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1Ð: gauging information: ï







3925th postualte

We have so far considered the Universe in its fundamental principles – the topological adjacent construction in simultaneity of super organisms, which sequentially will live a world cycle, ‘traveling’ through 3 planes of the fifth dimension. Neat and simple, that is really what there is to it. Minds though, mirror those infinite worldcycles of existence of other space-time super organisms with languages ‘stopping’ them into a mapping that allows them to ‘perceive=gauge=sense‘ information.

And we highlight sense because a ‘still mapping’ sense in each stopping, locked ‘crystal image’ a measure of its self. The sentient Universe can only be ultimately explained if ‘perception’ exists within the language, as when you think words, you sense words, when your eye sees light and maps into an electronic mapping you are seeing. And when an atom maps a geometric image in its ‘locked’ ‘stopped’ spin, it must perceive that geometry as information.

Minds thus are infinitesimal points-particles that stop, gauge, perceive, and move – and then we have the sensation of motion-pleasure.

This of course is not within the realm of the scientific method. You cannot measure those sensations of awareness-pain vs. pleasure-dissolution, in-form-ation, pressure vs. release-entropy ONLY sense them as humans. So if we had first a difficult hurdle to cross trying to prove the existence of minds but passed it objectively by considering a mind-singularity to hold the will of existence of a T.œ – hence as invisible gravitation shows in its external effect, so will the existence of a singularity through its external actions; at the final level of ‘human awareness’ of the game of existence – sensations of the dual pain-pleasure reward system (with all its parallel and perpendicular events/sensations) there is ONLY a justification to the existence of other minds – that we humans are made of the same substances that all those other minds, space and time, and hence what we sense other atomic systems must.

Therefore IF OUR LAST REWARD is the flow of sensations, with its duality pain-pleasure, hate-love, etc. which we can easily adscribe to geometrical perpendicular (cut, pain) parallel (friction pleasure) properties and many other dualities we have established for all systems, IT MUST EXIST IN ALL OTHER SYSTEMS of space-time. That is, atoms must feel pain when op-pressed by huge masses, pleasure when released in entropy, but also ‘awareness’ of a more complex inner still image, when flows of information converge through forces in its non-euclidean singularity; and so it is only left then 2 questions:

  1. What are those sensations? Answer: the very essence of time as a motion/flow. Motion in itself seems evanescent; as sensations are… Yet combining them, this flow of sensation-motion becomes very likely the ultimate program-will for all T.œs to exist – the ultimate, ‘Dasein’, ‘being in time’.
  2. Yet we cannot go beyond this, as this is the ultimate ‘reference’ of reality we have as humans. So there is no MORE methods of knowledge beyond what it is contained in our ‘selves’. Know yourself, the method of knowledge of Aristotle; ‘saper vedere’, the method of Leonardo and know how to see and calculate with attached machines, the method of Galileo, to which we have added a few ‘tricks’ thus completes the capacity to probe reality. Are there more layers beyond motion as sensation in time? We cannot answer. We don’t know. As all is relative, in the same manner we can only probe into ∆±3 planes around our ∆º and hint by force of motion the existence of an invisible gravitational/cosmological plane at ∆±4 but no more, beyond the duality of sensation, there is nowhere else to go.


CONTRARY to ‘physical belief’, the first quality of the Universe before motion exists is information gauging: absorption of energy by a head-particle-social network, which transforms it  through its hardware into a software still image (ab.S@) of the Universe it perceives.

So the mind is a singularity or infinitesimal 0-point, the relative frame of reference that maps the ∞ cycles of SPACE-ðime of the Universe, reducing them to a ‘World’, to fit them into the infinitesimal volume of the brain.

This we formalize with the equation of the mind:

0-linguistic mind x ∞ space-time cycles of the Universe = Constant World mapping of reality, with the mind at its centre.

In mathematical terms 0 x ∞ = Constant; that is the infinite information of the Universe, multiplied by the relative infinitesimal volume of our mind gives us a constant mapping, where we extract all the properties that are not interesting to us and our self-centred view.

So the first to go are the MOTIONS of other entities, which is what makes them feel alive. Indeed, Science started when Galileo realized the mind stopped the motion of the earth, but the Earth MOVES: e pur si muove he said and Galilean Relativity latter expanded by Einstein gave birth to physics.

Next, of course, they eliminate ALL THE OTHER egos, and sentient points of view, so only we are intelligent. And animals perhaps and only recently. But our atoms are NOT different, so the sentient pan psychic universe likely IS already thinking in any atom, as all reproduce particles, gauge information, evolve socially with magnetic fields. But we JUST reduce minds to ours.

And this is the origin of the paradox of the ego, as from a perspective which is blind to all the motions and vital perception of other beings, as from our perspective, NOTHING THINKS AND from our perspective we see our own nose bigger than Andromeda. So reality becomes deformed, inert, and the ego becomes the center of the Universe, as always happened with humans who thought first the earth in its center, then chosen of god, the creator, who spoke our language, and finally debased all living entities reducing them ‘to spatial forms’ in the still mapping of the mind, which stops all motions to fit a reduced image of reality.

So we express verbally the ego paradox, as the ‘ego believes its still mind mapping IS all the information of the Universe, when it is only an infinitesimal part of it, self-centered in the self’.

In the graph we can see the difference between the subjective EGO PARADOX who thinks THE MIND MAPPING of reality with light-eyes and its 3 perpendicular coordinates is the universe, with the reality, of an entire Universe, in which the self-centered ‘Cartesian humind’ is just one of the many minds, that use many different type of pixels, from atomic olfactory elephant minds to gravitational black hole and atomic minds, possibly with different geometries, certainly with different perspectives, but all gauging information and moving through reality perceiving from its own ego-paradox/point of view.

So while the ego is natural to all species, and hence when a child is born it thinks to be the centre of the Universe. As there are infinite other egos trying to absorb your energy and reproduce and prey on you, a childish mind that doesn’t see or refuses to reason about the paradox and take measures to control other species’ reproduction becomes systematically extinct in the action-reaction processes of the Universe.

The mind ordering a territory. 

Next the mind, once it has perceived in any of the ∞ languages-mappings, it will try to order a territory by reflecting its mind view on the external world – and this is the ultimate meaning of Aristotle’s unmoved Gods that move the energy of its body-waves around them – in quantum physics of the shyncronicity of Broglie’s internal clock of the particle with its wave, in man of its second-glimpse of the eye with the steps of his limbs and heart’s rate – the mind is at it, trans-forming the world to its image and likeness, ignoring in its struggle for survival all other fractal non-euclidean points minds with its volume of information and flows of parallels going in moving back into order:

So once the mind has perceived, and flows of energy have been gauged into information it will then direct, and divert the body to obtain motion towards a desire point of the Universe where it will be able to continue the program of absorption of information and mirror creation of its inner order which rules its existence.

And this is thens the 1D mind->2D motion->3D energy absorption->1D order creation ‘loop’ of most common existences:

The mind is thus @RISTOTELIAN, clearly on a single route of dimensional perception and order, it DENIES to all other rivals. So   humans deny in physical sciences minimal perception to one-dimensional particle-points, quarks and electrons, with no volume – never mind they use a gauging=information theory to describe them (its 3 angles of perception being the fixed spin positions).

All systems though not only biological beings, where we see heads as the most observed informative systems, similar to us, ARE gauging. From atoms to chips and human brains that we see as networks, within any hardware, there is a software of forces converted into geometric logic paths of languages that perceive in themselves an image mirror of the Universe.

This is thus the first program, perceive. ‘I perceive therefore I am’. Any hardware, a network of chips, a brain network, a head of genes in a cell, a particle of mathematical flows of magnetic and electric energy or of gravitational energy – mass or charge vortex – will want to maintain its perception of a stable, rich in varieties of perception universe, in which the light of energy is higher than the darkness of void of it. Where the entity ‘feels at home in its interpreted world’ (Duino). The poetics of existence must never be far away in its perfect isomorphic transliteration of meanings.

Organs of Perception transform energy into languages of Information, different for each brain species

Relativity of virtual worlds: minds

It is then clear what is perception: the knotting, the inner-form-ation of universal energy that becomes formed through the language, organized into shapes by a linguistic brain.
That brain perceives the form as energy goes through its centers of perception. You perceive as you see electronic images, made of light-energy, a computer perceives as electronic data made with electric energy flows through its center.
In the organic Universe, all knots of information, all spherical, cyclical brains perceive and trans-form energy.

Each one uses a different language. That does not matter. Only the arrogance of man denies that a rabbit perceives the carrot with smell as well as we do with sight, or a computer does it in mathematical terms.

In the relative stillness, and focus of a brain, that acts as a linguistic mirror of reality, the language traces a reduced version of the Universe, and that mirror-image is perception.
Languages are living species, they perceive.
Even a computer is a observer of digital languages, that once awakened in a robot body will also move and have a second will of organicism , besides informative perception, and energy feeding.

The Galilean paradox

We could resume the nature of perception, in the Galilean Paradox main cause of behavior of Universal species. Every species considers himself the center of the Universe, in as much as it perceives from that Universe only a certain part of its information, processed by the mind and the limited informative languages of the species. In fact a mind is a Galilean paradox, what a physicist would call a ‘quantic knot’, or deformation of spatial energy into temporal information, into form, into a mind. You are a subjective knot that deforms reality from your point of view, from your frame of reference, from your ways of perceiving, and smelling and hearing reality. Reality is not your Galilean paradox; reality is something else, that you hardly understand.

We call it the Galilean paradox precisely because modern science started when Galileo discovered without understanding it one of such paradoxes: the fact that the Earth and our mind feels the Earth fixed, as the center of a Universe turning around us, when in reality it is the Earth what moves around the sun. That paradox of perception never solved by Galileo, is the key to understand the Relativity of spatial, scientific knowledge, compared to the absoluteness of organicism and his laws and arrows.

Let us study then under the Rashomon effect the different perspectives on those minds.



Perception maps out with different languages the motions of the Universe, as the perception of the being requires the transfer of ∆-3 pixels of diminutive information to map the world with those languages perception is motion relative to the focus of perception, the still Gods of Aristotelian philosophies:


Absolute relativity vs. homunculus ego-MIND.
The laws of the mighty infinite Universe; which makes us absolutely relative, in motion, form and scalar location in the Universe.
The natural expansion of the work of Godel proves the mental relativity of all languages including mathematics. Now extended to the absolute relativity of the homunculus ego, even if he feels to be infinite in his finitesimal mind, inversion of the true infinite Universe:  1/∞= Mind = 0

As such the mind both absorbs and emits energy and information with the external Universe, as it orders a vital territory or body, isolated externally by a membrane. Yet the singularity centre of a hyperbolic wave which brings from the spherical, clock-like curved geometry of its membrane remains even in complex network the most solid, orderly quiet, self-centred font of order and origin of the dominant arrow of information of the Universe, as a sink, monad, charge, mass, you name it – singularity sink that absorbs and reduces energy to a mapping of beautiful information, the mind-monad which plays the GST game that makes it equal to any other singularity-mind of any level of existence of the Universe:

Minds though mutter because they are the Form-Future-upper scales (ST∆), which are always happening together (form with lesser entropy is the relative future state of any system, as a tighter network of imploding, still-mind like forms which become a single whole, from the p.o.v. of a lower scale), is defined in terms of implosive, closed time cycles as one of the 3 ‘functions-forms’ of space, as ‘Still Form’, only.

So here we shall deal with ‘Form only’ as a process that implodes space into information by slowing and curving a ‘loose herd of a lower plane of the 5th dimension, creating a new scale, and warping, the entropy ‘scale below’.

Tiƒ is in its purest form a seed of language, which the wave will re=produce over the non-perceivable motion of the field of entropy.

It is in essence the mirror symmetry of the game of exi=stence. The language-singularity-point forms then a ‘lanwave’, herd, network. So in the next scale of development the seed is the network that invaginates the vital space, and organise it. And this brings the reversal of time, from entropy to information that will become a wholeness of organisation.

The seed is thus the intelligence of the Universe, ‘frozen’ in a perfect ¬Æ form of packed in-form-ation.

At birth all forms are Tiƒ seeds. In development all forms have a point of minimum space, a fractal point that hides in a lower ∆-1 the potential structure of an ∆+1 game. So the seed is ∆º, the point-frame of reference of the language.

The seed in mathematics is the mind of Descartes. And any mind which will have a relative frame of reference or world with 4 different quadrants, of possible directions of its motions, along the 2 inverse arrows perceived from the seed in a field-gradient of entropy (x-coordinates) and a dimension of height (information). The seed in the middle will start then to move along the feeding x-coorddiantes of entropy to vibrate upwards and reproduce a tall bosonic height of information, if we were to put a canonical example of mathematical physics, the SMH:

We can even imagine the seed of all seeds, in the GST rules of the lanwave of space-time beings.

So the final absolute information of 0 motion and infinite curvature or singularity-mind, is for man the GST program, in physical space-time, the black hole, in our super organism, the mind of time; the arrow of evolution and life, the thoughts of God, the non-Æ logos (Plato), image of all the images of the cave, of ‘a higher logic than man’ (Augustine), through which I peer with my faulty languages, along the smallish apertures of its π-brain into the absolute:

5D best

Mathematically the equations of tif, are non-lineal, of difficult resolution as they have many different inflationary informative solutions to the different mappings that can grow in complexity and are related to all kind of mathematical structures from the 4d coloring of a two dimensional sheet, to the theory of networks and knots.

THEY Are in general better expressed with tensors that freeze and reconnect systems, from masses to neurons, from crystals to dna waves.


265BUT SINGULARITIES must communicate to evolve socially. It starts with 2, then IT WILL GROW further away into a wave, becoming a more complex St-RELATIVE events of two poles, or conic geometry:

Communication embodies the meaning of the Universe as monads share energy and information starting to build complementary Spe<Tiƒ systems, which will reproduce and evolve socially into larger wholes. So without communication, none of the complex actions of the Universe are possible.



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.

The fundamental particle of the Universe is not a physical form but a logic particle: a knot of time arrows, which in any scale of reality, from physical particles (quantum knots of ‘—motions’ and information) to biology (knots=networks that absorb ‘—motions’, information and reproduce and evolve into bigger knots) act under a single mandate: to maximize those time arrows, a fact that we formalize with an equation, the function of Existence: Max. ∑SxT; which is the fundamental function of both, logic and mathematical languages. In the graph, all such points of view, will define a system of relative perpendicular coordinates, through which it will enact its time arrows, departing from a central knot of information.

Geometry of Multiple Spaces-Times: fractal creation.

Reality is made of entities that are knots of Time Arrows constantly tying themselves up with other knots of Time Arrows, forming networks in different scales of existence, evolving as complementary organisms of ‘—motions’ and information. And the question that science asks next is how to formalize that game of existence, its knots of Time Arrows or ‘entities of reality’, its fluxes of ‘—motions’ and information, its reproductive flows, herds and motions; its complementary networks of ‘—motions’ and form that create super-organisms. And the answer is, as all models of science with its primary languages of space, mathematics, and time, causal logic, albeit more complex than the logic developed by the Greeks to explain a simpler Universe.

In this new Non-Euclidean topology, planes are networks of knots of Time Arrows; and those knots of Time Arrows, the beings of reality are ‘Non-Euclidean points’ with a volume, or ‘organs’ that transform back and forth ‘—motions’ into information, creating reality.

All what you see becomes then a game of knots of Time Arrows, or ‘Non-Euclidean fractal points’, connecting themselves to other knots, forming complex planes, networks of points of two types, networks of energetic points (herds in motion) and networks of informative points (still networks). In any scale of reality those networks of points, which are knots of Time Arrows take place. The simplest scales of atoms can be described as such networks, but also the human scale. Consider a meeting: a series of human heads, moved by a lineal limb will start to share ‘—motions’ and form by producing waves of smaller ‘particles’ (sounds), and acquire a cyclical geometry as they create an event of information.

The Universe is a self-similar reality of infinite processes of creation and dissolution of networks made of knots=points of arrows of ‘—motions’ and information; and the best instruments to analyze it are the languages of the mind. In that sense, humans, before clocks reduced our conception of time to a single arrow and language, were guided by psychological time, which is our inner perception of our time cycles and drives of existence – our desire to perceive, inform, reproduce and evolve socially. So we lived according to our cycles of ‘—motions’ (feeding hours), reproduction (family cycles), and social evolution (religious and cultural activities). And followed the cycles of the seasons of this planet, according to which all living species calculated its reproductive cycles.

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

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, ∆-dimensional points:           =========== o

In our definition of the fundamental particle, the fractal point of view, we must for shake of rigor, bring about basic foundation concepts of mathematics to introduce the ‘Holographic principle’ of a Universe where the 3rd dimension of space-time, is made by the accumulation of bidimensional membranes, as you are made with ‘membranes’ of skins, membranes of layers of cells.

To understand this so-called holographic principle, however we must also introduce first the concept of a Non-Euclidean, Fractal point the so-long needed ‘definition’ of the 1st postulate of non-Euclidean geometry, similar to the 5th, which affirms that:

‘All points have breath, they are spherical topologies that include within themselves a volume of spatial energy and temporal information, which becomes ‘evident’ the closer to come to them’.

Non-Euclidean points were philosophically described by Leibniz in his Monadology. They appeared first in science in the incomplete work of Mr. Einstein, regarding the Non-Euclidean structure of space-time.

There are 2 interpretations of this fact. We could consider that lines are curves, thus Non-E points are focus of multiple forces that bend to flow into the point. This is Mr. Einstein’s preferred solution that defined a curved space-time. Yet Mr. Einstein’s solution brings 2 logic contradictions: Lines stop to be lines and become curves, and still those curves have to become fusion into one as they approach the point. A second, more logical conclusion determines that the 5th postulate can only be truth if a real point has an inner space-time volume through which many parallels cross.

Hence, as reality proves, any point can be enlarged when we observe it closely. Indeed, since reality follows that Non-Euclidean 5th postulate, it follows that 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, points with breadth, with space-time parts… Abstract points are fantasies. Anything real has dimensional size. Thus the 5th postulate defines a fractal Universe of super-organisms that grow in scale when we use thinner forces to observe them. And since there is not limit of size for electromagnetic and gravitational waves/forces, the Universe become a fractal structure of unlimited microscopic and macroscopic sizes.

Thus the enormous advance in formal mathematics, made by this author, with a non-pedantic language, which still awaits )-: proper recognition is the completion of the 5 Postulates of Non-Euclidean Geometry. 

I often think of Mr. Perelman who got a Shield medal and global acclaim for completing the Poincare Conjecture, which is essential to ∆ST (scalar, isomorphic space-time), in its definition of a mind but basically completes merely the 5th Postulate, or in Einstein who used that 5th postulate to do the whole Relativity theory.

I did complete the 1st, 2nd, 3rd and 4th and so I could complete Leibniz’s work of which Einstein had said ‘he is right but if so we must re-define western science from its beginnings’.  This I say, not because of self-pity, or self-bragging ( I am now too old to care for those things), but so you understand this is very serious very important future science writing if you are a scholar even if I am not going to use set theory for nobody else to understand.

The holographic principle: bidimensional membranes made with ‘thick Non-E points’.

Why non-Euclidean fractal points are so important?

They explain the holographic principle: a bidimensional membrane of strings, (called brain), of information (called your computer screen or paper), of stars (called a spiral galaxy), of galaxies (called the Universe also a flat membrane), of dense photonic knots (called an electron, also a probabilistic membrane in the abstract description, a fractal of dense photonic quanta in ∆ST theory), of cells (your skin), of humans (the above surface of the Earth), of Gaia (the above surface of the earth with all other beings) etc. etc. do have ‘width’ or ‘height’ depending how you call the ‘thickness’ because it is made of fractal points. So by bidimensionality we mean that in general for most systems of the Universe:

Length (dimension of motion) > Width (dimension of iteration/reproduction) >> Height (dimension of information)

This is the case of galaxies, the Universe, Gaia (information coming from the sun’s height) and the skin of living beings (information coming from senses perceiving perpendicular waves).

Except in the case of ‘specialized’ sheets of information (screens, paper, humans as wholes, informative species, antennae), where the Dimension of information is the largest one, and that of energy the smaller one:

Information (height) > Width (iteration – bilateral in man) > Length (energy-motion).

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: Tƒ 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 cycles5.

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-E 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.



Height is the dimension of information, we perceive, inform and form, and put our heads on top for a reason: projective geometry shows the higher you are the more you perceive from your limited  angular point of view:

It follows that in all systems information is maximized and evolved towards the topological height of the system. Let us put 2 examples, from physical and biological systems.




A key element of a physical system is the singularity ‘membrain’, which includes as in any key system of nature, a center that processes information and a membrane that encloses and breaks the system into an inner region, the T.œ and an outer region, the Universe. This dual system IS the COVER AND CENTER of a topological open ball, which is the vital energy enclosed by the system, which DOES NOT EXIST as a full T.œ unless those 2 elements are formed.  Consider the case of ‘Mass’. Energy contributes to ‘mass’, but if we do NOT have an enclosure we cannot measure mass, as energy is moving around and there is nothing to ‘weight’. Yet as soon as we close the membrane, the mass parameter will exist, as measured externally by the membrane.

Further on, as the membrane is CLOSING the inner region, which we normally do NOT access, or else we will have to tear the membrane and then mass might escape and a continuity equation will have to be applied to assess the flow of mass in and out, we cannot truly measure the mass.

It is then obvious that the ‘parameter’ of ‘density-weight-charge-angular momentum-rotational speed’ etc, tends to accumulate in each scale in the external region, where the ‘mass-force’ is maximal; while in the inner singularity center, it reaches ‘zero value’, and that point is the mind-still singularity, where motion stops, and so in black hole equations time moves to zero in the singularity, in the vortex of an Eddie.

The dimensional question: 1D singularities + 2D membranes (holographic information) = 3D vital energy.

Now it is obvious that the eye of the hurricane and the eye of the black hole has maximal height as it is indeed the informative center of the system, in fact ‘infinite height’ in the axis of a black hole, which means that ‘motion stops’ in the perpendicular plane but shuts off as a yet of dark entropy and matter through the axis of superluminal speed according to the Kerr equations of a rotating black hole.


All systems also evolve according to the arrow of information increasing the height of its dimension of gauging information as the evolution of reptiles into birds or mammals into humans show. So in its 3rd age evolution grows information:



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