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I. Reproduction is The name of the game.

II. Epistemology: Mathematical and Logic Languages:  Max.∑exi≈st

Experimental proofs:

III. Physical systems.

IV. Biological systems.

V. Social systems.


The method of the first line is simple. We study the existence of all ∆ºst beings of the Universe as super organisms tracing worldcycles, WITH EMPHASIS on the spatial view, of ‘simultaneous’ super organisms, made of fractal points joined in functional physiological networks of entropic, energetic and informative processing; which live to reproduce survive and make immortal the system in time:

” 5D    ¬Æ    ðime§paœ points    åct to Maximize its existence,  by reproducing  in network supœrganisms  triping ωorldcycles of  st¡enœ:

So we first define each of the words of that sentence which resume dynamically in time (‘timespace arrows’ ‘worldcycles’), simultaneously in space (‘reproducing’, ‘supœrganisms’), ºmentally through formal languages (‘¬Æ’, ‘stience’, ‘Max. ∫exi∂st’) and organically through ∆-scales (‘5D’, ‘tripping’), the existence of all beings.

And then consider in more detail the element of the space-time being under the experimental method, by studying it in physical, biological and social systems.

The project is a ‘work in progress’, as i copy-paste or translate 30 years of research from old files, ordering, eliminating repetitions and adding experimental proofs… My apologies then for its poor form, which hopefully won’t obscure the essence.

I.  Reproduction.

Screen Shot 2016-05-15 at 15.31.07

The Universe is a fractal that reproduces information. This is the single expression of reality in its organic terms, function and form. So the question is to properly study in each scale and discipline of reality how the acts of supœrganisms and species, flux into the creation of new similar species, to ensure the immortality of the whole – how the swarm intelligence of reality brings about once and again apperceptively the act of reproduction and conservation of form, of in-form-ation, embedded naturally in the repetitive nature of worldcycles and time cycles, from the simples to the most complex aggregate of them.



Fractal Reproduction of information.


A mathematical fractal like the Koch curve is an ‘—motions’ line that triples its in-form-ative bits every iterative cycle. But since it doesn’t grow in length, it exhausts its ‘—motions’. An organic fractal also starts as a single cell that clones its in-form-ation. But since it can absorb ‘—motions’, it can iterate billions of times. In both cases what defines a fractal is its reproduction of in-form-ation that bends ‘—motions’ into form, creating the arrow of futures. So the abundance of fractals proves the existence of an arrow of information in the Universe. We are all fractals, Cantor dust of ‘—motions’ and information: we fractalize so much that finally we lose ‘—motions’, volume and return to the dust from where we departed in the process of death. For that reason, the only solution to death by excess of information is fractal reproduction of a younger micro-form, when the being has enough ‘—motions’ to replicate in a discontinuous zone of space-time, ensuring the immortality of its logic in-form-ation.

The evolution of Time-space requires giving motion to Euclidean geometry. This is done by uniting fractal mathematics and Non-Euclidean Mathematics. Mandelbrot in the 70s considered the fact that self-repetitive forms diminish and grow in scale maintaining its forms invariant. The why of this grow ultimately responds to the arrows of reproduction and social evolution: A fractal can be seen as a reproductive process, which is common to all generator equations of information of the Universe.

Fractals can also explain in more detail the reason of aging and the life cycle. The 2 arrows of time follow a natural order from yang=young ‘—motions’ into yin=old information, which defines the existential cycle of most beings in the Universe. For example, the life and death cycle can be explained as an iterative process of reproduction of information that degenerates into aging, when the organism has exhausted all its ‘—motions’ in a 3rd age in which instead of reproducing, it wrinkles and fractalizes its cells.

Recap. An organic fractal always iterates its form over new ‘—motions’ not to become fractalized. Yet after a young age, even natural fractals start to lack ‘—motions’ end up becoming wrinkled. In fact, all forms in Nature including the Universe in the future big crunch, suffer some aging process, guided by the time arrow of information.

Information theory. Why informative membranes are bidimensional.

For example, Information Theory proved (Shannon) that a perfect Universe with no entropy in which information can be transferred with no loss must be a 4D Universe with a 2D coding language (0,1 in his studies), which transfers messages of 10D spatial elements.

H (entropy) = p1 logs(1/p1) + p2 logs(1/p2) + … + pk logs(1/pk)

H = 0: -> Dimensional being: 4 D, equal value dimensions;   Information message = 2 D;   Spatial length-> 10 D

And we shall see that in the ‘perfect Universe’, information membranes as the screen/page you are reading, has 2 dimensions, X≈Y>>>Z, and systems perceive only the external membrane of information of the system, where the sensorial feelers are. And we shall see that in space the fundamental form, the triangle has a canonical form, the tetraktys, of 10 elements, where the central point communicates and organizes all others, as the zero-point of the triangle, which transcends into a unit of larger 10-dimensional scale, which will be the fundamental scale of organization of the 5th dimension.

This example that connects Information Theory with 2-manifold geometry and the relational model of space-time is the kind of insights we shall reveal constantly in our analysis of the Universe with relational space-times, which will show the whys of an interconnected Universe where all the discoveries of different sciences find its harmonic whys in the laws of Cyclical space-times.

  • This simple equation, Se>ST>Tƒ, which describes all systems as assembles of 3 topological varieties has its symmetry in the causal logic of time cycles, which is no longer a lineal single time arrow of future, but as all cycles, do have 3 relative phases, the initial, energetic accelerated impulse of maximal energy or young, past age (Se), the steady state, inertial constant speed of the reproductive/body wave or present age, and the final informative age or Tƒ or warping of energy into cyclical form. Thus we shall find 3 phases or ages in all systems, from gaseous, energetic, liquid, steady state, solid, informative state of matter, to the young, energetic, mature, reproductive and old, informative age, to the 3 solutions of Einstein’s equations that describe a Universe ‘warping space into time’.

And so the ‘spatial topologies’ of bidimensional space have its symmetries in the 3 ages of time, which constantly, warp, >, energy into information, till all energy is exhausted and then in a single time cycle, information explodes back into lineal energetic space, in the moment of death: Tƒ<<Se.

Thus we can define a worldcycle for all species between birth and extinction and 3 arrows of time, expansive past, repetitive present and informative future, which can move forward (life arrow) or backwards (death arrow), causing a zero sum which makes the Universe immortal as all life arrows are cancelled by death arrows, all particles by antiparticles (that are explosions of energy in zero time, and have past arrows in Feynman diagrams).

And this fascinating understanding of the 3 arrows of time cycles, and its complex ternary logic, which substitutes the Aristotelian, past-entropy single arrow models of absolute lineal space-time, inaugurates an entire new discipline of logic, symmetric to our widened discipline of 2-manifolds and non-Euclidean fractal points.

Thus since the Universe is in terms of logic ternary, Non-Aristotelian, and in terms of mathematical space, topological, Non-Euclidean we talk of the formal, logic-mathematical new model for the study of cyclical time and fractal space, as the discipline of ∆-topo-logy. I-topology is thus the formalism of cyclical, fractal space-time.

This ∆-topo-logical Universe, and its 2 formalisms, Non-Euclidean geometry of fractal 2-manifold points and the Existential algebra of time cycles and its ages between birth and extinction, requires only a 3rd set of formal principles to complete its scientific analysis, the metric of the 5th dimension, that is the organization of all the relative scales of parts into wholes and the classification of its ‘åctions of space-time, ∂( æ,e,ï,œ,û).

This can be done departing from the new co-invariance, Se x Tƒ = ST0±4, which merely expresses that as we become smaller in size our time cycles accelerate, but the product of both parameters which are closely related to the energy and information of the system remains constant (as energy is stored in the fractal points that create the smooth continuities we call absolute spaces, when we do not distinguish those points from atoms in a water space to strings and photons in a vacuum space; and information is stored in the frequency and form of time cycles).

Again this co-invariant law applies to all systems, and explains when the specific number of dimensions and cyclical forms are clearly defined, all kind of laws. In physical systems it explains from the vortex law, Vo x Ro = K, to the Kepler’s laws (the inner planets turn faster), to the meaning of charges and masses, which are according to Einstein’s correspondence principle accelerated vortices of the larger cosmic scale (gravitational vortices≈ masses) and the lower atomic scale (charges≈accelerated electromagnetic vortices), its hierarchy (charges turn faster and have more curvature≈form, hence more information and are also more attractive as attraction≈speed of vortex), and it will allow us to deduce the equation of Unification of forces.

While in biological systems explains the law of metabolism (rats process energy and information faster than elephants), the laws of genetics (which code information of larger systems), and the entropy and chirality laws (lower U scales have more information and larger scales more motion, hence information transcends from lower to upper scales as in genetics but not the opposite – no Lamarckian evolution; while motion transfers perfectly from upper to lower scales – so when we move all cells and atoms do move synchronically but lower scales of molecular heat do not transfer fully to the upper scale).

Thus entropy is defined in terms of transfers of energy between scales and information such as there is entropy in U-∆<U transfers, but not in U<U-∆ transfers, and U≈U-∆ transfers (Shannon’s laws of informative communication).

But this chirality, which explains the 4th non-spatial, temporal form (electro-weak force that trans-forms particles and has no spatial range), and many other phenomena, which constantly increases information across planes (reproduction of messages) and upwards, (Genetic information) is Balanced by the explosive destruction of information from upper scales in Death-energetic processes, which do destroy information ‘two scales downwards’, from the human scale to the atomic scale, from the material scale, through big-bangs to the radiation scale. Thus information constantly creeps across planes and upwards: i>∆+1 but this long slow life arrow is balanced by the explosive, no-time big-bangs of death, i<<∆-2.

Fractal reproduction in a discontinuous Universe.


In the graphs, fractal systems are self-generated by seeds of its cellular scale, which encode all its information, compressed in very limited space (an equation, a DNA code, a Unification equation that generates the ‘—motions’ and forms of the Universe). Then the seed replicates its form in ‘biological radiations’ that multiply the fractal cells of the system, which finally follow the plan of network evolution of all systems, recreating the original species.

The process follows a series of ‘beats’ that change the arrow of time of the system from reproductive, energetic waves to informative, self-organizing phases in a pattern proved mathematically for chemical systems by Mehaute, which showed in the 80s that for time to continue when a system was not releasing ‘—motions’; it had to create fractal information, the 2nd arrow of time in the Universe. Thus, the Universe never stops its Sp->O->Sp rhythms.

When ‘—motions’ ceases is because the feed-back equation changed side. In Nature those micro-structures detach themselves from the being and absorb ‘—motions’ in the environment growing in size, self-replicating. So the fractal transmission of form is the most important event taken place in the Universe. From genetic information transferred between living beings through a fractal process of palingenesis to the creation of mental ideas that we convert into bigger machines, fractal replication between different planes of fractal space-time with finite dimensions, is the essence of reality.

Fractal, transcendental reproduction iterates cells and reorganizes them in decametric scales of growing social complexity till reaching a limit number of 1010-11 cellular units. The organization of those scales follows a simple law:

‘—motions’ flows from ∆-1 into a future st-scale: Sp-1->Tƒ.

Information flows from st into a simpler ∆-1 scale: ∆ST>E∆-1.

Reproduction happens in the same ∆-scale ΣS∆<=∆ST

Since those planes are networks existing with different space-time constants, disconnected from the other planes, how a given space-time scale, the cellular or atomic scale, relates to its higher st-plane? Riemann hinted at such scalar structure of space with his analysis of Riemannian surfaces, polynomial planes which communicate through a narrow path that transfers ‘—motions’ and information between them. Those paths between light and gravitational space are in Relativity ‘Rosen Bridges’ – black holes and other massive regions of the Universe. Yet the concept can generalize to any dual system, in which there are asymmetric flows of ‘—motions’ and information, according to a fundamental law of fractal space-time:

Information flows from the macro-plane of relative future to the micro-points of simpler ‘—motions’ and ‘—motions’ flows from the micro-points, ∆-1 from past to the relative, more evolved future macro-points, from the microcosms to the macrocosms.

Thus there is an asymmetric, hierarchical single flow of information from a relative future, the higher ∆+1 plane, to a relative past, ∆-1 plane and vice versa, a fact which explains the lack of parity of ‘temporal, informative flows’ (weak forces in physics, hierarchical social classes in sociology, etc.)

Thus the order between those scales is hierarchical. Species in different planes of space-time interact within each other transferring ‘—motions’ and information. Yet the bigger structures control and order the smaller pieces – its parts that become wholes through the arrow of life or disintegrate those wholes back into parts through the process of death. Such interaction is possible because in those different Planes, from microcosms to macrocosms, ‘—motions’ and information have self-similar forms that make the shapes of atoms similar to the forms of galaxies and stars. And follow self-similar isomorphisms of harmony. In terms of hierarchical order, we observe that the bigger an entity is in space, the longer it lasts in time, ΣS<=>Tƒ. That is, the amount of time and space of the different structures of the universe is in balance. While in terms of hierarchy the bigger scale orders and transfers information to the smaller scale that transfers mainly ‘—motions’ to the bigger form. Those 2 arrows of time, ‘—motions’ and information imply that the bigger scale or network – for example, the nervous system in man – controls the lower scale of cells, which in turn feeds the upper scale.

So we describe Temporal, Organic fractals with 2 terms of increasing complexity: a fractal system or network, which is incomplete, since it doesn’t reproduce internally and might not be able to self-organize itself, but requires the collaboration of an external agent; and a (super)-organism in which the arrow of reproduction is internal, iterating the initial fractal units of ‘—motions’ and information into 2 networks that finally combine its ‘—motions’ and information creating the 3rd reproductive network that perpetuates the self-sufficient species.

In biology such processes of self-organization and reproduction of parts into wholes are called Palingenesis – a term, which complex sciences that use both the jargon of physics and biology, extracting self-similar isomorphisms that apply to all those scales, uses also to describe physical processes of creation of matter and social processes of creation of cultures. Since all social and physical systems display complex, palingenetic behavior, from physical particles to organisms, from minds to nations.

All of them constantly reproduce seminal information – called åctions of ‘—motions’ and time in the quantum world, offspring in living organisms, ideas in the linguistic mind, technology and culture in human societies. And in all those cases, the seminal information grows into a species self-similar to the mother. So forces reproduce particles, cells become organisms and nations create self-similar cultures, called colonies.

All of them are organic fractals whose different planes (the cellular, individual and social planes) are connected by flows of ‘—motions’ and information: Life reproduces in a smaller space-time plane (∆-1) seminal seeds that grow into replicas of original st-mother; human existence is a travel between 3 Planes of relative existence, the cellular Plane (∆-1), the organic, individual Plane (st) and the social Plane in which a human can be considered a cell of a social organism, a nation, religion or civilization (∆+1). But electrons (st) also produce smaller photons (∆-1) that evolve into new electrons, which become cellular units of electric flows (∆+1); while galactic black holes (st), made of billions of social quarks (∆-1) emit flows of matter that evolve into new galaxies, cells of Universes (∆+1).

Thus, Social Palingenesis explains also why in all the scales of the Universe, the geometry of ‘—motions’ and information remains invariant; since a ∆+1 Plane is born by the social evolution of ‘—motions’ bits and information bits of the inferior Plane, which repeat its self-similar forms in all the multiple, self-similar relative ‘planes of existence’ of the universe, from the atom to the galaxy, from the cell to the factory. Thus, social palingenesis is not exclusive of living organisms. All systems display those complex, social Planes.

The 2 simplest particles of the Universe self-reproduce and socialize: quarks absorb ‘—motions’ and reproduce smaller quarks. Electrons produce a seminal light ray that becomes a new electron. So happens to the heavier form we know: the black hole, which reproduces its form when crossing through a star. Even the Universe is a space-time fractal, which might have reproduced its ‘cellular’ particles in the big/bang.

Recap. All systems of the Universe reproduce through a fractal, palingenetic process, in which the system produces a seed of information that reproduces and evolves socially till surfacing in the same plane of existence that the parental form.

Complex, reproductive motions.

In the Universe there is a simplex cycle, e<=>Tƒ, that converts ‘—motions’ into cyclical motions, and can at best be made to exist in 3 dimensions (spherical motions) of space and 3 of time (expansive youth, or big-bang, steady state and implosive 3rd age). Yet complex motions – acts of reproduction and social evolution – are different from simplex motions, in as much as they take place between at least 2 planes of different space-time. This difference between the simplex and complex arrows of time creates jumps between space-time planes:

The most complex phenomenon of the Universe is the fractal jump in space-time. Both bidimensional cycles of time, and planes of space are fractal and so their changes and displacements are also fractal. And since time is geometric, bidimensional, as space is, it has also 2 directions of motion.

So the oldest fractal question of philosophy is: how can continuous movement exist in a fractal world filled with discontinuities? Zeno, a Greek philosopher, put the example of Achilles running against a Turtle: Achilles will never reach the turtle because there are infinite fractal spaces it has to cross. Parmenides gave him the answer: continuous movement doesn’t exist in a discreet Universe; it is a mirage of the senses. Since a wave is not really moving, but reproducing information over the potential ‘—motions’ of the vacuum in a sequential, fractal jump, through a series of wave-lengths, drawn one after another, which appear to the senses as a moving wave. Movement is always a discontinuous displacement either in space or in time, in any of its 2 directions, towards the past or the future.

The simplest analogy is a television screen where new images are created constantly without hardly any cost of ‘—motions’, because they are virtual images created by illuminating 3 colors that are already potentially in the screen. In the case of a wave, the relative ‘—motions’ imprinted by the logic form might vary, from the vacuum ‘—motions’ of a light wave to the placental ‘—motions’ of a mother, yet the process is always the same: a form imprints another region of space, changing its spatial position and temporal morphology.

So speed is synonymous of reproduction, the main cyclical action of the Universe. Thus we can explain all physical events in terms of organicism. Since even movement – the external, mechanical change physicists study – turns out to be also an organic cycle of reproduction. We distinguish, according to their quantity of ‘—motions’ and information ‘translated’ in the process from a place of space-time to another place, 3 fractal, reproductive jumps:

– S=T: Space-time reproduction dominant in spatial displacement that implies a minimal movement of information that fluctuates from a future to a past form and returns back to the future. For example, when an electric impulse arrives to the end of a nerve, it becomes translated into chemical information and then it is transferred chemically through the synapses to the other cell, where it becomes translated back into electric information.

That process implies a ‘spatial, fractal jump’ from a neuron to the next neuron, but also a fractal jump in time from a level of informative complexity, the electric language to the lower level of chemical languages, which is the relative, past informative system of life. The informative essence of the process implies a transcription of form from each discontinuous point to the next point but also a movement in space, since ‘all yang has a drop of yin’, all is temporal ‘—motions’, also spatial and temporal reproduction requires a minimal dual movement in time and space.

-Max. Sp: Spatial, wave reproduction of a wave a particle that jumps from one place to the next place, reproducing a minimal temporal form. It is very common in physical waves, defined by its speed of reproduction, V=S/T. Depending on the density of a form, its speed of reproduction will vary. So the most massive forms are slower than those whose informations are minimal and can imprint the ‘—motions’ of vacuum very fast. Those forms that hardly move however evolve a lot in time:

– Max. Tƒ: Temporal, palingenetic reproduction, when an organism produces a past, smaller, simpler seed that reproduces the being, evolving faster towards the future. So a fetus is ‘born’ when it comes out of the body of the mother to the next discontinuous region of the Universe, making a minimal spatial jump and a huge evolutionary, temporal jump.

Recap. There are 3 types of reproduction: self-reproduction by a complementary system that mixes its ‘—motions’ and information, without concourse of external agents; spatial reproduction, or motion of a wave that imprints a simple form of ‘—motions’ as it translates in space and enzymatic reproduction when an external agent assemblies the parts into a whole.

Reproduction of physical, biologic and mental fractals.

reproduction good

In graph, cosmological, chemical, biological and mechanical fractals during their reproduction cycles.

All fractals iterate=reproduce by absorbing ‘—motions’ transformed into fractal information by a Mother cell or external enzyme- as it happens with carbohydrates or machines iterated by ‘enzy=men’.

Unlike mathematical fractals, made of fixed, spatial forms, Nature’s fractals are made of temporal, iterative cycles, in which ‘—motions’ is transformed into information and growth, as the fractal family becomes detached from the mother cells. Organic fractals are not fixed, geometrical forms that merely repeat in spatial scales, void of life and temporal change. They are temporal beings, whose bio-logic cycles and functions reproduce at different scales and time intervals. Since not only space has a fractal structure. Time is also discrete, made of cyclic trajectories that repeat themselves, as it happens with the cycles of a mechanical clock. It is precisely the repetition of the organic cycles of ‘—motions’ feeding and informative reproduction, what makes natural organisms fractal structures. The Universe is made of such temporal, organic fractals that reproduce into multiple clone forms that latter re-organize themselves, giving birth to macro-forms similar to the original ‘cell’.

The most obvious natural fractals are those created by the iterative, repetitive nature of 3-D space. They are similar to mathematical fractals where geometrical form dominates.

For example, an ice crystal is a chemical fractal that jets up triangular, tall spikes, in its relative dimension of height, growing into a fractal; a salt grain is a cubic crystal that reproduces its form as it grows in scale and recomposes itself into huge cubes. While a hurricane fractalizes air streams into a vortex of wind cycles that grow also in height, the fractal dimension of information. Those physical fractals already iterate its form, despite the simplicity of its fundamental elements; since all natural fractals reproduce the shape of the ‘mother-cell’ into multiple clone forms that latter re-organize themselves, giving birth to macro-species similar to the original ‘cell’.

In Biology, fractals are used routinely to explain how the iteration of simplex growth processes gives birth to complex botanic shapes: Branches, leaves and roots are all easily created by the iteration of an initial mother-form. A DNA molecule, which iterates its form both in micro-fragments (amino acids) and at macro-scale (recreating a cell). While a tree repeatedly fractalizes its form in 3 branches, ever slimmer, with less ‘—motions’ but ever increasing the information of the tree.

A human being is also a temporal fractal, made of fractal cells, whose organic functions repeat themselves at individual macro-scale in a longer time-interval: the feeding, reproductive, informative (sensorial), and social behavior of human beings are a macro- repetition of the same cycles that take place in cells. Cells feed on ‘—motions’, absorb information, reproduce themselves and form social groups, as human beings do, at a smaller, faster scale. The fractal sum of those cellular cycles creates a human being. And then, the fractal sum of human cycles at a bigger scale creates socio-biological organisms, called nations and civilizations. A human is an organic, bio-logic, temporal fractal, extended in 3 scales, the cellular, organic and social scale.

Recap. The arrow of information and ‘—motions’ together describe all kind of natural fractals, not only the well-known biological fractals but also social and physical systems that display complex, fragmented borders, (from physical particles to organisms, from minds to nations) and constantly re=produce information (åctions in the quantum world, offspring in living organisms, ideas in the linguistic mind, technology and culture in human societies). They are also organic fractals, since once we understand their structure in multiple scales connected by flows of ‘—motions’ and information, the old distinction between organic and inorganic matter loses its meaning, beyond its anthropomorphic role to make man the center of the Universe.

Linguistic fractals. Paradox of inflationary information.

Minds can also be modeled as fractal systems that replicate the forms and movements of the Universe in a smaller scale, through the syntax and semantics of a certain language. Indeed, modern science concentrates in the study of the parallelisms between the hardware of the mind, the neuronal brain, and its software, the depiction of the Universe made with visual and verbal languages. But what truly matters is the bio-logical parallelism between those mental structures made of syntactic and semantic, fractal units (numbers, geometrical forms, phonemes and sentences), and the external Universe they map out. Since organisms survive thanks to their accurate, mental perception that orientates them in that bigger Universe. So fractal minds are a fundamental tool of evolution: The mind acts as a virtual, fractal mirror, allowing the being to interact efficiently with the Universe, absorbing ‘—motions’ and information from it to replicate its form. This means that we can study minds as mental fractals similar to its 2 main languages of space-time; mathematics and logic.

For that reason, mental and geometric fractals are both defined as entities whose informative boundary tends to ∞ while the ‘—motions’/space of those boundaries tends to zero:

δe/δt->0 x δi/δt->∞: Mental Fractal.

Thus the information of a mathematical fractal is found in the boundary. It happens also in black holes, where information is attached at the boundary in a bidimensional space (holographic principle, which we proved in a simple manner as result of the 2 dimensions of a cycle of time that carries information and now we can observe from a more complex perspective). It is also the case of the human mind, an i=eye+wor(l)d, created by the eye’s retina and the electromagnetic waves of the cortex brain. Thus the informative parts of organisms, what we call ‘senses’, are also external, attached to the boundary and one of the fundamental functions of Nature’s fractal arrow is to create senses, systems of perception of fractalized information. Minds and senses are similar to mathematical fractals. It should not come as a surprise; since mathematics after all is a mind’s language, and minds fix most cycles of Natural fractals into still images that don’t capture the vital ‘—motions’ of the Universe.

Mathematical and real fractals share the properties of information, inverse to ‘—motions’. Information increase when the fractal becomes smaller in its surface. This paradox, that the smallest regions of space hold the maximal quantity of time: Min. Tƒ =Min. Sp is however essential to full grasp the Universe.

Languages hold more information than the forms they describe. Information is bidimensional and can be warped and cut. This essential property, that information is in the void, the cut, not the substance, as it will be first perceived by a mind in order to exist, and so it is not real till the perceiver observes it (quantum paradoxes), is however the reason why the smaller regions, in which voids multiply are more conductive to information frequencies that long ones. This paradox already understood by Gödel simplifies the distinction between mathematical physics and reality. Information is inflationary.

The Universe is not all the possible mathematical models. As Riemann, the key mathematician of the XIX C. explained, we cannot consider all possible spaces real, because the physical universe has selected only one geometry6, to which we shall add – it selects the most efficient geometry that maximizes the 4 main arrows of time of species and helps the organic, Complementary, Sp X Tƒ, bio-logic forms of reality to survive. Unfortunately neither mathematicians nor physicists today accept restrictions to their imagination, so they invent ‘multiverses, cosmic strings, multiple, infinite dimensions’ without ‘upgrading’ the concept of a continuous space into the reality of fractal discontinuous scales. The confusion of languages with reality is one of the main ‘errors’ of science we must resolve in order to improve the ‘logic/mathematical mirror’ the mind uses to perceive reality.

This distinction often lost to physicists in modern times, clearly expressed by Riemann in his ‘foundations of geometry’ and further proved by Gödel implies that not all possible mathematical spaces and mathematical particles exist. The space of the Universe is far more restrictive in form and dimensions than the space of mathematicians.

Why this happens can be explained ‘bio-logically’ by the fact that the inverse function of existence, extinction, eliminates all forms which are not efficient even if it creates them a priori – in the same manner all mutations in Nature, which are not efficient disappears. While our informative mind keeps producing imaginary models of geometry, which are pumped up by the scholar who seeks to convince the world his geometry is also right. For example, in the field of physics, multi-universes, super symmetries, ‘—motions’ in black holes, etc. are mathematical theories with no equivalent in the world because they ignore the arrow of information in mass and the need for no more than 2×2 dimensions to construct the Universe.

While the Copenhagen interpretation of quantum physics in which an organic wave of photons, parts of whole electrons, guided by the 4th arrow of organic evolution is considered a herd of ‘probabilities’ is wrong. As in the case of the Mandelbrot set that doesn’t exist in nature, unable to resist energetic motion, in all those cases the 4 main time arrows of reality and its need to be performed by all entities that wish to exist, limit the information that becomes real.

All this requires understanding 2 of the basic properties of information – the fact that ‘fractal information’ is constantly created by the motions of reality and the paradox between ‘—motions’ with maximal spatial extension but minimal information vs. information with minimal ‘—motions’ and extension. In brief, information increases, as in fractals, when we diminish in size. So brains are smaller than bodies but have more information. And a language has maximal information packed in minimal space. A language in fact has more information than a huge surface of vacuum space, which makes theories more abundant than the forms we find in the real Universe. Information is inflationary and so are physical theories with bizarre space/times that reality never will select.

Mathematics is, as all languages, an informative, ‘fractal’, whose self-similar forms/theories multiply in excess (ΣSe->0; Tƒ->∞). Thus, if certain sentences of verbal thought can be imaginary fictions, despite its beauty, so happens to many ‘quixotic’ geometrical forms, which do not exist. The Universe selects only efficient geometries, based in forms that can move and perform the arrows of time in the real Universe. So for example, the most beautiful fractal form of the mathematical Universe, the Mandelbrot set, does not exist in reality, because all its small self-similar attachments would easily break if they were moving as reality does.

Hence the importance of having a geometric theory of space-time that describes accurately the forms of the physical Universe. This was the key discovery of Einstein. He realized that Euclidean, lineal geometry, used to describe ideal space, could not describe the cyclical paths created in gravitational space-time. So he switched in his description of reality to a space called Non-Euclidean, where its minimal fractal unit, the point, could be crossed by multiple gravitational curves and hence, unlike the abstract point of Euclid, it required inner volume, inner form and ‘—motions’. This point, which has always in Nature a region that can absorb /gauge information and a lineal or cyclical, rotational motion, is what we call a Point of View= Measure or Non-Euclidean point of view, the relative unit of Non-Euclidean mathematics.

Philosophers of science have wondered often if mathematics is merely a construction of the mind or an image of reality and why they are all pervading in the description of any ‘system’ of self-similar forms in the Universe. The answer is both: languages are construction of the mind that reflects the external universe’s information in a small space, hence they must reduce the total information to fit the mental mirror, trying also to make an image the closest possible to reality. This is what logic languages do with time and mathematical languages with space; because the Universe is logic-mathematical, albeit of a type of logic and mathematics more complex than the abstractions without motion devised by the Greeks 2300 years ago.

Indeed, the same concept applies to the new logic of time, which is based in multiple causality, either a dual ‘biological causality’ in A<->B events in which an element A is predator and the other B victim; hence B is considered by A mere ‘—motions’ when B considers itself an informative entity worth to exist (so A is both A and B, victim and predator, ‘—motions’ for the predator information for the I-self of the victim); or ‘multiple, spherical causality’, when multiple agents create a certain network or form. So for example a real circle is not drawn in abstract by a single pen, but happens when multiple self-similar points of view converge and form a cycle.

Ultimately we are all made of spatial ‘—motions’ and temporal information, whose synoptic descriptions are achieved with 2 languages, mathematics and logic. And so the search for knowledge by the human mind is not only the recollection of experimental data, but its description with the languages of mathematics and logic. Hence even more important than the collection of data is the creation of a mental container – those 2 languages – efficient and evolved enough to fit properly all the data of reality we observe.

Yet since the revolution of thought represented by Evolution Theory in Biology and quantum /relativity in physics, there is a gap between the behavior of universal entities and the linguistic syntax of mathematics and logic, hardly evolved since 2300 years ago, when Euclid and Aristotle founded those 2 sciences.

Thus, we shall in this work summarize the new advances and isomorphisms of spatial geometry and temporal logic that are needed to describe a complex Universe of multiple, fractal space-times in which points are Complementary systems – entities that gauge and feed on ‘—motions’ with an informative and energetic center (body/brain, field/particle system). What still stands is a simplification of reality to ‘fit’ it into the mind. So while we are not concerned with the specific ‘—motions’ and information the point of view process (the details that don’t fit), we cannot longer hold truth the syntactic errors of Euclidean mathematics (points, lines and planes without breadth, width or height), and Aristotelian Logic (single causal events of the type A->B).

We call the evolved syntax of those 2 space-time languages, i-logic geometry, or simply i-logic geometry (as i represents ‘information’ and it is the next vowel after the A-ristotelian and E-uclidean languages used till now. Yet it also represents a ‘complementary system’ with a cyclical, informative ‘head’, O, and a lineal, energetic ‘limb-body’ |, which are also symbols used in ‘complex algebra’ to represent energetic and informative functions)).

Thus, we affirm that the Universe of multiple space-times follows the complex logic of information or ‘i-logic, fractal geometry’ pioneered in the XIX and XX C. by Darwin, Riemann, Planck, Einstein and Mandelbrot whose discoveries were the first steps of a ‘new paradigm of science’, which this work completes, upgrading philosophy of science (mechanism and monism), stuck in Aristotelian, Euclidean theories since the XVII century. So we shall talk often of the ‘i-logic, fractal paradigm’ as opposed to the ‘A-logic, Euclidean paradigm’ of a mechanical world of single ‘ceteris paribus’ causes and entities which are supposed to exist in a single, continuous, abstract, non-moving space.

The second part of this work after this brief introduction to ‘metaphysics’, the description of the ultimate meaning of existence – the accomplishment of the 4 main arrows of time – will be dedicated to the development of those new formalisms of mathematics and logic needed to make detailed, rigorous analysis of the events and forms of natural, organic fractals.

In that regard, since all languages are fractals of the entire Universe perceived in a slower, shorter, memorial pattern, a mirror of information with less dimensions of ‘motion’ and ‘form’ than the original. So these texts could be also considered a fractal, linguistic mirror of all Realities.

Recap: Information is inflationary. So are informative languages, reasons why we must differentiate fictions from theories that truly describe the universe. Multiple Spaces-Times improve our logic and mathematical tools to describe the Universe. This is done advanced the Aristotelian logic and Euclidean geometry into the next vowel of the alphabet: i-logic geometry, the logic and geometry of information.




II.≈ Max.∑exi≈st

The purpose of the actions of all beings, is ultimately to reach discontinuous immortality through its reproduction, as entities which do not reproduce become extinguished. So we shall define reproduction in this post and show that all entities reproduce, since a motion that repeats its form, is in fact reproducing, and time is motion and time is everything. We show then how all systems, physical, biological and social systems do reproduce.

Thus if we were to pick up a single function on the Universe, we would say that all is about conservation of present through the dynamical reproduction of its forms. Even motion can be understood in terms of reproduction, as  the previous graph from the 92 book, ‘god, man and universe’ shows.

Reproduction is the essential game of the Universe – to iterate information, first – and then evolve it up and down the block of time of possibilities, along the informative and entropic dual arrows that take the system out of balance. There is no mystery to it, as forms become with time implosive and explosive, so if reproduction did not dominate the game, the universe would die away, and would not be immortal (as reductionist physics with models of a single arrow of time) expect.

Momentum is a present ‘dharma’, a minimal step, an action. And the sum of those actions of existence, reproduced with different beats and rhythms, creates a wave of reproduction.

What the function of existence as a sum of infinitesimal number of actions of space-time, absorbing and emitting energy and information, ±∆e, i, combining it into reproductive seminal seeds of the whole, e x i, and associating it into social scales, allows is the description of the whys of the larger world cycles and ensembles that form the super organism in space and its time cycle.

Thus the main action of exi=st¡ence is reproduction, achieved in the age of balance, when the motion an form of the being, exi imprints on its lower ∆-1 field of space-time, bringing both together into an exi=st-ential form. To reproduce once and again, ∑exi=st, and maximise that function, Max. ∑exi=st, becomes then for all systems, the purpose of exi=st¡ence. The many jargons and languages we can use to mirror that process are just details of the ‘large picture’. The series of actions that bring re=production into fruitful realisation tend to be similar, departing from the monad, which first:

i: perceives->a:moves to fields ->e: of energy where it feeds, or meets an inverse ‘mirror symmetry’ (gender) communicating with it ï-> to finally reproduce->œ & in the most successful reproductive waves, it will evolve socially into a new whole, a new Universal->∑œ=U

So all those actions, which ultimately are partial equations of the acronym expression of the generator (entropy=motion, information, reproduction, exi, ∑exi= social evolution is really all what is about the game for those ‘beings-monads’ who successfully still exi=st.

Dûst, momentums of the function of existence, journeying to perform its survival actions, trying Tº exi≈st, combining all its actions of existence with the aim of survive not as individual but as ‘clone form’ -that is, simply speaking the art of living, which is the same for any monad, on charge of a supœrganism of any scale of the Universe. Moreover the game of each monad is not only the same but when adjusted in terms of its ∆-metric (spe x Tiƒ) it gives us similar range of space-time actions, as smaller beings live shorter but act faster.


Motion as reproduction of in-form-ation.

Space-speed as reproduction of form.


In the graph, a particle moves, reproducing a quantic wave or ‘field of matter’, since in fact all physical movements reproduce a form in a field of energy. Thus the reproductive speed of a wave that imprints a surface of spatial energy is also a quantic jump in space-time. The spatial energy will vary but the process is always the same.

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

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

Communication towards a balance of parameters is thus natural to the laws of the Universe.

‘—motions’ must be understood in its simplest laws – 2nd law of thermodynamics, heat flows from the hotter to the colder source till balancing both, expansion of a gas till fill uniformly a volume, etc. – as a proof of the function of existence that balances the parameters of all systems. This balancing tendency might seem to favor a final ‘—motions’ or death in disorder of the system but it is more subtle. The system balances to achieve a faster constant switch off of states between energy and information, accelerating the feed-back cycles, E<=>O, which are the dynamism of it all.

This feed-back cycles reduced to the maximal i-rational expression, such as Pi, or √2, means a constant feed-back loop a space-time cycle, SP<=>Tƒ…

Now, this will even confuse you more. We defined the present active-reproductive dimension of space-time in other posts as:

Se (past-entropy-lineal motion)  x  Tƒ (Future-form, cyclical motion) = Present-wave reproduction.

And above we saw that a wave speed, V = Sp x Tƒ

So a wave strictly speaking is reproducing its form into a present speed over its lower ST=∆-1 plane of existence, feeding on energy, putting its form and reproduction. Motion is truly reproduction of form, in a lower plane of existence and this solves the Zeno’s paradox, why motion is possible? It seems impossible in Zeno’s concept of quantum space-time. Today quantum physicists still have to accurately explain Zeno. Now we explain it. It is in fact impossible because motion is NOT motion but reproduction from quanta to quanta of pure space motion of a form.

And this works with higher planes which have more content of form as mass does. Energy = Mass x C2 is the case.

Strictly speaking we add to the mass, the ∆-3 scale of space-time bidimensional light-space to get that much energy. It is more of a ‘reaction’ than a transformation, but we humans have our ‘limited means of measure’, so that is what we ‘see’. Point.

Strictly speaking a mass moving is ‘interacting with the ∆-3 plane of light-space time also, as the wave of its particles of information is becoming imprinted in each step on the lower planes, it is being redrawn as a wave does step by step, reproducing its form side by side. So speed is reproduction, Sp x Tƒ = Present reproduction = Speed. This is truly what happens in ∆ST complex physics. When you move your hand, you redraw your atoms and electronic nebulae from ∆-4 to i step by step. And so it follows that waves which draw only the form spend less time drawing information than masses than human organisms, and so they move faster at c-speed.

So here we have another logic ∆ST way to deduce the previous deduced infinity of speed of gravitational waves:

Max. Tƒ = Min. S≈Min.V

And this has two limits: gravitational quanta are perceived as moving at infinite speed because they carry no information and black holes which are forms at 0 K of perfect form, information, seem anchored in their point of view with no motion relative to the Universe that ‘moves around them’.

This advanced analysis for those who have gone so far shows the extraordinary power of ∆ST to explain much more in a logic way than the mere equations manipulated in an artefact of absolute space-time.

This motion thus requires to print a form, departing from the ‘energy’ of the plane. And we can therefore do an explanation of the entire Universe as a reproductive, living organism of present reproductive waves of form with motion.

Energy though will still be dominant in motion. And this is proved by the fact that we do calculate energy and work in physics, considering only the lineal vector of motion not the height-informative component. And so indeed energy is related to motion. We talk of energy as the ‘food’ of motion for cars and planes. Energetic people are people that move a lot. Energy is biased to space-motion.

All this said as truly energy and information are considered in the ∆±1 planes around us synonymous of motion and form, we shall use them as equivalent S≈e, T≈information and use i to symbolise information.

While space-time planes will be referred as ST=±∆ or abbreviated as ±∆

Still we will use very often the concept of temporal information, Ti, and also the concept of spatial energy, Sp, as roughly equivalents to Spatial speed, S and Temporal form,  (i do confess to have been careless, exchanging all those terms in other papers, but this blog should be when finished the foundational texts of the 5th Dimension, so I will try to standardise and be precise in all its definitions).



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