±∞ ¬∆@ST:

‘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.

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 purpose of Non-Æ mathematics is clear: to vitalize the foundational concepts of mathematics, to make them reflect better the 5 dimensional motions or actions of reality (Dimotions): entropy, motion, perception, social evolution and reproduction.

At present mathematics in its abstract forms, treated in all other previous posts, can be closely related to the vital Universe in a painstaking illustrate of its main components and theorems, which unfortunately will always collide with the @entropic mind frame of mankind which denies the complex Universe to come on top and mirrors it with its mind frame, and simplicity, so it loves ‘simplex explanations’ of it; instead of trying to mirror its mind with the complexity of the Universe, and further evolve it. 

Now humans are what they are, and you are not going to get them out of its æntropic mind view. Nobody of the few huminds, which have gone further, which are hardly a few hundred of them, from the Axial masters to the very few you could put on that category on the modern western culture (people like Leibniz or Einstein, Picasso or Beethoven, Darwin or Spengler)…


Generational spacetime 


Each advanced language of reality thus CAN BE UPGRADED, AND IT WILL BE UPGRADED IN THIS BLOG, TO A PENTALOGIC ANALYSIS in its basic Grammar.

Why the Universe is pentalogic should be obvious to the reader. Its fundamental element are the 5 Dimensional motions of space-time – the 3 usual dimensions classic science considers spatial dimensions, plus the two scales of space, ‘above’ (social evolution) and below (entropy), them (of the organic whole and parts of the system). Yet in reality space dimensions correspond to time motions, as we cannot distinguish motion from form (Paradox of Galileo, we see the Earth still but it moves, so motion can either be perceived as such or a a dimension of space). This means essentially we can consider always a spatial, dimensional still view; a motion, time view, or a space-time ‘dimotion’ combination of both. Let us then define in its 3 ‘ceteris paribus, spatial, temporal and space-time analysis reality’ to set the main 3 descriptions of ‘pentalogic’ that studies the 5 elements together:

Motions are perceived by minds that stop motion into form, into information, as distances. So if we see slow motion in the night a light it seems a long distance. Distance and motion CANNOT BE distinguished so they must be taken as two side of the same being, a Space=time ÐIMOTION (ab. Dimensional Motion):

S= T; Dimension-Distance = Time-motion = ST Ðimotion:

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.

For a slow mind the Earth will seem a disk, denser the faster it turns converting its full worldcycle of time into a form of space. Reality thus is MADE a blocks of time for its ‘wholes’, which in 5D metric are the slowest parts that perceive the largest reality. For the universe is the definition of an ¡logic impersonal God, the laws of the game of ∞ fractal existences.So there is NOT really a Dimension of pure spatial form or a pure time motion but a combination of both, even if mentally we tend to reduce motion and focus on forms, all has motion=time, and form=space, and this is truly the meaning of ‘spacetime’, the messing of both into 5 DIMOTIONS, THE FUNDAMENTAL ELEMENT OF ALL REALITIES:



It follows that since space and time are more complex than humans think, our language of spatial thought, geometry and temporal logic must be upgraded to formalize properly the description of‘superorganisms’ perceived geometrically in simultaneous space and logically in sequential time. At present the dominant geometry of science is Euclidean (save 5th postulate) and static; while Logic is lineal, Aristotelian, A->B. So we shall evolve both into a non-AE-=i-logic topology of space, next letter, i also meaning information and the fractal scales of reality and a ¬Æxistential algebra of time to formalize the ‘stœps’, stops in space and motions in time that move the relative futures of each system, made of vital scales of space that last a finite time duration, which are generated by the bio-topo-logic properties of its vital space and cyclic time. 

¬Æxistential Algebra: the complex pentalogic of supœrganisms of times-pace.

The entangled Universe generates its spatial over through the synchronous connections between the 5 elements of reality, fractal space and its scales, cyclical time and its repetitive causality, minds that perceive with synoptic languages the system as a whole and project its territorial order and survival will through its actions, and the entropic limits (¬) the infinite universe imposes to that will. So ANY aspect of reality must account for 5 elements to express such entanglement. It is the fractal principle of 5D in time and its pentalogic structure in space.[/caption]

In how many different ways can we perceive the 5 Dimotions (Dimensional motions) of space-time? As they are the only 5 elements required to understand the entangled Universe it follows that as in a kaleidoscope the number of possible perceptions of them are so many as events of reality we can observe.

3 are however paramount, as 5 Dimotions (a dynamic analysis) as 5 dimensions (a static analysis) and as 5 entangled elements (combined analysis).

T-Motions: The ilogic 5 logic motions of time are clear: entropy, «, locomotion, <, reproduction, ≈, perception, >, and social evolution, ».

S-Dimensions: They correspond to 5 dimensions of space: entropic dissolution into a larger spatial plane; length-locomotion, height-perception, width-reproduction and social evolution into a smaller cyclical vortex of form.

The entangled Universe generates its spatial over through the synchronous connections between the 5 elements of reality, fractal space and its scales, cyclical time and its repetitive causality, minds that perceive with synoptic languages the system as a whole and project its territorial order and survival will through its actions, and the entropic limits (¬) the infinite universe imposes to that will. So ANY aspect of reality must account for 5 elements to express such entanglement. It is the fractal principle of 5D in time and its pentalogic structure in space.

ST-Dimotions: Each of those Dimension and motions, then can be seen combined as a ‘structural element’ of reality. So Entropy becomes the limits in space and time of a T.œ (Time§pace organism), ¬; perception, its mental form, @; social evolution, its scalar structure, ∆; motion its lineal time flow, T; and reproduction, its spatial population, S.

Thus the key translation ads Dimensions + motions of exist¡ence into 5 structural elements of reality, which allows to move from ceteris paribus dynamic motion analyses or dimensional ones into structural studies of those Dimotions as ‘entangled’ elements of a being made of ‘dust of space-time’: ¬∆@st.

All dimensions of space have a motion in time.

This was realized in mathematics, as the still Geometry of the Greeks evolved into a much vaster, generalized concept, a topological variety, where a topology as opposed to a geometry has internal motions-changse. As the only case in which the inner dimensions of a being don’t seem to change is external locomotion most 5D motions need ‘geometries’ with inner motion, which are topologic varieties of which there are only 3:

All systems have ternary topologies with 3 organs of motion-information-reproduction that absorb energy, move and perceive to survive.

In the graph, the diffeomorphic Principle of Einstein’s 4D analysis acquires an organic nature, when we see the Universe as the sum of ∞ Complementary ternary, topologic systems whose dimensions have organic functions: Systems feed on their relative dimension of energy-length, perceive in their relative dimension of height and reproduce in their relative combined dimension of width, which are assembled into each specific species, to best satisfy the systems’ in taking of motion, energy and information.

I.e: An animal has its informative height in the high perceptive light dimension, but a plant, which uses light as energy has its up and down dimensions inverted respect to the man and its chemical brain buried on the Earth. So both have opposite energy-time coordinates, with an ‘antero posterior’, lineal’ ‘outward’ energy oriented structure due to the oriented arrow of light. But in a 3D world with no preferred orientation, a sea or vacuum, cyclic forms that maximize information dominate from plankton to galaxies that have a cyclic, informative, inward structure, as the stars’ body absorbs energy from intergalactic space, reproduces matter with it and feeds the internal informative knot of gravitation, with a higher height dimension the black hole.

So as all are dimensions of space with time motion, its science is topology that allows a system to deform= change its inner form. Yet a 4D Universe has only 3 ‘topological varieties’ that restricts ensembles to only 3 topologies, each one best suited to perform the 3 organic vital functions of any physic or biologic system – gauging information (1D), to move the system (2D) to an energy field in which reproduce (3D):

1D: T>S: angular cyclical motions of information (Ab. §ð): the minimal ‘geometry’ of reality, a spherical particle/head or fractal point, the geometry that stores maximal form in minimal space, hence suited for ‘organic functions’ of gauging, storing and perceiving information (particles, heads).

2D: S<T: Lineal Locomotions, (Ab. $t) which will move through its lineal limbs/fields the system, as the line is the shortest distance between two points… towards a…

3D: S≈T: Fields of vital Energy (Ab. ∑≈∏): with its hyperbolic body-waves that iterate the forms of both the spherical particle/heads and lineal limbs/fields; as the hyperbolic topology combines the other two, so it can generate them, in the same manner Energy adds as the third CONSERVED space-time quantity the lineal and cyclical momentum of 1 and 2D. To which we must add the 2 ‘scalar’ Dimotions of

5D: entropy («, ∂S) whereas motion is dual internal dissolving the information of the being and external, scattering its parts, hence we use an « ¬Æ symbol; so the system explodes into its ∆-1 parts: ∆«∆-1 (death). 4D: organic evolution (»,∫T) of parts into still locked simultaneous ‘linguistic seeds or mind forms’∆-1»∆

So the structural view to perceive reality in 5 terms works through the analysis of its ¬∆@st, BY FINDING ITS ¬ limits of validity, its ternary Universal grammar or structure in space, ages of evolution in time, as huminds reached with it higher levels of understanding of pentalogic (with different results in each language, maximal for classic music, SVO languages and Analysis), and scales…


This said mathematics is a language and as such it orders a territory with its syntax that reduces reality to a mind mirror of those 5 Dimotions and then projects it into reality. This is likely the topologic mind of atomic systems that reflect forces as its 5 Dimotions, studied in physics with mathematical geometric laws – reason why mathematics is so extended. In the next graphs w see the process for any language:

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.

Because mathematics is in its basic grammar, ‘Geometry’ of points and collections of points that are social groups of identical beings (hence by force regular polygons, which are the ONLY mathematical forms in which social points are all equal in Nature, hence numbers of collections of equal beings in pure number theory), the IDEAL of mathematics to make it look like the real vital, organic Space that GENERATES all entities in existence along the laws of pentalogic is the COMPLETITION OF THE concept first advanced by Non-Euclidean geometry of a point with parts, with volume through which infinite parallels can cross.

It then becomes clear that the point MUST grow in size to FIT multiple parallels, and so it is A FRACTAL POINT, A CONCEPT that substitutes Euclid’s axiom of definition of a point.

The result is pentalogic Geometry.

This is showing the graph in what we shall call, Non-Aristotelian, Non-Euclidean=Non-Æ=¬Æ=¡logic Geometry (as if it is not A and E the next vowel is ¡, our index of the scalar Universe).

(To notice also that because entropy is the negation of all other Dimotions, its dissolution most systems can be considered to be written in 4-logic, as we shall discuss for all of them).

While there is also PENTALOGIC ALGEBRA, concerned with the 5 Fundamental operands and its inverse that define the main Dimotions of the Universe (sine/cosine; ±, x ÷, √x² Log xª, ∫∂); and in modern Algebra, concerning groups and symmetries, the 4 different symmetries of congruence, arising all form the asymmetric ‘entropic energy deformed symmetry’… This of course can be extended to all languages, which will then be casted in terms of tetralogic or pentalogic that includes the entropic negation of it all (hence the non symbol, ¬).

Negation thus in Algebra is represented by the inverse operation of each positive one (whereas the difference powers and roots, exponentials and logarithms can be considered part of the same ‘operation’)… In Non-AE geometry the two sides separated by the membrain of the fractal point, the inner one with closed order, the outer one with infinite entropy=motion… which the mind distinguishes. 

But this post will be strictly dedicated to the pentalogic of geometry.

In an ideal world obviously we could then RETRACE THE ENTIRE DISCIPLINE OF  mathematics as it was invented through its ages, departing from Æ-mathematics in the Greek era, to recast everything in terms of pentalogic, a task which I started enthusiastically with Mathematics and Physics as well as all other sciences in my youth till life got complicated and I abandoned Academia.

This would have been a task that in my years at Columbia University a team of specialists could have also completed decades ago. But I didn’t find much interest on the project, and so at this age, at best I will try to annotate the posts of this blog with work of my notebooks and old diskettes, my apologies for errors and repetitions.

Since even languages, as mirrors of reality have the same inner structure – reason why we can use the axiomatic method to prove maths, outside reality – even if ALL LANGUAGES ARE INFLATIONARY IN INFORMATION, AS THEY CAN JUST COMBINE its bits without caring to ‘Imprint’ and ‘bend the energy of reality’, that stubbornly tends to disentangle in pure motion. What this means is it is ESSSENTIAL TO USE THE EXPERIMENTAL METHOD AND KNOW THE ENTROPIC, ¬ limits of validity of non-fiction languages, or else we would believe that because words describe Quixot with beautiful inner syntax he is real, and Skywalker will walk into the future galactic confederation as we believe in mathematical physics without any proof that black holes travel to the past to evaporate (Hawking’s fantaphysics), and other fictions of harmful consequences to mankind such as monetarism (the idea that money is the language of god that must rule beyond its natural limits, not only financial but also productive and social systems, as it does inner placebo democracies).


We are all ¬∆@st beings, made of scales, space, time and the minds that measure it all with languages, which can be of different complexity and exist in different domains with different dimensional motions, all of which WILL FEEL TO BE EXTREMELY INTELLIGENT AS THEIR MINDS and languages will select a limited information, they will confuse with the whole:

O-finitesimal mind (languages) x ∞ Universal space-time beings/cycles = Constant world: o x ∞ = C…

Thus is the fundamental equation (mathematical mirror) of those minds and their limited world’s realities.

Which we also study as it is the essence of the @ristotelian monologic of the egoist mind.

Because mathematics is in its basic grammar, ‘Geometry’ of points and collections of points that are social groups of identical beings (hence by force regular polygons, which are the ONLY mathematical forms in which social points are all equal in Nature, hence numbers of collections of equal beings in pure number theory), the IDEAL of mathematics to make it look like the real vital, organic Space that GENERATES all entities in existence along the laws of pentalogic is the COMPLETITION OF THE concept first advanced by Non-Euclidean geometry of a point with parts, with volume through which infinite parallels can cross.

It then becomes clear that the point MUST grow in size to FIT multiple parallels, and so it is A FRACTAL POINT, A CONCEPT that substitutes Euclid’s axiom of definition of a point.




¡maths should in an ideal fractal planet of enlightened people have started NOT with Euclidean æntropic geometry that reduces all beings to points with NO parts, and all numerical forms, to IDENTITIES with NO form, thus allowing man to ‘itify’ the Universe of fractal organic beings as a lesser form than himself (gifted with inner parts and obsessed by differentiating its ego unrecognizing any organic, social form, as the only free different being).

WE STUDY many of the deformations of æntropic parts, which resume in the loss of inner form of the points and the denial of its motion, which will only be regained by Differential geometry

It is the Paradox of formal space (@nalytic geometry) v. Time motion. As we defined ‘all distances are also motions’ to explain Galilean paradox (why we see Earth still when it moves), this simple duality of all ‘Dimotions’ explains why in differential geometry, to represent a curve we trace of a continuous motion of a point. as we can always think of it as the path of a point moving along it:

If a moving point X traces out a curve from time t = a to t = b, then the coordinates of this moving point are given by the functions of the time x(t), y(t), and z(t); the flight of an airplane or a projectile are examples. Conversely, if we are initially given the functions x(t), y(t), and z(t), we may let them define the coordinates of a moving point X, which traces out some curve. Consequently, curves in space may be given by three equations of the form:

x=(t), y=y(t), and z=z(t),

This is the most general manner of defining curves in Differential geometry (Monge). And so when we add those 2 advances, Non-E points with parts crossed by ∞ parallels, and curves as points in motion we find out that each point is a time cycle:

The 5 postulates of ® Vital, sentient Geometry.

We thus recast the axioms and postulates of Euclid into five new postulates to define fractal points, Non-Æ lines as wave of fractal points, Non-Æ planes as ternary networks of Non-Æ lines, which become supœrganisms, whose relative ‘congruence’ in its 3 ‘elements’ (singularity point, membrane and vital space) defines the type of ‘perpendicular or parallel’ relationship between them:

1st Postulate: ‘¬Æ point are discontinuous time cycles with an inner content of vital space-time’.

2nd Postulate: ‘¬Æ lines are waves of fractal points’

3rd Postulate: ‘¬Æ planes join 3 ¬Æ lines into a supœrganism’.

4th Postulate: ‘2 ¬Æ points are congruent when both its inner parts and outer perimeter are equal’

5th Postulate: ‘¬Æ World points focus multiple ¬Æ lines of energy and information into a still linguistic mapping of the Universe’

As space-time is ultimately cyclical the fifth postulate then becomes the first postulate AS THE INFORMATION AND ENERGY that crosses the point enters inwardly the system. So let us now explore in more detail those Postulates starting from the 5th and its definition of an outer mind. 

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.

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.

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.






Why points have volume is obvious: because they are timespace points and as such they have a cyclical time clock component, a membrane that returns to the origin and encloses a vital space, breaking the inner and outer world of the point. So first we must define cyclical time.

Time is cyclical, military physics made it lineal

Time is cyclical, all clocks of time and laws of science are based in the cyclical patterns of nature. But physicists developed ballistics and denied the obvious truth that we can know the future because it will repeat the causality of the past, and we can change it by changing that causality, in History by repressing the lethal memes of the tree of metal and enhance the welfare memes that make us survive. Of course, lineal and cyclical time render the same equations as one is the inverse of the other, measured by frequency, T=1/ƒ, but the philosophical implications of cyclical time, are ginormous and the in-form-ation provided by those cycles, erased by lineal time, a handicap for humans to truly understand the cycles of history and economics, the ‘deep time’ scales of the fifth dimension, and the whole workings of super organisms and its physiological structures.

It follows then that from the definition of a fractal point as a time cycle, with motion, an inner volume of information and energy, we can deduce that lines are waves that communicate those points, or fractal networks that control the inner parts of the point – its vital energy cells, by branching to them.

And so we can redefine the 5 non-Euclidean postulates from the translation to vital geometry of axioms and postulates of classic geometry, restarting from scratch the science of ‘generational space-time’ where we shall PROVE SLOWLY THAT ALL THE MAIN POSTULATES OF GEOMETRY HAVE AN EQUIVALENT VITAL DEEP MEANING IN NON-Æ geometry.


FRACTAL points. The fundamental particle of the Universe.

Yet to understand that formalism in detail we have to define a Non-Euclidean point, the fundamental element of any network:

‘A non-Euclidean point is a knot of spatial information and temporal energy, joined by a non-Euclidean line=wave or geodesic flow of energy and information’.

Thus, the first important change that generational space-time introduces is the expansion of Non-Euclidean Geometry through a more realistic description of Euclid’s point defined now as a point with parts; giving birth to lines that are waves or forces of communication, creating topologic planes that are physiological network which become vital supœrganisms, whose relationship will depend on the relative congruence=equality between 2 of such non-E super organisms.


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.

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.


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.



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’.

Supœrganisms of networks of waves of fractal points.

In Euclidean geometry a plane is defined by 3 Euclidean lines that intersect. In generational space-time, its vital ¬Æ Geometry defines each of those lines as a ¬Æ wave of information in a single plane, or as a fractal network that probes an ∆-1 plane in its 5Dimensional analysis, origin of the 3 physiological networks that make ip a super organism and we shall call ∑, the ‘herd-like digestive entropic network’ of the system, Si=Te, the present ‘reproductive network’, and ∏, the informative network.

The choice of ‘symbols’ is well-behaved (though the reader should understand this is a systematization of 30 years of disjoined work and so it will take some time to reduce multiple symbology to the canonical one, only developed in the 2010s), since ∑ expresses the herd, unconnected nature of the entropic cells the system ‘digest’, ∏, the neuronal axon-like nature of those of the informative system (since if a group of x cells connect each other through an axon the number of axons will be ∏x); while the Si=Te (information=energy) nature of the present-reproductive ‘blood work’ shows its capacity to ‘balance’ both extremes, carrying entropic nutrients converted into usable energy and formal languages, converted into useful organizing information to each part.

We distinguish thus two type of non-AE lines: those who happen in a single plane of the 5th dimension or waves proper.

And those non-AE lines which penetrate other planes of the 5th dimension. They are ‘fractal non-AE lines’ or ‘networks’ which branch into the i-1 scale touching fractal points (atoms, cells, citizens), forming physiological network.

Then 3 of such fractal networks that intersect in a mind-point form a vital plane.

The most complex of those vital planes are  thus topological supœrganisms, as they co-exist in a plane but also intersect 3 ∆±I planes of reality, internally with its fractal ¡-1 points (atoms, cells, individuals) and externally with its ∆+1 world or ecosystem.

So if 3 lines form an Euclidean plane, 3 non-AE lines form a non-AE plane and 3 Non-AE physiological networks connected by a mind-point form an organism.

The third postulate thus defines finally the construction of super organisms through ‘networks’, which messed in ternary forms create a super organism as a fractal plane, which co-exists in three scales of reality:

3 scales

In the graph centered in human beings, both from a physical and biological perspectives, we see the 3 main scales of the scalar Universe and its 5th organic dimension:

Let us now express it in terms of physiological networks, which in the organic paradigm are the right way to interpret the abstract concepts of modern topology, which build ‘topological forms’ as ‘networks of points’. In 5 D metric those abstract topological networks, merely mean that any form of the ∆ø-plane are made of smaller cellular/atomic/citizen ‘points’ that build the whole.

So besides the 3 space dimensions ≈ 3 time dimensions (seen as still in space, as moving in time) we do need to consider at least 2 more dimensions, one for the lower scales of the being, which we shall call the fourth dimension of absolute past and one for the upper dimension of the being of absolute future.

We do have then mathematical and verbal, logic mirrors to express those 5 dimensions of space-time, the ultimate substances and unify with them ALL SCIENCES, departing from the properties of those dimensions its structures in space and travels in time, each ‘stience’ of space-time studying an scale, including those who describe man.

Thus this is the Universe in a nutshell, repeated ad nauseam in all scales, and we shall repeat with kaleidoscopic variations the previous paragraphs to describe the thoughts of ‘god’, to make organic systems tracing world cycles, regardless of the huge details scientists have obtained so far.

So the organic paradigm has taken longer to be formalised, as we do in this blog, because it requires to ad to the motions in space studied by physicists, the arrow of in-formation, of form, stored in the form and frequency of the clocks of time cycles of reality, which are along its lineal motions in space the two elements that conform all realities, by combining and integrating into ‘vital energy systems’.

Those 3 arrows spreading across different scales of size, which add 2 more space-time dimensions of ‘wholes and parts’ to the mix, will allow us to describe all what exists as an organism of space-time, the long-seeked ‘sound organic philosophy of science’;

In all species studied by science a common phenomenon occurs: the existence of parallel groups of beings organized into a single social form. Molecules are made up of atoms and electronic networks; economies are made up of human workers and consumers that reproduce and test machines, guided by financial networks of information (salaries, prices, costs); galaxies are composed of stars, which orbit rhythmically around a central knot, or black hole of gravitational information. Human bodies are organized by cells controlled by the nervous, informative system.

A tree is a group of leaves, branches and roots connected by a network that provides energy (salvia) and information (chemical particles) to its cells. Cultures are made of humans related by verbal, informative isomorphisms and economic networks that provide their energy and information.

Stiences study those organic systems, tied up by networks of Ðimotions. In the graph, we see the main st-planes studied by human sciences and their 4 main time arrows, Sp x ðƒ, which in static space give birth to the ‘organic elements’ of all species: social cell of energy and information and the reproductive networks that relate them. Thus, there are 4 basic elements in all organic systems:

  • Cellular units.
  • Networks that move the system (limbs/potentials)
  • Networks of fractal information (heads/particles).
  • Networks that reproduce vital energy (body/waves)

So what we mean by an organism? A very simple system – NOT to confuse with the most evolved, complex of them all, that of human beings, reason why so many people, having a natural biased ego-centered belief in man as the unique organism, reject the concept:

An organism is just a group of similar forms, which organize themselves with at least two ‘networks’, one that provides the ‘clone cells/citizens/atoms’ with the vital energy they need to feed, move and reproduce (blood-economic system-electromagnetic forces) and one that provides them with information to guide their survival actions (nerves system, political system, gravitational in-form-ative forces). This simple dual system IS the minimal, fundamental particle of the Universe.

The formalism of super-organisms describes them as networks of non-Euclidean points, a concept developed in my earlier work on quantic space-time that describes the smallest scale of the Universe as a network of spins of temporal gravitation joined by strings of spatial energy. Those microcosmic networks have evolved into the bigger, more complex networks of the macrocosmic world through a process of social evolution, triggered by the higher efficiency of networks in all processes of survival. Yet, despite growing in complexity, non-E, informative points and energy flows have maintained the original properties of any quantic space-time network.

So we can define in mathematical terms any super-organism as a fractal space-time network extended in i-scales of information and composed of n, non Euclidean points or individual cells: Σœ¡-1<=>Œo.

Thus any super-organism is made of fractal points joined by networks of spatial information and temporal energy of particles/heads and waves/ bodies.

And further Heads exchange lines=waves of energy and information forming networks.

The 3rd 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 oldest graph of 5Ð: Human ¡±4 perceived planes


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.



Anti-Symmetry. And social parallelism.

Anti-Symmetry is the fundamental property in terms of logic thought of the Universe. To fully grasp it we consider the ternary symmetries of scales, ages and adjacent topologies, which structure the being internally through ∆±1 scales, in time through 3 ages and in space externally through its 3 topological forms, all of them expressed in the generator equation:

∆-1: Generation > ∆º: $t |-lineal limbs/potentials (dominant in a past young age) <: ∑∏ iterative, hyperbolic ø-body-waves (dominant in an iterative present) > ∆+1: O-Particle-head, which commands the being as a whole in an external world, dominant in its future 3rd age, before the system explodes entropically ∆+1<<∆-1.

To notice then how reality can be observed through those anti-symmetries, which mean the properties of each of the two extremes of the 3 ternary elements of reality are anti-symmetric to each other and so they cancel each other. That is cells/atoms/individuals are to the wholes antisymmetric as they maximise information vs. energy-size; limbs/potentials are to the heads/particles also antisymmetric in lineal and cyclical form; and the first age of life or relative past dominated by lineal motion is antisymmetric to the 3rd age dominated by cyclical form. 

But because the system is ternary, the anti symmetries of time-ages, space-topologies and scales become merged into the present-hyperbolic body-wave interacting and mixing together to form a single one. 

So the best expression of the game is a present body-wave breaking constantly its symmetry into two opposite functions that can either annihilate each other, as waves do or complementary reinforce each other, concepts those hardly used in science beyond physics and even there ill-understood that now we expand to all sciences.

Indeed, in physics much has been done about the term symmetry which is NOT really that relevant, because even when physicists define symmetry they are in fact talking of a mirror symmetry, which is an inversion or a bilateral symmetry which is also an inversion so they are forms of topological antisymmetry, of two identical social parts.

Yet the game as a game of identical social parts is an element of fractal organicism. This parallelism of beings which are clones by reproduction of each other and the asymmetry between systems that are complementary to each other and meet in the middle term, are essential elements to make sense of how reality, comes together and pegs into a single being.

So that is the future of stience, in any planet in which similar huminds have kept expanding our connection with the entangled Universe.

The law of behavior in the organic Universe is simple: beings who are similar or complementary and speak the same language of information come together as couples, herds and social wholes stronger than individuals. Those who perceive each other as different,will simply act in a Darwinian, perpendicular  manner. 

A case of Darwinian devolution among men that perceive each other as different and enter into a perpendicular, Darwinian relationship and a case of social evolution between 2 forms that perceive each other as equal and enter into a parallel relationship of social love. The fourth postulate of non-Æ topology thus ‘vitalises’ the laws of mathematics, establishing the three fundamental geometrical≈behavioural relationships between T.œs, according to its:

  • Informative (Particle-head) communication, possible in cases of relative similarity≈parallelism (which determines parallel herding and social evolution).
  • Perpendicularity≈difference in particle-head, which will determine if one system is related to the other and there is body-similarity, hence can be used as energy its darwinian destruction,
  • Or IF THERE IS NO similarity NEITHER IN BODY OR MIND, its existence as ‘cat alleys’, that never cross (relative invisibility). We talk then of Skew T.œ.s.

Indeed in three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. It follows that two lines are skew if and only if they are not coplanar, which IN 5Ð AS 3 ±¡ planes co-exist in the same organism and systems feed in T.œs, two super organisms down, IMPLIES SPECIES which are not in the relative planes of action of the being.

The different degrees of Parallelism, Perpendicularity and skewness are thus essential concepts of vital Non-Euclidean geometry.

And as all has degrees of ‘grey’, it is also a relative concept and essential to many branches of sciences, notably quantum physics to know the relative angle of parallelism, perpendicularity and skewness (here we redefine the concept NOT using it only for probability theory), of a system (and to make things more complex in which type of geometry, of the 3 ‘analytic points of reference’ – Hyperbolic, euclidean, polar & complex or lineal=cylindrical we are talking of)…

All those are hints for future researchers. We won’t be so detailed.

In the jargon of 5Ð specially to study physics, we also use for those 3 concepts, the concepts of a(nti)symmetries:

The Universe always starts with an asymmetric being, which can go both ways: towards a social evolutionary symmetry that lasts in time and implies a mirror parallelism, or an antisymmetric destructive, perpendicular event in which one part punctures and absorbs the energy of the other. It is the topo-biological ternary principle of non-Euclidean, Non-Aristotelian I-logic geometry that puts together both the biological and mathematical properties of reality.  The concepts of symmetry=parallelism, antisymmetry=perpendicularity and asymmetry are mirrored by the 4th Non-E Postulate of similarity. But we can extend the concept of asymmetries also to asymmetries of time, between the young age of locomotion and the old age of information, of actions=Dimotions between the step and stop similar actions, and the entropy and social evolution actions, which bring us the final asymmetry of scales between the upper arrow of whole with more spatial size and the lower arrow of parts with more information. When those dualities: step-motion/stop-perception and scale up (5D: social evolution), scale down (4D: entropic dissolution) are put together we obtain the most complex balancing dimotion, reproduction, and when they are all added up in the existence of a being, we get its world cycle.

We have introduced in the graph with a bit more of complexity the logic dimensional laws that define how systems IN ANY scale of the inverse, from Atomic Ions or crystals to human societies relate to each other in darwinian, perpendicular ‘tearing’ topological relationships that ‘break’ the closing membrane of one species disrupting its existence, or will keep a mean distance to form social networks of communication that will grow into super organisms, starting the emergent process of evolution of species into a new ∆§cale of social existence, so you understand that in the Universe organic, geometric and scalar relationships are symbiotic to each other. 

In the graph, symmetry is close to parallelism reason why social systems evolve into symmetry forming herds. Disymmetry is a mirror form of parallelism, or ‘inverse parallelism’, which is complementary and needed to form pegged ‘genders’, bilateral systems, etc.

Antisymmetric forms are therefore the perpendicular ones, and its Darwinian relationships are also essential.

Asymmetric systems on the other hand are NOT equal to Skew systems, but is the closest concept. Why we do NOT have another ‘concept’ for Skew systems IS FOR THE SAME REASON ORGANISMS CODE ONLY 4 DIMOTIONS (4 quantum numbers, 4 genetic numbers, 4 Human dimensions of spacetime, etc): BECAUSE entropy=death and Invisible beings that do NOT relate to us, are of NO importance.

Still this Asymmetric concept is intuitively perceived as ‘skewness’ in probability where the distortion of a bell curve is the measure of its skewness:


4th postulate in terms of 5D. 

In that regard the 4th postulate DEFINES BOTH the entropic and inverse social evolutionary elements of reality, as it HAPPENS in most coded systems, in which the negative or absence of Coding numbers IS what defines entropy (themes those of advanced quantum and genetic studies we will likely never pour on those posts before exit Mundi).

 Logic and geometric postulates.

Why geometry needs 5 postulates if the 1st, 2nd and 3rd 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 4th 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 4th 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 4th postulate:

4th  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. 


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

Aristotle on the mind.

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

All this said it would seem obvious that the first and fifth postulate are the same, as a fractal point has parts, and those parts hold the parallels that penetrate them. But the view of the two postulates differs, as the first postulates has an internal perspective of the point with its inner parts, which are then developed in the 3rd postulate of ‘organic planes’. While the fifth postulate has an external view, observing the fractal point from the outer world it perceives through those flows of energy and information (parallel waves). Thus one refers to the inner organism as an island-Universe while the fifth postulate refers to the point as a mind-singularity that perceives the external larger world that hosts it:

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.

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.

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 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.

  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 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.

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. 


What is the Universe? A 5D Game of Non-Euclidean Points of view.

The mathematical unit of the complex universe is the Œ-fractal point, better defined as a Non-Euclidean knot of infinite cyclical parallels f energy and information that converge into the Œ-point.

Œ-points are both points of information, with form, fractal points, non-Euclidean points made of 3 bidimensional geometries. And they are Energetic, points with ‘momentum’, with motion, Œ-points pushed by the E-nergy or E-ntropy motions behind them.

Hence the importance of ‘momentum’ in physics, given the fact that we do NOT see a point without motion (though we can extract mathematical properties from it). So by definition we do prefer in physics, the Lagrangian and Hamiltonian canonical analysis, which uses momentums rather than ‘pure scalar’ masses (Newtonian formalism), in the description of ‘physics of motion’; which for this reason is also along bidimensional ‘foliated’ analysis (fluids, General Relativity, Hamiltonian version), and the duality of finitesimals (point-particles, undistinguishable Bose statistics) vs. Wholes, 3 ever pervading ‘realities’ of physical systems.

If we add the understanding of the two asymmetric arrows of 5D geometries (information moving upwards, energy downwards) we have the fundamental elements that we shall use to ‘explain’ properly and correct some of the gruesome errors of the physical Universe.

Thus the units of reality are dimensional points. And all Realities are constructed with them.

This is what we are. Points, which grow in size as we come closer to them, and grow even larger as we enter the region of the ego, till reaching the ultimate essence of it.

The zero point, the fractal point, the Non-Euclidean point, the first postulate of existence, the I…

The Universe is a mathematical, i-logic game of Non-Euclidean points of view that web waves of exi-stence, communicating, cyclically forming wholes that decay back into parts in the process of death, cycling in time and space.

And the understanding of the Is and its i-logic and Non-Euclidean mathematical rules of existence is the game we all play and each mind reflects with a language.

Aristotle was perhaps the man who better understood the Universe as a sum of non-Euclidean points of view, and after him Leibniz, who said that ‘we must regard each point as a Universe in itself’ and indeed, in the fractal Universe each atom is a galaxy, an island Universe of a bigger gravitational scale, and this infinity of self-similar games that are played in different scales is what we talk about, which is resumed in the widening i-logic of those i-points of view, which have internal parts, which have breath unlike the simpler non-e points of view.

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.

Non-Euclidean Points of view have perception, they have mathematical view, they have Non-Euclidean i-logic paths or structures of causality in its built-in organic systems and as such can be described as living entities.

All beings are points which are a world in themselves, and so the point world is the unite of it all. Externally it might be always reduced to a mere point of a bigger field, in actions of collective experiences, but internally it feels itself so important.

Yes even the ant feels itself important s an ant.

And we might be seen as ants by systems of national power that control us.

Our Space thus is the bidimensional magnetic wave. Our time is the charge-electric field bidimensional wave, c-speed is the space x Time combination of both, c=1/√µ x ε0   (the peculiar positions of human equations with inversions squares etc. does not matter much here, c-speed is a 4 Dimensional space-time wave, and most properly should be treated as c2 ‘always’, as it is always positive, and it appears in that sense in the next equation whose meaning we must find now:

E= Mc2

That is, E<c2>M

A 4 Dimensional space-time of pure motions E(Spe) becomes a 4 Dimensional space-time present wave (C2) which can be curved in the largest of all perceived planes of physical space-time as a mass, a clock vortex of gravitation (Principle of equivalence of Einstein).

The constantly of light follows immediately because it is our space-time.

In terms of the action of information it follows and latter will be studied in more detail from the fact that electronic Tƒ, our minds, ‘stop motion into still space’, and to do so they must in the beat of stop and motion of the Universe stop gauge light space-time information sent by other particle and hence entangle with the other article.

How it is done, it will be analyzed latter. My hypothesis is that it happens through 2 neutrinos, which are first fixed as space (neutrino theory of light of which Jordan, Fermi, and Bohr were enthusiastic proponents).

Neutrinos thus would be the strings (its size is in fact that of the Planck string) of the minimal space perception of our Universe, rounding on the lower scale the parameters of the Physical world.

All this of course can be established with far more complex mathematical equations as we shall attempt to do in the 4th line in the future…

At this stage we just will consider the parallelism of the 3 scales, the human biological and economic/mechanical scales, with those 2 bidimensional fields of space and time, which create all systems of Fractal Space-times and its bi-Dimensional Lines, Waves, and Cycles.


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