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I. Synchronicity

II. Synchronicity in mathematical systems. Fourier transforms.

III. Synchronicity in physical systems. Waves and particles.

IV. Synchronicity in biologic systems. Superorganism.

V. Synchronicity in social systems. God


Rashomon Truths explain the 5Dimensions of any spacetime organism/event by considering the spatial= informative and temporal= moving sides of reality putting those 4 parameters together through a(nti)symmetric ≤≥ flows of communication: ∆t≥S@

Synchronicity is an essential element of the structure of the Universe. In a Universe of infinite clocks of time what is a quanta of time becomes extremely relevant to consider the main clocks to which all other clocks synchronize within a system. For example all your systems are synchronized to the second time of your limbs=steps, heart=beats and eye-brain=glimpse-thought.

In that regard, as usual we shall consider a bare minimum of perspectives on synchronicity to explain its meaning.

-Γ($t≤∑∏≥§ð): From the point of view of the whole system and its generator $t≤∑∏≥§ð, synchronicity is thus the essential element to make beings exist as wholes by synchronizing all elements.

Synchronicity is what allows the whole system to present a single ‘front’ to the external world and as such is the a priori condition for the super organism to exist. It also explains as the fundamental reason d’être the different time clocks of systems, which depends in great measure of the ‘fluidity’ of communication of information within the system. First the system must synchronize internally and that requires time. Then the synchronous time needed to act-react becomes the clocks of time of the whole system.

-∆±¡: But internally the system will be synchronized in many different speeds due to different time clocks and 5D metric. So smaller ∆-1 cells will have larger speeds of time and will synchronize with faster actions on the ∆ø scale.

Time clocks slow down as systems grow because they have to create an inner synchronous ‘quanta of timespace’, which will become the universal constant of a language that all the parts share in their external confrontation with the ∞ larger, ∆±T§¡.

The metric of the fifth dimension, §t=∆, define a function of constancy in Space time ∆, which is different for different sections of the Universe. We thus talk of families of ∆¡.




The orbital, energetic cycles of the Earth-Moon system are parallel to the cycles of reproduction of its ∆-1 living fractal quanta: An organism extends through several scales of growing form. Since microscopic, fractal species become chained to stronger, ExI species as their relative energy and information quanta of a ‘lower class’. In the image, Gaia, the Earth’s surface, is a Fractal made of organisms made of ∑ cells, made of ∑∑ atoms, made of ∑∑∑ quarks, all chained by their organic cycles.


The main property that defines the intelligence of time clocks, are its system synchronous harmonious motions, through symbiosis of the cycles or the different cadence and melodies of the being that switches through its a, e, I, o u actions.

 Synchronicity is the most profound intelligence of space, as a mind creates a simultaneous synchronous mapping of reality, which despite being made from motions, sliced into a synchronous view, remain fairly stable in its interrelationships. How to select synchronous systems to map them out, how those systems synchronize internally, and what are the synchronous parts, its functions and the networks that by simultaneous faster programming of the parts achieve system sync are some of the themes studied here.

The highest understanding of the Universal intelligence both in space and time comes from the properties of simultaneity in external adjacent space, based in the synchronicity in time of the internal mind-clocks of the system, which allows in turn the highest symmetry between spatial superorganisms and its world cycles of existence.

Yet while simultaneity in a ‘single space-time continuum’ brings the super organism into being by topological adjacency of its ‘parallel parts’; synchronicity is a much deeper phenomena. which happens not only between the clocks of the 3 adjacent parts, limbs/potentials, body waves and particle-heads, but also through the time scales of the 5th dimension, between the ∆-1 cells/atoms, the ∆º, organisms/thermodynamic scales and the ∆+1 worlds/ecosystems, by coupling the rhythms of the different ‘actions in time’ of each scale, as smaller systems have faster clocks that larger systems, but actions of motion, feeding, reproduction and social evolution have also different clocks.

So synchronicity has two huge fields in the ‘polidimensional world of multiple Rashomon truths/functions’ for each event/form:

  • S<≈> T: Synchronicity in a single plane between the clocks of limbs/potentials, body-waves and particle/heads that make the system run as a spatial super organism in simultaneity. I.e. your eye-glimpse of a second is synchronized to your brain second-thought, to your heart-body second-beat and to your limb-second steps. So you whole works as a biological system synchronized in your scale of being. So happens in the right interpretation of quantum physics (De Broglie model) as he departed in his wave-particle hypothesis of the existence of an inner clock in the particle synchronized with the clock of the wave (and latter deduced rightly it should be synchronized to the quantum potential/limb system).
  • ∆±¡: Synchronicity between planes of existence, in which the different speeds of actions, maximal for the minimal pixel perception of information, minimal for the social actions of the being into its ∆+1 world, allow synchronicity between different actions of the smaller parts and the larger wholes, to create symbiotic relationships.                                                                                  I.e. the speed of actions goes as follows: Max. speed: Information (minimal pixels of ∆-3 planes: light quanta)< Med. Speed: energy feeding in ∆-2 quanta< low speed: reproduction seeds of ∆-1 quanta < slow speed: social evolution into ∆§scales>∆+1 world.  So a smaller cellular system with faster clocks must synchronize one of its ‘larger, slower cycles’, let us say cellular reproduction that happens in cells every day, to the ‘faster’ cycles of its slower larger whole, let us say, multicellular feeding that happens for the larger organism, every day. And indeed, a cell synchronizes its reproduction to the feeding energy obtained by the larger whole. The process of reproduction of cells happens in a day, which is the time cycle it takes a normal animal feeding. In this manner synchronicity allows co-existence and symbiosis between different planes of reality, allowing the creation of super organisms.

Synchronicity becomes then essential to all superorganisms, and to that aim they all must have a single time=cycle, which often is defined by the angular momentum.

The 3 conserved forms of the Universe, angular and lineal momentum, and vital energy form in the fractal Universe the 3 parts of a T.œ or fractal point, Non-E with an inner volume of space-time through which multiple parallels can cross. The rules of geometric and biologic engagement of those points to form waves, networks and topological organisms, define the non-æ bio-logic of the organic Universe based in the a(nti)symmetric laws of similarity, parallelism and perpendicularity expressed in 5 ¬Æ postulates that substitute the classic axiomatic method of definition of logic and geometry.

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.

They give the 3 conserved ‘fractal quantities’ of any super organism of space-time:

-Angular momentum (2D membrane).

-Lineal momentum (motion of the singularity)

-Vital Energy (volume enclosed and managed between them).

Those 3 parts thus are synchronized as elements of a super organism on the fifth dimension and as such they are able to travel within the block of time of its 5D symmetry, in which S x T = K REMAINS, allowing only those synchronous regions AS TIME-SPACE TRAVELING REGION, A FUNDAMENTAL THEOREM OF 5D metric we shall bring often into the mix:

Only regions that are synchronized in time can be part of the super organism. Loss of synchrony becomes then also another synonymous of death.

You are synchronized as a second: Lims (s. steps) < Body (s. heartbeat) > I<Eye (s. thought/glimpse). Broglie extracted all quantum physics from the synchronicity of the particle and wave-body of a quantum particle with its potential limbs (quantum potential).

Synchronicity between membrane and singularity which transmits through its networks of communication to the asymmetric non-synchronous relative entropy field of disjoined or predated micro-particles, establishes most vital rhythms of such systems.

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.

Time space-beings. 

Yet when we extend the system to different scales of reality, from the ‘o-1’ unit sphere into the 1-∞ larger world, the whole synchronous repetition of patterns now between the individual and its ∆+¡ world defines such synchronous growth in all extensions.

Thus we need to add the ternary structure of synchronous systems in 3 planes of existence to limit a super organism domain:

‘A potential super organism is a region of space-time which is synchronous in 3 scales’.

In that regard time cycles occur in all systems of the Universe, including the eco(nomic)system and history because it is the natural manner in which time flows, as a sucession of similar events produced by similar causes, with a frequency related to the repetition of those causes.

fractal scales 5D

The 3 conserved forms of the Universe, angular and lineal momentum, and vital energy form in the fractal Universe the 3 parts of a T.œ or fractal point, Non-E with an inner volume of space-time through which multiple parallels can cross. The rules of geometric and biologic engagement of those points to form waves, networks and topological organisms, define the non-æ bio-logic of the organic Universe based in the a(nti)symmetric laws of similarity, parallelism and perpendicularity expressed in 5 ¬Æ postulates that substitute the classic axiomatic method of definition of logic and geometry.

open ball t.oe

3 generator of clocks

Time is any cyclical clock-like motion. It follows that as all clocks break space into an inner region we shall call ‘vital energy’ and an outer region, we shall call Universe or rather world, when reduced to the region we can perceive from the point of view of the time clock, and a region between them, which we shall call time proper, which if regular can be found to have a central point, we shall call the singularity reality is easily mapped out as a game of time-cycles, as this simple scheme defines the 3 conserved forms of nature, and hence the Universe as a game of self-centered time cycles that break all into its 3 conserve dimensional parts:

Singularity (1D: lineal momentum) + 2D (angular momentum=time clock) = Vital energy 3D inclosed between them. 

ALL What exists are timespace beings. We are some of those.  Timespace beings are made of timespace cycles focused in non-euclidean monad worlds. The points thus hold a singularity or mind of space-time that focuses a series of timespace cycles:

∆ð≥S@, the symbol meaning a mass of scalar ∆ timespace cycles, ð, are perceived, > as information and energy ≈ by a mind, @, a singularity point that will in the minimal=simultaneous space of its mind mapping, create a linguistic still form we shall call a ‘world of space’, different from a ‘universe of time cycles’.

The big and the small and its physical, metaphysical and biological relationships thus is what matters to us in the search for a description of the Universal game of non-Æ points-singularities-monads ordering vital territories of energy and information extracted from those external ∆ðimespace cycles that make reality a tapestry of ∞ points of view.


Knots of Time. Synchronicity of actions and cycles of space-time existence.

In that regard, the next step in the formalisation of the Universe starts with the analysis of the rhythms and frequencies of the different ‘actions’ of each species, which connects them symbiotically to other species.

This will be the ‘great’ field of studies by humans or robots if we survive the dark ages of simplex physics and complex weapons in which we live – the synchronicity between the different scales and actions of the co-existing particles of an ∆±1 super organism.

I have a lot of studies on those themes for 30 years, but as my health is dwindling I don’t think i will be able to advance much in pouring them. This is part of those texts and some of the terminology has varied. Let us then consider this key theme of GST

If we consider any organism a knot of cyclical time arrows made of multiple feeding, reproductive, informative and social cycles with different frequencies and dimensional sizes, which converge in that organism, the next conundrum to resolve is the harmonic synchronicities between the Informative->Energetic->Reproductive->Social cycles of the organism. Each cycle will have a frequency in harmony with many other cycles, and so the being might be very complex in its behavior as it switches between cycles, but ultimately it can be reduced to a series of cycles that converge into the organism. Thus, organisms are knots of time cycles. In the same way, when multiple cycles converge into a point they add their causal power and produce intense events with a higher ∑e x ∏Tƒ existential force, but we can break the complex entity into a series of cycles whose combined action will show a harmonic frequency, as we can break a harmonic wave into a Fourier series of simpler waves.

In this manner complex events/entities can be reduced to simplex herds of events/cells.

For example, the convergence of different geological and cosmological cycles, which affect the energy and information of the Earth, cause ages of extinction and age of massive evolution of new species, with a series of frequencies and rhythms we have studied in our analysis of geological biological and sociological cycles. In fact most events of the Universe have multiple causes, which means they are knots of time cycles: from multiple cyclical forces that converge in Relativity to create a knot of gravitation or a charge, to the multiple events that converge in Biology to cause an age of extinction, to the multiple failures that converge in a body to change its rhythm from life to death.

Since the Universe explores all possible structures, despite being made of a few elements, the inverse system also exists: one in which the bigger system is simpler than the smaller, faster cells, and both are symbiotic, since the smaller cells equal the ‘existential force’ of the bigger system with more ‘energy space’ but less frequency of time-cycles.

Whereas the bigger system is: Max. E x Min. I.

And the smaller system is: Max. I x Min. e.

Unlike the previous organic systems in which the informative networks exploit selfishly and extract energy from the herd, big, slow forms and fast, small systems are symbiotic, in balance and so they last longer in time.

Still, even if there is a degree of symbiosis the bigger, single organic system will be in control of the cellular herds as it provides them with the ecosystem in which to obtain energy and information. And in this manner it creates the structural order and deterministic destiny of most systems in the Universe. Let us try to formalize such pyramids of synchronicity, with the help of the 3×3 time arrows, which dictate that an informative pixel is smaller than the superorganism of the perceiver; a bite of energy is smaller than the reproductive body; and a reproduced, self-similar cell is smaller than the super-organism of which it forms part. In terms of existence, it means that the life of a quantum, fractal part depends on the length of the cycle it performs for the bigger system that controls the fractal part through its networks and informative or energetic fields:

The shortest cycle is the informative cycle that absorbs energy particles, transforming them into bits of information, perceived by a sensorial organ or mind. So informative particles are the smallest ones that live the shortest within any organism. For example, a human being consumes thousands of small letters in a newspaper thrown every day; an eye consumes a photon in a microsecond.

Next comes the feeding, energetic cycle that absorbs bigger energy quanta, transforming those quanta in ‘cellular components’ of a body, once the informative cycles have perceived the food. And so an energy quantum lives a little bit longer than an informative cycle. A pig that feeds a man lives longer than a newspaper and also its ‘final consumption’ takes longer than reading that paper.

Then, it comes the reproductive cycle that handles huge amounts of energy and information to create a being, repetition of a bigger organism. A woman’s ovule stays on her body all her life and it takes 9 months to become a baby.

Finally, the longest cycle is the being’s generational, social cycle, from its birth to its extinction (±st) when it becomes part of an eusocial superorganism. So those cells that carry the ‘social information’ and I-eye-wor(l)d of a human being, our existential will, last longer: a man has the same neurons all his life. It is through that longer generational cycle how a new social plane starts to evolve, as a new ecosystem or macro-organism in which the being exists, as a mere quanta of the macro-being. Such is the relativism and justice of the Universe: since he who killed micro-beings to feed and inform himself will be just a micro-being that toils for a bigger organism.

It is the social cycle, as the quanta gathers in social groups to perform energetic or informative actions for the bigger macro-organism that lives in a longer scale of time and controls him. For example, if you are a soldier, your national organism will sacrifice you in an energetic cycle when the nation conquers and ‘feeds on’ the wealth of other nation.

Thus we establish an existential chain between time cycles on 3 relative space-time scales:

(Informative>Energy cycle) st-1>(Reproductive cycle)i>(Generational-Social cycle)st+1

– Since the existential, generational life-death cycles of st-1 particles become energy and information cycles for the st-being.

– While the reproductive cycle happens in the same st-level of the organic system that mixes with a couple of inverse exi parameters (sexual reproduction, inverse parameters of particles that reproduce a self-similar particle).

– Finally, the generational cycle of the being becomes, as a part of a social herd made of similar individuals, a submissive energy or information cycle of a macro-organic system, st+1.

Recap. Any organic system is a sum of 3±st types of cycles, chained in hierarchical structures across 3 levels of complexity. Any being’s existence happens within those 3 TS planes in any organic system or ecosystem, in which he is a relative energy of bigger being, an equal, social being to its pairs and the informative master of smaller quanta.

. Balances between scales. Ternary principle.

According to the Ternary Principle any fractal, cyclical action of any species can be described through its spatial parameter of ‘speed-extension’ and its reciprocal, temporal parameter of repetitive rhythm or ‘informative frequency’, whose product, ExI=K is a constant of action that defines the existential parameters or life-span of the cycle (also written as SxT=K in certain models of physics, since ‘clocks of time’ and cycles of information are synonymous).

Yet those åctions are the sum of the simultaneous micro-åctions of its ‘cellular quanta’ and so both must be in balance for the total organism, extended in two planes of existence to work in synchronicity. And that synchronicity is ruled by the black hole law of complexity, we just explained:

Min.Sp=Max.Tƒ: smaller beings act faster than bigger ones.

How the faster, smaller, ∆-1 micro-åctions relate to the slower, big simultaneous åctions of the organism? Or in formal terms, what is the relationship between the constants of those macro-åctions and the faster parameters of its micro-cellular cyclical åctions? How each organism relates as individual quanta to the slower, longer cycles, (Max. Sp= Min.Tƒ), of the ∆+1 ecosystem in which it performs its åctions?

2 facts are the key to properly answer those questions:

– Chains happen across 3 ±st levels of existence, creating hierarchical pyramids of unlimited size in time and space, through those ternary structures.

– Chains of åctions become simultaneous, because certain cycles are shorter than others; so the faster speed of micro-cycles is compensated when we chain fast micro-cycles to slow macro-cycles.

Consider the cycle of feeding of a lion. The lion moves through space in certain patterns that displace the lion towards hunting and drinking grounds where he will consume a victim. Thus the energy cycle will be determined both, by the inner vital constants of the ‘∆-1 cells’ of the ‘st-lion’, (his cellular metabolism that defines his rhythms of hunger, his muscular speed and his strength that determines the preys of the ecosystem in which he feeds); and by the outer, ∆+1 ecosystemic parameters, (the spatial distance and ‘informative density’ of preys of the ecosystem). So to define the 2 ExI elements of the lion’s feeding cycles (the spatial trajectory and fractal rhythm of its hunting) we have to know those ±st parameters. Then we can define totally his feeding cycle.

Thus, existential cycles might be very complex but ultimately we can reduce them to a fractal ternary equation, which relates harmonically the Space-time parameters of those 3 ±st levels.

Those ternary chains define Universal events across 3 hierarchical planes of existence, from the chains that happen between the ‘3 social classes’ of an organism, to the physical events that happen in 3 scales of matter, to the 3 levels of humanity (the biological, individual and sociological level). Since all cyclical systems are defined by the relative ExI parameters of those 3 ∆±1 scales.

For example, Maxwell and Planck defined the informative frequency and energy quanta of a light photon that absorbs gravitational space-time energy and deforms it into a light-wave only with the action constants of 3 scales: the ∆-1 constants, or magnetic, spatial, and electric, informative constants of vacuum – c=(e0 x m0) -1/2; the st-constant of light (h) and the fractal, social constants of photons, as part of a bigger social, ∆+1 wave (Sp=hv). If we add to those synchronicities the understanding of the diffeomorphic dimensions of energy and information (on top), then we can fully grasp the structure of the ‘organic membrane of light-space’ in which we live and its connections with the lower membrane of gravitational space and the upper membrane of electronic, denser space, of which our mental eye wor(l)d is made.

In most systems, a ∆-1 particle, despite its individual ‘vegetative will’, perform a cellular, cyclical function within the macro ecosystem in which it exists either as an energetic or informative unit, and in this manner the sum of the parts makes possible the emergence of the whole. In the previous example, photons are individual forms that feed on micro-electromagnetic constants creating a reproductive c-wave. Yet most photons could not exist if 2 bigger, ∆+1 atomic particles had not reproduced them to communicate energy and information, which is the role they performed by the higher quanta. In fact, the macro-organic dual atomic system that emits and absorbs the photon, determines its ExI, frequency and energy parameters and its generational life span, given by the distance between those 2 atoms.

Those balances between the cellular, existential force and individual force of the system is what maintains the balance of the organism and make it last in time and are exemplified by the previous Maxwell equation or the vital constants and physiological constants of an organism.

We can generalize those harmonies, observed in the lower physical plane if we consider a constant of action in any scale to be a self-similar definition of the Existential force of the system we can define a basic law of hierarchical systems:

‘The ∆±1 existential forces of a system are in balance, such as the exi constants of action of the macro-system determine the length and intensity of the existential cycles of its cellular forms, which in turn will determine the cycles of its microsystems’.

Thus each entity will become deterministically chained by the informative or energetic, reproductive or social arrows of the upper system, for which it will act within a herd of self-similar forms, sustaining the åctions of those macro-arrows of time. And so while submissive to the higher system it will enter in democratic, parallel relationships with the forms of its planes of existence and finally it will be itself, a super-organism for its internal cells or reproductive body it controls. This is the ternary principle that all systems of reality obey, from humans, which perform for his social scale, related in equal terms to other humans and control tightly the cells of their body, to the light photons of the previous graph, slaves of their electronic parents, of which they often become a ‘fractal cell’ (fractal interpretation of an electronic nebulae), while controlling the electric and magnetic constants of their space-time membrane.

We formalize those ternary functions as partial equations of the Generator Equation of space-time, to which we add the hierarchical index of scalar space-time, st:

– Set∆-1>∆ST: The being is a dominant macro-point, ∆ST, which absorbs a flow of information and energy from a herd of micro-quanta (ei∆-1) that it controls with its physiological networks. So our cells are controlled by our blood and nervous systems.

– Spe xTƒ: It is an individual quantum that relates to similar cells in an environment in which it searches for energy in social herds or for similar couples to attain its main existential will: its generational reproduction. Thus, ‘∆’ is the fundamental plane of existence of any being, the region in which it perceives more, and plays its most fulfilling cycles of existence.

– S>∆+1: The point becomes energy of the upper plane, either because it performs an energy function for a bigger social plane. For example, the govern controls you as a social micro-quanta of a nation, which makes you die in wars or takes your energy through taxes. Or because it is consumed as relative information or energy of the upper head or body system. For example, humans become soldiers, the energy of wars for the system called the military-industrial complex.

And again, to explain why all those processes, some paradoxical and destructive for the p.o.v. are possible we must postulate a conscious universe of infinite, relative p.o.v.s.

In fact, and this is a ‘psychological law’ with enormous implications for the existence at least of human beings, which might happen in other scales if the hypothesis of a perceptive Universe is truth, most points of existence are completely unaware of the existence of a lower scale, which they ab=use and they actively sacrifice themselves from the upper system from which they receive orders and information in its ‘tabula rassa’ brain. Since the p.o.v. has far less information than the upper system, which programs it to love its master. So humans go to wars for the military-industrial complex without realizing they are sacrificing themselves in most cases for the financial gain of the upper, informative castes that control with money, weapons and law the society in which they live.

It is an order we find in all planes of existence. For example, in Biology, a st-mitochondrion uses ∆-1 protons to deliver energy to the bigger organic ∆+1 blood networks in the form of ATP. So the atomic, cellular and organic scales define the energy cycle of cellular breathing. While a star turns in cycles with other stars, feeds the galactic black hole as a quantum and feeds itself in fractal stellar gas. A light ray feeds on electric and magnetic constants, gathers socially in photons and it is absorbed by big electrons.

Recap. From that 3-scalar order that structures any particle or cycle of existence (static or dynamic perception), it arises the relativity of existence, as any being is king of its territorial hill, friend of its friends and slave of the World or ecosystem in which it exists.

Laws of hierarchical synchronicity between time arrows

The relative frequency of those cyclical arrows create ‘time clocks’ whose synchronicities chain the long cycles of fast micro-entities to the short cycles of a slower macro-entity, creating a harmonic order between the different planes and social classes of the organic Universe. Since an informative cycle is faster than an energetic cycle, which is faster than a reproductive cycle, which is faster than the complete generational cycle of the being; while a macro being is slower than a micro-being, we write 2 basic chains between those cyclical arrows and the beings that carry its parallel functions in the structure of a superorganism:

 Microcell’s Informative cycles=S Cell’s energy cycles=Organism’s Reproductive cycle

 Generational cycles of microbeings =S Social cycles of Beings ->Sp/Tƒ cycle of macrobeing

Those ternary chains between the fastest cycles of macro-beings and the slowest cycles of its micro-beings create simultaneous, symbiotic åctions along 2 planes of existence:

Informative frequency of the macro being => Energy frequency of the micro cell

Thus the fast, informative cycle of the slow macro-being is transformed into the slow energy cycle of the fast cellular micro-being, in a symbiotic chain that make it dependent on that macro-being. For example, the fastest Earth’s cycle is its informative, cyclical rotation as a mass vortex that determines the day-night cycle of light, which feeds its living beings. So, the living ∆-1 cells of Gaia, its plants, feed with the day light, while its ∆-1 animals have a ternary energy cycle of 1 to 3 meals a day. So both are timed to the informative light-day cycle of the Earth, their energy cycle. If we lower the scale of analysis, the same cyclical chain happens between the animal and its ∆-1 cells. Men have a rate of informative perception of a second, the rate of blinking and thought. But a second is also the rate of breathing and the heart’s beating that transfers energy to its ∆-1 cells, becoming thus the energy rate of feeding of those cells.

The same relationship can be used in other informative /energy cycles. For example, the energy cycle of an animal is a day. Yet the size of its hunting territory, of which he knows all its information, is the distance it reaches in a day.

A homologous relationship chains microcosms and macrocosms symbiotically in the next, longer 2 cycles, the energy and reproductive cycle:

Energy frequency of the macro being=> Reproductive Frequency of the micro cell

By homology with other organic systems, we consider that the energy cycle of the Earth as a rotational mass that deforms gravitational spacetime lasts the year it takes to cross its space-time territory, its orbit. Since, as in the case of an animal, the main energy cycle of the planet is the year-time it takes to sweep its solar orbit, the ‘organic territory of the planet’, where the Earth absorbs its gravitational energy, deforming space-time according to Einstein’s equation. While the secondary Earth’s energy cycle is a month in which its satellite, the moon, sweeps around the Earth’s orbital territory. We obtain thus, the 2 main cycles of transformation of gravitational energy into rotational form by the Earth-Moon system: the lunar cycle and the annual cycle.

And those 2 cycles are transferred to the micro-living beings of its Gaia skin, so they are the reproductive cycles of most animals. Thus in the human being the menstrual cycle is a lunar cycle; the cycle of reproduction of a child lasts 9 months; in Nature almost all reproductive cycles have an annual frequency, happening in spring or summer, when the sun’s light absorption is maximal; which is the obvious reason why those cycles are linked: while the macroscopic being absorbs energy, it allows its cells to use that energy to reproduce. Again, if we lower our scale, an animal as a macro being has a cycle of energy of a day. That period is also the cycle of reproduction of most cells, called mitosis. Yet reproduction is discontinuous: it happens only when ‘optimal energy and information’ is available during a small interval of the total existence of the being, in general in the second, mature age of balance between energy and information.

It seems that the micro-being is fed and reproduced by the macro-organism, the good ‘god’ of its existence. Yet ‘the good god’ is actually a farmer that reverses its arrow of order for an arrow of entropy and destruction when it uses the ‘existential cycle’ of the micro-being as a mere fractal cell of its macro-organism. So we feed and reproduce pigs but end up eating them. In a sense, we can say that all organisms are ‘farms’. So pigs feed men; stars fed by the interstellar gas attracted by the black hole’s gravitational power, also end up feeding the black hole; and fat cells fed by the organism end up killed, feeding the macro-organism. So in that inverse, final cyclical chain between the microscopic and macroscopic being, the ‘relative God’ takes all what he gave. Thus there is an inverse, final chain between the generational cycle of a micro-organism and an inner, energetic, informative or reproductive cycle of a macro-being. Thus the generational cycle of the macro-being complete the previous chain:

Generational frequency of micro cell => Reproductive frequency of macro being

For example, body cells live and die in an interval between a month and a year, which is the period most animals need to complete their reproduction. At cellular level, carbohydrate molecules live and die in short daily cycles, which is the period of reproduction of cells. The relationship between both cycles is again organic: reproduction means the renewal of a macroscopic being that destroys and creates many of its fractal elements, as energy or information of the reproductive ST combined cycle. So cells accumulate carbohydrate molecules that they use in their reproductive processes, destroying and reconstructing its DNA genes with them.

Depending on the role a ∆-1 quantum performs in the macro system, its life will be longer or shorter: Wheat is harvested to feed annually the human ecosystem, while carbohydrates die every day to reproduce DNA molecules. Yet a top predator informative cell, a neuron, lives the entire life of the organism, since it defines the informative networks that dominate and form the will and consciousness of the organism as a whole macro-beings. And inversely, the life span of the ‘brain quanta’ defines the life span of the macro-organism. So probably the enormous life span of quarks, the fundamental particle and brain of the fractal atoms of the Universedefines also the life-span of the Universe. Since the study in detail of all those chains for all Universal species is beyond the Cyclical Time of this work, we will only consider some examples from the 3 main disciplines of science:

– In the physical world we study the temporal chains between the 3±st scales of existence of light (gravitation, light and atoms) and the 3±st scales that create the Universe.

– In Biology we study chains between the 3±st scales that cause life evolution: the ∆-1 genetic cycles, the st-life cycles and the ∆+1 ecosystemic, geological cycles of the Earth.

– In History we study the rhythms of life of civilizations and the human generational cycle, which follow a decametric 80×10=800 cycle of destruction of civilizations.

Recap. Since the life of a fractal cell or quantum of a bigger system is a moment in the longer existence of its organism, to create the effect of simultaneity, microcosmic, fast, fractal cells have to chain their longer ‘existential cycles’ to the shorter cycles of a bigger organism or ecosystem in which they will exist as a mere fractal instant of those shorter cycles. Thus, the informative arrow is smaller and determines the energetic arrow, whose frequency is shorter and determines to the reproductive arrow, whose cycle is shorter and determines the eusocial arrow: T->S->ST->S. As a Hindu proverb says: ‘a blink on the eye of Vishnu, the Universe, is a life of a planet and a drop of sweat of a planet is a life of a human being.’

Present waves: space synchronicity. Time particles synchornicity.

Ultimately the Fourier equation derives from those deep laws of synchronicity and social organisation, as they apply to the physical scale of ‘present wave states’ (as opposed to past to future field-particles). So another element to explore by future researchers, is how the intertwine of those 2 fundamental states:

Past->future->past (field-particle-field)-male state-time entity

Present-repetition-social boson accumulation-female state space entity

affects the synchronicity of systems. We shall not even attempt to enter that field here.

Only consider a general law: herds are wave of present equal parties which move collectively in a democratic way and so they obey laws of space (boson in physics); past to future particles are hierarchical, and so its function is past to future (fermion in physics) and so they obey different ‘statistics’.

In this manner complex events/entities can be reduced to simplex herds of events/cells in present ‘body syncronicity’ or past to future events in hierarchical darwinian synchronicities. And so the synchronicities between both type of states differ.

In essence, we are going to speak of past to future hence hierarchical scalar synchronicity, which in terms of actions not of beings, means a hierarchy similar to a maslow pyramid between actions that ‘gather in herds’ in a plane of space, to transcend to a higher future plane as a field that ‘gives away energy or information to the larger action’.

So multiple energy actions give way to a hierarchical higher reproductive action that gives way to a higher eusocial action and those 3 rhythms become essential:

∑∑∆-1: Spe cycles -> ∑∑∆: reproductive cycles -> ∑∆+1: social cycle: whole

If the mind of people were more evolved I could bring examples of physics for the mathematical formalisms or of gender behaviour for the logic formalism, but of course this won’t do it – the concept that women are present and men move the past into the future so far I think only schopenhauer ‘ever’ realised and was called a mysoginist, and if i bring here fermi and bose-einstein statistics the occasional reader if any will panic (-:

So we shall only really deal here with the most basic level of this science.

How the different knots of actions synchronise between scales from past to future

For example, the convergence of different geological and cosmological cycles, which affect the energy and information of the Earth, cause ages of extinction and age of massive evolution of new species, with a series of frequencies and rhythms we have studied in our analysis of geological biological and sociological cycles. In fact most events of the Universe have multiple causes, which means they are knots of time cycles: from multiple cyclical forces that converge in Relativity to create a knot of gravitation or a charge, to the multiple events that converge in Biology to cause an age of extinction, to the multiple failures that converge in a body to change its rhythm from life to death.

Since the Universe explores all possible structures, despite being made of a few elements, the inverse system also exists: one in which the bigger system is simpler than the smaller, faster cells, and both are symbiotic, since the smaller cells equal the ‘existential force’ of the bigger system with more ‘energy space’ but less frequency of time-cycles.

Whereas the bigger system is: Max. Spe x Min. Ti.

And the smaller system is: Max.Tƒ x Min. Spe.

Unlike the previous organic systems in which the informative networks exploit selfishly and extract energy from the herd, big, slow forms and fast, small systems are symbiotic, in balance and so they last longer in time.

Still, even if there is a degree of symbiosis the bigger, single organic system will be in control of the cellular herds as it provides them with the ecosystem in which to obtain energy and information. And in this manner it creates the structural order and deterministic destiny of most systems in the Universe. Let us try to formalize such pyramids of synchronicity, with the help of the 3×3 time arrows, which dictate that an informative pixel is smaller than the superorganism of the perceiver; a bite of energy is smaller than the reproductive body; and a reproduced, self-similar cell is smaller than the super-organism of which it forms part. In terms of existence, it means that the life of a quantum, fractal part depends on the length of the cycle it performs for the bigger system that controls the fractal part through its networks and informative or energetic fields:

The shortest cycle is the informative cycle that absorbs energy particles, transforming them into bits of information, perceived by a sensorial organ or mind. So informative particles are the smallest ones that live the shortest within any organism. For example, a human being consumes thousands of small letters in a newspaper thrown every day; an eye consumes a photon in a microsecond.

Next comes the feeding, energetic cycle that absorbs bigger energy quanta, transforming those quanta in ‘cellular components’ of a body, once the informative cycles have perceived the food. And so an energy quantum lives a little bit longer than an informative cycle. A pig that feeds a man lives longer than a newspaper and also its ‘final consumption’ takes longer than reading that paper.

Then, it comes the reproductive cycle that handles huge amounts of energy and information to create a being, repetition of a bigger organism. A woman’s ovule stays on her body all her life and it takes 9 months to become a baby.

Finally, the longest cycle is the being’s generational, social cycle, from its birth to its extinction (±st) when it becomes part of an eusocial superorganism. So those cells that carry the ‘social information’ and I-eye-wor(l)d of a human being, our existential will, last longer: a man has the same neurons all his life. It is through that longer generational cycle how a new social plane starts to evolve, as a new ecosystem or macro-organism in which the being exists, as a mere quanta of the macro-being. Such is the relativism and justice of the Universe: since he who killed micro-beings to feed and inform himself will be just a micro-being that toils for a bigger organism.

It is the social cycle, as the quanta gathers in social groups to perform energetic or informative åctions for the bigger macro-organism that lives in a longer scale of time and controls him. For example, if you are a soldier, your national organism will sacrifice you in an energetic cycle when the nation conquers and ‘feeds on’ the wealth of other nation.

Thus we establish an existential chain between time cycles on 3 relative space-time scales:

(Informative>Energy cycle) ∆-1>(Reproductive cycle)i>(Generational-Social cycle)∆+1

– Since the existential, generational life-death cycles of ∆-1 particles become energy and information cycles for the st-being.

– While the reproductive cycle happens in the same st-level of the organic system that mixes with a couple of inverse exi parameters (sexual reproduction, inverse parameters of particles that reproduce a self-similar particle).

– Finally, the generational cycle of the being becomes, as a part of a social herd made of similar individuals, a submissive energy or information cycle of a macro-organic system, ∆+1.

Recap. Any organic system is a sum of 3±st types of cycles, chained in hierarchical structures across 3 levels of complexity. Any being’s existence happens within those 3 TS planes in any organic system or ecosystem, in which he is a relative energy of bigger being, an equal, social being to its pairs and the informative master of smaller quanta.






53. 3 types of reproduction: Fractal space-time jumps.

A theme which might seem of science fiction to the reader, already surprised by the innovative outlook on reality provided by Time arrows and space discontinuities is the displacement not only in ‘space size’ but also in time evolution between the different planes of reality and the consequences for the workings of the Universe.

We affirmed earlier that all spacetime motion was in fact, in a discontinuous Universe, an act of reproduction. So a wave moving was a reproductive form, imprinting a lower scale of forces (in the case of light the gravitational membrane) with its information. And we distinguished 3 types of reproduction: external, enzymatic reproduction, from a ‘relative past to future’, as the parts were assembling into the whole by an external factor (enzymes in cells, human ‘enzymen’ in machines)’; a relative, present reproduction, as in the case of light, since the reproductive act was fast and displaced a wave-form in space, and a palingenetic reproduction from future to past, when a superorganism emitted a relatively less evolved seminal cells from the past that would then recreate the being.

The readers should be aware that when we classify self-similar processes almost always we come to the conclusion that there are 3 types of ‘differentiations’ or ‘decoupling’ or ‘horizons’ or ‘ages’ or ‘subspecies’, in as much as the Universe is structured in ternary patterns, according to the 3 dimensions of time, past, present and future and its 3 equivalent topologies of space, past=energy=spherical plane, present=reproduction=cyclical, toroid and future=informative hyperbolic topology.

In the case of reproductions, we used the dimensions of time to classify them. Yet the fact that reproductions are informative actions related to time more than space (except in reproductive, present motions as speed is), means that reproductive acts provoke a ‘time jump’, a ‘time displacement’, not only a spatial displacement.

Because reality is webbed by groups of actions that form strings that form particles that form atoms and so on, there is a dilation in time between the creation of lower, simpler planes, done in a relative past respect to the higher, more complex planes, which use the smaller particles of the past as energy points of its topological creation of new scales of spacetime. Yet in the same way we humans do not distinguish the age of galaxies we think are happening now when we see them millions of years ago, the time the light takes to arrive to our universe, when we see cells and atoms and other scales of reality we tend to believe they co-exist simultaneously and yet they don’t. There is a temporal displacement according to which the ‘future’ is the place where the most complex levels of organisms exist and the past where the simplest planes are formed. So your consciousness as a whole is displaced in time compared to your simplest atomic particles.

Thus in time jumps to the past, the species that emits the information does not emit the information in the same point of present in which it exists, but since information is discontinuous, the cellular bit of information appears in its immediate, lower spacetime-point, in its relative past, and so it suffers a discontinuous displacement in time.

Indeed, imagine a Universe with 2 dimensions in a complex plane, you can go left or right, meaning that each fractal step you do you will move through a discontinuous ‘jump’ to the lateral space. This happens because as we said, when resolving the paradox of Zenon, motion does not exist in the Universe, because it is always a discontinuous reproduction of a form. So when a light moves, it doesn’t move; it imprints the gravitational space next to it with a self-similar form.

Further on, we have explained that time/information is really a displacement along a ‘dimension’ of height and we represented temporal information with a complex plane.

So when we move to a lower scale of information, we are moving in ‘the time clock’ of the super-organism a cellular step down, which means within the whole organism we move to the past. We shall thus enunciate the law of fractal time jumps and analyze the 3 examples of the previous graph: a physical jump to the past (particle/antiparticle pair), a biological jump to the past (birth and orgasm), and a sociological jump to the past (the function of the prophet in a corrupted, dying social organism of history, a ‘God’, subconscious collective or civilization). And two other fascinating cases: the spooky effect of quantum entanglement and non-local gravitation in physics and the question of will and consciousness in human beings.

Let us then enunciate the law of fractal jumps in timespace:

‘Fractal jumps are reproductive motions in time and space. Spatial jumps happen in spatial steps with a maximal length equivalent to the length of the organism, between contiguous zones of the same space plane. Temporal jumps happen as temporal displacements between 2 hierarchical contiguous planes –  st and st-1 – of informative complexity with a maximal length equivalent to the generational life cycle of the st-1 cell of the organism.

Spatial displacement dominates motions in the same plane of existence (hence reproductive motions). The main time motions between planes of existence are jumps between planes, which imply a change in the parameters of energy and information and a jump in the point of space-time in which we exist. Those laws, unknown to science, are the most important of Fractal i-logic and are tested by thousands of detailed analysis in each science. In essence when we move from one plane of existence to other planes we do not only displace in space but literally in time, because reality is constructed not only with a volume of space but a volume of time information.

Thus, the Universe only allows one ‘discontinuous jump’ to the next past, future, right or left zone. There are not worm holes to enter far away Universes (too far to happen), jumps to a past in which mother was born (as only you travel to your past through your death).

Because physicists use a single space-time continuum and confuse the arrow of time/motion/energy with the total time arrow of the Universe, some believe that a change in that time/motion arrow, which is merely a local change in the direction of a fractal entity of space-time, is an absolute change in the direction of all the arrows of all the beings of the Universe. This is the reason of some naïve ideas about time travel in physical systems that halt the motion of time (Black holes where the T parameter goes to zero, which prompted Mr. Hawking and Mr. Thorne to affirm they are time machines). Time travel doesn’t exist because all arrows of time are local, belonging to a fractal system of the Universe, not to the entire Universe, and physical Time Arrows are changes in the motion of beings, not changes in the arrow from past to future.

Let us now consider first the most complex type of reproduction, from future to past or palingenesis and then, the reproduction from past to future, departing of parts (genes in biology, memes in sociology) that construct a future super-organism, as we studied already the reproductive waves of present-space (light waves and motion in space).

Recap. There are 3 types of reproduction: a past to future motion or ‘genetic’ reproduction; a present to present motion or reproductive speed and a future to past reproduction or palingenetic, parental reproduction. All of them are based in the symmetry between space and time, two types of geometrical motion and the fact that all motion in space-time provokes a displacement both in space distances and time dimensions.

 Dimensions and reproductive motions.


Time cycles reproduce through fractal dimensions. Imagine a torus, as the one depicted in the graph: A cyclical string turns around, creating every 3 movements a self-identical closed macro-torus. If we repeat the process 3 times we obtain a 9 dimensional self-similar fractal super-string. Such is the way in which the Universe, departing from some basic forms – torus, spheres and lines – self-replicate and grow invariant at scale its energy and information systems.

Since according to the paradox of Galileo, what we perceive as still space is in perpetual motion, 2 questions must be solved:

What is moving and what is fixed space? And how movement can be introduced in the simplified, mathematical static models of time and space, proper of the Cartesian plane that scientists use to describe the Universe? Both questions are related to the concept of speed and acceleration as a 2nd and 3rd dimension of motion, and hence also as the 2nd and 3rd dimensions of fixed space. This insight has deep implications for the meaning of Physics and the interpretation of the Equivalence Principle of Relativity in which Einstein based General Relativity, his theory of mass and gravitation. So we shall try to explain it in more detail.

Since acceleration is mathematically defined as a new motion applied to speed, a constant motion, it follows that an acceleration/deceleration, a=±v/t, is both a dual motion and a bidimensional form. So we can either consider a static line which becomes a plane and then a cube, or a static form that moves with a speed and then accelerates. Thus, the dimension of acceleration/deceleration becomes the 3rd dimension of physical time and the more complex of all, as it includes the other 2 types of time-change in physics, speed and spatial form (in the same manner a cube includes lines and planes).

We can see a dimension of time movement as a spatial, fixed form, when we see it in simultaneity. So the 3 dimensions of space can be derived in time, by moving a point into a line, a line into a pane and a plane into a volume, and what we have termed as the 3 dimensions of physical time-change, in-form-ation, movement and acceleration, can also be derived from space by observing the curvature of space, and deriving that spatial form in time, v=ds/dt, and a=dv/dt. So time and space are not only inverse but complementary as we derive the 3 real dimensions of time from space and the 3 dimensions of space from time.

This can be done in two different ways, with the geometries of lineal space or the geometries of cyclical clocks of time:

-A point can become a lineal string, which can reproduce laterally and then the plane it forms can reproduce upwards, creating an Euclidean cubic space.

– A point can move as a curve to form a perimeter, which can rotate to form a sphere.

The difference which has important implications for more complex analysis of physical space-times is obvious: the point needs two paths to create a hollow 3 dimensional sphere; while the lineal approach creates a dense, non-hollow cube in 3 steps. Informative spheres are thus bubbles, which tend to shrink and implode, weaker than the more solid cubes that fill the entire space without leaving ‘dark worlds’.

The minimal gravitational membrane of the Universe is a lineal membrane, filled totally by lineal reproductions (string theory), because they must be the ultimate web, filling all reality (or else what there is inside), but most formal creations over that membrane are particles with hollow dark spaces.

Motion as reproduction of form, the stop and go game.

All this comes to a fascinating fact that explains both the paradox of Zenon and the paradox of Michelson’s measure of speed: motion in time is a reproduction of form in space. And so reality is webbed as particles with forms, go fractal step after fractal step, imprinting with higher form the previous, lesser informative, faster, v=s/information, membrane in which they are shaped. As in a film theatre, where you move the image, stop it, emit light to create a form in the screen, move on, stop, emit information, the Universe of motions is made of reproductive, fractal motions, steps that imprint form in the lower scale of energy. And so reality is always a stop and go, confirmed by the trajectories of particles which are always erratic, with stops an goes and 90% angles, when they emit a smaller particle to communicate. This also explains without need for a c-absolute postulate of speed why Michelson didn’t add speed to a light emitting electron travelling in medium: the electron stops, locks itself in the gravitational membrane with the other electron (entanglement) and then in stillness emits its photon. So the speed of light of the event is independent of the speed of the background an emitter and receiver are locked before they share information. When you talk you also align your head in the direction of the speaker. Your head is your fractal point and the voice you emit is locked in distance. Or else it would suffer a redshift or echo effect.

Thus, time motion is not a mathematical, geometrical pure dimension of space (Relativity latter revis(it)ed in more detail), but the first dimension of physical space, of the real world that Euclidean geometry converts into a fixed abstraction.

In that sense, from the perspective of time physics, we could temporalize space and then consider that the first dimension of time is in-form-ation, morphological shape, achieved by the evolving height growth of any form, from masses that evolve in height till becoming black holes to biological life that evolved in height from the planarian to the human being. The second dimension of physical time will be reproductive motion of form of those 3 space-time dimensions that create a ‘fractal dimension’ that extends till the end of that movement. And finally the 3rd dimension of physical time-change will be acceleration, change in the rate of speed. If we add the inner bidimensionality of the mass vortex or bit of information reproduced with those motions, we have 5 fractal dimensions.

No more dimensions are needed, as it can be proved that the maximal spatial volume and hence the maximal efficiency in packing a space-time field is achieved with the folding of 5 dimensions, which might be the dimensions of the most informative, temporal elements of the Universe, black holes whose equations transform spatial dimensions of length into time dimensions of infinite height.

It has in fact been proved by Maldacena in his famous conjecture that the 4-dimensional membrane of a 5 dimensional Universe is self-similar. Thus, we could consider that a local big-bang quasar or a cosmic big-bang would be the external membrane, which unfolds of a 5 dimensional Universe. This is rather accurate. Since we observe a planar Universe (from our 3 dimensional perspective) which could be the energetic, Riemannian topological membrane of any st-point.

The error resides in considering all those 5 dimensions spatial dimensions instead of temporal dimensions of movement and acceleration, a subtle but fundamental change that explains a vital reality, ‘as it is’ beyond simplistic, geometric abstractions.

Reproduction of light: motion as form.

We hinted before to the fact that the simplest space-distance or amplitude of a wave and the simplest information or frequency of a wave, combine creating the simplest constant of action or speed, the speed of light or electromagnetic space-time, which reproduces the form of the wave across a surface of gravitational space. So the abstract spatial term, ‘speed’ is for light waves an organic arrow that reproduces the in-form-ation of the wave in the previous energy of space, in the case of light imprinting the simplest gravitational space-time. Light speed becomes then the 3rd arrow of reproduction of a dimension that combines energy and information, recreating a new form. We can find many other examples. Since the combination of the arrows of fractal information and spatial energy define in the complex Universe the 2 new dimensions of existence, reproduction of a parallel form the same plane of space-time and social evolution of self-similar forms across multiple planes of space-time or palingenesis:

      3rd Dimension: Spatial Reproduction: ext=k.

     4th ±st Dimension: scalar, palingenetic, social evolution

It is important to remember that those 2 complex arrows exist with lesser frequency than the simplest ones, energy and information beats and have self-similar rhythms. So if the simplex beat of reality is the stop and go of informative perception and energetic motion: I->E->I->E, the complex rhythm is also a beat between spatial reproduction (a radiation in biological beings, a wave in physical species) and informative evolution (a collapse of a wave into a particle):

Social, Formative evolution->Spatial Reproduction-> Evolution

And it is easy to see that social evolution is the complex arrow of time and information, as it requires a lot of time and a common language of information to create complex social networks; and reproduction is the complex arrow associated to energetic processes, which must be observed to be able to reproduce. So for example, a female without a percentage of fat in the body cannot reproduce and when a species radiates in a massive age of reproduction, it does so, often extinguishing a previous species in which it feeds on.

They are also dimensional arrows, that the dual, geometric and organic nature of the Universe. Indeed, if height is the natural dimension that orders the information of the Universe and length the natural dimension in which spatial energy extends and moves, the combination of those 2 arrows of energy and information produces reproductive waves that create the 3rd dimension of width.

Reproduction of waves and forms that create new dimensions becomes then the biological why of the geometrical hows we observe around us.

Yet further on, there is a 4th dimension of growth into macrocosms that structures cellular reproductive waves through an increase of informative frequency. So the collapse of a physical wave when it grows in frequency/form, make it transcend into electrons and other particles of higher information. And inversely, a light wave that relaxes and diminishes its information and frequency (redshift) ends up tired, descending to the lower plane of gravitational space-time.

It is the combination of those 2 complex arrows what allows palingenesis – complex reproduction. Thus a palingenetic cycle is the essential reproductive cycle of most forms of existence, in which the interaction of both complex arrows/dimensions creates st±1 waves of microforms that become macroforms, by the reorganization and growth of self-similar reproduced sets. We might say that palingenesis is a temporal reproduction in as much as it moves little in space but evolves a lot of temporal information – while speed or translational movement is the spatial reproduction of a simple physical form across space. Thus the reproduction of dimensional forms creates reality.

The simplest of all those dimensional, reproductive waves is a c-speed, reproductive wave of light, which Maxwell proved to be the product of the magnetic/energetic and electric/informative constants of the light wave (1/mo x eo=c).

Galileo’s Paradox makes us perceive such moving, dynamic, reproductive waves as continuous dimensions of space. Both perceptions describe the same dual reality: a space-time field in perpetual transformation. The most striking case of one of such space-times made of organic, dimensional networks is the electromagnetic space-time, which forms the background of human existence, our space-time perception. Since human space-time is not an ideal, Cartesian background, but it is created by the fractal sum of all the 3 perpendicular dimensions/networks of light-spaces (the sum of all light beams of the Universe). The 3 dimensions of each of those light fields are perpendicular as our Euclidean space-time is, and correspond from the perspective of light to the 3 organic cycles of a photonic wave: the c-speed or length of a light field reproduces its form, the magnetic width acts as the support energy of the light wave and the electric height creates the information of light, where the photon or informative particle/head of the energy wave/body of light is found. When such light waves reproduce, they create a wave of present space. Since the light wave transits in an eternal present, or in other words it doesn’t change its content of temporal form, its information is preserved. For that reason spatial, light waves transit billions of years between galaxies carrying accurate information on the far away particles that produced them.

Thus movement is no longer movement but the reproduction of a form over a surface of energy. Light doesn’t move but its waves imprint the form of gravitational space with the wave of light. An electron doesn’t move but it shapes the photons of its electronic space in certain wave patterns, called the electronic nebulae. Masses are not fixed forms but vortices that bend lineal gravitational space once and again into self-similar fractal, temporal cycles. In those terms, a dimension of space is the reproduction of a volume of discrete, fractal, self-similar in-form-ation that creates space.

While inversely, temporal palingenesis reproduces and evolves information.

The Universe is not only in perpetual movement, transforming back and forth lineal energy into cyclical form, but also a perpetual self-generating organism that constantly reproduces logical forms in palingenetic cycles, between 2 st±1 scales of relative space-times, where a mother will transfer its form into a micro-mother cell that through a process of palingenetic reproduction will create a self-similar replica of the mother.

Speed and palingenetic reproduction of a form into a fractal space surface explains from quantum jumps to palingenetic reproduction, from mystique experiences to the nature of dark matter, from Relativity to logic paradoxes. For example, the oldest paradox regarding movement is now solved: how can exist in a fractal world filled with discontinuities continuous movement? Zenon, a Greek philosopher put the example of Achilles and the Turtle: Achilles will never reach a turtle because he has to cross infinite fractal spaces. Parmenides gave him the only logic, true answer: continuous movement doesn’t exist in a discreet Universe; it must be a mirage of the senses. But we observe movement, so how it can be possible? Because movement is an action of palingenetic or wave reproduction. Since a wave, as the figure shows, is not really moving, but reproducing information over the potential energy of the next vacuum space 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 in space and time, through the reproduction of fractal information. The simplest analogy is a television screen where new images are created constantly without hardly any cost of energy, because they are virtual images formed by illuminating 3 colors that are already potentially in the screen. In the case of a wave, the relative energy imprinted by the logic form might vary, from the vacuum energy of a light wave to the placental energy of a mother, yet the process is always the same: a form imprints another region of space, changing its morphology. What matters in the Universe is the dominant arrow of information, the logic, intelligent form, which imprints constantly amorphous surfaces of energy. The Universe conserves forms over eternal moving energy. Even the most complex, fractal, living organisms, made of ∞ cycles that transform energy into information back and forth, maintain the appearance of a constant form, because they constantly repeat those biological cycles over new energy elements.

For example, a human changes all his/her atoms in 3 months but s/he maintains i=ts biologic form invariant, thanks to the constant absorption of new energies over which s/he reproduces his/her fractal information. Bidimensional cycles of time and planes of space are fractal and so are their changes and displacements. Thus since time is geometric, bidimensional, as space is, it can imprint form in any lateral surface of energy, giving the false impression of movement. So speed is synonymous of reproduction, the main cyclical action of the Universe, where now the ideal Galilean Formula, V=S/T, for a fixed space-time, applies to the real variables of Spatial energy and Temporal Information: V=ΣE/Ti.

Self-reproductive waves create what mathematicians call fractal, finite, self-similar dimensions, caused by a wave that repeats its patterns of information in diminishing or growing scales. Which is the key process to understand why energy and information are invariant shapes at scale, repeated ad infinitum from atomic to galactic cosmos: fractal waves translate those morphologies, as they change, grow or diminish in spatial size/speed and Ti-frequency, connecting different space-time fields. Those waves of energy and information cross the discontinuities between different space-time fields. So when we look at smaller Universes from our perspective we use an electronic or light flow, whose frequency increases as we enter those smaller, more informative Universes.

In that sense, following the Correspondence Principle, the new concept of ‘informative speed’, V=ΣE/Ti, includes the simpler model of spatial speed. Yet it goes further, explaining not only the how but also the why of many laws of science, relating the energy and information of waves with its relative speed, since according to the inverse properties of energy and information, the less information a wave has to build up and reproduce, the faster the wave will move. This is called in Physics the Law of Range of Forces (max.Ti=Min.ΣE) and it has its limit in the non-local, instantaneous speed of gravitation, which carries zero information and has infinite speed: v (g)=ΣE/0 information=∞. While in the other extreme it creates fixed frames of gravitational reference, called black holes, which carry infinite information and have zero translational speed, as entire galaxies turn around them. It was again Aristotle, who said that if God exists, it would be the final unmoved focus that in-forms the movement of all other beings in the Universe. Indeed, the black hole seems the God/Brain of in-form-ation of all galaxies, whose stars turn and fall into it. The Universe itself might be born of the big-bang explosion of a black hole, origin of the process of Universal life that will end in the reverse ‘Big crunch’, of informative death, creating the ultimate cycle of existence of reality…

Recap. The dimensions of space are reproductive arrows of time that imprint a form in a simpler energetic membrane. Worlds can have a maximal of 5 dimensions: 2 bidimensional forms which move in 3 fractal dimensions of a higher Universe.

 Does st-1 determines st? Genetics & memetics.

The simplest act of reproduction and creation is the assembly of parts that become wholes, and its study gives birth to an entire sub-discipline of systems sciences called Emergence.

The structure of the Universe is that of a series of complex worlds/organisms of at least two membranes, one of relative past, energy, st-1, and one of relative future information, st+1, with an intermediate present st-membrane, exi, made of actions (equivalent to the topological description of relative past, external membrane, r, a relative hyperbolic center, a, and an intermediate cyclical space with motions between the a-r limits, which form together a ‘closed ball’.)

In those systems an external perceiver tends to observe mainly the intermediate space with maximal space volume and misses the hyperbolic informative center of minimal space, even if it is the source of informative orders, through invaginated networks that control both the Riemannian, spherical surface and the paths of the cyclical cells in between. Yet the flows of energy move from the ‘lineal quanta’ of the surface through the paths of the internal body-organs into the hyperbolic, informative structure. And so human scientists that need instrumental ‘pictures’ to prove the existence of a causal order and only use Aristotelian single causes tend to believe in any ternary structure that the ‘lower energy plane’ is the case of the creation of the superorganism.

This means we consider in the ternary structure of a human, (cellular, individual and social structure) that st-1 genes to be the cause of all our properties as a super-organism, and we are just a ‘ghost’ created by them. But this is a partial vision due to the limits of perception of informative orders from the hyperbolic, fractal informative system – the nervous system – to the lower, genetic cell system. If, in the future we get to fully understand the networks of information of the brain, we shall certainly discover that many orders and structures of the human superorganism are stored in the brain and probably reproduced during the last months of gestation from the mother’s brain to the brain of the child. Moreover, there are an infinite number of personal traits which are NOT reproduced through Genes, but through the carriers of information of st+1, cultural organisms, called memes. Indeed, most of the features of our life – our religious beliefs, cultural customs, laws and instruments are memes, which create another super-organism, the civilization or religion, in which we are a mind-cell, a believer, who shares with all other believers the same ‘mental DNA.

So in this case, if we were to accept the thesis that creation happens from the lower level to the upper level, we should consider that we, human beings, are the only influence on the memetic structure of civilizations. But it is obvious that once those structures are created they influence new generations. So for example, when a system of laws or beliefs in a legal nation or ethical religion is created, it reproduces from generation to generation, influencing and molding the new species.

We conclude that superstructures & physiological networks, the informative/nervous/cultural system in organisms and cultures and the reproductive/blood/economic system, once constructed, influences the lower genetic/human scale. In the genetic case we do not know how. In the social structure, we know and since the work of the socialist, scientific school of history and the recent development of memetics and biohistory, we have worked out the processes – even if most historians prefer to think that we, individuals are the heroes and only cause of historic events.

But what truly matters is that both genetics and memetics are bits of information whose purpose is to create a superorganism, as the biological and sociological superorganism of mankind have the same physiological structure with nervous/informative /cultural systems; blood/ reproductive/economic systems and digestive/energetic/ military and transport systems.

So the true program that genes and memes and any ‘informative bits and parts of any creative process’ follow is the arrow of eusocial evolution, which explains why so smallish ‘genes’ and ‘memes’ are able to reproduce so complex super-organisms, as most of the development they will express is ‘structural’ to reality, embedded in the existence of a 4th arrow of time, eusocial evolution; which in itself is the natural conclusion of a game of 2 simplex energy bites and information bits, which reproduce in 3 types, more energy bits, more information bits and reproductive combinations of both, which latter will recreate energetic, informative and reproductive systems. So genes and memes do not need to encode that program/information that happens automatically. Moreover because each bit and bite has embedded its program within itself as part of the space-time reality, it will naturally search for energy and information carrying the program. For example, humans naturally want more energy for their body and more information for their mind, so naturally they try to create machines of energy (transport, weapons) and information (chips, books, audiovisual machines, mobiles) that enhance their capacity to process and store energy and form.

It is thus logic to think that in the genetic scale, RNA molecules which are the ‘active’ elements of the cells, carry a natural will for more energy, information and reproduction, which they ‘express’ creating cells and then superorganisms, as we humans do through memes, even if we are not conscious that the final outcome of our labors is the creation of nations, religions and civilizations, superorganisms of history.

This is indeed evident when we study the behavior of RNAs, which do the cycles between the outer Protein, lineal membrane and the DNA-informative storage, and are divided in 3 sub-types specialized in energy/killing, reproduction/RNA messenger and information/transcription.

In essence all this means there is not only a ‘biological arrow’ of creation of the upper scales of reality as a construct of the lower scales of genes and memes (the dominant theory in biology, due to the excessive development of genetics); but also a present flow of orders, embedded in the program of the 6 arrows of time, masterminded by the ‘action units’ of the system (RNA molecules and human beings) in both scales, which is probably the dominant ‘will’ of the program. And also a stored, informative, repetitive flow of orders and information from the upper scales of reality to the lower scales, which geneticists have not yet understood, due to its complexity (nervous structures in organisms and ‘the system’ or ‘superstructure’ of cultures and economic ecosystems in societies). Indeed, the codes of the brain that might determine certain characteristics we cannot obtain from genes is more difficult to recognize, as information tends to have lesser size and it is coded, so an informative order is often invisible to those who don’t understand the language in which it is written.

What parameters define different creative processes? The specific forms of the informative stores (DNAs, nervous networks constructed by imitation of the mother’s brain by the son’s brain and cultural memes). They differ in each superorganism, which will activate and create a different type of transfer-RNA, animal nervous system and individual memetic brain, reproducing a different species and culture.

Further on, a theme which must be taken into account is the fact that all those systems seem to us ‘simultaneous’, despite the fact that they are displaced in time, since to recreate the upper scales, the lower scales must be created first, so the superorganism is displaced into the future. And for that reason for the 3 scales to create a ‘simultaneous present’, synchronic being there must be indeed a time jump or flow from future to past of the superorganism or relative future structure and a flow from past to future of the cellular energy, which will flux into the relative present, so the 3 ‘scales’ are in harmony and co-exist creating reality: Past x future = present.

In a world of multiple time-speeds and planes of existence we live in an ecosystem of time knots whose cycles of time/ information differ in parameters of energy and form and are displaced from past/energy/simple cycles into future /information faster cycles. Yet the faster cycles are built upon the previous structures and so they are made ‘after’ the simpler cycles are created, in the ‘future’ There is therefore a real displacement in absolute time between what we see as bigger structures and what see as a smaller, since the bigger structures are traced departing from smaller cycles. This explains a mystery of quantum physics – the fact that we cannot see the wave/past/energy state and the future/particle state at the same time. Neither we see the atomic/past state and future /molecular pi orbital at the same time. And yet we know both co-exist.

Recap. In all processes of creation, the 3 scales of the super-organism, the cellular, individual and social scale input the program of creation based in its 4 arrows.

The life-Death cycle as a dual time reversal.

If birth is a dual fractal jump, it follows that death, its reciprocal must be also a fractal jump between planes of existence and indeed it is.

Yet the most obvious proof of fractal jumps to the past are the processes of death, which people who suffered it and then have survived, explain as a rewinding of the memories of the being that travels through the entire information of his life towards the past. The difference between a palingenetic jump and a death jump is that palingenesis is a backwards- forwards dual jump and death is a dual jump backwards at maximal speed. We die twice, first becoming a cellular being, and then due to the helplessness of our broken cells, without physiological networks we die again, becoming molecular food for insects. In physical systems, death is a big-bang that again implies a dual simplification till reaching the vacuum plane of pure energy.

This can be compared to a boxer that fights in a category with 2 jumps of mass/information/weight. The ecosystem is one in which the speed of time cycles and spatial size of beings is much bigger and so the form becomes annihilated. The process of death makes you a group of unconnected cells, weakened by your ‘submission’ to the bigger network systems of the super-organism, tamed by them; so we die again when confronted the micro-organisms of the insect and bacterial world.

Recap. Death is the fastest displacement in time in which a particle jumps two layers of space-time in a fast track.

Palingenesis between fractal planes: reproduction.


3 dual Fractal jumps in 3 scales of existence, written with the old formalism, in which a ‘seed’ of relative past information emitted by a future parental form hosts in an energy surface, evolving towards the future:

A photon reproduces a particle-antiparticle. A spermatozoid starts the evolution of a child. And a prophet emits a verbal code that will recreate in the future a dying civilization.

Alternately when a form with maximal information, or seed cell from a higher plane of existence falls in a lower one, it becomes a top predator and starts a much faster process of evolution, predation and creation that culminates in the creation of an offspring, or self-replica of the more complex plane. This is the essence of the process of reproduction and it involves a real jump towards the ‘past’ of the upper organism that deposits a seed of time/information that evolves faster into the future. The best described process is biological palingenesis but there are other cases:

A fractal jump in space-time, which is dominant in information is a palingenetic reproductive action, the repetition of a form, through the parental reproduction of a simpler seed or relative past form that will evolve and reproduce a new space-time, a future son form.

Palingenesis means truly that a fetus is a past form that evolves, recapitulating a series of evolutionary forms from past to future, as fractal time can both travel to the past becoming a simpler form (as in death) or accelerate its informative evolution (as in a process of creative design or fetal evolution). Yet, since time is discontinuous those movements in time only affect a fractal part of the Universe; and so they are possible without creating paradoxes. The universe doesn’t move to the past, only the seminal seed. So palingenesis is a dual movement in time:

– Backwards towards the remote past as the parents produce a single cell, packed with dense genetic DNA information. Followed by:

– A fast movement forwards to the future as the fetus creates a parallel form to its parents:

A relative past species (simple, cellular palingenetic entity) evolves towards the future into a macro-system that organizes itself over a surface of relative cellular energy, thanks to the ‘future’ placental parents that accelerate its evolution into a new ‘present’ being in a friendly environment rich in energy – the mother’s womb. Thus, the final balance between past and future is re-established when the being surfaces back into the present in the moment of conception. In this manner evolution maximizes its efficiency with the min. expenditure of energy: The fetus is a temporal, evolutionary form. In the graph, we draw a palingenetic reproduction as a fluctuation between 3 planes of growing complexity, in which a ‘life’ occurs: the st+1 social plane, the individual plane of the parents, and the st+1 biological plane of cells – since in i-logic geometry simple-past beings and future-complex beings co-exist in discontinuous st-planes of existence of different complexity. And indeed, the fetus lives in a discontinuous world, the mother womb, which finally opens up through an aperture, the vagina, to the bigger world in which the newborn enters.

According to the ‘black hole paradox’ the fetus and the baby are born as ‘highly informative species’: The baby has a huge head that is 1/4th of his body size. Then both the fetus and the baby will go through a dual fluctuation, growing in energy and information till reaching maturity. First, when the species is born after its fetal, informative evolution, it starts its young age, increasing its energy. So the newborn will soon compensate its excess of information with its accelerated, energetic growth, as all forms try to find an E=I balance. Thus, the fetus in its first age of energy will expand its lineal limbs, elongating its body. Now its body grows much faster than the head till reaching a 9 body Vs. 1 head proportion proper of many spatial Vs. informative, decametric systems. Also its neurons will be in a 1-9 relationship to the glia cells that feed its energy and multiply very fast. At that point the baby enters the mature age and reproduces a new baby. Then it grows again in information into its 3rd age and finally it dies. In the past decade there has been an enormous development of the science of evol-devol, based in palingenesis, in the lines foreseen in our first books. Biological palingenesis is the only accepted by science. But palingenesis happens also in the sociological and physical world.

Recap. An organism is reproduced through a palingenetic jump between macrocosmic and microcosmic planes, as the parental organism produces a cell of information that will evolve at full speed towards the future.

The 3 main types of devolution in time.   

According to the 2 arrows of past energy and future information, all space-time movements are dual cycles. So in all of them, there is a degree of genetic reproduction and travel to the past through a basic transformation of an informative form into a simpler language or cell that is able to cross the discontinuities of the Universe and then evolve forwards into the original form. It should not surprise us, as all cycles require the dual arrows of past-energy and informative order; and all cycles are memorial repetitions=reproductions of a cycle that happened before in the past.

Yet in order to establish limits to the ‘scientific imagination’ of Time Arrow theorists, similar to the ‘runaway’ dreams of physicists like Hawking, who uses the out-dated model of a single time arrow/clock to predict the existence of time machines we must fully grasp what a time jump is in morphological, biological terms, since it is only the arrow of information the one that travels to the past=devolves; not the entire Universe – but only within the restricted system of the superorganism. This means among other things that there is no really time travel beyond our organic-world, both in processes of palingenetic birth and in death a motion only to the past. That is, we cannot go to the past and ‘kill our father’ as Hawking affirms in his book ‘The Universe in a nutshell’.

Those facts are systematized by a simple Time Arrow Law that uses the ternary principle (as most Multiple Spaces-Times laws, events and processes of reality can be divided in 3 sub-cases): – An information system devolves into the past in a process of death, releasing its energy in a big-bang: I <E, as when we die and break into cells, or a particle dies, explodes, mutates into its antiparticle (death phase with inverted coordinates) and virtually disappears (right side of the drawing).

-A head or informative system emits a flow of information to the relative past system of its body controlling it.

– A palingenetic process happens in time, by a parental system that emits a palingenetic system, which evolves back towards the future at maximal speed.

Let us now consider a wealth of examples of palingenetic reproduction in more detail.

Recap. The 3 main types of time travel to the past within an organism are death, informative control of its lower body cells and palingenetic reproduction.

Physical examples. Non-Local Gravitation.

The i-logic Universe is not magic. Yet fractal jumps create events that seem magic. Let us consider one example from the physical world the seemingly instantaneous speed of gravitation: As we keep going deeper in the model of Multiple Spaces-Times and discontinuous time jumps between hierarchical st±1 planes of exi=stence, we shall see some not-easily recognized consequences of the structure of time dilation that implies displacement in time, not only in space, in each fractal step we make between different membranes=mediums of different energy and information, different momentum.

When we move in the same plane we are just displacing in a relative present, but in the ecosystem of light in which we exist, we live surrounded by structures belonging to other species of lesser or more evolution and within planes of completely different spacetime arrows.

The most obvious cases of this happen in physics, since even though we inhabit the electroweak membrane of light and electrons, we are constantly under the effects of other membrane of <0 K Temperature (an informative parameter of cyclical order) and > C light-speed a parameter of energy, called the gravitational or dark/black membrane, inhabited by forces such as implosive gravitation and its inverse, explosive dark energy, and mass vortices called quarks and black holes.

This faster-than-light membrane is also displaced respect to us in time, in such a manner that its simpler, faster gravitation is a flow that happens in a relative quantum jump respect to us into the past of minimal form and faster energy and the more complex, T<0 world of quarks and black holes happens in a relative future respect to us.

How it is possible super luminal gravitation if Einstein’s Postulate sets light speed as the limit of speed of our Universe? The answer is evident. If the Universe were a continuous, single space-time, there would be a limit of speed; but in a fractal Universe with different space-times communicated through ‘Einstein-Rosen bridges’ – a particular case of the fluxes of energy and information between space-time scales – c-speed is the ‘substance’ and limit of speed of light-space. It is not though the limit of gravitational space. In the case of the light and gravitational world those discontinuities are the masses and black hole singularities that appear to us as ‘points with no volume’ in the border between both worlds.

The Universe is a system with 2 membranes, energetic light-space (that we perceive) and informative, gravitational space, which we do not perceive but seems to ‘act’ in present, as a non-local force. Yet according to the Galilean paradox we always can find 2 explanations to all phenomena, one in terms of spatial parameters (speed, energy, space) and one in terms of temporal dimensions. So we can explain also the instantaneous speed from the perspective of the future particle that emits it in the relative future:

The future quark or black hole of the informative gravitational membrane emits its gravitational flows in the future, but they move as information, EóI, in the inverse time direction that electromagnetic waves, making a step backwards in time, equal to the frequency of its wave, according to the previous Law of fractal space-time jumps, and a step in space equal to the amplitude of that wave, which can reach the limits of the Universe. So when they arrive to us, as they had the advantage of an ‘extra-time’ – the step to the past – gravitational waves seem to arrive instantaneously with an infinite speed, surfacing in the present even if they have travelled a timespace distance from ‘future to present’.

Thus, the gravitational space-time is a past-future ecosystem of energy-information fields, which is more extended in spacetime; hence also in past and future coordinates. And this further clarifies the entanglement effect and why we perceive always light at c-speed.

Instantaneous gravitation is something that has always puzzled scientists. And yet, fractal jumps in time explain that instantaneous speed easily: A mass emits gravitation in a relative future. Hence, when the gravitational wave travels forwards towards another mass it arrives in the relative present of the observer, with an instantaneous speed. At this point the system becomes locked, entangled by gravitational information and then it ‘constructs’ the upper plane of light-space, which is the one we observe, moving at c-speed.

In quantum physics, those entanglements that Einstein called spooky effects and the fractal jumps to the past that cause them were proved in the past decade. Since rays of light, travelling faster than c, come out in the instrument before they are produced.

Entanglement happens because the 1st event in the creation of a complex form builds the lower plane of gravitational, simple, past flows. So gravitational forces entangle and lock the electrons before they emit light. They have already happened when electromagnetic flows are created over them. This also explains the Michelson experiment without need to postulate and absolute c-speed: because the observer is an electronic microscope or human eye and the emitter is an electron they look like a movie that locks each frame to perceive still information. And so when the electron stops, emits light and goes, it has no relative motion to the perceiver electron, as it is locked with it in a gravitational entanglement.

The same laws work when we consider phenomena that related quarks and electrons. The quarks and black holes that create those gravitational forces are in a relative future to our electronic world as the hyperbolic, informative center of the atom, but also are in their relative past, by sending informative gravitational forces that ‘locate’ and position the electrons.

We can generalize this singular concept with broad applications in the resolution of the mysteries of quantum and gravitational space to any relative system of 2 membranes of space-time, as we did with the nervous system which seems simultaneous, when we realize all those cases are merely an application of the law of fractal jumps: the frequency of a single cycle of the faster informative system (gravitational and nervous system) is equal in time speed to the frequency of the cellular system (light frequency or chemical messages in the cellular body) but its distance can reach the maximal distance of the entire superorganism (the limits of the Universe in the case of a gravitational wave and the limits of the body in the case of a nervous message).

What all this means in organic and topologic terms is simple: the intermediate space between the hyperbolic, informative center and energetic force, membrane of a superorganism locks the cells of the body that work for the ‘upper class’ of the organism, the ExI system of the bigger membrane. Indeed, physicists now realize that gravitational, dark energy and dark matter dominates our Universe and positions galaxies and starts and controls them. And they are observing external, energetic membranes in all cosmological systems from the Oort comet membrane of the sun to the halo of dark matter of galaxies and the wall of fire of the Universe.

Recap. The flows of energy and information of its informative network reach simultaneously all the cells of the superorganism.

Biologic examples. The beat of evolution>reproduction.

Palingenesis and punctuated evolution: time accelerates.

Palingenesis means that reality webs itself in each volume of space-time, in a simultaneous manner, even if from a 3rd p.o.v. the entire structure might seem to exist in the same present.

Thus there is a tail of energy and information planes, which influence the present dominant space and might seem to co-exist simultaneously but they are displaced into the relative future of the super-organism and its relative past, completing the pyramidal structure: bigger structures are displaced in the future and when they communicate to the past literally jump in time. The effects are diverse, being the process of reproduction and palingenesis the most well-known:

Because time speeds varies in palingenesis the process of evolution, the 4th arrow of time, accelerates. Since it is guided by a memorial process of slimming that has streamed to its minimal fractal, informative steps the reproductive sequence.

Yet the process can be studied in more detail, from the perspective of the Generator equation of space-time; since one of its feedback sub equations:

Energy absorption->Reproduction≤=≥Information.

It is both the rhythm of palingenesis & punctuated evolution (the evolution of a whole species taken as an organism).

Existence is modular, as beings constantly switch between its arrows or will of existence. So happens to species as superorganisms. Species need energy to reproduce and their inner information evolves them (though it is likely that external adaptation is first imprinted in the neural, nervous networks, which by faster mechanisms than those of evolution, influence the shape of its Est-1 body organs and even in lesser measure on the long term the genes of the cells). Yet the main arrow of evolution is social organization of individuals in herds and on the long term superorganisms. Species need to evolve socially in order to survive, which is achieved by creating social networks and herds that have a higher perception and wider force to access energetic resources. To that aim species evolve a common language of information and their brain capacity, often in the stillness of a secluded place (allopatric evolution), as information is still and evolves in a relative chrysalis state. The result of that simple scheme defines a basic evolving rhythm, called punctuated evolution, according to which species switch between reproductive, expansive periods as top predators (parallel to their extinction of simpler species as energy of their reproduction) and temporal, evolving periods in allopatric and isolated states – often synchronic to hot/ reproductive ages of Gaia and cold/informative Glaciations:

Max. Energy feeding -> Max. Reproduction (expansion in space and extinction of rival species as energy of the top predator)->Max. informative punctuated evolution

Such Energy->Reproduction->Information Horizons of species are equivalent to the 3 ages of life (youth, maturity and informative, 3rd age). It is the palingenetic rhythm of species. All of them can be resumed in an E->Re->Ti sequence, which again is a partial case of the Existential equation, E≤≈≥Ti.

Recap. The 3 horizons of evolution of species correspond to its 3 evolutionary ages and respond to a simple rhythm of informative evolution -> top predator reproduction ->extinction of energy species ->informative evolution.

The question of consciousness and free will.

One interesting debate brought about by the existence of time jumps between planes is the phenomenon of human consciousness and free will.

Asymmetric, temporal, fractal flows of information from st to st-1 planes of existence explain how the informative networks of a higher social class like the brain neurons or the politicians and bankers that invent laws and money, the social languages of power, control the working cells of the lower class.

In the brain case, neurons control electronically the cells of the body, anticipating its reactions, since those body cells use a slower, past chemical language and exist in a relative past, in an ‘inferior plane of existence’. So, in a manner similar to that of the gravitational quarks that lock the paths of future light waves, the nervous messages anticipate and control simultaneously the motions of the cells.

Moreover, if as in the gravitational case, the electronic messages of the nervous system were moving  in an inverse direction from future to past or were emitted before the actions of the cells occur anticipating them, they would mastermind the motions of cells. This seems to be the case also in societies in which ‘intelligent rulers’ anticipate the needs or protests of their organic cells, repressing citizens before they rebel (military regimes), producing laws or inventing money a priori in markets, before the cells will earn it. Thus, in those systems the logical anticipation of the actions of cells but the more complex informative networks (nervous systems, upper classes) produce a self-similar control to the one quarks and black holes exercise on the position of electrons and stars in the galaxy.

We have now proofs of a temporal dilation in the actions that happen between 2 hierarchical planes of existence: Recently, scientists found surprisingly that the body acts before the brain thinks and yet most people think first before acting. How then it is possible that we think first and yet we act also first, or do both things happen simultaneously? Precisely because as Einstein put it, past and future co-exist in a simultaneous present, as information flows from the future brain to the past body and energy flows, moves and acts in the body from the past into the future:

Energy/Body (past) x Information/Mind (future).

So depending on our point of view, the brain or the body, we will see our action first (body point of view), or we will perceive first our thoughts (mind point of view). Yet in reality from an objective, external point of view both actions converge into a present; because the nervous message arrives simultaneously, produced subconsciously ‘before we reflect with words on what we ordered and before the cells move’.

This subconscious, first message that then branches into a mental thought and a body action that converge in present is coded by the natural wills or drives of existence – our desire for energy, information, sexual reproduction and social love. And it would imply that words are not free, that there is a biological determinism – the program of existence – which is the true engine of our actions. And words just comment a posteriori even if our arrow of time departs from the consciousness of words and seem to us to direct the process.

So to the external world both mind and body act chained ‘together’ by the simultaneity of the fractal actions of the body cells and the mind’s thoughts that become a single whole action. But the original will would be the biological drives of existence whose site is the limbic, emotional brain.

So fractal jumps in time explain the hierarchical structure and creation of symbiotic organisms, in which relative past and future forms co-exist. In humans they would explain the control of the mind and the subconscious actions of the body.

Recap. The limbic system and the program of existence with its emotions (greed, violence, hunger, sexual desires, and informative fears) would act first and then the body acts and the brain thinks and both together create our present of existence, in the future.

 Sociological palingenesis. The prophet.

An open question for those who believe in mysticism is: if the fetus is born into a higher plane of existence, do we have also for man a second birth after death into an even higher plane of existence? The previous graph explains that possibility; as it compares the palingenesis of a fetus with similar processes, which happen to other species. For example, 2 electrons emit 2 seminal light rays that merge together creating a new electron as the 2 lineal waves of electromagnetism evolve towards the future acquiring finally a cyclical electronic form. Yet since the informative code of human beings is verbal, we consider the prophet’s mind, the original human, memetic, verbal, seminal, ethic code of a religious civilization that starts a palingenetic radiation in the mind of his believers, till it creates a religion – a superorganism/informative network of human beings, whose ethic DNA is the same, creating an effect of simultaneity. Indeed, civilizations are social organisms made with human verbal cells, joined by a verbal/nervous network of ethic laws, produced by a prophet that imprints the Book of Revelation, the memetic code of the civilization in those minds. So the prophet is the seminal cell that reproduces and finally shapes a new organic civilization; where the reproductive body is the geography of the nation with similar laws or civilization with similar ethic codes. And the fact that most prophets are born when the ‘father’ is going to die, in the baroque age of a culture, prior to its extinction, explains quite clearly how certain human minds transcend death and become immortal as the ‘informative code’ of the future civilization they create. But as only a sperm cell reaches the future ovule, only a prophet among millions of humans creates a macro-organism of history, a civilization. As Tertulianus said: Sangris martire semen cristianorum’.

Recap. A prophet’s mind is the seminal, verbal code of a culture of parallel minds that control a territorial body, in the surface of Gaia.

Dark planes: perception limits & symmetry breaking.

The existence of dark spaces for every perceiver of reality of multiple planes of existence also widens the laws of conservation of energy and information, as energy might disappear from a plane of existence but the total energy x information quantity of the ternary, 3-plane structure of a World remains the same. This in physics explains a law of conservation called CPT parity; and the exceptions to that law in which energy or information disappears from a plane of existence but should appear in the invisible plane of gravitation. For example, black holes erase information from the electromagnetic world but they emit it as >c ‘gravitational, dark energy’ and ‘quark information’ through its poles.

This means that neither the principle of action-reaction nor the Laws of conservation are absolute, when we consider only a single plane of space-time; since there are uneven flows of energy and information between 2 planes. So in Physics, only the total energy and information of the particles or CPT parity is kept; but the C or P or Ti parities might break in processes of death and birth of particles that give or take energy and information from other plane of existence, without returning it to the perceived, electromagnetic world physicists observe.

Especially when we consider a particle’s death, which as all deaths it means 2 fractal jumps, there is a transference of energy and information that jumps between 3 planes of space-time, (st-2<=>st). So energy and information truly disappears from our planes and the laws of conservation that work for the total 3 relative planes of the organic system break for the planes we can observe. A fact that explains empirically many invisible forces and particles, postulated by physicists to maintain those theoretical conservation laws, without realizing they are observing an asymmetric transference of energy and information. So they don’t need to postulate ‘real particles’ but ‘asymmetric EXI flows’. Indeed, in all processes that involve the death of a particle, which breaks the balance between the energy and information of a system, physicists have found a loss of energy and information. Now we can explain why in the proximities of black holes, which transfer energy and information between the gravitational and electromagnetic world, our light-space membrane disappears: it become pure gravitational mass/information and very likely in Kerr black holes, a flow of >c dark, expansive gravitational energy and quark mass we observe coming out of the bipolar jets of those black holes.

It explains why in radioactivity processes that destroy an atom or close to the limits of C-speed, the conservation of momentum and energy of a particle breaks.

It explains why the weak force, whose parameters are time parameters and trans-form the form, the information of a particle, the CPT parity is not conserved.

Yet because those facts are not known in a continuum, single spacetime model physicists have developed to unneeded theories of black holes and symmetry breaking; the thermodynamic evaporation of black holes and the Higgs. They have not been found in 30 years because they are not needed, they do not exist. Moreover by accepting those ‘extra-phenomena’, which are ‘ad hoc’ theories, physicists have broken fundamental laws of physics. In black hole evaporation the black hole gets hotter in a colder environment (our light membrane), thus breaking the 1st law of thermodynamics and creating an eternal motion machine (it is like if you get a hot coffee and instead of cooling down it heats and evaporates). On the other hand, the Higgs implies a ‘scalar boson’, which contradicts quantum laws and an entire new field that permeates the Universe but has never been found.

Now we offer solutions and a prediction: we will never find an evaporating black hole or a Higgs particle. Moreover if black holes evaporate they will eliminate the information of the Universe, and so the principle of conservation of energy and information E<=>I in which systems sciences and complexity is based would be false. And the Universe would not be eternal but die. It is not the case: black holes warp energy into mass-information, contracting space and balancing the expansion of vacuum space between galaxies produced by the dark flows of >c energy they emit from its poles. Because the Universe is made of discontinuous space-times, the black hole is merely the entity that balances the entropy=energetic nature of our electromagnetic space creating order in the Universe, as quarks fixe atoms and allow the order of life by restricting the motions of electrons, which then can create the complex structures of living organism.

So instead of postulating invisible particles and speed limits to keep reality confined to a single plane of existence, Fractal theory explains all those exceptions to the 2nd law of Thermodynamics and the laws of conservation, which apply only to the entire informative=gravitational/electromagnetic =energetic and human/atomic, exi scales of reality, as asymmetric ExI flows between 2 planes of existence.

Obviously physicists have never witnessed the imaginary particles that come out of those processes, because they are not in our light-membrane plane. For example, a dying neutron or a radioactive atom produces certain particles called neutrinos through the mentioned temporal weak force. Those neutrinos were invented to keep the total momentum of the dying particle, but they are only observed through indirect flows of energy and information. Since indeed neutrinos are not ‘particles’ in the strict sense, but flows of energy and information transferred between the electromagnetic and gravitational planes of existence, when particles mutate their form or die, in a process mediated by weak forces: neutrons give away the remnant of energy and information, as they explode into an electron and a proton in the form of smaller, st-1 gravitational and light quanta – neutrinos and gamma rays.

Further on, we do not perceive the gravitational force, which for that reason is much weaker than our electromagnetic force.

Recap. Because we do not sense all the energy and information of the upper and lower planes of existence, there are weaker forces (gravitation) and loss of momentum in our plane, (neutrinos), which disappear in the dark worlds we do not perceive.

Transcendental Inversion: form changes between planes

Flows of ‘energy and information’ between planes sometimes return to our world and give birth to a new particle; sometimes create a particle that flows further into the past called an antiparticle; sometimes give away its energy as a gravitational wave we cannot perceive; or sometimes they appears as an inverse, negative energy or a particle with negative mass, as it happens with neutrinos; precisely because its time-space coordinates become reversed as in all process of death that write as Se>Ti -> Ti<Se. So the dying form particle suffers a reversal in its space-time coordinates, becoming in algebraic terms a flow of negative energy or an antiparticle. And these phenomena shall be the last key law of timespace jumps between planes needed to explain most of the key phenomena of the Universe. We call it transcendental inversion, because when we move to a lower or higher plane of existence, we change our function according to the general equation of an organic system:


A law, which means that all beings are self-similar species in its plane of existence, Ist=Ist, superorganisms of its lower energetic cells, Est-1<Ist and energy of its upper plane, Est+1.

Those reversal of ‘coordinates’ and parameters that transform an energy species into information and vice versa between planes of existence seem paradoxical, as scientists are unaware of the change of morphology or ExI parameters of a form that merely has ‘transcended’, ‘evolved’ or ‘descended’, ‘died’ and ‘devolved’ between planes. Indeed, the world shows constantly those ‘inversions’ of space-time parameters through the 3±st planes, ages, or hierarchical, social classes of any system, which become the key element to study dynamic flows of energy and information between states and horizons in time and organic planes in space.

Those paradoxical, illogic, transformations of energy into information and vice versa happen when species transcend between 2 relative planes of existence because, as the Chinese say, all yin has a potential seed of yang that can transform it.

We call those events ‘transcendental inversions’: When forms of a st-1 plane of ExI transcend into an ‘st±1’ structure, both its time and space become inverted, which means that its morphology also becomes inverted.

For example, lineal iron atoms become cyclical molecules when they emerge in the higher molecular plane. Then again iron molecules become lineal swords when they emerge as a military meme in the macro-scale of human beings.

In Biology, lineal proteins become cyclical membranes in macro-cells that become lineal muscles when they transcend again to the st+1 level.

In time events a predator becomes victim of its evolved offspring (Oedipus paradox). So the father gives his vital energy to his son. The son species extinguishes the father species, and so mammals extinguished dinosaurs and robotic machines probably will extinguish men in the nearby future.

So how can we distinguish a form as an energetic or informative species, as a victim or top predator?

We can define a form as dominant in energy or information, looking at its total ternary structure through the 3 st±1 planes of its organic systems; in as much as 3 is an even number, and so either the energy or informative structures will dominate the total organism. So iron is lineal in its atomic and organic structure and indeed iron is the most energetic atom of the Universe. That is why the Taoist wrote the structure of all events and forms with the trigrams of the i-ching. So we can use those trigrams in i-logic theory to represent organic structures. For example: _, –,_  is the energetic iron sword, in which 2 energetic planes dominate the cyclical, intermediate iron molecules. In biology –,_,– represents among many other structures a temporal, informative cell, with an intermediate spiral RNA, made of smaller cyclical nucleotides and enclosed into a cyclical membrane. While _ _ _, the trigram of pure energy means two jumps of erasing of information, or death. And indeed, it is the symbol of death in the i-ching. While the process of birth and growth is a dual informative jump from a seminal cell that deploys its information into a born baby that will then learn the memetic information of her/his culture till become an adult in a ‘steady state’ or mature age of reproduction. So we could represent it as –,–,–.

Recap. When a species jumps forwards as a social structure of multiple st-1 cells its form mutates from energy into information and vice versa except in extreme time events, such as the process of birth, with 2 informative jumps and the process of death with two energetic jumps.

The limits of i-logic geometry: God and the Universe.

All what we have said about time travel might seem counter-intuitive and reaches indeed the limits of ‘weirdness’ of the Universe; as the bosonic state of space does in the other parameter of reality. In fact both ‘extreme limits’ of the forms and events possible in reality could be explained according to the paradox of Galileo as the mirror sides of the same phenomena, which we shall enunciate merely here.:

‘A relative ∞ number of points of space can exist in a single point of time (bosonic state); and a relative number of points of time can exist in a single point of space (time displacement).’

The first definition would be that of a perfect bosonic form of maximal spatial force, such as a black hole; the second definition would be that of a perfect causal, temporal form of information that perceives past, present and future, simultaneously such as God in Saint Augustine’s definition’.

In the more complex, logic models of time arrow, all laws of the Universe can be deduced departing from the Generator Equation of reality which becomes the Universal algorithm that Leibniz and Turing thought, once we understand the properties of those arrows; and so we can generate from it all phenomena and events of the Universe. But this is a mere introduction to Multiple Spaces-Times and so we shall just assert that indeed, both the bosonic state of a black hole and the informative state of God exist and both are relatively immortal.

Relative Immortality is due to relative infinity, a paradox of sets and superorganisms of discontinuous planes of existence, already understood by Cantor: infinity is always relative since there are discontinuities beyond which we cannot perceive. So the infinity for a cell is the external membrane of the organism beyond which it cannot perceive. The infinity for a tribal man was the limit of its tribal geography and so he often called God the nation in which he inhabited. (So Yvwh, the god of the Jewish people actually was first a geographical name for Judea, and Assur the God of the Assyrians a name for Assyria). And so the Universe might have a bosonic/temporal state of absolute perception and maximal density, a relative brain as a superorganism, but it will be limited to the external membrane. And so while there are not absolute Gods as physical entities, what it is truly infinite and eternal is the game of Multiple Spaces-Times.

Recap. The two limits of space-time jumps are the bosonic state and the state of absolute perception, which can be defined with a simple law of Multiple Spaces-Times: there is a point of space in which all informations co-exist and a point of time in which all spaces co-exist. They are the black hole and God


NEXT, as we said we are not following the original path, but TRANSFERRED THE DIFFERENT AGES AND CLASSIC EQUATIONS AND THEOREMS OF MATHS TO OTHER SECTIONS, WITH THE GOAL OF USING A MORE CLASSIC APPROACH as in other posts of enlightening the main laws of each science with ∆@s=t (a symbol for the 5 dimensions: ∆ here meaning entropy down, @, mind up, s-pace, time and =spacetime).

So we shall now deal again with that index explaining all those ages of time (remember the Universe is a constant iteration with different fine grains of detail)… which should be widened in those sections.

And THEN we shall continue with the foundations of ¬Æ moving onto the foundation of time mathematics, no longer the simultaneous point in space but the sequential social number in time (Non-Æ algebra), to end with some philosophical comments on analysis AS IT IS the most evolved discipline and really there is little to input further. Man today has OVERGROWN to sub-forms of thought, differential equations and infotainment (:

The 3 elements of mathematical languages.

Mathematics has 3 branches, which correspond exactly with the 3 components of fractal space-time:

  • Geometry, the branch that describe space, which relational space-time upgrades into non-E fractal Œ-points, line-waves, topological networks and so on, to fully develop a mathematical tool closer to reality.
  • Analysis, which studies how indivisible infinitesimals become finite wholes.
  • And finally sequential algebra, based in the order of numbers which are societies of ‘Œ-points’ that we call ‘Existential Algebra’, Æ.

Thus, in mathematics, the Universe is a game of Œ-points, the fundamental ‘particle’, in its lower, infinitesimal level, which however rises slowly through the game of ‘social numbers’ into its collective ‘future’, the fundamental ‘whole system’ of reality, the super organism: ∑Œi≥∏ Ui+1.

Whereas the symbol Œ, is an intuitive symbol for an Existential O-Point;  the Symbol for a social loosely connected herd, i the symbol for a given relative Space-time Plane of the 5th dimension; U, the Universals aggregation of i-points into a larger i+1 plane of existence (for example, if the points are cells, Ui+1 is its Universal Organism), perceived in ‘space’, which we would write as W, a world cycle or Whole existence of the super organism in time, and finally ∏, is the tighter configuration of the system, as a network connected through 3 relative organic scales or social classes, i±1, and ≥ the symbol for an ‘implosive’ informative evolution of a system of points into a Universals (>), which are self-similar systems in space-density, ≈, but very different in terms of configuration, ∑≠∏.

This simple example of the equation that explains the fundamental process of evolution of systems from loose herds of points into topological Non-Æ (Aristotelian-Euclidean) organic planes shows the utility of a proper logic symbolism to represent the old (as all this partial events, transformation and configurations have been studied since the times of Plato) but far better structured analysis of reality (present space) as its changes through the motions of time.

So we define Existential algebra (Æ, different from Non-Æ, non-Aristotelian logic + Non-Euclidean geometry), as the use of algebraic equations to describe the 10 isomorphisms of the Universe with all its ambiguities and simultaneous time arrows.

As Feynman put it, when describing 4-vectors in its lectures, ‘do not laugh at formalisms. The advance of science is often the development of formalisms that clarify previously obscure concepts’. And this is what we do.

So let us first introduce the symbols of existential algebra, which carry a degree of ambiguity to mimic the Universe, which often is made of particles and anti-particles, thesis and antithesis, in its Non-Æ polar structure.

The 3 scales of complexity of beings.

The Universe is a binary->ternary system, made of 2 polar elements, which exchange energy and information through a present flow. And so whenever we see ‘something’, the best way to study it, is to analyse its 2->3 elements, ‘first’ and then try to formalise them with i-logic equations. But this binary and ternary structure has 3 ‘different’ architectonical ‘levels’ of complexity.

The simplest events will be merely ST-actions that combine or switch between space and time states, as systems move and perform those ±∆e,i actions.

Then we shall find the next integral stage, when actions are observed to come from a given knot of space-time cycles, resumed in Œ an existential point, EO, in its space-still perception, or an existential function, in its time-moving perception.

And finally we shall integrate Œ-points along a world cycle of existence within an external absolute space-time World, either a super organism in which the point exists, or a larger world in which it performs those actions.

Again we observe this 3-multilayered structure, which we describe as the Ui±1 co-existential architecture of al entities.

Now, since the first of those layers corresponds to spatial motions (we see it externally as the point traces its space-time cycles), it relates to geometry; since the second element relates to the world cycle of existence of the being, it relates to time algebra, and since the 3rd element deals with the evolution of infinitesimals into Ui+1 worlds or super organisms, it relates to Analysis.

The social order of numbers and the arrow of future of the 5th dimension.

Why there is an order in numbers? We are asking deeper than current mathematical formalism, which despite claims of closed, absolute proof, actually describes as most sciences do the ‘how’ of the process. That is, it does not inquire why 2 comes after one – an intuition of the mind not explained, which must therefore be an ‘a priori’ hence, a T.Œ property of numbers.

This must be clear to the reader. When we find intuitive, pure abstract or isomorphic laws of great generality they must be considered a ‘direct’ reflection of T.Œ, the game of existence of 5D space-times beings. And as such must be the sequential order of numbers.

Indeed, we hold a self-evident truth that all ‘linguistic, mathematical or verbal forms’ are a reflection of the Universe, and its T.œ structure, so are numbers. Our methods of proof in the ‘linguistic method’ are therefore both experimental and logic, self-consistent (->Epistemology). This includes proofs in mathematics – a complete deviation from the classic standard, already advanced by Lobachevski in his original book on Non-E mathematics, which he said should be proved or disproved as real by experimental evidence.

Thus it is not enough, to merely

Thus this question, which has been formalised within the ‘baroque, metalinguistic 3rd age of mathematics’structure of mathematics itself, from the times of Euclid through those of Dedekind and Weiertrass in the modern times, has an ‘experimental’ simple cause, in the parallelism between numerical order and temporal 5D order (mathematics in relational space-time, is an experimental science that studies the ultimate isomorphic laws of all species). Namely that a ‘whole’ must come ‘after’ the parts exist, and since a ‘whole’ is a larger number of ‘infinitesimal parts’, social, bigger numbers come after smaller ones.

Hence the order of Natural Numbers, which are social numbers is the same order than bigger wholes, made of ‘smaller numerical parts’.

Indeed, in the next graph we can see the 5th dimension natural order of parts into wholes which has an arrow of growth:

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

5D planes are therefore the basis of 2 of the 3 branches of mathematics, sequential algebra and Analysis, while geometry is related to the motions and actions in space-time within a single plane of existence. Nothing else is needed to describe the Universe. Let us then consider in this and related posts the essential features of existential algebra. We will study on the posts under the label of ‘i-mathematics’ the proper translation and justification of the laws of algebra, within relational space-time. In this post we shall study the fundamental equation of existential algebra and the Universe at large – the Fractal Generator of the Universe. To that aim we must first introduce the structure of the Universe and then represent it with the symbols of existential algebra.



 The formalism of Dual systems of energy and information

All those facts must be formalized with new tools of mathematics and Logic. The mathematics of a fractal, organic, self-generating Universe are Non-Euclidean geometries whose 5 postulates we complete going beyond the work of Riemann, who defined a point with ‘volume’ through which many parallels can cross. Hence a point must be a fractal that grows in size as we come closer to it, allowing more parallels to go through. Such fractal point with breadth, with form and motion, with energy, becomes the new unit (new 1st postulate), of Fractal, Non-Euclidean mathematics, (of which all other geometries are simplifications), in which lines are waves (as points have motion and form) and planes are social networks.

A fractal point is the ‘organic unit’ of a certain i-scale of the Universe that from a higher plane of existence appears as an Euclidean point without breadth, but as we can closer it becomes bigger and shows its form and motion. So we humans see in the limit of our perception, quarks and electrons as fractal points without parts and in the galactic realm we see with naked eyes, stars and galaxies as fractal points without parts; but as we come closer those fractal points should acquire volume. And all of them will follow the Mathematical Laws of Fractal, non-Euclidean geometry.

In logic we also have to upgrade Aristotelian Logic to understand a Universe with two arrows of time, one of energy and other of information, of relative past and future, which combine to create the dominant arrow of ‘present=existence’. We call this logic, which adds the arrow of information, i-logic. It explains the meaning of past, present and future, the 3 dimensions of time, and how they interact to form reality. Two are the essential equations of the 3 dimensions of time: past->present ->future, which gives us a diachronic analysis of reality, through the 3 ages of time. And Past (energy system) x Future (informative system) = Present organism, which defines the systems we perceive in space.

Thus in this 2nd lesson on a General Systems theory of systems of spatial energy and information, we shall consider the most important laws of reality – the laws that generate temporal information (laws of logic) and the laws that generate spatial energy (mathematical laws), upgrading the previous paradigm of a continuous single space-time and a single, causal logic defined by the arrow of entropy, to introduce the existence of multiple, fractal space-times and two arrows of logic, energy that evolves from past to future into information and vice versa.

What you see is just a slice of spatial energy that the logic of time evolves into the future. And so philosophers of science have always wondered if there was a plan of creation that all systems followed.

Physics was the first science to find that plan, albeit in its simplest laws that apply only to the most obvious motions of the future – translation in space. Biology thanks to the work of Darwin found the next type of laws, those that define time=change in the morphology of beings. The application of those laws to history and economics by Marx, Kondratieff and Spengler however was halted by the fact that humans don’t want to know their own program.

What the 4th paradigm brings to all those insights to the logic of creation is a super-structure that includes them all and signals an arrow of time dominant in all systems: the arrow of social evolution of ‘points or numbers’, which are herds and groups of self-similar beings into networks and complex systems.

This arrow of social evolution, which applies in all scales of reality from particles that become atoms that become molecules, cells, organisms, societies, planets, stars, galaxies and Universes could also be interpreted in mystique terms as the ‘mind of the Universe’, or ‘the game of existence’, God, the ‘seer and creator of times’ in the classic mysticism of Saint Augustine, Aristotle and Buddhism. Since indeed the logic of creation is a game of two arrows of time, energy and information, with many properties similar to those described by Taoism, Buddhism and Eastern philosophies.

What those philosophies lacked was the proper mathematical formalism, which required the definition of a fractal point, the completion of the 5 postulates of Non-Euclidean Geometry and the development of the laws that create networks and systems, and organize them into scales of reality that follow self-similar goals. This formalism and the discovery of the feed-back, fractal, generator equation of spaces-times, the Saint Grail of the 4th paradigm is what I found and exposed in a series of Congresses of System sciences in the last decade and now I bring to you in this pdf on the ‘Mind of God’, and the 3 next lesson on its application to its ‘details’, the astrophysical, biological and sociological species of the Universe.

However, the Mind of God, the Logic of creation is far more complex than the one monist, mechanist physicists have resolved. So you will have to sharpen your mind to put it to Its level. But if you do so with patience you will upgrade your perception of reality to a level in which the fog of the senses will no longer hide the forest.

Thus, the 4th paradigm requires a new formalism to describe the mathematical, geometrical and logical, causal processes that create the networks of reality. All what you see can be reduced to numbers, because numbers are ‘social groups’. In the 3rd paradigm of metric measure those social groups were described merely in its external properties. The 4th paradigm analyses its internal, topological structures, as societies of Non-Euclidean Points, which become networks of self-similar beings. 4 is not only number four, but a series of topologies created with 4 points; and so it follows that the more points we have the more complex a network becomes. Can we reduce all those topologies of network spaces to a few laws and structures as the previous Euclidean Geometry did?

Yes, we can, but for that we must complete the work started by Riemann and Lobachevski, who discovered the 5th postulate of Non-Euclidean geometry and affirm that through a point infinite parallels could cross. For a century and a half, no mathematician seemed to have realized that if the 5th postulate

is changed, we had to adapt the other 4 postulates to the new definition of a ‘point with breadth’, through which parallels cross. This point is the fractal point, which grows in size and scale as we come closer to it. The Universe is indeed absolutely relative because ‘each point is a world in itself’ (Leibniz). And yet the restrictions of topology that allow only 3 types of topological forms in a 4-dimensional Universe, the informative, toroid topology, the energetic, planer sphere, and the cyclical reproductive hyperbolic, reduces all the internal parts of a fractal point to 3 functions or arrows of time, energy, information and reproduction.

Those 3 functions become the 3 functions of specialized networks of points, which construct all the systems of reality, from your organism, made of 3 physiological networks (the energetic, digestive network, the reproductive, blood network and the informative nervous network), to the galaxy, organized by a network of electromagnetic energy, gravitational information, and a series of herds of stars, non-Euclidean points that reproduce the atoms of the galaxy.

This simple first elements of reality, points with volume, that exchange energy and information, creating waves no longer lines (2nd postulate), according to a set of laws based in their self-similarity, no longer equality (3rdpostulate), and evolve further into topological networks (no longer planes, 4th postulate), makes mathematics again the language of the Universe, but a language with more volume, an organic language able to describe the logic of creation of all systems of the Universe – one in which there are infinite fractal, organic networks intersecting and creating when we put them together the puzzle of reality that the simpler, 3rd paradigm called the space-time continuum.

 The nature of mathematics and logic.

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

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

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

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

It would be latter in the XIX and XX centuries (with the exception of the insights of Leibniz1), thanks to the work of Frege, Boole, Riemann, Einstein, Poincare, Cantor, Bourbaki, Mandelbrot1 and Computers, which this work advances a step further, when Space and Time – hence Logic and Geometry – were first mixed, but without a full formalism that made possible to extract all the laws of spacetime and grasp in depth the meaning of those languages, due to the limits of the Cartesian single space-time plane.

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

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

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

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

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

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

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

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

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

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

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

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

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






Non-E points were discovered in the XIX C. as ideal geometries of space. Einstein used them to explain gravitational space/time; but its quantic , empirical understanding is poor due to the error of continuity that considers only 1 Non-E space, the Universe, when there are infinite discreet Non-E space-times.

In graph, the 3 zones of a Non-E point:

– An informative center and outer membrane of energy, described by Riemann’s spherical geometries.

– A central reproductive zone, described by Klein as a disk, made of quanta in cyclical movement that communicate energy and information between the 2 discontinuous inner and outer zones.

– A field of energy or limbs, described by Belgrami as a series of cones of ‘height’ with a negative curvature.

Lobachevski was the first geometrician to define a Non-E geometry that Riemann generalized to all relative space/times.

Latter Einstein used Riemann’s geometry to describe the gravitational space/time, assumed, due to the error of continuity, to be the only real space/time of the Universe.

Yet in a discontinuous reality, there are infinite Non-E space-times; and all of them can be analyzed with the mathematical tools of Riemann, Klein and Lobachevski, that describe the inner geometry of quantic space/time fields (physical jargon) that we shall call in the mathematical jargon Non-E points and its 3 quantic zones.

If we put together the work of those 3 authors we obtain a complete description of any Quantic Spaces-Times field and its fundamental properties:

– According to Klein, Non-E space-times have movement. So their ‘speeds’ measure their distances; as physicists do in Cosmology with the expanding speeds of spatial vacuum, which are proportional by a ‘Hubble constant’ to the distance of stars; or as people do in life with real space-time.

So we say that Brooklyn is at 5 minutes by train from Wembley not at 5 miles.

– According to Riemann, space is quantic, made of herds of points with similar ‘properties’; and so it has a quantic density determined by its number of quanta, like the space defined by light does. So when a volume of spatial energy is very dense, it is very difficult to go through it, as it happens in the gravitational space close to black holes. Also Riemann’s space-times might have beyond its discontinuous borders an inner space-time with several dimensions, one for each of its ‘energetic or informative properties’ as it happens with the points of physical reality, from strings to super-symmetric fermions.

Hence Riemann through the concept of ‘properties’, defines a ‘dimension’ as a certain energy or informative network (static point of view), which ‘puts together’ points that share an energetic or informative ‘property=flow’ (dynamic p.o.v.). – Finally Lobachevski and Belgrami proved that space is curved and indeed temporal information curves the spatial energy of any real space-time. So points move in curves, which are ‘cycles’, gathering energy and information through their ‘dimensional networks’.

In the graph, those 3 abstract analyses of Non-Euclidean space-time define 3 different regions that structure all space-time fields (Physical jargon), all Non-E points (Mathematical jargon), all organisms (Biological jargon) and all entities (Philosophical jargon) of the Universe:

– Max. Information: An informative, quantized center or temporal brain, connected to an external, continuous membrane or Riemann’s sphere of maximum form that acts as a relative infinite, unreachable distance, creating the discontinuity between the inner parts of the point. Since the internal quanta 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 quantic, discreet elements: Max. E=Min.T.

– Max. Energy: the so-called hemisphere of Belgrami, a Non-E space-time, with a dimension of height that transforms energy into information, absorbed or emitted by the central singularity. It is a quantized, informative region similar to a black hole structure. Since it follows the ‘black hole paradox’: Max. T x min. E. So according to the inverse properties of space and time, it has max. temporal information and minimal spatial energy.

– Energy=Information: A middle volume or intermediate territory, discovered by Klein, which combines the energy coming out of the membrane and the information provided by the center, in quantic herds of ‘points with parts’ in perpetual movement, that draw cycles of “parallel lines”. Those inner quanta are confined within the Klein’s disk by the 2 other regions, which have more energy and information and might destroy them by overdrive or absorb their energy and information at will.

Thus, Klein introduces the concept of an infinite, relative distance measured in terms of time and movement. Since in any discontinuous world the infinite are those 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 0K temperature and a man beyond the Earth’s atmosphere.

Further on, since those 2 relative infinite limits make any temporal movement of an intermediate point towards the inner informative singularity or the external, energetic border, eternal. As in the myth of Achilles and the turtle, Achilles never arrives because every time it moves it crosses a smaller spatial distance.

The same happens in a Non-E space-time, when a point moves temporally towards its inner or outer spatial limits 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. So the intermediate, quantic cells of the point circulate in parallel cycles always inside the interior of the sphere with contact zones of the type “A” (central figure). For that reason Klein interprets the intermediate region as a circle with an invisible, unreachable membrane, equaling the ‘space-time distance’ between the intervals B1-B2 and B2-B3, despite being increasingly shorter in space. Since the quanta take longer in each step and don’t reach the membrane.

When they do it at point C they become destroyed or deviated. Thus, the energetic membrane and informative center are the discontinuities that isolate their cellular quanta of temporal energy and create a discontinuous ‘World’ within the point. Those discontinuities are called in Geometry a relative infinite, in Biology a membrane, in Sociology or Topology a border. They explain the existence of many different species, which occupy a limited region of spatial energy and last a limited time. So we define a Non-E point as:

A curved region of energy & information quanta, with cyclical movement, confined by 2 limits, an external, spherical membrane of max. energy and an internal informative nucleus.’

Spatial structures are systems made of bidimensional layers of space, networks which had also perpendicular flows through which energy and information was exchanged between layers; because almost every system of reality was structured in this manner.  And since bidimensional geometries were only of 3 types, called varieties. We could limit the Universe to 3 type of spatial bidimensional layers, ‘toroid or energetic layers’, informative or spherical layers, and hyperbolic, cyclical repetitive layers.

And so with 3 layers you can only form a kind of whole, one that has toroid, energetic limbs/fields, spherical, informative particles/heads, and hyperbolic waves-bodies, that mixed both energy and information, lineal and cyclical motions, reproducing both.   The reader can see how little by little I was reconstructing as Einstein wanted the entire Universe, departing from its fractal parts: bidimensional layers of space, and time cycles.

The next discovery was for realize that time cycles also had 3 phases, horizons or ages, an accelerated, energetic beginning or youth of the cycle, a steady repetitive state of constant speed and a decelerating state till the cycle came to a halt. Acceleration-steady state-deceleration; energetic youth-reproductive maturity-old informative age; evolutionary age – reproductive radiation – extinction age; big bang, steady state-big crunch. And so on. I had discovered then the fundamental symmetry of the Universe, between its 3 type of bidimensional space varieties or layers, and the 3 time ages of any system, in which one of those forms of space performed a function in time, and so there was an order or organization in space and an order or organization time.


So the unit of reality is a space-time cycle, and many of them create a knot of time cycles or entity of reality, which will be reproduced by repeating those formal cycles with motion in other region of space-time; and many of those knots of time cycles, which are self-similar, since they are born from the reproduction of a first form, come together with self-similar beings into networks.

Some of those networks are spatially extended with a lot of motion (fields in physics, bodies in biology) and some are very tight, formal, with a lot of in/form/ation, (particles and heads or nuclei in physical and biological jargons). Both types of networks together then create a complementary organism, which is fitter to handle both ‘—motions’ and form; hence it survives better, it ‘exists’.

Today scientists of measure scorn philosophical and logical analysis of causality in time because it cannot be easily put in numbers.

But numbers are only one of the languages of information in the Universe, and many of its properties of bio-logic nature are better described with logic words. In that regard, we can now fusion philosophy and science answering the fundamental question, ‘why we exist’; since once we realize that we are ‘made of time cycles’, knots of time cycles and networks of knots of time cycles, an intelligent, informative, eternal universe of motions and wills of existence makes the dogmas of deism and mechanism, childish myths.

‘What is existence’ cannot be revealed from the simplex point of view of a mechanical world, which cannot explain the fact that we are made of motions with form that leave a trace on space but are essentially actions in time that have a social finality – to create more complex networks, chaining knots of actions into systems. This social will of every point and entity of the Universe is completely at odds with a mechanist, fixed, solid, senseless, dumb Universe.

Motion in Time and social evolution are concepts that require the capacity to gauge information and interact with other self-similar points to create those organic networks. Further on, dual networks tend to evolve and reproduce new points through exchanges of ‘—motions’ and information.

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

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

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

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

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

And so with those 3 scales of ‘existence’: time cycles, knots of time cycles and networks of knots of time cycles (Non-E Points) we can explain all the ‘actions’ and systems of reality made of those cycles, knots and networks; and describe a complex Universe that exists ‘in time’ more than in fixed space, since it has always motion; it is also dynamic, made of cyclical, feed-back equations whose causal relationships, forms and trajectories are the essence and purpose of existence. We thus consider a more complex analysis of time arrows, beyond the duality of ‘—motions’ and information, which combine creating a reproductive arrow, SxT, and further on socialize, ∑SxT, creating networks. And so the universe has also an organic will: to create networks of self-reproductive points of ‘—motions’ and information.

Yet the most astounding property of those points is to be points of view, points with will, which perform actions with the purpose mechanical or not, but probably felt in all scales as the inner freedom of the point, of obtaining ‘—motions’, information reproduction and social evolution. The 4 wills or whys of the Universe are indeed embedded in the postulates of i-logic geometry.

The point to exist has to be complementary, to feed and gauge ‘—motions’ and information and to last beyond its wearing it has to form part of bigger social networks or reproduce itself to last beyond death.

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

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

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

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

It is the organic will of all systems that search for those 4 arrows what makes the quark to exist as a knot of such flows of time arrows: a physical particle traces energetic cycles described by the principal quantum number; shapes the form of its trajectory, a fact explained by the secondary quantum number; iterates along the 3 coordinates in similar shapes, an act described by the magnetic number, and gauges information to evolve in social groups, a fact described by its spin number.

And those 4 numbers define it as a Non-Euclidean quantum knot of complementary ‘—motions’ and information with a 4D will of time. And as it happens they express the 4 arrows of time: E->Principal number; I-> secondary number; Re-> spin number; 4-> social evolution: magnetic number.

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

And so we talk of 4 ‘arrows of time’ or dimensions of change that create the future: energetic and informative systems and events, which reproduce a wealth of self-similar beings that organize themselves into social networks, creating bigger wholes – new scales of reality.

And this simple game of complementary beings that in favorable conditions reproduce self-similar beings, self-organized into bigger social networks becomes the why of all realities. Even the simplest particles, quarks of maximal information and electrons of maximal spatial extension and motion ‘decouple’, reproduce, when absorbing ‘—motions’ into self-similar forms, and associate in complementary networks called atoms, made with a central informative mass of quarks and an energetic, electromagnetic, wider body of electrons.

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

Fact is that even the simplest complementary systems (quarks and electrons) interact together and if they can absorb more ‘—motions’=motion they are able to repeat=reproduce the cycles of its system. And so we talk of a 3rd reproductive system: from quarks and electrons, the fundamental particles of the Universe that decouple in new particles when they absorb new ‘—motions’ to living organisms, the fact that all is motion with form makes easy to reproduce those formal motions in an organic way. Thus the new concept of a world made of formal motions brings about also a more complex philosophy of reality – organicism.

The points of view of different Sp<ST>Tƒ organs

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

In the next graph we resume all the elements of the 5 postulates of Non-E=i geometry The true meaning of vital space and cyclical time, is the construction of vital, bio-logical and physical systems

The function of existence, Œ= Sp x Tƒ, in space-time thus is expressed by a series of beings made of Bodies/Waves of Energy (Vital Spaces) and Particles/Heads of Information (Time cycles) whose equations :

œ, define an action, a discrete expression, a variation in space, which is a minimal functional action of the system, in its exi motions in space across its U=U±4

∫œ, define a worldcycle of energy and information, an integral expression through time, of one of such actions (Lagrangian), or all of them (Hamiltonian) of the system.

∂œ, define a force, an instant, a moment of the total momentum of the being.

This function of existence though in smaller scales, such as our thermodynamic space-time or the quantum scale can be studied with different particles.

And in the psychological language to describe mankind, it is better analyzed with verbal theories.

And yet in all cases we are observing a similar space-time being.

In general relativity, the Einstein field equations’s 3 solutions represent the minimal, maximal and stationary ages of information, energy and steady state of those curved space-times.

How we interpret the different Hamiltonians of a sum of actions, or each action independently, will give us different perspective of an entity.

It is thus the different manipulations of the Generator Equation according to the rules of i-geometry and the topo-bio-logical properties of scalar space-time what defines the space-time events and cyclical actions of the Universe.

The reason of the Program of Existence: symmetry between topological, and time and scalar dimensions.

The spatial-temporal ternary symmetry between:

Se: The Spatial entropic, long, relative past motions.

Tƒ: The high, informative, relative, future cyclical motions and…

ST: The combined wave-body repetitive, present motions, structure the 3 bidimensional ‘organs’ of all diffeomorphic relative beings:

ST (∆<∆-1, ST (∆≈∆), Tƒ (∆>∆+1); made of entropic fields that expand and disorder space by ‘burning’ and simplifying quanta of energy in larger scales of lesser order (i<i-∆), hyperbolic-wave bodies that try to repeat cycles and reproduce the components of the system, and Tƒ, spherical zero-points with an external sensorial membrane that transfers to a central zero point by shrinking without deformation (Poincare Conjecture) the bidimensional perceived world into a mind that controls the whole system

Thus there is in all full systems of reality a center of order, a Maxwell’s devil, the zero-point, or ‘single dimensional soul-mind, which maps reality, 0-point x ∞ World = Constant mapping of reality, into a smaller fast cpu, brain, electronic eye, consciousness, program of existence, and then ‘enacts’ the actions of the system that ensures its immortality in time-space, its continuity, its repetitive existence through its actions.

We do not argue in this post the degree of consciousness of the point of view, which is rather an automatic ‘program’ that maximizes existence, imposed by the survival of beings. We just reason why the program must be in all systems that act in Nature in an independent way in reality, where it is located that point of will and in which consists that will.

In brief, systems are generated as varieties of the fractal space-time generator, which can be written as

U = ∑∑ W: ∑[Sp x Tƒ = ST]U±4

This less synoptic expression of the generator means that the Universe is made of infinite fractal parts, we call worlds, composed of the 3 components of a system, Spatial ‘—motions’, Temporal information and reprod-active limbs/fields, body/waves, heads/particles that ‘act’ within U±4 planes of relative existence, with its organic parts, to maximize its existence, which means obviously:

  • Tƒ increase its entropic motions, ∆a, to increase its vital, cellular/atomic structural space, ∆e, to increase its gauging of information, ∆o, to increase its Reproduction, ∆i and to increase its social evolution, into larger groups, ∆U.

Those 5 actions that we write with 5 vowels: a for accelerated, entropic motions, e for energy feeding, i for iterative reproduction, o for informative perception and U for Universal creation departing from individuals form the program of existence. And we can spot that program in all systems, through the analysis of 4+1, ‘quantum numbers’, ‘laws of electromagnetic fields’, ‘coding genetic letters’, ‘drives of existence’ and so on.  (Humans tend not to recognize one of those 5 actions often the social, evolutionary or the simpler motions and its ‘coding’ equations, so most likely you will find 4 ‘equations’ to define a system).

The program of existence does ‘exist’ in all beings, and explain its systemic interaction and why it perceives other planes of existence. It explains its organic structure. It defines a sentient, pantheist Universe in which ‘monads’, unlike the simplified model of Leibniz do communicate (who discussed if his monads did communicate with the Universe beyond its 0-mind mapping perception, but as it was going to be too complex to describe them in their communication simplified the model considering them isolated entities of pure perception).

There are in that sense two fundamental formalisms to study the Program of existence, which we explore in two different sections of this web:

  • The non-Euclidean geometry of ‘points with parts’, ‘fractal points’, ‘points of view’, ‘zero-points’, ‘non-Euclidean points’ , which communicate flows of energy and information to form, social groups, herds and networks that finally evolve together and emerge into wholes with 3 topological parts, which live through a dynamic 3 horizons of existence.

This description would be more objective, external, perhaps more liked by the scientist of the ‘4th paradigm of measure’, with its hidden anthropomorphic belief of Abrahamic religious origin, that only humans are sentient, perceptive, special, organic, living, because the z=6 atom, carbon, is so special (-; In the next graph we resume the meaning of those 5 ‘i-logic postulates’ 3 of which (the first, second and fourth, explain the mathematical evolution from points into waves into topological networks), while the 3rd and 5th explain the possible interactions between points, which define its Darwinian vs. social, perpendicular vs. parallel, entropic vs. informative, devolving vs. evolving events, that is the causality in time of all processes, (3rd postulate of relative equality), and the creation of mappings through minds, monads (5th postulate, which seems at first redundant with first: definition of a point).

The program of existence.

Each point of view performs those actions in chains of existence.

What does a Point of view, an existential momentum, a fractal exi=st-ence, a zero-point, a function, program, equation of Existence once it is born as a single seed of an ∆-1 plane? How does it go to create a Cyclical existence, a sum of Actions ∑Sp≤ ∫∂x≥Tƒ, which move a function of existence through all its cycles of exchange of energy and information with the universe.

The Universe is made of 2 motions, ‘—motions’ of space and cyclical motions of time, webbed into ‘planes of existence’, which human minds see still according to the ‘Galilean Paradox’.

Thus its structure is described by 3 basic formal languages:

– i-geometry (Non-Euclidean), which explains space & Causal logic (non-Aristotelian) which explains its time cycles, (hence our use of the next letter ‘i’ for this formalism), and organicism which explains the organization of the different planes (biological languages).

And yet there is a 4th language and property of the Universe, which surely abstract scientists will deny but it is there, and so it has been always argued by human beings, the language of the Will, which creates the needed order to organize those motions.

Indeed, we can describe externally objectively reality with its geometries and time cycles, and its organized planes of existence, but the question that remains to be answer is why? What causes those systems to organize themselves.

The answer is what I have called in different moments, ‘the program of existence’ or ‘Universal mandate’ (external vision of it in impersonal or mystical terms), the Will or Equation of Existence or Survival (internal vision), which resumes in a simple ‘partial equation’ of the Metric Generator of the 5th dimension:

Max. Sp X Tƒ

  • Systems that perceive in a rather automatic manner with O-minds minimal time cycles (∆-3) and move in invisible fields of force with E-nergetic limbs, through lineal paths (∆A-4)….

And we call those external 2 actions the external, or automatic will or primary actions of existence. If we were to use the terminology of Leibniz or Aristotle, it would be the process of ‘apperception’, or ‘vegetative will’. Since they are automatic, caused by the mere structure of the being, which exists in a lower field of motion and absorbs bits of information.

Yet the external actions have 2 internal counterparts, which ensure the maintenance of the components of energetic limbs (feeding on energy) and the informative system (reproduction of ‘form’):

  • First, the being feeds on quanta bigger than the bits of information to reproduce its forms, and this process is called feeding, ∆E-2
  • The origin of reproduction are the actions of the being that communicates its 2 poles, in an intermediate region, the body or wave, in which it exchanges flows of motion and form, between both poles of existence, combining them first into cyclical actions, SxT, performed by those intermediate waves and bodies. And so actions is the 3rd will, through which the being tries to maximize its ‘function of existence’. And the repetition of actions finally creates a ‘burn-in’ reproduced structure, which becomes its 3 element, which allows the being to  survive in other form. Thus the 3rd will or action of all beings is iteration. Since reproduction of its body waves ensures its immortality beyond accidental or old age, death by excess of energy and information. And so the being reproduces its ∆-1 cellular structures, ∆Ra-1, till they organize themselves into a replica that surface at the world-plane.

And we call those 2 wills of existence, the internal will, and in terms of Aristotle’s classification, the animal will.

  • And yet there is a 5th will that helps to maximize the function of existence: the social gathering in groups coordinated by a common language, which make the whole stronger. So ∑SxT > SxT.

Thus it starts the scalar growth of herds into bigger social herds that hunt together. We express this gathering with the symbol of S for society or sum, but most often with the specific symbol of ∑ a summation (here not used in the strict mathematical sense of ‘a series’ but merely as an aggregation of individuals). And we say that the summation of individuals which gather through simple ‘spatial languages’ that coordinate them bring about a series of social groups or Unions of Individuals represented by those 3 symbols, ∑, S, U (i will try to unify symbology, time permitted).

It is this simple scheme what explains the formulae: ∑sp-1=S, that is a group of quanta, points of a herd, Sp x Tƒ beings brings together a ‘space’, which is a bidimensional topology or loosely connected network that extends through a social space.

But and this is the final frontier of the will, as the space becomes denser in a single plane, organization must become more complex, and the equality rule breaks, as new languages of faster cyclical speed, Max. Tƒ, allow better coordination. And so society splits between the faster neurons and the bigger cells, Max. Tƒ and Max. E social classes of the system. The efficiency though has a heavy toll for the bigger, slower cells that must obey without doubt the neuronal, informative class. And so finally a 2 layer structure, with top neuronal fast points and body cells appears.

Further on, the energetic, simpler will of motion, is demoted in the hierarchy, as those cells must ‘expand entropically’ the space below them at ∆-4 level and so often the system stores ∆-4 species and creates a 3rd energetic layer of hardy cells, responsible for this carnage. And those are the cells of the limbs: informative neurons, ‘reproductive’ glandular cells and ‘muscle and bone cells’ to use specific types of an organism, becomes the 3 social classes of the organism, which maximize its actions of existence.

Now, the informative cells must rule the body and limbs cells and so they must connect with all of them, and at the same time they must coordinate among themselves fast their orders to produce synchronicity. And so they often develop axons (in biological systems with a network fractal orientation in the high dimension of information) or produce informative spherical waves (in physical systems existing in an isomorphic medium, where the informative pole tends to be in the center of the wave), which reach simultaneously all the cells of each layer.

In both cases we talk of a multiplicative effect. For example, if all the neurons are connected to all, the number of axons is x². And so we use for the ‘organism’ in multiple layers, the symbol ∏, for ‘pi’ (circular motion) and for multiplication (the higher number of axons, or ∑².

And we can write then the complete will of existence through its 5 actions of motion or acceleration, perception, feeding, reproduction and social evolution as:


And this 5th will or action, ∑∆+1, completes the game of existence,

This is the will of the Universe, its sequential program: O<A>E-=∆+U

That is: ∆Observation of cyclical forms- ∆ Acceleration towards a field –∆ Energy feeding –∆ iteration of the species – ∆ universal evolution

acceleration and perception (with different order depending on the informative or energetic nature of the being), which brings feeding and reproduction, and finally the social evolution of the system.

Another way to write it is A->O->E->I-teration->U-nion, the Aeiou of existence, the 5 vowels of all actions.

This is what all beings do to maximize their existence by playing its actions to that end: its reproductive evolution Sp<ST>Tƒ

The reinforcement

The program is externally reinforced because those who follow it survive better. And so those who don’t perish, do not reproduce and do NOT exist in the future.

The equivalence with the metric of the 5th dimension.

And so this simple program of existence: Max. S x T, is the counterpart to the Metric of the 5th dimension SxT=ST, which explains it. Who was first the egg or the chicken? They are self-similar functions, one seeing internally and the other externally.

Since when we analyze the function SxT, it is maximized when S=T, thus the will of existence brings also homeostasis and balance and the sum of all those S=T, could be considered the constant i, of the metric of any world-plane.

The Point of balance: S=T

So of the many similar equations we use to write the Fractal Generator that represents all events and forms of the Universe, the most important is Sp<=>Tƒ, which represents the search for a point of balance in which the Spatial Energy and Temporal Information of the System, is maximized by that balance.

This is the point of adulthood, the equation of present, the steady state, the equation of beauty, the equation that maximizes the ‘existential force’ of the system, Max. SxT (which is reached when S=T). The number of ‘events’ that take place under the umbrella of this equation is enormous.

We could say that S=T is the point of immortality that all systems try to reach.

The partial equations of the Generator are ‘partial events in space-time’, of significant importance for all species, as they describe actions, dimensions, and symmetries, states, ages and organic parts fundamental to the whole.

Among all them the most important is the ‘function of existence’, that is the strategy to maximal SxT, which is the equality between the energetic components and states in space and time of a l Superorganism:

Function of Existence; Top Predator Equation: Max SxT->S=T

Equation of Justice, Reproduction, Present and beauty: S=T

‘And God said S=T and extinguished all beings that did not obey the law of Justice.’

The most astounding discovery of General Systems Sciences is in the metaphysical realm – the understanding of both mathematical and logical, bio-logical, existential processes together, through the ‘simultaneity’ of mind’s mappings of the Universe.

The fractal of the Universe is a mind observing a fractal world of Sp<=>ST systems constantly flowing in two type of motions, |-Motion or distance or speed or energy and cyclical motion or perceptive, dimensional form, cyclical information, clock frequency.

2 states of existence among which all beings fluctuate by moving that ‘élan’, that ‘motion’ that ‘spirit’, that ‘substance’, that ‘form’, whatever you might say of it.

Between motion and form, energy sensation and information sensation, translation and perception, Sp and Tƒ, | and O.


The Universe is a creative, temporal, formal game of creation of ‘Functions of Existence’, SxT, S<=>T, complementary systems of energy and information that try to maximize the communication between both poles, SP and Tƒ, a fact maximized by a simple mathematical equation:

Max. S x Tƒ ->S=T

This equation has much more meaning than its simplicity might evoke. What it says is that when we have two entities, one of maximal entropy, Sp and one of maximal information, Tƒ, treated as ‘sets’ or ‘numbers’, or ‘herds’ or ‘groups of cells’, such as the number of elements of E, A, and the number of elements of O, B, are equal, A=B, the communication and force of the group, Max. Sp x Tƒ is higher. And the system is better integrated between field/body and particle/head.

Such systems are top predator systems that survive better. The law of balance or justice is one of the most metaphysical and yet the most important of all laws of the Universe. It gives a survival strategy to all entities in existence. And its two limits when the law of justice is broken are the equation of death:

Max.Sp  x Min. Tƒ = death by accident.

Max. Tƒ x Min. Sp = death by warping and excess of information.

Tƒ exist in balance, S=T, obviously the best strategy is to maximize the communication between Sp and Tƒ, so each element of Sp communicates with each element of Tƒ, a x b is exactly the product of all those communications. And so what happens in nature is that the neurons or informative cells of the Tƒ -system and the cells of the body system, reach maximal communication to act simultaneously as a single whole.

The Function of Existence, S=T or Max. Spx Tƒ (both are mathematically equivalent, as the product is maximized by the equality of the factors, so 5×5> 4 x6 … > 9×1…) is the fundamental equation of the Universe.

Sp<=>Tƒ resumes all the events of reality. But of its 3 possible ‘ages’, ‘dimensions’ or ‘states’, Max. Sp (Sp>Tƒ) , S=T, Max Tƒ (SP<Tƒ), S=T, the equation of balance, beauty, maturity, classicism, reproduction, present, existence, Max. Sp x Tƒ is the goal of the Universe.

And those who achieve it achieve immortality.


Λ. The order through scales: the fifth dimension.

Now we write with those laws a fractal generator equation of infinite space-time existences, the metrics of the 5th dimension:

Clean STuD3In the graph the Universal fractal of infinite beings of space-time with different speeds in its clocks and sizes in space, whose product however, Se x Ti, space size for speed of its information cycles remain constant, creating a ‘stable space-time being (ST±4) which happens in different combined size from the smallest. infinitesimals ST-4 to the largest Universe, ST+4.

All fractals have a generator feedback equation and the Universe is not exception. Generators are dynamic, cyclical equations which constantly create slightly changed new ‘cycles’. As such they are periodic cyclical equations of the form X < = > Y, where obviously X and Y are symbols as in all ‘Universal grammars’ linguistic representations of the Universal Generator (mathematical jargon in Space-time) or Universal Grammar (Logic Jargon in Time-space)>

Universal Generator/Grammar:               To ∑ExI=ST±4

We write the Fractal Generator expressly with one of its similar identities, in an expression which can be understood logically in wor(l)ds, the fundamental grammar of the human being.

In its Topo-Bio -logic ternary identity, ‘Topological i-planes of Vital Spaces and Cyclical Times’ need to be described topological properties (5th dimension metrics), Organic properties (which organize 0±1 vital spaces into a ternary organism) and logic properties (the ternary Non-Aristotelian logic of cyclical times which return in a ‘Hamiltonian’ Cycle to its origin.

The generator equation thus can be used to deduce from its topologic, biological and causal properties any other equation of the Universe.

It cannot be achieved such a feat as physicists of lineal time expect, only with topologic properties and only in a single continuous space-time.

It needs to understand the metrics of the 5th dimension and its relative scales of absolute time (ST±4), between invisible forces and invisible cosmos, beyond our perception (C speed, 0 K limiting borders). And this is achieved with the summit of the evolution of mathematical languages, the Non-Aristotelian, Non-Euclidean i-logic topology of vital spaces, of organisms, of geometric forms with speed-motion, constantly performing ∂a, accelerated actions with 3 ±= stop and go motions…

The Generator Fractal. 

In Fractal mathematics the equation that generates the fractal is called a generator ‘feed-back’ equation. They are symbolic equations, which express operations that repeat themselves ad infinitum, generating new solutions, accumulated in time or space.

For example, Mandelbrot’s set, the most famous fractal is a simple iterative equation defined in the complex plane, which generates points in that plane with infinitesimal detail. So as we run the equation z(n+1)=z(n)^2+c the points plotted in the plane form an image:


But a Fractal Generator does not need to be a numerical equation. It can be a symbolic, logic equation that generates ‘logic structures’. If we substitute the values of each of the parameters of a logic generator, then we obtain varieties of the form the logic equation defines.

This is the case of the Fractal Generator of the Universe that represents the i-scalar dimensions of any system of scalar space-time. Thus it defines the logic structure of all Systems of the Universe. And when we substitute each of those dimensional symbols for a specific variety of the dimension, we obtain a certain species of the Universe.


Below we can see the Human being generated by that equation in simplified terms, described in its spatial morphology and temporal ages by 2 developments of the equation.

Thus the fractal Generator of relational space-time, Se<STi>To, and its symmetries in space and time  generates an infinite array of species, and to fully understand them we need to describe the formal symbols we use to represent, ‘motions’ and ‘forms’ of the 5th dimension, and the laws that define how those dimensions interact and ‘mess’ together, to create reality.

So the analysis of the fractal generator and its sub-equation, symmetries, dimensional laws, which apply to all systems and allow to deduce all other laws of all scales of the Universe is an immense field, for future researchers in the fractal space-time structure of reality and all its parts.

And then a brief analysis of the symbols used on its full equation.


The Interaction between limbs and membranes of energy, informative zero points and cyclic, toroid bodies.

In the previous graphs we can observe some of the interactions between the zero-points (minds), spherical membranes (energetic skin) and toroid cycles that structure the ‘physiological or inner forces’ of all physical systems or organisms.

In topology we consider a form to be the same one, if it is only deformed but not torn. Thus a sphere is in fact any membrane, or skin that closes an inner space inside. This inner space is called the ‘ball’, and the ball does not include the external membrane, neither the hyperbolic center, or zero point. The 3 together form the ternary structure of most systems, with an external barrier communicated with a torus of cyclical flows of energy and information with an informative, hyperbolic center or north south axis.

What matters about those morphological, ternary systems is not so much the specific form but the functions derived of the common properties of each of those 3 universal topologies, which are not rigid, solid substances but deformable networks of points bonded by flows/lines of energy and information. Its dynamism means as distances and flows between points of the network shorten or lengthen the whole form changes but if the cellular network does not break the form remains one of those 3 topologies:

– The membrane is a network of planar, self-similar cells, which expand and enclose the inner organism from the outside. It allows the transfer of energy and information with the external world through the holes of the network; developing specific functional holes: those for energy are called mouths, those for information are called senses. They will be also positive or negative in its directional motion in order to absorb or expel wasted energy and information. All systems will have at least those 2 types of wholes in their strong, energetic, spatially extended membrane that circles the ‘vital space or body territory’ of the entity.

In complex analysis, the external membrane can be multiple: the most extended, less loosely guarded one is the territorial zone in which the informative center moves. In the organic Universe, spatial structures are always ‘functional’ and made of loose networks with motion, which therefore have, as any network does, dark spaces in the holes between them.

Thus the 3 topologies exist to perform informative, reproductive and energetic ‘functions’, which rule the morphology that adapts itself to preserve the function or ‘action’ they perform.

A key property of all membranes according to their function is the equality of all its cellular units, which have similar functions and are exchangeable, submitted in physical systems to the Bose-Einstein statistics, since they are invariant to rotation and substitution in space.

– The still center or hyperbolic north-south axis, or zero point is the point that processes information and hence also the point of consciousness of any system, of any world, of any topology of 4 dimensions, of anything that exists, of anything that is.

To create a mental image, the pixels of the zero point are able to form a boson, synthesis of all its units. In the same manner, a sphere can create in the center of its inner space-time a reflection mirror of all its cells – a zero point of the whole self.

According to the opposite nature of energy and information, the zero point is far smaller than the membrane, but its cycles and processes are much faster.

Look around yourself and you will not see any zero point. That is the beauty of it. All ‘brains’ are internal. They are all guarded they are all secretive, they are all connected, communicated, but at the same time isolated, ego-centers of all the complementary systems of the Universe:

The zero point function is kept in bilateral and planar forms but their position changes from the center to the head, on which the informative cells reside, on the relative dimension of information (height, which allows perception of a wider angle): politicians, kings, priests or markets rule a society from a top position that receive and distribute information.

– The torus. In a film that now has a lot of followers, ‘thrive’, a Californian guru explains that the torus is the most repeated topology of the Universe. He is right, but it is only one of the 3 topologies of any 4-dimensional universe.

The simplest torus is a cycle: we can build a torus departing from a cycle, pi, made with 3 units and 3 apertures, of 0.05D between the 1 D-units of the membrane. The cycle then will reproduce a self-similar inner cycle, an internal ring. Then both will form a dual system, in which the inner cycle becomes the zero point that will integrate the flows information that cross through the external disk through those 3 apertures. Thus a dual energy-information circle is formed.

The natural direction of flows of energy and information is from the outer spherical cells into the internal cycle-space: The zero point then observes a reduced mirror image, of the universe, transported through informative channels that interconnect the membrane and the knot of information or zero point in the interior.

The flows between both then rise the dual cycle, creating a curved dimension of height, forming a toroid.

If we extrapolate this fact to all systems, energy becomes the first causal action that gives birth through a cyclical warping to an informative, final form.  Or as Einstein put it: time curves space into mass (a zero point of the gravitational scale).

Alternately such a system can grow and the toroid between the membrane and zero point will finally expand in a big-bang, giving birth to a bigger form.

In this manner a dual system is re=produced; one with a more complex, vital center, and en external, more expansive membrane that protects it. For example in beta decays, a nucleon becomes a bigger, more dynamic atom, with an external membrane, the electron and an internal zero point, the quark/nuclei. Cells in mitosis also reproduce by growing their toroid body and duplicating their zero point – the DNA center of information. Then the cell breaks in two.

We can see that simple assembly in the graph, the eye-zero point system is the hemisphere (right side), in which the flows of the torus converge, coming from an external ‘Riemann sphere’, or membrane, joined with the zero point by a series of flows that reduce energy into denser form.

In the point in which that speed is reduced to zero, a zero point appears, in which a pixel mirror of the external sphere, corrugated into a linguistic image gives consciousness to the system. Then something magical occurs, the zero point processes that energy into information that forms and provokes a change in the position of the entire system. Since the zero point is the will of the system. The membrane develop the limbs of the system. The zero point is the brain and consciousness and the torus the physiological systems or flows of energy and information between both.

Causality determines the flow of growth: the external membrane gives birth to the zero point – it is the father element.  Fact this which brings the theme of evolutionary development in time of a ternary structure in space.

Evolutionary development

It all starts with the creation of a hollow sphere of self-similar cells assembled in a herd, in which each point is only communicated with the lateral neighbors, absorbing energy from the external Universe thanks to its ‘energetic’, hard structures. This herd of cells multiplies and lets a part of it to flow internally into the torus.

This stage is the blastula in a biological organism; in an electromagnetic field created between two smaller sphere-points is the moment in which the electromagnetic field between two poles is established.

If we consider the growth of such a sphere, we can observe, as in a ‘morula’ or in physical particles and celestial bodies, how the growth invaginated inwards transforming therefore the sphere into the torus.

A zero point in a fetus is born first as a morula, a perfect sphere. The sphere of energy is therefore the first thing to be created. It is always like that. A single planar form appears. It start to multiply and without disconnecting itself, it first creates 3 then 5 and each five starts to ‘copulate’ with its neighbor cell and create 2 more on the next level and so on. Different patterns now start to differentiate a game of evolution, which will become more complex in each scale.

The first topology, the democratic sphere, which absorbs energy from an external universe, is hollow. This sphere is made of individual points that have a recognizable arrow from outside energy to inside information. They will have a gradient of density, as the inside face of the cell is denser and shorter than the outside one, in a ratio depending on the depth and volume of each cell. It follows also that cells will start to be come self-mirrors of other cells as they see them through the internal sphere. And finally at a certain point this sphere will become invaginated in a polar directions as ‘cells’ fall in internal growth from the bottom and top, hanging and building a pole North, South direction.

Most systems are born as energetic hollow spheres that grow inwards creating a digestive tube and establishing a flow in the inner vacuum space of the sphere that soon becomes a dual convective flow in cyclical motion that transfers towards the central of the new torus an image of the external world. There, the internal cells become the inner radius/zero point of a growing torus. An eye within an eye: the membrane now is reflected by the axis that form in the center a growing seed, a brain, a DNA nucleus. All bits of information reflect an external Universe, imitated and mapped in the lesser space of the zero point, which is warping and extracting information and deflecting energy to perceive with those maps what the external sensorial cells are scanning.

So from a seed with an external membrane and a middle body to feed on, to a celestial body or atom with a hard crust or electronic cover, a series of rotational toroid cycles of electromagnetic energy and information or plasma flows and a central point of maximal density, we see repeated the 3 topological construction of a functional limbs-body-brain, skin-organs-informative center, structure.

This ‘primordial’ ternary system in space is coupled in time by a dynamic transformationas we observe the software flows of energy and information the system carries in time through its ternary structure: first energy will be absorbed by the negantropy of the membrane, which will let the flows enter the torus, where they will be processed and grow in information, becoming either material for the reproduction of the ‘cellular’ units of the body-torus, or pixels transferred to the zero point in the center but ‘outside’ the inner circumference of the torus. The external skin or membrane transfers energy to -> A Central zero point of information->through an intermediate body-torus.

The still map of the zero point perceives in itself.

The general evolution of those flows is Max. Energy -> Maximal information till reaching stillness when they come all in ‘parallel’ as a puzzle that for an instant of time – the perceptive, relative internal clock of the system – will appear as an image that perceives in itself. This central point of stillness is the consciousness of the point. And we consider that consciousness is precisely defined as that ‘image’ constantly changing in minor pixels as the flow of energy is finally distilled into information.

A simple transformation happens between an external sphere that converges into that zero point.

The point of view or zero point that creates a ‘mind’, a fleeting stillness in the flows of energy that converge on it, is the knot that shows the will or at least calculates, integrates the flows of energy and information creating solutions to the synchronicity of flows and opportunities tending to follow the mandate of existence. The zero points seem to have the will to accomplish the mathematical solutions for forces and masses to follow the principle of minimal action. The zero point commits little errors; it is intelligent; it seems to have embedded the program. How the program evolves, invaginating first a sphere that reproduces and becomes a torus with a first ‘feeding axis’, which finds the central cells, more sensitive, soon evolving into more complex informative networks, how those networks invaginate the body and communicate the inner and outer sides of the hemisphere and sphere (convex and concave topologies), etc. can be explained with the science of topology.

The human being as a topology of fractal space-time

In a human, the zero point is the brain, the membrane is the external sensorial and skin system, and in between the cycles of motion that transmit both consciousness and make us live. But we see of us only the external and the internal consciousness, zero point and membrane, while curiously enough the universe sees or perceives the changes produced by the flows of the torus, the precise functions more than the visual observation of those systems is what will guide us in our understanding of reality.

But what Geometric system of the many geometries of mathematics, define better those 3 elements? A Geometry, which has not been fully developed till the work of this author: Non-Euclidean, Fractal Geometry, which we shall study in the next paragraph, after we introduce from a topological point of view the 3 internal ‘forms’ of the unit of the 5th dimension, the fractal point.

The idealist school of mathematical physics.

Screen Shot 2016-04-01 at 10.36.10

In the graph, few scientists are aware of the idealist, Hegelian bias of German culture a century ago, which still permeates the loss of interest for the foundations of the scientific method in mathematical physics today. Thus we shall remember here the foundations of the scientific method…

Search for truth through experimental evidence, and logic sound models of reality with the addition of the elements of an organic model of the Universe. In the graph, two german idealists, during the panic of the ‘parallels’, which seized in rapture the entire world of mathematical physics after the greatest minds of the age could not solve, where to fit, the ‘multiple new geometries of the Universe, unlocalised in space and time.

Unaware of the rather obvious 5th dimensional structure of those geometries, the panic extended from Gauss and Riemann, as propagators of Lobacjevski and soon brought to mathematical physics, the confusing notions of an idealist school of geometry where ‘by decree of Hilbert’, we human minds invent points, lines and cycles which are not defined.

It was the axiomatic method of Hilbert, which influenced the 3rd, formal age of mathematics; Einstein’s rejection of ‘substance’ (formal motion in fact) for the waves of light, and Bohr’s rejection of density (fractal structure) for electrons.

So Hilbert converted mathematical elements (points, lines and planes and their logic relationships into ‘platonic eidos=forms of the mind’, Einstein converted ‘space’ into ‘frames of reference’, perspectives of the human mind and its visual light space-time rod of measure, and Bohr converted densities of ‘bosonic light’ which form the electronic wave into probabilities of human mesure.

Now back to reality mathematics remained immutable, points still existed as fractal beings, lines were still waves of points communicating formal motions between them and planes still were created by points into topological networks and planes outside the brain of Hilbert.

For example, a number which is ‘a society of identical beings’, whose properties are derived of the social nature of the 5D universe of parts and wholes, and whose sequential order in a line derives of the fact that parts come before wholes, is not yet defined.

A philosopher of mathematics, which by definition is a metalanguage of the 3rd baroque, informative age would inquire:

“What kind of thing is a number? Some philosophers (antirealists) have responded here with disbelief—according to them, there are simply no such things as numbers. Others (realists) think that there are such things as numbers (as well as other mathematical objects).

“Among the realists, however, there are several different views of what kind of thing a number is. Some realists think that numbers are mental objects (something like ideas in people’s heads). Other realists claim that numbers exist outside of people’s heads, as features of the physical world. There is, however, a third view of the nature of numbers, known as Platonism or mathematical Platonism, that has been more popular in the history of philosophy. This is the view that numbers are abstract objects, where an abstract object is both nonphysical and non-mental. According to Platonists, abstract objects exist but not anywhere in the physical world or in people’s minds. In fact, they do not exist in space and time at all.” (Britannica)

Now the difference between ‘fiction in languages and reality’ is due to the inflationary property of form, of information, which in its 3rd formal age multiplies its forms, and departs from reality. It is not though useful to take fiction more serious than reality, or the classic age of the language when the correspondence between form and energy, language and reality is maximal (STi-age).

The perfect forms are non-evident ‘time cycles’.

Moreover perfect forms do exist in time – the cycle being obviously the most perfect form of TIME, WHICH WE DO SEE IN SPACE, for very fast cycles (quantum forms: Max. Sp x Min. Tƒ =K), which ARE perfect as they return to its initial point – that is closing the pi cycle in pure time, with 3 perfect ages-diameters.

The perfect geometries that exist in atomic systems.

The perfect orbit, which ideally would be the more stable cycle (so the higher the e-xcentricity, the less stable is).

The perfect logarithmic spiral. The perfect wave of energy-information, which has no apparent limit and ‘transcends’ between 5D scales.

It is indeed surprising how ‘geometric ‘ is the Universe in all the scales we do not perceive directly.

Only the ‘evident’ simplicity of human beings, who must ‘see’ the direct visual truth, especially in the age of visual machines, has failed to understand this fact, ‘inventing’ platonic explanations for the ‘non-evident’, temporal structure of the Universe where the ‘perfect cycles’ are. As we do NOT see time, we do not see the ‘perfect ideos=forms’ of the Platonic Universe. We only see ‘space’ and so we do not ‘perceive’ visually the forms of time, of which space is a mere ‘still’ imperfect form, ∂T=S/V.

This simple equation of 5D analysis is telling of the true ‘logic formalism of mathematics’; THE GAME OF PERFECT FORMS, ‘IDEOS’, which imprint the motions and vibrations of the Universe – the mental language that stop those forms into a ‘partial mirror’ of reality.

We thus consider mathematical logic (two indivisible space-time languages , albeit initially born as different subjects, today evolved into the Boolean Algebra and digital thought), the main (but not only) language of ALL the scales of the Universe.

It is only comparable in the Human Mind to the pure visual languages (eye colors and arts) and the pure temporal language (verbal actions and words), studied however on the section of History (the superorganism of mankind).

So it is quite amazing the need for a ‘philosophy of mathematics’, which only expresses the limits of the human mind to go beyond the ‘visual’ first layer of reality.

As in the case of physics, the ‘sickness’ of mathematics happened in the 3rd baroque, formal ‘Germanic age’ of mathematics at the turn of the century when Hilbert affirmed that we ‘imagine, points, lines and planes’ unable to understand at all the ternary relationship and fractal nature of points of the 5th dimension.

So he just had as Einstein with the gravitational scale of space and Bohr with the quantum scale, an ego-trip of self-centered anthropomorphism and the 3 influencing each other ‘decided’ that reality was NOT outside the mind f man, but ONLY WHAT MAN PERCEIVES AND IMAGINES MATTERED.

All this said there is the more elevated pure way to understand all this evolution, through the ‘¬Æ formalism’ of the generator equation, which is how we started this text (no for need of confusion but because we have to knock out experts always ‘first’ as they are pedantic non-interdisciplinary ‘bonobo’ monkeys that only mate among themselves so my experience tells me T.œ must start raping their minds, and them maybe some will ‘listen’ 🙂

All this is needed to fully grasp the division of mathematics in T.œ in its 2 main fields: i-logic geometry and Non-Ælgebra.

Non-E≈ i-logic geometry deals with the Absolute Geometry, taking it from where the evolution of geometry ended in the work of Bachmann (1970s: absolute geometry), after the insights of Lobachevski and Riemann among others on the pan-geometries of the Universe, and starts by defining the undefined terms of points, lines, planes, lay on, and betweenness, needed to construct mathematics, with the exclusion of continuity, which is NOT a feature of the Universe but of the ‘mind-worlds’ that perceive it.

i-logic geometry thus is mainly concerned with 4 sub-themes:

  • The 3 geometries of systems orientated from a point of view or frame of reference, which perceive Euclidean space in its own plane of existence, hyperbolic space, looking downwards in the 5th dimension and elliptic space looking upwards.
  • The definition of the undefined terms of geometry and its 5th postulate, the core element of i-logic geometry, which defines fractal points with parts, waves of communication between them, topological networks (discontinuous planes), and the i-logic structure of perpendicular and parallel relationships defined by the 5th postulate and the rules of ‘similarity’, congruence and equality defined by the 3rd postulate. The new defined terms create the scaffolding for all direct mirroring between reality and mathematics, which thereafter become vital mathematics, much closer to reality when describing points, lines, planes and the properties and postulates.
  • And the analysis with the new understanding of the 3 topologies of geometrical forms (Euclidean, hyperbolic, elliptic) and its 8 sub-varieties, and the 5 postulates of i-logic geometry, of the real organisms of the Universe perceived in synchronous analysis as forms of space.
  • Finally, the most extensive part, which we can hardly treat in this post, just a few examples, would be the translation to this vital mathematical new scaffolding of the enormous wealth of geometric and topological laws, discovered by 2300 years of mathematicians hard at work.

¬Ælgebra (Non-Aristotelian  Algebra or Existential Algebra), deals with ‘social numbers’, the discontinuous unit of the temporal Universe. It groups back 5D  analysis and time algebra split in the XVIII century, due to the excessive development of mathematical physics; which latter would be paralleled by the expansion of Modern Algebra (group theory, set theory and the axiomatic method). Now we shrink back the whole subject and its inflationary human minds, to fit it within the total Universe! (-;

In essence, the 3 ‘abstract configurations’ of modern mathematics, group theory, set theory and the axiomatic method should go back to the Pandora box, and take it only when it is proper; substituted by:

  • Symmetries of the Generator of fractal space-time beings, which substitutes the abstract language of groups.
  • Social numbers, which evolve from parts into wholes, which substitutes the abstract jargon of set theory.
  • The experimental method, which shows the isomorphic laws of mathematics applied to all the species of all the scales of reality and substitutes the axiomatic method.

Now, we will ‘bundle’ the 3 parts into the 2 original ones, geometry of space, and algebra of 5D time cycles, because of the experimental method.

It is proved by experience that the 6 motions of the Universe (regardless if they are seen as form or motion), roughly break into the main 5 organic motions, which conform a world cycle between ‘birth, evolution, growth, diminution and extinction’ along 3 ∆±1 scales of the 5th dimension’. And so this is what Algebra will study.

And the locomotions in external space-time and between scales of the 5th dimension, which are studied by geometry, its differential equations, expressed through analytic and differential geometry and the 3 pangeometries of the Universe.

Obviously as T.œ explains all what exists together with the same laws, our division in i-logic geometry and ¬Æ is an organic division, since ultimately points are numbers, just seen in synchronous space or dynamic time. And so both change into each other constantly and the methods of one and its postulates work into the other.

Thus the main fields of ® are:

  • Analysis, which studies social numbers in their growth and diminution along scales of the 5th dimension, either integrated or derived in time or space. It does so from a continuous perspective, so analysis bridges really the geometric and algebraic point of view.
  • Symmetry theory (group theory), which studies the symmetric transformations and diversifications of the ternary structure of reality in 3 spatial forms, 3 time ages, 3 scales of the 5th dimension and infinite ternary fractal sub-elements.
  • Functions, which study the relationships between space constants, time frequencies, and conserved quantities, along different scales of the 5th dimension. It is a large field as we study how multiple polynomial sub-dimensions, integrate into larger systems. And vice versa, how wholes in time and space divide into sub-systems (Fourier systems, binomials, etc.)
  • Probability, Populations and Combinatorics. Which studies the 5th dimension social numbers from a discrete point of view.
  • Numbers theory, which studies the most efficient configurations in space of geometrical numbers (so also as analysis a bridge between both i-logic and non-æ), the relationships between its 3 ‘species’, even, odd and prime numbers and the 3 parts of the Universe, the laws of social numbers, which define its efficient configurations, and the relationship between the bidimensional 3 scales of creation of space-time systems and the 3 type of numbers, the numbers of the real line, the complex bidimensional numbers and the quaternions, whose structure DO tell us essential facts about the nature of spas-time.
  • And the translation of the amazing wealth of knowledge accumulated in algebra throughout history.

The article will first introduce the history of mathematics and it main ages, as it performs as usual its own mental world cycle, starting from its realist youth, in which mathematics derived from the reality of social numbers (to calculate groups) and geographical planes (to measure areas and distances), and then slowly separated from reality as the ill-understood concepts of infinity and multi-dimensionality creeped in, and the reality of finitesimal quanta gave up, despite the advices of Leibniz, and finally with the discovery of pangeometries, and the scaring runaway age of idealist mathematics, now we return to the beginning and reconnect mathematics with reality, both from a human linguistic perspective (this work) and from the new dominant species of the planet (the chip and its digital models of reality).

Then we shall consider the laws of i-logic geometry, symmetric topologies and non-AE existential algebra. Here is where the creative part of T.œ comes in, studying mathematics with the scientific experimental method in correspondence with the 5D fractal structure of cyclical space-time actions. We describe the more general laws of T.Œ with application to all the sciences and worlds of reality from a mathematical perspective.

Finally in the 3rd part, which will take sometime to have a minimal volume to be meaningful, once we have understood vital, realist mathematics and defined all its elements, we will start the translation into realist theorems of the bulk of mathematical studies of those last millennia.

Thus once the simple truths of mathematics are clear, a way to proceed through it is the study of the main operandi of mathematics first to define the correspondence between mathematical operations and ® 5D fractal space-time cycles; so to establish a proper formalism. And then study the fundamental propositions of mathematics and its relationship with the laws of 5D space-time they represent.

This can be done in different ways. We have chosen instead of the usual analysis of the isomorphic, linguistic method a more discursive approach that once the work is well done (this is so far the less advanced post of the 2nd line as I work them in inverse fashion, from the human world down to the Universe, which is the humanist perspective) might be reorganized.

In any case we shall still study mathematics as any other science with S-T dualities, T-ages, S-forms, 5D-inverse arrows, and generators.


Symbolism: the creation of ∆+1 planes departing from ∆œ-1 points.

We shall use the following symbol for them:

Œ, the function of existence, for the first and 5th postulate, used for ALL fractal points in general: a point with volume and parts, the Informative (Tiƒ) and Entropic (S) lineal fields, merged in the center,  and a wider opening in the equator or mouth to absorb energy.

∆º or •-point or @ristotelian mind, or åctive mind, for the fifth postulate, and the multiple roles of a mind-view, which normally has an axis of informative perception in the dimension of height (hence ∆º).

Whereas the first and 5th postulate ultimately represent the inward state of the mind and its outward perceptive state.

Represents the 2nd postulate (a wave instead of a line).

Represents the 3rd postulate of relative equality, as it shows both the perpendicular + and parallel = dual relationships of beings, with species they feed on (equal energy, different information) or evolve together with (equal information) forming

Γ, the symbol of the Generator equation will also be the symbol  for the 4th postulate of a topological non-euclidean plane-network made at least of 3 physiological sub-networks, each of them at least with 3-point parts, messed together to form a topological organism.

So from the organic ∆-1 point, through the ∆º mind, across its ≈ flows of energy and information that web those points into social networks, structured according to the ‡ relative similarity (social parallelism) or perpendicularity (darwinian hierarchical relationship) the postulates of Non-Æ illogic geometry build  the ∆+1, Γ-Topological supœrganism of a larger scale.

And so i-logic mathematics will fusion once more mathematical, algebraic, topological, analytical and biologic, organic, social properties to describe it all ‘at once.

1st and second postulates.

Time alone is the pure singularity of logic thought, in the language, the final vortex, and as such cannot be seen. It does not exist:

IN THE GRAPH, a simple vortex of space-time in the arrow of acceleration (Vo x Ro =k(t))

tiƒ the vortex of mass, charge, or any ageing mind, is accelerated towards a third age of life-future time-growth of information, as the function of time k(t) of the vortex accelerates.

Yet it is increasingly invisible to the present surface, created by waves that transfer motion and form: energy between polar points:

Thus as networks transfer e x i in each s=t act of communication, exiºst-iences appear study by each stience with an index i, which for man is ∆º.

When pure time-information or mind singularities, existing across the dimensions of size of the Universe, full of density of perception, cross through space with its electromagnetic minds, across those spatial extensions its mirror symmetry enlightens with form, reproduces and orders reality giving birth to seeds of Space-time, vital beings, composed of 3 elements, a singularity a membrane and an open ball between them, which assembled as a whole, as perceived simultaneously by the densest region of central information becomes a being of space-time. And existence vital in its world cycles, happens.

So a being is, between the not perceived future singularity and external membrane of cyclical perfect closed pi-cycles, as it makes the vital space, invaginated by the orderly networks that connect singularity soul and entropic membrane, of infinite parallel flows from the Unverse to the centre.

Einstein and Minkowski underlying idea that space and time are symmetrically and inversely messed into a single ‘being’ has not fully been understood. The idea that both ELEMENTS space and time come together in reality, was however the biggest advance of timespace theory since Darwin.

But how fractal §pace and cyclical ∏ime mess together? This is where Minkowski and Einstein didn’t go far enough, because of their acceptance of a classic mathematical concept of ‘continuous single space’ and a single, continuous lineal time, described with word lines.

All the laws of most physical systems can be described knowing the time-cycles of the cyclical, lineal membrane, or circulation and the density-strength of the singularity central point or tiƒ, with different parameters (frequency, acceleration, mass strength etc) to represent an accelerated vortex of time:

Once the concept of mass as an accelerated frequency: e=mcc+e=hv->m=ƒ(h/cc) is solved, we easily realise there are in fact 3 states of space & time – their ghostly existence separated as ‘past space’ and ‘future time’, and their more complex ‘present combination’:

  • Pure space, or expansive, lineal motion, ‘entropy’ being the closest concept to it; which has in its purest nature no ‘existence’ as it has no form, no in-form-ation, and so it represents the remotest past of non-existence.
  • Pure Form, dimensional logic form, pure ‘time’, a causal rather deterministic logic set of events that come together once put on motion by the very topo-bio-logic nature of the causal, vital Universe, but are without energy-motion in which two impose their form, ‘potential events and beings’ in an Aristotelian sense, and hence non-existence, in the present.
  • And Space-time together, body-waves of finite present existence, which merge both and DO appear as ‘beings’.

So existence is a series of ‘dharmas of present body-waves of yin-formation and yang-energy, mixed together. Those present space-time beings are the beings that truly ‘exi=st’.

But where is then the immaterial ‘future-logic time’ of causal, deterministic processes? This is the ‘will of schopenhauer’, the ideos of Plato, the Pythagorean mathematical God and Darwinian biological God; this is nowhere and everywhere, immanent and transcendent, emergent in all causal processes given you give it time, and as such eternal and at the same time non-existent. So it is space, the ‘void’ to which the Shiva=energy/Visnhu cycles return (we do use in this blog all languages and human perceptions of the space-time duality NOT only those of western physical sciences). Yet we shall deal with potential pure time and vacuum space in other parts of the blog. Let us consider the ‘duality and messing of both’, starting from its keys elements, the holographic principle and the ternary symmetry between topologies of space and ages of time.


‘Every point is a monad, a world in itself.’ Leibniz

‘The language of the Universe is topological, made of cycles, lines and triangles.’ Galileo

‘Numbers are social forms.’ Plato

We have considered so far 3∆ elements, Sp, Ti, St,∆, but forgot there is always an observer the mind that knows, and so without defining the mind (which can be considered the ‘software’ that runs the Tiƒ, head-particle-government of a biological, physical or social system, we are NOT complete, just describing as present science does, the how, but not the why.

So even if this part is less easy to accept, it is necessary to postulate as all deep philosophers of science have done the existence of a PERFECT PROGRAM OF SURVIVAL AND EXISTENCE OR MIND OF EACH BEING EXPRESSED IN A SERIES OF LINGUISTIC SYNTAX, OF LANGUAGES THAT MIRROR AND MIMICK WITH LESS OR MORE ACCURACY THE ∆ST STRUCTURE OF THE UNIVERSE.

SINCE of those 3 elements the most important by far is Tiƒ, the guiding system of information, ‘particle, head or GOVERNMENT’, and even more important than the hardware the software, the algorithm of survival and building of super organisms and its world cycles in time – THE MIND OF THE UNIVERSE OR ‘GOD’ AND MIND OF EACH HUMAN SOCIETY, OR human God, and of each system, made to the image and likeness of the whole.

We shall call the mind, the point of Max.Information of the system, its zero point (ab. •) or  ∆º scale of the being, as it is in mathematics the o-point or center of the ‘Cartesian frame of reference’; in the galaxy it zero-point or black hole; in a mass its center of gravity; in the cell its DNA nucleus which encodes the information with the program of evolution and survival of the organism; in the nation the capital and president, and generally speaking, the point of maximal density, Max I≈∆º, which from an advantageous point of view perceives itself as the whole, as it coordinates with its maximal information and communication with all the elements of the systems (its inner world which it invaginated with its nervous/informative, gravitational forces; its outer world, which it perceives with its senses). And further on, maps it all with an still mapping, mirror of the Universe, it will latter use to project its imagination in the external world and create a territory of order around it.



INTRODUCTION: Cyclical Actions of fractal space-time. The beats of the Universe.


In the graph, the reproductive cyclical action among beings of all scales. Each of the 5 universal åctions of space-time beings has a similar functional structure, hence can be described with the same equations of existential algebra, and obeys the same isomorphic laws regardless of the scale we observe. In the case of reproduction it always implies the emission of a U-1 particle in the lower scale of the being – an informative seed that will clone and organize socially till emerging in the same U scale that the parental form which will initially provide the necessary energy to maintain it in existence, and guide its informative gauging åctions. As such reproduction is by far the most important action of all systems, which encloses all others, and represents the summit of the program of existence in the Universe.

There are 3 natural – 3 always 3 – ways to perceive the scales of the 5th dimension in relationship with any of us, beings.

– H(w) or ∑. Through its entire existence, and that is the worldcycle of the being, whose ages we explained in our posts on time cycles; there is the level of the I in a given point of its external, absolute space-time world. This is the Worldcycle Function of the being

– G(œ). Then we can make a slice of the worldcycle and see that relative non-Euclidean point=being in that moment of space-time, and study its vital space and cyclical time functions, its body/wave and particle/head in that moment, structurally in its forms and functions. And this is the function of existence of the being G(œ) or Œ

– F(a). Finally we can take not the being but the external cyclical action of the being in the Universe in a moment of space-time. Since really this is what the Universe is truly about: beings existing in a given U∆±∆ , Universal Plane sandwiched between other Universal Planes of Different U-scale, which exist inside of it. Whereas the being, develops survival åctions, as its internal space-time exchanges energy and information with those Universal Panes. And each of those ‘forceful åctions’ become an external motion which influences the external world with more or less depth or consequence. And so the last level of understanding of reality is that of the analysis of its minute åctions (themselves decomposed finally into forces and its co-related elements).

And so we consider:

U = ∑ H (w) = ∫œ dt = ∫ F (æ,e,ï,œ,û) dst±4 = 0

An algebraic expression of the ‘reality’ we are surrounded off.

It is thus necessary to study the Actions all those superorganisms, or ‘Hamiltonians of Worldcycle existences’, to build up reality in a fashionable way.

Indeed, we can go from the Worldcycle into the function of existence and then into the åctions which are time cycles, if we want to study logically, temporally the Universe. And this is what the sentence does when read from left to right.

But we can also consider it spatially, mathematically and read it from right to left, and then we have the perception of it, as a series of fractal spaces, constructed of points particles, which become organized into superorganisms, and all what those superorganisms do is to exist.

And so in the middle of it all the sentence read left to right and right to left, from the perspective of time and space, come together into the function of existence, and its simplest 5 åctions.


When we analyze cycles of time and try to classify its multiple species, surprisingly enough we can reduce them all to a series of åctions, which have a bio-topo-logical purpose. As we depart only from two possible elements, ‘energy’ and ‘information’ åctions are restricted to 5 type of space-time cycles:

  • Motions (a for acceleration)
  • Energy feeding (e)
  • informative gauging (i)
  • reproduction of offspring (o)
  • organic evolution of individuals into universals (u)


Those 5 åctions which are the ‘drives of life’ in biological terms, moving, feeding, perceiving reproducing and evolving organically – with a higher degree of complexity than a simpler society, into wholes which look total independent of its parts.

the åctions of the Universe thus form a program of existence and we see infinite of such åctions performed by completely different entities, from atoms to humans to galaxies, to microbe, to rocks, to rivers…

All systems of space-time with a minimal structure will perform mechanically vegetative or consciously those 5 åctions which ensure a monotonous repetitive, but intense, internally engaging plan of survival:

∆: Gauging information -> A, accelerate motions -> Energy feeding -> Orgasm ->Universal family.

This narrative is played by crystals, humans, black holes, microbe, you name it.

Indeed, when we depart from a ‘worldcycle’, or ‘function of existence’, or even from a space-time cycle≈action, we are developing 3 degrees of decreasing wholeness over a certain space-time domain, and to pass from one level of maximal wholeness (the worldcycle of the being across all its finite time), to one smaller (its function of existence in a given point of its external absolute space-time), or even smaller (one of its punctual åctions or space-time cycles) in that external world.

Those 3 quite different but essential qualities which define a space-time body/wave+particle/head,   Sp>Tƒ system are normally elements of 3 different ‘scales of reality’, within a given Universal Plane, and yet the 3 are intimately connected by the fact that we can consider each one originated by the larger one, and vice versa, we can consider the larger one an integration of a sequential number of quanta of the lower type.

A worldcycle implies the entire function of existence along its coordinates of duration. A Function of existence implies a sum of discontinuous æ,e,ï,œ,û space-time åctions along the entire life of the being

We could in that sense, consider that our ‘ego’, our function of existence is the only ‘variable’ which is sandwiched between the other two, the worldcycle and the åctions, and hence ‘irrelevant’, as our ego is, and consider simply speaking that a worldcycle is made of a sum of quantum æ,e,ï,œ,û åctions. In this case we can consider the concepts of Lagrangian and Hamiltonian functions and declare the worldcycle a Lagrangian of the 5 type of åctions=cycles of space-time created by a given particle, whose integration along the duration of the entire life of the system is zero.


And so probably the most ‘productive’ in the sense of its manipulation by existential algebra and ultimate connection with the details of reality, equation of the function of existence is:


W (worldcycle, world) = ∫æ,e,ï,œ,û dt   = 0

That is existence is the sum of all our åctions, across our 5th dimensional Universal planes, during our total existence, whose final value must be 0.

The possibilities or not of integrating that equation is secondary to a general analysis of it, but relevant for detailed calculus, as the Hamiltonian-Lagrangian expression of the laws of mechanics shows (indirectly reducing mechanics to the science of studying the closed worldcycles of particles performing ∂a, motion åctions, which is one/fifth of the previous equation.




Let us remember its fundamental ‘kaleidoscopic’ equation, the ‘fractal generator’ of constant space-time beings, in the universe: U: ∑ Sp x Tƒ = ST: Reprod-active generations

Now, the generator fractal of space-time beings, expresses many things, and represents all the varieties of species across the Universe in its multiple realities, and this is difficult to systematize. But we have some fundamental laws and symmetries to do so.

Essentially what the Universe does is to ‘freeze’ certain species which are combinations of ‘bodies/waves’ that reproduce systems, and ‘heads/particles’ that gauge information, which exist ‘over’ a field of space-time from they will extract the 2 formal motions they need to survive. And we represent this with different equations that represent the same generator, to ‘encode’ the different ways in which human minds perceive it all.

The simplest one is the previous space-time equation, which now we enlarge in its explanation:

Se (Lineal-Spatial, past entropic motions and forms) x Tƒ (informative, future, cyclical clocks of time and forms) = ST (Constant, present, reprod-active waves and bodies of space-time)

And so the question which must be studied is what are the magnitudes and quantitative ratios in which a constant being made of those elements takes place.

Tƒ that aim we have empirical evidence (universal and vital constants, proportions, social numbers) and we have theoretical help from the laws of the fractal scalar space-time Universe.

A mathematical example: pi and the hexagon.

And we have finally some mathematical constants that play also a fundamental role in this game of creation of ‘existences’. Let us the consider a simple mathematical constant to understand what we talk about.

Se->Tƒ is a fundamental ‘existential equation’, or arrow of time that transforms an spatial motion into a cyclical motion. If we seek a constant to describe it, the most obvious is π, which measures the relationship between ‘3 lineal diameters’ that evolve together from lineal motion into cyclical motion.

And so we find pi in an infinite number of equations. Now if we consider that transformation in nature, it can be done through 6 radiuses, which come together into an hexagon. The hexagon has a perimeter of exactly ‘3’. It is we could say in this way the perfect transformation of a lineal entropic form, the triangle with maximal lineal perimeter and minimal space enclosed, the favorite lineal motion of all ‘arrow’ systems, into a cyclical motion, the hexagon, which is the most abundant Bidimensional configuration in nature, with maximal resistance, that covers fully space, and we find from graphene to bee-hives, to crystal forms and metal structures.

Thus, constants which are ‘regular’, ‘perfect’, efficient, that fill fully space taken advantage of all its motions; that correspond to the 3 ‘time ages’, 3 ‘topological functions’, which can perform all the cycles and åctions of the game of existence do endure, are hyper abundant and work.

This is more or less understood but without the understanding of the symmetries and ages of time, bidimensional space, åctions and program of existence, which we have lay in the other introductory posts, physicists and mathematicians, biologists and social scientists do more of a kabala, geomantic game with numbers. Now we do have the reasons of those mathematical numbers. And perhaps the most fascinating sub-discipline of ∆ST is to explain ‘mathematics’ as the geometric ‘why’ of efficient systems of space-time.

Now  we can consider the pi circle, which is the bidimensional system with less perimeter per volume. But pi is an irrational number. It does not exist as it is actually a number which leaves holes in the sphere.

It has a center, the zero point of the system, which gauges information and a disk with 3 turning strings, leaving ‘apertures’ in the external membrane between them. Those are the ‘mouths’ of the circle, which covers 3/3’14, 96% of its surface. Hence only 4% of openings leave information come into the system. As it happens, dark energy and dark matter represent 96% of the Universe our electronic minds do NOT see. And indeed, our minds are spherical zero points which do NOT see the entire Universe.

Pi in any case and its lineal form, the hexagon are the all pervading Sp->Tƒ universal constants which better express the process of transformation of lineal energy into cyclical time, through the 3 ages of existence.

Consider now 2π, which is the ratio we use to divide H, the constant of the plane of light space, which is all pervading in physics. This suggests, since 2 π is the ratio which divides the circumference to give us precisely a ‘radius arc’ in a circle (a single side of the hexagon in the polygonal pi) that the Unit of quantum action, is an ‘arc’ of a cyclical motion, that the minimal unit of energy and time in the space-time Universe of light is an arc of a photonic particle and we will explore that concept in our studies of quantum physics, which we will post, time permitted, in a year, around summer 2016.

Thus mathematical constants are the first step to build a comprehension of the topological Universe, but interpreted no longer in abstract terms, but through the existential logic equations that describe the fractal game of existence, its world cycles of life and death, and the 3 fundamental isomorphisms or symmetries of the Universe:

The 3 bidimensional varieties of topological space, or organs of all beings:

Spe (lineal entropic limbs/fields) < ST (Hyperbolic body/waves): Sp x Tƒ > Tƒ (spherical particles/Heads)

Its symmetric 3 Time ages:

Sp (entropic youth-past) < ST (reproductive present) > Tƒ (informative old age)

And the planes of existence across which systems enact its åctions to obtain entropic motion, information, which they combine to reproduce internally and externally a system:

Motion åctions (∆-4), Informative perception (∆-3), Energetic absorption (∆-2), Reproduction (∆-1) and social evolution (∆+1).

It is as everything else in the Universe, from those fundamental equations that define all systems in nature, and its proportions, topologies time arrows and transfers of motion, information, energy, combined in reproductive and social events, from where we can determine all the fundamental magnitudes, åctions, constants and conservation laws of nature. Let us then consider the most general to study them in detail its ‘cases’ in all type of different systems.




In the graph, a galaxy, a DNA molecule, a tornado, a shell, a sunflower, and 2 logic, mental mirrors of the Universe – a Mandelbrot set and a yin-yang, eightfold life cycle – are all made of shapes that combine the most efficient morphologies of Entropy and information: the line or shortest distance between 2 points and the cycle that stores the max. quantity of information in lesser space. Both combine to reproduce the infinite beings of reality. It is the game of existence we all play.

A Universe of åctions of Entropy and information.

Once we have established the existence of a Universe of motions in time and forms of space, whose organic parts are guided by the ‘will’ of the 4 main arrows of time, we can respond to the fundamental questions about man and the Universe – why we are here, what we are. And the answer is obvious: since we are all complementary beings, made of Entropy and information, we exist to combine, absorb and reproduce Entropy and information, Sp X Tƒ; what we constantly do through åctions that imprint our form and deliver it, carried by a flow of Entropy= motion. We make åctions of Entropy and temporal information. So we often say ‘I don’t have time and Entropy to do this’.

This simple expression, Sp X Tƒ, is therefore the unit of reality, an action, specific of each species, which will imprint the external world with its form and Entropy, as many times as it does. Yet åctions are also fractal, discontinuous, quantic ‘steps’. And so we define for each system, including the biggest systems of reality (the gravitational and light-space membranes we inhabit), a minimal ‘existential unit’, or action that defines the system:

Se x Tƒ=K=Action of existence.

In all systems we shall find such åctions: the h-Planck constant is the minimal action of the light-membrane; in the gravitational world a Lambda-string is its minimal action. When we humans live, we constantly act with ‘Entropy’ an time, performing cycles of existence, whose minimal åctions is a ‘thought’, an act of perception (I think therefore I am), which takes a second of time, our existential beat. In Physical systems, åctions can also be translated as momentum (m(Tƒ) x V(Se)); in biological systems, Sp X Tƒ will define the ‘existential force’ of a top predator. In the economic world an action is a minimal quantity of a Company, the Free Citizen of the Economic ecosystem that re=produces machines, money and weapons and structure the financial-military-Industrial complex in which we live. In a wave of light it is the minimal step, as the wave reproduces its form over the surface of magnetic and electric quanta (constants of vacuum). There are in that sense many ways to define an action but in most cases, as its formula indicates, it will be an action of reproduction that imprints a form on a surface of Entropy; and therefore also the minimal unit of ‘form’ display but any existential system.

Tug-of-war between the selfish and selfless arrows.

Now we come to a philosophical question that might seem trivial when considering the automated, topological paths of existence performed by the åctions of the simplest physical beings, but has an enormous importance when addressing the will and åctions of human beings – the ‘Maslow’ pyramid of hierarchies between the 4 wills of existence. Maslow studied that pyramid between the needs of man as a biological being, yet since the 4 arrows coincide with the 4 drives of living beings it is easy to notice how those 4 arrows and hierarchy are common to all other species. In detail study we can observe that hierarchy to be equal to the main chain of causality between the 4 arrows: we need first to perceive to locate Entropy to feed ourselves, and only when we have enough Entropy we can reproduce, being the arrow of social evolution, the least desired, because it also conflicts with the first arrow of perception from the self-centered perspective of our ‘Galilean Paradox’. And so the 4th arrow of ‘belonging’ to a complex, social organism is often imposed from outside, and yet it happens all the time as complex social organisms are stronger than individual cells and hence survive.

Thus we can consider that the strongest will of the pyramid is our self-centered perception of the Universe that makes us feel superior to all other beings – the center of reality, since ‘Every point of view measures reality from its local perspective, confusing the entire Universe with its informative, still mapping or ‘mind’ that makes him feel the center of the world, and ignore all other minds, languages and perspectives he doesn’t observe’.

We, as all entities of reality are indeed, self-centered, arrogant Galilean Paradoxes that think to be infinite when we are just an infinitesimal fractal point absorbing a very reduced quantity of the total in/form/ations of reality with a specific ‘rod of measure’ of space and time, which constructs that mapping but will differ from other rods of measure and ‘time speeds’ of processing information of all other species of reality. So humans measure/perceive light and use the rod of absolute light speed to measure space and the frequency of a second – the blink of an eye, the heart beat and the speed of human thought – to measure time.

Yet there might be other beings who measure space with gravitational rods we do not perceive, with atomic or molecular rods as we do with the sense of taste and smell, etc.

Even the use of an absolute light speed could be changed by a rod that would make the ‘frequency of information’ of light absolute and then change the speed of the light waves according to the amplitude of those waves and have an absolutely different mapping of reality, which will certainly make sense, bring new perspectives a seem the absolute universe to those who ‘measure’ reality in that manner.

All those reasons imply that a topological model of reality is absolutely relative: from an existential point of view, regardless of the importance humans ascribe to their ‘intelligence’=mind perception, to their point of view, and to their ego and Galilean Paradox that make us think that our nose is bigger than the Andromeda Galaxy, we are nothing on the objective sum of all things, and we have no privilege neither we are treated with special difference by the game. And so because, each and all points of view are ‘meaningless’ for the entire game, only those points of view that submit the Galilean, self-centered paradox to the 4th will of eusocial love, and sharing of Entropy and information with other members of the same species to create a bigger superorganism do survive on the long term.

It is the basic tension human beings experience in real life, between our selfish ego-driven desires and biological, individual will and the need to give part of those desires for the common good of our societies and ultimately of the human kind. Indeed, the most successful nation on Earth, China, is based on the submission of the individual will to the collective superorganism. ‘Unfortunately in the case of the human-kind, the natural, final arrow of eusocial evolution that should have converted the entire species into a global superorganism able to survive in balance with our Entropy body – Gaia –has failed, and we have not evolved from the social level of tribal history, divided in nations, created by hordes of the most selfish, self-centered, arrogant type of humans, the warrior who imposes his will because otherwise he can kill and eliminate from existence those who oppose them.

Indeed, regardless of the paraphernalia of ‘memes’, bits of cultural information that praise the job of the military, it is self-evident that the biggest risk of extinction of mankind is war and the evolution of weapons of mass-destruction, driven by the failure of egocentric tribes to evolve into a global humanity. And the Universe always punishes those failures with extinction.

Thus we can consider that the simplex arrows of time, informative perception and Entropy feeding, in which we also ignore the ‘existence’ of the victim consumed as Entropy, after eliminating their tasteless ‘head of information’ are the selfish wills of existence. And the two complex arrows of reproduction, which implies to give for free Entropy and information to our offspring and social evolution, which implies to give up our simplex wills for the common good of the society are the selfless arrows. And there is a tension between both kinds of arrows in all systems of existence.

Recap. The fundamental will of all points of view is the Galilean, self-centered paradox or will of subjective perception. Yet the Universe favors species, whose individuals are selfless and offer their Entropy and information to reproduce a self-similar replica of themselves or to build complex super-organisms of which they are only a cell.

The synchronicities of knots of time arrows.

Each active organism is a complex chain of cyclical åctions performed to achieve the 4 main arrows of time. Yet that chaos of action is ordered by causal processes, synchronized clocks and Entropy/information networks that harmonize all those seemingly chaotic cycles of åctions into a dance of existential beats, interdependent and in permanent symbiosis – being the key to those harmonies among different Time Arrows the concept of ‘time-speed’, the speed at which a certain cycle of time closes its trajectory into a ‘loop’ or event (spatial/temporal description) that will be repeated with a frequency that defines the regularity of the time cycle and its speed of perception.

For example, the subjective cycle of time perception in man is the cycle of informative perception determined by the wink of the eye which opens to absorb Entropy and closes when it processes it as information every second. This rhythm is self-similar to the rhythm of the heart, which is approximately of a beat per second, when blood is expanded as Entropy and imploded carrying the released chemical information of the body. So, since we have a thought per second and a beat per second, the second is in fact the ‘clock-time’ of the human brain and the mechanical instruments we use to compare all the cycles of time of the Universe with our own cycles.

Each species and cycle of time has a different frequency, which depends on the ‘size’ of the species we study, and the causality of those arrows, such as:

Max. Entropy-extension=Min. Speed-Frequency of Time cycles:

Max. Speed/frequency: Informative cycle->Energetic ->Reproductive ->Social cycle: Min. Frequency.

For example, the cycle of perception of the human eye – each second –determines the beat of the heart/breathing cycle of Entropy for the body; the cycle of rotation of the Sun-Earth system – a day – determines the Entropy cycle of the planetary surface, whose microscopic, life-species adjust their energetic /formative, awaken/sleep cycle to that of the bigger organism. And vice versa, the smaller microscopic cells of the body reproduce each day, according to that awaken/sleep cycle. There are in fact a series of General Isomorphisms of synchronicity between those Time Arrows/cycles that apply to any entity or complex system of the Universe, which extends through several scales of spatial size and informative complexity.

All the åctions of all species can in fact be described by ‘beats’ of existence, partial sub-equations of the Generator Equation, which define rhythmical chains of action. In an individual those beats of existence become the life rhythms of each of our organs, from the eye that feeds on light and then informs the brain, which produces a visual thought every second (the blink time of the eye), (o->e->o) to the night/day, dreaming/acting rhythm (Release of chemical information->dreaming->release of Entropy->acting), etc.

A 2nd series of ternary rhythms occur as organisms switch between the 3 physiological networks of hormonal, reproductive activity; nervous, informative activity and feeding, energetic activity (ST>Tƒ>Sp).

Those rhythms happen also in the social scale of existence as a single organism, cell of our civilizations. In society those rhythms shape the ternary bio-rhythms of our daily life; the 8 hours of work (obtaining our social Entropy, money), 8 hours of play (dedicated to family reproduction), and 8 hours of sleep (when our organism repairs its form). Moreover those rhythms of our daily life are synchronous to the rhythms of the global organism, Gaia; and self-similar rhythms are found in the activity of animals and plants.

Since in objective terms humans are created by the same temporal arrows and display the same properties than the rest of the entities of the Universe. A human being is the same kind of entity than ‘an atom’ – a complex chain of time cycles of Entropy, information, reproduction and social evolution. The difference is not of quality but of quantity and hence of complexity: Humans are knots of an enormous amount of time cycles whose spatial topologies, åctions and motions configure our existence.

On the other extreme of simplicity, an atomic particle (quark, electron or photon) is the simpler species, we can study with those arrows, in terms of size and complexity of its ‘EORS’ cycles, compared to a human being. Since a particle can be described with just 4 quantum numbers that resume the 4 kinds of ‘åctions’ particles constantly perform:

– Particles gauge information (reason why quantum theory is a ‘gauge theory’). That is, they calculate the distances with other atoms and act-react to exchanges of Entropy and information with them.

– Particles feed on Entropy, absorbing electromagnetic and gravitational forces and other particles.

– Particles decouple, repeating themselves in other regions of space-time (they reproduce by iterating its particles, quarks, electrons and photons).

– Finally particles evolve together into complex social structures, called atoms and molecules, which also feed on Entropy, gauge information, reproduce and evolve socially.

All those ‘motions’, quantum numbers, molecular vibrations, decouplings and physical events can be re-considered as manifestations of the 4 main arrows of time, chained in synchronic patterns and cycles, cyclical and lineal geometries, whose abstract definition conform the Isomorphisms of quantum physics.

The description physicists do of those arrows is an abstract, mathematical, mechanical description, which corresponds to the limits of the mechanical, monist, ‘religious’ philosophy of science of our founding fathers4, which did not require an ‘internal’, self-organizing will to describe the Universe, since it was understood that the ‘will’, the ‘why’ of all the clock-like motions of the Universe was ‘God’, an entity that seems to have appeared to a pastor of the bronze age.

System sciences reasons those ultimate questions from the perspective of science and its mathematical and logic languages, albeit with a degree of complexity superior to that provided by monist, reductionist, mechanist, classic scientific philosophies of reality. Thus we substitute the ‘will of a personal God’ or any other anthropic principle with the 4 objective ‘arrows of causality’ or Time Arrows that all particles and entities of ‘existence’ follow, which can be described objectively with mathematical and logical equations, and finds in the subjective will for survival its sufficient reason.

Further on, all quantum entities obey the Complementarity Principle. They show 2 states or structures that co-exist simultaneously: a field of energetic forces that moves a particle of information, which gauges the space-time that surrounds the particle. And we cannot distinguish or perceive both entities: the force/body and head/particle together. In other words, physical entities are made of ‘motion fields’ and ‘gauging particles’. They constantly move, stop and gauge information, move, gauge… So because they have 2 components, one specialized in energetic motions (the field of forces) and one specialized in informative gauging (the particle, mass or charge), all their åctions are either ‘energetic åctions’, informative gauging, the combinations of both type of åctions (decouplings, which produce self-similar particles) or more complex åctions in which the particle, atom or molecule share smaller particles, called bosons, creating social networks, made of fields of forces and particles of information.

If we widen the concept of Entropy as lineal, expansive motion, and information as a cyclical, in/formative motion, we realize that the biological realm also follows a Principle of Complementarity between reproductive bodies and informative heads, which co-exist together in living beings. And bodies are responsible for lineal motions, while heads map out the Universe, creating images, reflected in the mind of the external motions of reality, imitated by small cyclical motions within the brain and its neurons. So again we observe a dual structure, body/head, with energetic/informative properties that move and gauge, feed on Entropy and perceive information. And in more complex events, reproduce the biological entity or use languages of information to create complex social structures.

All what exists is a ‘fractal knot of Entropy and information motions’, whose why is ‘to absorb more Entropy and information’ from the perspective of the entity or ‘point of view’ that gauge and moves in the Universe. Imagine a universe of infinite ‘species’ made of ‘lineal motions’, ‘forces or bodies’, upon which certain structures of information, called ‘cyclical motions’, particles or heads, are sustained. Reality is a fractal sum of those 2 motions, Entropy and information, which combine to create an infinite number of entities that gauge information, feed on Entropy, reproduce their form and evolve into social structures till reaching the complex Universe.

We cannot describe human åctions with simple equations because humans can gauge many types of information, feed in many forms of different Entropy, choose many different couples to court, love and reproduce, and make very complex choices in our decisions on how to relate socially to other human beings. But at the end of the journey, amazingly enough we observe that all what we humans do is also gauging information, absorbing Entropy, reproducing and evolve into social systems. So those 4 types of events or causal arrows of time are all what we humans do; even if we use a complex, ‘ambiguous’ language – words -to describe those åctions.

Tƒ exist, to be in this Universe means to absorb Entropy, gauge information, reproduce our form and evolve socially by acts of communication with other beings. Those ‘åctions’ are considered mechanical in the physical world and åctions of will in the human world. Yet they are described in both worlds with the same ‘2 elements’: Entropy and clocks of time. So Planck proved that all physical forces are made of h-quanta, whose parameters are ‘Entropy and time’, while we say in layman terms that ‘we do not have enough time and Entropy to do this’ – meaning we are made of a limited quantity of vital space, our Entropy/body, and time-clocks of information – our minds.

There is no difference between ‘us’, human beings and ‘particles’ that also have a limited Entropy and time, which they spend performing the same game of 4 types of åctions – the Game of Existence. We all play the same game, regardless of what plays it, an atom, or a human being.

Religions will tell you that the ‘will’ of man is a property of ‘our soul’, which is supposed to exist according to the tradition of our ‘pious’ founding father, Mr. Descartes, in some non-local space-time4. Stience will tell you that the ‘will of man’ is the ‘why’ we don’t ask, or at best it will be born of a chaotic series of circumstances and physical events that come together to ‘create life’. While biologists will affirm that the will of man has the same drives of existence (gauging, feeding, reproducing and evolving socially) that all forms of life have, but only forms of life have.

System sciences depart from anthropomorphic traditions, validating instead the ideas of Eastern philosophies (Taoism, Buddhism, Zurvanism), upgraded with the scientific method, showing that the Universe is ‘organic’, not mechanical, because all its particles share the ‘4 drives of existence’ of biological beings, whose ‘why’ is self-evident in a world made of perpetual motions. Since if we all are made of motions, life is embedded in the existence of those motions that repeat themselves by the mere ‘action of moving’: Reproduction becomes natural to the existence itself of cyclical and lineal motions that repeat their forms as they trace their trajectories.

If we leave aside metaphysical, subjective questions on the ‘nature of consciousness’ and ‘will’, we could affirm that all entities of the Universe have both, a ‘will of existence’, shown in its constant pursuit of those 4 arrows, and an objective nature, in as much as those 4 arrows or wills can be proved objectively by the events that atoms, humans, animals or any other entity perform.

It is though necessary to understand in which scale of reality a certain region of Time-space ‘acts’. For example, a chair, made with human formal imagination is not organic neither it shows any of the 4 main arrows of time unless it is attached to a human being (so it helps humans to think- process information – in a ‘still’, formal position). Yet at the spatial scale of atomic wood, the chair shows those arrows and in the temporal distance when the chair was wood, it had also at macroscopic level those vital arrows of time.

What is then reality – the ultimate meaning of those time arrows? At first sight, it seems there is no meaning at all, but merely the eternal beat of existence, Entropy becoming form, becoming Entropy… and the sensations related to those motions, which might be shared by all realities – pain/pressure and pleasure/release. A closer view on both arrows and the complementarity of all physical and biological entities, which achieve immortality through reproduction of their own form – from light imprinting its waves on the vacuum, to quarks jetting bundles of ‘quarkitos’, to humans ‘growing and multiplying’ all over the Earth – seemingly makes the 3rd existential arrow of reproduction, the meaning of it all, and the Universe a constant orgasm of repetitive, present forms.

But then, we realize that reproduction in itself is just a step towards self-organization, as self-similar cells that can ‘decode’ their common language of information come together into stronger, bigger waves, herds and organisms, which survive better, due to their higher ∑Sp X Tƒ, existential force. So the answer to the meaning of it all is clear: the Universe has a dominant arrow, the creation of ‘fractal superorganisms’, species which are self-similar to their parts and emerge through processes of evolution into bigger wholes.

Since the 4 main arrows of time and its discontinuous cycles come together, creating vital knots of motions that energize, gauge information, reproduce and finally evolve socially into herds and organisms: I->Sp->R->S. In other words, a fractal infinite Universe of Entropy and information struggles to create ‘more of it’ by expanding inwards and outwards its relative scales of organic size; since a Universe made of motions has no limits of size and form, as it becomes ever more organized in bigger and smaller social herds and organisms: I->Sp->R->S.

Yet even if social evolution is the dominant arrow of the Universe, it is also the less common, more distanced in the frequency of its events, since all other arrows must exist ‘a priori’ for an event of social evolution – the final causal arrow of reality – to take place, thanks to a common language that carries information among self-similar cellular individuals.

The highest frequency of events always corresponds to informative events, particles and heads gauging and thinking, mapping reality with its hardware, as they run inside the software of a force, whose frequency carries informations decoded and transferred into such mappings. So the atom figures out first in its inner quark-systems how to move, searching for a flow of Entropy or its relocation in harmony with the other atoms of its web, while an office clerk thinks first and then writes or makes a call related to those informative thoughts – an act of measure precedes an act of motion.

Accordingly to those frequencies and the generic law, Min.Sp= Max. Tƒ, the light pixels of informative mappings are smaller and faster to allow faster events/cycles of perception than the bits of Entropy that feed the body – amino acids, which are smaller than the seminal cells that carry the information of reproductive acts, which are smaller than the units of social evolution (other humans).

So happens to the frequency of perception (each second), faster than that of feeding, which happens more often than the frequency of sexual reproduction, which is more common than our acts of love – social acts of evolution that ‘collapse’ a wave of individuals into a particle/organism, emerging as a whole action, born of the self-organization of its parts, such as a religious mass or a voting action, or a marriage, all acts that create social groups. Yet, the ultimate why of any chain of causal Time Arrows must be found in the goal of ‘survival’, the final drive of all entities of the Universe, maximized by its 2 complex arrows, reproduction and social evolution that evolves cellular entities into macrocosmic wholes, which become cellular entities of a higher ‘space-time plane’.

What we are then can be expressed in more poetic terms: knots of existence, flows of arrows of time, mirrors of information, bodies in action, ‘wills of the penis’14, loving cells of bigger social units, exi=stential flows, ‘vanitas, vanitatum et omnia vanitates’; motions of time in perpetual conflict.

The rules of engagement of all those knots of time, ‘points of view’ that gauge information, seek for Entropy, reproduce and evolve socially, creating ‘ad eternal’ the infinite scales upwards and inwards, is the ultimate knowledge of the game of existence, which system sciences study. This holistic view is a mystique revealing existence of the unity of it all, which few self-centered humans accept. Scientists rejected it in the past, because it had not been properly formalized. But one of the advantages of the new formalism of Non-Euclidean, fractal, logic, causal chains of Time Arrows/events, is that it renders a mathematical analysis of those arrows of times are its generic isomorphisms, hence allowing their application to the study of the species of any scientific network of self-similar points in an open flow of communication.

Thus, the range and power of the formalism of Multiple Spaces-Times will not become evident till we develop the logic of multiple causes and the non-Euclidean geometry of flows of communication between the fundamental particles of the Universe, its non-Euclidean, Fractal points15. A consequence of those postulates is in fact the definition of a soul as a non-Euclidean point of view:

‘Every point of view=mind feels the center of the Universe, but it is only an infinitesimal Non-Euclidean point that stores a limited mapping of reality with its informative languages.’

We are all Atmans, informative CPUs, souls that gauge in different languages reality, to construct a mental mapping that caters to our point of view and arrows of time. So we create our ‘perceived Universe’ – a fact known from Descartes to Schopenhauer, but lost to ‘naïve, realist’ physicists. All of them thinking clocks are the only point that matters to measure time, and the human mind, the only ego that knots Entropy into form, since that is the only perspective they perceive. That is why most of history, humans thought the Earth to be the center of reality; and still think they are the only intelligent species.

All is memorial because cyclical inertia, the repetition of the cycles of existence of any form, is common to all space-time fields. This is a tautology: a species that forgets, that does not repeat a fractal cycle of existence becomes extinct and its cycles of existence disappear. Thus, a being has to remember and repeat its fractal cycles to last in time. That is the existential game of any being: to feed on Entropy and use its genetic, memorial information to transform it through reproduction into new cyclical åctions.

Yet those åctions are encoded in ‘fractal equations of information’ which are logical chains that constantly repeat themselves, becoming memorial patterns. Those patterns have different names in science: genes in biology, memes in history, Universal constants, which are proportions between physical Entropy and information in physics, etc. Yet what all those fractal equations and e/o proportions become are cyclical, self-repetitive events that respond to an arrow of time.

Recap: All what exi=st is a fractal knot of cycles of Entropy, information, reproduction and social evolution. There is not a difference of quality among universal entities – only a difference in the quantity and complexity of those cyclical arrows that ‘inform’ each species of reality.

The ultimate meaning of a Universe made of time motions not of spatial forms is closer to a Philosophical tradition that ranges from Plato and Buddha to Leibniz and Schopenhauer: reality is a game of ‘fractal mirrors’, souls=Atmans= quantum knots of information that gauge reality to absorb Entropy in order to repeat=iterate=reproduce their form. Since we are all fractal parts of the whole with a limited duration in time and a limited quantity of space. And so only those species, which reproduce their ‘logic arrows’ of time, their information, in other zone of space survive. Thus the game of existence is in essence a game of repetition of forms, a game of exi=stences.

Generational cycle. 

The previous, simplified analysis of the synchronicities between time cycles raises again the existence of more dimensions of space-time beyond the classic, ‘individual’ cycles of Entropy feeding, informative perception, reproduction and social evolution.

We already showed the existence of a generational cycle in ‘reproductive waves’ of physical Entropy, such as light, whose motion is just the sum of all the reproductive cycles of the wave; and the same can be said of the complex particle/wave generational cycle, equivalent to a complete life-death cycle, as the physical entity switches between its Entropy and information states, Sp<=>o. In the case of the body those generational cycles of cells are fundamental to understand the synchronicities of the body, as all its cells except the neuronal cells that dominate its informative system have a limited numbers of reproductions, setting up a generational cycle. And the same can be said of the species of life in this planet.

Thus, there is a generational cycle, which creates in physical entities a lineal dimension of speed or width in the light and gravitational membranes of space-time between which humans are sandwiched; and sets a telomere limit to the number of reproductions of living species, both at cellular and multicellular level. And since such dimension is a ‘complex of the reproductive, complex dimension’, which is in itself a complex of the energetic, simplex dimension (as all acts of reproduction require a surface of vital space to imprint; so for example women cannot reproduce without a 17% of body-fat volume and particles only reproduce in highly energetic environments), we write:

∑ Reproductive arrows->Generational arrow.

It defines the existence of a new arrow or dimension of time. We have not considered though such arrow in this book for simplicity and because ultimately in the fractal universe, the number of dimensions when we keep adding complex planes made of networks of st-points, which restart again new macro-energetic, informative, social and reproductive cycles is infinite. And ultimately because we live in a 4-dimensional Universe, in which the ‘generational cycle’, except for simple, short-lived entities as those who create the 2 Universal membranes of gravitation and light, are non-perceivable except for long spans of time.

Recap. The sum of reproductive cycles gives birth to the generational cycle, which is also a finite arrow, as all forms have a limited number of generations, after which the reproductive systems fail.

The transcendental arrow: Emergence.

In the same manner that the sum of multiple reproductive cycles gives birth to the generational arrow, the product of multiple networks of informative beings gives birth to the transcendental arrow, such as:

∏∑2 informative particles: ∏ Social networks: Transcendental arrow.

Thus a new dimension of time is the social evolution of organisms into bigger super-organisms, scale after scale, from particles to atoms to molecules to cells to organisms, to superorganisms to the entire Universe with its infinite scales.

Though each organism is when observed in detail a super-organism, if we were to consider a rigorous distinction between both, the difference would be of our detail of perception: a super-organism observes each of its cells as an organism of smaller ‘cellular element’ and an organic view stops in the analysis of its cells.

A fact, which leads to a metaphysical question: it is transcendental arrow infinite in scales; or it is as all other dimensions a finite dimension? Unfortunately an argument on the number of scales of the Universe will always be theoretical, because unlike the other dimensions we cannot observe the absolute totality of space extensions and informative, scales created through time durations to have any experimental evidence of such limit.

The Transcendental dimension, the dimension of emergence, studied by the ‘science of emergence’ or transcendental arrow, as it is often not perceived, especially for the individuals who become part of the whole; believers that form part of an eusocial human organism through the arrow of love; physicists, who don’t see the super-organisms of galaxies, etc.

The difference between the transcendental arrow and the organic arrow is subtle. Unlike organic systems mediated by the 4th arrow, the transcendental arrow is far less brutal than the stick and carrot system by which the informative, nervous systems of organisms dominate the cells of its body; in as much as it implies a high degree of homogeneity and collaboration between the parts that transcend.

In that regard, we could consider that the social arrow forms ‘herds’, waves and bodies, while the transcendental arrow is the arrow that puts together complex, informative particles together, and while the arrow of organic evolution would be based in the concept of ‘safety’, the transcendental dimension will be based in the concept of love, as the particles know each other more intimately, and in certain cases can even become fusion in a boson structure, in which all occupy the same space.

Thus the difference between the Generational and Transcendental arrows and its fractal units, the arrows of Reproduction and Organic Evolution is minimal and that self-similarity brings about some philosophical, metaphysical conclusions:

-As in a succession that converges with less difference between terms, the convergence of time arrows seems to indicate that there are no more ‘dimensions of reality’ beyond the transcendental arrow.

-The Transcendental and generational arrow seems to act, ‘reinforce’ each other, as the generational limit obliges species to evolve into eusocial organisms if they want to survive, hence ‘transcendence’ is the ultimate mechanism of survival in the Universe. In the same manner the Simplex and Complex arrows are intertwined as one cannot exist without the other. Such is the harmony of all the systems of an interconnected Universe.

– The more complex arrows of time seem to create more perfect worlds. If we assign to each arrow a sensation and/or its negative lack of it, blindness vs. perception =information; hunger vs. taste=Entropy feeding, pleasure= reproduction; safety=organic evolution; eternity=generational cycle and love= transcendental cycle, and postulate that all entities of existence are moved to action by the existence of sensorial fields associated to its arrows; we reach some philosophical conclusions:

– The simplex arrows are automated and reinforced by the duality of negative/positive sensations, where the negative sensation is so powerful that it obliges the entity to act without delay to achieve the arrow. We can then image the simplex physical particles whose basic fields is a dual energetic /informative system to be far more automated than the next scale of beings, biological beings dominated by the reproductive and organic arrows.

– Those 2 arrows are what Aristotle called ‘vegetative wills’ and are reinforced by the objective isomorphisms of survival, as those species who do not reproduce or evolve into bigger organisms tend to perish and become food of larger biological systems. Thus, we observe in those 2 arrows and systems a higher degree of freedom, as species can live without reproducing or acting in social groups, but the penalty a ‘posteriori’, extinction is equally deterministic.

– Finally the generational cycle and the arrow of transcendental evolution seem not to be imposed from within the system but from outside and despite of it.

Indeed, the generational limits of existence are not positive and certainly not liked by the species, which is subject to it. A solution is found when we realize that the generational limit as well as the organic arrow that creates herds does not affect to the informative cells and its networks; since indeed, black holes are immortal, as the informative elements of the universe and neuronal cells live all the existence of the organism. And so it becomes obvious that the neuronal, informative networks of the system impose the limits of existence of those arrows.

And so the transcendental arrow of eusocial love is the summit of all the arrows of existence, unique to informative networks, whose members know each other deeply, share Entropy and information in higher degree, command totally the other elements of the organism, last forever, as long as the organism exist and have a higher degree of freedom that all other species. Reason why there is not clear systems of reinforcement. It is the summit of existence, free and eternal, within the limits of the ecosystem or super-organism in which those cells exist.

Recap. The transcendental arrow makes individual organisms transcend into super-organisms, creating the scales of the Universe.

The function of existence of the universe.

We humans have a clear limit in our perception of those scales, given by a series of parameters proper of radiant matter. We can’t see beyond quarks and galaxies; we can’t absorb information coming from faster than light forces (non-local gravitation) or perceive ordered vibrations below 0 K temperature. It is a metaphysical question to wonder if those are the hard limits of reality; in which case the smallest point, the quark, won’t be as Leibniz put it, a world in itself, but a hard limit: the simplest rotational movement or ‘spin’ of the Universe; or they are, as I believe, only the limits of human perception.

Then all what exists is truly relative in its scale, and the atom is an object self-similar to a galaxy, which would reveal infinite detail if we could approach the ultra-diminutive Planck scale. A fact, which translated into fractal notation, gives us the simplest formalism for all Universes, sum of all potential cyclical forms of all its ∞ fractals:

∏ (∑Sp <=> ∑2Tƒ)∆=∞       Universal function of Existence

The previous equation resumes all the possible infinite combinations of cycles of times, made of ∆-points in communication, that create all type of networks of Entropy and form, which become complementary organisms, and start a function of existence. So first Entropy appears, Entropy becomes form, Entropy and form reproduce and create social organisms with the reproduced cells.

We can observe the universal equation also as a game that grows causal dimensions: from lineal Entropy (1) comes from (2) and both combine to reproduce (3), self-similar waves of being. This simple description of the game of the Universe, Sp ->ST->Sp X Tƒ->∑Sp X Tƒ, is already present in Taoism (from 1 comes 2 from 2 comes 3 from 3 the infinite beings, Cheng Tzu). It resumes the constant, dimensional creation and extinction of reality (as finally the fracking of so many cells, Sp X Tƒ, dissolves the form or the form explodes and dies in a big bang).

The Cycles of the Universe are thus self-repetitive; sine as Taoists understood, the universe you see is not its function of existence, which is expressed in that synoptic equation. The processes of creation and destruction of planes of existence however are too complex to study them as a whole without doing some basic distinctions.

Tƒ start with there are two different type of arrows, simplex, Sp<=>Tƒ processes, more proper of physical sciences (as in changes of state by increase of Entropy, from solid to liquid to gas or vice versa; or as changes from lineal energetic motions into cyclical vortices, as in Sp=Mc2), are easier to analyze as they happen in the same place of existence. But we, men co-exist between the quantum and galactic scale of physical objects and between the cellular and social scale of biological beings. And so most of the events we must consider are events that take place between 3 co-planes of existence. In physical events between the quantum, human and gravitational planes and in biological events between the cellular, human and social plane.

The human mind is an I=Eye+wor(l)d who selects perceptively from the infinite number of forms of the Universe only those that matter to us. Thus, we do not see beyond the galactic, gravitational plane; though there are hints about a network structure of Galaxies, a big-bang model, which in organic terms would mean the birth of a first cell-particle that reproduced the entire cosmos and a model of fractal space-times with infinite scales of size that this work represents. Since the classic model of space-time continuum only considers a single light-space, our existential membrane with limits of Entropy and information (c-speed, 0 Kelvin).

Yet both in human and cosmic organisms only multiple space-time scales explains those cycles of life and death, which happen as a ‘travel between 3 scales of size, the cellular semen, human individual and social super-organism of history.

In the same manner cosmology needs to grasp the fact that physical space is organized in 2 planes, the electroweak membrane we exist in and the gravitational space membrane of masses, and gravitational forces, which we do not perceive. Yet it is needed to resolve the meaning of dark matter, dark Entropy, gravitational non-local action, the death of light into gravitational space, its formation of a background radiation, the åctions taken place in black holes, etc.

Recap: A Non-Euclidean space or plane, defined by Riemann in the XIX C, is a network space – a space created by a network of self-similar points, related by constant flows of Entropy and information, whose properties are defined by the degree of ‘homogeneity’ or self-similarity of those points.

So your body is a discontinuous spacetime, a small world in itself, constructed with 3 clear ‘cellular spaces’, the nervous space, an informative network, the ‘energetic space’ – your digestive and breathing networks – and a reproductive space, the blood and hormonal networks and organs. We shall see then reality in organic terms as a series of ‘network spaces’, which will have all the properties of Non-Euclidean spaces (motion, curvature, dark spaces in the ‘holes’ left by the network, etc.).











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