cells, we could also say that the human organism is a network of cells joined by 3 flows of energy, information and reproduction mediated by those networks. Yet all the systems together are what form the Human organism.

Further on, the organism will go through a young age of energy and motion; a mature, reproductive age and an informative age, each one dominated by one of the 3 networks. And it will extend through 3 scales of existence, the cellular, organic and social scale; such as the human being will be born as a seminal cell, evolve into an organism, which will integrate itself into a society and when it dies, it will first erase its social memes, then it will dissolve its cells and so finally it will return to the lower plane of cellular existence in which it was born.

Recap. The structure of super-organisms across several planes of existence is based in 3 networks of st-points, the energetic, reproductive and informative networks. Those networks leave between them a quantity of dark space, where the other networks can intersect and connect with its st-points. Its ‘discontinuous borders’, are asymptotic bridges where through a change of state, the 3 network/membranes exchange energy and information.

Dimensions of organisms made of space-time planes.

Networks of st-point are dynamic ‘groups’ in motion; either herds or ‘rings’ extended in two scales of reality, which are tighter and still, due to the ‘connections’ established on its lower scale. We talk of ‘waves/bodies’ as herds of quanta or cells and of ‘particles=heads’ as networks where the quanta or cells are interconnected in greater measure. Thus, while groups/waves/bodies (mathematical, physical, biological jargon) extend in a single bidimensional plane, an informative network extends through 2 st-scales or perpendicular planes; one created by the points and the other by the networks or connections between the st-points and/or the st-points and its energetic herds. So it has 2+2 fractal, holographic dimensions.

Thus, as a consequence of the new definition of a point, a plane becomes now a 4-dimensional ‘holographic topography’ with 2×2 information and energy ‘dimensions’, needed by those points to absorb energy and information: informative height that allows the top head to observe the Universe, cyclical rhythms that allow the being to perform its existential cycles, length-speed that moves the being and width-energy that allows the being to store and reproduce its cells.  All this brings the theme of how many ‘real dimensions’ has a given system. And the answer is: depending on how we count dimensions and how many planes we study.

In fractal geometry a network has different dimensions depending on the complexity of its branches and quantity of space it fills up. This was already observed by Peano and Cantor who realized they could create a zigzag line that filled up the entire bidimensional plane. And as a general rule most networks of points can be considered to fill two dimensions and two systems of energy/information networks together to create a holographic intersection that adds up to a 3rd dimension, which finally if it has motions adds up the 4th dimensions of most organic systems of the Universe. Since dimension is a flow (dynamic version) or network (static version) of quantic, cellular points, gathered into bidimensional waves and 4-dimensional space-time fields.

Yet things become more complex when we consider systems that extend through several scales of size, and when we consider the ‘amateurish’ analysis of dimensions by most scientists unaware of the laws of i-logic geometry and quantum space-time systems.

For example, physicists, without those concepts wonder why strings have 3×3 inner dimensions of space and one of time. This means that they are calculating systems that extend through 3 planes of existence. Further on, those strings then gather in herds called electromagnetic branes, which warp into particles. Further on, 3-D particles form networks that become atoms, and the process repeats once and again till creating human organisms within which those organic points, now called cells communicate energy forces and informative bits.

There are many types of points with parts, gathering in scalar networks of growing size and complexity: atoms gathering in molecules, stars in galaxies, strings in particles, etc.

A fractal system keeps adding dimensions, as each point becomes part of a network that evolves into a point of a higher plane. Depending on the number of planes through which we observe a point, the total dimensions of the point will vary. As a general rule however, any species of the Universe is fairly described through its main Plane of existence and its lower and upper planes. So a human being is described perfectly as a cellular system in the st-1 Plane, an individual in the st-plane and a relative point co-existing with other individuals in a society in which s/he feeds on energy, information and reproduces. For those reasons we can consider that any point of existence will be described exhaustively when we consider the 9 dimensional networks of each of its 3 main st-planes.

Fractal ±st-point:  3 st-1 D > 3 st-D > 3 st+1 Dimensions

Finally, those planes are joined by ‘bridges’ of energy (from st-1 to st) or information (from st to st-1) called co-dimensions of ‘relative, perpendicular height’, the temporal, evolving  dimension that connects them to the upper plane of existence through their processes of iterative growth and social organization. Those co-dimensions measure the relative height or fractal accumulation of self-similar forms that takes place beyond the membrane of the Mother-Cell, as time iterates and evolves the natural fractal into a higher st-scale. Since informative cells accumulate in a relative perpendicular dimension of height, from living organisms whose informative heads are on top to audiovisual towers and satellites, to the perpendicular co-dimensions of microscopic growth of Mandelbrot and Koch fractal.

A fractal ±st-point exists as a 3 dimensional organism, which acts in the external world pursuing energy, information or reproductive goals (mechanically, consciously or in a vegetative way, or even micro-managed by a catalyser or enzyme – facts those, which won’t matter to its dimensional description). In all those cases, time, understood as a form of movement, will be a geometrical movement or cyclical trajectory but also a temporal cycle with a biological, energetic, reproductive or informative function; and a movement traced through a dimension of the upper st-plane of the point. So when a human goes to feed on a dinner, it will enter into a social network of human points feeding on that dinner, which will form an organic system of the upper st+1 Plane. When an electron flows in a metal network of atoms, it becomes a carrier of energy or information between those atoms, and so to its 3 inner dimensions we will have to add an external social dimension in the atomic plane (the only one physicists study in that case). Yet the electron has also inner dimensions, defined by its quantum numbers.

Recap. For more than a century, Physicists have been troubled by the need on their equations of Quantum Theory, Relativity and String Theory of odd dimensions, whose ‘ad hoc’ explanations varied from an author to another. Yet in fractal geometry the issue is resolved since the concept of an extra-dimension has a clear, mathematical and logic meaning, related to those scales, all of which will have:

– A 3-dimensional sub-space within their organic forms, as we come closer to them and observe their details no longer as points without parts but as full grown organisms. Thus the existence of 9+1 inner dimensions in objects like Strings means merely that there are at least 3×3 inner fractal micro-scales within the structure of those strings, where those dimensions will be located.

 The mathematical model of organic, scalar fractals.

We can now merge what we learned about the fractal structures of the Universe, and its creation through planes of existence, which are organic topologies made of networks of points communicating through flows of micro-fractal points. The Universe and all its parts follow the laws of super-organisms, which define all what exists as ‘organic fractals made of self-similar cells joined by networks of energy and information’. Where cells are knots of Time Arrows and fractal means a scalar, self-generated, organic, repetitive reality:

– A reality structured in several ‘scales’ of different spatial size and time speed, such as the smallest spaces move faster and show a higher frequency in its cycles of time (metabolic law, Chip paradox, etc.): Max. E = Min. Ti; Min. E= Max. Ti

– A reality generated by ‘informative’ cycles, which can be described with a generic feed-back equation, E<=>Ti, and any of its self-similar specific ‘generator equations’ of information that code the structure of any entity of reality (from DNA genetic codes to quantum equations of particles).

– An organic reality, which constantly reproduces its form in self-similar, micro-replicas of each point, and then organizes those self-similar ‘fractal parts’ into wholes, using them as waves of communication that relate points between them or forming with them an offspring of similar beings.

This organic, fractal, informative design of reality, explains why the Universe shows a scalar,  social nature, ‘transcending’ from smaller to bigger Planes, invariant in its e & i forms – the energy line and the information cycle – thanks to the fractal reproduction and social organization of self-similar forms.

All those complex systems extend through 3 main st-scales or ‘planes of space-time’, structuring reality as a ‘fractal, non-Euclidean topology of multiple, causal arrows of time’. Yet such complex reality requires new tools of geometry and logic to define properly the laws that relate all the elements and scales of the system. Since most sciences use still a single, continuous space-time plane (Cartesian), a single, Absolute Time cycle (clock-time), a geometry of forms not of motions (Euclidean geometry), and a monist, A->B causal logic (Aristotelian Logic). Thus, a great deal of Multiple Spaces-Times is dedicated to understand the non-Euclidean, fractal geometry of space, developed in recent years, which can study a space-time made of motions (Non-Euclidean geometry), divided in several scales of size and self-similarity (fractal geometry), in which reality is caused by multiple time cycles/causal arrows and multiple agents (Non-Aristotelian logic), tracing geodesics in search of those Time Arrows. Ultimately what you observe is a game of non-Euclidean points=particles=heads, each one associated to a lineal field of energy/body (Complementarity Principle). As entities of energy and information, they are constantly in search of more energy and information to reproduce and form social systems. To that aim each ‘Non-Euclidean point of view’, the fundamental, formal particle of the Universe, defined by the 1st postulate of Non-Euclidean Geometry (a point, which unlike the points of Euclidean Geometry, have organic inner parts), will start a line of Non-Euclidean communication, (a wave packed with energy and form, described by the 2nd postulate of Non-Euclidean mathematics), shaping ‘networks’ of energy and information points (topological planes defined by the 4th postulate of Non-Euclidean mathematics), which create a relative ‘space-time’ being of one of those ‘existential scales’.

Recap. Non-Euclidean, fractal space-time was defined by Riemann, who affirmed that a ‘space’ is a group of self-similar points, forming an undistinguishable ‘herd of points’ that becomes a homogenous plane. Riemann considered the ‘density’ and homogeneity of those spaces according to the degree of equality of those points (3rd non-Euclidean postulate) and developed the initial steps of a non-Euclidean, fractal geometry of ‘discontinuous points/knots of Time Arrows’ that gather into networks, which form organic planes of existence.

 The PLANES of reality: human organisms and Universes.


A human being exists simultaneously through 10 planes of space-time existence, from gravitational space to the cosmological plane of the solar system. The complex interrelationships between the points of each of those planes of existence, among themselves and its upper and lower scales, create our organism and influence our modular consciousness – as we feel the will of the Time Arrows of each of those scales through different senses: we feel gravitational weight and physical pressure, electromagnetic heat and atomic smells, photonic images and molecular tastes, social love for other human beings and the exhilaration of motion.

We are the most complex species of space-time, only because we are the species we perceive better, not because humans are the summit of informative evolution in the Universe. In any case, since perception is reality, we will always appear far more complex in form than the extended Universe, dominant in energy-space, of which we perceive very little according to the paradox of the ego (as we gauge from our perspective and so we see more detail in the closest entities). Thus the study of man as a complex organism should be the leading science, which offers more information. Then by homology we can apply the laws discovered in the study of our organism to other entities.

In the graph we see those 9 fractal space-time scales of increasing complexity, which emerge from the interaction, chains and evolution of the species of each scale: photons that become particles that become atoms that become molecules that become cells that become human organisms that become social cells of civilizations and economic ecosystems.


The fundamental particle of the Universe is a Space-time Super-organism that repeats its cycles and shapes of energy and information, co-existing between birth and extinction in 3 fractal planes, which can be subdivided each in 3 fractal energy->Reproduction->Information networks (spatial view), living 3 time ages (temporal view) as he fulfills its arrows of existence in those 3 planes.

If we extend that concept, the Universe becomes a hierarchical, scalar system, extended through a series of self-organized st-planes: particles gather into atoms, atoms gather into molecules, molecules gather into cells, cells gather into organisms, organisms gather into planetary systems that gather into galaxies that gather into Universes. the outcome is a scalar structure of 10 space-time planes, where fractal entities live self-similar cycles of existence under the same space-time laws, from the smallest, invisible plane of gravitational existence, till the Hyper-Universe in which ours is a single cell:

st=1 groups of ‘G-constants’ evolve, forming, curving the energy of gravitational space into masses.

st=2 groups of ‘Planck actions’ form the electromagnetic light space, evolved into cyclical charges.

In the st=3 plane of atomic existence, groups of particles became atoms.

In the st=4 plane, groups of atoms became molecules.

In the st=5 plane, groups of molecules became cells.

In the st=6 plane, groups of cells became living systems.

In the st=7 plane, life herds became ecosystems, societies, nations and global planets.

In the st=8 plane Groups of solar systems became galaxies.

In the st=9 plane, Galactic clusters become Universes.

Thus, humans are a st=5, 6, 7 species; since our organic system belongs to the st=5,6 scales of biological cells and living beings, and we belong to the st=6, 7 scales of individuals and social organisms – as cell of a nation or religion.

How many scales reality has beyond the 10 scales humans perceive3? Given the flexibility of size and speed of gravitational forces, whose waves Einstein calculated could extend to the size of the entire Universe those scales might be infinite as each galaxy becomes an atom of the next scale. It is also the logic result of thinking in mathematical terms, as the simplest informative fractal, a disk, given the irrationality of π, can reach any infinitesimal size. Ultimately it is a choice of the reader: if he is objective he should observe that for survival reasons, spatial perception always puts him in the center of all his observations of Nature. Thus in the same way space is infinite but we are in a limited, perceived self-centered space, the scales of temporal complexity should be infinite, as the arrow of eusocial evolution should be acting for ever in the eternal universe of time motions.

Thus even though the perceived Universe displays only i=10 scales to human observers, ‘i’ probably tends to infinite.

Recap: the universe is a fractal structured in ternary scales that create decametric social organisms. We cannot know if those scales are infinite but the eusocial arrow of love should have act ad eternal since time and space are absolutely relative.

The complex causality of Multiple Spaces-Times.

The key law of flows between 2 planes of existence is:

‘Information flows from a more complex, ‘upper’ plane to a ‘lower’ more extended plane, Ist+1->E; energy flows from a lower, spatial plane, to an upper, informative plane; energy and information flow within the same plane of existence’.

This self-evident law determines the outcomes of events and the form of structures, from the 3 perspectives of reality:

Geometrically, in relationship with the 3 topologies of the Universe; as it will determine the flows and channels within a certain organic st-point.

Temporally, in relationship with the 3 dimensions of time; as it will determine the relative flows from past to future and future to past, and the simultaneity of certain events in present, between complementary systems.

And organically, when we combine both approaches, as it will determine the key events of existence: the why palingenetic birth and evolution, the process of death, etc.

Departing from that law, we can tackle the most complex level of understanding of reality – the i-logic of systems, created by multiple time arrows, which no longer follow the Aristotelian laws of single causality, A->B, but the logic of simultaneous present creation, either by the confluence of past-energy and future information, or the simultaneous confluence in a formal ring of multiple, self-similar time arrows. Those complex systems of causality were partially studied by Einstein with its concept of simultaneity and ‘convergence’ of past, present and future, and by quantum physicists with its analysis of particles and antiparticles and the invariance of physical phenomena regardless of the direction of time we study, but now we can analyse it with more rigor in this and the 2 next paragraphs, since complex temporal causality and fluxes of energy from a relative past plane st-1 to a relative future plane st+1 (e->i) and the inverse process, a flow of information from a future plane, st+1 to a relative to past plane st-1, is at the heart of the structure of superorganisms (i->e).

Unfortunately, lineal time introduced in science the concept of single-causality (ceteris paribus analysis), which is only a partial analysis of the causality of most phenomena, in which acts a ternary causality (as energy flows from the lower plane, information from the upper plane and complex flows of energy and information happen between the cells of the same plane of existence). For that reason, most scientists constantly argue, considering their ‘cause’, normally one of those 3 relative events, the true cause. Yet in fact all events need at least 2 causes to exist, one from an energetic past and one from an informative future that converge into a relative present.

Let us then introduce the complex logic of organisms with relative future, informative systems and relative past, energetic systems (IX); studying next (X) the causality of a present system or knot of times, made of multiple time arrows/cycles; and finally (XI) some key events of ‘existence’ in which those flows of time take place, such as the process of palingenetic birth and its inverse process of devolution or ‘death’.

Recap. Events require to exist at least 2 causal arrows, EóI, which are 2 complementary networks of energy and information going through the 3 topological ages of the life/death cycle.. Such is how new systems are repeated: on one side all becomes a self-similar network of knots of time cycles that go through 3 ages and reproduce in certain topological forms. On the side of complexity of the time arrows of those Non-Euclidean knots, the iteration and combination of those simple elements that make networks, self-reproductive fractals and the logic complexity of the synchronicities of those feedback cycles create systems of enormous complexity.

Information networks control energy herds.

The beats of all species, as they absorb and emit information and energy in order to reproduce and evolve socially into self-similar or complementary networks, chain them into complex organisms and ecosystems. And since each st-point is always a cellular part of a bigger organism, finally all those beats, cycles and chains become part of an interconnected huge organism, the Universe.

The simpler of those chains are Darwinian events that connect victims of relative energy and predators with a more complex ‘form’; the sum of all those chains in a given ‘ecosystem’ or plane of existence form trophic pyramids.

Darwinian E->I events last a brief period. Yet Nature sometimes converts Darwinian events into symbiotic, dual body/head organisms, in which the ‘fastest’ temporal, informative beings tame, enslave and control the slower ones. So while the faster lion feeds on the slow buffalo, humans first feed in buffalos and then tamed them, creating a symbiotic organism – the herder and his herd. In the same manner, the first, faster electrical neurons probably devoured, smaller, slower chemical cells, but both together finally evolved into complementary organisms, while the fastest neuron controls the chemical cells of your organism, extracting energy from them. Thus, an organism is a chained system of top predator cells that control herds of tamed chemical cells; and an ecosystem is a loose organic system in which the top predator ‘cells’ only interact with the slower ones when they feed on them.

A 2nd element to understand such chains between faster ‘informative cells’ and slower energy cells is the fact that the faster cells can dynamically or statically (through a network of connections), control multiple, slower cells simultaneously and vice versa, it can process due to its faster time cycles, multiple messages coming from several slower cells that ‘cause’ its action. And this happens in all systems, including a human system in which a speaker talks to multiple ‘energy believers’. To that aim, we must consider a property of information we advanced previously: its fractal, reproductive nature that breaks a form of information or message into multiple self-similar messages (the speaker that reaches multiple people, the antenna that emits multiple electromagnetic patterns, etc.)

When we put together both properties of informative networks – to act faster and to act simultaneously – it is easy to understand why they can control the energetic cells of the organism. For example, the nervous cells act as fractals much faster than the chemical cells and so a single nervous cell can control an array of multiple chemical cells, because one of its ultra-fast fractal actions move a big distance that encompasses many chemical cells in the time those cells react. In this manner faster, upper class, informative species control slower middle class cells. In the other extreme a stronger ExI species can create waves of energy and information that extend over multiple cells, and so minute changes on its energy and information parameters affect all those cells, reprogramming them. So a small change in the Earth’s temperature provokes huge changes in the life of its species.

If we generalize those chains to enclose all organic systems of the Universe, the main systems of reality acquire a complex, deterministic degree of order and harmony that relates the different cycles of being (its informative, energetic, reproductive, social and generational cycles), as cellular units of the bigger cycles of the macro-organism or ecosystem in which it exists. Finally information cells form complex networks and so despite being smaller in space, the whole network of ‘neuronal’ cells is bigger than the individual, divided, energetic cells, making easier that control by the ‘macro-organism’ of information.The result of those structures is the 3-class structure of all organisms, in which a head/particle of information controls a reproductive body/field of cells/wave, which obtains energy from an ecosystem from a 3rd lineal system of ‘limbs/forces’.

Consider for example, the 3 elements of life, C, N, O. Today we are still in monism and so even biologists will tell you that Carbone is the basis of life. Yet carbon is only the reproductive body of life molecules. Some thus add Oxygen, the energy of life. And indeed, the biosphere has exactly the same mass of Oxygen and Carbone (24.9%) in your bodies, as limbs and bodies tend to weight and occupy self-similar volumes. But this misses Nitrogen, the intelligent, informative atom of life, which is only 1% of the biosphere (0.27%) and was called first ‘azoe’, which means in Greek without life. Yet with its cyclical forms and its Hydrogen 3-dimensional ‘eyes’, it perceives the external world and structures life, accumulating in the DNA and brain. And it is a General Law of all Systems1 that the informative system weighs far less than the 2 others (so your brain is only 1% of your mass, and 1% of ‘stockrats’, owners of corporations ruled the Financial-Military-Industrial System). Further on, beyond your organism, you are part of a world of water, the ecosystem of life. And so those 3 elements are exactly 50.7% of your mass, ½ of reality, the rest being mostly Hydrogen the primordial substance of water and the Universe.

The primary motion of all beings is lineal energy, in its relative direction of length, while the informative particle of any complementary system is on top, in the relative dimension of height. This leaves width as the natural direction for its re/product/ive, product equation: exi. Look at yourself: your height is your direction of information, your head is on top; your motion is forwards, in the length dimension of energy but your cells reproduce and multiply in the width.

All of us are knots of multiple cycles and arrows of time. So each of us is a multidimensional species. Complex beings, of course, do not follow exactly with geometrical precision those forms, because their vital functions must adapt to irregular ecosystems. Thus, perfect forms of energy and information exist only in the homogeneous, 3-dimensional ecosystem of interstellar vacuum inhabited by physical particles (and in lesser degree on water, life species, since water has complex motions and a general arrow of ‘light information and energy’ towards its surface).

For that reason, those geometrical rules of creation of vital arrows/dimensions of time/space, which are known to mathematicians as the product laws of vectors, are used to describe many operations between Time Arrows in the simplest geometrical systems of physical space: For example, light has 3 perpendicular dimensions. And Maxwell found that the product of the magnetic, energetic, flat field, given by the magnetic constant of vacuum (which is a membrane of light space) and the informative, electric, ‘high field’ constant, gives us the reproductive dimension of speed of the light wave. Further on since light-space is the ultimate substance of vacuum and light dimensions are time arrows of energy, information and reproduction, as unreal as it might seem to you, the 4 dimensions you see are not abstract concepts but vital time arrows, reason why they suffice to explain it all.

What is the speed of those time arrows and its frequency? The question is the key to unlock the complex synchronicities, quantitative laws and Vital and Universal constants of each species of the Universe, so it requires specific, detailed analysis of each entity, organic system or plane of existence, but certain general laws apply to all systems, due to the causal chain between those 4 arrows, as energy appears first, then it becomes bended and broken into information, whose product reproduces a field and finally the re-organization of self-similar reproduced forms creates a more complex super-organism.

Fast and slow dimensions of space and time.

Further on, we classify the 2 dimensions of information, cyclical rhythm (discontinuous frequency) and height, as the fast and slow dimensions of time, since height is often the accumulation of cycles of time one over another, which become in still space (Galilean paradox), cellular bricks of a sensorial system.

We classify the 2 dimensions of space, length and width as the slow and fast dimensions of energy, since width is often the reproductive accumulation of lineal speeds side by side, which stores in still space (Galilean paradox), new energetic cells:

– Length is a fast dimension that moves ahead a Non-E Point and gives it speed. All bodies follow a lineal inertia in its motions, signalled by its relative ‘length or body orientation’. Thus, length is the arrow most often associated to the concepts of energy, expansive destruction and devolution. It also follows that the absence of memorial height in an organism, is the key to increase its speed as it diminishes its dimensional friction moving forwards and the quantity of form it has to recreate in each ‘fractal step’ as it imprints its information in the lower scale of reality. And so the fastest known force with zero height and maximal linearity creates a perfect lineal motion of ∞ speed and 0 form: the gravitational space over which the forms of light are imprinted whose speed is: v=e/i=∞.

– Width is the slow dimension of space that reproduces or accumulates spatial energy from side to side. In current theoretical models, strings reproduce laterally, creating fractal spaces in the dimension of width. In our scale, people become fat and wide, as they reproduce their cells. All beings reproduce their energy in the width dimension of space.

We also classify the 2 informative, temporal dimensions:

– The fast dimension of temporal information is the speed of perception of information given by the frequency/ rhythm of a cycle, which determines the rate at which the system absorbs its pixels. It is the arrow most often associated to the concept of time; often defined by an angular speed or frequency, which defines a clock of time. Thus its parameter is the inverse of lineal time, measured in t-1 units as a scalar number; and when we correct the equations of Physics in terms of cyclical frequency, a whole array of fascinating discoveries and solutions to classic paradoxes – from the paradox of Information (Hawking) to the paradox of Quantum vs. continuous time-space – become resolved.

– The memorial persistence of a certain form traced by a time cycle prevents the drawing of the next cycle in the same place of space, causing an ‘Exclusion Principle’. So when the cycle repeats itself, it does so over the surface imprinted in the previous cycle, creating a tube of height, the second dimension of time, caused by the accumulation of cycles of information. Thus, the slow dimension of time is informative, morphological height, born out of the evolution of a species through aeons that accumulated informative cells in the height dimension. For example, the Universe was born flat in the big bang and now it is acquiring form, curvature; bilateral animal life was born as a flatworm that slowly acquired form, till rising to the height of man, the animal of maximal information; the first plants were algae that acquired temporal height; the Earth was born as a flat, rotating disk that became a sphere with height. Yet in duality, according to the Paradox of Galileo, events are created by the dual causality of formal, geometrical space and biological function. So a 2nd bio-logical cause is needed to explain why dimensional, informative height is all-pervading in the Universe:

The informative organs of a being are placed on top of its height to improve its perception of its territorial space: the human head, the speaker; the black hole of a galaxy, the photon of a light wave are all located on top of the relative energy of their bodies to inform themselves on the location of its feeding energy. Thus, height is also the biological dimension of information and the arrow of future evolution in life, which evolved from flat worms into the human beings. Both time dimensions are dimensions of change. Yet the motion of evolutionary growth or height is minimal: it changes very slowly, through the reproductive, accumulative process of evolution; while the mere displacement of a cyclical, physical movement can act faster.  The most complex arrow of time has the slowest dimension of change – evolution – which is shown as a change of form. Yet evolution sometimes doesn’t create height but it is often a contraction of space, as individual parts converge into a whole, herd, wave or organism. The 4th dimension of social evolution is therefore the only dimension that seems ‘static in space’ as a ‘form’, which doesn’t change from generation to generation.

So both geometries, cycles of time and planes of space are in fact bidimensional, adding up to create the 4 dimensions of space-time. Energy consists in an amorphous, relative surface of undifferentiated quanta, a plane without form – a network of small, cellular points, in which the creation of memorial time cycles imprints patterns of information and makes it recognizable as a complex system of multiple Time Arrows. Then, as the being develops those Multiple Spaces-Times, it acquires certain topological dimensions as an individual or as a species living in a longer time-frame.

Yet organisms are dynamic entities that change their parameters of energy and information and so they also change their dimensions of space and time, often transforming a dimension of space-energy into one of temporal information and vice versa: A space-time field is created and destroyed through the interaction of the 2 dimensions of energy, length and width, and the 2 dimensions of information, height and rhythm. To that aim, the 2 dimensions of energy and information combine and transform into each other in dynamic events of dimensional destruction or dimensional reproduction.

Finally to notice that according to the Galilean paradox we can do a description that spatializes time or one that temporalizes space: In a ‘ceteris paribus’ time model of reality all dimensions of space become temporal, as form becomes form-in-action, in-form-ation – exactly the inverse of what classic physics believes, when it affirms that time is the 4th dimension of space, by converting time into a clock-like, cyclical form of space. In the temporal vision, it is the lineal motion and lateral reproduction of information what creates the 2 dimensions of space.

Recap. Information networks have 3 advantages over energetic herds: they act-react faster, as they are smaller in space; they produce simultaneous, broken messages that reach multiple cells; and they act together as a single network, due to its multiple connections between them. Hence they can dominate the herds of energy in any dual, complementary organism.

In physics space has 3 dimensions of form and so motion only occurs through a dimension of time. This is false. Length is often the main motion of any system that displaces its body/wave in that dimension. Width is a slower dimension of spatial change, often related to cellular reproduction. Frequency is the fast dimension of time that defines the clock-rhythm of absorption of information. Height also changes; it has motion albeit slower than length, the longest/fastest dimension. It is associated to social creation. So we talk of Time-space as the perception of the 4 dimensions/arrows of time in motion, where the slowest 4th motion/dimension, social height, given by the arrow of evolution is the only one that seems to us static. Thus, energy displaces mainly in the dimension of length; information in the dimension of height; width stores reproduced cells, and then there is a 4 dimension of social evolution.

All dimensions of Time-space have motion, a fact which can be observed in all the planes of form of the Universe, till arriving to light space, the simplest substance of the Universe, which in the model of Time-space has also 3 obvious motions – magnetic width/energy, electric height/information and length-speed/ reproduction, and a 4th, less obvious time-change dimension of social evolution, represented by color.




 A case of Darwinian devolution among men that perceive each other as different and enter in a perpendicular, Darwinian relationship and a case of social evolution between 2 forms that perceive each other as equal and enter in a geometrical and causal relationship of parallel love.

 Logic and geometric postulates.

Why geometry needs 5 postulates if the 1st, 2nd and 4th define perfectly a fractal space/time in 3 growing degrees of complexity: the singleton point, the line of communication or wave and the network or plane with volume? Because the 3rd and 5th postulates are not about fractal space but about fractal time; about information and formal equality, about the logical scaffolding of mathematical equations, which so often is forgotten but shapes the underlying formalism of all mathematical statements (as per Frege and Gödel). Since:

– The 3rd postulate defines the degree of self-similarity between 2 fractal objects. Classic geometry considered equality based only in the external form, regardless of size and inner content. But beyond the idealized world of Euclid, equality never exists when we consider the inner form of those points made of inner networks of energy and information that contain dark spaces and inner parts, which make even twins slightly different. Thus fractal geometry defines instead the relative degree of equality of 2 forms, according to the self-similarity of its inner, informative content and scale, not according to the equality of its external, mutating membrane, which often is hiding, as in camouflage, a different form.

Self-similarity matters because the social evolution of points that become part of networks that deliver to all of them the same energy and information requires the capacity of those points to process the same energy and information, within its inner parts. Thus only self-similar cells with the same ‘genetic=temporal information’ evolve into organisms. And this happens in all scales. For example, the superorganisms of history which are ‘memetic organisms’, in which each human being is a cell of the super-organism with the same ideological mind based in the same memetic code (same religious code of ‘revelation’, same laws in a national super-organism, etc.) must have the same mental beliefs. It doesn’t matter to form the organism if the DNA code is this or that one, if the believer that forms a religious superorganism believes that Allah or a turtle, or Christ or Yvwh is the name of the God – as long as he has the same memetic code in his mind. Since the rule that matters is the degree of equality that triggers the creation of a social, tightly packed organism acting as a single whole. For the same reason, since reproduction is based in genetic information, only species with the same genetic information can reproduce and since they have the same equal form, it is a rule of nature that only reproduced cells of the same species form an eusocial organism – a key law to fully grasp the evolution of organisms and societies, in which a ‘prophet’ becomes the first DNA cells of a new civilization. While species that cannot share information to hunt through common networks or reproduce will consider the other point/species a form of energy and prey on it.

Thus surprisingly enough geometry determines behavior; form and function again go together and fractal geometry tends a bridge between physics and biology, explaining how species will communicate: if those 2 points perceive each other as equal, they will evolve into a social network co-sharing their ability to gather energy and information. If those 2 points are unequal, they will establish a Darwinian, hierarchical relationship, in which one becomes the victim and the other the predator. Thus the 3rd postulate is no longer an abstract, geometric postulate, but a postulate of logic relationships, fundamental to understand the why of motions and behaviors.

Since self-similar points evolve socially though networks and communicate through a common language of information to survive better as a single social species. So we can resume the main sub-laws and causal, geometrical chains of the Universe with the 3rd postulate:

3rd postulate of relative self-similarity:

‘Points that are self-similar in information evolve socially into a present network. Points that are different in information will treat each other as relative energy and evolve towards the future  into a hierarchical organism as a system of 2 points, one of energy and one of information, related by constant flows of energy and information. Or devolve towards the past into a Darwinian system is one in which both flows are not constant.’

The 3rd postulate explains why men do not perceive Universal entities as intelligent: beings perceive itify other forms whose flows of communication don’t understand as energy forces that they ‘destroy’ and feed on, without perceiving its ‘organic qualities’. However, even the smallest point known to man, the photons of ‘light-space’ show the 4 basic qualities of all organic systems that biologists use to define life, the capacity to process energy and information and the capacity to evolve socially and reproduce: photons carry energy and act like the minimal unit of information, because light transmits all type of images through its photons; they reproduce their form in the vacuum; and they gather in social herds of colors.

The 3+i arrows of space-time are the will of the Universe that all its beings share across all its planes of existence. Yet the rules that define behaviour between species, the limits of perception of the inner informative language of other minds and the need to use as ‘energy’ other entities, regardless of its inner information (so hunters feed on bodies and throw away the informative heads of lesser energy), imply that humans always deny the sentient, intelligent universe, and the invariance of topological form between those scales, itifying reality.

Recap: the 3rd postulate of relative equality define two forms as self-similar when their external, energetic membrane/surface and inner, informative minds are equal. Depending on the degree of equality species will evolve socially into tighter organisms (when they are self-similar) or hunt each other as different species.

Equality and social evolution. A new concept of truth.

Equality is the key concept in our definition of mathematical truth as, =, is the operandi of all mathematical equations and in logic, the necessary reason of all logical statements. Thus a fundamental change in our concept of truth follows from the understanding of self-similarity as a different proposition to equality: If Euclid defined equality based on the surface of objects, without taking into account their relative size and inner content, this no longer holds. Things might be similar in their surface and maybe in their content but they are never equal, at most self-similar, nor are equations and any linguistic state an absolute prove of truth, but linguistic self-similar images of the recurrent cycles and events they represent.

The 3rd postulate eliminates the word ‘equal’, which is so important to define truth as ‘dogma’. There is not absolute truth because we cannot perceive completely all the fractal information of the system and so we can merely consider the degree of self-similarity of two beings. Thus, a far more sophisticated and ‘real’ logic appears – that of the relativism of all truths which are related to the perception we have of reality, to our diffeomorphic=local point of view that will distort reality to cater to our selfish will (Galilean and Darwinian paradoxes), and to the quality of our senses and minds.

Thus we rewrite the 3rd postulate of Euclidean geometry, which defined the relative equality of 2 beings, based only on the external comparison between beings, as ‘points without parts’, to introduce the existence of inner energy and information parts in all beings. The new 3rd postulate of i-logic geometry establishes now the inner degree of equality between the parts of those beings as a previous requirement to judge the result of all social communication. The old Euclidean postulate of equality caused all type of errors. Since often points pretend a false, external equality. For example, the main stratagem of hunting in Nature is camouflage, based on the equality of external forms. So the victim accepts that equality as a sign of friendship and initiates a type of ‘positive’ communication, coming closer to the predator; but since the victim is different the predator kills ‘it perpendicularly’. That subtle difference between the real world and the abstract world is paradigmatic of the relativism of perception. If Euclid was right, hunting would be impossible, because camouflage could not exist. But real beings have internal, different parts. Some insects imitate wood to hide themselves but they are not wood although they seem it, because their internal parts are different. Otherwise there could not be hunting, based in the strategy of camouflage, as predators simulate the external form of victims or hide in dark spaces, from black holes to lionesses. It proves a fundamental theme of religion: forms that are equal, in this case all humans who have the same genetic information, since they can all reproduce, should love each other, and share energy and information to create a collective organism, a global civilization or God of History.

Recap: Truth is relative to the quantity of information we have. Thus truth is relative and never absolute.

Eusocial evolution Vs. Darwinian devolution.

Most systems are energetic and informative cells put together into 2 networks called heads and bodies that merge, creating organisms and species, where the informative network rules the energetic network in a symbiotic relationship (particles that rule fields of forces; gravitational black holes that rule electromagnetic, energetic stars in galaxies; heads that rule bodies; capitals that rule nations, etc.). How individual cells create complex organisms? How atoms evolve into molecules and molecules into the cellular Plane, cells into organisms and individuals into societies? Through Social, informative evolution, the most extended phenomena in the Universe by which individual beings become organized into herds and organisms when their cells share the same informative code.

Biological sciences have taken very long to accept informative, Social Evolution, influenced by the single arrow of energy and the subsequent excessive importance that its founder, Darwin, gave to the fight between individuals. Only in the XX century with the development of the sciences of information, Complexity, Systems Theory and Ecology, we have realized that the Universe is based in the social informative evolution of micro-organisms into macro-organisms. The existence of informative networks explains the growth of species in size, from individuals into societies. Yet according to another fundamental duality between energy and information, social events can be either energetic, Darwinian, destructive, or symbiotic, informative, reproductive:

Complementary, present, balanced events happen when beings share the same energy and informative language so they communicate and join forces in their fight for existence. For example, in gender, the female is a cyclical, informative entity that merges with the lineal, energetic male, only when both belong to the same genetic, informative species. Those social events evolve individuals into couples, groups, herds and cellular organisms, creating an evolutionary arrow of social love, based in the sharing of the same energy and information.

Among those social events the most intense is reproduction. Since the ultimate will of each point is to reproduce either by itself (since one is equal to its own being) or with a complementary species of energy (male) or information (woman). You can express that iterating will of all fractal species in mathematic terms with a Generator equation or in words with a logic mandate, as the Bible myths did, making God saying to man, a fractal species, ‘grow and multiply’, which means: ‘absorb energy and iterate yourself’. But the catch is that all other fractal parts of the Universe will want to do the same while energy is always limited. It is the Jungle Law that mechanically or biologically all fractal structures of the Universe follow. Because those who do not iterate become extinct and the fractal is no longer. So a fractal point has to erase the information and transform the energy of other fractal point to iterate itself. Galileo’s paradox motivates all points to ignore the rest of reality and take care of themselves, as relative self-centers of their own world.  Hence there are also:

Darwinian, energetic events, when the difference of form is so marked that both entities cannot share the same language of information to form a couple or a herd. Then the stronger predator will explode with the arrow of death the information of the prey into energy and absorb it to recreate its form.

Such duality of behaviors has set an eternal argument between Darwinians vs. love believers, which as most dualities of science, reflects the inverse nature of the arrows of energy and information: beings that speak the same language of information evolve socially to search for energy, inform themselves and when they are very similar, belonging to the same species, reproduce, accomplishing the wills/arrows of time in a more efficient manner. While individuals who do not understand their information interpret and hunt each other as energy. Thus duality proves that neither Love Religions nor Darwinism is wrong. Each one explains one arrow of time. Both together resume the foundation of all bio-ethic systems:

‘Love your neighbour and hunt all alien beings.’

So, there is an ethic duality, which derives from the degree of equality between communicative beings:

– Species that don’t understand their languages of information cannot form working social groups. Thus they kill each other to feed and extract their energy, making the best of their situation.
– Nevertheless there is a social, ‘loving’ evolution among equal cells of the same species that share the same language of information. And so they evolve from ‘individual bacteria’ into more powerful macro-organic systems of ‘parallel cells’ that add their fractal actions into simultaneous macro-actions; since social evolution is more successful that individual struggle. So, organisms based in the same genetic DNA-information kill zillions of individual gigantic bacteria; nations with organized armies such as the United States won over hordes of Indians, arguably better individual warriors; while ants rule the insect world, even if a cockroach is individually more powerful.

Yet since all men belong to the same species, we should love each other and evolve into a higher organism, the humankind, as prophets of love have always told us, in order to be more efficient and control properly Mother-Earth. Unfortunately humans still fight wars based in cultural tribalism, which makes us think our nations are different species because they speak slightly different informative languages or races are different because their skin has a different color. The result of such short-sightedness is that we have created partial, fractal social organisms with boundaries called nations. Thus Social Evolution deals with the fight between species and the way in which individuals of the same species organize themselves into societies, stronger than individuals, fitter to survive. Individuals fight for survival, but Evolution is a game of species. The key to survival is not the individual but the cohesive organization of a group of individuals belonging to the same species that act together with a higher energy and informative force than the individual and so the social individual survives better as part of the larger group.

Today we know that individual lions are less successful than hyenas and wild dogs that hunt in group (25% of captures in lions vs. 80% of captures in wild dogs). Even in the case of Germany, despite its ideology of Racial Darwinism, what really worked was the group – the German collective spirit that made the German army better than the individualistic Italians or disorganized Russians, till communism in II W.W. made them fight as a single organism. Thus social evolution, contrary to common belief, is much more important than dog-eat-dog societies. And that law applies to all systems in the Universe, including herds of stars (galaxies) or herds of molecules (cells) that capture interstellar gas and lonely atoms and explains the st-planes of the Universe as no other theory can.

The fact that the social organism is fractal, fractal, limited in its energy and information is ultimately the reason why individuals gather into social networks, evolving with other cells, since they require energy and information than the networks provide, becoming addicted to them. If the Universe were a continuous infinity with a single ‘immortal time’, there would not be social organisms, as our inner time of existence would be infinite. Thus survival is again the biological function that explains the existence of organic networks and its cells from the perspective of our limited fractal quantity of life-time.

Recap: Individuals who share the same language of information tend to evolve socially into ‘parallel’ herds and organisms. Species which share only a similar energy fight to use each other’s energy in perpendicular fights. Species without the same energy or information ignore each other.

Perpendicularity and parallelism.


In a prey/preying relationship, an organism absorbs energy from a simpler one. In those fights the being with better informative brain most likely will control a better reproductive body (in the graph, the black hole controls gravitation, man the rifle). So it will absorb the other fractal point.

Events are both, caused by the ‘form’ of the being’ and the ‘type of motion’ or geometry of the encounter. So even two particles that are equal can collide perpendicularly and destroy each other. In geometric terms there are ‘parallel’ or ‘perpendicular’ beings, according to the similarity of the information and energy they process within their internal organs. And so we formalize those 2 kinds of events through the 3rd postulate of illogic geometry that defines equality in terms of the inner energy and information of 2 space-time fields and the type of geometrical communication they establish. For example, 2 equal forms in a feeding, energetic cycle hunt together to enhance their survival, running in ‘parallel’, to ‘attack perpendicularly’ a victim, whose space-time they ‘penetrate’ because it is ‘different’ to them. In the image, we observe such Darwinian geometry:

2 spatial, energetic beings (a lion and a galaxy of stars), with a planar form and max. speed, confront 2 informative beings with a lot of information (a human and a black hole), dominant in the dimension of height. Since information dominates energy and time curves space, when they enter into a relative present relationship, man kills the lion and the black hole feeds on the herd of stars that become past, extinct species. Thus, the spatial ‘parallelism’ of particles and individuals that gather in waves and herds is homologous to temporal, informative equality; while the spatial ‘perpendicularity’ of predators that ‘cut’ their victims is homologous to informative inequality.

Given the infinite fractal information of any being, with multiple sub-scales of form absolute equality does not exist. At most we speak of parallelism or relative equality between 2 beings when their internal organs of information and energy process the same informative language and energetic food. Then they can establish a functional equality, communicating together, hunting in parallel social herds the same energy or even sharing genetic information to create a new being.

Those positive and negative events can be decomposed further according to the duality of energetic and informative networks:

Non self-similarity of energy and form.

No-events of minimal communication, when both the energy and information of the forms are different the forms don’t communicate, remaining in their discontinuous space-times in parallel, non-perpendicular motion, without contact.

Complementarity of energy and form.

Organic, parallel events of max. communication, when 2 self-similar or complementary forms merge into an organic system.

– Destructive, perpendicular events between complementary forms: when the 2 forms have inverse parameters/Time Arrows and come together in a perpendicular process, and become annihilated into the same ‘present’ spatial energy, dilating space and reducing the fractal, temporal depth of the Universe, as when a particle and antiparticle explode into energy.

Absolute Self-similarity=equality

 – Self-Reflective events, when the form communicates within itself and the degree of equality is absolute, which we divide into consciousness (i->i) and self-reproduction (exi->exi) in which the spatial present ‘expands’ in time and creates both, a past and future form, as when vacuum reproduces a particle and antiparticle.

Equality of energy

Darwinian events, when both forms share the same energy but with a different degree of evolution. Thus, a relative future more evolved form and a past form come together and the more evolved top predator ‘future species’ hunts and destroys the relative less evolved past species or victim, evolving the arrow of information towards the relative future ‘predator’ that transforms the past into a replica of its own cells. For example:

– A swallow and a man occupy different relative space/times and use different languages of communication so they ignore each other; they live in parallel worlds.

–  Your brain and mind occupy the same space-time because they are the same being. So their relationship is self-reflective and often our mind wonders about the brain and vice versa.

– 2 men seated in a room are parallel informative beings that speak the same language and have a positive communication, called a dialog. But if those beings belong to nations with different languages, religions and customs, as history shows, they will likely enter into a competitive argument or as nations will establish a competitive relationship that might end into a war. Then the nation with more information, with better technology and weapons that give it more Exi force, will conquer, penetrate perpendicularly and destroy the other.

– Yet if both systems have similar exi(stential) power they often destroy each other, as when a particle and antiparticle annihilate or when France and Germany entered war.

– On the other hand, when 2 similar forms occupy the same space, they create a new degree of order in the Universe. Since it is the most important, creative event, we study it further. According to the Ternary Principle we can sub-divide the creative events in 3 possible sub-events:

– A complementary event, when one form specializes in energy and the other in information. Then both forms establish a complementary relationship, creating a dual organic system with a body and a brain that share energy and information between them through physiological energetic and informative networks departing from each ‘pole’ of the couple, forming a single space-time field.

– A reproductive event. When both forms create a mixed, parallel form in other zone of space-time in which their combined energy and information creates a parallel being that mixes both exi forces.

For example, a sexual couple that makes love occupies for a while the same space-time, penetrating each other in a complementary way that reproduces a new being.

– A mystique event. When forms fusion into a single macro-form indistinguishable from i=ts parts. So cells become a body; or in a process of perception, the so-called bosonic forces, light particles, create in the focus of a visual organ in which they occupy the same space, a complementary image: In Non-E geometry, Riemann described a certain space according to the homogeneity of its quanta that diminish their distances till they fusion together when they are equal. So in Riemann’s classic example light quanta of the same frequency become the same color. In Physics we say that photons are ‘indistinguishable’ particles create a ‘bosonic’ space of relative infinite ‘informative density’, described by the ‘Einstein-Bose’ statistics. In Theology we talk of a ‘collective subconscious’, which fusions the ‘informative minds’ of believers into a communion of souls that create the mystique experience.

Recap: The degree of equality between points determines their type of Darwinian, energetic or symbiotic, informative communication: ‘2 points occupying different spaces with different information don’t perceive each other and remain isolated. 2 points with the same temporal energy are the same point and its relation is reflective. 2 points occupying different spaces, but parallel in their time-information establish a positive social or transitive communication. 2 points with different time-information, occupying the same organic space, establish a negative, Darwinian, perpendicular relationship, dominated by the point with greater exi Force or relative point of future, which destroys the lesser exi point. 2 points with different information but equal exi force, occupying the same space destroy each other, creating an inverse relationship.  2 points with complementary or parallel information, occupying the same space, enact a creative event, fusioning their existence into a new macro organic system or reproducing a 3rd being in a parallel space-time.’

Past x Present =Future. Creative and destructive events


In the graph, in more complex models of i-logic geometry, relative future, more evolved/informative species and relative past, more extended/energetic species create different type of events, which can be studied solely in terms of ‘time evolution’ as events between past and future, which will determine the creation or destruction of one or both of those entities in a relative present point, according to the degree of self-similarity (i=i) and complementarity (eói) between the 2 entities, which we have just defined with the 3rd postulate of i-logic geometry.

We talk of 4 possible outcomes of those events from top to right on the graph, which uses the standard time cones developed in Relativity Theory:

– Death Events, in which a complementary point splits its relative present form into its energetic and informative entities (particle/force field; body/head), which latter dissolve into a lower plane of existence.

– Life events, which are inverse to death events, in which a relative energetic and informative, complementary system form a stable, organic knot of present.

– Darwinian events of: A) Evolution. In which an informative, more evolved species with higher exI (existential force), destroys the past, less evolved system, advancing the overall ecosystem towards the future. Or B) Devolution: its inverse event, in which the simpler form, due to its higher Exi, existential form devolves the future, informative force, absorbed as energy. This event is chiral, in as much as there are more cases in which the informative form absorbs the energetic force, moving the overall time of the ecosystem towards the future.

– Anti-events, in which two species with inverted space-time parameters are destroyed, creating a relative present without form (inverted waves, particle antiparticle collisions).

We classify all events of reality from a spatial, formal, topological perspective and in terms of  causal, past-present-future time dimensions Then the generator equation of space-time, exi=k, can be written in time dimensions as:

Past x Future = present.

  Thus in temporal dimensions energy is the past and information the relative future of all systems. This hypothesis is consequential with the main arrow of all Time-space systems, e->I or arrow of life, and the causality that requires energy to create information, e->i. Further on, it is a fact of Darwinian Biology that more evolved systems (with better form) win in the struggle of existence, killing and extinguishing to the past, systems with less evolution. So we have a 3rd reason to consider our hypothesis that makes energy and past, on one side and information and future on the other, self-similar expressions

As Einstein put it ‘the separation between past and future is an illusion’ as both are ‘complementary’. Since relative past-reproductive bodies/fields and future-informative systems, heads / particles come together, creating the present forms of reality we observe. So the next step to consider this avenue of analysis of systems in terms of its ‘time dimensions’ is:

Thus, the 2nd/3rd postulates in terms of the 3 causal dimensions of time, past=energy, present=reproduction and future=information define how a single past and future point converge in a simultaneous present.

When we operate with those events and complex algebra of Multiple Spaces-Times, we can obtain some important results, which we can only enunciate in this introduction, such as:

– The overall sum of all the events of the Universe in terms of time is a zero sum, which means that the Universe is immortal and all the events of reality create an infinite eternal present. A trivial demonstration can be made using only the two simplest events of life arrows e->I and death arrows i->E, which gives us: SFuture Lives x SPast deaths =Eternal Present.

We however sense the Universe evolving because humans are dominant in information and perceive a much longer time-life than time-death. Or in geometrical terms death is basically an event of spatial energy, which releases and expands in space the form of an entity. Thus death has a maximal volume of energy release in a minimal time period:

Death= Max. Spatial Energy x Min. Temporal information.

Reason why death lasts so little in time. While life events are evolving, informative, warping, implosive events that happen in reduced space and stillness, but last a lot of time. So life has a minimal volume of energy and a maximal volume of information:

Life = Max. Temporal Information x Min. Spatial energy.

Those results are proved in all scales of reality. So in physical space, the death of a previous Universe (absolute scale), a galaxy (quasar), a star (nova) or a neutron (beta decay), release maximal energy in minimal time.

While in life systems, evolution happens in stillness and minimal space (allopatric evolution of species, isolated in small territories; palingenetic evolution of a foetus in the minimal space of a womb; chrysalis evolution in the stillness of a pupa). And death is almost instantaneous, releasing the energy of the organism that erases its upper, informative plane, st+1 (death of the nervous system), as the cells dissolve and become energy of herds of insects and microbial of lesser form.

Those diagrams resemble Feynman’s graphs that explain the possible events and outcomes of particle interactions, which also consider the existence of a relative arrow from future to past, which in Multiple Spaces-Times corresponds to a flow of information (Feynman’s diagrams can be considered a particular case of the model of Multiple Spaces-Times).

The graph shows the how of events. The why is defined by the self-similarity or complementarity, (3rd postulate) of the 2 Points, relative past and future entities of energy and information:

– If both particles are self-similar in energy and information (case not included in the graph) they will come together as part of a bigger social network.

– If both particles are complementary, energetic and informative systems (top graph), they will form guided by the arrow of life a complementary system that creates a symbiotic present from a past energy and a future form of information. Thus in geometric terms, in the point of collision (right side) the system will expand its space-time. Yet the entity will disappear as a relative plane of space-time in the explosion of death (left side), that will split and dissolve those networks.

– On the other hand, (bottom graph), Darwinian, destructive events happen among different beings that don’t decode their information. If both particles have the same energy, one particle hunts the other (left side). Then, the entity with lesser exi=stential force will die (bottom particle), and the one with more force will absorb and grow with the energy of the ‘victim’. Or both points might ignore each other when neither their energy nor information is self-similar and so the event of communication will not happen (right side with no space-time in the point of present).

Finally, all those events respond to a dual, spatial geometry:

– Darwinian events are perpendicular relationships, in which a predator invades and penetrates the vital space of the victim. While symbiotic, positive, social events happen among equal, parallel species that understand each other’s informative languages and maintain a parallel distance either as a hunting herd or an organism, acting with the same motions in space.

     – Exi=K: Present creation. Most events are balanced presents in which the arrows of information and energy collide in a symbiotic manner creating a self-reproductive radiation of a new balanced species.

Recap. The 3rd postulate formalizes the outcome of any communication event among relative informative/future and energetic/past st-points. The key factor to determine the outcome of an event between 2 Fractal Organisms is their degree of informative equality. Since most organic systems that can communicate by sharing the same type of information in a common language become symbiotic, as they prefer to share information than destroy each other as relative energy. 



‘The logic of Logos, mind of the Universe is of a higher order than man’s’ Saint Augustine

‘God is a supœrganism, with a mind called Logos, and a body, called the Universe’ Plato

Still mappings and its languages of information≈Perception.

In the graph we can see the difference between Newton who THOUGHT the mind of man WAS the entire Universe, hence converting the Cartesian mind graph into the ABSOLUTE BACKGROUND SPACE-TIME that still lingers in science and Descartes who thought it was just of the many minds, possible with different geometries.

The need to evolve the logic and mathematical ‘undefined’ elements of the Universe.

Now the key difference between a philosopher of science like Leibniz and a Physicist like Newton is this: Leibniz as Aristotle and Descartes before him, was conscious that the language first defines the world we perceive, and NOT the Universe. So it is a humble realization of the minimalist nature of human egos. The Physicist has reduced THE ENTIRE universe to the world-perception of a human light space-time ego centered point of view. So he lacks sense of humor and his arrogance is infinite. Because he confuses the infinitesimal of his mind with the infinite Universe. This we shall stress once and again. The physicist as all humans IS only an electronic mind that fits an infinite number of cyclical space-time beings, into a geometric linguistic mapping within its ‘monad’. And he is NOT aware of it. So his arrogance is supreme:

œ-point x ∞ Universe of time space cycles and worlds = fixed linguistic mapping

The 3 great philosophers of sciences of western thought (and their counterpart eastern philosophers of Taoist and Buddhist cultures) were always aware of this. The cut off happened when Kant rejected Leibniz and became a Newtonian. But at least Kant realized that the human Euclidean mind was a light space-mind and not necessarily all, as impressionist painters will latter.

So the human mind-language is a mapping made with light of the Universe,and uses the 3 perpendicular coordinates of light to simplify all the information of reality.

This mind on top is an Euclidean mind because it uses the 3 perpendicular dimensions of light:

All what we have done till now is fair enough but external in its description. It lacks the ultimate evasive question – the will, which creates the ‘world as a representation’ biased by the entity to ‘break’ reality into the outer and inner world, and protect the survival of the inner world with those actions.

In other words, we need a mind able to perceive the whole as a whole separated from the outer world in which it interacts. And this was the understanding that started modern philosophy of science in the work of Descartes.

Descartes  was not a simpleton. He was fully aware that what he had in the mind was not the whole Universe, so he expressly stated the fact, differentiating the ‘world’ of a human mind, from the infinite other worlds that exist outside, establishing in his little known book, the ‘world’, this difference, affirming that his ‘Cartesian Frame of reference’, was only that of the human mind.

So he affirmed that the Universe was the sum of infinite mind-worlds, which did not speak necessarily the same languages, and created the same mappings of reality we humans created.

Descartes was a contemporary of Galileo, and the true founder of modern science with his ‘Method of reasoning’ and the Frame of Reference of the mathematical mind, said that all what exists was made of:

– Open space, which he called ‘res extensa’.

– Closed, cyclical times, which he called ‘vortices’.

And then he added a 3rd element, the final stroke of a genius unparalleled since the times of Aristotle; after realizing that the only proof he had of the existence of those vortices and res extensa was, the fact that he perceived them: Cogito Ergo Sum. ‘I think therefore I am’.

– The mind or 0-point, the relative frame of reference that mapped the ∞ cycles of time of the Universe, reducing them to a ‘World’, to fit them into the infinitesimal volume of the brain.

ø-mind x ∞-cycles = World: equation of the Linguistic Monad:  ∞ Mind-Worlds in 1 Universe.

The EQUATION OF THE MIND explains the natural tendency of men to be self-centered and consider the world and the Universe around its ego. This is in fact natural to the way the Universe constructs points of view of measure, as still centers of perception, in which the I is bigger than Andromeda Galaxy. But science must account for those distortions of perception. Religions and tribes, nations and castes are NOT scientific points of view. But they do enter the mind of people who do science. And it is important to remember it, because the 5th dimension brings a much bigger jump into objectivity and lack of ego to our vision of the Universe.

Indeed, if information can only be obtained from a fixed point of view, it follows the Universe is made of egos. Or as Aristotle put it, God is the unmovable ‘ego’ that moves all the energy around himself and there are infinite Gods, particles that gauge information, heads that see, minds that smell… This must therefore be included in the next paradigm of science to build an even more objective, less anthropomorphic reality.

Now in 5D,  we have even a larger point of view. As we affirm there are infinite clocks of time, and infinite broken spaces and we adopt the point of view of all of them. SINCE THERE ARE ∞ MINDS, gauging information.

This is illustrated in the graph. In the right side we see our Universe, which Descartes affirmed correctly in his book ‘the world’, it was truly the ‘mind of man’ and Kant realized it was a light-mind.

The mind though believes to be the center of the Universe in the ‘ego paradox’ as he sees every thing turning around its infinitesimal point, which hosts inside all the linguistic perception of reality, or ‘world’ IT CONFUSES WITH THE UNIVERSE. So the mind is a fractal point•, but believes to be it all.

Indeed, we summarize the formal and functional differences between entropy limbs, intermediate boies  and information (minds) in a morphological equation:

Maximal Space-Entropy = Minimal Form=limbs/fields  Vs Maximal form = Information = Minimal Spatial extension=head

For example, the chip becomes smaller as it evolves into a better brain. Every 2 years it doubles its capacity to think, as it dwindles in size. Such process follows a generic law of evolution I call the ‘Black hole Law’, which computer scientists know as the ‘Chip paradox’ or ‘Moore Law’: maximal informative capacity= minimal spatial extension.

The reason is obvious: to think, to calculate you have to communicate in-form-ation, forms between elements of any informative system. The smaller the brain, the faster the communication that takes place within that brain and the faster you can calculate and process information in a logic manner.


The purpose of the Universe: creating world cycles.

We can assess the purpose of reality: motions with form struggle to exist as simultaneous supœrganisms elongating its existence. But for that to happen there is need for a mind-pov, which is able to control the system and enact exchanges of entropy and form, feed and perceive to ensure the maintenance and reproduction of the system.

Arrows of space-time are really cyclical and with a point of view; the singularity or Tƒi point of maximal information either in the center or top of the height dimension of information that commands the whole structure and enacts apperceptively, consciously or vegetatively a program of existence, which ensures the survival of the whole and has ‘appeared’ naturally either by selection or by trial and error after infinite eons – since those species who do not tender for their territorial vital space, and feed it with energy and guide it with proper linguistic mapping-information have not survived and reproduced. So the sum of the actions of those mind points is what becomes as observed simultaneously a whole supœrganism of ‘exi=stence’.

In that sense, the evolution of fractal points, into new wholes, super organisms and planes of existence, which form an ∆+1 emerging scale of reality, it has been the key question of philosophy of science: how individuals become universals.

In GST it means to understand that all systems are both, fractal ∆-1 dºst for the larger scale of the whole, but an entire Universe, û, for its internal ∆-1 minds.

We are all dust of space-time that evolves and emerges, as an ∆+2 whole, but alsodecay and dissolve into alower scale as ∇-1 d@st of space-time.

Only the Universe is eternal in its world cycle, conserving itself as a potential game, weaving its infinite dust into a finite number of repetitive patterns or species of being. Therefore as the number of dust particles and time frequencies is potentially infinite but the number of combined species is not, all forms have existed forever as all forms will be repeated again.

Hence the duality of fractal points minds, which after a process of social evolution emerge as whole ‘Universals’, Organisms that will live a world cycle ending in its final dissolution that completes its zero sum making the Universe immortal..

All this said we need to at least clarify the relationship between the mind of any being and the reality it perceives. Thus the mind’s languages influence reality? Most physicists today and by extension scientists who accept their paradigm, think actually the Universe is pure mathematics and so mathematics create reality. In fact, it is all the other way around, languages are mirrors. BUT they DO reflect back their image through the living actions of the organism self-centred in the mind, ORDERING reality according to that linguistic image.

Ƽst of space-time. Mind do exist.

What is the purpose of those minds? To exist through actions of absorption, emission and combination of entropy and form, which become repeated momentum, through the entire worldccle of existence of the being, Eω. exi=st in its many possible ‘representations’.

Let us then restart by defining in more depth the 4 elements of all realities. Cyclical time or ‘πime’, fractal space or ‘§pace’, the scales of space-time, or ∆-5th dimension, and the mind and world languages we use to describe them all (º,@,•, œ).

We shall use a simple function to study the holographic principle from where reality stems: e x i |s≈t.  We use a symbol | with long tradition on science to separate mirror symmetries. In this case, the main relationship of a system is between its 4 essential states, space (distance-dimension), entropy (motion), time (cyclical form with motion) information (slow time motion with maximal form) and energy (entropy motion with minimal form).

But let us stress it again: the Universe is NOT algebraic, the mind is. The universe is bio-topo-logical, and so biology, geometry and causal logic ARE the foundational stiences of it all. And an ‘image is worth a thousand numbers/words’ is a motto for GST. I.e. THE DIMENSIONAL FORM OF MICHELANGELO’s David is pure science of topological form, and it would be stupid trying to describe it with a mathematical formulae. So in general a revised Occam’s guide will be as follows:

‘All languages of Nature can map out any reality, but the simplex formulation of an event will define which language and state or entity controls and better describes the system’.

For example in the unending discussion of the particle-wave of quantum physics, Schrodinger gave us a wave description, but if we change frame of reference to see the wave as a ‘polar particle’ in polar coordinates, we get a simple formulae, which is the particle-field solution of the Broglie-Bohm model. SO THIS BB model which is realist, non local, deterministic, exactly as GST is, MUST be considered the proper way to describe quantum physics; and particles must be considered the Tiƒ state that controls waves.

In-Form-ation being essentially ‘DIMENSIONAL FORM’ is often much easier to describe with visual images in motion – a more direct understanding. And topological, geometric and bio-logical, causal, clear-cut, not algebraic, blurred concepts. So indeed, we shall see as in the graph, that art is the science of form, expressed in human languages, and as such it will appear as the subconscious collective mind of civilisations, which will go through the same 3 ages of life and death than the individual cell does, in one of the most beautiful isomorphisms (equal laws at scale) between man as a super organism in biological terms and mankind and its social organisms, which also go through 3 ages between birth and death by excess of technological information=war.

So once we have clarified a bit more the ‘ternary±@ STRUCTURE OF ALL SYSTEMS OF NATURE’,  we can go back and forth, with increasing ITERATIVE DEPTH, as the Universe does.

And study the 3±œ structure of the Universe:

Œ≈ ∆-1: Spe (entropy limbs/fields/territory) < ∆: St (body-wave-working reproductive class) > ∆+1 Tiƒ (head-particle-government)… with emphasis on its NETWORK, SOCIAL, organic STRUCTURE THROUGH 5D SCALES.

So we can now extend the generator to its natural ternary form, INCLUDING the concept of a central frame of reference, which is connected to the external membrane or sensorial ‘cut off’ ‘event horizon’ between the fractal space-time being and the Universe:

$pe < Œ: ExI(s=t) > ºTiƒ

This would be the most exact symbolic representation of the Universe. AS we include the lineal nature of Entropic Space (not money:)in $, and ad the cyclical nature of time, with the symbol of the mind, whose hardware IS often on the Tiƒ (but not always), and spread the more complex body-waves which ‘equals’ both through balancing exchanes of energy and information to create the ‘whole supœrganism’ (œ).

Epistemology of creation: feed-back mind mirrors.MIRRORSIn the graph – what is wrong with ‘physics’ and increasingly with mankind can be resumed in the ego paradox. The equation of the mind is rather simple:

We humans are just ‘finitesimals’ of the ego paradox: o-point x ∞ Universe = constant mind.

So the Universe is out there, one and single; but it does not fit in the mind. And the mind reduces it to languages to perceive it, which resumes the main properties of the Universe, which are first bio-logical rules of space-time existence (the Universe is a game of survival of space-time beings, which constantly try to reproduce their information in ‘fractal seeds’ that latter evolve socially; the Universe is a vital fractal, and the rules are simple), then logic (temporal rules only) and then mathematical (spatial rules only), and then the human vision of those rules (artistic space, verbal time, ethic, social evolution of parts into stronger wholes). And so all those languages are mirrors:

In the graph, the back and forth relationship between the infinite single Universe, its infinite partial minds, which become perceptive through a language-mirror, and then in the left its individual ego-centered singularity mirror projecting aback through limited arrows/actions of space-time, the linguistic image re-ordering a partial part of reality: its body and territory
. It is this feedback constant equation what creates reality and so we can also write another Γenerator equation, about the interaction of those three elements that orders each relative fractal partial being/territory of the Universe to the mage and likeness of those languages, images of the whole, they will therefore copycat with slight variations, in the being:

Single, ∞ 5D Universe <≈ Ternary Languages of perception ≈> Spe ‹ST›Tiƒ super organisms>Ø-Mind

This is the shrinking process, but if we take the scalar view, the Universe become infinite smaller minds, growing in volume as we count the inner worlds, (Cantor’s paradox: the set of subsets is bigger than the whole set: the sum of all mind mirrors is bigger than the single Universe).

So human minds alone are infinitesimal compared to all the languages and minds.

We ‘are’ only in that territory of order with the stif-human mind  and what we feel and sense, which we by homology imagine is the hidden mind of every synchronous form that lasts, and develops as the frequency of its happenings increase, a short of computer burn-in which becomes a consciousness of the stiff-processs. But can this self-awareness of the mirror change the mirror program? which is the mindless deterministic memorial game of reproduction of time cycles? 

Ah, the crystal of my mind responds, it wishes but it can’t hardly influence the program and purpose of mindless automated memorial time, iteration repetition conservation, the female present principle of the outer membrane cycle, which carries most of the Æxistential Momentum of the being.

Now of course, the ‘ternary’ level of self-awareness of the duality of pure perception of an infinite whole and mere action over a finite territorial ego; is seldom found among humans, reason why most beings are subjective and rather believe in abrahamic religions than objective science.

In the graph the dual function of the mind perceiving and ordering, modifying what it perceives.

It should not surprise the reader that the mind is the main element of all supœrganisms of ðime§paœ, as without the mind, ‘the will of existence’, using terminology of taoism and schopenhauer will not recreate a world as a representation of its self.

So the world cycle is felt by the mind alone, for the wholeness it orders, and in its tƒi consciousness of being the mind of a territory and fighting to make it last through reproduction and conservation the Universe happens in ‘its selves’.

To exist thus reduces the consciousness of the world cycle to the mind-point of the space-time being, in which order steams, through the networks connected to it, and the connections of the self to other parts of the being. The self thus is an º∆±1 mind, an º being, perceiving and ordering with the program of existence, the algorithm of partial actions, embedded in the Γenerator, enacted from the point of maximal communication a territory of space-time, ∆ across three ±1 scales, normally the center of maximal communication of the ‘solid-crystal’ network of minimal outer motion (maximal inner motion through the software running those networks): ∆º (Tƒi).

WHERE IS THE singularity’s will of each fractal point of existence, in the stillness of language, able to subtly reverse through the networks that connect it to all other points of the system? In the points of maximal communication, knots that try to achieve a balance S=T of all the flows it receives an re-emits after passing throughout a language mirror with capacity to ‘reverse’ the nature of the order.

Fractal points gauge information with infinite parallels.

The fact that all points interact with the external Universe is explained by the 5th postulate of Fractal Logic, which completes the 1st postulate.  The 5th postulate defines a point as a knot of communication of multiple flows of energy and form, which the point absorbs to obtain energy and information for its organic cycles of iteration.

Thus we introduce a new perspective in our study of a Non-Euclidean, fractal point of view: its capacity to gauge information and absorb energy, acting-reacting to the Universe. Since beyond those 3 internal regions the point feeds on an external world of relative forces, which provide the point with energy and information to map out reality and feed its body with motion. Thus, while energy and form will be different for each point according to the scale and form, all entities of the Universe will be able to absorb a relative number of ‘infinite parallels’ to create mental fractal mappings and keep on moving: light feeds particles, intergalactic gas feeds stars; plants feed animals that feed man; stars feed the black hole, and so on.

In science, mathematicians and physicists seek to describe reality as ‘made of mathematical entities’; while logicians try to explain reality as a series of causal events. But only when we use i-logic geometry we can mix both approaches, describing reality as a series of ‘mathematical points of view’, or entities that ‘gauge’ the geometry of the Universe, constantly mapping out the universe, to achieve a ‘selfish’ will, the desire of all entities to feed on energy, gauge information, reproduce and evolve socially. Those points of view are thus ‘mathematical minds’ because they gauge and somehow ‘perceive’ the geometry of the Universe, acting according to that geometry as they gauge and move with an ‘automatic’ behavior, trying to absorb energy for their body, information for their gauging mind, and combining both, to reproduce ‘self-similar points’.

So we shall consider that the Universe is made of i-logic, fractal ‘points of view’, akin to the concept of souls and Atmans in western and eastern religions’, of ‘Non-Euclidean points of view’, ‘monads’ or ‘Spinoza’s geometrical entities’, in western philosophy of science and mathematics; of ‘gauging particles’ in physics, or ‘informative DNA nuclei’ in biology and perceptive heads in biology. The size and form of all those points varies but all of them are spherical knots of information with sensorial apertures to absorb and emit energy and information, from boson particles to sound waves or light signals.



Foreword. The equation of the mind and the 5th postulate of Non-Euclidean geometry.

Now a hyperbola is perceived as a cycle from the 0point in the centre of reference. that is how we are. We are a zero point but perceive a hyperbola of the Universe. We are nothing and we perceive it all – the entire curve of the hyperbola has 2 focus, but the point that matters is the zero point.

In the beginning there was an observer, a focus point that let itself cross by infinite parallels and perceived a mapping of the Universe.

This original point might be considered infinite or infinitesimal, God or microbe, the unmoved one, of the eternally moving. But there was no other inertial frame of reference but the one he perceived.

And it was of course, a polar one, the perfect form, the 2-sphere.

Did he started the Universe by the mere fact of co-existing with it? Was he looking at its inside forms? We do not know this metaphysical questions but we can describe bio-topo-logically the first point in existence.

The infinitesimal point, O, saw the infinite Universe, ∞, and created a constant mapping of it, O x ∞ = Constant, in the stillness of the mind.

The point, the Observer the measure is the first action that starts any activity in reality. Prior to motion towards a field of energy or information that interest us or away from it, the point must perceive it. And for that to be possible, the point must have parts, an informative mind –like capacity to gauge information, and rotational motion to change the angle of view.

The point thus have to have angular momentum, the minimal unit observable in the Universe, the h action, a point of view a momentum moving and a radius of distance.

The fundamental Unit of the fractal universe thus is also a point that makes up an absolute space-time, but such points unlike Euclidean classic points of mathematics are fractal non-Euclidean points, which have breath, hence are cycles, the minimal unit of the Universe a time cycle, seen in statics as a cyclical point, dynamically as an attractive point-particle in a static position or a particle with momentum, neutral to a background universe.

Infinite of such points exchanges energy and information in infinite scales is the departing point of any scale of realty to understand how it builds above and below itself O±∆ superorganisms.

But the infinitesimal point to be noticed and exist must at least ‘think’, observe, perceive with a certain angle a part of reality converted into mind mapping.

And this can be measured with the simplest, smallest quanta, the angular momentum of a system, the h-derivative increase, the ∆minimal action of perception:

ƕ: angular momentum = h-derivate.

Objective vs. subjective perception

If the fundamental differentiating, ‘external’ property of species in the Universe are the Metric of the 5th dimension (i=SP x Tƒ), which makes them belong to different inverse scales of size in space and energy volume (SP) vs. speed of temporal information), the essential equalitarian feature is the co-invariance of that product, which gives them the same value when considered, internally’ from the inner point of view of the system,

Since from the inner ‘measure’ of time, the smaller, faster clocks of a diminutive being, process the same amount of information in its life span than the larger being. So an insect which lives a maximal of 7 years (queen ants, elephant cockroaches), since it processes information 10 times faster than we do – reason why we don’t catch a fly – it actually lives as much as we do, 7 x10=70 years.

This is the wisdom of the 5th dimension: all selves feel the center of the Universe they measure from their Non-Euclidean fractal point of view, which has from ‘its’ perspective as much information as the entire Universe do.

The mind self-equation:

Tƒ(infinitesimal point of view) x ∞ (infinite, perceived Universe) = ∆ (constant mapping of the whole)

nicely puts it in perspective.

Topology explains it: the sphere is the only topology that can shrink without limit of tearing, allowing the reduction of the infinite into the infinitesimal (Poincare conjecture).

The 5th postulate of non-Sp geometry also defines it.

Let us then start with the usual methodology of ‘building dimensional blocks’ of ST theory, by considering the Spatial location of Minds, as the center of maximal communication of a system.

 The Mind’s point of view 


In the graph, a mystical representation of the mind, as the central triangle of a tetraktys. The mind is the ‘fractal point of view’ (mathematical interpretation) or zero point, in which maximal flows of information converge, both from the external and the internal regions of the being, where the will of the ‘4 åctions’ resides. 

The Mind is the ‘point of view’, site of the will, that perceives each element, each part.

It is the ∆-centered dimension, in the sense that it is the most ‘connected’ point, in the center of the system, which ‘reflects’ upon the existence of the whole.

In mystique terms it is in a way the soul, the atman. It is the central number of maximal communication in the tetraktys that Pythagoras rightly considered the perfect number, illustrated in the Kabala graph above.

In Physic-mathematical terms it is the final black hole, non-Euclidean point of view of the system. It is the 10th or 11th dimension of Time on the string formalism, etc.

In biological systems it is the nervous, ’10th system’ that integrates the other 3×3, energy/reproductive/informative physiological systems of the human being.

Depending on which ‘human jargon’ with more or less errors – lacking the ∆ST formalism and ∆ST philosophy – we talk of, it will be ‘named’ with different forms.

I often use the term the 5th Dimension, of all ∆-scales of the being, to represent the ‘whole’. And so we have termed it also as the 5th ‘invariance’ or ‘isomorphism’ that all beings share, since the mind-self, the centered dimension of all scales, the 5 isomorphism of nature, the point of view, the soul is the most important dimension of all beings.

It wraps up all the other dimensions, isomorphisms and scales.

And it is therefore the center of its 3×3 ∆±4 scales, its 3 topological space organs, and its 3 time ages (the being is at its maximal force, in the SxT (s=t) steady state mature, adult age of balance, ST, age of maximal duration.

In man obviously is the brain, expression of the ‘Whole’ or ‘Soul’, which perceives internally the system through its ∑3×3 networks (our sensations of the energy, digestive system, the reproductive, endocrine system, and the mind thoughts and emotions) and externally through the senses. But in many other systems is a very different site.

So perhaps the best definition is that of Non-E mathematics: the ‘point of view’, the part of the fractal point that gauges maximal information. 


Non-Aristotelian Times and Non-E Topology

‘God is logos, of a higher logic than man’ Saint Augustine

‘Each point is a world in itself.’ Leibniz, On the Fractal, organic Point, the Fundamental particle.

”Nothing is new under the sun’ Spanish Proverb, on the repetition of all time beings & its cycles of in/form/ation.

‘To be or not to be that is the question’ Shakespeare, on the world cycle of existence.

 S<≈>T  arrows

The formalism of GST requires an upgrading of Euclidean Mathematics and Aristotelian Algebra and as a consequence of our epistemology of knowledge, which becomes the 3 fundamental new disciplines of formal sciences:

  1. Non-E mathematics with its definition of the 5 postulates of geometry in terms of fractal, non euclidean points.
  2. Non-A Logic which describes the ternary causality of the Universe.
  3. And the homologic method of truth of ‘stiences’ of space-time beings based in the same laws or isomorphisms across scales.

Because we are made of space and time, of energy and information, the sciences of space, topology and time, logic, and its combination (mathematics as a whole discipline, where logic enters in the demonstration and structure of its postulates), is the most REALIST of all stiences, as it deals DIRECTLY with the properties of the 3 elements of reality:

  • ∆nalysis, which studies how ‘finitesimals’ become larger wholes, integrated in time ‘frequencies’ or ‘spatial populations’ – often both, as frequencies become once created in time populations in space; which we greatly advance on the whys and explanations of calculus and its applications to sciences, through the enhanced concepts of ‘finitesimals’, ‘simultaneity’, ‘synchronicity’, ‘resonance’ and ’emergence’.
  • S-topology, which studies the ternary varieties of organic systems and how they peg together to form a system; which we shall explain by evolving the postulates of Non-Euclidean Geometry.
  • T-Algebra, which studies the rules of causality of a Universe with 3 time arrows, and its fundamental equations (generator equation, function of existence, equation of time ages).

Let us very briefly introduce those concepts which are the foundations of all stiences and it species in ‘exi=st¡ence’.

Non-e Mathematics: fractal mind-point, wave-line, organic plane and laws of similarity. 

Upgrading of philosophy of science needed to fully understand the fractal Universe requires to improve the main human language, which we use to mirror the space-time beings of reality, what we shall call from here on non-Æ, i-logic mathematics, which comes after Aristotelian logic and Euclidean mathematics:


In the graph, the upgrading of physical systems, to fully describe all its mathematical, logic and organic properties, requires to set the foundation of physics in more solid grounds that the ‘I imagine points, lines and planes’ of Mr. Hilbert, referring those lines, points and planes to real Universal entities (1st, 2nd, 3rd postulates of non-e mathematics). And expand the temporal logic of the Universe to include the 3 arrows of relative, finite past, present and future of all systems of nature. Finally the 2 postulates of Hilbert’s axiomatic method, of congruence, which can only be of relative similarity, as we never have the full information about a system, (3rd postulate) and continuity (which is false and not required in pan geometry, as all networks of points communicated by waves of energy and information, leave discontinuous dark spaces not crossed by those networks), must be clarified. Finally the 5th postulate of Non-E Geometry, the only one properly defined till date, which allows infinite parallels of energy and information to cross a fractal point, defines the structure of a logic mind-mapping, constructed with those flows of information, and hence the equation of any monad mind on the Universe: O (infinitesimal point) x ∞ (cycles of energy and information of the Universe) = ∆: constant mapping of a certain scale of the 5th dimension.

Logic mathematics is the language we humans use in science to describe the Universe. As such it is only natural that its 3 ‘linguistic mirrors’ or sub-disciplines, correspond to the 3 ‘elements’ of the fractal Universe:

  • Geometry and the 3 topological varieties corresponds to space and its 3 canonical, organic parts.
  • Analysis to the 5th Dimension and its scales of infinitesimal, derived points and integral wholes.
  • And algebra corresponds to the temporal analysis of the structures of the fractal Universe, resumed in its generator.

So an immediate task to upgrade human sciences to the fractal paradigm is to study its formalism, through a natural upgrading of the foundations of those 3 disciplines to match the 3 elements of the fractal, organic Universe.

Now as we said we have two LEVELS OF DEPTH:

  • THE FIFTH DIMENSIONAL UNIVERSE, as we have and will use to explain most of this blog.
  • The complete mathematical model of a 10 dimensional Universe, whose formalism we shall integrate slowly mainly on the 3rd line with 3 dimensions of time (ages) space (topologies) scales in a ∆±1 organism and the whole its mind. THIS IS THE FULL DESCRIPTION OF A SUPERORGANISM SO WHEN WE DEAL WITH SUPERORGANISMS IN ONLY 3 SCALES OF THE 5th dimension – which happens to be always as that is what our mind truly scans and integrates, so it can be also studied the whole universe in this manner as the graph shows, we shall bring the 10th concept back. And of course, THE 10TH CONCEPT IS WHAT WILL BECOME STANDARD: 10 DIMENSIONAL SPACE-TIME, 3 space 3 time 3 scales one whole ∆+1 mind-point that integrates it all.

The idealist logic of mathematical physicists vs. ternary reality

ALL THIS i-logic geometry IS completely NEW. Why?

Because humans do not have a basic picture of the 3 components of the Universe. We do believe in a certain mathematical structure called a continuum simple space-time. So our view of the first elements of the Universe, is very reductionist and simplistic, and so the mathematical mirror the ancients took of it, is also simplistic. And when in the XX century they found a much more complex Universe, of multiple scales of space, and multiple cyclical time vortices – particles, charges, masses, molecular clocks, galactic clocks, etc.as the initial mirror of mathematics was a distorted one, things got messy and remain so.

So the cartesian single space-time continuum is a geometric simplification, which despite the revolution of non-Euclidean mathematics, quantum physics and relativity is still with us.

It is based in a geometry called Axiomatic, which came after we found out that points were fractal points that could be crossed by ∞ parallels (5th non euclidean postulate) and so the definitions of Euclid were not good. Yet instead of defining as we shall do a fractal point, XX c. mathematicians left them undefined. So terms like points, lines, and planes still do not much its universal, referential reality.

In essence mathematicians scared of the non-Euclidean revolution, which was incomplete, invalidated the postulates of Euclid but didn’t find the new, real ones.

So instead, Hilbert, a mathematician said that he ‘imagined points, lines and planes’. So they must be undefined in relationship with the real Universe and what was an act of absolute arrogance, he implied that the human mind invented mathematics, the only language of the Universe, so somehow we invented the universe – no joke, today this means that physicists invent an equation that describes an imaginary particle, or evaporating black hole, or string theory and will affirm dogmatically without experimental evidence that it is real. While quantum physicists believe the Universe is made of mathematical symbols, which is exactly what religious people think, when they say that God created the Universe talking with words – so Allah created the Universe ‘naming’ it. And finally since mathematics are imagined, they require not evidence: only logic coherence not experimental evidence justify mathematics. And this is a dogma, even if Godel proved that mathematics without experimental evidence is not coherent.

IT MUST BE NOTICED THAT ®=i-logic mathematics is A REALIST stience, so the UNITS OF mathematics are again REAL:

  • Fractal points in geometry; numbers in algebra and finitesimals in Analysis, which are in fact 3 sides of the same being – the social St-point/number/finitesimal unit of all mathematical disciplines.

Existential algebra thus defines numbers as social wholes, and the laws of numbers the generic laws of those social wholes.

Hilbert’s axiomatic method is therefore not truth – as Godel proved with its incompleteness theorem, but arrogant, ego-centered mathematicians wanting to have the ‘exclusive language of god’ resolved, have been denying or a century.

Mathematics is the most experimental of all sciences, dealing with the structure of space and the logic of time, and so we need to evolve and defined its undefined elements. Only then the revolution started by Lobachevski aiming to substitute Euclid’s points with no breath, will make sense and mathematics will become again a proper mirror to look at the Universe – or rather we will understand why the mathematical mirror is so good.

So what is a point?: A unit of fractal space, which a mirror mind will see with less or more information the closer it is to the point. Hence while from far away it seems a point with no breadth, as we come closer it can fit infinite parallels. And so a line has also width, in detail carrying information and motion; and a plane is discontinuous, made of points joined by waves, which leave dark spaces between them. We thus talk of fractal points, waves and networks as the 3 units of i-logic mathematics.

Points then become defined as fractal points that grow in size, planes as networks of space points with wave-like motions in time, which become bidimensional, from far away, as we do not see the height of those points. And 3-dimensional systems, become the merging of perpendicular networks, which have more content of energy, when they are flat and extended, and more content of information when they are high and cyclical.

So for example in a previous graph, we can see 2 fractal space-time beings made of ‘mathematical topologies’: a field of space-time light, with a flat bidimensional magnetic field of energy and a tall informative perpendicular field of electricity merging into a light ray, which reproduces along the c-speed axis.

Yet we can see the final stage of evolution of light space-time, which evolved into particles, atoms, molecules, cells and human organisms, and surprisingly enough, in the same manner the probability of finding the particle-head or photon of a light system is maximal in the top of the electric wave, the informative head of a human being is also in the dimension of  informative height? Why, because geometrically, that is the point of maximal perception for both the photon and the human. And in both cases motion goes along the lineal direction of length, and in both cases energy is stored in the width dimension of the body and magnetic field.

Now, we are talking (-: It is indeed the most astounding truth of the Paradigm of relational space-time, first expressed by Leibniz – a Universe made of fractal space-time beings – that the properties of space-time and its mathematical topologies, perceptive, informative geometries, and ternary structures are carried and emerge in each new scale of social evolution of the Universe.

So while we have criticised the mathematical only view of earlier scientists, as we upgrade logic mathematics, in fact the Universe will become even more mathematical and logic that it was before, only that as Saint Augustine put it, the ‘logic of god, the mind of the Universe, is of a higher kind that our (Aristotelian) Logic’.



The first paradox of the Universe is that between unity and diversity, equality and similarity, numbers as undistinguishable social forms and points that must diverge at least in position, fermions and bosons, masses and individuals, wholes and parts, the one and the Universal…

It also come however to the concept of a fractal point, unit of reality, mind that has in itself a whole Universe made of infinitesimal pixels, an eternity could be spent talking of this paradox, which Parmenides first studied in the greek world.

Mind the reader, fractal points are NOT so new. Again, the great revolution of physics in the XX century happened when Einstein realized that a point was a ‘fractal point with volume’, since multiple parallels cross it. So it could not be Euclidean – with no breath, abstract, dimensionless.


The need to evolve the logic and mathematical ‘undefined’ elements of the Universe.

The key difference between a philosopher of science like Leibniz and a Physicist like newton is this: Leibniz as Aristotle and Descartes before him, was conscious that the language first defines the world we perceive, and NOT the Universe. So it is a humble realisation of the minimalist nature of human egos. The Physicist has reduced THE ENTIRE universe to the world-perception of a human light space-time ego centred point of view. So he lacks sense of humor and his arrogance is infinite. Because he confuses the infinitesimal of his mind with the infinite Universe. This we shall stress once and again. The physicist as all humans IS only an electronic mind that fits an infinite number of cyclical space-time beings, into a geometric linguistic mapping within its ‘monad’. And he is NOT aware of it. So his arrogance is supreme:

o-point x ∞ Universe of timespace cycles and worlds = fixed linguistic mapping

The 3 great philosophers of sciences of western thought (and their counterpart eastern philosophers of Taoist and Buddhist cultures) were always aware of this. The cut off happened when Kant rejected Leibniz and became a Newtonian. But at least kant realised that the human euclidean mind was a light space-mind and not necessarily all, as impressionist painters will latter.

Yet starting with Kant and then Hegel, which had the chuptzah (even if he understood perfectly the ternary logic of thesis-antithesis-synthesis similar to the Sp<ST>Tƒ ternary Universal Grammar of all systems) to affirm Abrahamic tribal religions were superior, because they only accepted the human ego-trip of tribal Yahweh, there is a growing anti quantum paradox in philosophers which yield as infinitesimal observers to the huge power of the observable, industrial world.

This paradox inverse to that of the physicist, so huge that influences the observer, made after Leibniz, all philosophers incomplete. As they no longer dare to criticise the makers of machines and weapons, and not even the Abrahamic tribal, lineal religions of the Bronze age that back the hate between members of the same species. So we of course show a complete indifference for all what has nothing to do with the larger Universe of infinite worlds, and find the arrogance of physicists, infantile.

Now I will state a provocation to the ego of physicists (-; Mind the reader though that my ‘selfies’ are ‘black humour’, i am an infinitesimal aware of it, but i like to bust the balls of ego-centered human infinitesimals, and none are so much ego-centered as physicists.

The advantage of being a philosopher of science, is that unlike a physicist, we DO know the essence of science which is ‘logic mathematics’. That is our profession. To understand the logic of mathematics. So despite Mr. Hawking’s quipping, that we philosophers of science are envious and that is why we criticize his evaporating black holes, because we ‘do not know mathematics’ the opposite is truth.

By definition the masters of philosophy of science HAVE created mathematics and logic, the languages of space and time, since the times of Plato and Aristotle to the times of Descartes, Leibniz and Hegel. And yes, this writer, duly ignored by ‘those who impose truth with power, to become the laugh of the Gods’ (Einstein, the only physicist I consider to the level of the best of our profession, which he greatly respected, along the rules of the scientific method, except when falling under the spell of Mr. Hilbert, and we will return to that).

Because the language of God is the logic of time cycles and the mathematics of spatial extensions. In this we are different from physicists who only apply the mathematics, we teach them. But especially we like the Logic behind the language of mathematics, which creates it. So let us rephrase it. Yes, Physicists do know as much mathematics as we do. And their computers even more (-;

But they do not understand the logic of it. And that is the problem. Because logic is a property of time cycles, and its repetitive causality, logic is more important that geometry. Logic is ‘the beginning’. So the Greeks called God the mind of the Universe, Logos, derived from ‘word’, not ‘geometry’ meaning “Earth measurement.” And that makes the whole difference, physicists do not grasp. As what they do is ‘geometry’, measure. We philosophers of science do Logos, (-;

Now, we told you, we will evolve mathematics, so we can fit the new concept of cyclical time and fractal space within it, as Descartes and Leibniz did to fit their time vortices and relational infinite times, as Einstein did (not by himself but by applying non-Euclidean mathematics to his description of space).

So to that aim, we just need to complete the scaffolding of mathematics and explain what a mind is, in geometric logic terms.

So we need to complete the concept of fractal quanta of energetic space of quantum physics, the concept of a Universe of multiple time cycles of Einstein, and the philosophy of science, made of causal repetitions of time cycles called laws of science.

Thus we affirm that the Eastern, O-Cyclical concept of Time; and the E-insteinian, Relativistic concept of space, which we shall call, Œ, is superior to the ‘lineal, Abrahamic, concept of time’ and Absolute’ Newtonian, concept of Space.

I like to play with ‘words’. So you could think that A-brahamic, Lineal, A-bsolute Space-time is a simplified, earlier version.

And we shall go even further, into the Non-AE, (Non-Aristotelian, Non-Euclidean), i-nformative concept of Space-time.

And build a new Non-Aristotelian Logic and Non-Euclidean Mathematic formalism, which will set the foundations for a new paradigm of science.

This new Geometry is simple and evident. It is based in the definition of the ‘terms’ which mathematics ill-defined in Euclidean Geometry, points with no parts through which only one parallel crosses, lines with no breath and shallow planes, equaled by superposition, and then once Euclidean Geometry was found to be a ‘limit’ of a larger pan- Geometry NOT lineal but curved inwards (elliptic) or outwards (hyperbolic), on those dark times of confusions, were UNDEFINED.

So we DID not resolve the issue. We CANNOT ESTABLISH the fundamental science of the Experienced Universe, by undefining its fundamental elements. This no way out sponsored by Cantor, who substituted points and numbers by sets, nowhere to be seen in experience, and Hilbert who affirmed ‘I imagine points, lines and planes’, is a failure.

In that regard, the founder of Non-Euclidean geometries Lobachevski was in the right track. We can summarize Lobačevskiĭ’s solution of the problem of the Fifth Postulate.

  1. The postulate is not provable. Because, infinite lines curve when we have a larger view, becoming exponential inversion of space-time.
  2. By adding the opposite axiom to the basic propositions of geometry a logically perfect and comprehensive geometry, different from the Euclidean, can be developed, providing we limit infinity, (as the 5th dimension shows) hence parallels do NOT meet on the infinity, and by curving them (hence lines are part of cycles)
  3. The truth of the results of one logically conceivable geometry or another in its application to real space can only be verified experimentally.

Thus we must observe the Universe to prove mathematical statements and reduce mathematics as we do with all experimental sciences to those equations which ‘are real’.

The evolved formalism of i-logic mathematics: Upgrading Geometry.

Now, we shall be less literary and start with very solid conceptual elements, namely describing the essence of the fractal paradigm.

And to that aim we shall bring, in the simplest possible form, the fundamental formalism of the Fractal Paradigm, ‘non-euclidean, non-aristotelian i-logic, o-rganic mathematics’.

We call it i-logic because in time, it is more complex, with multiple clocks and i comes after the A of Aristotle (the logic built with a single time clock and a single causal arrow) and we call it organic because in space is more complex, with multiple co-existing spaces, smaller parts that become wholes and O comes after the E of Euclid (geometry with a single continuous space made of points with no breath). But in brief, we shall just talk of Non-Æ, or i-logic mathematics.

So we shall now explain and complete at a very elemental level far more developed in the ∆±∞ posts on i-logic mathematics, the formal language of the fractal paradigm, what truly Non-Euclidean, Non-Aristotelian space-time languages are.

Fractal point with breadth and the networks and social organisms they make, connected together.

Einstein found that the Universe was non-euclidean, that is, points did have breath because they could fit many parallels of energy and information. And so they are ‘fractal points’ that grow in size when we come closer to it. But they forgot to change the first postulate of Euclid, and left points undefined, so this simple change of mathematics will open completely the world of science to the fractal paradigm. Let us see how.

Einstein found that gravitational Space-Time did not follow the 5th Euclidean Postulate, which says:

Through a point external to a line there is only 1 parallel

Euclid affirmed that through a point external to a parallel only another parallel line could be traced, since the point didn’t have a volume that could be crossed by more lines:

Abstract, continuous, one-dimensional point:

. ____________

Instead Einstein found that the space-time of the Universe followed a Non-Euclidean 5th Postulate:

A point external to a line is crossed by parallel forces.

             Real, discontinuous, n-dimensional points:           ===========o

This means that a real point has an inner space-time volume through which many parallels cross. Since reality follows that Non-Euclidean 5th postulate, all points have a volume when we enlarge them, as cells grow when we look at them with a microscope. Then it is easy to fit many parallels in any of those points. Such organic points are like the stars in the sky. If you look at them with the naked eye they are points without breadth, but when you come closer to them, they grow. Then as they grow, they can have infinite parallels within them. Since they become spheres, which are points with breadth – with space-time parts.

So space-time is not a ‘curved continuum’ as Einstein interpreted it, but a fractal discontinuous. The maths are the same, the interpretation of reality changes, adapting it to what experimentally we see: a cell-like point enlarges and fits multiple flows of ‘Ðimotions’ and information, and yet it has a point-like nucleus, which enlarges and has DNA information, which seems a lineal strain that enlarge as has many point-like atoms, which enlarge and fit flows of forces, and so on.

How dust of space-time becomes a complex system and organises the scalar universe of parts that become larger wholes, from atoms to galaxies, from amino acids to social super organisms of life, is then the ultimate process to describe departing from the properties of all forms of dust of space-time. Those fractal points do organise constantly into larger systems, whose summit of complexity is a super organism, in which all those points of different size, speed and form co-ordinate its actions, motions and forms into larger, synchronic super organisms, which however are never eternal, but end up dissolving after its world cycle of existence ends, back into its smaller, fractal parts, loosing its information in the moment of death.

And yet the whole Universe is eternal because motion, entropy never stops. It is the ultimate substance of it all. And so we could say the Universe lives an eternal present as dust evolves into organic forms, emerge as a larger whole in a scalar, bigger world, where it develops its algorithms of existence, absorbing energy and information for its body waves and particle-heads, repeating its structure in other regions of space-time, and finally dissolving back; once and again, per in secula seculorum, the Universe repeats those simple games.

And so it can be considered a fixed block of 5Dimensions of space-time, where certain paths will imprint certain beings, which will again dissolve, as a screen of a television can run infinite softwares, which will be waves of form that disappear while the hardware stays. That hardware is what we call temporal energy, the motion with form of which we are all made:




The second set of paradoxes incremental in complexity come from the 2, duality and its flows, which merge in the reproductive middle, iteration of both. But the I-logic paradoxes that matters most for a language are those of perception.

Such paradoxes concern thus with the duality of ∆-1 quantum discontinuity and ∆+1 continuous whole due to the different angle of perception, elliptic, minimal on the upper layers where the informative, invisible networks that enslave us but make us feel free reside, vs. the parts we manage to control below of which we extract almost all its information, while in the same plane we are cartesian, democratic equalitarian.

Thus we are slaves of the networks above we don’t see, enslave our lower planes and live with equal e-motions with those in the same plane.

It is in that semi plane when the continuous and discontinuous merge into variations of form, the mobile and immobile of faster smaller time cycles and slower larger ones merge into the variety of speeds and the lineal flat view from below and closed view from above merge into the variety of conic curves.

The paradoxes of duality were ill-understood by physicists making physics the simplex merely mathematical system it is today, but much better understood by Heraclitus and those who came from the east:


SCALE Dis-Continuity;  SPACE=Form V. TIME=Motion.
AGE: $t-open youth vs. ð-closed 3rd age.
How Dimensions in space, merge with motions of time? The answer is that all yin has a yang, all yang has a yin, all dimension has motion, all form has motion.
THE BEST WAY TO EXPLAIN IT is then through the paradoxes of the human mind that perceives often motion as form, often a cyclical complete world cycle as a mere open step or line, and cannot see the duality of parts and wholes proper of the 5th dimotion or social evolution. Let us then study those elements or paradoxes, which humans normally only study as either one thing or the other.

Yet both time=motion and space=form are ultimately mirror images of each other:

The 3 paradoxes of Galileo. T-Motion vs. S-Form, ∆… Continuity vs. discontinuity, $t-flat, open vs. §ð-curved order

‘The earth moves and doesn’t move’. Galileo: relativity and duality of space and time dimensions.

‘A Ðimotion can be perceived as a distance=dimension of space or a motion=change in time or both together’ l§

Einstein studied space as the simultaneous measure of different regions of the temporal Universe. His explanations though were a bit complex, dragging onto the tradition of lineal time and continuous space. It is all simpler. Space is a ‘mental’ perception in simultaneity of different regions of moving time cycles, which the mind simplifies, by extracting information in many ways (motion, scales, third dimension, etc.)

Physics has really been concerned since Galileo realized the earth moved but we do not perceive motion, with the paradox of RELATIVITY of motion vs. stillness. But the duality was not understood, neither the contribution of the mind to the ‘maya of sensorial stillness’ that gives us the ‘perception of space’.

Because all things move, and stillness is a maya of the senses, Galileo was right when he realized the Earth moved. But the important question science has missed ever since, and  Einstein would latter explain in relativity is why we see the Earth still if it is moving. Again, we shall fully solve the conundrum when we define the equation of the mind. But as this is the icing on the cake of the cyclical universe, we shall bring it now here.

The duality of motion-distance is similar to the way we see a car moving in a night picture as a fixed line, or the stop and go duality of a film projector, which is perceived as motion. And it has deep implications, which help to resolve many uncertainties of physics.

The next graph illustrates the 3 main dualities or paradoxes of endophysics (Physics in which the observer’s mind is also accounted for): motion vs. stillness; continuity vs. discontinuity, single §pace vs. fractal scales of spar, all of which depend on the detail of the observation – hence the quantity of information we have on the object we study:image005
In the graph, Saturn’s rings, first observed by Galileo, seem continuous, still and bidimensional from far away; but observed in detail they become discontinuous in motion and made of 4D spherical particles. THEY SEEM TO BE FLAT but in detail they are curved. And they seem to be still but they move. So those are the 3 main paradoxes of perception: MOTION VS. FORM, FLAT OPEN, VS. CURVED, ORDERED, and CONTINUOUS VS. DISCONTINOUS.

Moreover, what appears as a single ðime§pace continuum in detail becomes at least 3 scales: that of the rings with cyclical motion, of its particles, the rocks that turn within them and the not seen but known scale of atoms that create the solid networks of those rocks.

THUS Galilean relativity though was ill-understood, as the true question about time-change was why ‘we see systems still when they move’, and ‘why we see space as continuum, when in detail is made of quanta’, and why all systems are made of smaller self-similar systems. Those are pending questions solved with a simple statement, which shall double our dimensions of reality:

“Since we cannot distinguish motion in time and form in space, all systems are space-time systems with at least 2 dimensions, as to each motion in time corresponds a form in space: S=T”

So how physicists called the 3 arrows/dimensions/ages/motions of time? They have a conceptual mess made around them. Of course they study them but do not name it clearly as 3 different time dimensions.

The paradoxes of space and time is the key to understand the paradoxical laws that rule the exi=stiences of space-time species, which occupy a certain organic space and last a certain time. They are all embedded in the topological ternary nature of form, and the different quantity of information (discontinuous) and entropyy (continuous) we perceive in larger spaces (max entropy) and smaller ones (max. information) according to the deceptively simple metric of 5D:

Size in Space x Speed of Time cycles = constant: $ x ð = K

Dis-continuous paradox.

In the graph, Saturn’s rings are not a mathematical plane made of abstract points, despite their continuous appearance. When we look at them in detail they become in fact quantic planetoids in movement, tracing orbital cycles around the planet. They illustrate the fundamental paradox of perception:

Any piece of time/space seems continuous, from the lower ∆-1 perspective, as larger planes of reality with slower time cycles transmit less information, and we peg it together those bits of information, jumping over its dark spaces; but when we analyze its parts in detail, we receive more information so the system becomes discontinuous, made of space/time quanta moving in cyclical paths.

Thus of great importance for all sciences are the dualities between the ‘extreme scales’ of the being – its ¡-1 discontinuous cellular/individual scale and its ¡+1 continuous larger world, observable for example in the quantum discontinuous vs. Einstein’s continuous larger cosmological world, or the discontinuous cells and the continuous membrane that encloses the organism inits largest view, including the infinitesimal mind, and so on.

The key to the Unification of Organic and Physical Sciences is the solution of one of the longest disputes of Physics and Philosophy of Science regarding the nature of space and time: are they continuous as Einstein said or discontinuous as quantic Physics and Biology pretend? Time and Space are not a continuum as Einstein thought.

There are in the Universe infinite clocks, forms of reality that trace discontinuous, temporal cycles; and infinite pieces of spatial energy, quantic spaces, divided by membranes, borders and discontinuities, both in organic and physical entities.

The quantic nature of space and time today accumulates enough proves, despite the respect that Einstein’s work still causes, as to be the cover of prestigious scientific magazines. And it will revolution all disciplines of science, since all of them use those 2 parameters to explain their species and laws.

It also implies the equality between energy and space on one hand, and between time cycles and bits of information on the other. The only real difference between those concepts was the pretended continuity of time and space Vs. the proved discontinuity of information and energy. Thus now we talk of 2 concepts that suffice to explain reality:
- The space and energy of any quantic being, homologous concepts, both in Biology (where we talk of organic space) and in Physics (where the vacuum is considered a form of ‘dark energy’).
- And the bits of information or temporal, genetic memories and cycles of any being.

Since information is stored in memorial patterns that accumulate over time and it is processed in a cyclical manner, as time is. For example, we measure a computer’s informative capacity in Mhz, or quantity of temporal cycles of information the computer processes each second.
The 2 fundamental substances or states of reality are thus spatial energy and temporal information that we will call, when properly combined, temporal energy.
We are made of energy and time, which our mind often perceives as fixed space and fixed information, but are truly organic, moving forms.
And so the analysis of the relationship between fixed space and ‘moving energy’ and between cycles of time and ‘information’ is essential to understand what we are made of, and how we perceive those 2 elements in ourselves:

And we call its perceptive dualities of ‘Endophysics’ the Galilean Paradox, as humans perceive the Earth still as a whole space. But as we increase the quantity of information=truth we perceive it becomes a rotating, moving mass of atomic clocks (‘e pur si muove e pur no muove’).

Definition of a Dimension as motion and distances.

The first truism of scalar space-time theory, is the concept of a fractal, scalar Universe that becomes fractal, broken, discontinuous, grows in size, creating new ‘isomorphic scales’ and acquires motion, when we observe it in detail.

Thus the universe of space-time in a less detailed relativistic perception is unique, continuous, still. But in detail, in a quantum vision has motion-’—motions’, it is discontinuous, made of ‘fractal quanta’, which show cyclical clock-like motions – hence it is made of infinite time cycles and fractal spaces, which are organized in scales of size, which grow in information and speed of its rotary cycles when we come closer to them, as fractals do.

And this transition from continuous abstract, ‘background’, absolute space-time to relative, scalar, fractal space and time cycles, with more information of which all things are made is the essential change from classic 4D to 5th dimensional sciences.

The duality of motion-distance is similar to the way we see a car moving in a night picture as a fixed line, or the stop and go duality of a film projector, which is perceived as motion. And it has deep implications, which help to resolve many uncertainties of physics. The next graph illustrates this and other dual paradoxes of endophysics –motion vs. stillness; continuity vs. discontinuity, single space vs. fractal scales, all of which depend on the detail of the observation – hence the quantity of information we have on the object we study:

In the graph, Saturn’s rings, first observed by Galileo, seem continuous, still and bidimensional from far away; but observed in detail they become discontinuous in motion and made of 4D spherical particles.

Moreover, what appears as a single space-time continuum in detail becomes at least 3 scales: that of the rings with cyclical motion, of its particles, the rocks that turn within them and the not seen but known scale of atoms that create the solid networks of those rocks. The ‘present’ state of science deals mainly with the single space-time continuum of the more ‘obvious’ human scale studied in terms of ‘present’=differential motions, ∂t, with minimal latitude of time. The 5th and sixth dimensions deal with a longer duration from the absolute past (birth of the entity) to its absolute future (its death), when evolutions of form, frequencies of multiple åctions and cycles of creation and extinction happen.

The Paradox of Galileo – ‘why if the Earth moves, we see it still?’ – is the key question to understand the meaning of dimensions, which can be generalized to all forms: ‘why we see reality still, if all what we study in the quantum scale has motion?’

The answer-  given by quantum physics that we expand to all scales – is the law of complementarity: ‘all what exists is still and has motion at the same time; all is a ‘fixed particle’ and a ‘moving wave’, but we perceive a limited quantity of information about reality – either state, but not both dual, complementary states, a motion state and a still state, together:

All entities exist in a dual state of internal, ‘vital’ space with no relative motion between its parts and external time motion. All has a function in time and a form in space. As Schrodinger’s cat, all is dead and alive…

The Paradox of Galileo explains those dualities of motion and stillness, continuity and discontinuity and the fractal scale of non-Euclidean points, which grow in size and form according to the point of view of the observer. Yet since motion, discontinuity and fractal structure becomes evident as we come closer to the object, increasing our information and the truth of an entity is a direct function of the quantity of information we have of it, a Universe made of motions NOT substances, of discontinuous, fractal space-time, not of continuum fixed space is more truth.

Thus, all systems must, by the paradox of Galileo, be defined in time and space to achieve a complete description of an event. Yet the fractal, discontinuous, moving, scalar description is logically more truth. Indeed, in the formalism of Non-Aristotelian logic, ‘truth=information’ is measured in terms of probabilities and is a function which increases proportionally to our closeness to the entity we study and so it reaches 1, when information and truth become the same only when we occupy the same space-time than the being – that is, as Haldane put it: ‘Only the Universe (or any being) has all the truth (information) about itself’.

So we define the dual nature of dimensions: ‘A dimension is a motion perceived as still extension or distance.’

Hence motions of particles and reproductions of waves can generate dimensions. In the lower scale dimensions are in fact defined by the reproduction of lineal strings, laterally, into bidimensional planes and 3 dimensions by the reproduction of a cyclical closed string into tubes.

In the Universe at large, space is a planar vacuum, teaming with energetic motions that appear at a large scale ‘as fixed’ space-distances (quantum vs. relativistic view); and its ‘units of substance are rotating Galaxies, their time-clocks. Some consequences of this Galilean duality:

– The vacuum of our scale of space-time is made of light, which can be seen as a single sheet of fixed space-distance or as electromagnetic motion at c-speed. Since vacuum is filled even in its minimal energy density by a background radiation light – a fact that explains the creation of virtual particles, the first condensation of ‘—motions’- space into light waves or clocks of time (closed light paths, which start with the ‘first’ clock, the electron, a condensed density of light photons).

– Galileo’s paradox explains the immortality of the Universe, since a Universe made of motions cannot stop.

We are made of space and time, of spatial energy and temporal information. When we say I don’t have energy and time to do this is because we know subconsciously that we are made of a vital space that contains energy, our body and a brain that regulates our time cycles.

So it is a machine, made with a computer, sum of digital clocks and a body of iron regulated by those cyclical clocks.

So it is a physical entity made of energy that occupies space and particles, masses and charges that MUST be described as clocks of time, ‘vortex’ that turn in cyclical motions, as our pictures of them show – NOT particles with a substance but knots of time clocks.

Thus we consider that most systems of the Universe are ‘complementary systems’ made of lineal fields/bodies of energy/space quanta and cyclical heads/particles of temporal information. In the graph we can see how reality is made of infinite clocks of time that carry information. So we blow the absolute time of the 4th dimension in infinite details: T=∑o

And we blow the single Space, S in infinite surfaces of energy in motion: S=∑Sp.

Since in the new paradigm there are infinite clocks of time that measure with different frequencies different forms of information. And there are infinite spaces that store energy in motion.

And the duality between those 2 ‘arrows or motions of space-time’, |-Motion, space or ‘—motions’ and cyclical motion, clocks of time or information, either perceived in stillness as lineal or cyclical form or in motion as lineal speed or cyclical speed structures the Universe.

All what you see are combinations of those 2 essential substances, very complex sometimes, but combinations of 2 elements, and the laws of those combinations is what the 5th dimension studies, since once we group them all we find regularities, synchronicities, patterns tat allow us to define space and time as a whole.

In the graph we see ‘—motions’ forms (lineal bodies, weapons, fields of energy-light) and its complementary systems of information processing of time processing (cyclical eyes and cameras, electric fields of light).

Each clock creates a discontinuous space-time, whose cyclical perimeter of in-form-ation encloses a piece of energetic space breaking reality into ∞ formal patterns; different time cycles with specific forms and frequencies. Thus the use of a single human clock that equalizes all of them misses 2 features of each of those time cycles:

– Its specific forms of in-form-ation in space, which gives birth to the main topological laws and Isomorphisms of the 5th Dimension (I).

– Its different speeds or frequencies. Since cyclical time is measured not by duration but by frequency, its inverse function: ƒ(t)=1/T.

In the graph, galilean relativity was ill-understood, as the true question about time-change was why ‘we see systems still when they move’, and ‘why we see space as continuum, when in detail is made of quanta’, and why all systems are made of smaller self-similar systems.

Further on it reduced all time clocks to one, and made lineal time canonical ERASING our knowledge of the cyclical form, in-form-ation of those time cycles KILLING 2 essential features of time:

To be multiple and to be cyclical encoding the information of the Universe in the frequency and form of those cycles. THUS HE KILLED THE ARROW OF INFORMATIVE TIME, and as a consequence, as yin and yang no longer could combine, prevented scientists from defining properly energy as the combination of both, motion and form, streamlining our understanding of the equations of mathematical physics, which will from then on become mathematical manipulations void of most of its conceptual meaning, till arriving to the present ‘religious’ view of physical sciences, which shun off the whys they no longer understand.

Those are pending questions solved in 5D³, which the philosopher of science, Descartes, understood better than his mathematical disciple, Galileo, as philosophers depart from a ‘previous layer’, all the languages, hence all the minds that observe all timespace cycles; not a single language and a single clock-cycle, as physicists do eliminating all other ‘rival languages and beings’ AS IF THEY DID NOT EXIST. They do.

The paradox of Young, Motion vs Old Age, informative stillness: freedom vs. order.

A key element to understand the Universe of scales and its paradoxes of freedom vs. order is the perspective any mind has of reality when looking above, to its upper whole, which controls it through invisible networks of information, hence creating an elliptic perspective of decreasing perception – dark view of larger scales we do not observe, from invisible informative networks in galaxies to invisible financial networks in societies to invisible nervous networks for cells. On the other hand in the same scale we have a flat, euclidean geometry of maximal perception with minimal distortion:

While looking down to our smaller inner world we rule it with networks that break into fractal webs of simultaneous control, or hyperbolic view. This ternary view of reality has immense consequence from theory of knowledge, to mind constructs, from sociology of power to galactic organic models of a Universe ruled by invisible black holes and dark matter. We feel thus free as individuals but are controlled from above by the larger whole and rule over our micro-parts. As Shakespeare said: we are all kings from above, commoners or buffoons.

Another paradox happens between the dualities of the young, open, moving lineal age of the being and its old, still, curved, informative, cyclical one, which also manifests when we ‘expand in size’ and have a larger pov, where the flat earth to put the classic example becomes curved. And related to it the paradox of the opposition between time-motion vs. space-stillness.

It is the most complex and multifaceted of them all. As it defines also perception, and the wave-particle states… and ultimately the ego paradox…

When we add the fact that all systems move in a wave, mindless, ‘foggy’ state but gauge information from its still language/point of view, as a ‘particle-head’ they confuse with the whole Universe:

‘Every point of view considers the world it perceives from its self-centered still language the whole Universe, with ¡tself at the center’.

This is the paradox of egocy (ego=idiocy), which humans of course also show in extreme form, specially physicists with enhanced digital, mechanical instruments of measure. It is THE MAIN paradox of the mind.

Yet as the mind states are implosive reducing external motions to inner forms, the selfish-informative state is pposite to the young, mindless free moving state of the mind, focused on the external larger ¡+1 world:

The young moving state living externally ultimately sees an unbounded Universe; because the larger world in which it exists is only observed in its entropic and energetic parts; not in its information coming from networks above the being which are invisible.

This requires a bit of thought. Beings are nested beings, ∆±¡ structures, where ¡ is the larger whole and -¡ its minimal units used for the being to control informatively its inner parts. So paradoxically, the larger wholes which seem slower do have smaller parts in its inner informative networks which are faster; the larger wholes feed also in smaller beings. For example, the galaxy, which seems slower is regulated by non-local gravitation and dark entropy, we do not see because it is faster than our c-speed (so we think in a field of dark entropy that space is enlarging as we see its motion as invisible distance: paradox of the big-bang). The larger whale eats the smaller Plankton we do not see. The larger globalized metal-earth of company-mothers of machines controls nations and people with invisible flows of instantaneous digital money, we do not see or understand; the larger brain, with its giant neurons controls the smaller chemical cells with invisible flows of faster nervous messages.

So the being that lives in the larger world, sees it slower, and sees itself faster and free, but it is often bounded within the being that will limit him with its outer membrane and within, it will manipulate and strike it down, when needed with its faster informative network.

The ego paradoxes of the infinitesimal self-centered being.

∞º: EGOCY PARADOX Humans’  interpretation of the Universe is limited by their ego. It is NOT a problem of intelligence as many huminds have stretched our information but of ego. I.e. Self centered Huminds refuse to give living, organic properties to reality when it is too different from them. So physical systems are denied its Ðisomorphic properties.  The problem of human ego is so huge that we must always doubt of ‘science’ as culture and study a priori any human statement as biased by anthropomorphic egos – the sure path to discover the falsehoods of science. This is specially truth of physical statements, whose egocy comes as Goethe already noted from its higher technical senses, telescopes and microscopes that made him think more intelligent than other scientists. So man becomes the only intelligent being, the one who measures, the only one who speaks mathematics of measure, the language of God; reducing knowledge to locomotion numbers. In the graph, the homunculus physicus’ mind with handyman craftsmanship to kill with entropic weapons, a big mouth to talk idologies of human supremacism over the organic Universe he measures and a small childish brain filled with numbers that understands nothing.

Of all this dualities come the many paradoxes of the ego: The larger whole always appears to us dumb, because we do NOT perceive all the information of all its ∆±¡ scales, where our +¡ is smaller than its +¡, and our -¡, slower than its -¡.

So the intelligent Universe makes us feel our young ego free; and bold. The older mind though knows it won’t change the order of the larger world.

All of them in any case will see reality self-centered, in its mind that measures only a limited distorted amount of information, because the ∆º mind cannot perceive beyond its ∆±3 scales in which it performs its Ðimotions of exist¡ence, and thinks it is in the center of scale, as it is the region where its measure is more precise and from where more information flows into its mind.

Further on to fit in its infinitesimal all those dimotions, it eliminates motion and keeps dimensional form, in a fractal, smaller mirror images, converging towards the mind. So it sees reality still because it can gauge better its information, but unaware in its naive realism that its language is just a reduced mirror, it believes the being is still because it is dead. Reality is always dead for the scholar, academic mind that cares only about the language, without even realizing the language is WHAT IS DEAD, still, motionless.

The intelligence of the mind thus is truly a reductionist full paradox to keep each monad at its relative center, all of them, ∞º of existence. 

And so the ego paradox of the still mind confronts the entropy reality of the moving Universe; the ego-mind and the whole confronts the moving, disordering more powerful whole; and ultimately this is the eternal fight between the mind ordering, wanting to live eternally and the universe of motions, wearing, disordering it, killing it back to dust of space-time: ⌜𝝙@st.

So the 4 main ‘paradoxes of reality’ become then the paradoxes most common in all futile arguments of sciences in search of single humind dogmas. For example, those 4 paradoxes are at the heart of philosophy of physics. They are called in physics the paradox of relativity of motion vs. form that started classic physics, of continuity vs. discontinuity that divides quantum and relativity, hence starting modern physics, the duality of flat vs. curved, open vs. closed free vs. ordered, that is at the heart of ‘young physics’ (flat earth?!), and the ego paradox of the mind that measures and thinks to be above heavens and earth vs. the entropy arrow that will disorder it and physicists due to their worldly profession of making weapons prefer (without renouncing to feel as the scientists with better machines of measure, the ones that talk the only language of God, in their delirium tremens – numbers).

In this ultimate ego paradox we must inscribe the most important epistemological argument of science: the paradox of creationism, as each science believes its language and the limited properties it maps out of the whole are the only language of God and only properties of reality.

So we put in negrita the choices of dogmatic physics in those paradoxes, also in eternal disquisition between other scientists – so in medicine the paradox of the brain as a single block vs. the theory of neurons separated by synapsis was all the rage till Cajal draw them separated… not to speak of the systemic denial of the dimotion of reproduction in any system that doesn’t have our sacred ‘DNA’, when everything that moves and all moves by definition reproduces its in-form-ation when it reproduces its cyclical motion and science exists by definition because it observes repetitions of patterns of formal motions that we call laws of science. So ALL the paradoxes of ‘ceteris paribus’ analysis of science are ultimately also a product of the ⌜∆@§t dualities and the ego paradox that doesn’t see them.

Physicists on the entropic arrow. Partial theories of it all.

So on one side they use the entropic dimensions as the single arrow of time of the Universe, studied in entropic systems, gases and dark entropy expanding between galaxies (but here they call it mistakingly dark energy). Then most extend this entropic arrow as the only one, disregarding crystal, informative and liquid, iterative waves of matter, which make the 3 arrows of time. And in cosmology disregarding the vortex of mass-information, in galaxies that compress the Universe balanced the big-bang. So they by lack of clear concepts about time arrows, sponsor a big-bang only theory of an expansive dying Universe, eliminating on their equations the inconvenient truth of implosive time-like accelerated clocks of masses and galactic vortices.

Physicists on the present arrow: relativity and energy conservation.

Then they also study the present, simultaneous, iterative space-time, with different tools, but conceptually messed. On one side they realise the combination of relative entropic motions and future mass particles, is conserved in the Universe, either as momentum, or as its integral in a closed repetitive cycle of conservative energy. But they do NOT CALL ENERGY the present arrow of time, they just say it is ‘conserved’, and do not know what it is.

Also they study this kind of conserved time with a formula, v=s/t, t=∂s/∂v. Whereas they measure infinitesimal moments in the process of motion, taking ‘present pictures’ of simultaneous space to refine its measure of speed (Einstein and Galilean relativity) So this measure of present stills of space-time with derivatives, is another analysis of present space, performed by Galileo and Einstein (special relativity). And as it requires NOT a change of state in its form, it is truly always indicated for studying a single ‘present’ state. So relativity science deals mainly with the single non chaining ðime§pace continuum of the more ‘obvious’ human scale studied in terms of small quanta of ‘present’=differential motions, ∂t, with minimal latitude of ðime.

Physicists on the future arrow: vortices of accelerated time in different scales: masses and charges.

Finally Einstein realized that time curves space into accelerated masses (general relativity, principle of equivalence between mass and acceleration). So he defined a future, accelerated vortex of time-information, a mass, which we extend to charges in the smallish quantum scale, and to thermodynamic eddies inout scale (graph) which are therefore the arrow of future information nature. Yet they do NOT either recognise charges and masses as fractal clocks of accelerated future time, as we do. So they cannot unify them (the saint grail of physics is an equation that unifies charges and masses and we shall easily provide merely by adapting the obscure jargon of electromagnetism to the simpler vortex-like jargon of gravitation: Newton>Poisson>Einstein).

So while physicists have in front of them the 3 dimensions of time, parallel to the 3 forms of space, they have a conceptual mess, due to the use of a single time clock and a single arrow of time, entropy, which makes them NOT to recognise the arrow of accelerated time in masses and charges, and the relationship between steady time-cycles and energy conservative cycles.

They also deny the capacity of those time vortices, particles, to process and gauge information, even if they act as ‘mathematical minds’, controlling the organic territory, they perceive. And so they miss the logic explanation of the paradox of Glalileo: particles as heads do, perceive information and gauge it in relative stillness. So as in a film, the process is an stop-particle-gauge information go-wave duality, which explains the paradoxes of relativity (c-constancy of speed, emitted in entangled stillness) and quantum physics (perception always of the particle stopped by the perceiver, as systems move in waves and gauge information as stopped particles).

IN THAT REGARD, PHYSICISTS miss the fundamental conceptual truth behind Galilean relativity: the Galilean paradox and its cause – the fact that minds map reality with languages, that are smallish, fixed forms and so when we perceive we reduce the 3+3 dimensions of space and time to 3 dimensions of space, to have a still image, as your eyes give it to you – with hardly any motion, to fit it all in the brain.

Thus because that description is the simplified reduced subjective vision of the human mind, which ‘stops motion’ to fit reality in its smallish brain we must conclude that the ‘real objective Universe’ is made NOT of spatial forms (a mind mirage) but of motions, not of a single continuum but many scales and clocks of time that enclose and break space into internal regions and outer worlds. So reality is about:

-Dimensional ðime Motions not distances; Scalar Spaces, broken and discontinuous (ab.§) not single §pace continuum; and cyclical in form ‘ðime§paces’, not lineal (as we have proved previously).


Science started when Galileo realized that the earth moves objectively, externally but the mind sees still. So we cannot distinguish motion from form (Poincare) and as such, every dimension of form=space can also be seen as a dimension of time=motion. This means we shall see time-motions and space-forms together, giving origin to the first simpler topological dimensions:

In the graph the 3 dimensions of space and time. As we can see they correspond to the only 3 topologies of reality, and as such they combine in form and function to create in a single plane of space-time, all the systems we observe:  reality we see around is ternary made of 3 functional/formal space-time organs/networks that form super organisms:

In graph, different orders of the 5Dimensions of reality give birth to different entities, super organisms in a single present scale of time-space, ensembles of 3 basic forms, 1D particle-heads/3D wave-bodies and 2D lineal limbs/fields; but only when we add the lower dimension of ∑∆-1>∆º emerging seeds of information and its entropic dissolutions ∆º<∆-1, the full meaning of the game of exi=st¡ences, existences as space-time organisms studied by different stiences reach its full meaning.

Further on the 3 first dimensions are equivalent to the conservation processes of angular momentum – the first parameter perceived in the point, its motion, second parameter and reproductive strength, third parameter such as if we give an Active magnitude value as the scalar 1D and a vectorial momentum 2D number for the second dimension, we get equations of reproduction for the third dimension.


A dimensional definition of the Universe

So we talk also of 5D² systems of space-time meaning we divide and combine in ternary, s, s=t, t, groupings those 5D²

It follows that the sum of the tree, s + s=t + t gives us a full cycle, with the incissum that s=t = s+t, as it has coupled both:

The Universe is a supœrganism that re•produces information. And it does so towards a final aim, the reproduction of new super organisms, •5D² systems, of topo-bio-logical nature, with topologic, spatial, organic, scalar and logic, temporal properties.

As such the talking of it can be as detailed as a super organism is, which increases in complexity as it ‘covers up and down’ new dimensions of entropy and information brought together into a new ∆±i super organic structure:

In the graph, the three arrows of time of a world cycle are intimately connected to the three scales ∆±1 in which the supœrganism realises its existence, up and down the scales of the fifth dimension, from seminal birth into social existence and final extinction.

In the graph the ten dimensional organism, can easily be divided in ternary grouping according to topology or scale.

The most amazing thing about the dual fifth dimension of space-time that forms all the organisms of reality is that humans do NOT logically perceive it, despite being all around us, all being part of a partial perception of the •5D³ being, in 4D², 3D, 2 or • dimensions of existeence.

As such we humans have a hard time perceiving a full •5D³ being, let alone a simple 4D subject ordering around 3D objects, following the instructions of its holographic 2D mental sheets of information, as its moves in seemingly random lineal point-like cycles of exist¡enœ.

The whole beings in his whole action with his hole information only exists within itself.

How much information of the being we absorb to its stientific description is obviously relative to the mind that perceives it. At least a 5D³ being will need a thorough investigation of it at the three scales ∆º±1 above and below its 0-mind, pov; and through its three topologies of ðime$pace; as it performs its ∆±i ages of exist¡ence.

Existence rquires travels through the scales of the fifth dimension from that seminal to the emergent scales, in an ∆+1 social world back and forth through the eons of zero-sum beings.

As such a supœrganism is always defined from the human point of view of kaleidoscopic perception as a world cycle travelling through a given ∆±i symmetry we ‘perceive’ self-centred in ‘certain singularity-particles’ of certain stiences.

A super organism will be within the ‘limits’ of ∆±3 scales self-centred into the ∆º being (the seminal-world, ∆±1 scales; the energetic, ∆±2 scales, and the informative ∆±3 scales), a knot of Non-Æ flows of energy, information and, entropy, which make the ‘transference of’ motion and form’ between scales, as the being ‘lives’, grows, multiplies and orders a territory.

So each being is a knot-flow focused at ∆º and moving through an St±i ternary scale of stiences.

It is then this ∆º systems what we can study through different stiences and species, as the fundamental particle of the Universe, which will always follow the same ex i actions, trying to reproduce≈survive its complex ‘information’ as a knot of time-space cycles.

Dimensions are motions perceived as stillness.

The Paradox of Galileo, the key logic concept to understand the meaning of dimensions, astoundingly ignored by science for 400 years: ‘why if the Earth moves, we see it still?’, which can be enlarged to this question: ‘why we see everything still, if all what we study in a quantum scale has motion?’ IS the key to unveil the dimensions of the Universe.

The answer given by quantum physics that we shall expand further to all scales is the law of complementarity: ‘all what exists is still and has motion at the same time; all is a ‘particle’ and a ‘wave’’, but we perceive a limited quantity of information about reality – either, but not both, dual, complementary states, a motion state and a still state.

Thus, we apply this duality to the definition dimensions: dimensions are both, an extension of fixed space, perceived as motion or a motion ‘perceived as fixed space’. For example, the ultimate space of the Universe, vacuum, is teaming with energetic motions that appear at a large scale ‘as fixed’ space-distances (quantum vs. relativistic view); Galaxies separate from each other at huge speeds but we see their ‘motion’ as an expansion of space…Thus:

‘A dimension is a motion perceived as still extension or distance’.

Hence dimensions can be generated by motions of particles and reproductions of waves. In the lower scale of string theory we can describe those dimensions as the reproduction of strings. But what matters to us is the vacuum of our scale of space-time; which can be seen as electromagnetic motion at c-speed, since it is filled of light and background radiation, or as vacuum space.

This duality of motion-distance is similar to the way we perceive a car moving also as a fixed line of distance in a night picture, or the duality of stop and go of a film camera, which is perceived as motion. And it has deep implications, which help to resolve many uncertainties of physics.

It explains the generation of dimensions:

A point with motion creates a line dimension; a line in motion creates a bidimensional plane of information; a plane in motion creates a mass-volume and a volume in motion creates a life-cycle or world-cone – the concept used in Relativity to define the 4th dimension of time.

The reader might notice that those motions become perceived by human senses as a duality of motion-stillness, so the 1st dimension is seen as speed, the second, a plane or sheet of information as the page you are reading as ‘still form’ or information the 3rd, a volume or mass becomes again a stillness, and the 4th a world line, which is substituted by a time cycle, as motion again. Thus again the past, the 4th dimension becomes ‘still’ and the future, the 5th dimension, an uncertain motion.

Indeed, theoretically, prior to Absolute Relativity there were in physics only 3 dimensions of space and one of time.

But under the duality of the Paradox of Galileo, in reality those 3 dimensions of space are also motions. And indeed, it is obvious at quantum scale that ‘space’ is really a bubbling world of electromagnetic energies and particles condensed from those energies.

This also applies to our scale. So if we consider the motion of a gas, volume is proportional to that motion/temperature: PxV=knT. But volume is space; so space grows as motion grows. And it applies to the aforementioned cosmic scale of galaxies moving/creating distances.

Moreover we observe that each ‘bigger dimension’ includes the previous ones. So the line includes the point; the plane, the line; the volume the plane and the world-cone the plane.

Can we extend this growing game of dimensions in motion that create a new dimension? Yes, we can, when we do a proper analysis of what the 4th dimension of time in General Relativity really means – something which as most definitions of physics is far better understood in mathematical terms than in logic, conceptual ones. Indeed, physicists, unaware of the paradox of Galileo still draw higher dimensions as weird spatial drawings, when beyond the 3rd dimension our ‘senses’ spatialize, by creating the stillness of light-space, all other dimensions are perceived as motions in time. Hence there are not ‘weird’ impossible drawings of dimensions beyond the 3rd one of ‘volume’, for reasons that go beyond this introductory lesson on Absolute Relativity.

Physicists spatialize time, in terms of its ‘present’ dimension.

Few physicists understand that time has also 3 dimensions, since they only study ‘simultaneous measures’, mathematically described with derivatives, ∂t, which are an ‘instant of time’; that is, a slice of present in the total flow of the 5th-6th dimensions.

This was further proved by Einstein’s Relativity a theory, which is concerned with the values of ‘simultaneous measures of space-time’, hence with the values of a relative ‘present time’.

This concept of present time derives from Galileo’s measure of speed, V=s/t, ∂s/∂t; hence ∂t=∂s/v. which is the meaning of time in standard physics.

Time is defined then in terms of space and speed (which are according to the paradox of Galileo, similar concepts of fixed space or motion space). Hence physics ‘spatializes time’; and vice versa. In those terms, space is just the perception of present time in simultaneity. Or in words of Einstein:

‘Space is measure from a simultaneous frame of reference’.

Thus physical time, ∂t, only shows a very limited ‘dharma’, or part of the entire flow of time from past (the fifth dimension) to future (the sixth dimension). In physics the fourth dimension is only present time, which is what the Riemannian geometries of Einstein’s and Minkowski’s models of space-time study.

Time though as any child knows before it learns General Relativity, has not only the present time, the spatial ‘dharma’, or slice of the flow of time that ‘freezes’ in the field equations of Einstein. Space is a fixed perception of a time motion.

Thus, all systems must, by the paradox of Galileo, be defined in time and space to achieve a complete description of an event. Then both will be an equivalent perspective on the same event.


A true understanding of reality in its fundamental logic principles is missed among huminds because the founders of modern science missed the not-so ‘evident’ visual duality of the Universe between the 3 motions of time (lineal t, iterative hyperbolic ∏, cyclical ð) which form billions of different beings in all scales of reality, and its 3 fixed forms as perceived by its ∞ monads≈ §patial minds, @, which stiffen those motions into forms (lineal distance, $, hyperbolic bidimensional space curvatures, S and cyclical space-information, §).

And the other two logic dualities between lineal, flat, small, open and cyclical, large, closed forms; and small discontinuous and large continuous parts. The 3 dualities we illustrated with the picture of Saturn’s rings also discovered by Galileo ARE all over the place in mathematical physics (i.e. lineal small steps of momentum described by Newtonian 2nd law vs. closed cyclical energy paths in the Hamiltonian/Lagrangian  formalism; ∆-1 quantum discrete eigenvalues in quantum physics vs. continuous differential equations in the other extreme of ∆+1 gravitational relativity, algebraic still ‘Groups’ vs. analytical ‘steps’, matrix’ Heisenberg descriptions vs. wave Schrodinger’s dynamics, etc. etc.). 

It is then all the more surprising that a serious philosophy of dualities and ternary symmetries have never been explored. How is this, has to do with the automaton, mechanical praxis of modern science. In fact, the years I tried to spread among scholars 5D², as the world chair of the science of duality in the milieu of systems sciences, I was receiving questions about the ‘utility’ of this work which simply puzzled me about the nature of the humind, as I live in awe of those symmetries, like the one just explained between simultaneous superorganisms and time worldcycles. And simply concluded that huminds are not much interested in ‘the territory of truth, which is like a path on a cliff, a thin line we fear to walk through’…  as a polish poet concluded. Poetry indeed being the higher Disomorphic form of verbal mirrors.

But it is not the mathematical formalism as mirror of reality truth? It is, but only a single mirror of the poetic disomorphisms of the universe, which are all based in symmetries, dualities and ternary forms.

But, and this is the biggest handicap of mankind, huminds are self-centred and one-dimensional. They want single truths. They abhor polidimensional views, as the Universe abhors vacuum – a meaningless word as all space has motion, and all time has form, and when both do not exist nothing exists.

So the concept of multidimensionality, symmetry, duality and ternary forms puts ill-at-ease most huminds. And yet without exploring the dualities and ternary symmetries of space and time dimensions we cannot start the game of existence we all play.

Of them, the most important trinities is that of co-existing planes in super organisms, the present scale, and then two ‘extra scalar dimensions’, entropy or dissolution, 4D and social evolution into wholes rule by singularity minds, 5D.

Of all this humans understand very little as they are ‘evident beings’ with a hard time looking at time, specially at the future, with its intelligent variation, always focused in the past, with its memorial forms. So we shall repeat the basic notions of reality hoping the human or robotic ‘future’ reader can memorize them.

Now we shall bring a new fundamental law or fundamental symmetry between space and time states, which illuminates its constant interaction.

As we cannot distinguish time from space states, they must appear as ‘pairs’, but as time is always a sequential flow those pairs must appear consecutively, and we shall call that flow of sequential states of which there are only 5  dimensional variations, THE 5 motions of time & space:

t≈t (3D), s≈s (1D), s<t+t>s (2D), ∆-1 s>>∆+1 s (5D), t+1<<t-1 (4D)…

A minimal MOTION in time and/or space, thus becomes the fundamental ‘dynamic flow’ of reality. Let us see then how the Universe moves through ‘repetitive’ or ‘s<≈>t’ feed back variations.

Motion and form, the two elements that combine into energy beings.

This is the fundamental principle of physics, called the principle of relativity:

“We cannot distinguish a motion from a still dimension (form or distance).’ Poincare…

‘as each dimension of space= form is accompanied b a dimension of motion=time, ST≈ST≈ST’.

SO WHAT WE CALL MOTION IS IN FACT A BEAT OF CHANGE, AN S-S, OR T-T, OR S-T OR T-S STEP… in a  constant form-motion, information-entropy, perception-reproduction st-st-st beat; as all motions can be reduced to that constant reproductive beat.

Let us then explore the concept of ðime cycles as carriers of information, and its three arrows and the systems made with them as organic elements, entropic limbs/fields, body-waves and informative particle-heads – its simultaneous perception in §pace – departing from its simplest forms, which are topological bidimensional forms.

So what IS the proper way to make sense of the galilean paradox?

Conceptually the way to go is to accept the stop and go, the dual dimensionality of all systems which are motion and form, momenta, energy, and so we move from Galilean relativity, the single being, to the holographic principle, the mind seeing it as dual motions and forms.

BUT AND THIS IS THE BREAKING INSIGHT, the still view is that of the mind – the motion view that external to our mind. So we must recast the question of relativity:

‘why minds still the motion of the Universe” And how this through relativity, distort our in-taking of information as human beings?

The answer is ontological: to perceive you need a still mind mapping; motion is unfocused, and adds too much information which a small mind cannot fit if it wants to portrait a still , perceivable image of reality.   THUS PARTICLE-HEAD states are informative minds that stop, and wave states move the system.

But why we do see form with the mind, motion when we adopt an external point of view? To understand why we have to understand first the mind.

Because IT IS OBVIOUS THAT WHAT WE SEE AS SPACE IS A MAYA OF THE MIND, WHICH CAN BE MATHEMATIZED, OR TALKED ABOUT OR PICTURED, BUT STILL WILL BE THE ELECTRONIC MIND AND ITS CAPACITY TO PERCEIVE LIGHT IN ‘STOPNESS’ (Constancy of c-speed, which conceptually means simply, we, or rather our ‘electronic minds’ – and the electronic digital minds of atomic computers – SEE LIGHT as stopped in its source, with always the same speed.

The mind is as in that case, since electrons ‘perceive’ waves of light as stopped photons, always present in the way mankind perceives, measures, and so with its electronic instruments.

So let us then consider what the mind is, as it is obvious that there is a feed-back equation going on in reality:

§@ ≈ ∆ ð 

The Universe is made of ‘Motion and Time’, ‘Lineal and Angular momentum’ Motion with form. But motion dominates form. Even if the mind thinks otherwise because of the Galilean Paradox – the duality of stillness and motion, as we perceive the Earth still but it is moving.

Yet this paradox is indeed the proof that form, information dominates motion, because the mind prefers to see still information to blurred motion.

The perception of time and space as a moving cycle or line or a fixed form or distance is obviously an effect of the mind. It is NOT there, it is the mind that stops time cycles and lineal spatial motions.

This must be understood from the beginning, the ultimate reality is motion not form, time moves and space moves. They just move in different shapes. And then minds, lock those motions into a simultaneous, ‘informative’, ‘dimensional’ shape because it sees those motions in ‘slow camera’. The arrival of filming makes this easier to understand. Stillness is just the perception of very fast cyclical motions, as when we see a turning wheel as a fixed form.

So often we see motion as distance – we cannot distinguish motions from dimensions of form (this is the meaning of relativity, the relativity of all motions).

The duality of motion-distance is similar to the way we see a car moving in a night picture as a fixed line, or the stop and go duality of a film projector, which is perceived as motion. And it has deep implications, which help to resolve many uncertainties of physics.

It manifests in different forms in different scales. Perhaps the most important expression is the duality wave-particle, still ill understood in quantum physics.

We shall consider of its many consequences 2 of them – an objective explanation of the constancy of light speed from relativity and a footnote on its duality in quantum physics.

The physical world is dual  from ‘above’ (the cosmic scale) to ‘below’ (the quantum scale), to quantum discrete motion to go ‘actions’, from the duality of motion vs. still perception or ‘Galilean->Einsteinian relativity’, to the basis of our understanding of science is the finitesimal small vs the finitely large (infinities do not exist in the metrics of the 5th dimension, hence the use of finitesimals and finite, minimal and maximal n-1 quanta and U+1 worlds).

EINSTEIN’S RELATIVITY: adapting discontinuous scalar space-time to continuous single space-time.

Now, the next instalment of the analysis of galilean relativity between motion and stop was einstein’s special relativity and again, he, unaware of the duality of dimensions of motion and form, merely went further into the obsession of measure, translating the effects of ‘warping’ of space that shortens it, when information is imprinted by light in the previous quantum potential of lineal form, adding to the measure a -ct factor of warping. This was special relativity concerned with that translation to our world where we do not see the quantum potential – hence we add the warping to scale up the process into our ‘terse’ space-time.

And further on, we do not see the stop and go of particles and waves, and so we added the lorentz transformations to compensate in our continuous Universe, and in this manner special relativity maintained the fantasy of a continuous derivative motion universe (when it is a stop and go), and a single space-time (when it is a scalar space-time warped in the whole scales).

Motion and form go in pairs, advancing space-time.

The st beatings of the Universe define 4 dimensions immediately of motion, s≈S, T≈t,  S<T, T<S, which are the four fundamental motions of the Universe. BEING THE FIFTH DIMENSION, the no motion of them all in the still pure space-time of the Mind, @.

So departing from 4 motions, we must first consider if an S≈s and a t≈T is motion: it is in the scalar growth OR DIMINUTION. WHILE the stop and Tgo, Stop, Tgo motion and form gives us the other two:

we cannot see motion and form together, the whole and its parts, we confuse lineal detailed view in short space-time intervals with cyclical, larger slower view… such galilean paradoxes are the reflection of Space=time dualities that the mind tries to ‘con-form’ into space-simultaneous view to ‘perceive them’. (Perception being always in space-simultaneity as still form a quanta of space=time).

The Universe is a fractal superorganism of 5 dimensions of space-time, where the fourth dimension of parts and the fifth dimension of wholes create its scalar, organic structure, as it is made of smaller and larger super organisms of space-time.

Those super organisms follow a fundamental logic rule, which started modern science – the realisation that ‘we cannot distinguish motion from form’ (Poncaire, Principle of Galilean relativity) according to which all motions in time can be seen as form-distances in simultaneous space and vice versa.

So we conclude that space-time, what we perceive as motion and form is composed of 5 dimensions of space undistinguishable of its equivalent perceptions as motions of time, hence:

5 D ST = 5 T-motions + 5 S motions (S=t).

This simple equations of the logic behind galilean relativity will suffice to explain all what exists.

As it happens two immediate consequences of the formulae is that being S=T, the maximising function of S x T (S+t being equal to K, in this case 10 dimensions), what the Universe maximises is Sxt+S=t, which given the relationship between space and information and time and entropy we write as exi+s=t, which is the function of existence of the Universe, maximise your function of existence is what all systems, do.


The simplicity of the first beats of existence, S=t, s=t, and its s=s, t=t apparent congruencies is only the beginning of an incredible adventure, the motions of reproduction of information across the five dimension of space-time that we call reality.

The first beats of existence.

We start with 2 states: space-form and motion-time. Space is the mind-intelligence, motion the constant original substance the minds try to stop.

The mind tries on the other hand to be also in constant motion, switching perspective not to be bored, so stop and go, but as go is reproduction of form, is really inform and reproduce, and reproduction being st, and inform, @-S.

The maximisation of an s=t balance happens obviously with the maximal number of s=t beats, as s and t become equalised by smaller moments and forms of it, the moving reproducing st>t>st>t ‘actual beat’ is sparkled by explosions of Ss,death.

RECAP.The 5s +5t=10 Disomorphic space-time organisms & the Galilean paradox.

The Galilean paradox simply means there are two realities, as Descartes, founder of modern science, its method and mathematical frame of reference, rightly understood. One the @-mind, which creates the fixed forms of ‘fractal §pace’ we observe (ab. @, §):  §@≈∆ð.

The equation with 5 symbols, each representing one of the dimensions of the Universe of space-time is a conceptual logic deduction of the Galilean Paradox, that expands the concepts of Galilean relativity and Einstein’s relativity to the Absolute relativity of the fractal Universe. So it is worth to detain ourselves in their understanding.

So if we consider space-form and time-motion in its 3 parallel ‘lineal, cyclical and mixed, hyperbolic forms’ we can define 3+3 Ds:

  • @: $, S, §: The perception of time cycles by an space-mind, still, linguistic, mirror of the whole Universe, which ‘seems’ in words of Descartes a devilish virtual form put on the mind. As the mind, @, generates it; we cannot deny this spatial virtual reality, even if it is not the ultimate motion reality. As the mind generates a still=spatial reality, ab. §, we need to describe also space, as generated linguistically by minds in synchronous mappings. We use again different symbols for the different ‘dimensions’ of space: $ for lineal form-distance, S, for the combined wave-forms and § for cyclical and lineal space, which is CAPitalized as present is its dominant element.
  • ∆: t, T, ð: An absolute external Universe, made of scalar dimension, which in each one of them shows 3 varieties of motion, lineal time motion (t), cyclic time motion, ab.ð, and its ‘combinations’ for which we shall use the CAP symbol T, as present is dominant. Where ð cyclical time is measured by frequency, ƒ=1/t, inverse to lineal time s all has in detail motion, and it is structured in ‘scales of space’ (ab. ∑§) or rather ‘planes’ (ab. ∆=∑§).
  • ≈: Operandi that relates them, most often a relative equality. Since  the only way we can make logic sense of it is to consider that the mind view of reality in space is parallel, similar, congruent, equal but NOT identical TO THE OUTSIDE UNIVERSE IN MOTION=TIME, with real obvious fractal scales from minimal forms in space to maximal forms.

The  inverse properties of cyclic time and lineal space.

How can we translate the dualities of line and cycle, motion and form? They are inverse in a logic and geometric way. So we can describe easily the concept of space time inverted properties with a hyperbole. We shall find then that hyperbolic functions, such as e, are fundamental to define the different transformations between space and time:

In the graph a hyperbolic function between a line and a cycle. In general certain cyclical curves follow the relationship between a point of time and a lineal distance of motion.

The Universe is a 5 Dimensional fractal that reproduces vital topologies of time-space, ternary forms of motion and form, which organises into larger, slower scales of fifth dimension of ðime§pace.

Motions on 5D are either topological βidimensional changes (Galileo’s paradox) in D³, or full worldcycles (motions in 5D), and so we must be aware of both.

The main bidimensional motions of a space-time being are motions with form, bidimensional units of:

§, $: Lineal form x Lineal form=plane of space-distance

E, ∃: max. motion x min. form = wave of energy, entropy, expansive motion

ð: min.. motion x max. form= cyclical time, information, harmonic motion

ƒ: max. form x max. form= informative time, implosive motion.

This initial conditions set the combinatorics of topological motions as each of those bidimensional elements combine with other forming ternary, fully-functional, efficient systems, Γ• that can act feed, perceive, move and reproduce and evolve socially, the five actions, of survival of the vital program of any fractal of information of the Universe.

This basic motions then become repetitive in fractal self-similar beings as each compose motion leaves a memorial trace of previous traces that continue being traced in the same place ‘reproducing the facto the being’.

In this manner physical systems grow in form and dimensions:

Thus the CONSTANT AMBIGUITY in normal and scientific discourse, which confuses entropy and energy on one side and form and information. We can’t escape that ambiguity so we often confuse terms entropy and energy and form and information but we will try to BE PRECISE, when writing equations or explaining fundamental facts.

SO WE TRY TO DIFFERENCIATE ENTROPY AND ENERGY, and CALL FORM, in/form/ation, as here the ambiguity is far more entrenched in the normal discourse, so when we highlight form, we use ƒ and in/form/ation.

For example in E=mc²; E is e, entropy not Energy; m is ðime, an inward vortex of gravitational forces (principle of equivalence of acceleration and mass), and the energy is c x c a wave of light ðime§pace, whose hyperbolic form is in fact a combination of the cyclical mass form and the lineal, expansive entropy of the explosion.

For example, in ‘colour codes’ used by minds to differentiate the four terms, blue is the colour of pure form, red the colour of pure entropy, and its combinations are green the reproductive colour of information with more form and yellow, the colour of energy with more motion. And so the brain classifies reality with those two extreme and two intermediate colors, and we shall observe that all mind-languages are combinations of those four elements.

Some languages are simpler, and then we have the two unperceived limits, black of form, white of entropy and combined greys. Words also have:

Form-subject (human) < energetic-informative verb or ‘action’-momentum: e x i > Entropy of subject (object ab=used by the subject).

Since existence is a game of those 2, 3, 4 elements/dimensions of reality. So we define a conceptual acronym, the ‘Function of existence’:

Entropy x form = energy + Information

But in a license of the inherent ambiguity of those terms we write: e x i = st   entropy x Information = ðime§pace Momentum (integrated for a long period as Energy).

To exist is thus to combine entropy-motions and in-form-ation, form,  in a series of actions of existence, pure motions, energy feedings, perception of forms, communication of information, reproduction of both, social evolution with other forms through ‘ties’, which are flows of sharing of those elements…

Do not be scare by the ambiguity of terms, try just to realize the deep connections between them at a topo-logic level of form and function and when you are familiar you will learn to see reality in a much deeper way. To help we shall consider a simplified graphic of the two poles, temporal form and lineal entropy, and its energy-information combinations.

I apologize because I tend to use in-form-ation instead of form, very often as my texts of 30 years of lonely research started with the simplified model of energy and information (as that is what we perceive)

It is important though to be precise when using those terms in equations and detailed descriptions of beings and its events. So the first question is how can we measure those terms? Even if we don’t perceive. Alas! the Universe is wise and has given us ‘parameters to measure’:

PURE §pace can be measure as DISTANCE and size, S. Pure form can be measured by the frequency of the cycles of the form-clock, ƒ, which in turn becomes perceivable externally as ‘density’, ‘inertia’, ‘mass’ and similar terms for each scale.

Once those dualities are understood, we can compare the properties of both, spatial entropy>energy and temporal form< information, observing the inversion of its qualities and yet, in as much as both have the same number of dimensions, energy and information can transform one into the other by transmuting those properties:

Time cycles, Tƒ                    Vs X       Entropic Space, ΣEs            ≈ST-momentum-actions- energetic information

Time-clocks: O-form           Vs.        Space motion: Lineal        ≈ waves

Small, still                             Vs.       Large,  moving fast      ≈   Open curves

Tall, Perpendicular                     Vs.             Long, Parallel   ≈  wide, intersecting

Hierarchical  Order                           Vs.           Democratic chaos-freedom

Bidimensional Height                Vs.            Bidimensional Length  ≈ tri-dimensional entity

Cyclical, Rotation, imploding     Vs.            Lineal, uncoiling, exploding   = beating rhythm

Informative Frequency         Vs.             Lineal Speed                        = momentum

Broken  form                           Vs.               Continuous, differentiable

Intelligent, perceptive             Vs.                   Strong, fast.   =        energetic top predator

Social, organic, creative              Vs.           Darwinian, destructive behaviour   =

Future, logic path              Vs.            Past, trailing motion

Life arrow                                Vs.                      Death arrow.     = existential world cycle

Waves of §pace                      Vs.                     Particles of Time

Female, yin principle             Vs.               Male, yang principle   = reproduced child

Masses, charges                  Vs.                       Forces, fields       = energy

Heads  & senses                     Vs.                    Limbs               =  Bodies.

The formal=functional differences between entropy and information (organs) is a duality – the ‘Black hole Law’:

Limbs/fields of Maximal Space=Entropy x  Min. Form Vs.Max. speed of Information=Minimal Spatial extension= heads & particles

For example, as the chip becomes smaller halving its size every 2 years it doubles its capacity to process information (‘Moore’s Law) The reason is obvious: to think, to calculate you have to communicate in-form-ation, forms between elements of any informative system. The smaller the brain, the faster communication takes place within that brain and the faster it calculates and processes information in a logic manner.

If we consider that each being can be in a time or state of space, the question now is. What defines then its state?

In mathematical terms the answer is its curvature, its form, FORM becomes then the definitive element of being, as you cannot change so fast from cyclical to lineal form and viceversa, as you can between state of form and state of motion.

Cyclical time and the world cycles of existence of beings, made of a sum of ‘actions’, which become ‘arrows of time’ (spatial entropy, temporal form and its e x i =st combinations) which are ordered in sequential world cycles of time, which gives us the sensation of a cyclical time program of past to future, which we can also see as a sum of synchronous minds in which ‘knots’ of timespace actions converge, through several co-existing scales.




Trinity is the name of the game, which is natural to the fact that causality exists, and so there is always an up and down scale in the fifth dimension, a left-right, back-forward element in a system, and a past-future. What we have unveiled further is the symmetries between those three ∆-s-t components, and the capacity of linguistic minds to put it all into still ‘continuous image’ as a whole. 


3 numbers could resume it all, 1,0 and ∞. Amazingly as it seems they can be seen as the ternary sides of the same structure, 0,the center, |-the membrane, ∞, the internal cycles between both that mirror the infinite Universe.

Thus infinity only reaches till the limits of its Whole:

The |-membrane,  the • singularity & the ∞ cycles between them form an island universe, a fractal superorganism and its world cycles.

The study of the interaction of those 3 elements that compose all §upœrganisms is thus an essential part of GST, which can be inscribed in an even larger concept: the ternary, Universal grammar of all systems, and its fractal ternary sub-divisions ad infinitum.

So in this blog and related ones, we shall deal with ‘TRINITY’ (-;

screen-shot-2017-01-08-at-09-37-22screen-shot-2017-01-08-at-00-22-33In the graph, trinity is the structure of reality, its Universal Grammar, scalar, ST variations and ultimately all what we care to study from the most sacred to the most mundane:

-Trinity is the mystery of christianity, where the ∆+1 Γ•∆, OR subconscious collective of mankind (Jung) communicates its laws of ethic survival which express the fifth dimension of eusocial love, in human verbal languages, through its ‘nervous, informative system’, the language of the wor(l)d through its prophet≈scientist of history, where ‘the word, our God, becomes man and inhabit among us’, as the ‘canon’, or ideal form of the game of existence that humans should imitate to form with its revelation books and memes, a collective ‘DNA’, which brings together all its cellular citizens, supporting that collective mind God, who foresees the future of eusocial evolution; which if humans obey, will help them to evolve and survive from species into super organism, but if not, will bring them likely its collective death through hate-memes and weapons, the ‘bad fruits of the tree of science’.

So the prophet, who foresees the future logically (though a physical interpretation will mean, as information can jump a quantum cycle into the smaller ∆-1 past, which co-exist with the future whole, that actually the future death of a cultural God co-exist with the past life of the cells that host it),  spells those laws to its quantum cells back to the past a generation. THUS the entropic death of God into the language, ∆+1<<∆-1, imprints with the genetic memes of the super organism of history the mind of the prophet, a biological generation 72 ages, exactly the moment of death of Yhwh when 1/3rd of its believers died in the roman holocaust, the month of Ab, 72 years in ‘lineal time’ latter, in the same moment in co-existing scales of the 5th dimension, of the birth of Jesus . Alas, GSTheology is born and we have proved the most debated questions of Christianity – the mistery of trinity, the proof that Jesus is Son of Yhwh, the god-mind of the jewish people, and that he is a prophet  (: hem… ‘believe it or not’.

But trinity is also the cutlery ternary division and its Gst equation: ‘|-Spe (knife) < Ø-ST-fork > O-Tiƒ (spoon); as the knife delivers entropy the food, the spoon acts as the spherical membrane that surrounds it and the ‘last to come’ and more complex fork, with one of the 2 ‘hyperbolic geometries’ of space-time (fractal branching), which performs the functions of the other 2 (perpendicular holding and lateral cutting). We deal with trinity in depth in this post, its sub posts on Æ,  Universal grammar and those ‘attached’ to the Fractal generator.

Just two examples that show you the power of the GST formalism, which besides the usual questions about mathematical physics, will be explaining such seemingly ascientific questions as religious mysticism and table etiquete (: As a TRUE T.Œ, HAS INDEED TO EXPLAIN IN AN EFFICIENT UNIVERSE, all what exists, including good and EVIL≈ANTI-LIVE≈DEATH. And all the arts of the human mind:

Why I am so positive about GST laws? Obviously because of the experimental method, and its FUNDAMENTAL LAW OF TRUTH, which we can resume in a sentence:

‘A theory which is simpler (Occam’s razor) and explains more things with less elements (efficient Universe) is more truth’.

SO FAR NO MODEL OF REALITY CAN MATCH GST on both grounds, as it explains it all WITH ONLY 2 elements, space and time (in fact inverse formal motions, hence ultimately with one element, ‘temporal energy’). Not a single human theory has been able even remotely to explain scientifically the 4 biggest realms of human thought, science, art, religion and the machine…

The fundamental particle of the Universe is a ±∆ super organism, which extends within the U±∞ scales of reality in 3 of such scales, which co-exist tightly related to each other to form a super organism of space-time ‘Œ±1 points’.

∆± ∞, this is the potential of the game and Œ,Æ, i-logic mathematics the language that shows all those potentials as a mere logic shape of information, a still mapping of the Universal game.

But in most cases the system is just 1±∆, a super organism. This is the logic game the Universe plays, the construction of Universals from infinitesimals. Then all the other games are details of this one. Thus we should consider the queen of all sciences biology, and the fundamental particle of the Universe once we have all the information about a region’s domain of vital space and cyclical times, the super organism.

It is a good moment to reflect on what all this means for the scientific understanding of the arrow of time and the nature of the Universe at large.

‘The 5th dimension is scalar, Time is asymmetric, informative; space is symmetric, entropic – with those 3 elements and its fractal parts and combinations, the Universe creates itselF.

A fractal, isomorphic organico-mathematical universe is a proposition quite different from the standard comfort zone of anthropomorphic science. It means we are in a living, organic universe where our importance is absolutely relative, and our dumbness born of the limited view of each point of view of this living universe.


In the graph, the 3 5D Space-time elements that structure all physical/biological/social systems of the Universe:

  • Τhe 3 only topological forms≈functions of Nature, lineal, energetic fields/limbs/territories of space; hyperbolic waves/bodies/reproductive space-times and cyclical, informative particles/heads/languages, which create  in space all ternary fractal organisms of reality:

|-Spe (limbs/fields/territories) < Ø-St (wave-body-reproductive class) > Τiƒ (particle-head-ruling class)

As topologies are form in motion, we can see those 3 topologies synchronically in space and they form a ternary organic structure, or we can see them in actions throughout time:

  • Τhen those systems enact a series of actions of absorption, emission and reproduction of energy and information (±∆e, exi, i), which develop in time in 2 phases, a long period of increasing information with 3 ages (youth: Max. e, reproductive age, Max. e x I , old age, Max. I) followed by a short period of erasing information or death, such as both become a zero sum:

Life arrow of information (E>I) + death, big-bang arrow (I < E) = 0. Whereas > is an informative, implosive motion and < an energetic, entropic one. So we can write the fractal generator in time

Spe (youth) > St (reproductive age) > Τiƒ (old age) << Death-big bang: Spe

So the interaction of the topologies of information and energy and its combination define a Universe made of fractal beings of space-time, which complete world cycles of existence, across all the scales of the Universe.

It is the 3rd element needed for an organic description of reality, as all those systems, will not only have 3 organic topologies in space and 3 ages in its world cycle, but will be organised through 3 scales of relative size that co-exist as parts of bigger wholes:

∆-1 (atomic, cellular, memetic scale) > ∆ (thermodynamic, organic, individual scale) >∆+1 (gravitational, ecosystemic, social)

We can see in the graph, above, some assembly of ternary systems made with the 3 topologies of the Universe, and below the scientific scale of spatial sizes and time clocks, which compose the different space-time beings of the Universe.

SPACE BECOMES FRACTAL BY REPRODUCTION OF PRESENT BODY-WAVES-WORKING CASTES, of the ternary topology of the Universe, Space = Max. E x I, a 5dimensional fractal reproductive space with 3 motions upwards, downwards in scales or with a present simultaneous speed, in present-past-present waves of simultaneous motion, networking in information, non local at distance, as the wave of form, of information, reproduces through a fertile space of energy, the being becomes and as it becomes emerges, fetal entity of a perfect supeorganism, the wave of motions who resembles organic livings living and dying travelling through the scales o the 5th dimension.

We can see the different scales of the Universe all of them including humans, below, described with those 3 elements , ∆SΤ, and its sets of 3×3 + œ laws – to notice that the minimal and maximal scales, both theoretically (cyclical-lineal nanoscopic and macroscopic scales, and atoms and galaxies) have very similar parameters;hence the hypothesis of a scalar Universe of infinite, ∆±∞ scales.

Below we see a human being and its 3 topological digestive-energetic, reproductive-hormonal and nervous/informative systems, which sub-divide in 3 more systems, for a total of 3×3+0 sub-systems which are used in medicine to describe completely the human being; whereas the 0-integrative whole system is the brain, itself a ‘fractal point’ of the next ∆+1 social, memetic scale of mankind. In the left we see the 3 ages of human beings, between conception in the ∆-1 seminal scale and death back to the flat energy world of disconnected cells.

As such we shall be able to describe existence, as a travel through 3 scales of the 5th dimension.

Τhe beauty, precision and essential homologic poetry of the fractal, organic, self-reproductive, scalar, absolutely relative, infinite, immortal Universe we shall describe with the formalism of 5D Space-time systems, is a new door to our communion with the whole Universe of which are all a mere part, made to its image and likeness.

Networks of simultaneity and resonance (informative axons): consciousness and emergence.

All this said there are elements in the Universe which are difficult to understand in terms of ‘classic’ human thought and science, which are at the heart of the processes of ‘existence’, and emergence of information in upper scales, and organisation of parts into wholes. They deal with the fact that ‘Tiƒ’ particles-heads-upper informative classes must be fully connected with its lower ∆-1 scale to synchronise, make it work together as a whole, resonate its orders in all lower systems and finally be conscious of a whole – and the key to all those processes are fractal branching networks, which unlike herds loosely connected in a single plane, conned the upper scale of a being with all its lower parts/regions.

It must be understood that those networks have many levels of connection between scales. They are though basically always the same. Informative networks break information in reproductive waves through axons and so they can produce informative actions of multiplication of information both ways through effects of simultaneity and resonance.



The resonance of all resonances, one can consider an imaginary space of dimensions of time – the 3 first dimensions those of a space of lesser form on which we transit – in our case the 3 perpendicular dimensions of light space – all other dimensions becoming dimensions of scalar growth of information, through resonances between the larger and the smaller scales with self-similar forms, merely differentiated by its TIME metric:

Max. Spe   = Min. tiƒ, the larger resonance encodes the smaller one.

How whole minds imprint smaller parts, through the simultaneous fractal network division of an impulse of maximal energy into multiple quantum’s of information. Such as E = h v, is proportional to the information the system emits (v) along an ‘H’, constant of space-time, or ‘lower field’ (S=t), from where the E(e) x V(i) body of ∆+1 extracts its energy of motion.

On the other hand, parallel networks of energy ,pipes and blood flow are less concerned with the form but with the energy it provides to the motion of its cells, and are based in adjacency and other topological, spatial properties.

The devil though is in the details, so once we understand this general picture of the whole, its parts and its common time world cycles, sum of all the frequencies of its space-time actions, which construct a super organism that will go through 3 ages between birth and extinction, as it carries as a whole its 3 ∆±1 scale of beings, we shall realise we just have explained they very surface of a extremely intelligent and complex world in which almost magically, all works together because of the complementary connections between simultaneous parts in space and synchronous rhythms in time and ‘resonant’ effects in scales.

So 4 ‘magic phenomena’ will be of enormous importance to fully grasp how ∆, S and T, dynamically organise (or inversely become disorganised):

  • Space Simultaneity, which is an a priori condition for a vital organic space to exist, and act efficiently as a whole.
  • Time Synchronicity, which is an a priori condition for a temporal ensemble of parts to exist, and act as a shoe.
  • ∆-Scale Resonance, which is the a priori condition for ‘parts and wholes’ to interact together.
  • Consciousness, which is an a posteriori condition of complexity in a panpsychic Universe: consciousness arises within any sufficiently complex, information-processing system. All animals, from humans on down to earthworms, are conscious; even the internet could be. That’s just the way the universe works.


The few scholars i have been able to lure into this web (: are taken aback by the sheer size of its posts, its excessive disorder :(my fault), its polymath structure and complex ‘syntax’, that is logic formalism (the fault of the Universe:)

i am trying to improve my faults, but I am not of the opinion of my predecessor in the illustrious series of humind infinitesimals that in the modern age have evolved our paradigm of time-space … Descartes>Galileo> Newton>Leibniz>Darwin>Marx>Planck> Einstein>i-man (my old pseudonym, back in the 90s when at Columbia U. I used to self-publish books and send it around the globe)…

‘If General relativity is wrong, God should correct the Universe, so beautiful it is’. Well God is correcting… relativity, into Absolute relativity and who knows what else he would correct>improve in the future. So far this is the deepest view of his thoughts, as ‘the seer of time’ (Saint Augustine) And so we need to correct our humind mirror, maths and logic; maths by correcting geometry adapting it to fractal space, logic by introducing the ESSENTIAL CONCEPT OF ALL LANGUAGES WHICH OBSERVE REALITY, THE TERNARY SYMMETRIES BETWEEN THE MIND LANGUAGES AN THE S-T-∆ elements of reality.

In essence the key changes are the concept of an Euclidean point, which now becomes a non-euclidean fractal point that has breath as it has a vital inner space of energy, enclosed by a membrane or cyclical time-clock, focused into an informative still singularity or mind. So all points are fractal ternary points.

And for that reason, the logic of the Universe IS TRINITY, the study of its three parts in space, three ages in time, three scales in ∆; and the symmetries, mirror reflections and interactions between those 3 x 3+0 dimensions of reality; as the Universe is really in a visual simile, like a kaleidoscope, with four mirrors, the mind, the scales, the time ages and the spatial topologies communicating with each other and creating relationships between them.

Now, while the mind can be studied by its own linguistic elements it is often placed in the head-particle, Tiƒ, so for sake of simplification we accept except for detailed analysis and epistemological philosophy its ‘equality’ with the Tif element of its spatial topology. So in general we eliminate the mind of our analysis (given also the difficulties to be accepted by anthropocentric humans). 

It is then when trinity can be resumed in a generator equation: ∆-1 Past Sp (limbs/fields) < ∆ Present TS BODY-WAVES> ∆+1 future Tƒ particle-heads.

And this Generator equation is the basic formal definition of each species (naming its parts), whose formal study gives birth to NON-Æ=I-LOGIC SCIENCE (i for information and next letter to a and e).

The use of the generator helps a lot to make simpler as Feynman diagrams did in quantum physics the complex symmetries, similarities, reflections of time ages into space topologies into scales and so on. I.e. we just change the reverse order of the generator and it becomes a time symmetry: Ps (past) < ST (PRESENT) > ft (future). We reverse the symbols of > into < and information becomes entropy, and so on.

So the symbolism of ® is very useful to define all kind of events between the 3+0 elements or reality.

So trinity is a complex logic, but the simplex way to deal with it is the ternary principle, basis of our division of those four forms into 12 more detailed isomorphic elements to study in depth each species and its properties; which we can resume in many ways. Some are:

  • ‘Every element of reality can be subdivided into three ∆ST sub-elements diminishing in ∆§cales and viceversa, every three elements of reality with enough complementarity to create a larger whole can be assembled into an ∆§+1 system’.

i.e. your leg has a Tiƒ ankle joined to the feet, a middle and and upper part; your fingers in palingenesis broke first from 1 to three and then the lateral ones into 2 to make five, which are the different type of fingers of all animals.

  • DUAL s-t and trinity s-st-t evolutions in time establish then the creative processes of the Universe. In languages from one a-languages we went into three vowels and five and then seven…. Complexity grows by subtle differentiations on the trinity principle.
  • THE TRINITY principle in kaleidoscopic terms means also: every phenomena in space, time or ∆-scale has A REFLECTION in the other two elements. Ie the three parts of space have three dominant ages in time, limbs in youth, heads in old age, bodies in the middle age, and relate closer to an ∆±1 scale: limbs to the ∆-i fields of entropy it absorbs, ∆º to the organic plane the body ‘mates to reproduce’; tiƒ, to the ∆+i worlds in which it performs larger cycles as part of a larger whole.

And finally as trinity means indeed reflections into t-s-st, ∆º±1 scales, topologies an ages, we talk of multi functionality:

  • Every system of reality to exist efficiently is able to develop three relative functions in its whole as entropic, informative and reproductive partial part.

Besides trinity there are then lower duality principles of logic of which two are important:

  • Entropy and information are inverse functions.
  • Species subdivide in gender states, wave-female states, s>S=t<t and male, particle-field state: S>T+T<S.
  • The ‘postulate of existence’ which requires at least two poles of entropy and information in a dynamic event for an entity to exist. Since without software and hardware, entry and information, without a dynamic flow/motion, the seed of information is latent, the vacuum space has no form. It is then the fusion of both, and its intermediate growth of a body-wave of communication, which introduces into present existence a being, and for that to happen there shall be a certain similarity between software and hardware; slowly comming together through its communication.

In the graph, the syntax of all languages can be reduced to dual and ternary structures that reflect the ternary elements of the fractal generator, Spe<St>Tiƒ. Thus we can consider all languages mirrors of the generator, which in turn species use to order and project its imagination’, reproducing those mirrors through those languages into actions that mold the future of reality. Mind stiences therefore are essential to the way the Universe creates. The graph shows how a minimum of two parameters to represent entropy and information can create a mapping of reality, even though ternary languages are more precise. In the right the human verbal, temporal language and mathematical, spatial one, can be reduced to ternary dimensions (height-information, width-reproduction, length-entropy), ternary topologies, ternary symbols G(spe) <action operandi>T(ƒ) and ternary sentences. Above a simple mathematical statement that relates a spatial function, D, and a temporal one, written BOTH in cyclical 1/ƒ=T and lineal time, below a scheme of the Universal grammar of all systems made of Names (informative element), verbs (actions) and Objects (energy of the Name). Both suffice for a whole mapping of reality.

So let us go part by part. We first upgraded your mind to black and white and then to the three colours/arrows your mind uses to view reality.

Now we shall enter into the territory you don’t see – the mind itself, behind those languages that simplify reality into information.

So we need only a final element, the mirror mind of information or central singularity that apperceives it all.

As those three time arrows in each instant cannot be seen, systems become mirrors that visualise the motions of time in simultaneous measures of space, a mind can conceive a linguistic mapping/mirror of those three topological motions and see how through time they develop structures synchronised as ‘space-time organisms’.

The Universe is a fractal of 3 timespace arrows, entropy, energy and information. This simple elements in its infinite variations and combinations defines the Universe, with a logic and mathematical that present science lacks, despite its awesome achievements in terms of mathematical description and praxis of manipulation of reality.

Philosophy of science though is not so much concerned with the capacity to manipulate reality with precise measures and a posteriori accounting of all process as ‘patterns’ that will repeat in the future and can be manipulated. But with the reasons and whys of those processes, which are considered to be ‘rational’,  ‘selfish’ and ‘biological’; that is, systems act to survive, and they do so from their central point of view or singularity-mind of information, by controlling and ordering a territory around them, enclosed by a cyclical time-like membrane.

And so the 3 functions-forms of time-space, ‘spatial lineal entropy’, ‘repetitive energy’ and ‘informative cyclical dimensional form’ combine together to create ‘entities’ which are the essential ‘particle of reality’, not some arid physical parameter, but an organic structure of scalar space-time, the supœrganism (Ab. œ, following the rule of slightly change terms in english to serve the new paradigm). 

Thus we can rephrase our definition: ‘the Universe is a supœrganism, made of 3 timespace functions/forms, assembled into ternary physiological networks, that process spatial=motion, informative dimensional form and its iterative combinations, in order to survive as a balanced structure’.

It is then time to connect this seemingly new view of reality with the tradition of philosophy of sciences, as philosophers have always understood it.

Culture over science.

Now, all this clear a big question hauls over our understanding of the Universe. Why mankind has been unable to describe scientifically its three arrows of time and only ‘admits’ entropy; even if in earlier time of history, Asian cultures with its duality visnu-shiva and yin-yang, equivalent to the duality information-entropy, were so closely to make sense of all of it?

The answer will surprise the reader, who mistakingly believes today as it believed in the past, that ‘science is truth per se’ and proved with no errors or cultural attachments – as people though religion was proved by dogma. Here the element missed in his discourse is ‘cultural bias’ in science and ‘postulates without proof’, ‘ceteris paribus analysis’, ‘anthropocentrism’, ‘power’ and ‘hyperbole’… all concepts natural to the human psyche a priori of any scientific statement.

In that sense entropy only theories are indeed a bias of the military, power-profession of physicists making weapons and motion machines, and it has always been so, becoming dogma. Entropy was discovered in the study of steam machine motion, as a product of gaseous heat; which is ONLY one of the three states of matter:

Gas (entropy state) < liquid (balanced state) > Crystal-solids (information state).

So it is obvious that the laws of kinetic gases are entropic but it is absurd to expand them to the whole of Nature, by simply ‘eliminating’ from philosophical analysis the other two arrows. And the same happened when in an astounding ‘hyperbole’ Helmothz from the ‘military culture of Germany’, expanded it to the Universe, affirming it was dying and further more, Gamow, a Nuclear-weapons maker affirmed the Universe was always and only a ‘gas-like expansive state’, again reducing the three arrows of the Universe; so well resumed in Einstein’s awesome equation: E=CCM, which he inferred in fact from the inverse arrow of informative, accelerated vortices of mass information, in his landmark: can mass be created out of entropy? So in this formula we have again the three arrows: 

Entropic expanding intergalactic space E< c²≈st  constant wave of light space-time > M Imploding masses and charges (galaxies)

And yet again, physicists and western cultures just used it to make entropic bombs and declare the Universe had only a similar big-bang exploding arrow.

There is here the side of dogma, and repetition and the believers memorial nature of the human mnd. As 1/2 of mankind believe that a  bronze age donkey-breeder tribe who saw a bush burning, understood the meaning of the Universe (Abrahamic religions) and react offended to any attempt to ‘reasoning’ historically this hallucination, just because the word ‘god’ is sacred; 1/2 of them believe the Universe is in a permanent state of entropy, dismissing the other so evident, experimentally, arrows of time, proper of all the generator equations of all systems of nature.

There is nothing though you can do to change a ‘believer’s mind’. In religion is called dogma, in science ‘first postulates’, which always show on the long term to be partial, ceteris paribus, analysis of the whole ternary reality. So for example, euclidean flat space turned out to be one of the three possible geometries of reality, because it was a postulate.

And an entropic Universe shows to be both in space and time one of the three parts of it. So in EFE (Einstein’s equations) the three solutions, steady state, big bang and big crunch are the equivalent processes in time to the three parts in space, and we will see that beautiful time-space symmetry soon).

In that sense, we can say that the entropic postulate of a single arrow of time is a product of the white western male war oriented culture and its manifest destiny, throughout the whole history of the western world, opposed to the dualist and ternary cultures of the west. So we can now introduce a historic view of those cultures, because its postulates today pass as science, and are by no means scientifically proved by experimental evidence, which shows a ternary Universe always.

So we shall use exactly what we have proved – the ternary only topologies of the Universe and its three space-dimensions/time functions, to the racial make-up of mankind, since as it happens is the origin of a new of the many sub-sciences derived of gst that studies…

The three cultures of the mind.

WHAT IS MANKIND? The answers of philosophy of science, the only ones that should be accepted  by a rational enlightened mind of the III millennium, beyond myths and selfish ego-trips is obvious: a single species, as we all can mate with each other, divided into three  races of the mind, the dolichocephalic white  visual people, lineal entropic with its longitudinal axis larger and dominant, likely by influence of the European Neanderthal of larger eyes, visual brains, consonantal sounds, red hair and hooked nose; which has in consequence developed lineal culture, mostly based in lineal agglutinative languages, as German and Arab are, the original language of its most extended groups ,  has fallen in love with lineal weapons that deliver entropy motion and death, and has consequently imposed by force its culture based in the bad fruits of the tree of metal, since the age of bronze, its imperial, hierarchical concept of concepts of lineal time in science, and a lineal manifest destiny in culture, above the two other races of the mind.

In the opposite side of the three dimensional topologies of the Universe, there is the mongoloid race, whose wide word axis between the ears through the Brocca region of temporal verbs, more developed make their cultures dominant in the social language of man, words, with a full understanding of the cyclical nature of all time clocks, which as any kindergarten child knows has more dimensions of form, more information than the simplest, fast moving line.

Hence it developed a more complex, cyclical culture of information, where the creative cycles of nature and the curves of female, yin, Vishnu, women were preferred over the lineal body-mind of the military, entropic, destructive white macho male. Communal social evolution was preferred, conflict avoided and so the Asian cultures with less metal-weapons and tribal warfare survived in larger numbers, the only true measure oaf success in evolution and still today represent the majority of mankind. But when they were discovered by the lineal, entropic white male, soon were submitted by raw power, massacred in huge numbers, and adopted the lineal culture and obsession for the false glare of metal, gold and iron weapons of the west. THE PARADIGM of that conversion being Japan, which copycatted the Germanic cultures and the cruelty and manifest destiny of war and machine-making that have characterized the western world.

But as we said there are three dimensions and topologies which structure the form of all bodies and brains, which in the human case, is the only organ that truly matters; as we are after all at least in paper the Homo Species.

So the third space-time topology in the Universe, mixture of lineal visual entropy of fast motions and destructive power, Shiva or yang in the oriental philosophies, and the cyclical informative arrow of temporal words and social gathering in circles and get together are not the whole tale.

We still have a third axis, that of height, which the racist anthropologist all of them white macho male of the western colonial imperial enslaving cultures didn’t even account for in his classifications, so we will have to invent a new word, psylocephalic people. They are thus dominant in the height axis of the brain, site of the inner soul, the emotional and motor elements, in close connection with the body. It is the black culture, with its rich emotional development, physical powerness and love for nature, Gaia, who have preserved the wild animal life of the planet. Because children are also dominant in the emotional, physical brain, it has been often said that the black people and their cultures, are less powerful than the white, military men who came to dominate and slave them with the fetish tool metal, but again biology tells us that childhood is the happiest of all the states of being; and in all ternary systems constructed with the three topologies of space-time, the body-wave sustains the particle-head of the system, and both are complementary to each other; none is better, they both need each other.

If any of the three elements with whom all systems of nature are constructed, one is the less complex, in fact is the gaseous, entropic, lineal, limbs and fields over which body-waves, guided by particle-heads run.

Indeed, if we extend the topological analysis, to the whole organism of a human being, the entropic limbs, reproductive bodies and informative heads are ALL needed, all are complementary, but if you were to loose a part, a lizard will cut-off his tail, and you rather loose a leg than your body or your head.

So alas, what topological biology tells us, is exactly the opposite of what the supremacist white, lineal military cultures has been claiming for millennia, entropy, big bang weapons and war the leit motif of the white culture and its philosophies of the Universe, are completely disposable. And we cold live perfectly as a species without them. But ethic Languages of social love that enlighten the mind, Nature that sustains our body and children which bring happiness and renew are future are not.

So the next question the philosopher of science should wonder about history is why then the white, male entropic lineal simplex culture has come to dominate all the aspects of our world, from science to culture, from territorial power to the authorized version of history, as it comes in the books of social science. What went wrong with mankind to be guided by entropy, not by life information, by the wrong arrow of time; giving supremacy to the simplest view of the Universe and its death culture?

And the answer is clear: the entropic white man discovered a harder attachment to its teeth and hands, metal-weapons; and so the natural balance between the three races of the mind, and its complementarity was broken, suddenly by a boost of power on the side of entropy.

So we should give the entire mindset of the entropic culture of physics a turnaround showing that even its concept of a Universe of worldlines of motion, as the only ‘arrow of time’ IS IN FACT yet another manifestation of the reproductive nature of the fractal Universe, solving the never quite understood Zeno paradox on the ultimate nature of motion as reproduction of form.

Now the application of the ternary principle to the study of medicine, physiology, the mind, cultures and brain structures is so rich in meanings it could take an entire book in itself. The symmetry between space regions and ages is the most amazing.

A simple example will suffice. The upper brain has three regions, in topological structures: the cerebellum, whose role is to control ‘entropic motions’ and as such is the FIRST developed in the child, with maximal youth activity; the middle brain, which is the emotional brain; and as such is the second in development – the present state, the larger one; and the third region, the frontal, cognitive, maximal Informative region, and as such is the third to be developed. The Dunedin study famous from following 1000 people through life noticed criminal, entropic people develop faster and maximal the cerebellum (properly advised become also better athletes).

In that regard, while this web might seem too abstract for the skeptic scientist, as I focus on GST theory its connections with details of each species is what causes on my mind (cognitive:) a constant orgasm for 30 years, as I read often Nature, SciAm and some specialised scientific magazines – I have not written down more than a fraction of it all, but as Descartes put it, ‘I have left most of it for future researchers to have something to do’ 🙂


Our interest, in a Universe in which there are constantly 3 choices of paths, S, T or ST to act or no to act (-1 action), with equal probabilities. is to map out a new existential algebra (ab. Æ) of all nature systems, with those 3 -1 possibilities.

Why the Universe has 3 positive ternary actions (and a negative, passive no-action) is self evident:

-1: The mind might merely observe and stops motion (•),.

+3: Yet the system might evolve towards higher entropy (+Spe), higher information (+Tiƒ) or might reproduce its space-time in repetitive cycles, which on the long term will become a larger ‘whole’ (∆).

So the existence of 4 elements, ∆•ST, 3 of increasing motion along the 3 paths of space-time (S, st, ∆st) and one of growing stillness (•), implies a more complex logic with 4 potential actions for each bifurcation of past-present into the future.

Of course, if we were to study a ‘fresh beginning’, the probabilities of those futures would be the same. But as the Universe is a game of memorial, informative motions, it follow that as the game proceeds, the future paths become determined by the long cyclical causality of individual actions and past cycles to be completed into the future.

screen-shot-2017-01-08-at-00-22-33So while paths do have a possibility to be modified without expenditure of energy, closed time cycles impose their ‘inertia’ and so the perfect potential ‘fourks’ of space-time (four point forks). The image is meaningful: as always we have a ‘lineal, entropic knife’; an informative, cyclical ‘spoon’ and an ∆•ST, 4-dimensional fork to both cut and  form the food in present space-time. And you would choose, if given a single pick, the fork precisely because it can cut laterally and it can scoop the food. Everywhere the rules of GST will enlighten ‘why things are as they are’; and the causes of the past or the fourkations of the future will be ternary±1.

The causal ‘bifurcations of timespace’ thus are now ‘fourkations’ of space-time. And so the extraordinary one-dimensionality of human minds and its languages are out of meaning. Those arduous arguments between wannabe geniuses sponsoring their ‘point of single view’ as the real cause must cease. Ceteris paribus is simplification. For a being to exist, for a cause to act, for an event to happen in fact it will be because 3 past causes have converged to form a whole time-space ternary symmetry. Think of your actions, when you move, the mind first ‘thinks’ in the motion; the body then provides the energy; the limbs convert it into entropy. It would seem there is only one cause to action, the motion of the legs, but actually 3 actions converged in a ‘dharma of time-space’ to make it happen. Yet for the non-action only the mind is needed to stop action; which therefore is an ‘easier path’.

So the languages we use to portray that process are naturally different from the classic ones. And unlike analysis so close to the social scales of GST and fractals & topology, essentially ‘the’ spatial science of the fractal Universe, algebra as it is understood today, is basically a synoptic way to deal with topological and analytical theorems. And its proper structures, sets and groups must be understood as expressions of our social groups and ITERATIVE, MOVING laws, based in symmetries, transformations and motions through ‘polynomial scales’. But as the language is so different, we rather start afresh and include as we go along the main field worthy of classic algebra, which is NOT sets but group theory.

Temporal, Æxistential Algebra, studies the organisation of systems, through time=change; that is by means of transformations that provoke motions of a system, and create variations of systems, according to Group theory. Still it is worth to remember the basic elements of Algebra and its equivalence.

The ternary operandi of Æ… and its symmetry with ∆ST elements.

Actions and its causes are thus the ultimate inquire of existential algebra. Why and how motions of space-time happen. And what is the formal way to define them?

What we are interested here, beyond explaining the laws of classic algebra, such as group theory, with so many practical cases in science, which translate the TSymmetries and motions through ∆-scales, is the nature of existential algebra and the different equations of motions and species creations, through those motions and actions, which always render a certain ‘syntax’:

Past ‘Operandi’ Future= present.

The operandi between past and future, entropy and information, thus define what kind of present space-time event or entity appear to us. Because we have 4 elements to define existence, operandi are many, not only a simple ± symbol to ad or rest the same type of beings or motions, as when physicists study only locomotions and reduce all to a Hamiltonian ± operandi between the two O-potential and |-kinetic ‘states’ of form-entropy.

So each motion of time will have a different ‘algebraic operandi’, departing from our initial ‘Universal Grammar’.

We shall consider in this introduction the main operandi of the 7 motions of the Universe of which the 3 more important are:

Locomotion: Hamiltonian (Entropic, kinetic Past motion ± Future, Potential motion = Present (superposition motion of waves).

Reproduction: Past (field)  x Future (information)  = Present (iteration)

And the rule is simple, from classic algebra: a superposition or sum is of the same ‘species’; hence ‘energies (time-like)’ or ‘momentums’ (space-like), etc.

A Product can however combine different species. So it is normally a motion, which involves a space and time-like parameters:

Reproduction mixes the Spe and Tiƒ, different ‘genders’.

Finally, the 3rd mode of algebraic equations, polynomials/logarithms, correspond to the ∆-scale of growth or diminution.

So again we find an immediate relationship between the 3 elements of reality, S or T, ST and ∆ST, in its growing complexity and the 3 basic operandi of algebra, sum, product and polynomials.

What about the more complex scalar ‘motions’ of space-time? They are not that simple, as they combine elements of the pure ones. But as all ternary, Universal grammars, the complexity is born of the iteration of those elementary motions:

  • Evolution is a change in the topology of a system, so essentially a process of space-time morphological in-form-ative change better described with topological elements.
  • Growth and diminution involves reproduction and evolution of topological form and its inverse.
  • Birth and extinction represent an ∆±1 change, combined with an ∆T increase of information or a loss of it all ∆S, which are often expressed with logarithmic scales.

And so most motions involve both a Past to future, ∆+1, social evolutionary arrow accompanied with changes in topology. And as such are pure ‘GST’ Ælgebraic motions, better described with the formalism of Æ and its symbols S>T, T<<S, ∑∆-1 Λ ∆… and so on.

Since in its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; the definition holds. And as algebra is a unifying thread of almost all of classic mathematics, so happens with Ælgebra.

In that regard, classic algebra (we shall call arithmetics) includes everything regarding those 3 operations, ±, x, % and log, x². And its symmetry as we have seen is immediate.

While modern algebra deals with the study of abstractions such as groups, rings, and fields; sets and Boolean algebras; and categories and elements… So we can subdivided Æ in 3±1 age subfields:

  • Birth: THE study of æ proper (existential equations).
  • Youth: of classic polynomial equations or arithmetics (S,t; st and ∆ systems in its interaction).
  • Maturity: of abstract structures, or algebra proper concerned, with group theory (the internal social structures of the Universe).
  • Old age: of inflationary information (set theory and other ‘weird’ algebras)
  • Extinction: the transference from human minds to digital minds (computer algebra, boolean algera)

∆•st of space-time and its limits in space, time, ∆-scales and mind perception.

So space-time is always in its whole ‘plenum beings’ made of 3 elements, which in topology, are called:

-Tiƒ: the singularity or monad-mind in its centre of maximal communication

-Spe: the membrane or limiting, hard entropic circular system that encloses

-ST: the space-time much larger reality that mixes lineal expansive outer membranes and internal singularities:

circular motionScreen Shot 2016-05-09 at 23.56.35

ALL systems of physics and biology and sociology show the same ternary elements: the membrane singularity and space-time between them.

In the graph physical systems, from electromagnetism to fluid dynamics to  gravitational gradients, charges in physics, have the 3 parts. In biology they are cellular protein membranes and nuclei and cytoplasm, skins and brains and organs. In sociology they are national borders and capitals, and the internal territory. In non-euclidean geometry (right side, the inner parts cannot reach the membrane, and so it appears as a relative infinity, and the central singularity (A point), connects with all the points within the membrane, as its focus of information. It is that constant interaction between membrane and singularity what moods the internal vital space of energy/momenta, of the being.

In physics all Maxwell’s laws can be deduced from the existence of an external circular membrane (magnetism). So happens in gravitation, (orbits which ‘scan a bidimensional aerolar surface). And all systems will be centred in a singularity (attractive vortex, charge).

Moreover we shall see that TIME has also those limiting membranes (death) and informative centres (seeds of information at birth).

And the scalar Universe will have also those non-E unreachable limits, (Universal Constant limits of c-speed and To temperature).

All this is the essence of topology that defines an ‘open ball’ as the space-time volume limited by a central singularity and an external membrane, which are NOT perceivable, included within the open ball. 

So the concept of finite infinities, limiting membranes in space, time (birth-death) and scales (limiting unreachable constants of maximal information and maximal extension) are essential to understand formally and logically the Universe.

We are limited in time by the birth-death finite enclosure of our world cycle of existence, in space by the skin/membrane that breaks space-time into us; and in the scales of size of the ‘5th dimension’ by the increasing ‘blurred uncertainty and dark spaces’ which limits our perception of them beyond the ∆±3 scales of atoms and galaxies.

And so we are also limited IN THE KNOWLEDGE THE MIND MIGHT ACQUIRE OF ALL THE INFORMATION OF THE UNIVERSE, WHICH ONLY A BEING HOLDS ABOUT ITSELF, making ‘absolute truth’, 1, in terms of probability, only ‘existing’ in the being in itself.

Those four limits of birth and death, of absolute seeds of information (seminal seed) and entropy (explosive death); of singularity (the mind of information) and membrane (the skin) in space; of organisation above and below, in ∆±1 levels; and in knowledge provided by the limits of the language ARE ESSENTIAL TO ANY UNDERSTANDING OF MAN AS A LIMITED BEING, IN A ∞ UNIVERSE, BUT MAN DOES NOT RECOGNIZE THOSE LIMITS. Hence the astounding arrogance of scholars, scientists, dogmatic axiomatic methods of ‘truth’ (Hilbert in mathematics, which still denies Godel’s incompleteness theory). And the result of course is that you have a human astounding ego, who thinks to be so special, so unique, so unlimited, so galactic and Universal and YET IT IS SO IGNORANT.  And all what it does is to hold its pretension of infinity.

The decametric scale: 3 x 3 +o = 10.

8266397157164128‘The universe is written in the language of geometry, lines, spheres and triangles’. Galileo had a point – all reductionist views of reality are indeed half-truths. But in this case it is a huge truth.

The languages of the Universe are mainly 3, Topology, the most advanced form of geometry with a ‘bit of inner motion’, which describe the 3 ‘timespace’ only forms of reality – hence the determinism of topological evolution and the awesome capacity to describe it all with the ternary generator of those 3 topologies. 

Regarding triangles, intuitively humans both in earlier religion of words (Judaism) and Pythagorean religions of the number, were considered the ‘tetraktys’ and symbol of the ‘tetragrammaton’ (graph) – the symbol of it all.

As indeed, the 3 topological organs of all systems (lineal, toroid limbs/fields; hyperbolic, body-waves and spherical, informative head-particles, shown in the graph, which need only a little imagination to convert into a woman’s body – first surface, a leg, second, and a head 3rd one), suffice to create reality.

Yet as all ‘is scalar’, all subdivides into ‘ternary fractal sub-elements’. So to include the co-existence in the 5th dimension of parts and wholes, we can immediately subdivide the 3 topologies into 3 ‘sub-elements’ and put them in each of the corners of the tetraktys/tetragrammaton; while the central point, which is perfectly connected to all others, is the soul-mind-0-point, 10th dimension – the system that is apperceives the whole, connects its and tries to preserve it, through the world cycle of being.

(The reader should get accustomed to the ‘taste’ of GST which is the HOMOLOGIC, ISOMORPHIC METHOD, of putting always a physical, biological and socio-economical example of the 3 main sub-disciplines of knowledge to show the unity of it all as we illustrate reality).

Alas, the growth in the ‘5th dimension of scales’ happen through 10 dimensional ‘social organisation’.

Thus the previous graphs of Eames’ ‘Powers of 10’  is also the game of social existence.

Since it is also the number of quanta of space-time needed either in frequency or in population (spatial organic or temporal world cycle view of a system), either through time or space to create a new social scale (ab. §) that ‘becomes a new larger functional whole’ able to apperceive and process entropy-motion, informative forms and combine them through the ‘3rd corner’ to ’emit seminal’ reproductive particles, coordinated by the central whole.

Let us though then, once this is understood depart from reductionist ‘mathematical physics’ , and realise that what truly MATTERS IS organic FUNCTION, NOT the triangular form, beyond the obvious fact it is the most perfect ‘packed’ functional way to put 10 elements together.

So when we study specific species what we shall see is that ‘fractal points’  of space-time (beings) gather through networks of entropy, information and reproduction (in man, the digestive: spe, blood, st, Head, Tiƒ systems, which define our physiological structure), into a being. So humans in medicine are DEFINED by 3 x 3 + O sub-systems to which fractal points≈ cells attache themselves. This is the essential formal way to study in detail beings: through its 10 sub-dimensions of being; WHICH FOR the whole known Universe would look like thi::


In the graph in the creation of the whole Universe, and any of its fractal parts, ‘worlds, super organisms or island-universes’:

The being passes through scales of organisation that can be put in symmetry with the 3 topologies, 3 ages, 3 scales and final ‘warping mind/program of action’ of the being as it emerge into the new plane.

WE ARE ALL 10-DIMENSIONAL SCALAR BEINGS, when we consider this more ‘correct’ formal approach that the concept of the ‘scalar 5th dimension’ (the use of 5D though is useful for general studies of all those scales, given its METRIC FUNDAMENTAL S x T = K equation; and further on, it is a good first intro for the sceptic  4D physics that respects more the correspondence with its 4D formalism –  but I ultimately abandoned it, leaving the concept of the 5th dimension for discussions on the inverse arrows of entropy and information).

So the ‘numerology’ explained is rather simple with 2 clear numbers, the ±3 and the 9+0=10. Then on those themes we shall find some fascinating variations. We already talked of the +3 constant, the pi-cycle of time, where 3 lineal diameters convert into a whole time cycle with 2 dimensions.
But then why pi is not exactly 3? Because its curvature varies as we change slightly the ‘density and geometry’ of information of the space-time plane, so in black holes the curvature of such awesome c-speed event horizon accelerating inwards do come closer to 3. Still we do have here the first fundamental ‘event of space-time of the Universe’: 3 lines of entropy becoming a cycle of information:

3 D = π; whereas the porous ‘0.14’ holes between cycles will be found to have a fundamental function on ‘organisms’ with a spherical pi-cycle membrane isolating it from the external world.

While on the other hand – π, will turn out to be also a universal constant the e number, used for a different ‘common event of space-time’ the emergence by social reproduction and organisation or inversely by decay and death, the dissolution of a being through its ∆-scales.

Thus we can see then all systems as 3 x 3 +o scalar social organisms, with 3 dimensions of space, time, and ∆-size become warped in a new whole, which EMERGES into the new plane of existence in space, when it is COMPLETED, and a new world opens to it in scale (as when a baby is born) or emerges earlier.

Now it is important that you realise that despite the claim of ‘exactitude’ of mathematical physics, there is nothing exact about it, but rather fluctuations and variations around the perfect tetraktys being; only the whole display the perfect immortal game of time-space, we are all ‘nebulous fleeting platonic shadows of the GST canon and its games of topo-bio-logical existence, in S∆T. (For example, physicists need Wilson’s renormalisation tools to include the effects of ∆±1 scales in a given system; often put ‘ad hoc’ to match experience; differential equations that tabulate actions across several ∆-scales are not SOLUBLE only by approximations, etc. etc. AS IN THE FRACTAL UNIVERSE, ultimately every fractal domain of 10-dimensional organic existence with an apperceptive monad at its centre does make its own calculations which will have hidden variables for the external being – so something as simple as the motion of 3 bodies in gravitational attraction CANNOT be solved exactly.)

This does not mean though that the Universe is chaotic but that obviously the astounding arrogance of the selfie-scientist-mathematician claiming to have the exact language of God and absolute truth/knowledge/information about any entity is just more of what Humans do best, pumping their ego to ‘galactic, Universal hyperboles. Ultimately’ only the Universe has all the knowledge/information about itself’ Haldane).

Further on only the Universe is the immortal, perfect super organism and that allow us fleeting variations of the ‘platonic canon’ to exist and fancy our imperfections.

So those ∆•ST variations around those TETRAKTYS scales and numbers make the the morphological growth of forms between scales through the palingenesis of an i-logic memorial repetitive being born out of a seed of information, fun to study – they are, we are, the details of Γ•∆.

Then as the system is born from an initial seed – particle/semen/memetic prophet of the world – it will reproduce into parallel particles/cells/believers minds, and grow till it emerges as a whole new super organism in another plane with close to decametric scales of growth.

Alas, a religious subconscious, memetic collective civilisation (social systems), a biological being or a crystal world will be born.

IT IS THIS GAME OF CREATION OF COMPLEX SOCIAL ORGANISMS, THROUGH SCALES AND cycle of existence, WHAT THE UNIVERSE that constructs ONCE AND AGAIN logic ∆•st, 10 dimensional games of BEINGS is all about.

The final epistemological element of all systems that co-exist in several planes of the 5th dimension is the organic structures and biological properties it displays due to such co-existence symbiotic thanks to the metric equation, as smaller parts code the information of larger ones that provide them with energy and motion, so both scales become symbiotic.

The co-existence of planes of space-time can only be explained through organicism one of the two eternal philosophies of science.

This, true scientists know, as the mechanist view of physics was too simple and rather theological. Indeed, as Leibniz put it to Newton, a mechanical model of the cosmos, needed a God that started and created the mechanism.

While an organism, which is a system that co-exists in several scales of size, from smaller cellular/atomic scales, to individual thermodynamic/organic scales, to social, gravitational/ecosystemic scales, can easily reproduce by emitting seminal seeds of information in a lower scale, which then organise back, emerging again into the whole system, and further on can evolve socially into larger scales.

In this manner the Universe becomes a self-reproductive organism of information, and each of its parts becomes also a self-organising system made to the image and likeness of the whole – with no need of a mechanical clock to put it in motion, as Newton and Kepler thought.

Such view of the Universe and all its parts was called the organic view, and the aim of the science was considered to find a formalism of mathematical and logic nature, able to translate this more evolved philosophy of science in a model that without renouncing to the precision of simplex physical models, had the complexity required to explain not only the ‘how’ but also the why of all sciences and it species.

The science that studies the organic nature of the Universe, its planes of space-time and the common laws or ‘isomorphisms’, which exist between them, is called General systems Theory (Ab. GST). However it is simpler and more realistic to consider merely the formalism of the 5th dimension of space-time without any prior jargon as that developed by Systems Sciences. Even if we acknowledge the fact that this blog is the only ‘formal’, logic-mathematical model of both disciplines, known commonly the science of Complexity.

There are other efforts worth to notice. Notably the work done in Santa Fe Institute and the congresses of the International Systems Sciences Society, among collaborative efforts and the work of Mr. Troncale at Ponoma U. among individual researchers have tabulated many isomorphisms in the Universe (self similar laws across different disciplines of science, which as it happens are ordered by space-time planes of relative size, hence according to ∆ST metric: fig.2). But collection of data is only the 1st step of the scientific method, which requires to fit data into  a ‘general mathematical and logic model’ good enough to fit new discoveries in different fields – to test its veracity.

In any case since there has been always a ‘Philosophy of Science’, or discipline of disciplines, General Systems can be considered merely the formal attempts to convert into hard science the ‘scientific philosophy of an organic Universe’, as opposed to the other simpler model of a ‘mechanical one’.

And so we could put in both sides – the simpler, more accurate mechanical model vs. the Organic model, most of the thinkers of the past. Mechanism is easier so it has triumphed, Organicism has taken more time to become – still needs a lot to be done – a standardize system.

Thus the 5D model fits all the data of all the sciences of those scales to the extent of the knowledge of this polymath writer. Thus it is probably the better tested model in terms of the Principle of Correspondence and Ockham’s principle (a theory that fits more data in simpler laws, is the most truthful.)

Thus the site studies mainly those 10 isomorphisms in great detail ³.

The whole site, on general systems sciences, when I rewrite it properly, will be a small encyclopedia of all sciences, seen through the focusing, orderly mirror of the 3+3 Dimensions of the Universe, its 9 planes and scales and isomorphisms. I started to do this, in august 2015. Though the work is much older.

While the model was published in a very reduced format  in a series of peer reviewed conferences at ISSS during the last decade, this blog is the place where I will pour 2 decades of independent research in the aforementioned formalism.

You might then wonder why nothing of this is well-known in science (and why this blog i assume won’t change that trend).

In the field of social sciences we explain the anthropomorphic causes. In essence, humans as all systems are ∆-centered, and so they don’t like objective science. They like myths and that make them the center of the Universe. So religions are always more successful. And i attribute to that fact the delay on understanding the 5th dimension: human anthropomorphism. Since the 5th dimension shows an organic, ‘vital’ Universe ruled by Absolute relativity. Since humans simply occupy a relative world-plane of an infinite 5th dimension, self-centered in its point of view, an infinitesimal point with no importance whatsoever, ruled by the same laws that define the form and functions of all other systems and ‘scalar social herds and superorganisms’ .

Thus the ‘organic philosophy’ of the 5th dimension of isomorphic, scalar space time (∆ST), called ‘General Systems Theory (∆ST) ‘ is a philosophy of an organic vital Universe:

“All type of Universal systems can be described as social networks of energy and information. Its similar=isomorphic laws are the content of the formalism of the 5th dimension, from where we can deduce the main laws of each science that studies a relative ‘scale’ of spatial size of the social, organic Universe, from physics which studies its smaller and larger atomic and galactic scales to biology and social sciences which study its intermediate life and human scales.”

So what is really time? Change≈motion, as we see the passing of time when something changes, hence it moves externally in space or internally changes its form, its information. AND SO two fundamental modes of change=time exist:

Physical time, which is change in your lineal loco motions or translations in space, well studied with the formula v=s/t and the ad ons of Einstein, in which time is merely the parameter of space (the fourth dimension of space) needed to measure those motions.

But then there is change in the JUST DESCRIBED CYCLICAL INFORMATION, FORM of time cycles and systems, and this is biological change, which we shall see IS also the basis of historic change as we are BIOLOGICAL beings. In this different form of change, what matters is the change of information, which is MORE complex than entropy, lineal motions. And so there are several different forms of CHANGEs of information, which can be studied all together as a CAUSAL series OF CHANGES, WHICH TOGETHER FORM THE LIFE-DEATH CYCLE, or ‘world cycle’ in 5D jargons. The main types of biological and sociological changes thus can be described as Aristote did with the causal world cycle of informative life-death changes:

  • ∆-1: Generation, ∆ºs: growth, ∆st: evolution, ∆t:perception of flows of information, (∆s: Locomotions), diminution and dissolution (extinction)

But with lineal time you won’t understand all those life-death cycles of all systems of space-time, including the whole Universe.

Lines of time, without FORM, INFORMATION, relevant to the essence of what time is, but just as an v=s/t secondary parameter in the measure of space and its ‘locomotions’, DOES NOT reveal the full power of those EFE equations, which are NOT lineal.

And yet physicists keep trying to approach all cyclical motions into lineal locomotions, which is the only time=change physicists study of the 7 sub-species of times=changes, already defined by Aristotle, (which he roughly divided as we do, in changes in the in/form/ation of beings, as evolution, which biology studies; change in the mind position and control of its body-motions, as in process of perception; and so on, again another HUGE field completely ignored by lineal time sciences).

Now if physicists stick to their profession, which is the study of locomotions in physical space, ALL their talk on time locomotions, despite being not that important, is useful and MAKES SENSE, and that is fair enough, but time ‘cycles’ are many. So it is important to understand from the beginning this concept. And have a bit of healthy cynicism about their dogmas.

All those changes=time cycles that trans-form the information of beings ARE also time-space changes, which mankind HAS shunned off as if they ‘were’ a different thing, since Physicists became the leading scientists of humanity, mostly because they became over powerful, as the makers of lineal motions/weapons/machines. But power is not truth. Praxis is not theory. So while acknowledging the power of physicists and the usefulness of their discoveries, as a philosophy of science I am not ‘impressed’ just by lineal weapons and artillery masters’ thoughts, as Galileo pretended.

As it is a new dawn for all sciences, never seen since Mr. Galileo put time to measure space, with huge benefits for our sciences of measure, notably physics and the making of machines and cannonballs. As all sciences use time as its fundamental parameter, and so all have new revelations coming from the switch from time lines to time cycles.

The funny thing about physicists is that they know I am right, because they do know modern physics, when Einstein and Planck, my favs, crashed the delusions of Newton and Galileo absolute space (which was the Plenum, sensorial organ of Yhwh according to Newton) where he put it its creatures on-a-box.  Einstein found there were infinite time clocks. And so he quipped, ‘Leibniz (the discovery of fractal timespace he called it relational time-space, ridiculing Newton for his religious thoughts) is right, there are infinite time clocks on the Universe’. And Planck that the Universe was spiritual broken in in finite parts with energy and motion, and so ultimately we are made of space-time ‘actions’, of motions with form.

So what we say here does ONLY contradict, the already dismissed Newtonian absolute space-time paradigm created by God, as the plenum of his body… Bull$hit. It Corresponds (fundamental principle of truth) and explains further modern physics.


The will of survival: mind actions.  

5d organic ∏ime§paœ ∆ûst arrows exi:s≈tº act, live and survive.

All what we have said can be simplified ad maximal with an equation of survival, Max. e x i ±s=t, that is to maxmize the entropy, information and its balanced combinations in body, limbs and heads/particles.
This simple ‘action’ is what all supœrganisms, automatically, consciously or through some other species, as enzymes of its reproduction, is what all beings do.

We are all knots of discontinuous, cyclical actions of energy and time.

Energy and information have inverse properties. Energy is lineal motion; informations are cyclical forms. Thus both are two types of motion, |-energy and O-information, equal in power and interacting and transforming into each other constantly. This principle of conservation and transformation of energy and information becomes the new fundamental law of science: ‘All what exists is a complementary system of bites of |-spatial energy and bits of O-Temporal Information: E<=>Ti.‘

And that duality of substances/forms/function structures all our actions:

Indeed, all systems are complementary systems with heads that absorb, perceive and process information and bodies that absorb, perceive and process energy.

But the previous graphs and equations refer basically to a bidimensional system and we live in a 4-Dimensional system with 3 spatial dimensions and a 4 dimension of motion, which puts together all the cycles of time, all changes of the Universe (and we shall explain with far more detail, including the meaning of its own 3 dimensions, past, present and future, in this work) Thus the next step of a complete analysis of energy and information is to consider those forms of motion in 4-dimensional space.

 There are only 4 actions of energy and time that all complementary systems perform.

The science of General Systems or complexity describes all entities of the Universe with the same laws explaining the reasons why those entities exist, its forms and functions, its actions and its life/death cycles and reasons why they become extinguished. So its laws of creation and destruction of all Universal species can be considered that ‘program of the Universe’ or ‘program of existence’, which traditionally in mythic terms is equivalent to the concept of the will of God. Yet it is not a personal God-will but rather an impersonal, biological, evolutionary program which reinforces itself through evolution and survival:

Those who do not obey or seek the 4 arrows/actions of the program, which is the strategy of survival of all species, die away, and so the will of the Universe must be obeyed, or else we become extinct.  We are free to deny the program (as humans, we shall see do in this moment of history) but if we do not gather energy and information for our body and mind, if we do not reproduce and we do not evolve socially and interact with similar species, chances are we shall not last too longer and die away. And so the program will be carried further by those who did obey the ‘Law’.

All systems perform 4 actions to survive that define a simple program of ‘existence’, which all species of energy and information follow, to survive. 

The deduction of the program is simple. First, all what exist is an action, which has 2 components, exi=k or exT=k (depending on which self-similar concept you choose information or time) and there are many quantic actions. So all what we can do is 4 type of actions that we shall call ‘arrows or motions of time’:

Those arrows or actions all species made of complementary bodies/fields of energy and heads/particles of information perform to last in time and space will be:

–     ∆E:  They feed on energy for their bodies/fields.

–     ∆I:   They absorb information for their heads/particles.

–      Exi:  They act combining both, and the most common action as we shall see is to combine them both to reproduce you in other zone of space and time and survive after death (or become reproduced by an external catalyzer, enzyme or ‘enzyman’ – machines).

–     ∑ e x I=Ii+1 They evolve socially in more complex networks that survive longer in time and space.

The 4 arrows are ‘necessary’ for any complementary system of energy and information to exist. As any system will die if it doesn’t replenish its energy and information, or reproduce before death.

Further on the 4th social arrow creates stronger top predators, either herds (loose groups of self-similar organisms of the same type) or organisms proper (more connected systems that organize 3 sub-systems, heads, bodies and limbs, specialized in information or formal structure, reproduction and energy, all of them connected by a 4 system, the linguistic system that organize them all).

Consider yourself as a being, which will follow its path of time motions unaware that the sum of them all will be a spent life without anything but a trail of forgotten actions, which only your finite ego commands and understands. What is your freedom? rEALLY NONE, except to think you are free to manage your actions, but at best you would just perform an excellent game by closely following the rules of justice and balance in the golden mean path of maximising your function of existence, max. exi (s=t) the same boring strategy that all systems do follow.

First definition of the Universe

The Universe is a system of networks of knots of actions of energy and time, perceived in static space as forms and organisms, and in time as motions and causal chains of cyclical actions all of them put together into the causal chain of life-death cycles.

The Universe perceived in time is a game of beings performing cyclical discontinuous actions as they switch between feeding, perceiving, reproducing and acting in social networks.

The most important of those actions is the reproductive action that preserves the game, and the most important ‘time cycle’, born of a series of causal actions that chain each other is the life and death cycle, which thanks to reproduction allows generational immortality.

The interaction between beings performing those actions between the limits of life and death causes its selection, extinction, recreation, fusion and fission in bigger or smaller network-entities.

The interaction of all those cycles in perfect harmony can be defined by a single function, which resumes the 4 actions of time between life and death, max. ExI, where E is energy and I information, quantum terms closely related to the universal equivalents, Space and Time cycles; as Space is the sum of all energies and time the sum of all informative cycles, all the discontinuous repetition of the being’s actions which carry different frequencies and intersect each other.

Thus the function of existences is the mystique, final equation of the grand design of what you see.

In this post we will resume in a decalogue those actions, its laws, the forms and functions that accomplish them, how those actions are organized in ages, and how their frequencies and balances define the actions of the main species of existence.

The creation and reproduction of new forms-in-action,informations, existential Spe<St>Tiƒ beings, follows simple rules which can be resumed in the constant reproduction of waves of existences, Max. Exi (s=t) functions, which maximise the energy and information of a domain,  Max. e x Max. I by maintaining a balance and internal communication between its Se and Ti elements, in a point S=T, which maxmize its product.

All thus can be reduced to the function of existence, which decomposes in the basic actions< max. e (feeding moving) max. I (perceiving information communicating) Max. e xI (reproducing) E= I (balance and beauty), Max. ∑ E, I (SOCIAL evolution and quantisation).

The feed back function, E<=>I BECOMES FIRST a static, balanced e x i (Spe=Tiƒ) organic system of two poles and then develops this maximal function, through a series of quantised actions, directed by a point mind that acts as the knot of those space-time cycles, trying to increase them all in quantic balance and synchronicity. It is then the stud of those harmonious synchronous chains of space-time actions, Max, e, i, exi, ∑, what brings us the details of the different functions of existence of Spe<St>Tiƒ, SUPEROrGANISMS & its world cycles, integral zero sum of all those actions, ∫∑ e x i ds dt=0

The discontinuous nature of cycles of actions.

Actions are discontinuous because they happen from time to time as systems require new energy, information, reproduction and social interaction. This creates discontinuous frequencies and formal patterns that relate cycles of actions and information.

We obtain information from those patterns that allow us to describe those actions and cycles.

Any cycle in which a being performs an action has an end in time and a discontinuous, quantic size in space. Thus, the Universe is continuously differentiable during the cycles of time their beings performed, but when the p.o.v. switches its action it has a point of discontinuity, what we see is the trace of those cycles of actions that ‘draw’ the 4 dimensional space-time universe

Beings constantly create actions of energy and time. What you see are knots of such cyclical actions… fabricating time. What we see are the trajectories of beings performing in an alternately causal way their cycles of time. One of the most common cycles is to have a p.o.v. become a focus of a force, which acts as its source of energy and information. A first paradox of Galileo happens here, as we can perceive the point as static and feeding, moving along the field of energy and so we can establish a static or dynamic analysis.

Those points then ill feed along that path and a certain moment satisfied that action will try to fulfill others, and in that switching on and off actions will seem to disappear and new, different trajectories motivated for another action appear. If we see densely packed in time and space those actions they will be sequential and those causal sequences are the stuff that latter (paradox of Galileo) seen as a package of space-time or organism, are the reality we see in its infinite fields.

 The organic whys of the Universe: The 4th paradigm of knowledge.

In the graph, the geometrical perception from Ƽ, the human self-centred perspective (ab.pov) differs from the way we perceive information from the upper scale, seen as an only attractive gravitational vortex of future time-masses (relativity theory, equivalence principle) from the perspective of an elliptic geometry that reduces the size of the whole masses by speeding up its perception as motion.

In the left side the perception of lower scales is a lovacheski’s geometry, which multiplies the whole in its self-similar parts to get to the infinitesimal, which is the ‘piece’ on the membrane of the border o the whole, such as tƒi=∑Spe-1, the infinitesimal components of the membrane. Thus quantum and relativity descriptions of upper and lower scales differ

The Universe evolves from simple light space-time into particles, that gather socially into atoms, molecules, cells, matter, organisms, and social super organisms, planetary systems, galaxies and universes. Such scale means in mystique terms that the Universe ‘loves’ and wants members of the same species to evolve socially into larger wholes that survive better than individuals.

The fifth dimension of space-time (physical concept), the laws of evolution of ‘SPECIES’ (not individuals) into more successful social systems (ants and humans being the most successful animals precisely because of its social evolution) and THE LOVE messages of prophets=historians of the future, who express the law of eusocial love in human verbal terms to make humans understand that survival means to evolve together into a global super organism, UNO/EU style are just expressions of the same Universal law. And this indeed the stuff of this blog: to prove that departing from the simple principles of time, space and social organic evolution we can explain it ALL including sciences, arts and religions and deduce from those simple laws  all the equations, events and species of the Universe.

And so this is the Universe in a nutshell, cracked to see its core, what Einstein called ‘the thoughts of God’. Since indeed the rest, all of us space-time beings are ‘its details’; which important as they are, we study with  ‘stiences’ (sciences of space-time beings), each one dedicated to the analysis of the species of one ‘scale’ of size of that fractal Universe of growing space-time wholes. So what the blog will do is to explain the ‘thoughts of god’ in the first line in a more discursive, easy way; formalising those principles on the second line, to connect them mathematically, organically and logically with all the laws of equations of ‘stiences’, scale by scale in the 3rd line.

Since all what exists has mathematical=spatial properties, (S), logic, casual, temporal properties (T),  co-exist at least in 3 ‘organic’ planes of parts and wholes, your inner cellular world, your individual being and the larger world in which you exist (∆±1) and finally do have a ‘mind-point’ (•), whose ‘languages of information’ stored in cyclical logic patterns, perform the actions of energy and time that ensure the balance and survival of the being, by first mapping out the ∞ universe in the small infinitesimal mind of the being, and then acting on that mapping searching for entropy of motion, energy for its body-wave and information for its mind-particle.


We deaL in the first ‘iteration’ with the immediate truths of mathematics, which are topological and geometric. Let us now introduce the other great field of mathematics, which uses instead of the spatial point, the temporal, sequential, causal number to represent reality. It is to put in GST terms, the ‘holographic duality’ of spatial maths (geometry), temporal maths (algebra), to which we add the 3rd great branch of maths, ∆nalysis, obviously dealing with finitesimals and wholes, the 5D scales.

Line 1

 ∆±i: (scalar, fractal  view):                   5D  Ternary ∏ime-§pace        ¬ Æ points

 ∆º: (mind view):                  do Maximize its ‘function’ of exi≈st¡ence  

S: (spatial, organic view):                 to reproduce as superorganisms     

 T: (Temporal view):                        triping    isomorph    worldcycles

The first line is about philosophy of ‘stience’, and its jargons and languages ‘evolved’ to define a dual entropic/informative reality:

  • Made of dust of space-time revolving in world cycles that for reasons of survival and efficiency organise its form into:
  • Planes of space-time, which are topological organisms, which exists to reproduce ≈ iterate its energy and information ensuring the  survival into the future of the complex organic system.
  • And the formal way to describe those worldcycles of existence as ‘travels through ∆-1 3 scales of the 5th dimension (final 2 posts): Thru 5D planes ±∆t Symmetries.

We do follow strictly in-depth the ternary±0 ∆•st  method that reality has to fully create the complex multi causal, multi-spatial, fractal, organic Universe.

So the upper sentences do have in fact also a 3±0 structure explaining the key elements of the game, its ∆-scales, time-space symmetries and vital, organic nature from the point of view of ∆-scales, S-pace, @-mind and T-ime. And this ‘detailed’ sub-structure of the line is explained in the way we have written it above. So let us consider the first ∆-view of it all.

5D  Ternary ∏ime-§pace  ¬ Points


The greatest achievements of the human mind are generally received with distrust. Schopenhauer

The principle of Unification: A scalar reality of space-time beings.


The reason why we think of time in lineal terms, since physicists made of locomotion the only form of time=change canon-ical to science to measure cannon-balls.

We are all beings made of: Networks of quanta of lineal, spatial energy with motion & cyclical, temporal clocks of information.

And so to start with a truly comprehensive time theory as the one provided by 5D metric equations requires to explain besides ‘physics of time’, biology of time, and further on study historic time, which as we shall see is close to biological evolution than to physical time-measure. Space then appears to us as fixed, still or at least with less motion than time.

But then there is the fact that all systems of measure of time are cyclical, even those used in physics. And so we must also define time in terms of form, of in-form-ation as cyclical motion.

The Universe and all its parts are made of ‘dust of space-time’, ‘fractal non-euclidean points’ of spatial entropy with speed, with ‘lineal motion’ and temporal information, with form, with ‘clock curvature’, which come together in ever more complex networks, ‘weaving’ the systems and structures we see around us.

The biggest error of science is the concept of an abstract mathematical, Cartesian ‘background’ of something independent call absolute space and time, first defined by Newton, opposed by Leibniz and finally dethroned by quantum physics, who found space to be broken in pieces with ‘energy-motion’ and Einstein, who found different regions of reality have different time speeds.

Thus we are NOT in a background space-time frame of reference set by Yhwh, as Newton thought, to put in all its creatures, but rather we are made of spatial energy and cyclical clocks of temporal form, information, as when we say ‘I don’t have enough energy and time to do this’. And for that reason when our clocks of time stop (telomeres in cells, age in life), our existence stops, our ‘time’ runs off. And for that reason, when another entity, a ‘predator’, cuts through and occupies our limited vital space, breaking the membrane that closes up, our organisation as a space-time being enters in disarray and our fragile web of space-time dust, organised into a super organism collapses, and we die.

 But what is an organic system? The answer was not clear mathematically, till the discovery of fractal mathematics in the 1970s. Hence because the organic paradigm lacked its fundamental tool of study, a mathematical, logic language to add to the other properties of organisms, discovered earlier in biological and social and logic, mental languages, the fractal paradigm has not made it into the mainstream discourse of philosophy of science, changing our worldview, from the obviously outdated mechanist, entropic vision of the Universe sponsored by physicists for 4 centuries into the much richer in meanings, reasons and answers, paradigm of fractal organisms.

It is then necessary to change the underlying paradigm of science, and upgraded it to ‘stience’, that is the science of fractal space-time beings. Of course, as all descriptions of reality are relative truths, with a certain distortion, the scientific analysis, made till today with that single frame of lineal time and single space continuum, works to make measures in reference to the fixed space-time background, but the cartesian space-time continuum is an ‘artefact’ of measure that has obscured completely our understanding of the ultimate principles of science.

But what is an organic system? The answer was not clear mathematically, till the discovery of fractal mathematics in the 1970s. Hence because the organic paradigm lacked its fundamental tool of study, a mathematical, logic language to add to the other properties of organisms, discovered earlier in biological and social and logic, mental languages, the fractal paradigm has not made it into the mainstream discourse of philosophy of science, changing our worldview, from the obviously outdated mechanist, entropic vision of the Universe sponsored by physicists for 4 centuries into the much richer in meanings, reasons and answers, paradigm of fractal organisms.

This paradigm was born as a ‘wishful form of thinking’ in time of Aristotle, who wrote in his ‘Organon’ the first reasoned philosophy of science, hence rightly considered the founder of logic, biology and the experimental method. Then Galileo completed the method with the addition of mechanical instruments of measure, but also reduced in its scope by making mathematics the only authorised language of science, and reducing the organic clocks of the Universe and its world cycles of creation and extinction, with the 6 canonical motions of time=changes in the form and position of beings – generation, evolution, growth= reproduction, locomotion, diminution and extinction.

We shall use often as a reminder of the cyclical, discontinuous nature of time, instead of T, ∏, which means ‘pi’, the symbol of the cycle, it breaks the T into 2 pilars as ∏ime, the discontinuous factor does with nature, and it is associated to the product, which as we shall see is the mathematical trademark of Time processes, connected through several ∆-scales (hence if ∆ has n elements, ∆-1 will have n x n) as opposed to ‘superposition=sum’ in spatial ‘herds’.

Science has completely missed the most important of those WORLDCYCLES OF TIME: the world cycle of creation and extinction of systems, which makes them evolve from seminal seeds into larger, slower organisms and dissolve back in the moment of death.

TIME tends to be as in the 3rd graph an accelerated, cyclical informative shrinking clock that ‘warps space into time’, ‘wrinkles life into 3rd ages’ and ‘corrupts societies into entropic wars’, as when all the entropy=motion is consumed and the system is pure form, the system explodes back into pure entropy in the moment of death.

Because we are beings made of vital space with motion and cyclical clocks of time with information carried in its frequency and form. We are time space beings.
In the graph, we are networks of vital space, made of ∆-1 atomic or cellular space quanta, surrounded by time cycles, membranes of finite volume of information (holographic principle), that create our ∆-being; which then will be performing further time cycles in larger networks, as part of a bigger ∆+1 whole or world.

The interaction of those 2 elements, vital space, lineal motion, entropic, kinetic energy, res extensa, all similar concepts abbreviated in the symbol ‘Spe’, and cyclical, tall, time clocks, membranes, closed paths, Tiƒ, which carry the information of the Universe, across 3∆±1 scales, structure all systems made of fractal ‘space-time’ that ‘thinks, therefore exists’ as a world in itself.

It is then easy to connect with the perennial dualist philosophies of the Universe those 2 Spe<=>Tiƒ concepts in a reality that constantly transforms lineal entropic motions (E) into physical time vortices (M, charges). So we talk of  beings made of energy with forms, which will be the 2 similar concepts to space in motion and cyclical time clocks with more dimensions of information, the fractal spaces and times of which we are all made.

So what is time? We have two versions of its widest meaning: time as change, and so all type of motions can be defined in terms of time, of which Aristotle defined 6, generation/evolution, growth, reproduction, locomotion, diminution and extinction. So physicists study one of those motions, locomotion. Biology most of them in its dualities (growth and imitation, reproduction, generation and extinction). And a 7th one he did not define as motion, called perception by a still mind which ‘is the focus of the motions of the world around it’ (so it is the external motion and focused flux of informative waves what causes perception)… In that regard yes, nothing is MORE IMPORTANT THAN EINSTEIN’S work to understand…. locomotions at c-speed. But i doubt you will ever learn anything about your existence and changes (generation, growth, evolution, etc.) only with locomotion. As it is in fact the simplest of all the motions=changes of the Universe.

The next step of the metric is the Generator equation of space-time systems.

Ok, maybe before everybody abandons this blog with an attitude, to state that I do have a problem with physicists as my ‘known-known’ career has been as an activist against the Nuclear industry, but i have none with the Universe and its awesome logico-mathematical time-space structure. So before going further into concepts and biological and social analysis, it is about time to put a bit of mathematical quantitative numbers, and logic formalism on it, as it is at the core of reality.

So we shall state now that as GALILEO said: the ‘main’ (but not only) language of God are geometrical figures, (he didn’t say mathematics but geometry – important detail): lines, triangles and circles. He could have said also ‘hyperbolic waves’, but of course he did not know yet.  So we shall say here:

‘Because we are all made of scalar space and time, form and motion, 3 are the underlying fundamental stiences:

  • Geometry with motion, which is called topology, the formal stience of space forms.
  • Analysis of finitesimal parts and wholes, which is the formal stience of the scales of the 5th dimension.
  • And i-logic causality, based in the 3 arrows of time, which I call often ¬ Ælgebra, or simply ¬æ, connected to logic, algebraic structures and time theory, but so much r=evolved respect to single-entropy theories that in the hard models of it, we shall not use much of contemporary algebra beyond group theory.

But how we express in a logic formalism (mathematical details are obviously the final analytical phase of a synthetic theory, kept for line 3) all those similarities? Again it is quite easy once we realise we are not in a background space-time ‘mathematical’ cartesian graph, nowhere to be seen in reality – what we see and experience is that we are made of entropic space, informative time and the vital space that mixes both (the intermediate body-wave).

In that regard, we must consider that all systems are made of:

|-Spe (limbs-fields of spatial entropy) < ø-iterative body-waves > Tiƒ (particles-heads of temporal information)

which becomes the ‘Generator feed-back equation of all space-time systems/beings’ of the fractal Universe.

So we will use the same abbreviation, GST, to define the formalism of the 5th dimension with the Generator of Space-Time and the conceptual ‘stience’ behind it, General systems theory.

It is then a fascinating adventure of the mind to study the common laws of all systems made of fiefs-limbs of space≈entropy and particles-heads of cyclical time, merging in hyperbolic body-waves that iterate the system, as we will find the 3 kind of stiences and systems, physical, biological and social follow the same 5D laws of structure, topology, energy, information, function and form.
In the graph we resume all physical, biological and social systems, which ensemble the 3 ‘topological forms/functions of space-entropy, time-form and its body-wave combinations into real ‘existential beings’, as we are all made of space and time.

And this fully connects organic evolution with topology since in those are the only possible varieties of form of the Universe. So ultimately all what exists is a ‘living topology of space and time’.

So what is the ultimate causal relationship of those 3 arrows. Initially it is a simple equation:

  • Past (entropy limbs/fields) x Future (informative particles/heads) = Present-iterative wave/bodies

It is a deep equation, which for the time vein merely means that the informative particle-head and entropic field/limb become connected by the dominant body-wave element of the system, the most visible and relative dynamic unchangeable present, as it keeps reproducing the system as if it were always ‘the same present form’, even if the parental element has died away.

So there are 3 elements in topology: entropy-pure motion or lineal space; form-pure dimension/curvature or time clocks. And its combinations, space-time beings.

The 3 arrows=motions of times in sequential order.

this ternary ‘reality’ in ceteris paribus analysis is  made of 3 pure time motions. Entropic expansive motions, repetitive body-waves and informative, time vortices. BUT when we put them in sequential order as it happens in beings it gives us a sequential world cycle of an organism as it lives and dies through existence.

Suddenly I realized, I had solved the way the universe created its beings, from the mystery of quantum physics, (the so-called wave-particle duality, as all physical systems were wave-particles moving on an entropic, accelerated field), to the reasons why evolution always worked right, choosing despite its seemingly infinite options the few ‘efficient’ aforementioned topologies (so wings were flat energetic members, and eyes spherical ones).

Namely they were the only available choices of topology. Alas! Curiously enough the great ‘mystery of Darwinian biology’, which he had also wondered about – the ‘right choices of the seemingly chaotic process of evolution made sense, because after all there were a mathematical planning NOT of course a religious design. And the biggest Mystery of Physics (the complementarity wave-particle) also became resolved.

And this was to me the proof that I was indeed on the right path of T.Œ, because the 2 principles of truth, ‘Simplicity, Minimalism (Occam’s razor)’, and Correspondence (a theory proves previous ones besides bringing more solutions), were met.

Equations of physics and biological designs kept pouring into the model and finding its whys, fitting all nicely. Something scientists did not even try to understand merely describing it now had easy whys, in the ternary symmetry in time and space of the Fractal Generator of the Universe, truly the ‘Equation of God’, not a ‘Particle of God’, not a ‘substance’, but a Logic, mathematical Symmetry of space-time that created us all, the details of that ‘thought’.

But if we were made of time-space cycles and forms, of this ternary ‘Generator’ structure seen static in space as a formal organism, and moving in time as a series of cycles, it was necessary to analyze each of those 3 parts of all beings, and decide its inner structure and hierarchy.

Now, I am afraid we are going to refound also logic. I know I’m nuts. But what can I say. We cannot go further without a new logic, because if time has 3 arrows, then the simple A->Causes b does not work. It is more about ternary logic and symmetries in space, time and 5D. It is more about the GENERATOR fractal equation of the universe and its infinite variations.

So Non-A logic is a huge new science – the study of the symmetries between the 3 motions of time and its sequential ages and the 3 spatial forms and its organic parts. Its ‘Generator feed-back equation’ will be essential to describe all the beings of the Universe:

Γ.   Sp (young-past-entropic limb/field) ≤≥ ST (iterative, adult, present wave-particle) ≤≥Tƒ (future, informative head/particle)

Where the symbol < means an expansive, energetic motion, > an implosive, informative one and = a repetitive present motion.

So all systems of nature will be made of those 3 elements, whereas the present body-wave combines lineal fields (faster motion) and cyclical heads-particles (since the sphere is the form that stores maximal information) or in the ‘second fundamental state of nature’, will be made of S-fields/limbs<=>T-particles/heads as particles absorb the field entropy and move.

This first differentiation between an S>T System (particle-field) and an ST-wave-system WILL be enormously important to understand from quantum physics (Bohm’s classical interpretation in polar=particle coordinates of the quantum potential field that guides the particle, vs. Schrodinger wave description) to gender (women are present waves, men are particle-fields:)

Indeed, that equation seems simple, but as we fully understand the conceptual meaning of those worlds so ill-defined in science (particles, waves, time, space, energy, information, entropy, etc. etc.) a fascinating new ‘form of homologic knowledge, with deep insights on the unity of it all will come to the readers.

So this equation of ‘ternary topologies of space and ternary ages of time’, which call the generator fractal of space-time beings will be to XXI century space-time studies, what EFE was to XX century – the next step in the evolution of our comprehension of the fundamental principles of Nature.

Indeed, essentially this equation UPGRADES the principle of conservation of energy to include  the co-invariant conservation of the 3 elements of reality: pure motion or entropy, pure form of cyclical time, and its energetic combinations.

And further on, breaks the space-time continuum into infinite ‘infinitesimal’ fractal parts made to the image and likeness of the whole: all of us space-time beings, made of energy and time, as when we say ‘I don’t have time and energy to do this’.

And so as a consequence of those 3 elements we shall describe a fractal, organic, informative ‘sentient’, living universe.

  • And so the key to understand reality is to consider ‘formally’ that the fractal scales of the Universe form all together a new ‘5th dimension of scalar space-time’, whose metric equations and properties that relate different scales of ‘size’ and speed in the clocks of information of its ‘systems’, truly are the ‘hidden variables’ and ‘whys’ that give us an explanation to reality much deeper and complete that the present system of physical sciences, which study only as relevant the properties of entropy and ‘locomotion’. Whereas the proof of this dimension is reality itself, as it is evident that there co-exist in such Universe from the smallest atom to the largest galaxy a series of beings, which are similar. And so we talk of a fifth dimension of scalar size, which is philosophically a dimension of social evolution, of ‘absolute time’ as points reproduce its fractal form, organise themselves into networks and create new growing scales of the fifth dimension.

So instead of a simplex world of physical motions and entropy as the single arrow of the Universe we shall construct a complex world with 2 arrows of ‘time’, entropy and information, which ware akin to space and time (to yang and yin in classic philosophy), and combine in ‘present body-waves of energy’ (yin-yang beings if we were to use the philosophy that better described them).

So entropy and information and its space-time, ‘energetic body-wave combinations’  will become the dual and then ternary principles that structure all the systems of reality made of complementary fields/limbs of entropy and heads/particles of information, which combine in ‘present body-waves of energy’, and the 3 together create the infinite ‘yin yang’ beings of the Universe.

‘Fractal scales’ (ab.∆), topological space, (ab.S) and time cycles and ages (ab.T).’, understood in terms of human mental languages of thought (Ab.•, @,º), mathematics the language of space and logic the language of time, thus become the 4 elements needed to describe reality:  ∆•ST.



We say that there are 2 arrows of time, information missed in Physical Models. So if, for the sake of simplicity and the principle of correspondence between old and new theories, we consider ‘entropy, the arrow of past-time, we shall call Information the dominant arrow of life and future, the ‘fifth dimension’ of time and study in depth what it means, and how it applies to reality.

First the obvious fact that information it is the future can be proved by several concepts. In brief: it is the future because particles and heads guide locally bodies and waves, so they anticipate the future of the System. It is also the future because informative species win the struggle for existence so less informative ones become extinct. Thus both in the physical world and the biological world, more informative species dominate the future.

The galaxy is dominated by the ‘only informative’ pure force, gravitation that in-forms, attracts and forms bigger wholes, and so black holes dominate galaxies and end up eating it them into dark matter. While humans dominate life, and have developed the ‘arrow’ of information more. Which leads to the concept of parts that become social wholes through a common language of information creating super organisms. So black holes form with gravitation, galaxies, super organisms of stars; humans form societies, super organisms joined by legal, informative networks in the human verbal language; company-mothers of machines form with digital money super organisms of re=production of ‘mechanisms’, and finally the most informative insects, ants and bees form super organisms sharing a language of pheromonal or magnetic visual information. And they survive into the future better as superorgansms are stronger and more intelligent.

It finally follows that the arrow of information which defines a fifth dimension of scales in the Universe is the future, because a whole needs its parts to appear ‘first’, to build over them. So larger organic wholes are the future arrow of the Universe.

In the graph, the fifth dimension of scalar space-time and its dual arrows of spatial entropy (ab. S, $pe), studied exhaustively by physicists and temporal information, Tiƒ (grossly underated and misunderstood, as the view of a Universe with a single entropy arrow dominates physics). The interaction of those 2 arrows, in fact, create the complexity of the Universe, which CANNOT be explained only with the lineal entropic motions of simplex physical models of the universe, only apt to describe the simplest scales of space and matter.

All systems of the Universe can be studied with that simple, fractal generator, but to do so, we must be aware that those beings, made of ‘atomic or cellular’ fields/limbs<body-waves>particles-heads have also a ‘scalar, network, social structure’, as those 3 topological parts, which are the ONLY 3 forms that exist in geometry (proving further we are all beings made of the 3)  are in fact what mathematicians call topological networks, shaped by the ‘atoms’ or ‘cells’ or ‘citizens’ of the physical, biological or social systems integrated into hole organic beings:


So we talk of a scalar, organic, fractal Universe in which parts become wholes through networks of entropy, information and energy. For example, your nervous, digestive and blood network, or the vacuum entropy, energetic electromagnetic field and gravitational≈informative force of the Universe… Thus we can build the Universe as a series of scales of growing network size, which all together form a new dimension of scalar space-time.

The organic description: Biological properties.

5D structures are based in social scales, not only on the lower scales of the graph (physical systems) but also on the middle and higher scales, as ‘social systems’, which can be described mathematically (as numbers are just social groups of indistinguishable clon beings), but also organically, as networks of parts that become wholes, because the scales also apply to biological systems and HISTORIC and ECONOMIC super organisms (civilisations, nations, company-mother of machines). This organic description is far easier to understand: ‘fractal points’ (any being) become social numbers joined by networks that deliver motion≈entropy and in/form/ation, to all the systems and in this manner systems grow from parts into social organisms.

And this can be expressed with mathematical numbers, or algebra, with topological networks or geometry and with ‘finitesimals’ integrated into wholes (analysis), which are for that reason the 3 sub disciplines of mathematics.

But also with organic, physiological networks, which deliver motion (limbs, digestive systems, raw materials), information (nervous, legal systems) and combine them to reproduce with energy the whole system (financial, economic, and blood, hormonal networks) which are for that reason the 3 networks of all socio-biological systems.

So in history the most efficient nations are super organisms properly designed to take advantage of those laws.

So we shall unify with so simple truths all the scales of the Universe, each one explained by a science, by fusioning the biological and mathematical properties of the Universe, which are two jargons, one quantitative the other qualitative to describe the same laws; as the ‘languages of God are ∞’ (Upanishads), but all have the same ternary structure to describe the same game of creation of parts into wholes – and needless to say we can also ad the mystical language of eusocial love of religions, which express in our verbal language the Universal mandate  for all beings: grow=evolve into wholes and multiply your finitesmal parts.

So the organic description parallel to the topological one, talks of similar beings connected through PHYSIOLOGICAL NETWORKS, that ideally deliver energy to all cells (blood, money, digestive systems) and co-ordinate them with faster nervous/electric/legal information which synchronise the motions of all those parts.

Never mind humans are so bad at designing their super organisms of history that we are the only system that does not deliver free oxygen/money to all its cells, but lets them die of anoxia, and do not emit just, synchronous laws to all citizens to work as a whole, but divides people into castes; and so such ill-designed human super organisms live short and die in entropic explosions of war.

The physical description:  Energy scales

But how we are so sure, the scalar structure of the Universe define a new dimension of space-time? Easy. Let us just check the most authoritative definition of a dimension, from XIX c. mathematician Klein:

‘A dimension of space-time exists, when we can move through it, while leaving its parameters of space and time co-invariant’  Klein, on the expansion of Non-euclidean geometries and its new dimensions.

What this means for example is that when you move up and down, your parameters of size in space and inner time clocks remain invariant. So ‘up and down’ form the height dimension.

SO HAPPENS when something move through the 5th dimension: when it grows in size it diminishes the frequency of its time clocks, from the simplest entity, a ray of light that literally grows, diminishing the frequency of its wave-length to humans that emerge from a fast seminal, evolving fetus into the slower rhythms of life, which can be formalised as a journey traveling between scales of size of the 5th dimension, from seminal birth, to emergence as an individual part of a larger, slower social world, or supœrganism (œ, ab. super organism), its nation and civilisation, returning back to the cellular aggregation that we are, in the moment of death.

Present Energy. The equations of physics.

Each of those scales of reality is made of smaller quanta, which have a peculiar property: their cyclical motions run faster the smaller they are, but the product of both (Spe & Tiƒ) remains invariant, creating a metric equation that defines the 5th dimension:

Γ.             Past-entropy:     Spe           x      Future: Information   Tiƒ     =      ∆ST = Present body-waves of energy

This simple equation that shows the product of the time clocks of a system and its size to be invariant (hence allowing travels through the 5th dimension, as when you are conceived as a seminal cell with smaller size and faster time clocks and grow=travel in the 5th dimension till you emerge larger and slower), is poised to become the most important equation of XXI century science, which will correspond with all the main equations of all the different sciences, each one studying a scale of the fractal Universe.

We see 3 physical parameters of those 3 arrows: entropy, as the minimal space-quanta of thermal scales, light speed, as the iterative present arrow of quantum space, and angular momentum, as the O-arrow of the same scale, which transcends into the gravitational concept, for gravitational orbits. What matters thus to localise a parameter of entropy/present space time/ or cyclical motions, is its topology that transcends scales.

Why then energy=present can be equalled in the 3 scales of the organic Universe? This is the strongest prove that the Universe is connected through the metric of the 5th dimension; as it shows the 3 ∆±1 scales equal in value of ‘energy’ and co-existing with different Tiƒ parameters (T, M, V) and 3 different Space quanta (k, h, c). So ENERGY is ultimately the ∆-constant of the immortal Universe

Let us then in more detail the 3 components of each system of the Universe, starting with the more important,  cyclical time of which lineal time is a mere simplification, to allow ‘frequency derivatives’, t=1/ƒ.

Now it is obvious that body-waves transport more of the energy of a physical or biological system, and the working re=productive middle class of society provides most of the work≈energy of the system. So again we must realise always the ‘symbiotic parallel levels of the organic Universe’ and how its properties reinforce.

Energy is in fact obtained adding potential energy (of position hence of form, of in-form-ation) and kinetic energy of motion, hence of ‘entropy’. but information matters more:

So a static mass does have potential energy, and to calculate it, you multiply the motion of the in-form-ation (the mass) only by the vector component that runs in the ‘formal path’ of the mass.

And when you close a path of lineal motion into a closed cycle of information, ENERGY IS CONSERVED IN AN eternal UNIVERSE WHERE PRESENT ENERGY EXISTS FOR EVER, as long as it closes its paths into clocks of temporal information (something only Feynman, among physicists seems to have noticed, when he quipped that energy and time are seemingly the same in its closed paths).

Now this is just the very surface of the r=evolution of thought which makes uddenly all quantum entropy only theories a thing of the past, both literally (entropy is past with no information in relative terms, and absolute terms as ultimately death-entropy is just a moment, an explosion, but time-information runs the whole range of existences).

And we shall explain much of it. It is though needed for you to realise that entropic earlier PHYSICISTS ARE not the ‘holders of absolute truths’ .

Why the fifth dimension is the dominant arrow of futures.

In the graph the space-time planes of the Universe, ∆±i , which according to scale structure the 5th dimension in parts that become wholes, and since wholes come after parts, which must exist to sustain them, we talk of a temporal absolute arrow of future, regarding its ∆ scales, such as ∆-1 will always be the relative past of ∆. The Fractal, organic structure of the Universe in scales of size is what we call formally ‘the 5th dimension’.

As we study in depth all the elements of the scalar Universe, a fact will surprise us; when we try to localise ‘mathematically’ the fifth dimension. As it will turn out that it encodes the algorithm of time, all the potential waves and particles of time, possible, according to a probability related to the ‘closeness’ they follow the program of the algorithm. 

But that is far way out, for advanced 5D students along the century (-; For now we shall try to keep it simple, and explain you why the 5th dimension encodes all the flow of time, from ‘past-simpler space’, through present (the human scale of perception) into future, with multiple probabilistic paths, which do collapse at a point in a single future->present->past.

It follows from the fact that the simple, iterative scheme of evolving from individuals into universals – from social evolution, that there is a new dimension of time and information more than space & entropy, which in poetic terms we can call the dimension of eusocial love, which is the arrow of future of the Universe, in as much as those ‘whole’ new scales need casually to have its parts born ‘before’ (logic meaning of causal future); and because they survive better as wholes, stronger than individuals (biological meaning of  evolutionary future).

Same happens in human societies. Since those nations, which are able to share efficiently and justly energy and information among its individuals, do NOT collapse in wars and r=evolutions. It follows that we can deduce from the general laws of systems ‘stiences’, the laws of social sciences that could create an efficient, just perfect human world.

But as we shall see when study in depth some specific systems, in as much as those scales co-exist in the same ‘space’, they must be displaced in time, to be part of reality, due to a simple ‘Pauli exclusion principle’, better known in physics than in other systems. There are indeed forms equal in information-time, which occupy then the same region of space (bosons) and forms with different information-time, which occupy different regions in space. This rather mystical fact will have enormous consequences for the motions on the 5th dimension, we shall explore in depth in different posts.

We can say in that sense that the ‘physical existence’ of those scales and its parts are displaced in time; through very real but ‘spooky effects’ (resonance, simultaneity, synchronicity etc.) which in the more formal parts of this web we shall explain with enough mathematical rigor to connect it with classic science.
The integration of all sciences under similar laws is the goal of Philosophy of Science achieved by the organic, fractal models of Systems Sciences or Complexity (ab. GST: General Systems Theory), which explores how ‘parts’ come together into wholes, through networks that share its energy and information.

So physical, ∆=1,2,3, 7, 9 systems evolve from particles into atoms, molecules and states of matter, through in-form-ative, gravitational networks, exchanging energetic, electromagnetic flows.

Biological systems, ∆=4,5  evolve from molecules into cells, organisms and social super organisms, through genetic networks of information and golgi and blood networks that distribute energy to all the cells of the system.

And human beings ∆=4,5,6 form social super organisms, join by verbal, legal networks of information and economic networks that re=produce the welfare, energy goods our species need to survive.

Finally company-mothers of machines, ∆=5, 6 evolve into a global super organism, ruled by digital networks of financial information, (prices, salaries, stocks, internets) and energetic networks (roads, electric lines).

Now an important ‘prime’ about the 5th dimension of space-time.

Now this is the ‘Non-Euclidean, expanded geometry of the fractal world’.

What about its non-aristotelian temporal logic of multiple ‘time clocks”?

This again must be also understood from the beginning. And the easiest way to do it is with the so called holographic concept.

Because the change of paradigm implies huge changes in the underlying truths of the universe and the old simplistic human ways of thought, so as we change the concept of space and break the continuum into infinite scales of non-euclidean growing points. We must explode the concept of a single time-duration into infinite time cycles of a finite duration, as the cycle of life and death of all beings.

But when we convert time into a cycle, we must add a new dimension to make the cycle. A line is one-dimensional, a cycle two dimensional, it has ‘height’. So where we get that second time dimension? I just have said it: in the height of the cycle. It is the holographic principle, a trendy word physicists coined without proper understanding – as they found that information is bidimensional. And indeed it is. Information is carried as in a computer that measures in hertz its in-form-ative power in the form of time cycles, and the faster a time cycle turns (remember there are multiple clocks and multiple speeds of its beats), the more information it accumulates.

But if information and time is now bidimensional, so must be space, flat planes of bidimensional space, made of networks of points, each point a cell, an atom, a galaxy… part of the bidimensional plane.

The proof of this of course is also available for decades. We have found the Universe as far as we see it is a flat plane, made of cyclical clock-like vortices of time, called galaxies, where information grows as the cycles accelerate towards its central black hole, and the rise in height around the black hole, towards its tall singularity.

General Systems sciences therefore is the formalism of the ‘alternative, far more advanced philosophy of science’ to that of Newtonian physics, with its concept of a single background absolute space-time in which entities like-mechanisms, whose ultimate substances are ignored, move in simple lineal motions.

In general systems sciences, as Leibniz affirmed, and then quantum and relativity proved, we do not exist in a background, abstract space-time mathematical plane, but we ARE MADE OF clock-like bits of information of different speeds (time relativity) and fractal, moving quanta of spatial energy, which are complementary systems (quantum theory), co-existing across 3 relative scales of the 5th dimension. So all systems can be described with the same laws, derived from the properties of spatial energy, temporal information and the metric of the 5th dimension, which together give birth to a set of 3 x 3 + 0 ‘isomorphic’=equal laws, which describe the ‘existence’ of all beings. For that reason we call also the Fractal Generator, the Function of Existence.

As we all beings follow a ‘world cycle’ of existence, made of a series of actions of absorption and emission and reproduction of energy and information, which might vary in quality and quantity but are essentially the same process for all beings of Nature. So in Gst, we go much further than a simple shallow, external description of the motions of beings, as physicists do, fully exploring all the whys of reality, with all the languages available to human thought, in a jump of understanding that should start a new age of knowledge, once the model is fully related to the details and specific laws and jargons of each science.

It must be understood that if the formalism of GSΤ is verified as all seems to prove by the laws of the scientific method, it represents a remarkable change in our scientific look of the Universe, unlike anything that has happened since Einstein and Darwin and Copernicus, made previous extreme revolutions of human thought, regarding the nature of time and the cycles of existence of its beings. A change of paradigm of course does take time, but it is unavoidable that humans and its growingly organic machines, do that jump of awareness about the full properties of the Universe, which go well beyond the reductionist view of putting on it a mirror with a single motion of time, entropy or energy, as physicists do.

The Universe constructs super-organisms, through a causal process, departing from simple, amorphous flat surfaces of energies – herds of Non-Euclidean points with lineal motion.

It is a simple ternary causal event, which is different from the causality of what we call the cycle of life, Sp->X->Tƒ, yet still an essential chain that we shall see constantly in the Universe.

So the next question is how the universe constructs reality, departing from its generator equation. And the answer is: constructing superorganisms, in a causal order, e->∆->X->S.

A form fractalizes, becomes in-formed, and loses energy= speed=motion. For example, a line becomes a Koch fractal or breaks into a Cantor dust of self-similar cells; a line becomes a p∆-cycle. In this, simplest and most repeated Sp->Tƒ, we can write 1->3>Pi: a line has reproduces from past to future 3 self-similar motions, then it coils into a p∆-cycle.

The next stage would be then the reproduction of that cycle in a lateral, new dimension of height. In this manner, we have obtained 3 fractal iterations: the line has become a cycle (or a Koch curve or any other fractal topology with more form and dimensions), which has become a tube.

Sp->Tƒ->X (symbol of Reproduction and sex, born of the product and combination of Sp X Tƒ).

If duality covers simple events, mostly SpTƒ combinations, when we construct an organism we are playing at least with a causal 4-sequential arrow of time, Energy becomes fractal information, which reproduces laterally and so the light of length-speed becomes a time cycle with rotational speed w, whose frequency curries more information, and such form moves like a Maxwell scree reproducing in the 3 dimension of width. Sp->Tƒ->X.

Yet, this rather mechanical sequence of creation of a fractal 3 dimensional Universe becomes far richer in forma and meaning when we add the 4th Eusocial love, of Social time the longest arrow that finally creates a form of stable space-time that exists, a superorganism: Sp->Tƒ->X->SP X TƑ. Since as time goes by, entities evolve into more complex organisms by the power of love – by sharing energy and information in social networks. The 4th arrow of time evolves socially parts into wholes, waves, herds and organisms:

Particles gather into atoms that evolve into molecules that associate into cells that gather into organisms that create social networks – planetary ecosystems, which are part of solar systems, herded into galaxies that form Universes. Those processes of social evolution occur thanks to the creation of social networks among self-similar (hence reproduced) beings, in search of the same type of energy (hunting herds) or information (organisms joined by nervous/informative and blood/energetic networks).

Thus, the arrow of organic evolution derives from the arrow of information that allows entities to come closer and ‘act in parallel’ under the command of an informative language, which we formalize with the social symbol, S. And its reason of existence is to elongate the survival of the organic system: Any cyclical vortex of time accelerates inwards, losing energy/surface as it increases its informative speed.

When we generalize that concept to all Time-space systems, it turns out that the arrow of information dominates the universe, wrinkling and warping any cyclical system, which will exhaust its energy, converted into form. Thus, our time clocks and vital spaces increase constantly their information, diminishing its energy space, towards a 3rd age of excessive warping and limited energy that will not last forever.

Since the cycles of exchange of energy and information, the geometric beats of reality between expansive and implosive, entropy and informative states, are limited in their repetitions by accidental errors of all kind, which establish the need for reproductive and social arrows in order to ensure the survival or immortality of those ‘patterns of form’ – entities made of lineal fields and bodies of energy; cyclical particles and heads of information, who must be reproduced to ensure a longer existence. This means that only those species able to increase their existence in time by reproducing its form and in space by evolving socially into bigger entities survive.

Recap: The 4 main arrows of time cannot be reduced without losing detail, but they can be philosophically and ‘bio-logically’ grouped as ‘organic systems’. Those organic systems that synchronize accumulate and organize clock-like arrows of cyclical time, are in fact all self-similar, as all can be described with the 4 elements, ∑S<=>T of organisms: cells, networks of energy and information and reproductive systems.

Dark space: cat alleys and parallel Universes.

Now, each super organism is a network because it has an enormous amount of dark space-times it does NOT see, the cat alleys which the mind does not neeed.

Discontinuity is essential to pangeometry and the continuity axioms no needed to build them.

The i-logic of Non-Aristotelian, Non-Euclidean geometry, of the ternary causality of a π cycle, made of 3 diameters in its perimeter means that the diameters of the protective membrane blind the system, who only sees what its connected sensors see.

Thus the 3 diameters in the simplest 1-sphere system (a disk) cover 96% of a pi-perimeter surface, letting the point of view in the center, see only a 4% of light, through the holes of the membrane, leaving π-3/π 96% of dark matter for the logic mind to see without the glaring of light.

This is in fact what we do NOT see of the Universe across the halo membrane of our spiral galactic disk (proportion of dark energy and matter).

So we can consider that our electronic eyes miss 96%, which is the volume beyond our perceived scales of the 5th dimension, which however exists in the larger russian doll of gravitation.


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