Home » ‘GST: » ¬Æ: Fractal generator

®: Fractal generator

±∞ ¬∆@ST:


Log: 5D growth

∆∞:  ði-1≈Si

The fractal generator is an equation that expresses in the symbolism of 5D the 10 dimensions of space-time of a being and its main but not all operations and relationships. As such is the synoptic expression of T.œs and existential algebra the study in formal terms, to connect it with previous rigurous formal languages. As the all pervading development of maths have superseded other languages we shall use more often its concepts.

But ultimately what reproduces the generator is not numbers but planes of space-time, starting for the 1st dimension, the point, followed by the second dimensions, the motion of the point to form in the 3rd dimension, the productive body-wave that completes the being which then will leave in a new wholeness of existence along the up and down paths of entropy and in-form-ation of the 4th and 5th dimension:

3D: •, 1D: t, 2D:∏, 4D: X¯ª  5D:∫  <≈>     3D: @, 1D: ±2D:  X,  , 3D: ∏ , 4D: ∂, 5D:Γ

Operations are frequency of times applied to quanta of space thus for each s=t we must find an infinitesimal quanta and a motion in space, to create existential present momentum St. Operations are better suited for different scales and forms.

Space is better multiplying, time is better adding. Wholes are better integrated, parts, derived…

So steps are dimensions of space quanta stopping and going through one of the motions of the 5 dimensions, most likely expressed in math through one of the key operators over points and numbers, ±, ∑, x÷, ∏, ln xª, ∫∂, Γ.

The fractal generator studies operations on the algebra of existence with 5Disomorphisms as the elements of the group.

The fractal generator is a group of 3 operations on inverse elements, past-information, present generation, future death.

The unwelcome fact that future is death, entropy, expansion in space sets a high barrier for humans to understand existential i-logic thought as they would like the seminal age of life to be at the end of the cycle. But the five dimension of mental information displaying the construction of a new T.œ happens in the first age of existence.

Since it is the zero dimension, limiting as the fifth dimension between 0 and 1 a template of the entire game written in a smaller dimension, ∆-1 of existence. BIRTH THUS is the end of the 5th ‘certain’ dimension of man as a living being, then we exist in a level which is a ghost that hardly connects and gives to the higher even level of ∆+1 human society, to die and desegregate what was created in birth:

NON-AE studies the Γractal Γenerator, T, the operation of the 5th dimension and beyond, which completes, the last of the operations studied by humans, ∫. A new operation is needed. We use often concepts of all sciences, including math. So in group theory we could consider the Fractal Generator of TimeSpace Organism (t.Œs) the Group with 3 equivalent type of elements, quanta of past, present and future. If we consider each of them a single element, then we define past and future as the inverse elements, and present and the identity element, considering the construction of the Algebra of the generator group:

  • The Fractal generator is a an equation defined with 3 operations, ∆, the scalar operation, O, the topological operation and §ð, the operation of the Mind generation, @.
  • It has an identity function, called present, Ø
  • Two inverse functions, past, | and future, O.

For example for the Time mind generator, the operation gives as:

| @  Ø = |;  Ø  @  O = O;  | @ O= | @ Ø;  O @ |= O @ Ø

The the fractal generator of timespace has the structure of a group. Regarding if it is or not Abelian, it is relative. As  WHILE PAST x Future creates a present, then first ‘element’ to arrive in time will also be the first in a second generating operation to relate to the created present and then | x Ø = |  ˆO x Ø = O

So in two operations a dominant past will convert a future into a present and then in a second probabilistic equation into its past.

The best graph two study it is the Complex squared graph where i² is the negative real, its conjugate the positive real and the real the squared positive with a slight tendency to negative in the negative squared, which externally seems a squared 2 -dimensional positive, but within its vital energy it has two negative elements, unperceivable outside the squared circle.

Squared circles in geometrical form are circles in numerical form squares, as the graph shows (1 is a square space, over which we can lay the spherical 0-1 form.

The previous translation to mathematical space of existential algebra though is a mere, consideration to show that we can study it with the tools of group theory but this is not the purpose of future analysis of beings. RATHER IT IS BETTER TO TREAT the operation of the fractal generator,⌉⌈, in its two inverse elements and identity axis, with the language of past, present and future and 5D we have been built, forgetting any pedantic language of Modern algebra.

It is though useful to consider as the next ‘operation’ of stience, the study of the generator and its group in isomorphism with the groups of classic algebra, because we could consider that such isomorphism makes a strong claim for the generator of timespace organisms to be also the generator of those groups, and in that mood i have casted the posts on classic algebraic groups.

Now to the operations they mean really what they say:

Past x Future = Present (x past) = Past = 4D: S for entropy and ∂ for the finitesimal quanta ∂S

Future x Past = Present (x Future) = Future = 5D, ∫ for integral sum and Γ for the generator equation it integrates

Present x Past = 1D: motion $ for lineal motion, t for lineal time.

Present x future = 3 D motions: Ω for the arrow of time, § for the log.

Present x Present = 2D Iteration: Pi for networking between points, ∑ for a herd configuration.

which we can write also with the symbols of space-time to obtain even more varieties of the Algebra of Existence in which two dimensions are operated by ±, x÷, S†: Log; ∂ ∫, Γ…

 t,∏,Ω,   ><≈><  ∑, $,,§,S,∫ 

The 3 operations of existential algebra are thus, ≤>≈, the 3 symbols used in those texts, which mirror two different kaleidoscopic dimensions of space and time through operations known to science.

The first being is not motion but form, as we do not perceive pure motion. But then the operation is obviously counting numbers, the line.

Both are thus connected to the postulates of non-e:

5th dimensionL ∑∆-1>∆º Generation (Social evolution)

____Emergence: Birth:

1st dimension, fractal point, perception and growth: operation counting numbers.

2nd dimension, second postulate: line, operation, moving polygons: Operation, speed momentum

3rd dimension: network organism. Operation Energy: Reproduction, ∑∆i(ego)>∆i+1 (world)

4th dimension: power entropy: ∆i<∆-1

___ (Death) Next generation:

∆-1: 5th dimension, generation.

It is then obvious that the ∆-1: ∆º(∑=∆1):∆-1 is the cycle to express here.

And as such the operation, ∆, is a view of those planes of existence, the world, ∆+1 where the whole ∆º exists made of ∑∆-1



The simplest equations of science are those generated by the S=T symmetries.

‘God is the seer of time, of a higher logic than the logic of man’ Saint Augustine.

‘The Universe is a ternary space-time fractal. made of infinitesimal parts, that co-exists in three simultaneous topological regions of space, three sequential cycles of time extended across three scales of the fifth dimension’. ls

How the Universe reproduces its actions, super organisms, species and planes of energy and information? Through its ternary logic as nothing exists, if it does not have three topologies of space, three sequential ages in time and extends through three scales of size. Reason why we can describe all systems of reality with the fractal generator.

We shall call therefore the study of the ternary laws that ensure the existences of all beings, ¬existential logic or i-logic, as it comes after a and e and it is a key symbol of GST.

Thus Existential Logic, ab. ®, deals with the rules of ternary logic that define the existence and extinction of beings and the algebraic equations derived of the fractal generator that define the possible events and species of reality and those who break the laws of existential algebra and cannot therefore be possible.


‘The separation between past, present and future is an illusion’ Einstein; on the deterministic world cycle of time beings and the 3 arrows of time.


What is worth of it.

As algebra cannot exist without the logic elements that connect its numbers, operandi and variables, which ad a new dimension of motion to each point that becomes then a curve in analytic geometry.

So it is necessary to make some statements on those logic statements.

As a tool for his thinking, Aristotle developed a magnificent system of formal logic, that is, cast-iron argument that starts from admitted facts or agreed assumptions and draws a compelling conclusion. In treating science he first tried to extract some general scientific principles from observations, a process we call induction. Then he reasoned logically from these principles to deduce new scientific knowledge. His system of logic was itself a magnificent discovery, but it cramped the development of early experimental science by directing too much attention to argument. It has influenced the growth of our civilization profoundly. Most of us never realize how much our pattern of thinking has been influenced by the age-long tradition of Aristotelian logic, though many thinkers today question its rigid simplicity.

It argued from one absolute yes or no to another absolute yes or no; argued with good logic to a valid conclusion, provided the starting-point was valid. “Is every man mortal?” “Do 4 times 3 make 14?” “Do 2 plus 2 make 4?” “Do all dogs have 7 legs?” We answer any of these with an absolute “yes” or “no” and then deduce answers to questions such as, “Is Jones mortal?” “Does my terrier have 7 legs?” But try the following: “Is self-sacrifice good?”, “Should I escape dine for work?”

These are important questions, but we can make fools of ourselves by insisting on a yes or no answer. If instead we spread our judgments over a wider scale of values (those of ∆-arrows of social evolution) and are aware of the ‘branching’ of actions to choose at any moment of existence (between ±∆e, i, œ, u space-time cycles), we may lose some “logic” but gain greatly in intellectual stature.

So we can say yes, self-sacrifice is good when it is for a higher good – the social group; it is NOT good when it is imposed by hate-memes against the nature of being human (religious inquisitions); since we ad the ‘logic arrow of causal, social wholes’, that structures the Universe. And the same goes for the second question: No, to feed is the second ‘actions’ on the pyramid of choices, and we cannot ‘deny’, the survival actions of the Individual, unless they result in a higher good for society, which most work, today dedicated to create and work with machines won’t.

Now we realise then that as arithmetics was the beginning of ‘number theory’, Aristotle’s logic, was the beginning of ‘causality’ in the Universe – its most simple forms.

In the complex scalar, multi-choice Universe, while there is still a strong determinism, there is a constant branching of futures (you can eat only food not oil and you need to eat each day, but you can choose between work and eat, sex and social leisure, making slight variations on your world cycle).

And in that sense, the paths of modern logic, which has tried more of the same – dogmatic yes/no, computer-influenced simple one-dimensional causality and ‘Axiomatic methods’ of absolute truths, is not very enlightening on how the deterministic-branching Universe of logic works.

So we shall just merely comment on Aristotle’s work as a first step, a first doodle on the sands of logic.

Aristotle’s logical writings comprise six works, known collectively as the Organon (“Tool”). The significance of the name is that logic, for Aristotle, was not one of the theoretical sciences. These were physics, mathematics, and metaphysics. Instead, logic was a tool used by all the sciences. Hence for the first time, the ‘superiority’ of logic, the language of time, above all sciences, INCLUDING physics, the science of motion, appears, justifying that a T.Œ must depart from Philosophy of science and its temporal-logic, spatial-geometry (and yet to be found 5D-organic) and 0-point (mental), properties common to all systems, NOT from physics (first scales as originating through ‘material substances’ all other scales in a ‘mechanical’, how way).

Of those properties the Greatest of all Minds of western mankind till Leibniz, DID in fact recognize them all:

– Mental properties. Aristotle affirmed all beings are ultimately moved by a 0-point, or unmoved central god (the mind of each system, antecessor of the Monad and the fractal Non-AE point)

– Logic properties of time causality, studied in this sub post.

– Organic properties, as he was a biologist first and foremost.

– Mathematical, geometric, spatial properties (which he saw as secondary unlike Plato, and indeed, they are the ‘details’ which allow us to ‘study’ the contingent beings.

This was also recognized in Taoism, where the Tao-logic properties, of dual nature (yin-yang combinations) were above the ‘details’ measured. Taoism as Buddhism and Hinduism, did understand better that dualist logic of the Universe. But as science in the west is born of Aristotle and Plato, we do not treat it here (I was though the world chair of duality for a few years at the International systems science society’ conferences, where I did talk of all this often.)

Let us then deal with Aristotelian logic, which has 2 fundamental simplifying errors, transcended to modern science and maths:

– The error of single causality, A causes->B means B does NOT CAUSE A . THIS IS FALSE. A(Past) x B (Future) cause C is more proper.

– The error of equality, A=B is possible, if B has the external similarity with A. This was the 3rd Euclidean postulate, source of many errors today in physics and science, = is either ≈ (similarity, as we cannot see all the information of the being) or ó transformation, or change of state. So A=B, might be A(S state) <=> B (time state) as in E(S) <= > M(TO) in Planck’s notation (c=1).

Yet there are many important advances worth to mention. Let us summarize them.

Aristotle’s logical works, in their traditional but not chronological order, are:

1.            Categories, which discusses Aristotle’s 10 basic kinds of entities: substance, quantity, quality, relation, place, time, position, state, action, and passion. It MATTERS as a forebear of the properties of Space vs. Time, SE óTO dualities.

2.            De interpretatione (On Interpretation), which includes a statement of Aristotle’s semantics, along with a study of the structure of certain basic kinds of propositions and their interrelations. It is a forebear of Universal Grammar.

3.            Prior Analytics (two books), containing the theory of syllogistic (described below).

4.            Posterior Analytics (two books), presenting Aristotle’s theory of “scientific demonstration” in his special sense. This is Aristotle’s account of the philosophy of science or scientific methodology. It introduces the Experimental method, today so often ignored by Platonic mathematicians like Mr. Hawking (no evidence of black hole evaporation, rules out its mathematical beauty as real).

5.            Topics (eight books), an early work, which contains a study of no demonstrative reasoning. It is a miscellany of how to conduct a good argument, irrelevant, source of future rhetoric mistakes. As it shows its:

6.            Sophistic Refutations, a discussion of various kinds of fallacies. It was originally intended as a ninth book of the Topics.

TOPICS. ITS MODERN VIEW – the webbing of the future

Aristotle’s work thus is limited but alas, amazing for the age.

Further on his interrogative techniques as a universal method of knowledge-seeking, DO resemble the way TERNARY logic constructs its present, from THE KNOWLEDGE OR limiting PARAMETERS OF PAST, AND FUTURE, which will become the flux of present reasoning.

Indeed Aristotle was especially interested in strategies that could be used to “win” such “quizzes.”

Aristotle noticed that in some cases the answer is completely predictable—viz., when it is (in modern terminology) a logical consequence of earlier answers. That is, the future is most often deterministic as a causal chain. Hence it ALREADY EXISTS, when the past appears.

But that’s all what his absolute simple truths can master. As we have said the branching of future paths and the ternary causality of each point of time, which happens because at least an Spe, ST and tiƒ element fluxed to ‘create the space-time event’, was well beyond his work.

Its limits.

This said, Aristotelian logic is a ceteris paribus analysis of reality based in a single causal arrow of time, A->B, when as we shall show in existential logic reality is webbed through the ternary logic of entropy < energy > Information, which is the content of ‘existential algebra’, treated in a whole post of its own, the logic of the fractal generator of timespace organisms (t.œs).

Hence the incapacity of the axiomatic method based in Aristotelian logic to find the absolute truth of mathematical statements and discern its fictions from its truths, which require both a proper upgrading of fractal points sequential numbers theory and the experimental method to see what is ‘real’.

Of the first consequences of considering the logic of the ∆st universe we must highlight the LACK OF EQUALITY as all forms in a vital fractal space-time Universe that do NOT occupy the same space and have the same form (property of bosons), DO NOT have equality, but similarity, and congruence of its ‘external membrane’, which means we use ≈ or ≤≈≥ >≈< instead of = and this implies we cannot beyond abstract algebra merrily move all kind of ‘real symbols’ around in mathematical physics and other equations, beyond the algebraic methods of resolution of equations to accept that everything goes and everything equal (the classic case being e=mc2, where mass is NOT energy, but rather E($) < c x c (ST) > M(ð), A FUNDAMENTAL EXPRESSION OF THE fractal generator in physical systems.

So a HUGE subfield of 5D² is the proper analysis of EVERY equation of physics under the rules of the Generator and its ternary logic and laws of similarity (5D postulates of non-E geometry) to discern what it is allowed as ‘final results’ beyond the algebraic methods of resolution, as ‘real’, and what turns out a false result/parameter born of the manipulation of those equations and operand.


The formal stience of 4, 5 Disomorphisms in the mathematical mirror is analysis, which deals directly with the relationships between  ∆-1 ‘finitesimal’ parts’  and (in)’finities’. Two new terms we still accompany, with the lost inflationary  term ‘in’; since infinitesimals and infinities are a Kantian paralogism; as all planes have a limit in its quantic units, and all wholes a finite circle that encloses them into a relative 0-1 ‘circle unit’. 


So we might wonder if the ‘group’ of all motions in space-time studied with group theory would be the best approach for existential algebra.

The answer is not, because now that we know what reality is, and have the fractal generator, it is much more realist and meaningful to use it, while borrowing whenever needed concepts from algebra and analysis.

What matters to us is to solve the Disomorphisms, the common laws of space-time motions and how one transform into each other. To understand this let us consider the first huge discovery that put analysis on the center of science since its inception:

Alas! Due to the scalar duality, derivatives in time turned out to be inverse to volumes of an integral of space; when they were considered first two different operations not related to each other; derivatives of time motions and volumes of spatial form.

Yet according to the Galileo’s paradox, in 5D², time and space are the two sides of a holographic 2-manifold dimension.

So a motion in time quiets becoming a new dimension of space, and indeed a moving curve is equivalent to a surface, it generates when we measure as space. And so lineal time-motions produces space surfaces:

In the graph, the seemingly simplest of all equations of analysis, still encodes some relevant information about reality.

This of course must be done because reality is bidimensional and a dimension of space goes accompanied by a dimension of time, generating as in the previous graphs, the motions=changes, S≈T≈S≈T that shape reality.

What kind of beat we study is normally a symmetric beat around a central ST element, which we might call if we were to adopt die-hard mathematical creationists, (we won’t) Group theory, the S and inverse T dimensions, being ST the neutral element…

But as we have already mentioned group theory which was the best available form of existential algebra at the time quantum physics was discovered and so it has been used as a pest (Weyl) to classify and fix mentally all the elements, is obscure in its meanings. So we shall work better with the fractal generator. 

This said, there is a certain ‘loose ‘isomorphism’ between the Dimensional motions described by the Generator and GROUP THEORY enough to be able to study one conceptual system with the other.

We consider a few kind of motions in ∆st with the concepts of groups and its operations, to see in that sense if a Group would describe everything in the Universe as the monkey method seems to indicate.

-. Motions in present space are either unisexual reproductions along a line of space of a single form, or mirror symmetries between ‘2 genders’ that reproduce a third element. We shall call in the jargon of group theory, this operation, +.

And immediately we realise they are NOT associative. If A makes love to B, generating c, and then C makes love to D, the T.œ generated will NOT be the same that if B makes love to D and the result makes love to A, unless we talk of identical genetic pooling, that is identical reproductive processes happening on the lower scales of indiscernible beings. Then 2 identical electrons but with opposite spin do produce a third identical electron.

More troublesome would be if A reproduces in its adjacent place B and then in the next place C, A->B->C. It is not though possible as there is a non-adjacent vacuum in B to do A->C first, plus we are talking of a single element ‘copulating’ so to speak with himself. Then we are into a possibility to be a ‘magma’, a ‘loop’ or a ‘quasi group’ but as it happens none of them have ‘commutability’, and this do happen in reproduction, AxB = BxA, doesn’t matter who is up or down as long as you copulate, but of course, we could go on and think that copulation is lineal, and so if A man copulates from behind does not carry a child (: yes, obscenity brings here clearly the whole thing.

More seriously if we return to the only elements that associative – IDENTICAL elements things can be worked out to look like an Abelian group, but the question is for a why vital purpose, why not to describe merely the reproduction of particles into identical particles as an action of reproduction instead of being pedantic and talk as a isomorphic, or homomorphic, transformation or representation, etc. etc. that reveal nothing of its purpose and meaning?

Group theory thus is mostly an attempt to classify all what exists in different properties, which are NOT that relevant, beyond mind categories, what Kant calls regulative concepts. 

Of course as it is a method of exhaust combinations, permutations of parameters, it did help to find when those groups of permutations of the elements we know should resolve a parameter can find the solution (Galois groups).

-What about motions in TIME?

LET US now try the inverse concept of a group, with 3 only elements, motions from past to future or future motions, from future to past or past motions and present motions that leave the system unchanged.

It is then obvious that present is the identity element, as a present motion repeats the being that does NOT change. Past and future are the inverse elements, as they combine to give present (entropy x information = energy, S x T = ST).

And so if we call the simultaneous being in Space, any DISOMORPHIC T.œ, the ‘operation’ completely reversing the intuitive image of a Universe made of spatial beings – the maya of the senses, but rather made of time events, past, present or future flows, alas, the Universal Generator becomes a non-Abelian group, the operation being ‘creation of T.œs’ and the elements past, <, present or identity element, ≈ and future >.

So if we call motions, slides of the Generator, > < ≈ and the operation, the Generator itself (any TOE) ONE motion≈element slides the Generator, which is any TOE, from past-$t to present, or from present to future.

But a present quanta of time leaves either past, present or  future unchanged.

and a motion of future to past, §ð <$t does not commutate but activates ∫∂-4D entropy and death, which must be considered as in most simple systems, where the death of the father feeds the new generation (as in arachnids among higher species), a resurrection of the cycle.

So the Maya of the senses would the being – a mind simultaneous view, NOT operating with other element of the set but with himself and hence NOT proper of any classic or Non-Æxistential algebra.

Yet if the elements are changes in the state of the being from past to future or future to past, there is indeed an identity element, present, as a system that operates with present, does NOT change.

So we could then consider a group view IN WHICH the operation is a motion in time defined and the group elements are the infinite §œT of all T.œs in existence. We need then to define two operations, + present and x time motion which in a world cycle can be from past to future to past to future from youth to old age and death and alas, we have our desired group which is non-abelian (commutative).

The concept is deeply interesting in fact to connect existential algebra with quantum physics and study what is REALLY a particle as a pure motion in time and we shall return to such concepts as today quantum physics is casted in the language of SU3 groups (but increasingly more realist and less interested in the ‘pest’ of group theory or rather mathematical creationism).

Logic proof of ¾xistential logic.

‘2 things i deem infinite the universe and the stupidity≈lack of existential logic of man’

The proof of the existence of a ternary logic depends on the infinity of the Universe, which is in itself a property derived of the nature of fractals, which can be divided ad nauseam, that is, of ∞ scales of the fifth dimension.

(I am not though using formal logic, pedantic forms of expression to prove but classic logic, the logic embedded in the verbal syntax of reason, which is FAR MORE POWERFUL FOR MAN THAN ANY pedantic version ‘imagined by Hilbert like individuals who pretend to substitute the logic of the whole human species)

Indeed, the ONE DOES NOT EXIST PERSE IN TERNARY LOGIC, because if the one exists per se in a dynamic universe, of finite parts, its existence will be limited to the space-time occupied by the one, which is an infinitesimal compared to the infinite duration of the Universe in time, and its infinite extension in relative size in any scale. We just need to realise that a larger scale will be so vastly large in its ‘point-sizes’ compared to the infinitesimal, that the o-will not exist.

So it is necessary to extend backwards and forwards in time, in space and in scales reality. And as systems are dynamic, that motion upwards and backwards can only be real if it is ternary.
In the graph, the ternary principle in physical and biological systems.

This is experimentally evident. So the second ‘proof’ which must be besides ‘theory’, ‘experience’, shows you that if you want to exist you have to reproduce in three discontinuous generational cycles. You exist because a father conceived you and you will keep existing because your son reproduces your genes, and generally speaking the three generations co-exist together.

This is also the rule in space: you exist because you have three topological parts, body, head and limbs. Physical systems also coexist in ‘three wave-packets’ and three parts (complementarity principle, particle-weave-field: pilot interpretation of quantum physics). So the ternary logic makes possible existence.

In the graph, we see ternary logic in quantum physics, the system is ‘both’ (i have no found a good adjective for 3, so we settle for 2 showing indeed human logic faulty with wording) field, particle and wave. And it goes through three generations in any possible event (the graph shows the transformation from a moving wave into a stop-particle.

The examples of ternary logic would be infinite.

So, Why then we are NOT aware of it? BECAUSE THE MIND WHICH DOES NOT EXIST without the other 9=3×3 dimensions, HAS A SINGLE DIMENSION THAT GATHERS THEM ALL. So the mind tends to have Aristotelian logic, @ (expanded symbol for the mind). But for the mind to exist it must order a ternary super organism, in space time and scales, to become at least ∆•±ûst (dust of space-time).


‘The smallest point is a world in in itself’ Leibniz, on the fundamental particle of Reality: The fractal Mindworld of space-time.

‘God is the seer of time, of a logic higher than that of Man’. Saint Augustine

In the graph the existence of 3 topologic arrows of space-time, make the Universe more complex in its minimal principles:

Spatial entropy (-Spe) and In/form/ative time clocks,  (+Tƒi)  combined its present space-time (ST) actions with momentum.

And yet, once this first burden passes, things become far more enlightened and simple to understand. Indeed, the next stage is the organisation of the three arrows of space-time into ‘space-like, simultaneous super organisms’ and time-like, sequential world cycles that integrate the three arrows of time.

It then becomes evident that the fundamental principle of science, the principle of conservation of energy derives from the zero-sum value of a world cycle of life and death of a system.

So when we add up the three arrows in a finite duration we obtain the integration in time of present momentum that become a conservative energy world cycle.

And when we integrate in space the whole system and its arrows we observe a synchronous super organism made with the 3 arrows in its spatial form as the sum of three topological networks:

In the graph we see the form of those three arrows as the topological components of all systems of the Universe.

So in the same way small steps are integrated into full cycles, the three arrows that seem separated, become a full cycle of existence and a full beings.

There is though a more complex, detailed view of those systems, if we consider what they do in the ∆+1 world scale where they exist.

We can then observe that each system will be a sequential sum of ‘cycles’ the being perform in the external world to ‘replenish’ its internal physiological networks/arrows: feeding its body with energy, moving its limbs, absorbing information for its brain and so on. So we can perceive the being as a knot of time-space cyclical arrows.

And finally in its simplest most abstract mathematical view, we can compare any world cycle with a π cycle, where the entropy-energy-information, ternary arrows are equivalent to three diameters rising and falling the wolrdcycle of the sπcies structured by those time arrows:

In the graph, the interaction of the three arrows of time as the description of a world cycle. In the left the three arrows sequentially between birth and extinction, when after the third age of maximal information the system collapses and returns to its zero sum, dissolving into cells. In the middle the first rational explanation of the sequential order of those arrows, where form, in-form-ation arrows are yin, — broken lines, and entropy with less information, yang_ single lines. In the third graph a vortex of time, or third age of increasing form and diminishing entropy/energy, prior to the final death of the system by an entropic explosion of all the warped form. Time arrows thus combine both sequentially in time and simultaneously in space, and the symmetry between both ternary parts is the essential nature of reality, but we can also do as in the graph ceteris paribus analysis of the arrows in time and in space, giving birth to the concepts of a world cycle of existence (graph) and a super organism of topological space.

So there are as usual several ∆-scalar, Spatial, Temporal and space-time views of a being made of time arrows, as we can observe them in the internal ∆-i part of the being, its external ∆+i world, or its ∆º membrane, which is the being as a ‘topological surface that relates internal and external, physiological and world-like space-time actions through transfers of energy and information between the inner and outer world.

So time arrows interact in many different ways, which makes its rules of ‘existential algebra’, more complex than the ways we represent today space-time phenomena. We resume this added complexity stating merely that in GST, time logic is not one-dimensional hence not-aristotelian, and spatial dimensions are non-euclidean, as points do have volume parts and an inner ∆-i world.

Hence the use of the concept of ®rrows of space-time.

This section thus will be dedicated to the  Non-Aristotelian logic and  Non-Euclidean mathematical formalism of GST (the generator of space-time systems). As such it is the more complex. It is also the post and sub posts where we upgrade the sciences of logic causality and euclidean mathematics to its needed non-ae versions proper of a fractal space and cyclical time, scalar, organic Universe departing from the Generator of all ∆ST structures.

How do those time arrows knot in topological networks, it is easy to formalize departing of classic Non-E geometries. It is just a question of complete them.

In that sense mathematics and logic as languages do have also a ternary generator.

The generator of mathematics. Mathematics as a language also follows the rule of ® ternary logic, fractal space and scalar space-time, and so we can define a simple generator for mathematics as a language, considering its 3 sub disciplines that roughly mirror the 3 elements of the Universe:

∆: analysis;   S: topological, fractal spaces;   T: algebra;   •: logic and mathematical syntax.

Mathematics thus is the most accurate experimental stience, substrata of all of them as it deals primarily with the most general law of the ∆ST universe, when we properly translate its concepts and equations, upgrading them to an ∆@ST universe.

The generator of Logic: ternary Logic & Universal grammar

‘ The languages of God are Infinite’ Upanishads.

Even more fascinating that ¬E mathematics is ¬A-logic or ‘existential logic’ (ab. Existential Ælgebra), which deals with the causality of events in a world with 3 active potential arrows of time in each decision and event (max. entropy max. information, max. exi: reproduction). Consider for example the simplest space-time event: a clock-like cycle. You can try 3 things on that cycle: to repeat it with a π-motion, to implode it, increasing its informative vortex, or to expand it increasing the entropic space and decelerating its time speed. So the Universe is both probabilistic (the 3 outcomes are equally possible) and deterministic (with only 3 outcomes, there are  a fixed number of variations, as all time world cycles are also finite to develop them).

THE SAME happens for all languages, which all display a ternary ‘Universal grammar’.

Accordingly all languages have 3 elements to represent those 3 dimensional space-time symmetries across several scales:

Universal Grammar: Subject (Information pole) < Operandi (actions) > Object (space-time point).

In any logic language 2 symbols suffice to represent any being of the Universe. All languages have a syntax based in 2 parameters, one of information and one of relative energy that combine through a 3rd active principle, an operandi or verb, that merges them. We talk of a ternary Universal Grammar:

A (Informative subject) <Operandi/verb> B (energy/object)

The ternary, Universal grammar applies to all languages able to represent the systems of reality: from the code of colors (red that represents energy; blue, the color of information and green, the reproductive color) to verbal languages, where an informative subject relates to an object through an exchange of energy and information, described by a verb, shaping the genetic structure of all human languages 8. It also happens in mathematics, where f(x)= g(y) is the universal equation that summarizes all the others.

A fundamental sub-discipline of i-logic, existential algebra is the study of variations on the fractal generator, according to variations in the simultaneity (in space), synchronicity (in time) and resonance (in the ∆-scale) of the ternary topologies, ages and scales of any system. I.e: Spe < ST < Tiƒ is a different space-time event (an organism in which limbs/fields move, < entropically a body-wave, ST, which moves a head-particle, Tiƒ that an Spe>Tiƒ (where the body-wave is absent, hence we talk of a field moving a particle) than an Spe << Tiƒ (where the limb/field ‘destroys’ entropically the particle-head).

So the fundamental question of existential algebra is to map out all possible combinations in space and time of the scales and symmetries of ∆ST; establish the rule of engagement between them and apply the rules of ‘similarity, perpendicularity and parallelism, resonance, synchronicity and simultaneity, that are the bottom line of the causality, determinism and probable solutions of any system of space-time.

Diffeomorphic Dimensions. Each P0INT is a relative Universe.

In the graph, all systems perceive at least one language, interpreting with the same ‘grammar’ reality, to localize its energy, information, reproduce, evolve socially and try not to devolve, becoming preys of other systems. In the next graph we observe how different species perceive with different languages the Universe, but all of them ‘share’ some of those codes, specially the geometrical one. So all heads are on top. Yet each head is different in each scale and talks a different grammar, albeit with the same universal grammar, which reflects the fundamental equation of the Universe: E<=>I.

Given the simplicity of the Game of Existence – despite its infinite complexity in its details, iterations and combinations, all species, from the simplest atom to the biggest structure can play the game and understand it and relate to all other species, which will play the same game from their selfish point of view. And so all individuals of each species plays the game, and ‘talks’ about it, with similar species and understand it with information provided by self-similar ‘ternary images’ provided by a language that shares the properties and emergent qualities acquired in each scale.

But of more interest for General systems theory is the ternary structure of all linguistic systems in all scales; what we call the Universal Grammar, such as:

Space-Dimensions: Height (informative dimension) <Width (reproduction) > Length (energetic motion)

Mathematical languages: X < Operandi> Y

Forces:  Particles (information) < Universal constant: action, exi or ratio e/I > forces (energy)

Code of Colors: Blue (information) < Green/Yellow (Reproduction) > Red (energy)

Verbal code: A (Informative, I-subject) <verb/operandi (action) > Object (energy)

A(Human) < verb (action) > Object (energy of human)

The ternary Universal grammar expresses the arrows in verbal languages and human super organisms.

It follows that not only mathematics (geometry) is a mother science but also logic (the analysis of the causal processes determine by those arrows) is even more essential, and further on ‘evolution’, the evolution of forms and functions in temporal patterns summons them all. So those 3 sciences, spatial geometry, temporal logic and its combination, evolutionary theory, are the ‘3 subdivisions’ of general systems sciences, which apply to each science explain it all.

Over them, there is general systems sciences, the science this book can be considered its foundational book (as it formalizes and structures and advances all previous works done on it.) Below them, each specific science studies a scale of social evolution in the universe from the smallest physical systems, to its complex biological organizations and beyond its social organizing systems.

Since science consists in the definition of the type of points of each relative scale of size of reality, from the quantum scale studied by physics, through the intermediate human scales studied by biological and sociological sciences to the higher scale study by cosmology

Once those points are defined, each science studies their 4 actions, which define all its events and forms.

Study of the 3+1 actions: its bits of information, bites of energy, reproductive seeds and grammar.

Yet we study those actions through the 3 scales of size of the system, its bits and bites, normally of the smallest scales of existence, since:

–   We perceive with the minimal bits we can process to create the more detailed maps (<i-2).

–    We eat sometimes, similar species but break them into smaller parts (i<2). For example we eat meat but break it into amino acids, below the cellular level.

–   We reproduce a seed from the lower plane of existence (i-1). So we produce seminal cells and electrons reproduce emitting photons that collide and recreate an electron.

–   And finally we communicate with a language of information at the same level we exist (i), in order to create a more complex whole (i+1).

Thus we observe, as in many other laws we will be developing in this book, an infinite number of harmonies between sizes, ages, forms, functions in all scales of existence.

Actions are expressed with bites and bits of inferior scales. We perceive the smaller possible ‘bits’ (<i-2), eat bites of the inferior i-2 scales, reproduce with seeds of the i-1 scale and share energy and information with species of the same scale to create.

The bits of information (i-2), will usually be entities at least two smaller scales of existence.  The smaller they are, the more detailed the map made with its ‘pixels’ will be. So we can consider the possible existence of ‘gravitational minds’ that perceive a scale inferior to us.

For example our eyes perceive light photons, the minimal scale of form. Ants perceive chemical pheromones; computers perceive electronic flows; all of them ‘forms’ of a minimal scale in relationship to the species that perceive. The bites of energy will be pieces of the same or inferior scale. So we eat ‘living beings’; electrons feed in the lower scale of light; and black holes in stars. Yet once a system feeds it will further reduce what it feeds on another scale to obtain basic bricks to reconstruct once form through ‘2 scales’. So our body reduces food to amino acids, the minimal parts of life. And electrons probably reduce light to its magnetic and electric constants to create their fractal nebulae. And nations that conquer other nations reduce their people, minimal unit of the nation to slavery and take their gold to print their own coins.

So as we move upwards in the complexity of the actions we study there is a ‘growth’ of informative similarity of the bites and bits and a growth in size, such as informative bits are less similar and smaller than the bites of energy we feed. And this pattern continues when we consider the ‘expressions’ of the actions of social evolution and reproduction.

The expressions of social evolution are languages, which are naturally produced by the informative center of the system; except in the case of enzymatic evolution in which the language is external to the species (a species which acts as the reproducer and catalyzer of evolution of other species; cells with viruses, humans with machines metal atoms with carbohydrates and so on). So the language is a ‘part’ of the being, often corresponding to an i-1 inner structure, though transported by an external force.

Finally the larger, closer form to the organism is its reproductive seed. And hence by the law of parallelism between species, the ‘bit’ of information for which the organism cares more: small quarks among simple particles, cellular seeds in life; jets of matter in galaxies.

Æxistential ¬ælgebra.

Another conceptual expression of algebra is Existential Algebra (ab. also æ¬æ), which translates the rules of ¬Æ to the vital, first ‘simpler æ view’ of selfish points of view practicing its local algebra of existence, trying to last and through its åctions achieve a maximal reproduction of its self.
Existential algebra is thus more complex than either æ or non-æ as it works on the troublesome relationship between aristotelian, euclidean beings in a single space-continuum with a single time arrow as present humans are, ‘subjective one-dimensional minds’ vs. ‘objective, polidimensional non-ae’:
In the graph the subjective æ view, confronted with the objective multiple logic of a non-æ reality, is the next stage of ‘evolution’ of non-se and ae algebra. We shall consider this the proper level to marry the non-euclidean point analysis, which is externally mostly aristotelian with points producing ONLY an arrow of time at each time. THIS FUNDAMENTAL LIMIT OF ALL POINTS hardly understood by A-logicians is the key to jump into the i-logic of multiple points of space acting the same time-action and SINGLE POINTS OF TIME, PRODUCING SIMULTANEOUS TIME ACTIONS, something we humans do not make.
So we shall also consider the basis of æ¬æ seemingly contradictory confrontation.
 The existential algebra of fractal points is thus a decisive element of the understanding of reality. I have kept the ¬, as we are indeed virtual zero sums, so existence is also non-existence itself. It is essentially the philosophy of stience we can ‘perspire’ from ¬æ i-logic postulates.

Our interest, in a Universe in which there are constantly 3 choices of paths, S, T or ST to act or no to act (-1 action), with equal probabilities. is to map out a new existential algebra (ab. Æ) of all nature systems, with those 3 -1 possibilities.

Why the Universe has 3 positive ternary actions (and a negative, passive no-action) is self evident:

-1: The mind might merely observe and stops motion (•),.

+3: Yet the system might evolve towards higher entropy (+Spe), higher information (+Tiƒ) or might reproduce its space-time in repetitive cycles, which on the long term will become a larger ‘whole’ (∆).

So the existence of 4 elements, ∆•ST, 3 of increasing motion along the 3 paths of space-time (S, st, ∆st) and one of growing stillness (•), implies a more complex logic with 4 potential actions for each bifurcation of past-present into the future.

Of course, if we were to study a ‘fresh beginning’, the probabilities of those futures would be the same. But as the Universe is a game of memorial, informative motions, it follow that as the game proceeds, the future paths become determined by the long cyclical causality of individual actions and past cycles to be completed into the future.

screen-shot-2017-01-08-at-00-22-33So while paths do have a possibility to be modified without expenditure of energy, closed time cycles impose their ‘inertia’ and so the perfect potential ‘fourks’ of space-time (four point forks). The image is meaningful: as always we have a ‘lineal, entropic knife’; an informative, cyclical ‘spoon’ and an ∆•ST, 4-dimensional fork to both cut and  form the food in present space-time. And you would choose, if given a single pick, the fork precisely because it can cut laterally and it can scoop the food. Everywhere the rules of GST will enlighten ‘why things are as they are’; and the causes of the past or the fourkations of the future will be ternary±1.

The causal ‘bifurcations of timespace’ thus are now ‘fourkations’ of space-time. And so the extraordinary one-dimensionality of human minds and its languages are out of meaning. Those arduous arguments between wannabe geniuses sponsoring their ‘point of single view’ as the real cause must cease. Ceteris paribus is simplification. For a being to exist, for a cause to act, for an event to happen in fact it will be because 3 past causes have converged to form a whole time-space ternary symmetry. Think of your actions, when you move, the mind first ‘thinks’ in the motion; the body then provides the energy; the limbs convert it into entropy. It would seem there is only one cause to action, the motion of the legs, but actually 3 actions converged in a ‘dharma of time-space’ to make it happen. Yet for the non-action only the mind is needed to stop action; which therefore is an ‘easier path’.

So the languages we use to portray that process are naturally different from the classic ones. And unlike analysis so close to the social scales of GST and fractals & topology, essentially ‘the’ spatial science of the fractal Universe, algebra as it is understood today, is basically a synoptic way to deal with topological and analytical theorems. And its proper structures, sets and groups must be understood as expressions of our social groups and ITERATIVE, MOVING laws, based in symmetries, transformations and motions through ‘polynomial scales’. But as the language is so different, we rather start afresh and include as we go along the main field worthy of classic algebra, which is NOT sets but group theory.

Temporal, Æxistential Algebra, studies the organisation of systems, through time=change; that is by means of transformations that provoke motions of a system, and create variations of systems, according to Group theory. Still it is worth to remember the basic elements of Algebra and its equivalence.

The ternary operandi of Æ… and its symmetry with ∆ST elements.

Actions and its causes are thus the ultimate inquire of existential algebra. Why and how motions of space-time happen. And what is the formal way to define them?

What we are interested here, beyond explaining the laws of classic algebra, such as group theory, with so many practical cases in science, which translate the TSymmetries and motions through ∆-scales, is the nature of existential algebra and the different equations of motions and species creations, through those motions and actions, which always render a certain ‘syntax’:

Past ‘Operandi’ Future= present.

The operandi between past and future, entropy and information, thus define what kind of present space-time event or entity appear to us. Because we have 4 elements to define existence, operandi are many, not only a simple ± symbol to ad or rest the same type of beings or motions, as when physicists study only locomotions and reduce all to a Hamiltonian ± operandi between the two O-potential and |-kinetic ‘states’ of form-entropy.

So each motion of time will have a different ‘algebraic operandi’, departing from our initial ‘Universal Grammar’.

We shall consider in this introduction the main operandi of the 7 motions of the Universe of which the 3 more important are:

Locomotion: Hamiltonian (Entropic, kinetic Past motion ± Future, Potential motion = Present (superposition motion of waves).

Reproduction: Past (field)  x Future (information)  = Present (iteration)

And the rule is simple, from classic algebra: a superposition or sum is of the same ‘species’; hence ‘energies (time-like)’ or ‘momentums’ (space-like), etc.

A Product can however combine different species. So it is normally a motion, which involves a space and time-like parameters:

Reproduction mixes the Spe and Tiƒ, different ‘genders’.

Finally, the 3rd mode of algebraic equations, polynomials/logarithms, correspond to the ∆-scale of growth or diminution.

So again we find an immediate relationship between the 3 elements of reality, S or T, ST and ∆ST, in its growing complexity and the 3 basic operandi of algebra, sum, product and polynomials.

What about the more complex scalar ‘motions’ of space-time? They are not that simple, as they combine elements of the pure ones. But as all ternary, Universal grammars, the complexity is born of the iteration of those elementary motions:

  • Evolution is a change in the topology of a system, so essentially a process of space-time morphological in-form-ative change better described with topological elements.
  • Growth and diminution involves reproduction and evolution of topological form and its inverse.
  • Birth and extinction represent an ∆±1 change, combined with an ∆T increase of information or a loss of it all ∆S, which are often expressed with logarithmic scales.

And so most motions involve both a Past to future, ∆+1, social evolutionary arrow accompanied with changes in topology. And as such are pure ‘GST’ Ælgebraic motions, better described with the formalism of Æ and its symbols S>T, T<<S, ∑∆-1 Λ ∆… and so on.

Since in its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; the definition holds. And as algebra is a unifying thread of almost all of classic mathematics, so happens with Ælgebra.

In that regard, classic algebra (we shall call arithmetics) includes everything regarding those 3 operations, ±, x, % and log, x². And its symmetry as we have seen is immediate.

While modern algebra deals with the study of abstractions such as groups, rings, and fields; sets and Boolean algebras; and categories and elements… So we can subdivided Æ in 3±1 age subfields:

  • Birth: THE study of æ proper (existential equations).
  • Youth: of classic polynomial equations or arithmetics (S,t; st and ∆ systems in its interaction).
  • Maturity: of abstract structures, or algebra proper concerned, with group theory (the internal social structures of the Universe).
  • Old age: of inflationary information (set theory and other ‘weird’ algebras)
  • Extinction: the transference from human minds to digital minds (computer algebra, boolean algera)

Let us consider them.

The simplest equations of temporal algebra which form together a plan describe the creation and destruction of super organisms, through its motions of existence, most of them established in a sequential order given by a world cycle.

If the world would be a single scale this would be a simple analysis of Spe<st>tiƒ changes of topological varieties without the need for its internal network structure and its external motions. As those parameters of the inner ∆-1 and outer ∆+1 surface allowing constant exchanges of parts and motions on all those scales we must talk of the different arrows/dimensions, which a being has to manage in all its ∆•st cycles of existence:


In the graph at any moment a being can be defined by its state in the ∆•st scales of existence, that is, a certain ∆±1 location in its modular consciousness, a certain |xO=Ø topology in its flows of energy and information, a general Ωge in its total worcycle and so the best way to consider physics is as 3 different ‘huge sub-fields’, according to the general planes we observe, the quantum, thermal or gravitational plane, and under the hypothesis of ‘isomorphism’ and the quantum paradox of uncertainty, declare as reference the thermal scale, which is the better known in detail by humans ∆o thermal beings and above it the ∆+1 gravitational scale in its simpler mechanical locomotions, which are those that affect humans in its outer ∆+1 cycles of existence in its geological worlds.

Thus, he was led to the study relations of logical consequence, the four other books of the Organon, which transcended modern mathematics.

screen-shot-2017-01-28-at-08-52-16Aristotle nevertheless continued to conceive of logical reasoning as being conducted within an interrogative framework, which is in a way how the Universe webs the present as past to future to past back and forth, ‘interrogative paths’, stretch to the ‘principle of least action or most probable path, present, answer: In the graph, the best representation on how the future is webbed, by back and forth feed-back Spe (past)<≈>tiƒ (future) events is the fourier transform, of time-frequencies, which show between two end-points, how time cycles become ever more ‘informative’, and less energetic, but as they accumulate into a memorial tail, finally surprisingly loose its ‘informative form’ into a lineal, entropic, square wave, which is the end of the informative wave, dissolved in ‘lower ∆-1’ scales. Since ‘the separation between past, present and future is an illusion:


‘The possible ranks higher than the actual’. Heidegger, on the potential paths of future, which are never perfectly made.
Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being.

On the i-numbers of future times

II. ‘Generator’ equation of space-time beings: its ternary logic.

Γ. The Generator Equation and Universal grammar

The Universe can be reduced to a single equation, the ‘Generator Equation’ or Universal Syntax, Se≤Str≥To, which describes the 3 motions of time (<past-entroPy, ≈ pResent-Reproduction and >Future-Form) an its 3 relative ‘static’  forms of space, Se, the entropic pole, To, the informative pole, and Str, the reproductive mixed pole; AND ALL ITS COMBINATIONS.

Those combinations might be symbiotic, in which case we use the ≈,=, symbol, embedded in the central symbols, ≤≥, as the systems will stay in ‘parallel’, that is with the same relative motion-stillness to each other and form a larger stable structure of space-time (a super organism), or they can be ‘perpendicular’, ><, x, which means the system will transfer energy or information in a Darwinian manner that means the end of one of the 2 poles.

Think for example, of a a head, To, and a limb, Se, joined by a body, ≈, which are stable, parallel combination that maintain its distances and communicate energy and information.

Or think of a system with a predator, max. ExI and a prey, Min. ExI, which therefore act as the To, dominant informative pole that absorbs the prey as an Se, energetic source, which it will ‘inform’ and convert into its own predator form.

Thus we resume in the previous equation, the 3 motions of time (<≈>), the 3 forms of space (Se, Str or STi, To) and its two fundamental forms of relating to each other, ≈, parallel, symbiotic interactions, and ><, x, perpendicular, darwinian ones.

In dynamic terms the Generator is a feed back equation, which describes the < entropic motions delivered by the Se< limbic/field upon the system and the information produced by the To future pole that guides and hence decides logically the future position of the system. In static, spatial terms it merely means the structure seen as a harmonious interdependent whole. So the generator is a ‘Fractal generator, an equation which repeats the same patterns as time goes by.

Thus with those 3 simple elements in its 2 space-time states we can describe all systems and events of the Universe.

The Generator Equation is therefore a simple feed back equation, whose infinite variations, on the properties allowed to vary without changing the whole structure of the system, allow to describe all systems of the Universe. Those

Moreover, since the mind, O-∂till point x ∞ moving Universe = Linguistic mapping of reality, is merely a mirror of the whole, simplified into a linguistic syntax able to fit the image within the smaller finite space-time of the being, we can build a Universal Grammar of all languages departing from the previous equation.

Thus Logic and mathematical, even visual languages merely are ‘Codes of the Universe’ that help a species to interpret the space-time actions of other beings, in terms of its value as ‘Se, Str, and To’ elements.

So for example, in visual languages, we have the Universal Grammar that codes our perception of Nature around us:

Red-energy: Se<+Green – Yellow ≥ To: Blue-information.

In verbal thought, the equations found by Chomsky is:  To (Human, informative subject)≤Verb-action≥Se(energy-object).

And in mathematics is, F(t) ≈ G(s); where F(t) is a parameter of a time function that through an operandi (≈) integrates together a series of spatial elements or steps into a Time function, of larger duration, G(s).

Thus we affirm that the structure of all languages has a common Universal, ternary Syntax or Generator Equation.

Those 2 terms thus define the metalogic of all languages (we used the concept of Universal Grammar for many years, but after a few letters with penpal Chomsky, on the theme, I decided not to confuse terms, so we shall try to use more often the terms Universal Syntax, while Generator Equation, is the term used in fractal mathematics for any ‘seed-equation’, which by iteration will generate a fractal system).

Thus the Generator Equation≈Universal Syntax is merely the linguistic mapping of the whole, mirrored in a given o-point mind; and as the barebones generator equation is dressed with more complex elements, and multiple layers of iteration and complexity, it ‘becomes’ a being.

This Generator equation is written in different ways. So we sometimes write it as: E xI = ST±4,  an acronym version, whereas a pole of maximal motion, and one of maximal form, I, come together and perform a series of space-time actions across the different ±4 scales of the 5 Dimension, from where it obtains energy and information, to create a stable space-time, ST±4.

So besides using synonymous letters, to define the similar concepts of space and entropy-energy (S≈E), and time, information and cyclical clocks of form (I≈O≈T), in the previous equation we introduce an scalar 5D element (±4), needed to complete the description of the being NOT only in a single space-time plane as the Universal grammar does, but across the multiple layers of the 5th dimension.

Thus, we shall consider some aspects of the previous  2 equations in this post and how they are at the foundation of all mental forms of knowledge. First we will give a fast review of the structural elements of the duality of Space-time and the scales of the 5th dimension, and then we shall translate them into the elements of all languages.

Finally for those interested ‘mainly’ on human languages, there is an article on topological linguistics (the syntax order of the 3 elements of sentences, which define the character of cultures, according to the position of subject, verb and object), with a better discourse from an earlier age of higher lucidity in the section of U+1 social super organisms of mankind.

Unfortunately the beats of the universe are difficult to understand because the logic of present man, especially that of physicists seems ‘lineal Aristotelian’: A causes B.

Reality though is more like the Eastern philosophies of Vishnu-yin-information and Shiva-yang-energy/motion:

A<=>B, that is A and B interact to create a ternary <=> present element.

Reason why there is conservation of Angular and Lineal Momentum, there is Space and Time,  Energy and Information, O-Particles/Heads that store time cycles and limbs/fields that move them, mixed in bodies and waves that reproduce both of them.

Humans of course, naturally have always expressed this ‘Ternary’ Structure of the universe.

And so the parallel syntax of the languages of knowledge we use to describe those Universal beings  – verbal, mathematical and visual languages – all have the same ternary ‘grammar’, which I have called the ‘Fractal Generator’ of the Universe:

Tƒ (Subject or Function of ‘temporal information’) < ST: action, operandi or verb ≥ Sp (Object of ‘spatial energy’).

We associate counter-intuitively ‘cycles with motion’ and ‘lines with Still space’.

It has to do a lot with the limiting errors of classic physics, where only lineal inertial motion matters. Fact is big-bang explosion DECELERATE speed till it becomes Still lineal distances and dimensions, that is pure lineal space with no motion or vacuum space (as in any physical big-bang of entropy). While the equation of cyclical vortex, is Vo x Ro = K (2-manifold, simplest variety), which counter-intuitively accelerates (∆V) when distance becomes smaller, (-∆R) to maintain K constant.

Thus clocks, frequencies and vortices accelerate ,and have more ‘time’ content, that lineal motions that decelerate to a halt.

Now, we explained before that in duality Space was slower, extensive, Sp, Size, and time was faster, cyclical, accelerated (so are its maths). But now in ternary symmetry we have the need to ‘extend’ the meanings of time and space to the duality of the 3 motions of time and the 3 organic parts of spatial bodies and this makes some confusing choices of terms, such as:

Space will be the still, formal view of reality and Time the motion view. And so we shall talk of 3 ‘topologies of formal space’, and 3 ‘ages of time motion’, which together shape the fundamental duality of reality, the view of organs in simultaneous space and the view of beings living a worldcycle of 3 ages of time:

Sp (limbs-fields)≈ Young, past, expansive age < ST: Present, repetitive, hyperbolic body-waves, adult reproductive age>Tƒ (Temporal, future informative, cyclical old age).

Now here the convention I have adopted is to Use the same symbols for either symmetries, the limb-field<body-wave>head-particle or spatial simultaneous view of an organism in space, and the Young-past-expansive < present-Adult-reproductive>Old-Informative 3 ages of time.

This is where things seem confusing because the whole thing transmutes. The old age of future time has more information and it is cyclical, properties of time cycles, but it is also slower, property of space decelerating motions. The young expansive age has more motion, a property of time more than space and so on.

But as I have told you B & W and 3 color view are new worlds, and this is the closest way to express past references and correspond with human expression of all this.

A way out to avoid confusions with the ternary symmetry is to use more when dealing with the still, simultaneous spatial view, the ‘symbols of geometry-topology, |, O and Ø:

|-Limbs/fields < Ø-waves-bodies> O-Heads/Particles

And the same for time ages with the reference of time motions:

|-young past < Ø-present, reproduction > O-Information, future, old age.

So it shows the symmetry with the symbols | , Ø, and O.

And the ® formalism that better express them.

Then I realized why mathematics was a language, so closely related to 5D space-time.

Since geometry was the science of space, logic algebra, with its sequential social numbers, the time language, and analysis the 3rd branch of mathematics, the study of the 5th dimension, of infinitesimals and wholes.

So it IS easy to translate the laws of mathematics into isomorphic laws of 5D space-times, with the proper corrections to account for the fact that each point was a world in itself, when we came closer to see it – the true meaning of the 5th non-Euclidean postulate which defines points as crossed by infinite parallels; part of waves, connected into planes, that grew through the fifth dimension into co-existing organisms, which used the clocks of time of different speeds to build up its complex forms. It did not matter so much that form, as knots made it convoluted, but the functions of those networks, which now became the 3 ‘physiological networks of all systems’, again described by the Generator equation:

Sp; Digestive-energetic network of Non-AE points < ST: reproductive, ‘blood’ networks > Informative, nervous networks: Tƒ

 Of those elements, the most important is the most spiritual of them, the mind, defined by the 5th Non-AE postulate of pan geometry:

5) Definition of a mind: O-Point x ∞ cycles of space-time (world)= Linguistic mapping (mind).




¬Æ Algebra. Main symbols of relational space-time and its isomorphisms.

Now, Existential Algebra, another term I use to develop the logic equations and a(nti)symmetries of 5D fractal space-time IS an entire new logic symbolism, which departs from ‘algebra’ in the sense used in mathematics. It is not though completely removed from it, once through these post and in more detail in the last line (∞ scales, aka ‘God’, the mind of the Universe:), we get into a full detailed analysis of all its elements and put them in relationship with classic mathematics. Here in these posts we will merely give indications of homeomorphisms and mappings between both algebras.

In the sense that 5D space-time Universal symmetries can be mathematized with classic terminology, as we advance on the details of both, we shall see those relationships, as FUNDAMENTAL THEOREMS OF CLASSIC MATHEMATICS become THEOREMS OF ¬Æ Algebra, giving realism to abstract mathematics and giving abstraction to real 5D space-time. Such is the symbiosis we aim to achieve in those texts; both in classic mathematics and mathematical physics, which is a step closer to the 5D space-time formalism.

Consider for example the case of ‘Groups’, the fundamental structure of classic Algebra. Now it is evident to the reader of those texts that the fundamental properties of the Time-Space symmetry is to have a Group structure, as it has an SE state, which is inverse to its TO state (both in form in space and time parameters of energy and information). Since Sp = Max. energy x Min.Information and Tƒ =Min. Information x Max. Energy), and have a point of maximal ‘existential force’, SE x TO on the point of balance (SE=TO, which for SE+TO=K, maximizes the product).

A group in that regard is considered a system with an operation (G,•), such as there are an element and its inverse, whose product gives us the neutral element. So its definition is quite similar to that of fractal space-time world cycles. To which extend this similarity is an identity will be explored along this pages. As we can define several operators in the symmetry of space-time, >, < and ≈ being the 3 fundamental ones.

Further on, if we add the 3rd group of symmetries, those of 5D which are a process of social evolution and superposition, it has many properties of an Abelian group. So it is easy to observe the close relationship between the 5D asymmetries and the second most important Algebraic structure, a ring in which isomorphisms are essential.

But here the relationships are far more rich in symmetries, as we extend them between the Œ-point and the external, larger world, with its U±2,3,4. For example, the symmetry between a Tƒ point and its Sp field belonging to the U-4 scale defines all the translation symmetries in an isomorphic space-time.

In mathematical physics, obviously we can directly and we will relate the symmetries of particles and motions with those of 5d fractal space-time and its generators. And again here both will enlighten each other.

The operations and equations of relational space-time are written with a new logic/mathematical formalism that upgrades Aristotelian and Euclidean logic and geometry into I-logic (next letter) Geometry, which includes and fusions both, the laws of the 3 arrows of time and the laws of the networks of fractal points, which through its symmetries or dualities of form and function, O and |, lower and upper I-scales of the 5th dimension, and the common laws extracted from them (isomorphisms), define all the events and forms in existence.

Thus to define any system of reality we need to define the 5 logic ‘isomorphisms’ proper of any system of space-time, its 0-point or function of existence, its spatial membranes, its time ages, its universal planes and its actions of existence.

And the related 4 organic isomorphisms, related to the 5th dimension, and its metrics and quantitative values: the ‘6th isomorphism’ of social classes, vital constants, creative diversification and social planes.

Thus all equations of all sciences that explains all space-time events of the Universe will be related to those 10 isomorphisms, themselves related to the 3 (x3) isomorphisms of time, space and the scalar fifth dimension, themselves derived from the 3 inversions of space-time (inversion of form-motion, O-| and | _).

Equations of world cycles and ages.


In the graph, the fundamental equation of Existential Algebra, ab.Æ, is the world cycle, decomposed in 7 motions, 5 actions and 3 ages. While the world cycle and its 3 ages is better analyzed in pure GST terms (equations on the bottom for ‘space-like in the description of left organic parts’ and ‘time-like’ in the description of ages), when we deal with motions and actions, at a more detailed scale, standard mathematics is of use.

In both cases we depart from the generator of space-time:


In all its possible combinations.


On the other hand the second commonest set of equations to describe motions, as transformations of time forms, is the equation of reproductive motions. And assemblies of bidimensional space sand time planes

Past-entropy x Future-information = Present space-time.

Whereas at least 2 flows of conflicting inverse information and entropy come together to form a 3rd entity, present time, which is a dual system. The laws of existential algebra become then the laws that structure the creational processes embedded in those flows, which we shall call tensors of existence.


In the graph, the basic tensor of existence. 265

In the graph from the original c.92 book, ‘A theory of Unification’, the creation of flows of communication between points starts the creative process of the fractal Universe. Its formal study is the field of Existential Algebra, which along i-logic geometry (the study of fractal points and its topologies in space) and 5D analysis (the study of the laws of transfer of energy and information between scales of the 5th dimension and how its finitesimal parts become wholes), complete the formal mathematical and logic analysis of General Systems Sciences, reason why they are the 2 first isomorphisms, which resume all others that will develop that formalism, and the partial equations of the Fractal, ternary generator, in great detail, for each species of the Universe.



The 3 elements of the Universe: 2-manifolds, 3 time motions and ages, and 5D scales.

In the graph, the 3 type of motions of the Universe, expansive, decelerating, Se-entropic, past motions; present, vibrating, wave-like repetitive, present motions and future, informative, implosive, accelerated, vortex like motions.

Its sequential combinations in life-death cycles (world cycles of the ‘existential function’), its simultaneous adjacent construction of ternary organisms, with moving, entropic toroid limbs/fields, repetitive, hyperbolic body/waves and cyclical spherical heads/particles of information, and its complex, architectonical design of the co-existing planes of the 5th dimension that build together the systems of the Universe, require the formalism of existential algebra, Æ, departing from the symbols that represent those motions, forms and scales. It will then be easy to represent all space-time events and define the simple symmetries, transformations and inversions of space-time that define the Universe and all its parts.

In the graph, the Universe has 3 different arrows of time, which being time broken into infinite events can travel simultaneously in different regions of space-time towards a local future or past, as when we die ( a past dissolving event) or we live (a future, informative arrow). The combination of both arrows creates a repetitive present, which reproduces a certain form in space-time. Thus we write:

Ω.  Tƒ (future, informative arrow) x Se (past-energetic arrow) = ST: Present iterative arrow.

The 3 arrows of time must be always understood in relationship to the 3 ‘scales’ of growing complexity and organization of the Universe. That means, they can be the phases of a single, ±∆e,i space-time action, or they can be part of a larger, sequential order, as the one represented in the world cycle of life and death, which is a journey through 3 scales of the 5th dimension (seminal-cellular/atomic->Idividual-organic->social/gravitomagnetic), between birth and extinction.

In the case of the perception of those 3 arrows in space, we shall observe beings with fields/limbs of entropic energetic motions hyperbolic bodies/waves that iterate those motions and particles/heads that project into the future and guide the system.

This combination is the one we most often observe, and so we can say that it generates most systems of reality:


So what existential algebra does is to consider the logic processes that build up systems in the Universe, allowing the vital realisation of the 5 postulates into super organisms.

What algebra today does is to talk of this game but in a completely abstract unrelated way which greatly obscures the meaning behind it but allows a maximal generalisation and also ‘inflation’ of forms of algebra which have nothing to do with reality.

Against this inflationary algebra we shall reduce our posts to themes and structures of classic algebra better connected to the Universe we observe.

However the ¬Ælgebra of the 5th dimension is quite innovative and well beyond the abstract jargon of present algebra (the one of the 4th dimension of Einstein’s space-time). So on the secondary posts time permitted we might introduce the 5th roots of sufficient reason (-;

Algebra forms a duality with Topology, since their fundamental units are the ‘hierarchical, sequential, temporal numbers’ (Algebra) and fractal, spatial, adjacent, network points (Topology), but both, obviously have space and time components.

As all ‘evident’ entities are dual, present systems: all yin has a drop of yang, all motion has a minimal form to become energy, So the study of pure ‘past-entropy-space with no form’ and pure forms with no motion, is quite barren.

So we could rephrase our classification and say that Topology is dominant in ‘yang-space-geometry’ by virtue of studying its units, points and networks of point…. with a little time motion:

Topology: Max. S x Min. T

And Algebra is its inverse, as it studies with sequential numbers, the hierarchical, causal time unit of maths, structures that develop dynamically in space; yet what matters in groups are the moving transformations, not the static space-forms:

Algebra: Max. T x Min. S

Thus, this page will be loaded slowly into the future with a full study of Algebra with special focus on Group theory, and its ‘space–time symmetries’.

A it will be more technical, I do not expect to tackle it till summer 2017 when the simpler upper hierarchies (¬ æ, ¬e mathematics) are completed.

Algebra & Algorithms.

One of the main fields of existential algebra is the study of the algorithm of existence, a simple, feed back generator equation of 3 dimensions in present cyclical time, 3 in spatial past, 3 in temporal futures, and one mind that occupies vector space with all of them, into a monad, or will of existence, reflection of the game, which it deploys through such symmetries internal or external as they are available to a 3 ∆ST, NINE dimensional group:

Sp  ts   tƒ  meaning space, timespace and temporal information and it inverse symmetry

Ps, st Ft  meaning past flow, present iteration nd future inform

∆-1 ∆ ∆+1 meanin micro, scale and macro

So the question is how we move between those 3 x 3 dimensions? what operations  state can be found in a being,w which isin 3 of such states at the same time?

It is easy then to resole the all possible combinations of flows of existence, as motions that happen between 3 possible combinations of the algorithm,

Then we can establish an order through actions and flows between those algorithm possible tensors of existence, such as a form of relative past, moving towards a future form (evolutionary emergence of a phonetics), or a macro form, exploding into microforms (death arrow), an so on and so on.

IT IS THEN AN interesting logic exercise to prove that all laws and events are combinations of those possible arrows of existence. As such we are all knots of cycles of space-time, whose will would be a mechanism that manages the switch on and off through those actions of existence themselves flows made possible by the switch on and off of possible different configurations of the mind of the 9 dimensions represented in the language of the being.

However as here is a maximal point Max e x i|s= t, of the 3 parts of the being, S, Exi and T, this configuration can be consider the golden mean point of a ny field system and we will find it at the top of the life of any being.

So the first thing we find out s that the function of existence, in its maximal point, Max. e xi (s=T), IN WHICH A BEING is a synchrony with time and adjacency in space, S=T, MEDIATING with the same parameter values in shychronicity and simultaneity with both, emerging as a resonance of the field in which absorbs its being, and iterates itself, since max. exi is a function of reproduction, which Maximizes through reproduction the existence of the e x i, combination in present space, around a time space constant, which we consider to be an as=t, point in which an e xi particle travels through in tune of synchornicity particle-clock with fields wave rhythm, speed, back and forth thus the field of the turning round a constant energy origin of the particle which will collapse ahead the wave in the pit of measure timespace…

∑|-Spe <≈> ∏O-Tiƒ          :              ∆ = |∞  x To          :                  To< ExI≈st

We have written the 3 elements of the fractal generator, purposely above, in  different forms, from left to right, as an algebraic, dynamic equation; as a mental, geometric equation  and finally as a semantic philosophical function that shows the fascinating homology of all languages. 

So in the centre we write:

∆ = |∞ x To ,  which is the equation of the mind as a geometric game of creation of new forms of time made by mapping together into a still image of the Universe its lineal and cyclical motions.

In the left we write the ‘Function of Existence’, as an acronym verb of the 3 parts of the system, its future guiding Head, To, which controls with its information, < its present body wave of energy and information exi, that feeds on an external s≈t field.

The equation shows a fundamental equilibrium that exists in all survival body-waves of the Universe, where the Product of the energy and information or vital constants of the system is kept in a balance maximised by the equality of its space and time parameters. Since when we have 2 numbers, to maximise its product, they must be equal. So 5×5>6×4>7×3. Hence: Max. Exi->S≈t. And indeed we shall find that all surviving functions of existence achieve a balance between body and mind, in its adult age of reproduction, when they combine proportionally their energy and information to reproduce in similar forms. And we shall use this equation to define beauty as the balance between lines and cycles, forms and motions.

So the Fractal Generator in its simplest most meaningful expression is full of hidden meanings.

Finally in the left we have written both in geometric, logic, causal and dynamic terms the equation, showing its symbolic meaning as a lineal spatial entropic flow of motion that constantly transforms itself back and forth into cyclical, temporal information. So the equation represents the ‘Principle of conservation and transformation of energy and information, the fundamental principle of all sciences.

And if we were to put them all together the Fractal Generator  will be:

[|-Spe x O-Tiƒ=Exi:S≈t]∆±1

We can in that sense play with infinite variations and languages to describe the essence of the fractal universe and its correspondence with all languages, which themselves mirror all kind of species. The Fractal paradigm is thus more closer to metaphor and poetry, mysticism and communion with the whole and all its parts, as it unifies the essence of all beings than to the measure-seeking detailed precision and classification in different parts and compartments, which is our concept on how to do science. And yet, as we shall show in the 4th line, this detail can also be achieved.

Let us then build on the fundamental relationships and symmetries of the 3 elements of that fractal generator, starting from its space-time dualities.


‘If you want to understand the future, look at the past’ Confucius

Abstract; The cycle of Existence.  The causal order of the 7 motions of time.

Temporal, ¬Æxistential Algebra, studies the organisation of systems, through time=change.

We SHALL therefore be a bit more exact in this post for future stientists if any is left, human or robot by the end of the century…

The motions of existence are ‘displacements’ through the 4 elements of reality; hence they have a ± direction, which in space is conventionally left and right for locomotions…

; that is by means of transformations that provoke motions of a system, and create variations of systems, according to Group theory.

What we are interested here, beyond explaining the laws of algebra, translated to TSymmetries and ∆-scales, is the nature of existential algebra and the differen equations of motions which always render a certain:

Past Operandi Future= present. We shall consider in this inrodution the main operandi of the 7 motions of the Univrerse of which the 3 more important are Past ± Future = Present (superposition classic of the motion of a wave), Past x Future = Present

(Product, normally of space and time different states) and Pastˆfauture = ∆+1: social evolutionary arrow of future across the ∆-dimension.

Æ generator

the fundamental equation of Existential Algebra, ab.Æ, past – future = present space-time, of which there are as many versions as regions in which flows of past, present and future entropy, information and space-time find itself in a simple relationship:

Past <Motion Operandi> Future ≈ Present

This is the most generic equation of existential algebra, and depending on which type of motion we study the Operandi between past and future will be different.

The most studied ones are locomotion, (Operandi ±) on terms of Hamiltonians of Potential INFORMATION & Kinetic Energy; reproductive fields which create a 3rd dimension, using the product operandi, and growth and diminution ratios, using logarithmic scales.

Consider the simplest of those equations:


Where Present (left side) is the sum of the kinetic energy and potential energy, V (hence often with negative symbol). Why the future rests from the past? It does, also in relativity:

screen-shot-2017-01-04-at-20-03-58 screen-shot-2017-01-04-at-20-03-29

We observe again that the c2t2, is rested from the pure spatial coordinates, dx, dy, dz.

The particle-future in that sense feeds on the entropy of the ∆-1 field, and absorbs its energy from it, parasitising its motion and as it is this combination what we see, the wave is equivalent to the value of the past minus the particle.

It is then possible to play with the equation,

Future = Past – Present

being obviously the most intriguing.

What this means? How can the present be the past resting it, a future? Pure mystical thought for initiated

Just think of it, what we have not yet discovered, the 3rd man:

Past = Present + Future

The past is thus balanced with the present future, which is meaningful for an immortal Universe in which the present is the middle point which in fact means it is an ∂st portion with minimal value, and as an infinitesimal we can also talk of:

Past ≥ Future

which is the particle state in simultaneity in a moment of present in which it absorbs energy into form from the past, in such finitesimal moments of time, as to create a balanced closed motion with no expenditure of energy. The immortality of the universe, and the relative ∞ and yet 0 value of the present in each of those equations, opens a deep philosophical analysis of the meaning and creative processes between each of the 3 stretches of a flow of time.

In the next graphs we can see different encounters between flows arrows of relative past and future, > < in its ‘collisions on a relative present, which gives us different tensors and motions of existence, with different operandi:

The 3 Past, Present and Future ages defined as ± combinations of 2 inverse arrows of time, future information & past entropy, above, below, as Present reproductive waves, and Past>Future, guiding fields of particle forms:
Screen Shot 2016-06-05 at 18.53.23

Further on, this is only the commonest expression of the 3 dimensions of a motion of time, but as there are 7 motions, more operandi are needed to study a certain form of motion or symmetry along the S, t and ∆ 3 dimensions of reality.

Each of the 3 dimensions will have ± operandi motions of time, products, integrals, potentiation and logarithms between the most common.

So has i Æxistential algebra an equation, hence the multiple operandi expressed above, as the relative 3 type of dimensions, simultaneity, resonance and synchronicity imply different displacements in past to future arrows depending on which S-T-∆ direction we displace.

In the graph the present wave and past-future, field-particle configurations of physics; and  the 4 sub-equations that combine past, present and future producing either death-annihilation or creation processes, illustrated with ‘time-space’ cones (borrowed from relativity). THEY ARE all consequences of the fundamental equation of simultaneous equilibrium among the 3 topological functions-forms of time beings:

Present (wave-body) = Past x future (field-limbs x particle-heads)

The classic event of relativity then would be a ‘relative present, simultaneous event of measure’, which is really the dimension of time used in physics in their study of locomotions, in as much as those v=∂s/∂t equations (including Einstein’s expansion) are always about ‘simultaneous measure’ in an instantaneous present ‘derivative’ slice of the flow of a time-cycle. But the events that merge space and time components, past and future, entropy and information are far more in a catalog that departs from ±2 arrows (with inverse direction). To fully grasp those variations on the theme of space-time systems, we though need to explore in depth the meaning of ‘equality’, ‘perpendicularity’ and ‘parallelism’.

So we will not go so far in i-logic till we do not clarify fully the structure of Non-Euclidean geometry. To notice though that only Schopenhauer seemed to have realised that the true fundamentally flawed Euclidean postulate was the one on equality, which shall become the MOST transcendental of them all in i-logic geometry: equal forms do indeed merge together and reproduce, complementarily; unequal forms will engage into destructive events.

So we love to communicate with another human speaking the same language but go to war with other linguistic neighbours; atoms form huge crystal networks with equal atoms but very small ions with different ones. Vital, i-logic geometry will achieve in that sense a fascinating result: make mathematics far more real by giving vital, i-logic, bio-logic properties to geometric figures.

What does it mean to live in a Non-Aristotelian, Non-Euclidean Universe? In this post we shall study the i-logic nature and causality of space-time events, according to the existence of 3 non-Aristotelian causal arrows≈dimensions≈ages of time-space cycles≈events≈frequencies, past≈entropy, present≈iteration and future≈information.

The interplay of those 3 dimensions of time-space and how they ‘manifest’ in human languages, species and perceived events, is the fundamental theme of i-logic.

Whereas Aristotelian Logic means merely a logic of time with a single arrow. We are doing a dishonour to Aristotle, which is far more complex when you do understand his work than this single causal arrow. In fact, we refer more to a physicists’ view of causality as motivated by an entropy-only Universe.  As we use 3 arrows of space-time for all finite domains-beings, past-entropy, present-iteration and future-information, we call this ternary logic, i-logic, Non-Aristotleian logic.

And so the first question to answer is how to put those 3 ‘terms’, past, present and future in causal, mathematical relationships.

In that regard i-logic is the most surprising and yet fundamental part of ®.

Its fundamental equation is the equation of presents that generates by split a field of past and a particle of future such as:

|=Past-entropy (Fields/limbs)  x O-Future-information T(heads/particles) <=> ST-Ø present reproductive body-waves.

The fundamental equation  of time arrows of the Universe is enormously fruitful in understanding all kind of Nature’s phenomena, and of course it does have the usual variations, explained according to the structures we observe in reality:

Past-entropy field (gravitational pilot wave in quantum systems) > Reproductive body-wave > Informative particle/head

Existential equations, its syntax

The study of equations of number is such a vast genre because both herds of energy in motion and networks of bits of information are sums, with different dimensions. So they are essentially polynomial functions, which vary as energy becomes information or vice versa. The way in which one variable grows or diminishes to the expense of the other is thus an equation plotted in a bidimensional plane – the most common event studied by science. The difference is that of the unit. Since by fusioning the concept of a Non-Euclidean Point (Riemann, Lobachevski) and a Fractal Point (Mandelbrot, myself), we defined a new unit of mathematics, the ‘point’ (Geometry) or number or set of points (Algebra). And since equations treat points-units in social groups/networks/numbers, we cast more insight in those equations knowing the properties of its elemental unit.

Those Non-Euclidean points are knots of time arrows, with complementary functions and forms that combine Logic and Mathematics, Time and Space in actions, where motion with purpose – with form – create the 2 sides of the same action. For that reason the new postulates of i-logic, Non-Euclidean geometry (the geometry of multiple spaces and the logic of multiple, causal arrows of time), are both logic and geometric postulates. In Algebra and all its branches, numbers are the units used in equations, all of which follow a rather simple ternary structure: f(y) = f(x), which we shall write as F(i) <=>F(e); that is, all equations are descriptions of certain events, which can be described also with the wider syntax of all languages ‘generated’ by the Universal Grammar of the feedback equation of space time. The corrections are minimal but relevant. Equality, = now becomes dynamic, <=>, since many errors in science are derived by the fact that scientists tend to think that an equation is based in equality (3rd Euclidean postulate) and not in self-similarity (3rd non-Euclidean postulate). So for example: E=mc2 is not an equality, Mass is not energy, but a self-similarity in which at least one property of Energy is transformed by the symbol of self-similarity, <=>, in this case lineal energy coils into cyclical information, mass.

Algebra is a sequential, synoptic language of time used to operate with complex groups of points/numbers, either expressed with the modern concept of Set theory (Cantor) or the old concept of Equations and Operandi. Those operandi that defines F(x)=G(y) relationships are a reflection of the permitted operations Generated by the Feed-back equation, <X>, E<=>I, or Generator equation of space-time that expresses the foundational law of physics: ‘energy and information never die but transform into each other ‘ad eternal’.

In essence the 3 operators of the generator, ∑, <=>, ∏ are dynamic operators that encompass most of the operations of mathematics.

The sum defines the way in which herds communicate, the multiplicative and integrative symbol defines the way in which networks tie themselves, the flow symbol defines processes of diminution and enlargement as energy and form is transfer from one side to the other of the equation with different rates according to the ages of life of the system or event. As energy flows from the herd to the network, the network reproduces more informative bits and the herd diminishes till it halts its growth and the asymptotic curve is formed  – this is the region of death established by a peak or non-differentiable discontinuity where the function collapses, and all the information returns to energy.

All those possible transformations of  a life/death curve are indeed, what mathematical operations done with equations of the form F(x=e) <=>G(y=i) describe.

Many errors of science are caused by the ‘mechanical’ approach, which operates with mathematics without understanding the deep meaning of equations. In essence any equation, F(Y)=F(x) can be reduced to a transformation or relationship between 2 functions that represent complex and simplex knots of time arrows or events between them that become transformed  through an operandi, which represents one of those basic transformations. So we could write instead as the Universal Grammar of all algebraic equations, either the Generator equation of space-times or any other notation that reflects the fact that equations describe events and forms born of transformations between structures of time arrows. For example if we write:

F(­,®,¿)i±n≤=≥ F(­,®,¿)i±n

We describe all possible equations in the ‘dimensional notation’ of time arrows, where ­ is the Time arrow of information, ® is the time arrow of energy, ¿ is the time arrow of reproduction and i±n is the transcendental arrow of social evolution or emergence and social devolution or death.

The basic concept of algebra is that of number, briefly explained in this text and that of operations between numbers which are herds of time knots and its properties and the structures they create (grupoids, semi groups, groups, Boolean Algebras and rings). All those operations describe in fact the possible events that take place between points that create either a herd/simplex plane of existence, or a complementary organism extended in 3 relative planes, st+1 (informative system), i (reproductive, reproductive body) and st-1 (ecosystem in which the herd or organism absorbs its pixels of information and bits of energy). The meanings of the basic operandi are:

Sum, +, S is the fundamental operation that creates ‘body herds’, in which the individual cells are simply connected (each one relating only to the cells that surround it) and so their ‘exi’ existential force merely adds up. Their reciprocal, destructive event is subtraction, -, when 2 herds enter into a Darwinian event and one herd extinguishes the other.

Multiplication, x, P, is the key operation that creates ‘informative networks’, in which the individual ‘neurons’ are complex connected, each one, joined through its ‘axons’ or ‘subsets’, to all other neurons (ideal network) and so their ‘exi’ existential force multiplies them. Thus for example, 5 neurons with a complex connection, each one will have 5 axons/subsets, and the number of connections will be 25.

The duality of planes of space-time, proper of informative systems is the first ‘complex’ structure extending beyond a single space-time continuum used to define energy-only processes (and hence deforming the understanding that physicists have of information systems, which cannot fit in a single plane and their obsession for models with a single arrow of energy/entropy). Essentially an information network can ‘operate’ both in the language of the energy herd it controls (so quarks, which are bidimensional vortex of mass-information, operate with electromagnetic forces to control electrons); yet they also operate as a network through the other plane of existence unknown to the herd.

This is expressed in mathematics with 2 concepts: energy herds are ‘groups’ defined by a single operandi and information systems are ‘rings’ which operate with 2 operandi. And ‘Groups’ and ‘rings’ are the 2 fundamental structures of algebra to the point that a ‘ring’ is called simply an algebra.

An important law of complementary systems of reproductive energy and information is given by the fact that the maximal product is always that between ‘self-similar subsets’, such as if we have 2 st-points with a total of 10 st-1 elements, axons or subsets, the maximal number of connections/products, will happen when Est-1=Ist-1 (5=5, 5+5=10): 1×9< 2×8<3×7<4×6<5×5=25.

It means that in the product exi that defines the existential force or momentum of a complementary system, those systems, which are balanced, are the most efficient.

Thus, the most efficient systems are those in which the 2 complementary parts are in balance between body and brain; a law fundamental to explain the survival of balanced organisms in its ‘2nd age’ when E=I; which is also the definition of beauty, as the classic age of balance between energy and form.

This laws explains why the fundamental algebraic operations are quadratic equations, as X= E x Ii=e is simplified with a square, x2 and defines multiple energy/information systems.

Yet more complex equations of the type xn normally respond to operations between different planes of existence, also described with Riemann’s complex planes.

– Division, which describes the inverse operation of finding the number of sets departing from its parts/subsets or network connections, but also another fundamental operation – the ratio between spatial energy and temporal information, origin of multiple Universal constants, E/I or I/E= K, related to our previous concept of balances between energy and information that sets the survival limits of any given system.

Integration and derivation. Those 2 ‘recent’ operations are related to complex operations between systems that extend in 2 or n planes of existence, especially in ‘neuronal networks’, whose cells/subsets ‘emerge’ into units of a higher plane.

In essence differentiation and integration are the 2 operations in which a flow of energy becomes reproduced into a bigger population or transcends and becomes connected by axons of a network of information – it becomes integrated and acquires a higher potency/dimension. While integration measures the curve of growth and diminution of the change of the population or herd. Integration creates a volume of a form with higher dimensions than the derivative and it can be interpreted in terms of a function of space and time. It can in fact be closely associated to the analysis of the Generator, exi=k.

Thus, we can consider the main operations of algebra to respond to the basic processes between time arrows. But a more important algebraic analysis is that of time arrows through time-space symmetries of the generator equation, ∑Se<=>∏Ti. What the generator is in poetic terms: a crystal that emits reflections of itself; and the densest in information the image emitted is, the more intelligent and complex the phase of the generator is. The tension, <=> between both poles of extinction is always dynamic, born of the cyclical exchange of matter and form between both poles but with a slightly constant derivative, Max. t->∞Se>Ti, or direction of life and pronounced slops of Max. Ti<Se s->∞ death.

The function of existence is – the reader at this time will have already noticed – the function of life and death of systems and organisms, and as such the two sides of the cycle, life and death, are notorious for their inverted properties. Death is an explosion of space and energy and motion that unwarps a network of non-Euclidean points probably on its highest informative point and minimal space. Those nutritive pills are everywhere to feed and feel a cliff of death, a discontinuous form, whose trace will be a memorial warped baroque angst in any language.  The slope of the function Se<=>Ti in any case determines where we are in the life cycle, because the life cycle is a bell curve with a known slope, in a coordinates of time (x) and space (y). The population of cells of the body for example, follows a bell curve and at a certain age the slope will be positive or negative but not cross.

In essence, what the generator equation means is the ultimate mirror of all equations of physics. A herd of bigger spatial forms, guided by a network of information, 2 different species and networks, messed together into a single body. The symbol <=> of the body, of the steroidal cycles of exchange and combination of messages between both poles of the being, the ‘vegetative and informative pole’.

The  study of the Se<=>Ti function in all its transformations of Se fields into Ti particles forwards in time and corruption and explosion of Ti particles backwards in processes of death in any of the infinite manifestations of the Space-time cycle anywhere in reality is in a philosophical sense the meaning of mathematical science: explosions of SexTi functions Sexualizing the universe with its creative orgasm of new smaller SexTi functions born as memorial, seminal motions within the exchanges of Se and Ti in the X-body of the System. The Human SexTi function is of course multipolar, taking into account the complexity of the human being. There is a Limb-Body-Head, Max.  S, Se=Ti, Max T structure that dominates the external architecture, and which is fractal dividing itself again and again in dualities and triads. When a function of time reproduces it divides in triads that latter will grow. That division is reproduction in its simpler sense.  Multiplication on the other hand is also reproduction but not within a single entity but a couple, which combine its inner, body-limb elements, multiplying the complexity of its Se-strata. The messing and sum of vortices that take place in Nature  might seem chaotic in any scale but play the organization of networks=numbers of great sophistication in its messing when we observe the apparent entropic disorder as a series of phases of synchronous motion among all the parts of the whole whirling landscape. The question is how to focus a certain dynamic structure,ó into its most ordered state or peak of information, or self-point of view of the system. Only in that point that we could well call with the Aristotelian name of God, the self conceives itself in all its subjective perfect form.

The existence of an animal and vegetal mind and body, head and limbs dual pole in the construction of all organisms is undeniable; the pole of motion and absorption of energy and the pole of information processing and sensorial perception. This complementarity limbs-body-head, spatial force-field-particle defines the exchanges:                  

                                           S (E: Body/Field) <=> T (i=Head/Particle)

Whose many particular cases gave form to differential physics of the type ds/dt=k Recap. Algebra is the science of sequential numbers; hence the mathematical representation of time events. Its equations reflect those time events as a language whose syntax is self-similar to that of the Generator equation of time events, once we substitute the concept of static equality, =, for the concept of dynamic self-similarity <=> formalized by the 4TH non Euclidean Postulate.

Creation: Inversion of ternary diversifications.

When we fusion the fractal principle of  ternary creation, the duality of form and function and the inversion of space-time processes we obtain a complex rule of creation that accounts for most speciations in the evolutionary process: according to this complex law:

Each process of evolution in time can be caused by 3 sub-causal processes in space, and each process of reproduction of a topological region of space can be caused by 3 sub-causal processes in time: 3Est-1->Ist;  3Ist-1->Rest

Thus, the event of reproduction can be branched into three possible causes that correspond to the three arrows of time: an energetic, explosive reproduction by the death of the mother, a balanced reproduction by self-similar beings (sexual reproduction), or an informative, seminal creation by a seed of pure form emitted by the father (asexual reproduction). For example, a species can put an egg in a living being, mate with a couple or reproduce spores. A quasar can blast and trigger the reproduction of galaxies; a cannibal galaxy can eject a jet of matter that reproduces an irregular baby galaxy, or it can merge with a bigger one triggering the reproduction of more stars in their body as it captures more intergalactic gas.

On the other hand each time age can be diversified in 3 topological modes of evolution. So a young species can halt its evolution (neoteny) and stay young for ever (alevin); can mature fast into a reproductive state, dying just after producing its eggs, or can make his youth a massive age of informative evolution (Chrysalis) and be born again as a complex form.

Further on, we can divide each ‘age’ in 3 sub-ages, which again will have an energetic youth, middle, steady state and a final informative vortex. So youth can be divided into the first age of geometric, massive growth of energy in which the head/informative organ diminishes in size in proportion with the body; a steady state of arithmetic growth and a final informative age (adolescence) of transition to the reproductive age, of maximal evolution of form.

We can in the same manner divide each topological space in 3 sub-topologies, specialized in energy, balanced and more informative, according to the adjacent regions; and so the membrane can be differentiated in the more energetic, external region, the intermediate balanced, and the informative inner zone; as the external cover must be harder in contact with the ecosystem in which the entity absorbs energy (outer skin), the middle zone is the region that reproduces the ‘lineal units of the system) and the inner zone, the one in contact with the more complex internal regions of the organism (region of the skin where the sensorial cells have its nuclei).

Thus when we properly merge the main laws of creation of multiple space-times, the ternary decoupling with the inversions of energetic spaces and temporal information, by dividing events in 3 sub-ages and spatial forms in 3 functional topologies (spatial, reproductive and informative layers). We can explain the Universe, which increases the complexity as we look in more detail a certain reality. It is the ‘fractal principle of differentiation’, which creates 3 and 9±st and then 27±3 and 90±10 sub-ages of time and 3 and 9±st and then 27±3 and 90±10 sub-forms of space in complex systems; which allow a detailed analysis that maps out the existence in time and main organic structures in space of most entities of reality. So the human being is defined in space by 10 physiological sub-systems and in time by 9±st sub-ages of life.

Recap. The fusion the fractal principle of ternary creation, the duality of form and function and the inversion of space-time processes explain the complex rules of creation and speciations as each age of time subdivide in a young, reproductive and informative sub-age; and each topology of space in 3 sub-topologies of energy, reproduction and information

Algebra operations respond to fundamental events between knots of time, tied by their time arrows. As such they can be derived of the Se<=>Ti function that represents all cycles of space-time between inception and extinction.

Equations of polynomials.

The fundamental mathematical solution is the polynomial double root solution, where the polynomial is a function of present and the 2 solutions a ± split fields.

Presents thus split in two dual solutions a ± dual field which is essential to understand all time of equations, from the equation of death where the complementary body-head, field-particle system splits, to the inverse equations of social symbiosis in systems that plug-both past and future systems into a present vital form of which the most important happens in social sciences:   Animetal Consumer: Humans (O or | function) x Machine

Examples in the 3 fields of science: De broglie’s double solution to quantum physics.

In quantum physics we can talk of 3 components, the pilot wave, the Schrodinger’s wave and the particle, which constantly split and come together in collapse.

Biology: the equation of death.

The split of the future-past, head/body & limb functions of a being produces its death. Inversely in viruses it provokes it birth.


The 3 social classes of sociology, the linguistic upper class in control of the information languages of digital money and verbal laws, are the future, because they create the future of societies. In that sense, paraphrasing Bohm, the ‘future can be determined because it can be invented’. Yet the result of the interaction of that future, informative, hidden elite class, over a body of present, re=productive beings, create a full organism that preys into a territory of land:

territory (entropic past) > re=productive class (workers, middle class) > Future (informative people-castes: politicos and bankers)


The Worldcycle of Existence: Order in the motions of time


In the graph the equation of the 3 motions of time and its 3 symmetric only varieties of 2-manifold spaces, seen in sequential order AS the 3 ages of all systems.

We can describe those ages from the perspective of its 5D metric order as systems are born in the i-1 cellular/atomic, relative scales of minimal size and maximal time speed.

And then it will evolve in growing scales of the 5th dimension sum of ‘layers of space-time’ that co-exist and organise beings through 3 such scales (the i-1 cellular, atomic electromagnetic scale; the i-organic, thermodynamic human scale; and the ∆+1 social, gravitational comus scale), infusing systems of an organic, biological, synchronic interactive nature…

Those 3 ages represent the symmetry of time space. As those 3 ages are in space, when we see them in stillness, the workings of 3 functional organs:

Lineal and toroid limbs/fields of energy/maximal lineal motion, since the line is the shortest distance; spherical, particles/heads of maximal information that command the system, (since the sphere is the geometry with maximal volume in minimal space); and its body/waves that reproduce the energy and information of the system. But of course our space is limited, and our time also.

This ternary symmetry will be everywhere in the Universe, from the 3 parts that assembly a virus (spherical/polihedrical head, injecting body and lineal legs) to the 3 ‘ages’/solutions to Einstein’s equations (big-bang expansive age, steady state age, and implosive big crunch age).

And so all systems assembly themselves by the interplay of its 3 motions that become 3 forms in space. The beat has now widened to the 3 canonical only varieties of bidimensional space-time. Since nothing can be made with other varieties, those 3 suffice to create the reality of systems of space-time including man.

And then we add the 3rd element of mathematics and T.Œ, that of analysis, of social numbers growing into wholes, creating new scales of the fifth dimension.

Since numbers, which are societies of cloned forms – so 2 are 2 pieces of something – requires that larger numbers come after smaller ‘parts’, we shall then find that besides the ‘fast time cycles’ of life and death, there is a relative dominant future, which is NOT as physicists pretend, the arrow of relative past, entropy disorder, but the arrow of relative future information.

As numbers grow in cardinal, as parts become societies that become wholes, after parts have assembled. So the Universe grows in scales from particles into atoms, molecules, cells, organisms, planets, solar systems, galaxies and clusters…

And this justifies our ‘definition’ of a relative future as the arrow of cyclical time, social evolution, order, organisation of loose spatial herds into tighter organisms, with its circadian cycles, of loose stars into spiral galaxies and then globular ones.

Ultimately we can also explain those facts in logic terms. The head/particle gauges first information, comes ahead and on top, and so ‘defines’ and designs the future motions of the whole, whereas the legs come downwards or backwards, last, in the relative past of the whole.

Thus indeed, physicists with their error of lineal time and single entropy motions got it all wrong.

They didn’t understand the thoughts of God, ‘the seer of time’ (Augustine), only some of their details.

Fractal Space; time cycles and its space-time actions of existence across its 5D social, organic scales.

The game of existence is simple but in its infinite combinations, enormously complex. Non-Euclidean points of different sizes and speeds, perform cyclical space-time actions, breaking and integrating motions into forms, building replicas of themselves, and using other’s species momentum to do so. Beings are out there hunting for momentum, exciting its energy to reproduce its form.

It is a vital game but of only 3 elements, the time cycles, the vital spaces they inform and the parallel planes in which its multiple time clocks and vital spaces order in a harmonic fashion.

We can thus build on the 3 simple elements of fractal space-time, ‘time cycles’, ‘vital spaces’ and the ‘fractal scales’ of the 5th dimension a Theory of Everything.

Since everything, is made of the duality of cyclical clocks that break space into vital spaces with energy/motion; who perform 5 cyclical actions of space-time to ensure their survival (hence a program of existence imposed mechanically as those who by chance or conscious behavior or mechanical one did not follow those 5 actions are systems that no longer exist), and through the 5th of those actions evolve socially from past simpler systems into future systems, creating a complex, fractal scalar, organic, pantheist universe.

Yet all qualitative analysis of reality requires a formal, logic model and so each of those 3 elements of ‘scalar’, ‘spaces’ and ‘cyclical times’, requires a more advanced, evolved mathematical≈spatial, logic≈temporal and organic≈scalar formalism.

The symbols of the Generator Fractal. Qualitative and quantitative analysis. 

Thus the fractal generator defines the logic structure of all Systems of the Universe. And when we substitute each of its dimensional symbols for a specific variety of the dimension, we obtain a certain species of the Universe. In the next graph, we see the entire Universe generated by the Fractal generator of 10 Dimensional Superorganisms, written above in simplified terms:


In the graph the dimensions and symmetries of the human being along its time motions ordered in 3 ages, integrated in the generational cycles, its spatial forms, organised around 3 symmetric networks of energy, reproduction and information, and deviated into 5 a,e,i,o,u actions of exchanges of energy and information with ±i scales of the 5th dimension. The formalism that studies all those symmetries in space is ‘Œ’, i-logic geometry and its expression on time, is Æ, Existential algebra… They require to adapt present mathematical and logic formalisms to the existence of infinite broken entities of space and time… but essentially work on the 3 classic fields of mathematics, the geometry of points, algebra of sequential numbers of increasing size, and analysis of parts and holes, to extract the fundamental laws of space-time from where all other laws will be derived.

ternary systems

Of all what we have said, one thing matters, to portray the super organism and its 3 regions, the boundary, Max. S, the brain, Max. T and the vital intermediate space-time world between both:circular motion

In the graph, all laws of electromagnetism resumes on those images: the existence of two perpendicular forms-motions, ith different speeds, the max. S, being the boundary, the central point, invisible, with no motion, though in reality a vortex,faster than the other parts, and the vital space, st between them.

We are all self-centered, fractal organisms of vital space, tracing world cycles.

So now we must deal with the consequences for knowledge of the ego paradox, which is mainly our belief that only human minds are intelligent and so its languages.

And so we must fully grasp the fact that we humans are not that important in the fractal Universe, but just a ‘fractal organism’ in one of its many relative scales, and our ‘intelligence’, that is, the languages of information we use to perceive the Universe, mainly logic words to perceive time, mathematical geometry to perceive space, are also not ‘special’, and they do not create the Universe or are the ‘languages of god’ as religious people and pythagorean physicists believe.

Since the main problem to objectively grasp, the  nature of reality as a fractal, organic system is that subconscious bias of all humans of all ages and all disciplines of reason or belief, against Nature, due to our ego-trips that make us happy only when we are the centre of the Universe as individuals and species.

Screen Shot 2016-04-02 at 09.17.48Screen Shot 2016-04-05 at 08.27.39



In the graph, the  centers of organisms, are the selfs, i-worlds, eyes mind of time, create the universe, by seeing from a single perspective cartesian space-time of simultaneous communication with all the points of the body-space o the point of time a wave of simultaneous networks of fractal existence, which is what we call a space, which must therefore be still and simultaneous to each other’s point, but only from the perpendicular point of space in the relative future-past which can move both systems in relative present time.


Reality Is a series of bidimensional sheets of space and time, of which 3 topological forms/functions are paramount:

In the graph, the complex Universe, is made of a repetitive series of bidimensonal space-time sheets, that can combined according to ¬Æ rules.

How those forms combine in more complex forms, are the basis of the processes of creation of the Universe. Of all those combinations of form and function,  4 BIDIMENSIONAL Spacetime SHEETS, are of great importance:

Pure Space, S, Pure time, I, the singularity-mind, and its combinations, < and > energy and information”

The symmetry between motions in time and space.

Space-still vs. time-motion duality is the causal alpha of it all (but not the omega, Ω, meaning, which we will find to be organic, biologic, embedded in the world cycle, represented by Ω). So we must go deeper into it, and follow now its ‘other fundamental expression’ – the ternary principle of ‘creation’, ‘diversification’ and ‘formation’ of entities departing from its time motions or still spatial states.

We deduce its original components from the interplay of the 3 motions of time:

  • >   The arrow of information that increases from upper to lower scales, faster in its time cycles: To (Ui)<To(Ui-1). This arrow appears most often in physics as an accelerated vortex (Vo x Ro = K being the simplest 2-dimensional form) or clock of time with increasing frequency, till it ‘collapses’ into a particle-point or reverse its time arrow into:
  • <    The arrow of entropy and decelerating expanding size that increases from lower to upper scales of larger size: Se(Ui)>Se (Ui-1)
  •    And their relative present combinations, in which the system combines, Se and To, fields and particles, limbs and heads of energy and information into reproductive bodies and waves which repeat in an eternal present the entities of existence.

In this case the entropy/energy arrow will show limbic/long fields of planar toroid energy, the arrow of accelerated cyclical motion the form of particles and heads that gauge information and the arrow of relative present iteration the body/wave form. And so in practice we tend to talk of ‘momentums’ of existence, that is Active Magnitudes that we shall call Œ, Functions in ‘existence’, which move through several planes of space-time.

This interconnection or duality between the stop and go dual motions/forms of entities in existence is a necessary complexity of the dialectic nature of the Universe, not only between relative Œ-points that communicate flows of attractive, imploding information and expanding, repelling energy, but within the entity which often displays both states, with different geometric position.

The previous symmetry defines all beings, as vital spaces whose ternary organs, perform the 3 functions=motions of time. Since all systems are  made of the same 3 components, the 3 2-manifold varieties, which accumulate in ‘layers’ to shape the depth of a 3rd dimension of thickness; and then move in ‘Time’ to accumulate the 3 ‘dimensional motions’ of time, past-entropic motions, present-reproductive motions and future-informative motions:


In that regard it is important that you understand those 3 arrows/dimensions/motions of time and its still present-spatial pictures as intervals. Since ultimately all clocks of time have different ‘steps/tics’, a relative instant of time varies, according to the perspective. If we have slow perceptive-time clocks we shall see a minimal time indivisible, which might represent for an atom or a cell an entire time existence. So how we differentiate the ‘time ages/phases’ of a system?

Precisely in mathematics, when the equation stops being differentiable or suffers a steep change of phase.

From energetic gas to reproductive liquid to informative solid in matter states.

From gaseous field of energy to liquid wave, to solid particle in quantum states.

From young energetic age to adult, reproductive age to old, warping age.

From the big bang expansive solution of EFE (Einstein’s field equations) to steady state to big crunch old age state in any physical system that follows those equations (galactic space-times mainly).

And so on. Time never ends because it switches its arrows, when one is exhausted. Or in terms of consciousness,  can you conceive the non-existence of time? Because we can conceive non-existence, but still time will happen when nothing else happening, the mind also has an a priori consciousness of the eternity of time.

In physics this becomes obvious when we realise that if Poincare’s/Einstein’s relativity 2nd postulate is truth and there is no way to differentiate motion from stillness, all has relative motion, and if all has motion, motion never stops. We can always choose the mind’s still perception of reality to fit all its information in its infinitesimal mind, or the moving objective, inner perception of the being. Atoms are moving vortices but we see solid matter. Yet if we consider the most objective moving reality, we realise time never stops as motion cannot stop and motion is the substance of reality in its 3 variations: expansive, entropic, relative past motion, Se, repetitive, iterative combined E x I motion and informative, formal motion, Ti, To.

This reality broken into infinite beings, of different sizes and time speeds is the ultimate reality science must describe. And in all its scales we shall find, the 3 arrows of time, its interplay and common ‘isomorphic laws’. Thus once we isolate the details and find its 3 arrows of time-space, we can apply the isomorphic laws of T.Œ and describe with them all what happens.

For example, Alain de mehaute proved long ago in a paper on chemistry, and his book on fractals, ‘l’espace-temps brisse’ ‘broken space-time’ that when energy exhaust, chemical systems DO NOT STOP TIME, but start to wrinkle as SPACE-TIME DOES in any scale.

For example, Einstein said ‘time curves space into masses’, which he said to be ‘accelerated vortices of gravitational lineal forces’. And E=Mc2 merely express that constant big-bang/big-crunch duality of eternal time cycles.

In fact, LIFE DOES the same in inverse fashion. Life is the arrow of growing form, growing information. Then, once you exhaust all energy into wrinkles, time does NOT stop in death. But it changes its arrow backwards into an entropic explosion/dissolution of our information.

So we can differentiate an interval of past, present or future, but it will ALWAYS have an asymptotic limit, where the equation breaks as the limit means a change of phase, even a bouncing back of time, reversing its arrows, to never stop.

It follows that as all goes back and forward between energy/information arrows, and we define present space as the confluence of both arrows, it is possible in the DYNAMIC, PARADOXICAL UNIVERSE OF TIME ARROWS, to define all as space-present, combination of ‘yin and yang’, if we take the larger perspective that adds two time arrows from past to future and future to past. In such a case, all becomes a zero-sum, an eternal present of conflicting existences that cancel each other.

Time never stops, but all ceases to exist for time to continue. So time switches in all possible combinations, between its ‘past arrow’ of entropy – expansive decelerating lineal motion – its future arrow of information, cyclical, accelerated vortices and its combinations into repetitive present spaces.

If we consider ‘space’ as still motion, as a differential of time, into an instant that combines the two arrows of past and future energy and information, into a repetitive motion, space is then also dynamical. But from an external perspective space seems not to change. It is then an interval without inner change, in which the external motion is continuously differentiable.

It is all that simple. In life≈biology the 3 arrows have a sequential order, the 3 ages of time due to an excess of genetic and nervous information that makes information the dominant arrow of the future – and make us choose information as the relative future arrow from the human p.o.v. of knowledge.

In technology information is also the future arrow as the human cult to the machine, makes evolving informative machines the goal of our collective subconscious suicide (creating robotic species that will substitute us).

In physical particles, which are dominant in motion, with lesser information, the opposite happens. There is in many systems a relative future arrow of entropy, and motion that dominates the system, such as in interstellar space where space expands; or in the interaction of particles of information, and antiparticles with past arrows, and inverse expanding motion.

Both co-exist and so antiparticles of past, which co-exist with future particles often come together and then, the following event happens: Anti-particle past x Particle- future = present entropic annihilation. This explains why we see less antiparticles, as they are the death-past arrow, which lasts only a time instant, so while they are as many lives and death as death is Maximal entropy expansion x minimal information, it happens very fast and the total space x time perception of an antiparticle or a corpse is far inferior to the perception of particles and living beings.

Now we shall consider the fundamental of those symmetries: the ternary symmetry between the 3 motions of time and the 3 dimensions of space.

B≈Ω. The fundamental symmetry of the Universe: 3 2-manifold varieties of space≈ 3 motions of time.

There are 3 motions of time, repetitive presents, inward, accelerating; future informative vortices, and outward, decelerating entropic past motions. But since space is a still picture of time motions, THERE MUST BE ONLY 3 TYPE OF SPACES. And indeed, when we realise that there are ONLY 3 varieties of a bidimensional space membrane (whereas the 3rd dimension of thickness is minimal, as in almost every ‘membrane’ of the Universe, from your thin skin, to the electronic orbital of an atom described as a planar fluctuating wave to the crust of the Earth.

So we talk of 3 types of bidimensional spaces, which are symmetric to our 3 time motions and affirm that all what exists is constructed with the iterative repetition, accumulation in layers and topological motion of those 3 space-time formal motions:

B≈Ω: Œ                        Symmetry between the 3 varieties of 2-manifolds and the 3 motions of time:                                                    

 |-Spatial entropic toroid limbs/fields <Ø-Present, hyperbolic, iterative waves/bodies>Future informative O-heads/particles

We call that symmetry, the function of existence, of any system of reality, Œ, a symbol composed of a cycle and 3 lines of space.

And we call Æ, Existential Algebra, its study with equations that use the formalism of relational space-time, which is in its origin a series of logic isomorphisms derived of the inverted properties of time and space (hence the use of Greek letters instead of numbers for its equations).

Those are the 3+3 formal motions of space-time and components that assembly all realities,: the 3 motions, ages, and networks of a time-space equation.

For example, in physics they correspond to the maximal, minimal and stationary points of its commonest equation, the Hamiltonian function, which studies the energy-mass=Physical Time of the system.

But in physical and biologic organs they correspond to:

Ω.B.—   The digestive, energetic, entropic system, maximal in the lineal, toroid limbs.

And they correspond to the planar fields in physics.

Ω.B.Ø   The hyperbolic reproductive body, which combine energy and information and reproduce the system.

And they correspond to the hyperbolic waves that reproduce information in physics.

Ω.B.O   The informative, cyclical sphere, or head/nucleus of a living system. And the equivalent particle, which gauges information in a physical system.

The key is the understanding that there are only 3 ‘topologies’ in the Universe we perceive, 3 sub-dimensions of space, 3 sub-dimensions of time, and 3 organs and elements in all physical systems, and they are all related. And there exists a parallelism between fixed space, moving time, topological varieties and physical/biological organs (fields-waves-particles; limbs-bodies-heads).761In the graph an amino acid fish in which the elements of information, iteration and entry motion are performed by N, C and O molecules. They will form the triad of all biological ternary organisms at the bio-molecular level.

So we shall write and then explain those 3 ‘symmetries’ between the 3 types of dimensions of the Universe, because they encode the whys of infinite particular events in time and forms in space and its organic combinations we observe in nature:

Ω.<    Past-youth-energy (Time D.) <=> Length (Space D.) <=> ∑i-1 Energy field

Ω.≈   Present-Reproductive-repetitive (Time D.) <=> Width <=> i-wave/body

Ω.>Future-3rd informative age (Time D.) <=> Height <=>∏ i+1 Particle Network

Now the first ‘symmetry’ both physicists and biologists ignore is that between the 3 dimensions of space and the 3 of time. Since:

Length is the dimension of energy and pure motion, as the line is the shortest distance between two points, and so it is the dominant dimension of young species and young individuals that ‘move a lot’.

– In the sample case we wanted to illustrate (the relationship between morphology and evolution in species), all species are born as ‘long’ flat forms. The first fishes were long, flat sharks; the first species were flat worms; the first earth-bounded animals were flat amphibian.

– Height is the dimension of information, as a tall position is an advantageous point of view of perception, as ‘projective geometry’ shows. So in social sciences we all know politicians and priests go up into a pulpit, and informative machines have tall antennas to distribute information and screens are flat, high forms.

And so are gravitational black holes in the center of galaxies that rule it with gravitational forces of in-formation that form the galaxy. And so on.

So in the biological case we study, life has on the whole evolved from a flatworm to a tall human being. And in each species the same process takes place. So flat sharks flip their body into the perpendicular dimension of fishes, flat amphibian ended up becoming tall dinosaurs and birds, and mammals become bipedal.

Finally width, the product of the other two dimensions is the dimension of cellular reproduction, and so bodies grow in the width dimension and stars accumulate into a width, spiral dimensions, and Maxwell’s rule of thumb make any student understand that the combination of the ‘energetic’ and informative, magnetic and electric fields create a perpendicular dimension.

And light is an existential being with 3 ‘perpendicular’ axis, where in this particular case, the magnetic, electric and speed axes are in a diffeomorphic perpendicular dimension to each other, each of them with an energetic, informative and reproductive function.

So the reader will notice again that as in the case of physics, knowing the ‘nature’ of the Game of existence and the meaning and symmetry between the 3 dimensions of space and its 3 functions in time helps a lot to understand the whys of reality. As it did, in the previous example the understanding of the symmetry between the 3 ages of time and the 3 social scales from cellular birth into individual and finally into a social being.

It is essential to understand this astounding new insights of complexity over physics, departing from the nature of the 3 type of dimensions – spatial, temporal and scalar – which bring 3 type of ‘properties’ – mathematical, logical (causal) and social (Organic). Since only now, thanks to those insights we can ‘integrate’ the true properties of reality together, unlike the ‘previous age of scientific knowledge’, based in ‘entropy-only’, mathematical, spatial measures, which limited to 4 Dimensions (where cyclical time was deformed into lineal duration), ignored completely the causal and organic properties of the Universe.



‘We are made of relational space, we occupy a vital space, and we are made of clocks of time, of world cycles of time, we are NOT in a background space and time graph, as Mr. Newton believes.

 ‘Letters to Clarke’ rephrased by author; Leibniz author of the relational model of space and time, fore bear of the 5th dimension.

‘The logic of Logos, mind of the Universe is of a higher order than man’s’ Saint Augustine

Humans have come to think science is just gathering data, put in 3D models of computer with algebraic equations, in a sort of automaton process of memorial learning rather than rational knowledge. In this huge detailed analysis, the forest has been blurred. And never evolved beyond its inception.

The Universe is a game of creation of ‘in-form-ative’ forms with entropic ‘motions’. Humans use the concepts of space and time to describe the game, albeit with a very primitive understanding of them (never mind their ego is so huge, whatever they think whenever they think seems to them an absolute truth, a new discovery, a genius insight). We shall try to upgrade the mind of humans in this blog, starting with the understanding of the complex logic of the three arrows of time, as humans use one aristotelian one-dimensional logic, and the fractal structure of the points of space, as humans still use the concept of an euclidean point without volume of information.

Thus the logic of cyclical time (ab. πime) and fractal, œrganic scalar space (ab. §paœ) is of a higher order than that of present man, which is stuck in the 2500 years old r=evolution of the mind of the axial age, and needs a new refurbishing.

So what is the logic of the Universe? The properties of it ∆º±st elements, and the way they combine and play together, synchronising its forms in space and evolving its motions in time.

Time is mindless motion of three types that singularity mappings, the synchronous miracle of existence put together into ternary ensembles that become.



In the graph, the oldest and most modern, precise derivation of the laws of ternary symmetries between space and time states and scales of the Universe. Below the 10 dimensions of all systems, in this case the perceived Universe. The rules of engagement between those 3 x 3 + œ dimensions of the being define how reality is created and extinguished, the world cycles of existence of  supœrganisms, all of them trying to maximise its space-time ‘being’. The 3 x 3 dimensions of super organisms

3 obeys to the co-existence of §upœrganisms with three topologies that dominate its forms in 3 planes of ∆-existence, which form the whole individual of an ∆º scale – just a finitesimal performing o-worldcycles in its upper social ∆+1 ecosystem or island-universe.

So 3 are the roles and scales of super organisms. And its study will allow us to go deeper into the questions that ‘matter’ about §upœrganisms in the fractal Universe and its translation into a few key mathematical differential equations (as analysis are the mathematics of ∆-scales), which apply to all §upœrganisms.

The 4 elements of existence: time-space, and information and energy, parameters which a few more ‘planes’ .

In each plane of existence of the Universe there are two fundamental elements, ‘space’ and ‘time’, or ‘energy’ and ‘information’. We humans perceive those 4 parameters in all systems. But in that perception the mind influences the way we see reality. What is then the ultimate reality?

The answer is simple but not easy to accept: Motion and form, of two types, lineal and cyclical motion; which manifests itself with different complexity depending on the number of ‘planes of space-time’ we perceive in increasingly complex manner. So the simplest perception, lineal speed and cyclical form, becomes acceleration and rotary motion, when we add a ‘new dimension of time-change’, and becomes momentum and angular momentum, when we add the concept of inertial mass, a scalar magnitude that integrates several scales; and further on becomes Energy and information, ‘form in action’, when we add the v/2 factor to momentum and a slightly more complex ‘reproductive factor’ to angular momentum.

This increasingly complex Universe born of adding dimensions and planes of existence to our perception, however is not the interest of this post. We are here trying to explain you the basics.

Thus in this introductory ‘first line texts’, we do NOT quantize excessively those concepts, neither we make strict definitions. We shall do this in sub posts and 2nd and 3rd lines. The interest we have at this stage is for the reader to have a feeling of the complex Universe and its paradoxes and dualities.

Now what matters is to capture the essential concept:

Space and Time  apply to the understanding of phenomena with minimal depth of ∆-scalar dimensions.

-Space would be the perception in a single plane of reality. Hence we talk of ‘lineal space’.

– Time will add motion, and form across ∆±1 scales, the seminal, individual and social scales. So we talk of time as change through those 3 scales.

– More technical physical parameters as energy and information very often used as synonymous of space and time, will start to add ‘parameters of the multiple planes of existence – Mass, which is in the concept of inertia a scalar parameter of the interaction between 3 scales of matter, the ∆-4 gravitational forces, the human scale and the cosmic scale of planets, stars and black holes; temperature is another scale parameter of the vibratory motions both cyclic and lineal of i=3 molecules. And so on.

Those are general ‘precessions’ for the quantitatively inclined scientist which we deal with rigor on the posts on mechanics, states of matter and other specific sciences. Here we want you to have and grasp a more layman understanding of those concepts, which make our existence: motion and energy as the substances and capacity to move and change our motion; form and information, the capacity to transfer form through a medium and disseminate it.

That is the simplest realities, motion and form, ad a little bit of the yin in the yang and yang in the yin to become motion≈ energy and cyclical form≈time≈information.

And existence consists in playing with forms in motion and motions with forms, energy and information, combining it into infinite beings, across multiple planes of space-time. Existence is to e x i = ST, transferring energy and information between different planes and entities with a single aim: to ‘act’, reproduce, perceive, move…

Action is the content of existence, and åctions are cause by the messing of those 4 parameters, by a ‘will’ a zero-point, across several scales.

So perhaps we should consider the 4 languages of existence, the languages of motion, space and energy, the languages of time, cyclical form and information, the languages of planes of existence and the language of zero-points of perception.

The languages of existence.

What are then all the languages of the Universe? 4 according to its 4 fundamental reality, space dimensions, time ages, social planes and zero-points that perceive it all and have a will expressed in its åctions of energy and information.

But to the Universe it matters, and any attempt to understand it requires to understand that ‘the languages of God are infinite’, namely 4, and without them it is impossible to understand more than some shallow details, as physicists do;

  • The language of mathematics, but of a higher ‘complexity’ to the present work (Non-Non Euclidean mathematics of fractal point with volume).
  • The language of causal, cyclical logic, proper of the 3 ages of time, past, present and future, which are essential to all systems and events including those study quantitatively, from the understanding of motion and its 3 ages (acceleration, speed and deceleration) to the 3 ages of the Universe (defined by the 3 solutions to Einstein’s equations, according to the ±0 value of the cosmological constant).
  • The language of biological systems, which are organized across 3±∆ scales, that is the languages of organisms co-existing across multiple planes of existence.
  • The languages of zero-points of perception, the will of the Universe, the sentient language of the 5 åctions.

Unfortunately of all this humans have been reduced to talk mathematics for all, including time. And thus there is very little they can understand. We talk here all the languages.  As all apply in a certain measure to every phenomena, or as ‘taoists’, the philosophers of antiquity that better understood the duality of yang-‘energy’ and yin ‘information’ said – the generic names we use more often for ‘motion’ and ‘form’, (perhaps wrongly as we are not defining them in a quantitative, physical manner as Helmotz and Shannon do, except in specific quantitative analysis but a generic term for the duality of the Universe) :

‘All yin has a yang.’

And this is perhaps the fundamental duality of reality: Pure motion is not perceived because it has no form. Pure form is not perceived because it is static and does not communicate. All what ‘exists’ thus has a drop of yin and yang. And so the concept of Motion and Form are ideal, mathematical. reality starts when motion acquires some form, becomes form in motion, which can therefore be communicated – that is becomes a transversal wave. And vice versa, when form acquires some motion, becomes a wave also, but of cyclical form. The ‘increasing’ complexity of the physical terms that we shall use to define existence beyond this primary limit of: Motion x Form = Wave shows how ‘deep’ the scalar Universe is. And how shallow the human perception of it, limited by our senses…

Let us not at this stage worry for the quantitative analysis, we shall do this where it is proper to do, in the 8th isomorphism ‘constants’ and in the first scale ‘forces’ and the 4th ‘matter’, as it is in those scales where we perceive in physical, quantitative terms the Universe. 

Just bear in mind that we are talking here of more generic terms, form or information (form with its little yang of motion) and motion or energy (motion with a little bit of form), as those ‘generic’ qualitative names for the 2 dualities.

And what matters to this first approach to existence, a game of ‘combining motion and form’, acting with both, and perceive them both, is how we combine them indeed into åctions, and how we perceive them either in fixed or moving terms, to which e will ascribe the 4 elements of reality, Space (energy perceived in static manner) and Information (time cycles perceived in static manner).

What differentiates them from ‘pure motion and pure form’ is precisely that pure motion would be merely a single ∆-plane of lineal length distance perceived in motion, and pure form would be a mere cycle of time perceived statically, but reality co-exists in several scales and that is the reason we have more meat in all motion, (mass with motion or momentum) and in all time cycles (cyclical change of living beings, etc.)

It is this mind’s synoptic messing view of all those ‘neat’ scales together, what makes so difficult for the human scientist of the ‘3rd paradigm’ of measure to get into ∆ST… He would like reality to be easy and simplex, but it is not. The mind messes from gravitation to the cosmos all planes of existence, reduces their information according to uncertainty rules and describes qualitatively many ways of change. So when humans reduce themselves to just a mathematical description, they can get little more than ∆-4 laws of motion. Let us remember that evolution, the theory of change in form is verbal.

All this said, we shall try to simplify so you understand or rather have an intuition of what existence as a being of energy and information (motion and form with ‘∆-scalar parameters added to it), is.



The generator equation of the Universe resumes all the invariances and scales of reality and its main symmetries and harmonies, in time and space, which are studied by the Ternary method of knowledge.

We have now all the elements of the game: the actions p.o.v.s. perform which are the ‘dimensions’ of spatial perception; the temporal dimension, integrated through a language by the p.o.v. and the Mandate – Game of maximal exi=stence they all play. And with those elements we can understand everything else in the Universe.


‘The Universe is simple and not malicious’ ‘Leibniz is right, space-time is relational… there are infinite time clocks in the Universe, but if so, we must restart physics from scratch’ Einstein
the Universe is a broken puzzle of three motions of time-space:

  • RELATIVE simpler past lineal entropy, |-Se (expansive, lineal motions, which disorder information and move faster as the line/plane is the shortest distance between 2 points; as in fields and limbs).
  • Relative more complex, future cyclical in-formation, O-Ti (cyclical motions with more dimensions of form than the line, which seem not to move and so become sinks of attractive forces (charges, masses) or heads/particles that process information in their spherical form – the volume that stores more information in lesser space.

Function and form coincides, so entropy functions of time correspond to lineal limbs/fields in simultaneous space. And spherical vortices that attract or process information become masses, charges, particles and heads. We thus realise first that ‘timespace arrows’ are broken into infinite beings, which assemble those parts, and we call the cyclical particle/head charge/mass the relative future arrow of the system as it is the ‘gradient towards which fields move’ (in physical particles) or the more complex dimensional form, as a cycle needs two dimensions and an entropy line one, so it comes ‘late’ in the future of evolution; or it is the head-particle that processes information, placed ‘ahead’ or in a ‘tall advantageous point of view’ and so it comes first to the future.

So physical systems are made of relative lineal-past fields/future-particles and biological systems are made of relative past limbs/ futureheads… and its intermediate:

  • Ø-present hyperbolic Se x Ti body/waves that combine both motions of spatial entropy (spatial as it is more extended in space) and temporal information (as it has the cyclical form of time clocks) into a third type of motion, hyperbolic body-wave iterative ‘momentum’, or its integral energy; which encompasses both lineal entropy and cyclical temporal information. It is thus the most important creative part of the Universe, the relative ‘present system’, which the Universe conserves.

And so the three parts put together form a world cycle, as systems of motions can also be described by an initial accelerated expansive impulse which reaches a steady state and then curls and stops finishing the three ages o the motion, and any other system of knots of space-time cycles, called beings and species, will show also to have a relative order in the dominance of its three arrows of time, as systems are first young, entropic, dominated by motions (childhood, youth), then are iterative reproductive finding a balance between its entropy and information, dominated by its body-waves (exi=st, the acronym we shall use to describe the ‘function of existence’ in time through its three ages and three organs fro all beings) and finally a third age of excessive information, warping and wrinkle, where the curved topologies of the Universe dominate.

And since there are only three topologies in the Universe, three functions, three times ages, after the system complete its world cycle, and all its entropy-motion is reduced into the ‘singularity of form’ of its mind, vortex force or warping third age, the system suffers a finite, time ‘reversal’, and its information erases into entropy in a big-bang or death process.

This extraordinarily simple but telling logic configuration of systems with three time arrows and three time ages, to form a world cycle of ‘exi=stience’ (acronym for the fact that exi=st systems are ALL THE SYSTEMS described by all ‘stiences’; which will allow us to do philosophy of science also in verbal, conceptual terms), was always known in classic philosophies of science both in the west and notably in the east (so TAO=TIME BEINGS, IN TAOISM where made of yin-information and yang-entropy combined in ‘waves’ of 10.000 beings’ Lao tse).

Humans used to be aware of this FUNDAMENTAL i-LOGIC STRUCTURE of all systems of reality, before Galileo applied a convenient artefact of measure, lineal time, discovered by pegging together the time cycles of beings, ‘erasing’ the detailed information about those cycles (frequency and form of the cycle) to measure easily motions which were repetitions of a time cycle, with its 3 time arrows (acceleration, steady state, deceleration). So Galileo unified those time cycles and its frequency and ‘steps-forms’: v= λ ƒ, into lineal time, V= S/t.

The reader will notice the fundamental characteristic of Galileo’s new definition of time, not in terms of times, as it had always been done, but of a single ‘sum’ of all the steps, without caring for the ‘cyclical form’ of the moving finite system (your legs, a wheel of a car, an orbital motion).

Ever since what we improved on the detail of our ‘lineal measures’ of motion – the arrow of entropic time, or lineal moving expansive disordered scattering motions, was lost in the understanding of the meaning of information, frequency patterns and the combined momentum/present and its ‘energy conservative world cycles’, which made the Universe immortal and infinite.

And it has brought gruesome errors in our understanding of reality, specially because as only ‘one lineal entropy-motion of time’ was accepted, all theories of reality leaned towards big-bang-death-entropy theories which re plainly false, as they describe only 1/3 of reality (one of the three arrows of time).

All what exists is 5 Dûs≈t, as such nothing matters anymore as all dust have the same ∆º  pov, equal amount of information, if we define a ¹¹11 bit of information for a given Universe, then all supœrganisms, will have that number of bits which we use for a Universe, or 11¹¹ for a world within it.


‘All what exist is a being of space-time, defined as such by a fractal generator, organised by networks of energy (fields/limbs: |Spe), information (heads, particles: Tiƒo) and its body-wave combination: Max. ExI(s=t).’

Function of Existence. L.S.

Another point of view on the understanding of the ∆ST• being, is provided by the fractal generator, which allows to analyse the interior of the being by the fractal method of decomposing it into its parts, systems and subsystems of spatial energy and temporal information. This is in fact the approach of medicine, which is physiology and studies the organs attached to the 3 networks, of energy-information and reproduction (digestive, nervous and blood systems) which define the entity in its first lower layer, departing from the whole. This study thus will analyse the 3 parts, ensemble according to the symmetry between space and time described by the fractal generator. Let us consider it.

The method of study of ∆ST species. 

The fractal generator:

∆-1 $pe < ∆S≈T > ∆+0 Tiƒ

and its 9=0 symmetries, its 3 topologies in space, 3 ages in time, 3 scales of the ∆-Dimension, resumes the essence of a being, its existence, which consists on tracing world cycles, of 3 ages, as super organisms, of 3 topologies, co-existing in 3 ∆±1, cellular/atomic, thermodynamic-organic, social/gravitational scales. So when we describe any being we depart from its specific fractal generator that explains in detail its 3 organs, 3 ages in time and 3 relative scales of the 5th dimension in which the organism co-exist.

Those 3 symmetries describe all beings in time, space and through its entire existence.

For example, in the next graph, they describe the existence of the human being, its parts, organs in space, ages in time, and relationship with its lower and upper scales through actions of energy and information:


Topology: tall spheres, long lines, wide waves.BIDIMENSIONAL

In the graph, the 3 only space topologies of the Universe, spheric informative, lineal, energetic and hyperbolic, reproductive (as it mixes the other 2) and its 3 equivalent functions≈ time arrows=motions  can combine in any form to create as synchronic organs the infinite varieties of species of the Universe.

So we shall find multiple ‘spatial organisms’, which are constructed following the combination:

Past-entropy (limbs/fields) x Future-information (heads/particles) = ± Present system.

Time. Past-present and future.


Those past to future combinations are either positive creative processes that forms balanced organisms or negative, darwinian processes that annihilate both (particle-antiparticle collisions).

Thus, the Universe is a game of 3 motions with form, and those 2 elements, the temporal motions with force and their still perception as spaces with form, with intelligence, structure the Universe.

The 3 motions in time, which we shall call, P, for entroPy and past, R, for pResent, Reproduction and Reality and F, for future, form and frequency, are complementary, often sequential, PRF, and causal; and while its perception as motions doesn’t bring much understanding, when we study them as fixed, still forms, we observe an astounding array of parallel structure on all those seemingly independent motions, which create a ‘spatial organism’ that works. It is the interplay between those 2 antithetic elements, the 3 motions of time, past, present and future, and the 3 still perceptions of space, toroid, hyperbolic and spherical organs, what gives birth to the dual space-time beings we observe around us.

In that sense the minimal Unit of the real Universe is a 2-manifold, space-time combination, as pure time or pure space, pure yin or pure yang, pure motion or pure form-stillness cannot be perceived. So all what exists is a 2 manifold that we might perceive as static space (a 2-manifold sheet) or as a point with motion, (where motion is one time dimension and the point, the minimal fractal unit also with a 1 dimension – as there is not 0-dimensional, ‘euclidean points’ in the Universe).

if we were to resume the essence of reality we would say that we exist in a reproductive fractal of energy and information.

The existential feed-back generator equation combines energy and information according to the non-æ rules of engagement of both forms, which become stable symmetries: Spe<=>Tiƒ, ternary equivalences between 3 motions of time and 3 topologies of space:

Spe <ST>Tiƒ thus becomes also a past<present>Future flow of actions…

that become world cycles of information and generate in its maximal point, Max. ExT: ext…

or middle point of its curve of existence worldcycle, a new generation and so the frequency of ‘generation’ of world cycles, which are ternary action-reaction waves formed by the creation of an Spe>Tiƒ:

SCALE: ∆-1: molecule > ∆-cell > ∆+1: organism.

3 scales

In the graph, the 3 scales of the super organism. They form together with the 3 arrows of time and the 3 topologies of space, the 3 x 3 isomorphic elements common to all systems of the Universe, which define the game of super organisms. 


From a theoretical point of view, both analysis related to the ∆o scalar mind and its S<St>t space-time topological parts are necessary to fully descry the organism, and since we exist in an intercommunicated Universe, in which all elements are constantly connecting through flows of energy and information with parallel beings and predating or being predated by smaller and larger, ∆-wholes, in fact each of those approaches can be decomposed ad infinitum into new perspectives, ceteris paribus analysis, and further on use the ternary method to sub-study each part into its ternary parts.

How to approach then a field so extensive as the Universe itself? There are always some themes and symmetries, which are the key to structure the being. So as this first line is a general introduction to the whole nature of scalar space-time supeorganisms and worlcycles, and the will of existence carried by its minds we have reduced the description of the program of existence that all systems of the Universe follow in its simplest terms, with a Decalogue of laws derived from the nature of all what exists as a complementary system of scalar, energy and time hence present in all systems.

These are the basic tenants of General Systems sciences that studies the program:


 Reality is made of actions of quantum energy and cyclical time.

The Universe is made of two substances spatial energy and informative time. We can see it with motion as energy and time or as fixed forms, as space and information. We can see it as a single reality, as space and time, or as a multiple quanta, as energy and information. We can differentiate them by form, as space and energy are lineal or planar surfaces and time and information are cyclical. And we can see it together into beings,  the simplest of which is an action of light, ext=k. And this simple duality structures all beings of the Universe. So we are made of cyclical heads and lineal bodies. Weapons are lines that release energy. Informative machines are cyclical, and all physical systems are made of lineal forces and cyclical particles of information.

The inverse properties of spatial energy and temporal information.

To fully grasp the dynamic transformations and properties of energy and information the most important quality is the inversion of its properties and the possibility to transform the forms of one property into the other.

Informative time, Ti                         Vs.       Energetic Space, ΣS 
Time-clocks:Information                 Vs.        Space motion:Lineal  energy
Small, still                                            Vs.        Large,  moving fast
Tall, Perpendicular                            Vs.              Long, Parallel,

Hierarchical                                        Vs.                   Democratic
Bidimensional   Height                     Vs.            Bidimensional, Length,

Repetition                                            Vs.                    Width-Growth
Cyclical, Rotation, imploding          Vs.            Lineal, uncoiling, exploding
Informative Frequency                     Vs.                            Lineal Speed
Broken form                                       Vs.             Continuous, differentiable
Intelligent, perceptive                      Vs.                         Strong, fast.

Social, organic, creative                   Vs.            Darwinian, destructive behavior
Future, evolved predator                 Vs.                 Past, energetic victim
Life arrow                                           Vs.                      Death arrow.
Waves of space                                  Vs.                     Particles of Time
Female, yin principle                        Vs.               Male, yang principle
Masses, charges                                 Vs.                       Forces, fields
Heads  & senses                                 Vs.                       Limbs & Bodies.

This resumes in its two fundamental equations: e x I = K (that describes any complementary system of energy and information,  in space) and E<=>I (which describes it in time as a series of flows of transformation of energy into information).

The constant transformation of one into another.

Despite their inversion, and this is the most important law of the Universe, energy and information constantly transform into each other. It is the principle of ‘conservation and transformation of energy back and forth into in/form/ation, forms in action’ which becomes the new fundamental law of the 4th paradigm, widening the principle of conservation of energy:

‘All energies, trans/form constantly back and forth into information, E<=>I’

Thus the Universe is truly an eternal infinite of beats of energy warping into dimensional form, information and informations uncoiling into spatial energy. And since both elements energy and temporal information have motion this is possible as they are truly just the two extreme types of topological motions of the Universe, each one associated to a series of ‘functions’ and ‘perceptions’:

Energy=Extension=Space= Fast motion  = Lineal, planar shapes = Pleasure = Reproduction = Death

Information=Implosion=Time=Slow motion=Cyclical ball=Pain =Communication = Evolution = Life

The infinite balances and combinations of those two fields and its forms are the essence of reality. The simplest of those combinations is an action of energy and time.

Actions of energy and time.

The why of the Universe turned out to be rather simple and biological, more than physical, even if it was a discovery that starts in physics with Planck’s realization that the simplest Unit of reality is NOT a substance but a cyclical action of energy and time. Quantum and cyclical are treated as synonymous, a quantum is a form that we might perceive as fixed and substance but it is really nothing but a morphological motion, traced by a being, that in the specific scale Planck studied, we could hardly see, the light-space. But all what that being did were actions of energy and time.

But can build the Universe departing of those two primary substances or ‘arrows of the Universe’? Yes we can. And that is what I did back in the 90s. The concepts are easy, if you are able to transcend your memetic imprinting and ignore Mr. Planck’s desperado dictum when nobody listened to his astounding discovery that we were made not of substances but actions and hence motions (‘for a new paradigm to be imposed all those who learned the previous paradigm must die’).

So try to follow me with a ‘Tabula Rassa’. You have two entities, energy and time, and they have motion, so they create actions. The simplest combination is called an h-Planck constant. That gives us a first ‘being’. Now forget your abstract, earlier Hegelian imprinting (this you might not know, but history of science tells us earlier German thinkers were idealist as philosophers of science and did not consider the Universe made of ‘realities’ but of ‘mathematical probabilities’). Think rational. h-Plancks are ‘real’, the simplest bricks of the Universe, and they are made of energy and time. In fact you perceive light, when you stop seeing light you stop seeing the Universe of space-time.

Therefore the space-time Universe we perceive is made of actions of light of energy and time. And physicists have discovered that indeed the vacuum is made of energy, which moves and change in time. But we said the Universe of space-time instead of the Universe of energy and time. Space has become energy. And indeed, space and energy are two ways of seeing the same thing.  Then we come to the other term Time…. But we use in many sciences instead of space and time, energy and information, so time and information, ‘form-in-action’, form must be related. And yet we use clocks of time, cyclical forms to measure time.

All what exists is made of space-time, in abstract, of energy and information, self-similar terms.

Now when you say ‘I don’t have energy and time to do this’, it is obvious that subconsciously you know the two substances of what you are made, energy and time and you are right. Because what you are, what we shall describe in this book in great detail is how you ‘become’ yourself, departing from the two primary substances of the Universe, energy and time, which together form an action, the basic unit of reality.

So Duality deals with that fact, and extracts the laws of energy and information. Now, think again, what else can be there? The simplest thing is to combine energy and information, and you get a 3rd entity. This combination e x i, or e x t, if you want to use Quantum or Einstein’s notation, turns out to be the essential equations of physics. So we are on the good path.

Thus now we have 3 arrows, energy, information and exi, that we shall call the arrow of reproduction or creation, as it creates a third entity, one which is made of two substances, and turns to be an ‘action’.

What else can we find there? Since there are many bites of energy and bits of information, we can combine them, and then we find the 4th arrow:

∑ e x i

This equation, which the reader should observe includes all the others, is what I have called the Generator equation of all the entities of energy and information or space and time of the Universe. And from that simplest equation and the interaction of its two ‘simple arrows’ or motions, we create its two complex forms, actions and societies. And this, my friend is all what we shall need to explain you all what exists and more… what you don’t see but it exists also in other fractal scale of reality.

Those two substances can be seen as a whole space-time or as two space and time or as a sum of parts, many spaces and times. So space can be seen through perception as a single, quiet space, adding all the ‘vital spaces’ of which is composed, or as a sum of ‘quantum energies’ and ‘vital spaces’ that entities occupy. Time also can be seen as a single clock-time for the entire universe, measured with our mechanical clocks or as an infinite number of cycles that all entities trace, each one with a different speed and rhythm, each one with a different ‘form’ or information, provided by the shape of the cycle and its ‘frequency’. So Space is synonymous of Energies and time of informations:

∑ E = S; ∑i=T

This is the first key concept you have to assume to understand the Universe beyond its useful measure by physicists with a single clock.

Further on, we recognize both types of entities by their form: clocks are cyclical, so it is information and its systems. Space is a lineal plane, so are energetic system. This leads to a key principle to understand and classify entities of reality: Form is function. And so the ball – the inner part of a sphere – is the perfect form of information as it is the shape that stores more form in lesser space, and the line or plane the perfect form of energy, as it is the fastest motion/biggest surface of space between two points.

So now it is clear what it is the game of existence, the Universe: a game of relative organisms, of each scale of reality, performing externally in an ecosystem, its space-time, cyclical actions, switching among its tasks of energy feeding, informative perceiving, reproducing and keep in harmony with the self-similar points of its energetic, informative and reproductive social netkwrs.

In brief, we exist in a series of parallel games of feeding, perceiving, evolving and reproducing. And all of us can be perceived externally as ‘points of view’, Non-Euclidean points, playing this geometric and biological, existential game:

We are all knots of discontinuous, cyclical actions of energy and time.

Energy and information have inverse properties. Energy is lineal motion; informations are cyclical forms. Thus both are two types of motion, |-energy and O-information, equal in power and interacting and transforming into each other constantly. This principle of conservation and transformation of energy and information becomes the new fundamental law of science: ‘All what exists is a complementary system of bites of |-spatial energy and bits of O-Temporal Information: E<=>Ti.‘

And that duality of substances/forms/function structures all our actions:

Indeed, all systems are complementary systems with heads that absorb, perceive and process information and bodies that absorb, perceive and process energy.

But the previous graphs and equations refer basically to a bidimensional system and we live in a 4-Dimensional system with 3 spatial dimensions and a 4 dimension of motion, which puts together all the cycles of time, all changes of the Universe (and we shall explain with far more detail, including the meaning of its own 3 dimensions, past, present and future, in this work) Thus the next step of a complete analysis of energy and information is to consider those forms of motion in 4-dimensional space.

2. There are only 4 actions of energy and time that all complementary systems perform.

The science of General Systems or complexity describes all entities of the Universe with the same laws explaining the reasons why those entities exist, its forms and functions, its actions and its life/death cycles and reasons why they become extinguished. So its laws of creation and destruction of all Universal species can be considered that ‘program of the Universe’ or ‘program of existence’, which traditionally in mythic terms is equivalent to the concept of the will of God. Yet it is not a personal God-will but rather an impersonal, biological, evolutionary program which reinforces itself through evolution and survival:

Those who do not obey or seek the 4 arrows/actions of the program, which is the strategy of survival of all species, die away, and so the will of the Universe must be obeyed, or else we become extinct.  We are free to deny the program (as humans, we shall see do in this moment of history) but if we do not gather energy and information for our body and mind, if we do not reproduce and we do not evolve socially and interact with similar species, chances are we shall not last too longer and die away. And so the program will be carried further by those who did obey the ‘Law’.

All systems perform 4 actions to survive that define a simple program of ‘existence’, which all species of energy and information follow, to survive. 

The deduction of the program is simple. First, all what exist is an action, which has 2 components, exi=k or exT=k (depending on which self-similar concept you choose information or time) and there are many quantic actions. So all what we can do is 4 type of actions that we shall call ‘arrows or motions of time’:

Those arrows or actions all species made of complementary bodies/fields of energy and heads/particles of information perform to last in time and space will be:

–     ∆E:  They feed on energy for their bodies/fields.

–     ∆I:   They absorb information for their heads/particles.

–      Exi:  They act combining both, and the most common action as we shall see is to combine them both to reproduce you in other zone of space and time and survive after death (or become reproduced by an external catalyzer, enzyme or ‘enzyman’ – machines).

–     ∑ e x I=Ii+1 They evolve socially in more complex networks that survive longer in time and space.

The 4 arrows are ‘necessary’ for any complementary system of energy and information to exist. As any system will die if it doesn’t replenish its energy and information, or reproduce before death.

Further on the 4th social arrow creates stronger top predators, either herds (loose groups of self-similar organisms of the same type) or organisms proper (more connected systems that organize 3 sub-systems, heads, bodies and limbs, specialized in information or formal structure, reproduction and energy, all of them connected by a 4 system, the linguistic system that organize them all).

Consider yourself as a being, which will follow its path of time motions unaware that the sum of them all will be a spent life without anything but a trail of forgotten actions, which only your finite ego commands and understands. What is your freedom? rEALLY NONE, except to think you are free to manage your actions, but at best you would just perform an excellent game by closely following the rules of justice and balance in the golden mean path of maximising your function of existence, max. exi (s=t) the same boring strategy that all systems do follow.

First definition of the Universe

The Universe is a system of networks of knots of actions of energy and time, perceived in static space as forms and organisms, and in time as motions and causal chains of cyclical actions all of them put together into the causal chain of life-death cycles.

The Universe perceived in time is a game of beings performing cyclical discontinuous actions as they switch between feeding, perceiving, reproducing and acting in social networks.

The most important of those actions is the reproductive action that preserves the game, and the most important ‘time cycle’, born of a series of causal actions that chain each other is the life and death cycle, which thanks to reproduction allows generational immortality.

The interaction between beings performing those actions between the limits of life and death causes its selection, extinction, recreation, fusion and fission in bigger or smaller network-entities.

The interaction of all those cycles in perfect harmony can be defined by a single function, which resumes the 4 actions of time between life and death, max. ExI, where E is energy and I information, quantum terms closely related to the universal equivalents, Space and Time cycles; as Space is the sum of all energies and time the sum of all informative cycles, all the discontinuous repetition of the being’s actions which carry different frequencies and intersect each other.

Thus the function of existences is the mystique, final equation of the grand design of what you see.

In this post we will resume in a decalogue those actions, its laws, the forms and functions that accomplish them, how those actions are organized in ages, and how their frequencies and balances define the actions of the main species of existence.

The creation and reproduction of new forms-in-action,informations, existential Spe<St>Tiƒ beings, follows simple rules which can be resumed in the constant reproduction of waves of existences, Max. Exi (s=t) functions, which maximise the energy and information of a domain,  Max. e x Max. I by maintaining a balance and internal communication between its Se and Ti elements, in a point S=T, which maxmize its product.

All thus can be reduced to the function of existence, which decomposes in the basic actions< max. e (feeding moving) max. I (perceiving information communicating) Max. e xI (reproducing) E= I (balance and beauty), Max. ∑ E, I (SOCIAL evolution and quantisation).

The feed back function, E<=>I BECOMES FIRST a static, balanced e x i (Spe=Tiƒ) organic system of two poles and then develops this maximal function, through a series of quantised actions, directed by a point mind that acts as the knot of those space-time cycles, trying to increase them all in quantic balance and synchronicity. It is then the stud of those harmonious synchronous chains of space-time actions, Max, e, i, exi, ∑, what brings us the details of the different functions of existence of Spe<St>Tiƒ, SUPEROrGANISMS & its world cycles, integral zero sum of all those actions, ∫∑ e x i ds dt=0

The discontinuous nature of cycles of actions.

Actions are discontinuous because they happen from time to time as systems require new energy, information, reproduction and social interaction. This creates discontinuous frequencies and formal patterns that relate cycles of actions and information.

We obtain information from those patterns that allow us to describe those actions and cycles.

Any cycle in which a being performs an action has an end in time and a discontinuous, quantic size in space. Thus, the Universe is continuously differentiable during the cycles of time their beings performed, but when the p.o.v. switches its action it has a point of discontinuity, what we see is the trace of those cycles of actions that ‘draw’ the 4 dimensional space-time universe

Beings constantly create actions of energy and time. What you see are knots of such cyclical actions… fabricating time. What we see are the trajectories of beings performing in an alternately causal way their cycles of time. One of the most common cycles is to have a p.o.v. become a focus of a force, which acts as its source of energy and information. A first paradox of Galileo happens here, as we can perceive the point as static and feeding, moving along the field of energy and so we can establish a static or dynamic analysis.

Those points then ill feed along that path and a certain moment satisfied that action will try to fulfill others, and in that switching on and off actions will seem to disappear and new, different trajectories motivated for another action appear. If we see densely packed in time and space those actions they will be sequential and those causal sequences are the stuff that latter (paradox of Galileo) seen as a package of space-time or organism, are the reality we see in its infinite fields.

Relationships between the simplex and complex arrows.

The dualities between external, spatial and informative, simplex forces/actions and complex, internal forces/actions/networks create a series of patterns and synchronicities that are repeated in all systems.

The simplest relationship is one of causality between the simplex and complex arrows:

∆ Energy->Reproduction and ∆ In/Form/ation->Social evolution through a common language.

Complex reproduction requires a great deal of energy to be achieved, so for example women cannot have children without a proportion of body fat, and most cells do not undergo mitosis without a cytoplasmic growth. So reproduction is the complex arrow of energy and we observe many causal relationships and ‘cycles’ of the type:  E->Re. On the other hand social evolution depends of a language of information that the different ‘cellular elements’ understand. Thus social evolution is the complex arrow of information and we shall also observe many relationships of the type:  ∆i-> ∑ e x I.

The most important inverse property of those space-time cycles is the fact that each cycle/action of time has a different duration and each scale and organism has a different speed, according to the ‘Generator equation’: Max. E = Min. I and vice versa. So in life smaller species have a faster methabolism. In physical vortices of information, such as mass… the faster they turn, the more they attract and the smaller they are, with a black hole vortex of gravitation, which turns at c-speed in its event horizon and attracts more than the bigger, slower turning stars, as a Universal limit.

Creation of social scales, in which each whole is a unit-part of the next scale.

Complex, social evolution helps most species to survive, especially when they reproduce in great numbers, creating a ‘new scale of reality’, self-organizing themselves with a language of information all those cellular particles share. And we measure this fact with a scalar, fractal index of new scales of existential functions, i. Normally all systems must be defined at least in 3-4 scales:

– The lower, i-2 (bits of information) and i-1 (bites of energy) scales defined with mathematical/genetic/memetic languages, depending of which systems we analyze in its details – a biological, sociological or physical system. We perceive this scale as bits of an informative language – which gives us a synoptic minimal information of the properties of the entity. As the i-1, i-2 levels, as it is far removed from us in size and so we introduce uncertainties and loose information.

Then it comes an i scale, of our size, where information is maximal. So we observe more information explained in a complex manner. Thus in the i-scale we deal with chemical molecules in physical systems, living cells in biological systems, humans in history and corporations in economics, using topological, organic, psychological or econometric methods to define their actions.

–     Finally in the i+1 scale we perceive ‘states of matter’ that define masses of molecules of energetic (gas), creative/reproductive (liquid) or solid/informative nature; we perceive organs and organisms made of cells and we perceive civilization and markets.

Thus it is obvious that function=action is the ultimate spiritual truth, to which form adapts; and the similar laws between entities are based in the ultimate program of functions, hierarchies and social scales of size. And so we can despite the details define a complex, spiritual, structural game of scales of i-nformation, organic roles and functions that will be repeated in all systems from the simplest particles to the more complex civilizations.


3. All are complementary systems made with 3 ‘topological functions’: Limbs, heads and bodies.

A 4-Dimensional Universe has 3 canonical topologies, which correspond to the 3 organs of all systems:

 Max. I: Head/Particle/Informative caste: They display the hyperbolic topology of information, observed in most ‘heads’ as an excess of warping and form (cortex, black holes, Chromosomes, Chip design).

Max. E: Moving Limbs/Forces/Energy class: They show a relative plane, or concave topology; such as the one observed in an external membrane, often the cover of a sphere of a bilateral form.

E=I: Reproductive Body/Atom/Working class: The topology of the reproductive system is a combination of the other two, performing cycles that communicate the energetic membrane and informative center.

In the graph, concave, energetic, toroidal, reproductive and convex, informative topologies are the ‘forms with most often found in the 3 main physiological systems of 4-Dimensional super-organisms.

Beings are not pure motions or just made of information. Hemingway understood , when he said to Dietrich: “Never confuse movement with action”. Indeed, energy ‘or lineal motion’ is not an action per se. It needs form, in/form/ation to direct it to create a purpose a goal, to change reality. So a Universe of actions requires some energy and some information to create a being.

Thus, all what you see will be a combination of both, and so we write a general equation to define all: ∑ E <=>∑I, and state that all what exists is structured with 2 complementary systems, one of information that gauges reality (cyclical particles and heads of physical and biological entities) and one of energy that moves them (lineal fields of forces and limbs).

This leads to a third system that combines both, energy and form, the reproductive system, exi or body. And all of them follow the principle that form is function. So bodies are conical, elliptic, combinations of lines and forms. And so Geometry and topology are fundamental sciences that apply to all ‘scales of reality’ and all its entities.

Thus topology proves that in a 4 dimensional Universe, there are only 3 topologies, which correspond to those 3 sub-systems: hyperbolic, informative topologies, energetic planes, and reproductive disks.

Thus Three Geometric Forms determines all functions: cyclical clocks of information, Energetic, lineal or planar limbs of space, and its combination, ‘complementary systems’.

Function and form: limbs and membranes of energy, informative zero points and reproductive, toroidal bodies.

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

All structures of the Universe are composed of only those 3 topologies. This astounding simplification is the result of 2500 years of mathematical evolution since Pythagoras discovered the laws that rule the bidimensional topology of those 3 forms, the concave-planar sphere (or cycle in a 2 dimensional world), the toroidal body with its regular cycles that transfer energy and information between the external surface of the sphere and its center; which is the informative region or  zero point, the ‘eyes’ that perceive in stillness a pixelled map of the Universe brought about by the flows of energy and information of the Torus.

After 2500 years since  Pythagoras discovered the circle as the most perfect form, geometer have come to the conclusion there are only 3 forms in the Universe: The sphere, the torus and the zero point.

With those 3 forms you can build all the other forms of reality. All is reduced to those 3. So what they mean? What is their function? And how they combine in the puzzles we call reality? Those are the 3 first questions we shall answer.

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, democratic, self-similar cells, which expand and enclose the inner organism from the outside. It will allow therefore through the holes of the network the transfer of energy and information with the external world, develop certain holes, those for energy called mouths, those for information called senses, and those positive and negative to absorb or expel wasted energy and information.

All systems will have at least those type of wholes and a strong, energetic, spatially extended membrane that circles the ‘vital space or territory’ of the species. The membrane can be multiple, the most extended, less loosely guarded is the territorial zone in which the informative center moves. The structures are always ‘functional’ and made of loose networks with motion and holes between them. Once we understand those topologies is essential to understand that they exist not per se, but as a ‘function of their functions’, which are temporal, dynamic more ‘abstract’ and yet rule the morphology that adapts itself to preserve the function or ‘action’ they perform.

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, absorbs energy from the external Universe thanks to its ‘energetic’, hard structures. This herd multiplies  and lets part of it flow internally into the torus.

A key property is the equality of all herd’s units, which have all similar functions and are exchangeable, submitted in physical systems to the Bose-Einstein statistics; hence able to form a news plane of social existence called 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. Thus the natural direction of flows of energy and information from the outer spherical cells is the internal space: The cells observe its mirror image, crates feelers that finally interconnect in a knot of information or zero point in the interior.

Function is kept in bilateral and planar forms but directions change. A two dimensional, planar herd can have a center or top or frontal head on which the language cells reside: politicians, kings, priests or markets rule a society from a center that receive and distribute information.

– The still center or zero point is the point of consciousness of any system, of any world, of any non Euclidean point, of any topology of 4 dimensions, of anything that exists, of anything that is.

In a human point 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.

Look around yourself and you will not see any zero point. That is the beauty of it. They are all 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:

ExI=K, the quantum equation, ExT=K, the Einstein equation, knots of actions of energy and time, centers of torus, hyperbolic topologies, brains, and cellular DNA, Cpus and black holes, vortices, eddies, time rushes, zero points are I=eyes, and the engine of form and quietness, stillness and perception, will and creation, and dis-creation.

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

We can build such tri-dimensional torus departing from a cycle, pi, made with 3 units and 3 apertures, of 0.05 between the 1 D-units of the membrane. It will reproduce and create a self-reflection – a similar smaller internal ring-son. Then both will form a dual system, in which the son will integrate the flows information and the external disk those of energy that cross through those 3 apertures. Thus a dual energy-information circle is formed. Then the flows between both will create a new curved dimension of height forming a toroid. That center is created internally by segregation and motion of a number of self-reproduced cells, imaging the father, which is always the bigger, external membrane of the system that appears first.

Again causality is determinant: the membrane gives birth to the zero point – it is the father element, hence energy is the first causal action that gives birth through a cyclical body to an informative, final form. Then when the father, external cycle dies, the internal cycle- son is exposed to the external Universe and in this manner all kind of waves are observed as being emitted, the father wave disappears as an explosive external energy the mother wave lives longer and reproduces an internal son wave that will repeat the process or you rather can see the father as progenitor hermaphrodite producing and internal, reproductive wave and an external explosion of death in the moment of giving birth. Thus many fathers die when their sons are reborn (as in mitosis). Yet a dual system is produced; one with a more complex, vital center, and en external, more expansive membrane that protects it. So in beta decays, the nucleon becomes a bigger, more dynamic atom, and in mitosis the cell breaks in two.

Most systems don’t have a radial form centered at a zero point but are born as 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 image. 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 toroidal 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, in time is coupled by a dynamic transformation, as 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 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.

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.

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.

This is the ‘perfect’, ideal ternary form, which evolves in time towards diversification of 3 forms and in space puts together the 3 elements in a ‘sphere’ and so it is often the perfect seed or organ of existence

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, the sum of the membrane, the zero point and the torus in between that acts as a body. The membrane are the limbs of the system, the zero point the brain and consciousness and the torus the physiological systems or flows of energy and information between both.

Observe in the bottom of the graph samples of the 3 form-assembly in different systems of the Universe. Man also is a complex system with 3 interconnected zero points, around cellular toruses, with external and internal membranes of exchange of energy and information with the external universe, and apertures called senses… So we shall first explain the general form of all zero points, spherical membranes and torus and then analyze in specifically the human one.

Diffeomorphic Dimensions. Each entity is a relative Universe.

 To understand that human form or any similar, lineal form evolved departing from a perfect, ideal spherical seed, we need to interiorize the most difficult fact of general systems theory: that the visual, topological forms respond always to  functions/actions in time, the commanding dimension of reality, to which the forms diffeomorphically adapt to obtain the maximal energy and information and accomplish their actions. So once a form is created, it will adapt and evolve , deforming their external membrane, creating complex warped, fractal, branched internal physiological networks that act as fixed paths of energy and information, diversifying its organs and yet at the end of the road, the same topologies, albeit sometimes difficult to recognize will form a ternary being, which will deploy the same 4 actions of existence with those topologies and internal networks/forces.

General Systems Sciences accepts the principle of relativity and diffeomorphic: local measures. Since each species is a ‘universe in itself’, with different relative, energetic and informative arrows that determine its ‘whole’ morphology. Thus, each species establishes its own up and down arrows or relative energy and informative directions. In the graph, animals use light as information and plants, use light as energy. So both have opposite energy-time coordinates. Yet both have an ‘anteroposterior’, lineal’ ‘outward’ energy oriented structure. Galaxies and other forms of the previous graph have a cyclical, informative, inward structure, where the stars body absorbs energy from intergalactic space, reproduces matter with it and feeds the internal informative knot of gravitation, the black hole.



5. Cellular, Social Networks. 

∞ beings: Whole and parts’ principle.

Though the specific combinations of energy or information of each species – defined by its ‘vital’ or physical, Universal Constants (energy/information ratios) – might vary, the space-time structures and cycles of all those social organisms will be self-similar: All entities are ‘cellular societies’ organized through energy and information networks that bring about processes of social evolution. In all species studied by science a common phenomenon occurs: the existence of parallel groups of beings organized into a single social form. Molecules are made up of atoms and electronic networks; economies are made up of human workers and consumers that reproduce and test machines, guided by financial networks of information (salaries, prices, costs); galaxies are composed of stars, which orbit rhythmically around a central knot, or black hole of gravitational information. Human bodies are organized by cells, controlled by the nervous, informative system. A tree is a group of leaves, branches and roots connected by a network of energy (salvia) and information (chemical particles). Cultures are made of humans related by verbal, informative laws and economic networks that provide their energy.

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

1.  Cellular units.

2.  Networks of energy or vital space.

3.  Networks of fractal information.

4. Networks that reproduce energy and information.

All entities are generated by reproductions and transformations of energy and informative cycles (ΣS<=>Ti), organized in cellular units, through networks, and ±st Planes of self-similar forms. Yet, since those cellular units st-1 are made of smaller st-2 cells, which show the same structure, we can define any organic system as a super-organism (made of smaller, self-similar super-organisms):

‘A super-organism is a group of cellular super-organisms joined by energetic, informative and reproductive networks.’

Thus we unify the properties of Universal Systems and the sciences that study them under a single template definition, according to which simple systems and complex organisms will differ only in the degree of ‘completeness’ of its networks and the specific energy or information they are made of:

‘A super-organism is a network composed of a population of (name a particular cell or cycle), related by an energetic, reproductive or informative arrows.

A fractal organism (name an organism) is a population of iterative (name a cellular species), related by informative (name a language or informative force) and energy networks (name a kind of energy), which combine into a reproductive network that iterates the organism.

A universal ecosystem (name a specific ecosystem) is a population of several (name the species), related by informative languages (name their languages or informative forces) and energy networks (name the energies).’

Fill the gaps with a specific species, language/force and energy and you can define any network-organism in the Universe. While if the system is composed of several species that occupy the same space but have different networks of energy and languages of information, we talk of an ecosystem: – An atomic organism is a population of (electronic) energy and (nucleonic) information, related by networks of (gravitational) information and (light) energy.

– A molecular organism is a population of atoms, related by networks of gravitational energy and networks of electromagnetic information (orbitals, London, Waals forces).

– A cellular organism is a population of molecules, related by energetic networks (cytoplasm, membranes, Golgi reticules) and genetic information (DNA-RNA.)

– A human organism is a population of DNA cells, related by networks of genetic, hormonal and nervous information and energy networks (digestive and blood systems).

– An animal ecosystem is a population of different carbon-life species, related by networks of light information and life energy (plants, prey).

– A historic organism or civilization is a population of humans, related by networks of verbal information and networks of carbon-life energy.

– An economic ecosystem is a population of human workers/consumers and machines, related by networks of digital information (money, audiovisual information, science) and energetic networks (roads, electric networks, etc.).

An economic ecosystem differs from a historic organism because they use different languages of information (civilizations use verbal or ethic laws while economic ecosystems use digital prices) and include 2 different species: human beings and machines.

– A galaxy is a population of light stars and gravitational black holes, related by networks of gravitational information and electromagnetic energy.

-A Universe is a population of galaxies joined by networks of dark matter and energy.

We establish thereafter a parameter of multiple space-time scales of growing volume of information, st=i, to classify all those relative scales of spatial energy and temporal information of the Universe, starting by the simplest scales, st=0 (mathematical cycles and lines), st=1 (Gravitational space), st=2 (electromagnetic space), st=3 (atomic particles) and so on, till reaching the most complex, macro-structures of the Universe (st=9, galaxies).

Cells and emergent scales.

Most beings are made of self-similar i-1 cells, particles or social individuals, which put together by networks become an i-organism, unit of a higher social i+1-scale.

In the graph, one of the fundamental properties of that structure is emergence. The properties of the simplest system emerge in the more complex. This means the geometrical properties of space-time are shared by all the new scales. The electromagnetic properties of quantum numbers are shared by all atomic species. The biochemistry of cellular life by higher organisms, and the individual behavior of human beings transcend into the socio-cultural behavior of social super-organisms; and our forms and vital functions are also expressed in the world of memes of metal we construct.

Wholes are made of smaller parts, and they interact and influence each other. The key law of those interactions between the cellular and network scale is simple: energy flows from lower i-scales into bigger i+1 scales and information flows from bigger to lower scales. And this paradoxically tends to cause a topic error in all sciences. Since all energy has information and vice versa, but energy bites are more ‘evident’, than smaller, coiled, often invisible or incomprehensible flows of information, scientists tend to overlook this duality or look at those interactions only in the path from the lower scale to the larger one.

For example biologists tend to think that the whole structural information of life beings is stored in its smallish scalar parts, genes. They think the whole, external ambient and organic scales do not influence the genetic parts. This is most likely false, as there should be ‘bigger scales that code information’ in ‘longer genetic codes’ and introns. There are morphological shapes, caused by the emergent properties of simple space-time (so all organisms follow the diffeomorphic dimensions of space-time with information on top, etc.) There is speciation based in the duality of energy and information systems.

There should be imprinting of neuronal networks by the mother emotional networks in the 3rd ‘informative’ phase of development of the foetus. And even there might be a Lamarckian response to external ecosystemic adaptation that might increase the random chances of mutation towards one of those ‘natural directions’ of morphology, as processes of punctuary evolution seem to indicate.

The same error happens among physicists, which are obsessed by entropy only theories (black hole evaporation, negation of the arrow of reproductive, fractal information, which Mehaute proved to happen always, when entropy no longer acts), etc. This is obvious in their obsession for heat solutions and the stubborn denial of the duality of all processes that can be done in ‘Max. E’, energetic, hot ambient and Max. I, informative cold ones – such as the fusion process.

Finally in social sciences, we build social models that stress the individual and not the systems, and superstructures. And yet it is a fact that networks, the whole, always influence its parts. And so many sciences must be completed with the study of that influence from ‘upper scales’ into cellular ones.


All those morphological differentiations and social elements can be resumed in a word: networks. Social individual systems acquire network forms, shaping forms related to energy or information, or combine them both. And so we find also in all systems a ternary differentiation between cells that become energetic, reproductive or informative networks.

Complementary systems are not ‘point-particles’ but cellular or atomic systems, made of networks of bits or bites of information and energy. Those networks are able to modify its distances and forms changing its topology and for that reason the Universe is dynamic in its transformations.

Because networks are flexible webs of points that can adopt different topologies by modifying the distribution of those points, networks evolve and switch between the 3 topologies of existence, hence creating a complex universe of constant transformations between the 3 functions-forms of the Universe.

Thus all networks = organisms often have two ‘sub-forms’ or states, the coiled, informative, radial or spherical state and the uncoiled, bilateral, anteroposterior, lineal form.

The first state is the informative state and the second the energetic state of motion; as systems are always dynamic flows and transformations between two poles of Energy and form joined by a body of cyclical exchanges between the concave and convex |-O E-I poles.

Thus the answer to the whys of the Universe can be resumed in a word ‘networks’ that defines the multiple realities we see around us:

‘All what exists are organic, fractal systems, made of self-reproductive, complementary, social, topological networks of energy (bodies and fields) and information (heads and particles)’:∑Se<X>∏Ti

Thus the why of reality is the creation of social networks that become complementary super organisms.

Complex and Simplex arrows: internal networks and external forces.

In essence organisms have internal parts, attached to ‘external apertures’ called senses that perceive two basic external forces of information and energy, elaborated and distributed to all cells by internal networks. When those external sources of energy and information saturate those internal networks the complex arrows enter in ‘action’. So the excess of energy is imprinted by the excess of information, exi,  reproducing a self-similar organism or it is shared with similar individuals, creating ‘bondage’ in herds or complex organisms.

Thus the external forces and actions of perceiving and feeding are fast in time and extend in a wide spatial range, to the point of creating a ‘continuous’ perceptive experience. While the complex arrows are of long duration in time, requiring little space and long time to re=produce its actions.

This is expressed in a law of inverse spatial range and time duration:

i-3 Informative pixels (Max. E x Min.i) = i-2 energy bites (ExI) = i-1 reproductive seed (min. e x Max. i)

This is the case of the forces that ‘express’ those arrows in atoms. Where the external forces of information and energy (gravitational and electromagnetic forces) have a wide range and the internal forces of reproduction and social evolution (strong and weak forces) have little spatial range, specially the weak force which is a ‘Temporal transformation’, not a spatial ‘force’, as it transforms particles in time, evolving them without motion in space.

Thus the Strong and Weak force are the complex ‘inner’ forces of the atom, which play the same role than the complex, inner networks of energy and information (blood and nervous system) of a biological organism.

And they describe reproductive and evolving processes. For example weak forces are the equivalent to other evolving processes like the chrysalis of an insect or the resting moment of pregnancy.

Both type of forces/actions are easy to spot. Since time and space are opposite in properties and so time processes tend to be ternary (with 3 dimensions states, a first more energetic, the reproductive middle event and the final informative one), and last longer in time (the weak force has a time related constant) and hardly have any range in space, but need quiet, small, secluded places (in species evolution this cause allopatric evolution).


7. The Universal Mandate: Maximize your existence.

Yet more fascinating than the philosophical argument is the mathematical formalism that explains the structure of those perceptive points, responsible for the general order of all parts and wholes of the Universe- the fractal, non-Euclidean points of the Universe, in mystique terms its souls.

Those points of view that we will define with Non-Euclidean mathematics in the next paragraph, represent the 4th dimension of social evolution and integration of 3 external ‘perpendicular dimensions’ of relative informative height, lineal motion and reproductive width (thought this 2 coordinates often vary, according to the environment and complex structure of the system, the height-dimension of information, which is the first to be established can be found in all systems).

For example, in the human mind, of electronic nature, the central S1,2 orbitals form a relative P.O.V. surrounded by 3 y,x,z p orbitals perpendicular to each other. The same structure is repeated in crystals and the NH+3 heads of amino acids in the 7.2 alkaline cytoplasm of the cell.

There is always a Point of View (biological jargon) or Non-Euclidean, Fractal point (Mathematical jargon) or ‘soul’ (mystique, existential jargon) that ‘integrates’ thanks to its control of a common language used for the system to code information (geometry in physics, electronic images in biological systems, verbal thought in sociological systems, digital languages in economic systems) the incoming flows of energy and information of the system. What is then the will or purpose of those points of view?

To maximize the function of existence, of its system, the Universal mandate of the program: Max. e x Max. I, which is achieved when E=I (mathematical rule: 5×5>9×1). This mandate of existence means that all p.o.v.s will try to perceive and absorb energy till they have enough to reproduce themselves, and then, they will be ‘forced’ to evolve socially in a dense environment of self-similar cells to survive.

In other words, the Universe is an infinite game of orgasms (-: Reproduction is the game.

∑: interactions and actions of all beings follow a pattern, of self-repetitive cycles, performed by each entity in a discontinuous cyclical manner, as the entity switches its modular ‘ego’ trying to maximize those 4 actions of existence, which is achieved mathematically for E=I, at ExI (Action of reproduction). The ego thus will have in any plane of existence a simple function to perform: Max E x I = K. For each domain of reality we defined therefore the field of an Ego-existence as, the function of God:

Max. E x I = K, which is maximized at points e=I, and max.I, which becomes the two first arrows of reality. The first one is called the arrow of space, energy, formless as both points equal, but the second function is a quantized function, which means the creation of more fractal information is the second arrow that maximizes the function of existence.

Once the function of existence of any plane of points of view that create linguistic worlds of truth is understood, you are into logic at the finest: The logic of existence, evolution and extinction, of the phases of the infinite cyclical actions its species perform.


The Bosonic point.

The creation of a bosonic zero point is the easiest form of maximizing the function of existence. This can be proved topologically and experimentally. The point is a Max.I, which strives to balance E=I, to create a max. ExI existential function for the whole EX I triple topological entity. This might be perceived as humans do with the perception of beauty (Max. I, i=e) and happiness (Max. E, i=e), which might be the ultimate will and sensations that resume the universal mandate.

Herds of undistinguishable bosons are also essential in the creation of membranes. They are also essential in parallel flows of bits and bites of information and energy transiting within or between planes of existence in the toroidal forms. Thus the creation of bosonic wholes from individual herds is key in the 3 type of networks that assembly together in functions of existence, E<=>I.

In the scale of particles all are bosons in the proper conditions, becoming undistinguishable. The result is the formation of a single new, condensed plane of existence to which each bosonic particle gives part of its existential momentum, creating a new fractal form, combination of the topological points fusion into the new form. The median of each S-T values for each individual field of  energy and information create together a new topology that looks like a single one, as it has become either a toroid, sphere or hyperbolic new whole.

The system integration happens in all kind of forms, from neuronal integration to cpus and gravitational fields of multiple bodies: An internal zero point once formed calculates easily from its p.o.v. the forces of energy that pass through it, ‘subconsciously’ as it creates a pixelled image to perceive.

The duality of eusocial parallel love vs. Darwinian, destructive hunting.

All systems of the universe display a dual behavior: they prey on other systems to absorb their energy and information for their bodies and minds and they evolve eusocially with members of the same species to reproduce and become bigger, more complex eusocial super organisms, sharing energy and information through common networks that create a new whole made of cellular parts.

It is the duality of the arrows of love and hate. Yet the arrow of love is a better strategy as it is the arrow of creation that the arrow of death and hate.

So we can describe the universe under the arrow of love, as a whole whose parts are all made to its image and likeness guided by the laws of all cellular systems who strive to survive by evolving eusocially to become a cellular part of that whole.

The duality expresses geometrically in the first scale as parallelism (love, flow of information invisible to third observer, separates at equal distances, two self-similar beings, who share energy and information along a small gap between them, this might lead to ‘fusion love’ the beginning of reproduction, when the number of self-similar, lower scales of existence of the couple in lower scales and higher ones is maximized. Then we find a quantization factor, ∑∑=∏ as the two polar species who have attracted each other, start to develop through its complex arrows of reproduction and love, more perpendicular networks of causalities that join its lower and higher planes of existence, with other forces and membranes that make the informative field of fractal information caused by the frequency an regularity of their get together arrows of shared experience…

From the first electrons that merge in spin/anti-spin sexuality till the last human being, this function is essential to complete the equation of existence, as informative ‘networks’ ∏ are stronger than mere, herds, ∑, which are connected only in the evident, i-plane of existence, while they perform their arrow. Herds follow the search for an arrow normally energy, sometimes information, but when information is what it is transferred, herds tend to evolve in networks in which there are causal memories that chain the system to other systems, neuronal networks of white matter in neurons and brains, electromagnetic cables in machines of information, etc. So we write:

i=∏, where i is the number of scales across which the network of information exists and controls with its bits and networks. Thus we write the equation of a complex organism as:

∑Ei<=>∏Ti±1= ∑ | x ∑i±1 O

The second notation is visual, geometric, as the universe is indeed a game of topologies in action, where the lineal, planar form of energy limbs/fields are ordered internally by mixed fields, X, guided by an informative head of bits of information that form both an internal language of control of the body/field and an external sensorial absorption of external information.

Evol-Devol. The cycle of life and death and the causality inferred by zero points.

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, and 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 why, the constant creation of cycles of life and wills and knots of time that want to order committing actions that maximize its function of existence, requires to fly further with your own will and empathize with the will fo all tknots of time cycles of the Universe.

All those individual, internal and external sub-scycles of a being are finally, disitilled once more by a new translation of the flows to a ‘alanguage’, in the human brain from chemical impulses and messages of hormonal chacater of ther est of the body. And all that appears as emotions and other neuronal fiels of electric energgy resumed in the mapping of perception of the mind, combined with the external mapping, with the 3 key mappings of the human brain (the verbal axis,s visual axis and emotional axis, z-x-y…, which reflects its maximal activities of energy and information)

The integration once and again of the will of each scale into new networks and the formation once and again of the same scales of reality deprting of the smaller, the printing an reprinting of reality – that is the intend,e huse, constant never stopping, in a universe of motions, game of realty.

The stillness of a zero point is a silent moennt of perception and the essence of the orgasm of a mind in peace with it all, ampped all it, and fluxed all it as lights of inner beauty to the hardware that the software runs with pleasure fields… the zero point seems to bee effortless but it is the final prouct of a a trillizon or zillion years of evolution of the game in its search for the ideal form.

And what you see what you perceive, whaat you undersands as beauty is the sensations of the fulfillment in balance of exi-k, your energy and infroamtion actions, forms and energies in balance is beauty and beaity is the state of the mind of full accomplishment of once thoughts and actions. In this manner in each being, in each language in each mind there will be a point of nivtante, in each insect orstar robot or human mind, mirror of beauty of a satisfying exi=K existence is balances… that is the art of existence, which all particles practices each in its own language.

RECAP. The 4-dimensional Universe is a simple game of 3 topologies of space, which correspond to 3 functions in time, the energetic, spatial, concave, spherical or planar membrane; the reproductive, cyclical, toroidal body; and the hyperbolic, warped, informative, still center of perception.

This simple a priori limited structure can adapt infinite self-similar forms as each ternary function absorbs energy that transforms in still perception or reproductive, self-similar clones of one self. Two primordial forms, the lineal, bilateral system or the cyclical, spherical seed are the most common of the Universe. Some forms might even switch between both states. Yet the 4 actions and 3 topologies and 3 ‘ages’ of dominance of one or other function and form remain in all systems that go from energetic young stages into informative ones.

All those simple similarities allow us to define a general system of simple equations that represent with topological symbols the causal and dynamic processes and events between the different parts of a ternary system and the system and the external Universe.

A new methodology and language, more advanced that the simple Aristotelian unicausal logic and Euclidean mathematics is needed; a new philosophy of science – organicism – and an emphasis in the qualities more than the quantities, in geometry more than arithmetic, in time functions more than spatial structures, in harmony and balance and feed-back, dual flows of causality more than in individual, entropy –based mechanist, digital, abstract models of reality. Let us consider this new method of knowledge to extract of the information relevant to the complex structure of its real systems.

It is this wave combination, that maximises the reproduction, evolution and perception of the being in balance with its external world (s=t), what we call the function of existence of the being. The logic we use here,the terminology, the search for a metaphor that relates the words of english with the equations of the fractal Universe is somehow magic, maybe embedded in the genetic linguistics but in any case, what we talk here is a body-wave which is a function that maximises the energy and information of the being, and its product combination (Max. e x i), which happens for any ‘product’ (5×5>7×3) when e≈i, that is the spatial energy and temporal information of the being is equal (s=t):

Human worldcycle
The methodology of ∆ST is simple. Reality is made of space-time beings, which are in full description of all its information a super organism with 3 topological organs in space, which perform 3 temporal functions, symmetric to their form (past-lineal entropy limbs/fields, cyclical informative heads/particles and iterative, hyperbolic wave-bodies). Such is the basis of the generator equation of space-time, which resumes the  3 x 3 symmetries of all beings:

The universe and its Fractal generator can be described as a game of 3 symmetries:

  • The simplest symmetry of synchronic 3 topologies of all organs of space.
  • The symmetry of those 3 organs in function in time, which dominate each of the 3 ages of life.
  • The symmetry along the 5th dimension of ∆-1 parts that become ∆-wholes, emerging into a bigger ∆+1 world, where those 3 organs of space, perform its 3 ages as a world cycle of time, co-existing in 3 relative scales of the 5th dimension.
  • Yet when we see the system as a whole, sustained by a O-mind/point of view, we can see the system as a series of smaller cyclical space-time actions that dynamically through those 3 organs in space-time exchange energy and information with other systems, performing a series of actions, which define the nature of the being as an existential discrete function of exchange of energy and information with its ∆+1 world:


It is then clear that the simplest ceteris paribus analysis is that of the 3 organs of space, in a single space-time plane and with a single arrow of time, entropy.

It is the present understanding of physical sciences, which by the principle of correspondence is the simplest limit of a Universe in which we consider only a single arrow of time, entropy and a single plane of the 5th dimension.

Yet, the next degree of understanding of the Universe, is to realise that those 3 organs of space, the lineal, energetic limbs/fields, the informative head/particles and the combined, St(exi) Hyperbolic body-waves, when seeing in motion in each fractal being, determine a relative arrow of time-future, that is a relative path the system will follow. If it uses the limb/field it will increase the overall entropy of the system, if it uses the head/particle it will likely absorb information, and if it uses the wave/body it will reproduce its form as the wave displaces or in the future as the body repeats its energy and information.

So the next symmetry is that of time. And we can build as taoists did, a worldview of reality that includes the organs of space and time ages/cycles of all beings, which tend to be dominated by limbs/fields in its youth, then reproduce and finally exhaust in its 3rd age of information, its energy, warping till they explode back into entropy and die.

But a final symmetry happens when we realise those processes of birth and existence do happen in 3 scales, as we are born as seeds of the lower scale of size, ∆-1, with a faster time clock and then emerge after a long process of reproduction and formal evolution into the ∆-scale, which will be a full being, exchanging energy and information with a larger ∆+1 world. So the 3rd symmetry of reality is that of the planes of existence of the 5th dimension.

7. Emergence and the scalar Universe. The 3 fractal scales of all systems.

The network structure of all systems and its complex arrows of reproduction and social evolution show a key property of the Universe, its scalar, fractal scale. As when the first cell is born, it feeds, reproduces, evolves socially and creates finally a new superorganism or whole of the new scale, a human being, which is born as a new unit of a social superorganism, nation or civilization. This happens also in physical systems: social particles become atoms that become molecules that either become cells that become organisms that become societies or become planets and social stars that become galaxies that become Universes. Two laws of all systems derive from the scalar, emergent nature of the wholes:

All systems share the properties of their lower scales that emerge in the higher scales of existence of the system. Thus the geometric properties of space-time are shared by all its upper, more complex scales; the electromagnetic properties of quantum numbers are shared by all atomic species; the biochemistry of cellular life by higher organisms, and the individual behaviour of human beings transcend into the socio-cultural behaviour of social super-organisms; and our forms and vital functions are also expressed in the world of memes of metal we construct.

–       All systems co-exist in 3 scales of reality:

The lower scale, which provides the bites and bits of energy and information the body, limbs and head of the system need to survive. This is the lower i-2 scale of the system. It is the scale of particles of information and forces of energy in the physical scale – for example, quantum numbers in an electron; the genetic scale of informative genes and carbohydrate molecules of energy in biological organisms and the memetic scale of instruments and ideological ‘neuronal networks’ in sociological organisms (memes of life or ‘human goods’ of the welfare state in human superorganisms; and memes of metal in economic ecosystems).

The i-1 intermediate scale, of atoms made of informative quarks and energetic electrons’ the biological scale of cells and the human scale of individuals in sociological organisms of history and corporations, the ‘free citizens’ of markets in economical organisms.

The i-upper scale of the Whole, molecular systems in physical organisms (of the size of entire planets sometimes), the scale of living organisms in biology and the scale of human cultures and economic ecosystems (markets) in sociological organisms. The reader could observe that the whole of biological organisms (humans) becomes in fact the i-1 scale of sociological organisms. So each 3 scales we can consider a ‘new game’ of emergence. And in fact the Universe is a scalar of infinite scales, as we can observe that the scale of galaxies is self-similar to the scale of atoms in many equations (black holes can be modeled as quark stars and star nebulae can be modeled as electronic nebulae; in fact Einstein modeled the Universe considering each galaxy a hydrogen atom).

The laws of emergence relate the different scales of reality and its functions. One subset of emergence laws is the laws of transcendence. How the arrows of the i-1 scale of ‘cellular’ existence transcend as bits and bites of information and energy of the next scale. The general rule is the following:

–       Arrow of reproduction of the lower scale-> Arrow of energy of the next scale. That is, the reproduction of entities of i-1 provides the ‘staple food’ of the next scale.

–       Arrow of social evolution of the lower scale-> Arrow of in/form/ation or form of the upper scale. That is, the social evolution of an entity of i-1 tends to happen when that entity enters the structural form of the upper scale.

For example, the 3rd quantum number, or magnetic number of social evolution of electrons is the key number to explain the form of complex molecular orbitals. The reproductive wave of photons and its speed becomes the feeding arrow of electrons that jump to absorb them.

The reproduction of cells structures the form of organisms. The reproduction of carbohydrates feeds the cell; the social evolution of amino acids in proteins and proteins and fats structures the form of cellular membranes.  And so on:

Rei-1 -> Ei ;  Social Evolution (∑i-1) -> Structural form (Ii).

The seven dimensions/scales of any system.

Shakespeare said we were all heroes or buffoons, depending on our perspective from above and from bellow. The paradox of the ego consists in the incapacity of humans to perceive the ‘above’ structures, which are ‘disconnected’ apparently because the networks of information that join them are invisible (so we do not see the networks of words that communicate us, or the flows of money that cre(dit)ate the economic system). So as we only perceive the smaller scales in detail as ‘wholes’ we feel like heroes.

In fact, if we consider for each ‘relative universe/superorganism’ a relative i-scale centered in the individual p.o.v. each system can be considered to exist between ‘7 scales of perception’ with clearly different roles:

There are scales at i-n that we do not perceive at all. It is the ‘nothingness’, in our case the gravitational space.

Then it comes the i-3 scale of pixels of minimal size that we use as information. In humans it is the light, and electronic space.

Then it comes the i-2 scale that we feed on. It is the atomic, amino acid, molecular space.

Next it comes the i-1 scale of our seed. It is the cellular scale.

Then it comes our scale of social evolution, or i. It is the human social scale.

But beyond we are for the higher scales exactly all what we perceive below. So we are sons of the next scale, which for any species will be called the generator.

We are food, energy for the next scale that we call the predator. In cultures, we are prey of those who exploit us as workers under salaries, citizens under laws, military… the people-castes of our society.

We are finally perceived as a mere pixel, a number, a poll vote, by the ‘system’, the whole social organism in which we exist for whom we are just an objective point of a whole.

And beyond there is of course God, the last scale, unperceived, the Laws of all systems, that explain all super-organisms, not only the social one we exist in.

Thus from our point of view, we are the most important point of the Universe, and all what we see is below us, our relative energy. Yet we exist between 9 scales, two invisible, 3 under us, 3 over us, and we, in the middle:

The scale of nothingness, the scale of bits, the scale of bites, the scale of seeds, the scale of Is, the scale of the generator, the scale of the predator, the scale of the ‘system’ and the scale of God. And this is truth for all systems and species. Because information occupies no space, lasts longer in time and all systems evolves towards those informative super organic scales, those facts leads to the 9th point, the relative dimensions of past, present and future.

The easiest question is here: how much of the external Universe the function ∏Oi, absorbs/perceives? The simplest of them, a pi circle, of 3.14-3 =0.14 apertures through its ternary membrane, is a paradigmatic, basic ‘function of existence’, and represents a 96% of ‘dark matter’ not perceived by the system, Curiously is the same than it is left in dark to the electronic image we perceive of the Universe (dark matter of the universe) Thus we could consider the electro-magnetic mind of a human being, to be in its ultimate, simplest structure of perception, the photon, limited to a possible ‘light, final structure of a pi 3-dimensional cyclical ‘worm’ like photonic H-Planck ‘snake’ that as it traces its 3-dimensional balls of electromagnetism, absorbed from the prior, dark matter universe of gravitational, scalar field (short of a Higgs, with improved equations), brings about the first jump from ‘nothingness’ to the first scale of perception.

But what is the nothingness, not perceived, the perfect form not perceived, the 0 x ∞ = K.

The limits of each perception of each knot of cyclical actions of the Universe.

Thus, the scales and species we observe between ‘nothingness’ (∞ E x 0 I) and ‘God’, (∞ I x 0 E) are:

1st scale: Euclidean Light-space-time and Non-Euclidean Gravitational space-time. They are the Energetic-Informative duality of space-times in which our reality is built.

2nd scale: Fundamental particles; energetic electrons, fractals of photons; and informative quarks, dominant in gravitational forces.

3rd scale: Atoms.

And so these 3 scales form together the simplest superorganisms of reality, the atom.

Then we start again, with atoms as the basic i-1 element of the new ternary superorganism:

3rd scale: Atoms.

4th scale: Molecules & Matter (states: energetic gas, balanced liquid, informative solid).

5th scale: Planets & stars.

This ‘energetic version’ of atomic structures has its duality with the informative version, life:

Life: 3rd scale: Atoms; 4th scale: Molecules; 5th scale: Cells.

And so we start a new ternary system through 3 more scales:

5th scale: Planets & stars; 6th scale: Solar systems; 7th scale: Galaxies.

Life: 5th scale: cells; 6th scale: tissues; 7th scale: Organisms.

And finally we arrive to the last scalar structures:

7th scale: Galaxies; 8th scale: Clusters; 9th scale: Universes.

Life: 7th scale: Memes; 8th scale: Humans; 9th scale: History.

Now the reader would observe that this classification of scales differs from the one of the graphic, as we stretch further the structure of living organisms. The point is that each scale can be divided in 3 scales, as all points are complex superorganisms. So descriptions might vary from 1 to 3 to 9 scales depending on detail and in this book we shall analyze in more detail life beings. Some obvious facts though of the previous scales: the i-1 and i+1 scales are ‘complete’ systems, tending to spherical, still, informative shapes and the intermediate scale is the more ‘active’ complex organism. So photons and atoms have the active intermediate scale of particles. Between atoms and planets we have the active intermediate state of states of matter. Between atoms and cells, the molecular active scale. Between cells and organisms, the active tissue-organs scale; between human’ heads’ and history the memetic scale.

This is the relative i-scale in which the entity that in the chain of scales might be just a ‘bite or bit’ i-1 form and an i+1 whole, works more and interacts, ‘lives’… To notice also that all systems are part of a chain, or as Shakespeare put it, we are all Gods, humans and buffoons depending on the perspective.

IF WE AD the whole as a mind-point which organises and perceives and guides to survival the system, then we have the 10 Isomorphisms  of the being…

0th isomorphism: Self: Œ-Point x ∞ World = Constant mind Mapping

The mind of a living or any organic form of the Universe is the ‘mysterious’ definitive engine of order of the Universe, by switching in actions of survival according to a clear program that maximises the energy and information of the system:

Max. Energy-body x Max. Information-Mind becomes a selected top predator ‘Program of cyclical actions’, which the mind performs.

So the mind normally is a knot of Maximal Information, which perceives a territory of order, where it will exist according to its mapping, WHICH IN LIFE SYSTEMS IS TERNARY, CHEMICAL FOR PERCEPTION OF ENERGY FLOWS, SOUND FOR AND LIGHT FOR PERCEPTION OF information.Screen Shot 2016-05-18 at 16.22.22

It is the alpha and omega, the 0 and 10th isomorphism: the point of the mind, site of the will, which orders the system internally in its ∑∆-1 parts and perceives it as an ∆-whole, part of its ∆+1 society. The topological center of a sphere, which can according to Poincare’s conjecture represent without deformation its whole world in the infinitesimal fractal, non-Euclidean mind point.

Screen Shot 2015-11-05 at 18.33.50‘Gods are unmovable, the primary cause which moves the energy of its vital space’. ‘We are all Gods.’ Aristotle on the mind.

‘Each point is a world in itself.’ Leibniz, on the Monad, mind of space-time.

‘Space is motion relative to a frame of reference.‘ Einstein on the Non-Euclidean point of space-time.


We start with 3 precise, logic, philosophical and mathematical definitions of the fractal point-mind, the minimal unit of existence in the fractal organic 5Dimensional Universe.

When we consider the minimum possible form in existence, the simplest action of reality IS not motion, but perception. This might come as a surprise to pseudo-scientists who uphold some magic properties to the creation of linguistic mirrors of the Universe – Leibniz’s concept of apperception, and the minimal mathematical unit of the fractal reality – the NON-euclidean point that grows in size when we come closer to it, and bends the lineal entropic motions of a field of energy into curved forms, ‘bits of information’, which shrink without deformation (Poincare Conjecture) creating mirror-mappings of reality.

So the first moment of existence was a point that became a focus of a flow of cyclical motions, which focused in an infinitesimal mapping, synchronous, in stillness created a ‘quanta of perception’, a mapping of information a…

….mind-point of view of the fractal Universe.


In the graph, we illustrate the fundamental particle of the Universe, a point-mind, which gauges information and creates a still image of reality, communicating in networks with other fractal Non-euclidean points flows of energy and information, building in this manner larger topological networks, whose growth and social evolution makes them emerge as new wholes, of a larger ∆+1 plane of the 5th dimension. We shall study with the tools of Non-Æ geometry such fractal points, to start the adventure of knowing how the Universe creates itself and all its parts, departing from those minds and their will of existence, as points that feed-feel pleasure absorbing energy in motion and perceive-gauge information, in stillness.

So when we consider the possible actions of a Universe of energy and information, which are deployed by any system in search of survival, it seems rational to think that systems, as we do first ‘perceive’, and then observe the fields of energy that they need to survive, so they move in order to reach them and feed, and only then when they have enough supply of energy will use it to reproduce, to communicate information and form networks with other beings. So we consider the following cycles of actions, departing from the first action that creates a shrinking point mirror of perception:

+∆i: perceiving information->-∆e: locomotion ->+∆e: feeding -> – ∆i: communicating information ->∆e x i : (∆œ) reproducing -> û: evolving socially.

So all what we know and exists departs from a first passive action: opening our senses and eyes to perception, from the simplest photon of light, to the largest black hole of the galaxy.

It is then the first step to found a general systems sciences of all the systems of the Universe, to define and improve our mathematical and logic truths, needed to describe those first fractal Non-Euclidean points of view, which opening its form to a simpler field of motion start to web the networks of in-form-ation of reality, as monads that first perceive and only then ∆a-ccelerate towards ∆-e-nergy fields in which to feed.



The 3 fractal timespace motions of the Universe.

Let us start in a more detailed analysis of the Universe for the simple truths of time motions and its 3 fundamental elements (which seen as static forms of space, will become the 3 topological organs of all beings)



In the graph the 3 finite, fractal time motions of the Universe; its 3 still topological equivalents of space, and some of the systems of nature they create by assemble:

  • Explosive, lineal big bang, past entropy motions (the initial, simplest motion, a ‘fav’ of the german physicists ever), measured with the dimension of Time duration.
  • Repetitive, vibratory waves (or present, as repetition made reality seems the same constant, repetitive present), measured with the dimension of Time Frequency.
  • And informative, accelerated vortices of time, clocks of the future, charges, masses, galactic vortices, which balance the entropic motions of space creating a fractal eternal Universe (since in the future all systems end in a 3rd old age of maximal form, and warping, of maximal information; masses that fall into black holes, men that wrinkle, societies that evolve technological information).

The cycle of time has more dimensions.

A cycle has more dimensions than a line. So we have to ad more time dimensions to define those time cycles.

For example, physicists generalize the first arrow of time they understood, ‘death’, ‘chaos’, ‘entropy’, and affirmed all will die, and created a theory of the Universe, called the big-bang based in its PAST death, not ITS FUTURE INFORMATION, to the point that when the arrow of information was discovered they called it ‘negantropy’, and to this date they HAVE not accepted it.

Never mind we live in a  GALAXY, that transforms the entropy of vacuum space into masses that grow in density of form, of information guided by a force which is ‘informative’ ONLY, gravitation, and so we live in a VORTEX OF information, reason why live evolves towards higher information, technology increases its information, and at the end we will collapse into the black hole of maximal information at the centre of the galaxy, or worse here on Earth as now PHYSICISTS are trying create black holes and dark strangelet matter of maximal gravitational information, which if it is born will NOT explode into ENTROPY but fold our light mass into information.

For a decade I tried people to understand this so obvious truth. Never mind. The physicist discovered the arrow of entropy studying the heat of gas in vapor machines 2 centuries ago and it will ‘repeat’ and ‘repeat’, with his believer’s mind this mantra.

And needless to say he also ignores this 3rd arrow of time, which he repeats when talking of ‘death’≈’big bang’≈entropy – ‘reproduction’, ‘repetition’, or ‘present’ time (as a present does not seem to change, hence we call it a present, as when we said, when we return to the slow time moving place we were born, ‘it is all the same here, it seems as it time has not passed’. Indeed, the speed of time in that region is slower, the arrow of information is not moving so fast, and things repeat as a present.

So here we are. Time has 3 arrows-motions-dimensions, past-entropy, present-repetition and future-information.

And we shall construct all what exists with those 3 fractal motions of time.

Now look at these simplest time cycle: π=perimeter=3 Diameters+0.14 for a cycle, or πerimeter=3 for an hexagon, or a mass with a lot of curvature. This is the simplest transformation of a line of space with 3 steps into a cycle of time. We use though because our clocks close the cycle a sexagesimal mechanism, based in the perfect hexagonal cycle of 6 ‘radius’=3 diameters, to measure time cycles.

Time cycles are thus the meaning of it all, the fundamental particle in which to base a Theory of Everything, or T.O.E. which is a sum of Time Cycles, T. that transform Spatial Energy, Spe, into temporal information, with cyclical Form, Tiƒ. back and forth, ad eternal into Present Space-time Beings – ST.œ:

‘The Universe is a sum of fractal knots of cyclical space-time actions that transform back and forth, spatial energy into temporal information, ad eternal:  ∑ Spe<≈>Tiƒ”.

This simple sentence and its equation, a ‘Fractal generator’ (a feed-back, dynamic cyclical equation that constantly reproduces and combines the 2 polar elements of the equation; in this case spatial energy and its quanta, lineal momentum, and cyclical information and its quanta, angular momentum), embodies the fundamental principles of physical sciences, the principle of conservation of energy, information, lineal and cyclical momentum (the 2 poles of the equation), and we shall see can be used to describe all the space-time cycles of the Universe.

Since all other systems of nature are also made with a cyclical or spherical pole (To-head-particle) the form that stores more information in lesser space, and lineal Se-limbs-fields that move them, the form that moves faster between two places.

So the ultimate principles of reality are rather simple. We are all knots of space-time cycles, lineal and cyclical motions, stored in our heads-particles and limbs-fields, combined into our <≈> body-waves that reproduce our energy and information. We are a game of time cycles, reproducing between birth and extinction. And the description of that game is what is all about.

All has a beat, a rhythm, and the most important rhythm is between the two fundamental states of reality, motion and stillness, energy and information, stop and go, time and space, function and form:


Where T is a time motion, S a still form, > the change of motion into form, or ‘informative flow’, and < the expansion of a still form into motion.  But if you take two of those steps you get an ST mixed motion with form, a present, repetitive wave.

All the varieties of those 3 motions and forms, the pure y-information and yang, energy and its infinite combinations, | x O=  Ø.


Φ. The inverted properties of space and time and its metric equations.


Duality in different sciences.

All those social networks and systems have 2 fundamental elements, spatial entropy and temporal information, and its social networks.

So what is the largest scale we know of, made with the smaller parts? Obviously the one between galaxies made of the smallest tiny bits, which seem to be neutrinos, whose ‘angle’ is the size of a theoretical string of ‘dark energy’

ANOTHER ONE: screen-shot-2017-01-17-at-07-18-22

You have likely heard that string theory ‘is’ the thing to learn, but it is soo complicated (‘if it is complicated you don’t know how to explain it’ Einstein) only those hyperbolic masters of thought and funerary ceremonies, aka artillery masters can know and enter the priesthood. Just believe on them… Well not so. At the end of the ‘string’ if you pull it out, all comes to the 2 drawings above, open expansive motions of lineal space (one strings in one D) and closed time loops with 2 dimensions of form, with more in-form-ation. Alas what string theory is telling us is simple, ultimately all what exists is made of time spatial lines and clock-cycles. But conceptually you need to understand the duality of space-time, to know what they don’t know they are talking about. Then departing from _and O, you can construct it all. Taoists called it yang and yin and constructed it all; computers | and O and model with them all; Descartes, vortices and res extensa and all came from them, Desargues circle and axis of a cone and all curves came from it… At the end of the journey all will be translated to it space & time; Line and cycle; lineal entropy and cyclical information, combined into ∞ bits and bites of energy (its Ø, 3rd element, the yinyang being, the conic, the space-time block, the being.

Yes it is that simple when you understand the FIRST principles: we are made of complementary ‘lineal motions of space without form’, or | and cyclical clocks of information or O, which combine into ∞ body-waves of ‘space-time’. So from yin-formation and yang-energy space-time yin yang beings are born, to use the terminology of the philosophy that closer explain those ultimate principles, in which the most successful human civilisation in terms of survival of its people and harmony with the Universe, was based. Simple principles indeed, so simple that a Chinese peasant could understand them 3000 years ago. It was the deformation brought about by the awe and reverence the mechanical clock brought to the western world, what changed the paradigm of time, improving our ‘measure of time clocks’ but blurring its qualitative nature as time cycles.

And further on since all sciences use time as its main parameter of measure, to extend the simplex concept of time as measure of locomotions in space to ALL sciences is the MAIN error to understand them properly. Or can you explain the cycles of evolution and history with Einstein and Galileo equations of space-light speed? Try (;

The isomorphic method of knowledge.

All this said it is obvious that we can expand the scientific method into the stientific isomorphic method, with the help of the isomorphisms of all systems, whose common properties in topological space, its similar time ages, soon discussed, and its  scalar arrows of time and space of the fifth dimension will show organic topo-logical common laws applied to all the beings of space-time of the Universe.

Now when systems have ‘the same’ form, it is called an ‘isomorphism’ from the Greek iso=equal and form=morph. So we talk of the first isomorphism of the Universe. Its 3 topological varieties, which process energy and move (limbs, fields), process information and perceive (heads, particles) and communicate both parts in exchanges of energy and information (that reproduce the system).

So we can put the 3 together:  Sp + ST + Tƒ = Constant (Being); which in more dynamic terms as parts are not really sums but ‘interact together’, exchanging flows of energy and information, we write:

  • Sp < ST > Tƒ

While we will often use spatial entropy and energy (entropy with a bit of form) and temporal form and information (form with a bit of motion) as synonymous is important when we get more technical and precise, to consider the ternary structure of all what exists.

As we have already introduced the theme, we shall now consider the 2nd and 3rd element together.

It it thus clear that the generator equation of the Universe is a ternary, feed-back equation that shows the inversion of properties of space and time, stillness and form, lines and cycles, decelerating and accelerating intervals, in its two polar maximal points and its intermediate point of balance:
n clocks

In the graph we can see the simplest TŒ, Time equation or function of existence:

∆(Ei): Tƒ x Sp

That is, Spe x Tiƒ = Constant, which is the SPATIAL PERCEPTION OF IT, as fixed form, and Spe ≤X≥Tƒ which is the dynamic temporal perception, to which we aggregate the entropy <, information >, parallel, social ≈ and X Darwinian possible combinations of those poles.

In this manner a feed back equation Se<ST>Tƒ, starts to create combinations by mixing the dualities of stillness and motion, line and cycles, individuals and wholes, which are the 3 games the Universe play. We can call those games as:

|>O<|: The game of life and death, whereas in the arrow of life |>O, the system increases form and in death, O<| releases it.

∑U∆-1<=>U∆, the game of parts and wholes, which then become joined into wave-particle systems, whereas >∆ is the arrow of future.

Se<ST>Ti, the Spatial game of simultaneous measure in space of 3 complex systems dominant in each of the 3 arrows (limbs/fields of Se; waves/bodies of St, and particles/heads of Tƒ.)

Now, all those combined games, make much more complex the dimensions of time and forms of space..

Whereas T is time frequency of a time cycle, hence the inverse of lineal time duration, T (reason why we use the To) Symbol.

And space is lineal motion seen as still form.

The first equation of time-space, deduced from the previous graph and its bio-topo-logical beats, space-form->motion-time->space-form->motion-time, is the generator equation of the Universe. We can with existential algebra, ®, define a wave-motion in time, which in its simplex generator will be hyperbola:

In other words we could write,  To =1/T, To=1/S, whereas T is lineal time, perceived in motion as still space.

This is thus the beginning of it all, the existence of cyclical, accelerated time motions and lineal time motions seen as circles and lines of form. The 2 dualities between motion and stop, and between cycles and lines is at the origin of all the realities we perceive and all its events and combined forms of space time.

Thus we could say:

The Universe is immortal because time never stops. Time never stops because time is motion. Motion never stops. It is conserved. Two motions are conserved angular momentum and lineal momentum. They can be seen in a slice of present space as form, or they can be seen in the interplay of its formal motions. Cyclical motion is faster so we call it time, and clocks of time are used. Nature has accelerated time vortices, from hurricanes to masses (equivalence principle of einstein between the curvature of the time cycle or mass and its speed or acceleration), to charges (similar equations to gravitation). Those time cycles of different size are ordered with the previous equation, converted into metric equations:

Spe x Tiƒ (substituting now cyclical time for lineal time) = K.

This means Time fluctuates along 3 points of the hyperbola.

Screen Shot 2015-10-31 at 10.58.01

And so one creates 3 points. Max. Spe x Min. Tiƒ , Spe =Tiƒ and Max. Tiƒ x Min. Spe

energy information good
In the graph, the Universe is a fractal of space-time symmetries across 3 vectorial dimensions of formal motion, the dimensions of space (and its 3 sub dimensions, length,w width and height) the dimensions of time and its 3 sub-ages (entropy, present iteration and future form), and the dimensions of Eusocial Evolution through planes of existence, or long arrow of time.

The interplay of those dimensions and form generate the Universe:

Now, in those graphs we can see the most classic ‘generation’ of ‘meanings’ in the Universe, by combining the 2 ‘forms’, the line and the cycle, and the two ‘motions’, the lineal motion and the cyclical one (and its SxT combinations of waves and hyperbolic bodies).

If we restrict to that first generation, and consider |-S <≈> o-T, to be the essential duality, we can study its combinations.

A perfect, still, lineal, ‘extended space’ with no motion and no perceivable form: |-S, or space.

A still cyclical form, or with minimal motion, as information. A lineal motion, entropy or with min. form, energy. ST.

A perfect cyclical form or’Time clock, Tƒ.

As the Universe starts to mess rhythms of motions that decelerate and expand into space, becoming still or accelerate inwards and become cyclical motions of time. As the observer changes its perspective enlarging and hence stretching cycles into lines of lesser curvature, and vice versa, the forms of the Universe also change. The graph shows our choice of 4 words to explain them, |-Space, res extensa with no perceivable motion, O-Mind, still cyclical form, |-entropy, expanding motion and O-Time, accelerated cyclical motion, and the somewhat more conceptual, less defined, energy (tending to lineal motion but with form) and information (tending to cyclical form that with motion), where we ‘put in’ as humans do, in a similar conceptualisation to that of spaces and times, the two inverse elements of the Universe.

Thus it must be cleared, that the logic equations of the Universe are fractal, conceptual, dualities, based in inversions and symmetries of two poles that come together vibrating into 3 points, of Max. S≈E, Max. T≈I, S=T, E=I, of maximal, minimal and balanced states, ages, forms.

This is the game, 2 limiting functions, opposite to each other, of relative past and future, combining into relative present, E=I balanced points.

The universe is not a quantitative but a logic not a material but spiritual game, and the quantitative and material reality and perception of the game as such comes only AFTER.

Let us define the symbolism of Existential algebra and study its main equation, from where we deduce all other isomorphisms of the Universe.


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