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5Ð ¬E Postulate: Minds’ Worlds

±∞ ¬∆@ST:

“The convention of perspective, which is unique to European art and which was first established in the early Renaissance, centres everything on the eye of the beholder, it is like a beam from a lighthouse – only instead of light travelling outwards, appearances travel in. The conventions called those appearancesrea/ity. Perspective makes the single eye the centre of the visible world. Everything converges on to the eye as to the vanishing point of infinity. The visible world is arranged for the spectator as the universe was once thought to he arranged for God.”

The art of seeing, Berger: The Mind’s point of view is NOT the Universe but an always self-centered partial world

Abstract. The first and fifth postulates of non-Æ geometry seems similar, as the first defines a point with inner parts and the fifth, the only one so far known to present science defines a point as crossed by ∞ parallels. But a closer look at its Euclidean equivalents show that they have ‘2 different perspectives’. The first axiom of Euclid focuses on the non-existence of parts to define a ‘self-evident’ point so its equivalent  In Non-AE will focus on the INNER parts of the Point, which we shall call a fractal point.

The fifth however focus on its outer parts, the parallels, waves of communication or fractal networks (2nd postulate) to which they are attached.

So we shall call the definition of the fifth postulate a mind.

Both of course are connected. The flows of information of the outer world focus in the inner linguistic still structure of the mind. But a more subtle difference is this: a mind is concerned with mapping the outer plane of reality or ∆+1 ‘world’. While the fractal point is connected to its physiological networks, which intersect in the mind and explores through them the ∆-1 scales of its physiological existence.

So the Non-Æ point or T.œ, ∆º, has an ‘outer mind’ defined by the fifth postulate, which focuses in the ∆+1 world; while its fractal inner self focuses in the 3 physiological networks that connect it to its ∆-1 cells.

This post studies them as mind-worlds, mirror of an external ∆+1 Universe.



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

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

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

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

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

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

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

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

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

We shall in this post study therefore the 5th Ðimotion of social evolution of parts into wholes, guided by the mind that perceives, the creative, relative God of the territorial energy it orders. We shall not obviously introduce well known geometric laws (this will be studied on the sub-posts on the language of mathematics, using a more classical approach) but rather concentrate in the theological and philosophical ‘point of view’ on the point as mind of the super organism, god of its territory of order, since as we said, the fifth postulate is similar to the first, albeit ’emerged into a larger scale’, concentrated into the internal parts of the being, as much as the first postulate concentrates into the external view of the being as a mind penetrated through infinite parallels of energy and information.


The i-1 mathematical perspective: points

In terms of i-scales, mathematics is the i-1, ‘point-like’, ‘atomic-cellular’ analysis of beings.

What complexity does, is to highlight those limits of mathematics and widen its ‘perspective’ by considering that the ‘points’ which are units of mathematical languages, are only ‘apparently’ points-with no breath (Euclidean points).

Generally speaking, physical laws are given in local form Physical laws are given for mathematical points but applied to extended objects. while their application to the real world requires a departure from locality.

For instance, Coulomb’s law in electrostatics and the universal law of gravity are both given in terms of point particles. These are mathematical points and the laws assume that. In real physical situations, however, we never deal with a mathematical point. Usually, we approximate the objects under consideration as points, as in the case of the gravitational force between the Earth and the Sun.

Whether such an approximation is good depends on the properties of the objects and the parameters of the law. In the example of gravity, on the sizes of the Earth and the Sun as compared to the distance between them.

On the other hand, the precise motion of a satellite circling the earth requires more than approximating the Earth as a point; all the bumps and grooves of the Earth’s surface will affect the satellite’s motion. All points thus have parts and details when we come closer to them, and this fact can only be explained accepting the complex metrics of 5 dimensions.

When in fact they do have the closer we come to them, ‘widening’ our ‘scalar perspective’, points with volume with inner parts, fractal points. And so a new/old form of mathematics, the study of the Universe as made of fractal, non-Euclidean points with breath, means a r=evolution in mathematical thought similar to the one complex sciences will cause in all other disciplines of human knowledge.

Consider for example a human being, in a match stadium. From above and far away it is a ‘point’, and it does matter little. As O.Welles said in the 3rd man, you can look at them, they don’t matter, if each of those points were money and you could grab them, how many would you take? Distance and lack of information make us indifferent to far away entities. yet if we come closer to the stadium we will observe them as i-ndividuals – this is the biological perspective – and as parts of a social organism, which move together with similar actions. This is the i+1 social scale and its laws of common motion, and social interaction are again of a different quality to those of a mathematical point.

So despite the common belief, since Galileo that the world is ‘written in the language of mathematics’, we must consider a Upanishad’s version ‘the languages of god are infinite’, or rather, the scales of the universe are infinite and when we look from above, we make a mathematical description and when we look from below we make a social one.
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.

“The Universe is the body of an organism (t.œ.), whose logic mind (∆§) we call God.’ Plato

‘We are all Gods, the unmoved center of a body of energy’ Aristotle – best ever definition of a mind-singularity, the linguistic mapping and will of existence of any super organism of space-time.


In the graph, the Monad, or center of the will of the system, or T.Œ (timespace super organism). But as we have already described it in depth in our first line, ‘@Monad’, we want now to consider a philosophical question: the mind as an aristotelian God, still linguistic center of all the energy-body that is its territory around which it orders ad totally controls. The singularity as the max. informative point or local god of a system is what Aristotle thought of, when he shouted ‘we are all gods’. As in those earlier pythagorean, Greek ages, the simplicity of the game without much detail, rationally analysed revealed as in CHINESE taoism, the first principles of reality in a clear form.

Leibniz, on the fundamental particle of Reality: The fractal point=world of space-time.

‘I know when mathematics are truth but not when they are real’ Einstein

In the organic paradigm embedded in the latin->European->Social culture, which reached it maximal truth in science, in the Wien school origin of general systems, the WHYS OF THE UNIVERSE are always organic, and the description are the linguistic mirrors of which mathematics is the best.

So only organicism is real in the whole sense of the Universe, while languages-mirrors are local orders.

The EGOCY of our present, entropic age of human civilization rejects this (Precisely because it is becoming dissolved). So we  reject the power of networks – self-mademan myths and tribalism in history. Yet  networks are more powerful and survive.

How this work on languages IS OBVIOUS: LANGUAGES ARE LOCAL, IMPLEMENTED BY BRAINS, AS THEIR SOFTWARE, which orders reality AFTER THE LANGUAGE MIRRORS IT, not the other way around as creationist religions and mathematical physicists think:

In the graph, which I re-designed from” road to irreality” (: a work by Penrose, one of the most staunchest creationists of physics (a mathematician along his friend Hawking, which shuns off the laws of the experimental method) his view of reality is VOID as in all PLATONIC (PLATO by the way never said that, they should be called Pythagorean, a much more primitive ‘magic view’) of HARDWARE MINDS and LOCALITY. In his view the Language creates the Universe.

In reality the Universe is a fractal organism, and as all its parts can be considered similar we can ‘make synoptic language’ with enormous power to reflect multiple similar images in its essence, which ultimately will be the laws of ‘Space-time’, which are Organic because that is the main property of co-existence in different planes (∆§cales), topological because that is the main property of Spatial adjacent topologies that form super organisms, and Logic, Multicausal, as that is the main property of the dimotions of time. 

So the ultimate causality ∆->T->S IS not Platonic mathematics but ∆organic properties -> T-Logic properties -> S-Topologic, mathematical properties.

In true form, the proper expansion of mathematics allows also to develop a lot of ∆§calar properties as numbers are ‘Social ensembles of undistinguishable beings’ and polynomial algebra and analysis studies how parts and wholes become one; but then mathematics properly understood become another proof of the vital, organic nature of the Universe. And since mathematics is based in logic in its internal nature and experimental proof in its outside qualities, the mirror is very good but we REPEAT, the true causes come from the ∆§ðructure of reality and its ∆-scalar properties, STopo-logic ONES.

SO WE ADAPT PENROSE GRAPh to show how reality is constantly going back and forth:

The ∆§T BioTopoLogic properties caused by spacetime beings, are synoptically reduced to what they have in common, since all forms are ‘generically’ speaking self-similar. And then THE LANGUAGES REINFORCE AS MIRRORS EXPANDED INTO REALITY those properties ordering local territories.

So the graph shows that back and forth  to adequate to how REALITY  IS created LOCALLY by ‘minds‘, which are the language software on the hardware brains of T.œs, ONLY after the language reflects the LIVING cycles (dimotions) of all time-space beings with those properties:

You can see in the graph how it works: First the whole Universe is ‘shrunk into the mind mirror’ and only then the mind mirror according to the efficiency of the language imprints bak ONLY THE TERRITORY OF ‘ARISTOTELIAN’ ORDER OR BODYWAVE ENERGY OF THE SYSTEM…

THE DRAWING in original Penrose ONLY had the mind ordering the Universe, as the source and only God in Aristotelian sense: ‘god is the unmoved causal point that orders the motion of the energy (body-wave) around it’.

So yes, languages do create reality but all of them, and all of them locally and all of them organically because they act as the mind of all kind of systems. Obviously atomic matter is AS IN CRYSTALS ABLE TO FORM mirror-images in geometric form, and that is why they do have such an efficient capacity to order – and that is why topology (dimensions with form or dimotions) are the language of it all:

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.

We are monads that hold worlds, mirror-perspectives of a mind over the whole, but we are not the whole much more complex and infinite in size and duration relative to the mind.

The mind we might say is a single ray with an origin and an end on that infinite horizon. Its mirror is shallow with less dimensions; specially those of time, as each point has its own time cycles. So the mind is orientated in his own time direction. The humind expresses its time view decoding the Universe into a single lineal parametrical language, verbal symbols that have a lineal syntax, where the subject man, comes first as we read in ‘lines’.

The mind is thus an infinitesimal lineal reduction; and even so its time speed of processing information of the whole spatial infinity it portrays in increasingly reduced forms till reaching the syntax flow of its primary language, goes much slower – as an electric current – than the maximal c-speed of our world. So even a computer that sees lineal codes of 0101 numbers in virtual minds of more complex atomic nature outpace enormously the words of humans.


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.

 IT IS THEN CLEAR WHY MATHEMATICS is so important and by enhancing the laws of logic and mathematics we shall describe better physics, but at the same time by realizing that organic properties are the larger why, we shall reduce the ‘obsession’ for platonic mathematics, and belief that all equations are real.
As languages like everything else in the Universe does have a 3rd age of excessive information, the Baroque age in which the language detaches from reality, warps in excess of form and creates imaginary thoughts. And this IS TODAY THE AGE IN WHICH LANGUAGES FIND THEMSELVES, due to the expansion of digital thought, allowing all kind of mathematical models of physics, specially in those areas (Black holes, dark entropy) of the ∆±4 plane we do NOT perceive and so without experience we just ‘inflate’ with ‘inflationary 3rd age excessive mathematical information).

WE shall thus explore the ‘metaphysical equations of God and its meaning’ in different scales, centering in the 2 final mysteries of existence: how gods singularities create reality through mirrors that project its linguistic still minds on the Universe? And what is the origin of the will of existence of those minds. Are they automatons of a mirror program of creation? Or there is even beyond perception a final level of awareness of existence that pull us into willing to fight for it?

The answer which can only search by considring the homology of all space-time beings, hence looking into human beings is Yes: SENSATION more than perception is the LAST DUAL, pain and pleasure game that seems to exist in man as its final will and should also exist in Nature.

instead of monads, we use here a simple symbol for GOD, taken from Greek letter, for the Generator of time arrows, for the topologic combination of lines and cycles, which form a spatial ternary symmetry: |x 0=Ø, and for the ∆-infinite scales of its ‘plenum’ body of space, where fractal parts of it become super organisms, gods of existence. Many variations on the same theme, specially on the central ‘vowel’ can be used, º•Œø∞, as a mind, as an infinitesimal infinite as a super organism as a topology as an infinite dries of scales.

We  highlight three components of all realities: Γ, the three ARROWS/ages of time that generate it ,Φ the three topologies of space across the three scales ∆, of its super organism.

it is god then just the program of creation of super organisms?  And as such always a ratio a balance, a domain within the limits of ∆±i of the domain?

I think so. Thus in this manner ΓœΔ will bring the three elements, time generation, organic topology, scalar, fractal form.

As we are all super organisms made to the image and likeness of god.

We all have Γime Φ-Space & ∆-scalar dimensions We are all gods, we are all super organisms. The existence thus of a Universal particle, or god’s particle, the suer organism, Œ=ΓΦΔ thus closes the third line between the mind and the whole, the first and final isomorphism that describe all beings as both dºst of space-time and a Universal God, dust=dºst.

We shall close this third line on ‘the different functions of exi≈st¡ence§’ of the Universe with the study of the concept of God, as the whole of all wholeness –  Logos≈Mind of the Universal body, in a platonic sense, as the absolute cano of the cave, of which all its fractal parts are  made to its image and likeness – the point of absolute future, of the 5th dimension, of two imaginary time parts, singularity point of no reference, that does not exist ever in present, asymptotic to it:

Max. i

When we say that pure form does not exist, neither pure energy is because the game is never perfect except in the whole that never dies block of 5Dimensions where all the potential games are written.

God both in the Universe at large and the Human Wor(l)d, our Space-Time domain of perception is the pure form of immortal logic time – the world cycle of all world cycles, which never ends as it repeats itself in simultaneity non-locality, at every scale, composed of:

G, Γ, Gamma, the Generator equation that defines its actions

0, •, its fractal 0-point, black hole Mind, Aristotelian still point of maximal density of information≈attraction of the Universe,

D, ∆, Delta its infinite scales.

Form in Space, Mind in time, Future in its infinite scales and hence in its distances – and yet purely as Plato envisioned a canon never to be reached except in the whole infinity itself



In the graph, the Absolute God of the Universe IS its mind of maximal information. Is that point conscious or impersonal? We can compare it with human Gods, the point of maximal information of a Human Superorgansim – its ‘self’ in the ∆ scale of individuals, a neuronal group of the brain; its prophets in the ∆+1 scale of societies; an informative master of the wor(l)d; its DNA in the ∆-1 scale of biological cells. All those ‘human gods’, ‘create’ the future of its systems, organism, society or cell with its logic patterns of information.

So such are the concepts of a personal God, or brain-mind with absolute control of the system that apply to a personal view of God and extrapolated to the Universe, gives the Black Hole, or gravitational brain of information as the God of the system, whose internal ‘chemical mind’ (Maldacena’s equations which show a black hole to have a 5D ‘homunculus’ representation of the 4D electromagnetic galaxy) controls the body of stars of its galactic plane, as the brain controls your cells.

But there is an impersonal Taoist concept of God as the game of existence and creation with the rules expressed in ¬Æ logic terms in this blog. For eastern religions, Ch’ang, God is the game of creation of yin and yang – the isomorphic laws of space-time that all systems obey, including the ‘God-brains’ of any scale of Organisms of the Universe.

And this God can be accessed by any part of the Universe made to its image and likeness, making you communicate and dissolve with the whole in a mystique experience I have lived now alone in this planet for 30 years and counting…

As we have studied in depth this impersonal god all over this web, we shall now concentrate a bit more in the personal God in the Human social scale of super organisms, which is the commonest concept of verbal god, humans better understand.

Personal God – Max. Tiƒ.

Perhaps the closest description of God is that of the mind of a territory of order, by a future fractal point that moves the territory in synchronous motions around its self.

For each discontinuous whole, god is it point of maximal information, or self with the will to order the super organism in which the point of knowledge is inscribed. It follows that god has more information than the point of knowledge, and as such there are degrees of god, regarding how high in the size of the god, we are talking on the scale of super organisms, from where we deduce that god is the logic mind of the Universe – in formal terms, the fractal generator:

Impersonal god = ∆±∞ ($t<∑e∏i>ð§)

which FOR THE SCALES OF DECAMETRIC infinity we perceive as human beings, is the scale of atoms-galaxies, which are the limits we perceive and the game of existence of its super organisms. In other words, the future is created by the Tiƒœ point of maximal information that is in the Universe, the relative quark-black holes of each atomic-galactic system. But humans do not use the word ‘god’ in that sense, so we must explore what ‘god’ as a human semantic word means in our scale.

God in its commonest verbal expression means the most intelligent, informative point of the Universe. Yet as the Universe is a fractal of infinite self-similar TSymmetries of space-time, God can be defined by a simple equation, as the relative point of future of a super organism or whole of wholes, common set of all sets of superorganisms of fractal points in a 5Dimensional Universe:

Personal God= Max. ð§



Mathematics is thus the perception of the universe with a distant perspective. Its units being points, which represent any form of the Universe, reduced to its i-1 minimal, ‘energetic’ perception.

Then the second level of structure of mathematics, is a collection of points, which mathematicians tend to refer to with two ‘structures’ of algebra, the set and the group, which is basically a set (a spatial collection in ‘present’), subject to temporal motions, caused by a ‘symmetry’.

Thus a set is ∑i, a sum of points…

And a group is STi, a set in ‘motion’ due to a symmetry between its dimensional scales.

Thus we can write an equation with ‘existential algebra’ to describe those mathematical levels:

∑∑i-points=∑Sets-> ∑Set x Symmetric Motion = i+1 Groups…

which define the 2 main scalar structures of mathematical systems.

Indeed, it has been said that mathematics is all about geometry, its initial configuration, whose fundamental unit are points; and in the modern age about sets and groups, the fundamental tools of algebra. And today they are used to define mathematics. Now, we will understand them in harmony with all other sciences, as a ‘manifestation’ of the 10 Dimensional Universe.  To notice though that mathematical analysis has only ‘2 fundamental scales’ – that of points and its elaboration by geometry, and that of groups of points, sets and groups with operations. Why there are not an intermediate i-ndividual scale? The reason is the aforementioned lack of ‘inner structure’  of classic mathematics, which we partially will remedy with our r=evolution of the concept of a point. So far, this means that the i-ndividual scale matters not in mathematics.

Mathematics is about ‘sociological’ properties, as ‘numbers’ are social collections of points where the individuality disappears. And so i+1  social scales are indeed an overlooked property of at the Universe, denied by the ego-centric human being, which the mere existence of mathematical numbers prove.

Mathematics thus is the essential, ‘primary’ language of the simplified i-1 vision of the Universe, but also fundamental to understand the sociological, i+1 qualities of ‘numbers’. Whereas, points are the ‘spatial’, geometric perception and ‘numbers’ the ‘ordered’, ‘causal’, hence temporal analysis of it.

We thus have defined for mathematics and its sub disciplines two fundamental symmetries of the Universe:

– The symmetry of its scalar dimensions

– The correspondence or ‘isomorphism’ between its spatial and temporal vision (points and numbers).

And both prove or rather ‘reflect’ the laws of scalar space-time (as mathematics as all other languages are secondary to the Universe and its fundamental language, the ‘existential algebra’ of the 10 Dimensional super organism).

Mathematics also reflect the properties of at the 3 dimensions of space, considered ‘alone’. In fact in combination with physics, (which adds motion, the dimensions of present-time duration to the static geometry of space), this field is the most exhaustively studied of all the aspects of the Universe by the ingenuity of man. If there is a subject where all the details are known is on translations, rotations and symmetries in space and at the motions taken place within it

But what about the symmetries and ages of time? How mathematics has dealt with it? It has done so in steps.

First mathematics dealt with the dimensions of present time, or ‘duration’, v=s/t, and its inverse frequency, 1/t and again it has done so exhaustively through the development of calculus and the corrections for ‘simultaneous’ measures discovered by Einstein’s relativity. But by definition calculus studies ‘continuous’ functions, which therefore do ‘not’ change phase, state or age, that is do not ‘abandon’ the relative duration of a present, in which the inner forms of the system do not change.

In other words mathematics has not properly understood the causal processes from past to future, which in any case are much better understood by Logic. And so if we were to consider the ‘limits’ of mathematics, they would be found in the proper understanding of ‘evolutionary’ and causal processes and the past and future dimensions, which are far better analyzed by logic, causality and biological theories of evolution and organisms, so we shall refer those dimensions and processes in those other sections. 

However in the XX century the last branches of mathematics to be developed – topology and fractal mathematics, have made inroads on different temporal motions than ‘duration’, which are essential to the understanding of the morphological processes of change – essentially directed by at the 2 manifold, membranous structure of biological organisms.  While fractal mathematics is essential to understand the repetitive scalar structure of the Universe. So we shall also consider those themes in depth, in this web ‘always a work in progress’, as i keep pouring the thousands of pages of analysis of all sciences done with the formalism of 10Dimensional Super-organisms.

Let us then start as the History of Mathematics did, with the initial postulate of geometry, the definition of a point, upgraded to includes its ‘inner, informative and energetic parts’. Since now the 5 postulates of ‘fractal, non-Euclidean geometry’ will further enlighten our compression of the world in one of the main ‘languages of God’ but not the unique, mathematics.


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 hyperbolic, 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 toroid topology. In the upper graph, it is the double ring, or convex, toroid 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 hyperbolic 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 3rdcanonical 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 hyperbolic 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.

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 hyperbolic, 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 toroid, 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 toroid 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.

Let us then cast upon the 3 regions of the point a more ‘physical description’ by using the conservation principles of science.


open ball t.oe

The fundamental element of any system is its vital energy, enclosed by a 2D angular momentum-membrane self-centered into a 1D singularity, establishing the essential equation of all systems: 1D singularity + 2 D membrane = 3D vital energy, and the 3 conserved ‘fractal quantities’ of any super organism of space-time, angular momentum (2D membrane), lineal momentum (motion of the singularity) and energy (volume enclosed and managed between them).

This is the simplest structure we find in all scales of nature, from atomic systems with an electronic membrane and a nucleus singularity enclosing fields of gravitational and electromagnetic energy, to cells with protein membranes, DNA singularities and vital energy enclosed in cytoplasms, to nations, with a hard-military border, a capital-singularity and a vital energy of middle working reproductive class, to galaxies with a halo of strange, dark matter, a center of top quark black holes and the stars, mitochondria  that reproduce them both, to yourself with a sling membrane a nervous brain singularity and a reproductive body.

The simplest mathematical representation will be then a 3-D volume of an open sphere, constrained by an angular momentum and beating at the rhythm of its singularity clock of frequency=1/t.

Yet when we extend the system to different scales of reality, from the ‘o-1’ unit sphere into the 1-∞ larger world, we need to add the ternary structure of systems in 3 planes of existence.

Let us then now explore in more depth that duality of locomotions expressed mathematically as ‘speed’ or change in the motions of being, studied by physics (v=s/t) and its inverse change of information, expressed with frequencies, T=1/ƒ.

As it will reveal the essence of the duality of time space arrows – the inverse properties of lineal time-duration and cyclical, frequency time clocks, which come together ONLY in the vital energy spacetime systems that combine both forms and properties into a ‘present being’.

Mathematic 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 toroid 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 toroid 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: A ‘mouth’ or opening that absorbs energy.

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

Max.+Ti: An ‘eye’ through which the informative center receives external information.

Max.–Ti: An ‘antenna’ 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 behavior 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 termsmathematicians 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, equaling 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 toroid, 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, hyperbolic 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 toroid, convex, warped forms, corresponding to the informative dual ring of a Belgrami cone. The toroid, highly warped brain is a double hyperbolic, self-similar to the toroid 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, toroid 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.

The fundamental unit of the Universe. The Non-E Point as a time cycle, its derived actions and integrated worldcycles.

Now Non-Euclidean fractal points are time cycles. It is therefore necessary to have a dual conversation through this blog and reality- between the idealized logic-mathematical world of i-points of view creating the Universe in any plane of existence, and the multiple varieties of them we find in each plane.

Indeed, what in common have a human and an atom? Now if we compare only the head/particle point of view, we suddenly realize we do have much in common. We are two spherical systems with an aperture to absorb energy from the Universe in the equator region (our mouth, the atom’s main S-orbital plane), and two spherical points of maximal informative activity, contently absorbing and emitting waves, which act as our eyes/receptors of information, whose information regulate the behavior of all our systems.

To which extend we want to ‘make up’ this reality with niceties is up to us, the ‘deep 5D coverings’ we add to the bare bone atom to become molecule, cell, human, is of course of interest, but it is ultimately a repetitive game.

So the point, number, Œ, starts a game of actions.

First it observes. It is the observer, the primary being and as such it needs one better 2 eyes, to perceive with an excellent angle, in the tropic North, of the sphere. Here the point achieves rotation, which means without disturbing truly the outer world, except for what the pi sphere can implode as bits of information in its rotational motion, the being perceives.

Rotation thus is the first form.

It is not lineal motion which occupies other’s space and enters in conflict

It is rotation.

And so the point said, let me be a point of view, let me rotate, let me have angular momentum.

And existence was born

We shall call this first existence which we know spin and give it value h/2, the first known angular momentum of the cosmos.

That the point perceives is clear. It is an oxymoron, as we perceive light, our eyes are made of light and light is made of h/2 angular momentums, 2 of which make an h, dual point of view, which scans a 3-Dimensional world.

For a while perhaps the point vibrated, but certainly it was only too soon that the point made an entire π circle, and so as H turned two pis around it became a Planck constant.

Those minimal forms, the radian of perception, the Planckton with a full rotation, the first time cycle with a complex M x V x R 3 variables – the point, the angle of perception and the moving object with p-momentum, which the point observes, are already a game of gauging information and perhaps future energy, a first act of communication and so it enters the second postulate.


An important quality of fractal points is to have a singularity center that gauges information coming from infinite parallels to map out the Universe. In that sense the 1st and fifth postulate study fractal points from different ‘points of view’ – the first from the external pov, the 5th from its internal point of view.

So we shall just briefly refer from other point’s text this singularity element of linguistic perception that all points-monads must carry.

The mind paradox: the meaning of Galilean relativity. The singularity as a mind.

“God is the unmoved (perceptive) center of a body of energy, moving around it”. “We are all Gods (of our super organisms” Aristotle

Now there is another way to observe the Equation, ∆ð≥S@, as the formal reduction of a temporal flow of cycles of space-time into a mind-mapping, from the infinite Universe into the linguistic, still zero mind.

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 §pace, which he called ‘res extensa’.

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

And then he added a 3rd element, the final stroke of a genius unparalleled since the ðimes 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’.

Euclidean mathematics, as Descartes and Kant understood is only the 3 perpendicular ‘space-time elements’ of a massless ray of light merely shrinks all other scales of reality to fit into the mind:

In the graph, as our mind is electronic, we feed on light energy and transform it into an informative mapping of the Universe, reduced to what light sees. Thus our space is light space-time, with its 3 Euclidean coordinates, a fact that was first understood NOT by physicists but by impressionist artists, Leonardo, whose motto ‘saper vedere’, guided my inquire as a young artist on reality behind the languages that describe it, and then by the impressionists; and finally by Picasso, who departed from reality, affirming he painted thoughts, so he studied the ‘elements’ of the mind mapping, its entropic lines (cubist age) and its cyclical forms (female portraits).

So let us consider the final element of reality to be able to build the whole… the mind that projects and co-exists in those three scales ordering the parts into a whole and helping it through its actions to survive.

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

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

Space is the simultaneous perception of multiple vital spaces by a still mind. Thus space is virtual. The true substance of reality being its temporal motions. On the other hand the description human minds  (@) make of the Universe is subconsciously biased by those ‘still, linguistic mind mappings of space’, (∫@) in which the ∞ of time motions (∆ð) is reduced and equalled to the spatial mind mapping.


This simple equation of similarity between the space perception of reality provided by a mind, and the whole Universe of moving time-cycles (as nothing is still outside the mind’s perception, being all observed in detail in perpetual motion), appeared in science as a philosophy of the Universe, when Descartes realized that what we see is NOT reality but what the mind ‘stops’ in its selective perception of all the information of reality. So the only truth we can depart from is the fact that we think and perceive still linguistic thoughts, hence we exist; making of informative perception in a still mind, the first ‘action’ of existence, even prior to motion which is unconscious of being.

Descartes astounding insight soon brought here to define mathematically, topologically and conceptually a ‘mind-singularity of order’, the ‘missing’ factor on our descriptions of reality, unfortunately was soon forgotten, and substituted by the naive realism of modern science – what we or our electronic instruments see is what there is there. But only marrying the spatial mind-linguistic view and the Universe of infinite time cycles, we can factor in all the elements and start to unknot the bias the spatial mind cast upon our objective comprehension of reality, which is our task as scientists.

In the graph, a fundamental truth of the Universe is the existence of singularities that order physical, biological an social systems, except when they are in a free, chaotic state of maximal entropy (gaseous state or dark entropy between galaxies), which cannot produce order, as they lack any ‘frame of reference’. Mental singularities, Monads, or Maxwellian Demons are the ‘missing variable’ needed to explain the whys of reality. In mathematics we call them P.o.vs.

Frames of reference, self-centred in a point, which we use as physical systems do, to calculate functions of space-time that WORK mirroring reality – hence they must exist. In that sense physical, atomic systems do indeed calculate as quantum-bit computers might do. Are they ‘conscious’? Likely NOT, as consciousness is just a self-reflection between two mirrors – what matters though is that they do process information, order territories that become time§paœrganisms and hence WITHOUT THEM there will only be entropy, not order, reason why physicists who don’t recognise those ‘poles of in-form-ation’ deny order and believe the Universe is a chaotic entropic state. YET WE OBSERVE order, so the experimental method oblige us to conclude there is a ‘darwinian automatic non-conscious selection’ of systems which develop singularities and ‘SURVIVE’ creating the order of reality.

Consciosuness would then be an unneeded dual mirror in which the first mirror perceives the spatial mapping of the second mirror, dialoguing with it (in the way I robot is consciousness by having a second brain). In the human case, the I=eye that sees space and the verbal cogito ergo sum temporal mind – the conscious languages. But it is not the verbal consciousness of man, but a mathematical consciousness which among humans only very good ‘mathematical physicists’, which can ‘see’ as musicians see ‘scales’ that provoke emotions, equations as dynamic visual forms.

So we affirm, as Aristotle, Descartes and Leibniz before us, that even though for physical measure it might be useful to equalise all rhythms of time and peg all ternary space-time beings into an absolute space and absolute time – that of the human light space view and mechanical clock, there are infinite clocks of ðime, and infinite broken §paces and we adopt the point of view of all of them.

Since there are ∞ minds, gauging information; and stopping the motions of time into the intelligence of formal space, as they try to ‘stiff’ reality into the mirror image of the language, which of course they confuse with the universe itself – and this is indeed the origin of the creationist theories of religious and scientific people, we must now debunk on firm grounds as we have a better grasp of why we see still the earth (our mind stops its motion) when objectively it is moving, why in other words we see ‘spaces’ when it is all about ‘times’.

A subject in itself fundamental to understand Relativity, is brought here to point out, the reason why in entropic only big-bang theories, we do see indeed light space-time expanding between galaxies, as light is space and so when it comes closer to the mass of the galaxy, elongates/red shifts its color (the only real effect observed; as we obviously are NOT out there in-between Andromeda and the Milky way with a tape). And vice versa, when Light collapses into our electronic ‘eye’ or any electronic source, it increases its frequency  balancing both effect to cancel the supposed big-bang death of the Universe.

But in the scalar REALITY, gravitation makes points LARGER when we observe them in the scale of the fifth dimension where they do interact above us, and will EASILY evaporate our ’empty bubble’ of light-light beings.

So Hilbert and Cantor who talked of ‘their imaginary paradise from where nobody would expel them, ass the Jihad warriors who die to enter paradise, just invented non-existen points, lines, planes with their imagination.

In the next graph, we see thus, the true meaning of the 5th and 1st Non-E postulate, which define both the real fractal point (1st postulate) and the real mind that bends it into a smallish mind. Since the fractal point does have breath, as it includes a volume of energy, entropy and information, carried by a relative number of ‘finitesimal’ parallel waves, but the ‘Aristotelian mind’, reduces it to an Euclidean point:

We have to introduce the first postulate of non-Æ so you realise how ‘limited’ is the homunculus mind.

Thus, human egos are just finitesimals with a huge ego, because they confuse their zero point-mind with the real infinite Universe, of fractal points, thinking the volume of information they store in their mind is all. 

Fractal points: the fundamental particle

Mathematics, as a language that represents reality with simplified symbols, has a limited capacity to carry information. Its symbols, geometric points and numbers simplify and integrate the fractal, discontinuous reality into a single space-time continuum, the Cartesian Space/Time graph, made of points without breath.

However the points of a Cartesian plane or the numbers of an equation are only a linguistic representation of a complex Universe made of discontinuous points with an ‘internal content of space-time’. In the real world, we are all pieces made of fractal cellular points that occupy spaces, move and last a certain time. When we translate those space-time systems into Euclidean, abstract, mathematical ‘numbers’, we make them mere points of geometry void of all content. But when we look in detail at the real beings of the Universe, all points/number have inner energetic and informative volume, as the fractal geometry of the Universe suddenly increases the detail of the cell, atom or far away star into a complex complementary entity.

So we propose a new Geometrical Unit – the fractal, Non-Euclidean point with space-time parts, which Einstein partially used to describe gravitational space-time. Yet Einstein missed the ‘fractal interpretation’ of Non-Euclidean geometry we shall bring here, as Fractal structures extending in several planes of space-time were unknown till the 1970s. So Einstein did not interpret those points, which had volume, because infinite parallels of ‘forces of ‘—motions’ and information’ could cross them, as points, which when enlarged could fit those parallels, but as points in which parallels ‘curved’ converging into the point.

This however is not meaningful, because if such is the case parallels which are by definition ‘straight lines’, stop being parallels. So we must consider that what Einstein proved using Non-Euclidean points to explain the structure of space-time is its fractal nature: points seem not to have breath and fit only a parallel, but when we enlarge the point, we see it is in fact self-similar to much bigger points, as when we enlarge a fractal we see in fact self-similar structures to the macro-structures we see with the naked eye.

That is in essence the meaning of Fractal Non-Euclidean geometry: a geometry of multiple ‘membranes of space-time’ that grow in size, detail and content when we come closer to them, becoming ‘Non-Euclidean, fractal points’ with breath and a content of ‘—motions’ and information that defines them.

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

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

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

Abstract, continuous, one-dimensional point:

. ____________

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

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

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

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

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

So each point is in fact a 3-dimensional point, and if we go to the next scale, a 3×3=9 dimensional point and so on. Yet those dimensions are the so-called fractal dimensions, which are not ‘extended to infinity’ but only within the size of the point.

In Euclidean geometry, a point has no volume, no dimension, but string theorists say that even the smallest points of the Universe, cyclical strings, have inner dimensions that we observe when we come closer to them. That is the essence of a fractal point: To be a fractal world, a space-time in itself.

‘Any Non-Euclidean point is a fractal space-time with a minimal of 3 internal, topological, spatial dimensions and an external time motion in the st+1 ecosystem in which it exists’

This simple law is the most important law of the 4th paradigm, foreseen by Leibniz in his Monadology, the foundation of the mathematical model of Multiple spaces-times that completes the 5 Postulates of non-Euclidean geometry and gives us the tools necessary to create a complex new logic and new mathematical model of the Universe, easy to connect through topology with the isomorphisms of the previous paradigm of a single metric space-time continuum.

Further on those points must be described always in 4 dimensions, with motion. This should have been obvious, but abstract mathematics simplify entities into numbers and static forms, and organic motion properties disappear. Yet we still say ‘San Francisco is at 8 hours from LA’, because we mean that journey is a combination of the motion of a car and the spatial distance. Thus we measure reality in Time-space, not only in space as Euclidean maths do.

Thus, in the same way Saturn’s rings stop being planes without volume when we come closer and observe them as fractal points, called planetoids; Non-Euclidean points acquire both motion and volume when we approach to them. In words of Klein, a sphere is not a continuous static form, but a group of points in cyclical movement. So in the same way the Saturn’s rings are a group of planetoids, a Klein space – the space-time that fills a point has motion – it is the sum of a series of cycles.

Einstein didn’t go further, adapting the other 4 Euclidean postulates to the new Geometrical unit: a fractal point with volume. Only then we will be able to define the 2 planes of physical forces, the plane of gravitation and electromagnetism, or any system in which several planes of space-time co-exist together (as in a human being extended from atomic to social planes of cyclical existence).

In all those systems planes are made with cellular points, Riemannian spheres with volume that form lines, which are waves between points that exchange ‘—motions’ and information and planes, which are organs of self-similar points that process ‘—motions’ or information in parallel networks. Thus the 5 Postulates of Non-Sp Geometry vitalize the Universe as a series of networks of ‘—motions’ and information of self-similar cellular points. Since the line and the plane acquire volume and become self-similar to the commonest forms of the Universe, the wave and the network of points with a 3-D volume.

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

All in the Universe are thus complementary systems made of networks. Now this might sound absurd to the anthropomorphic reader that thinks humans are different from the rest of points of the Universe, but it is a fact that those points obey in their actions and communicative flows within a network the same isomorphisms:

humans and electrons behave the same when they move through slits or in herds, the geometries of social groups are also the same and the ultimate purpose of those points, to feed on ‘—motions’ and information, whatever kind, is also the same in all networks of the Universe. And so that group of isomorphisms of networks becomes a primary why for all beings of the Universe.

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

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

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

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

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

O@ (infinitesimal Œ-point or mind) x ∞ð (Universe perceived) = Œ (constant mapping of reality)

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

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

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

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

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

The Universe can be perfectly understood when the human mind and its subjective vision of reality from the perspective of its limited ‘Aristotelian’ and ‘Euclidean’, logic, (temporal and visual, spatial perception of the human mind) is considered only one of the infinite points of view, performed by particles and heads that gauge information, move ‘—motions’ and constantly create the events of the universe. Each of those particles and heads create its own perspective and mind view, or mapping of the Universe to which they act-react accordingly.

 Mind languages do stop the 3 motions OR CONSERVED quantities, into space forms, and with its syntax mimic how those 3 elements combine to create the space-time super organisms of the Universe.
So we could say they map out superorganisms of space departing of infinite time-cycles, seeds of information, mind or simultaneous networks.
So the 3 main human languages, maths, words and images are ‘still images’ of a living, moving Universe of infinite time cycles: S@≤∆Τ
Let us then switch to the subjective mind view and include a first analysis on how the mind stops motion into form, and how it biases in this manner our perception of motion, despite the rejection of ‘naive realists’ that simply eliminate from reality all those spatial mental elements (as in the dominant philosophy of science today, logical positivism, which simply is not interested in study what cannot be measured, and unfortunately has substituted the perennial ‘pan psychic philosophy of reality’ that considers the existence of infinite such minds that stop linguistically reality to perceive it).

We can now give the explanation of the Paradox of Galileo, which started modern science but has never been quite resolved: ‘why the earth moves but doesn’t move’. Simple, because the mind-singularity that perceives it has as a function, to create within its language a still mirror image, a focus of reality that will allow to order it and try to deform it from its ego-centered perspective.






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