**SUMMARY.**

**I. 5D:** Mathematics as mirror of the 5 Dimotions and structures of ∆@s=t

**II. ∆±¡:** The elements of Mathematics: Points, numbers, operands, functions and graphs,.

**III. Evolution of mathematics:** Non-E topology: Point with parts.

**IV. Logic and mathematics:** axiomatic vs. experimental method.

**V. The 3±I ages of mathematics.**

**Abstract.**

Mathematics, after logic, is the most efficient language as a mind-mirror of the properties of space and time. As such it must be treated as an experimental science of those isomorphic properties.

The purpose of the upgrading of classic maths into Non-Æ mathematics is thus clear: to vitalize the foundational concepts of mathematics, to make them reflect better the 5 dimensional motions or actions of reality (Dimotions): entropy, motion, perception, social evolution and reproduction.

*THAT IS, to eliminate the magic of mathematics, explaining how the image does reflect a reality above the mirror, the laws of generational space-time.*

**Leibniz the ****pioneer: points with mental parts.**

This should have been done long ago if the school of Leibniz, the great forgotten genius of the modern Western tradition had dominated the development of modern philosophy of science, instead of the dual æntropic principle represented by Newton, with a modular paranoid brain, with a part dedicated to pure anthropomorphism (Abrahamic religions) and the other to pure entropism (lineal inertia, and absolute clock time, perfectly suited for the development of military ballistics).

The dispute between Leibniz and Newton, which we shall soon develop, thus represented the point of wrong inflection of the future of the humind. For Leibniz, every mathematical point was a fractal mind, with inner parts, a vital representation of future non-euclidean geometries.

And for Leibniz, the fact that differential geometry was about ‘finitesimal 1/n, parts of a whole’, points that ‘moved’ NOT lines OF FIXED greek geometry, vitalized motion with an inner vis, which again the æntropic principle denied.

THOSE TWO SCHOOLS OF THOUGHT have in fact existed in the western tradition since the military Plato, admirer of Sparta, who defined a Platonic abstract religion of mathematics, vs. the son of a doctor, Aristotle, who defined an Organic Universe. In the ‘repetitive cycles of culture and History’, Leibniz, the alter ego of Aristotle thus was defeated again by Sparta, his military German king, emigre to London where Newton ruled supreme with his studies on the bible and his job improving ballistics for the Empire.

**To get form to the abstraction of points with no parts, curves with no motion and a single plane of space.**

At present mathematics in its abstract forms can only be closely related to the vital Universe through a painstaking illustration of its main components and theorems, which unfortunately will always collide with the æntropic mind frame of mankind which denies the complex Universe to come on top and mirrors it with its simple mind; so it loves ‘simplex explanations’ of it; instead *of trying to evolve its mirror mind with the complexity of the Universe, and further develop it. *

The only thing we can try then, is to *upgrade its logic and mathematical foundations, to gift them with a more vital **complex mirror, based in space-time laws. *

Indeed, since the Universe is Generated by the properties of fractal space and cyclical time, better reflected in the mirror languages of mathematical topology and social numbers, and logic, *we could say safely that since ‘we think therefore we are’, that is, we perceive as humans a limited range of reality, with our space and time languages, for humanity, for humans the Universe of space and time is reflected by mathematical and logic languages. *

Hence the internal syntax of those languages will resemble that of the Universe, or else our mirrors wouldn’t work and we wouldn’t have survive.

It is then a fact that mathematics derived of visual thought and logic derived of verbal times, has been evolving in that path since its inception – which also responds to the 3 ages of evolution of all systems towards more complexity and more information.

So the proper way to upgrade maths would be to retrace the entire history of maths restarting from the beginning with the concept of a non-Euclidean point with parts, and a line-curve that moves and has volume… Those small first steps in fact were done in the XIX c. when non-euclidean fractal points were defined and differential geometry accepted that curves were points in motion, but routine weights too much and so the upholding stopped there.

And unfortunately it came then THE BIGGEST MISTAKE in the history of maths, the Cantor+Hilbert axiomatic method which changed completely the language of maths, away from its original elements points in space and social numbers in time. So the task today would be imposing. As there is a completely unrelated to reality metalanguage to talk of the otherwise real laws of mathematical points in motion and with volume and social numeric parts.

All what we can do though is to restart a bit the whole process by commenting in the main laws of mathematics, NOT through set theory but through the classic concepts.

*And so by studying the formal sciences of mathematics and logic, in the language that is MORE REALIST we can describe the Universe.*

*IT IS THEN NECESSARY always to consider that points have volume, that lines are points in motion, and frames of reference, points of view of Universal minds; that is, to restart from Geometry wth volume, motion, form etc.*

*We can talk then of a Universal topology, from topos, the language of geometry in motion and logic, the language of causal time cycles that create and repeat patterns of reality, which mirrors in depth those ultimate laws of reality.*

The result would be a refreshing new look to classic laws of geometry, number theory, algebra and analysis.

**Subdisciplines of realist mathematics.**

But simple mathematics work. Of course, because all languages carry a minimal information that is useful enough for certain minds in certain limited worlds.

How many world minds are then generated by those two essential languages of reality varies then according to the complexity of the being in exist¡ence.

The same happens with the original visual language: bacteria and electrons just perceive light-energy; animals dual B&W forms; trilogic visual animals have more colors and further on distinguish a dimension of time motion and so on.

In the ¡logic posts we study all those gradations and deduce pentalogic and decalogic as the more complex mirrors. Human mathematics then reflect those full elements of pentalogic in its sub disciplines, and even decalogic in the o-1 palingenetic scale of evolution and the 1-∞ scale of organic systems (as it does also in smaller scales in the o-1 probabilistic quantum scale and 1-∞ thermodynamic statistical scale).

So we start to see equivalences between reality and mathematical tools.

In general though trilogic in a single plane of reality is the commonest grammar of humind mirrors in all languages:

Light language: red-energy colors, blue-information colors and its green/yellow combinations.

Verbal Language: subject (information) < verb (action-combination)>Object (energy of subject).

**Geometry**: Height (Information dimension) < width (reproduction-Energy)> Length (Lomocotion, entropy)

**Algebra:** Y: Future-information < Operand-action> F(x))

Trinity is thus the logic of most beings. However as humans reached higher and lower scales of observation, a pentalogic was possible and its mathematical mirror became analysis, with its operands that extract finitesimals (∆-1) or integrate into wholes (∆+1) smaller or larger systems.

And further on motion was added to the mix.

Thus maths became with the inclusion of Calculus the most complex, best mirror language of human thought, arguably overcoming with the age of calculus the verbal mirror, which is the natural language of man, specially because of the arrival of instruments of measure which could also cast reality into the digital language of social numbers, identity species that further proved the social scalar nature of the Universe.

So with the modern age, past the simpler age of geometric maths, a new language of social thought and scale, numbers and calculus enthroned mathematics as the queen of all languages.

The fundamental purpose of this and all other posts on maths thus is to continue the UPGRADE on the understanding of mathematics as a language mirror of the vital, organic, scalar properties of the space-time Universe. So we are not so mucha advancing maths beyond the upgrading of Non-Euclidean mathematics, but interpreting maths as an experimental science, that is as a mirror of the space=geometry and time=logic, algebraic and scalar=digital social properties of all what exists.

Since we shall show there is enough math mirrors, in a classic realist way (ignoring the 100 years of Cantor and Hilbert and al the modern jargon) to describe the Universe as an entangled fractal game of Dust of space-time, ¬∆@st.

Further on, the main law of the entangled Universe S=T, means each of those elements can be perceived as ‘form=space’, in the stillness of a static geometric mirror or each element can appear as a flow of a series of ‘5 Dimotions’ (dimensional motions of time space), a motion of time, its true nature, since MOTION not form is the underlying substance of reality. So maths has evolved also from space still greek geometry into differential geometry and analysis. And then it has truly reflected reality.

And so the 5 elements of reality, entropy (¬), Scale (∆), time (T) and Space (S), are the elements all languages mirror either in a ternary grammar (if scale is missed), including human mathematics.

So we translate in this post and subposts mathematics to 5D.

# I.

# 5 D MATHEMATICS, MIRROR OF ∆@S=T

L’algebre n’est qu’une geometrie ecrite; la geometrie n’est qu’une algebre figuree.* Sophie on the S=T duality of maths as a topological, social, numerical language of form and scale.*

## ∆¡-logic Mathematics: **Pythagorism or organicism?**

**The pentalogic Universe.**

The method of the blog will then be able to deploy to further understand any mathematical law or structure, the ‘pentalogic’ of the five dimensional motions of the Universe.

Indeed, there is out there a larger ‘degree of logic understanding’ that the present axiomatic method of mathematics.

We talk of a MORE COMPLEX LANGUAGE of reality that justifies the structure of all languages as mirrors of the ORGANIC properties of the Universe, whose complexity as it entangles and (des)integrates, times=motions, space=form, language and scales, requires a higher number of parameters to do a dynamic study of exist¡ences (existence through scientific scales)… to resolve the question, *how far a mind can go in the imprinting of reality, because we huminds, cannot go further than the ∆±4 planes, decametric social scales, and ages of our lifecycle, around the 10±**I capacity we have to see, perceive, think, and order.*

So man, its logic, numerical systems, social scales, organization and territorial order ends in Decalogic. And yet IT IS STILL A GINORMOUS POTENTIAL UPGRADING OVER æntropic man, the present state of the species, worth to have a laugh at before we enter into serious work.

We have stated ad nauseam that in the Universe of 5 Dimensional motions or Actions…

Entropy(lower planes) > Locomotion (length) > Energy (width) ≈ Information (height) < Language-Mind-Form(upper planes)…

…the description of a being is based in the multiple symmetries between those Dimotions and the essential ways in which we can perceive them. As * languages are also consistent fractal entities in themselves, they will therefore be gifted in its complete form of at least 5 mirror reflections of those Dimotions, we know certainly to exist.*.

So for all languages we must first bring a series of pentalogic concepts that express in their syntax the pentalogic of the Universe. Most languages though act for limited minds and so they get away with the scalar concepts, which however in the full potential language, will still be expressed.

Pentalogic is then the fundamental tool to give deeper meanings to every element of mathematics and connect it as an experimental science with the Universe as it is, to be able to distinguish what of mathematics as an ‘Inflationary mirror’ of information Is truth and what is ‘Inflation, fiction’ proper of all languages, whose syntax allows to create combinations consistent with its inner structural grammar but with no reflections in the outer world.

Indeed, Pentalogic describes reality with 5 Dimensional motions in time parallel to its 5 Structural symmetric elements as an organic whole:

Scales: ∆, Topologic space, S, Temporal actions, T and mind languages that organize the whole, @, and the entropic negation-death of the system, ¬), which give birth to ¬∆@st, Time-Space super organisms generated by ‘dust of space-time.

And so when we apply pentalogic to any ‘system of Dust of space-time (¬∆@st), we can consider its scalar, spatial, temporal, linguistic parts. As we shall often ignore the ‘destructive’ entropic end of a system ¬, or consider it just as the ‘LIMITS’ of the system in space and time, this simple method of study of any structure of reality, including the languages that mirror reality, will also be applied to mathematics.

I.e. when we study a type of functions or elements or parts of mathematics, we shall discuss:

– its ¬ ‘limits’ in which the reflection of reality holds – which gives birth to fundamental truths of mathematics, such as the need for ‘Cauchy’ limits in the solution of differential equations and integrals.

– Both its algebraic, temporal expression and its ‘spatial, topologic elements’ and S=T symmetries and their use to describe the topology of the Universe – which gives birth to a fundamental law of mathematics, that all algebraic solutions have a similar topological way to demonstrate the model or theorem…

– And finally a temporal dynamic ‘analysis’, through calculus, based in the DEFINITION OF A DIMOTION, AS A DUAL SPACE-TIME element, by the Paradox of Relativity of Physics (paradox of Galileo: every form can be perceived both as a still spatial mind-form and as a motion in time, so we see the Earth still when it is moving, e pur is muove no move).

All this duly illustrated with the simpler findings of duality paradoxes caused by the Duality between wholes which are continuous and parts which are discontinuous, wholes that are closed, circular, curved and parts that are free, lineal (so all mathematical systems can be studied in differential geometry with lineal tangents and oscular planes, and in algebra, all curves can be approached with lineal tangential functions)… And a bit more complex ternary logic symmetries… of the 3 scales of any organism, its 3 topological varieties (the only ones needed to describe all forms, as Gauss proved) and its 3 temporal ages of a time worldcycle…

Pentalogic thus applies the laws of the fractal, scalar, cyclical timespace Universe to EVERY SCIENCE as they ARE THE UNDERLYING SYMMETRIES AND STRUCTURES OF REALITY COMPLETELY ignored by monologic man with its lineal time humind…

So while the data and equations we shall use are the same in any language, whose genetic structure IS INDEPENDENT OF MAN AS AN SPECIES OF ITS OWN in the vital organic mirror-making Universe (maths is an species of the fractal Universe as much as we are one, and so many species can have a fractal mathematical mind, and many might speak memetic linguistics and so on), we shall ground all ‘sciences’ in a far more profound philosophy of ‘stience’, based in the fractal, scalar properties of space, cyclical nature of time, and the organic, biological survival language derived from them. We shall always GROUND all realities in those topo-bio-logic PROPERTIES OF space, scales and time.

And the adventure of the mind that satisfied me for 30 years developing this Magna Opus, against the simplistic æntropic humind has been precisely to enjoy the perfect pentalogic grammar of all what exists, from biological species, to physical systems, from musical scores, to mathematical structures, from wo=men’s e-motions to physical forms, performing myself all kind of pentalogic exercises from the art of painting to the discovery of new laws of physics to the study of the life and death of civilizations, or the patterns of stock curves of reproduction of machines. When you know the pentalogic game of exist¡ence the mind holds not barriers in its perception of the perfection of the fractal Universe.

We have resumed the pentalogic of some disciplines of logic and mathematical languages in the next graph that shows what a structural analysis of a super organism in terms of the 5 Dimotions of pure causal logic and mathematical simultaneous space would look like:

In the graph we can assess the different 5 mirrors in which mathematical Space and logic Time reflects the game of 5 Dimotions=actions of existence, which then expressed by territorial monads GENERATES its logic REALITY. In Geometry fractal points=monads will other through waves of communication of energy and information that grow into reproductive networks a territorial plane, creating a super organism, which will related to the external world according to its relative similarity=congruence, assessed by its angle of parallelism or perpendicularity.

In logic terms, this means by breaking its formless asymmetry into different spatial configurations according to that congruence (social parallel systems, complementary gender-mirror systems, darwinian perpendicular systems, or systems that are disymmetric and do not share any reality) , as it builds a casual pyramid of growth from a fractal point through waves of communication into social networks that become a super organism, ready to move, feed, perceive and evolve socially. Since we __must add to the mathematical and logic languages-properties of reality the 5 actions, or organic properties of the scalar Universe as essential to the game as they are its logic and mathematical more abstract laws – a fact the egocy of æntropic men of course reject, as it must remain in its monad-subjective monologic the only claimant to life properties.__

Thus the PENTALOGIC OF GENERATIONAL SPACE-TIME is established by its Non-Euclidean fractal points, its ¡logic congruence with reality in which it will order a territory to perform its 5 vital actions=Dimotions of existence, and the mathematical, logic and organic laws of those 3 languages will be therefore the bottom line of the ‘Creative process’ of the Universe – nothing chaotic except the entropic Dimotion, which conforms the monologic of huminds.

Each advanced language of reality thus CAN BE UPGRADED, AND IT WILL BE UPGRADED IN different POST, TO A PENTALOGIC ANALYSIS in its basic Grammar. And so very often we shall start a post commenting on the pentalogic different Dimotional views of the system we describe.

The post of actions and Dimotions and Non-Euclidean Geometry; most of the posts on physics and studies of different species and properties will be casted from a pentalogic point of view. In terms of *the structural elements of reality, which reflect those 5 Dimotions, the method most used in the blog will be the study of ‘dust of space-time’, as made of ¬entropic destructive arrows that deny its 4 structural elements, the @-mind (1st Dimotion of *__perception), its scales (5th Dimotion), its spatial topologies (locomotion and organs) and its temporal ages and worldcycles. So we obtain a more concrete description of a ¬∆@st entity with reference to its organs and cycles of classic science.__

Yet in this post we are more concerned with the @-mind languages and its ilogic mirrors. In the previous post we have upgraded the logic postulates of geometry, the basis of mathematics. Because mathematics is in its basic grammar, ‘Geometry’ of points and collections of points. So we have also defined numbers as social groups of identical beings, which in geometry mean they are its next social unit – regular polygons, which are the ONLY mathematical forms in which social points are all equal in Nature, hence numbers of collections of equal beings in pure number theory.

We have then upgraded (work in progress) each subdiscipline of abstract maths into vital mathematics of fractal points = numbers to make it look like the real vital, organic Space that GENERATES all entities in existence along the laws of pentalogic, which we shall try to build up in this post. So while the fractal point is the COMPLETITION OF THE concept first advanced by Non-Euclidean geometry of a point with parts, with volume through which infinite parallels can cross, from where we evolve the limited connection human mathematics has between its theorems and reality; the concept of a Dimensional motion, is the unit which will allow us to upgrade the *even more limited command huminds have of the ¡logic processes of creation of futures and species of ∆@st in the highly intelligent Universe*.

But we repeat ad nauseam, the truth purpose of logic mirror languages and mathematical geometries is NOT the language per se, but the vital survival of the entity that wishes to perform through its comprehension of the Universe with those languages, its PROGRAM OF EXISTENCE, its vital actions. And so as the point MUST grow in size to FIT multiple parallels, and so it is A FRACTAL POINT, A CONCEPT that substitutes Euclid’s axiom of definition of a point; the first Dimotion of perception will move, feed on energy, reproduce, and evolve socially generating a new plane of existence. So we can cast our original question as to how many Dimensional motions exist in terms on how many ACTIONS are needed to survive.

And it seems then we can answer the first question: 5 actions suffice, as we have explained in our posts on the meaning of life=action, since a system that perceives can then move to feed on energy and reproduce its forms, which will maintain then its 3 topological parts alive; but by doing so it will both shrink its mind system into a lower plane and rise order into the outer territorial larger world.

So the point-mind perceives, moves, feeds, reproduces and evolves socially into larger wholes. And yet even if 5 Dimotions are enough, the mind’s program will mostly assess those dimotions, exclusively from its own ‘temporal subjective perspective’ but GIVE TO THE EXTERNAL UNIVERSE IN WHICH THEY WILL ENTROPICALLY FEED ONLY THE DIMOTION OF ENTROPY which is useful to them. This is what we mean by a monist mind. Humans performs its 5 Dimotions from its selfish point of view and languages as the center of the Universe and so they DO have a complex pentalogic view of themselves, and shun off ‘one-dimensional men’, but when doing ‘external science’ they have a monist view. And that might suffice. In this blog though we shall do objective pentalogic science ALSO WITH all other entities of dust of space-time of the Universe.

**æntropic man – (making friends):**

Now humans are what they are, and you are not going to get them out of its æntropic mind view. Nobody of the few huminds, which have gone further, which are hardly a few hundred of them, mostly from the age of Axial masters, prior to the domination of the Abrahamic, Entropic Military people of the gunpowder western cycle, to the very few you could put on that category on the modern western culture, mostly from the renaissance, the world of art, and the summit of organic scientific thought of the German school started with Leibniz and crashed with Hitler (people like Leibniz or Einstein, Picasso or Beethoven, Darwin or Spengler)…

Mathematics is the main mind-mirror of Space, itself the ‘formal’, static view of Nature’s time motions. As such is a fundamental language of Nature. We could say it is the language of the ‘Galatom’ and its immortal elements. Why is this though is ill-understood by mankind, specially in the ‘3rd formal age of mathematics’, when humind egos construct its foundations from the roof down and independently of nature (Axiomatic method that denies Godel’s theorem and its experimental nature as all languages mirrors; use of set theory – the roof – not its natural units, the point of space and the social number, etc.)

So as the philosophy of mathematics have become yet another ego-trip of the humind, pretending to speak alone with ‘God’, the language of creation, without reference to reality, 5D is at odds with those methods.

In that regard, the fundamental purpose of this and all other posts on maths is to UPGRADE the understanding of mathematics as a language mirror of the vital, organic, scalar properties of the space-time Universe. So we are not so mucha advancing maths beyond the upgrading of Non-Euclidean mathematics, but interpreting maths as an experimental science, that is as a mirror of the space=geometry and time=logic, algebraic and scalar=digital social properties of all what exists. Needless to say in a ginormous field as mathematics is, we shall just keep it simple.

The philosophy of mathematics of 5D then is the same that any other language as a mind mirror, and shows indeed its correspondence with reality, as all mirrors do. This becomes obvious when we consider its correspondence of its main disciplines with the ∆@st elements of reality, as stated in so many posts.

Needless to say in a ginormous field as mathematics is, we shall just keep it simple. To that aim, we shall often use texts from one of my fav books of my learning years – the 3 volumes of “principles of mathematics and applications’ by Aleksandrov, which if still alive would love to see as a member of the ‘dialectic=dualist’ soviet school of thought, the upgrading of his philosophy of science.

So we have selected pieces of Algebra, often copying the data from wikipedia and Aleksandrov, which I recall to have a special vital meaning to be illustrated slowly in ‘new layers’ of work, as we keep building up the web, and leave out all the work I have not resolved into vital mathematics or don’t remember (as most of my work on 5D was done in my 20s, before I escaped the military service and ruined my life as a scholar)… If I live longer and find my annotated notebooks and care to translate, we shall improve the web… So far my intention is to get to a level of work in which a well-intentioned, humble scholar soul realizes the discovery of a new gem of thought to improve with future researchers.

This post is the simplest one, a conceptual introduction studying the experimental vital philosophy of 5D mathematics.

l§**5 DIMENSIONAL DISCIPLINES: PENTALOGIC OF MATHEMATICAL SYSTEMS**

The Universe is a game of ∞ Sπcies of space-time making STeps and STops in its constant œxist¡ence (where we use π for time, in this particular wor(l)d according to the slightly changed rules of i-verbal thought for english to look more like the universal game), and so as Stops and steps (ab. œ) bring the being into exist¡ence we can measure them quantitatively as space-distances and time-motions. Stop and step then becomes topology and feed-back equations, where = is substituted by the dynamic symbol <=>, and the duality from = stops and ≈ wave steps.

Once the intuitive meaning of those symbols rises the awareness of the reader to the vital nature of our humind’s abstract rendition of reality things become then dynamic. ≈ for STeps, = for motions, and ≤≥ as the different implosive or explosive, informative or entropic ‘degeneracy’ of a system are easily quantifiable and translatable to both mathematics in its pure expression and mathematical physics.

**A definition of the Universe.**

All this said, , we can make a proper definition of the fractal Universe more suited to its mathematical description.

The Universe is a fractal super organism made of…

** A(nti)symmetries** between its 4 Dual components T, ∆, @, S, through parallel =symmetric or Perpendicular/antisymmetric communication, as theycan either evolve in Balance≈become symmetric or annihilate=become Perpendicular/antisymmetric:

**S:** space; an ENSEMBLE OF **ternary topologies,**** (|+O≈ ø)**… which made up the **3 physiological networks** (|-motion/limbs-potentials + O-particle/heads ≈ Ø-vital energy) of all *simultaneous **super organisms*

**∆: Planes of size**distributed in ∆±i relative*fractal scales*that come together as**∆º**super organisms, each one sum of smaller**∑∆-1**super organisms… that*trace*in a larger**∆+1 world…****ðime cycles:***a series of timespace actions of survival that integrated as a whole form a sequential cycles of existence with*each one dominated by the activity of one of those 3 networks: motion-youth, or relative past, dominated by the motion systems (limbs, potential); iterative present dominated by the reproductive vital energy (body waves), and informative 3rd age or relative future dominated by the informative systems, whose ‘center’ is:**3 ages**,**@: The Active linguistic mind**that reflects the infinite cycles of the outer world and controls those of its inner world, through its languages of information, which guide its 5 survival actions: 3 simplex,**aei**, finitesimal actions that exchange energy (**e-**ntropy feeding), motion (**a-**celerations) and**i**nformation (perceptions) with other beings, and two complex actions:**o**ffspring reproduction and social evolution from individuals into**U-**niversals that maximize the duration in time and extension in space of the being.

So that is the game: 3 asymmetries of scale, age and form, which can come together or annihilate and each language represent in different manners, those elements and its operandi.

Because the scientific method requires OBJECTIVE measure of the existence of a mind, which is NOT perceivable directly, we *infer its existence by the fact a system performs the 5 external actions, which can be measure objectively, in the same manner we infer the existence of gravitational in-form-ative forces by its external actions upon massive objects. *Hence eliminating the previous limit for a thorough understanding of the sentient, informative Universe. And further classify organic in simplex minds – all, which must gauge information, move and feed to survive, and complex systems, those who can perform a palingenetic reproductive, social evolution, ∆-1: ∑∆-1≈∆º.

Regarding the mind, which is the internal non-perceivable element, it requires the concept of an angle, which is not a number, and hence a ‘different’ element of mathematical representation of reality.

The study of the 5 Dimotions of all realities, with angles, numbers, operands and functions, its actions and ternary <=> similarity operandi, structures *the mirror of mathematics. *

So the first mirror we need to express is a METRIC EQUATION TO ‘MIRROR’ THE METRIC OF THE UNIVERSE.

**Metric equation of mathematics. ****1st algebraic S=T MIND EQUATION: 0x ∞ = K ****search for ‘wholeness’ in a single equation. **

*0-finitesimal spatial mind x ∞ time cycles = Constant mind-world: §@<≈>∆ð*

*The mathematical dynamic ‘Generator Equation’ of all Space-time Systems of the Universe, written in its simplest form as a singularity-mind equation is: *

*0-mind x ∞ -Universe= C-onstant world, which is therefore the fundamental equation of ‘number theory. *

* O x ∞ = K **Or in a structural way, S@<≈>∆ð.*

The equation represents all possible metric equations of all supœrganisms of the Universe.

As such neither 0 is an absolute zero, nor ∞ is an infinity, concepts relative in a scalar Universe, where the limits of scales in size and time speed and perception in each self-centered p.o.v. only allow to talk of relative infinitesimals, we call finitesimals, 0/~~∞~~, and relative infinities, whose symbol is ~~∞~~.

Two evident truths are then, the existence of an experimental finitesimal, h=m l² ƒ, the minimal unit of angular momentum or Planckton of the galatom, and a relative infinite, ~~∞~~=c, its maximal distanced-speed, which conforms the most extensive metric we know of with precision, beyond which dark space and time is unperceivable to mankind, so we write 0s (h) x ~~∞t~~ (c) = K

It follows also that mathematical infinities are inflationary mirrors whose contradictions (Cantor’s Paradoxes) are NOT solvable (the Zermelo axiom being an ad hoc addition, against the logic of truth), because precisely they limits of reality enter in paradoxical contradiction with the infinite inflationary mirrors of languages.

The study of those 4 elements of all realities, its actions and ternary operandi, structures *the dynamic ‘Generator Equation’ of all Space-time Systems of the Universe, written in its simplest form as a singularity-mind equation:*

*O x ∞ = K = ∞º=1*

Whereas the 01 finitesimal scale representsthe palingenetic first birth of any species and the 1-∞ its existence in the external entropic world.

Thus it matters more is the division of that interval between the 0-1, first palingenetic emergence, where the 1-whole is a closed space, hence without entropy (a placenta rich in energy) and the interval is time-like, probabilistic, embodying all possible generations of space-time species within its interval. While the 1-~~∞~~ is unbounded, open and hence entropic, meaning the being normally doesn’t reach its limit.

However as the game is one of 3 asymmetries of scale, age and topologic form, which can come together or annihilate and each language represent in different manners, those elements and its operandi; it is needed a ‘branched’ new plane besides the 1-∞, with the 0-1 sphere as a borderline, which happens thanks to the complex plane, where the function x=zª represents the 0-1 sphere and all its polynomials within it, and works as the AGE PLANE symmetric but not equal to the 1-~~∞~~ real plane which represents a population age.

**Operand as Dimotional functions.**

Within those 3 fundamental planes, there must then be operands, which represent Dimotions of a given function of exist¡ence. And so we define those DImotions in mathematics*, with the duality of **inverse operations, + -, X ÷, √ xª and ∫∂, and the universal ≤≥ symbols that put in relationship two sides of timespace event that connects adjacent, simultaneous parts of a super organism in space, or ‘moves’ and transforms a t.œ in time. So Dimotions are presented by those operand, and functions connected by similarity operand (<=>) express the connection of adjacent topologies in space: |<ø>O.*

Mathematics in that sense follows the same ‘grammar, syntax, semantics and synoptic nature’ of all languages that portray the world cycles of existence in time of super organisms, with synchronous adjacent topological chains of time§pace cycles, that all other languages of nature, albeit, seemingly with more precision, which has made it a ‘survival language’, likely to be the ‘mind-mirror’ of atomic structures perceiving in topological mind-spaces.

What those equations will then express are different motions of energy and information produced in the change between states of spatial form and temporal motion. The varieties of it, being mainly the 5 Ðimotions of space-time, and so relating equations of physical Dimotions to classic equation through those operandi allow us to convert classic physics in a subdiscipline of GST.

If we define the 5 Ðimotions of the Universe as S> T: information, S<t: locomotion, S t = s T: reproduction, §tð¡ ∑ §ð¡>ST¡+1: social evolution, ST¡+1<<∑ $t¡-1: Death then when we study mathematical physics, which is basically the study of different forms of the v=s/t original equation we shall find slight differences between mathematical dimotions which become then reordered within those 5 subspecies.

But what world-universe mathematics reflects within that equation? Obviously the largest possible world, where the o-mind will be the smallest infinitesimal and the body wave, the largest ∞. And this is the galatom (∆±4).

So we conclude that Mathematics is the language mirror of the galatom superorganism, hence it is the essential language of astrophysics. It does have also as all languages mirrors capacity to analyze all other systems, based in the fact that its numbers reflect the 5th dimotion of social evolution (a number is a set of undistinguishable beings), and its algebraic operandi can reflect the scales of reproduction and social evolution 3 ‘stages’ (±, x÷, log xª), its sin/cos operandi the cyclic repetition of those processes, and the ∫∂ operandi *any dimotion of time=change.*

We are thus going to try to translate in this post and subposts mathematics to 5D.

And to do so, as a fractal can always be divided in sub-fractals, mathematical disciplines subdivide further at all levels in 5 elements connected not so much with the 5 Ðimotions of existence, but with its 5 structural elements, ∆@s≤≥t, scales, minds, space, time and its a(nti)symmetries.

**Disciplines of Non-Æ Mathematics.**

**The main sub disciplines of mathematics as mirrors of the 5 Dimotions.**

It follows then from the definition of the 5 elements of all systems, an immediate classification of the five fundamental sub disciplines of mathematics specialised in the study of each of those 5 dimensional motion or similar structural elements of any space-time being.

Ultimately as the language of the Galatom, mathematics IS necessarily a language able to mirror the structural elements of the galatom and all its fractal inner parts. it follows then from the definition of mathematics as an experimental mirror of the 5 ‘entangled’ elements of all systems, an immediate classification of its five fundamental sub disciplines of mathematics specialised in the study of each of those 5 dimensions of space-time:

Mathematics in 5D becomes necessarily an experimental science, as its properties must come from the properties of space and time. This is at odds with the human egocy, of making it all coming from our mind as creators in contact with God. So we are supposed to speak the language of god which suffices in itself, and nothing will change that view – not even Godel’s incompleteness theorem. lobachevski’s experimental mathematics and Einstein’s view that ‘I know when mathematics is truth but not when it is real’, neither the understanding of the inflationary nature of information and its languages that produce fictions, done in this blog. So the task is daunting because as in all OTHER SCIENCES, humans have TRANSFORMED TRUTH THROUGH CULTURE AND EGO into A SELF-SATISFYING simplification that makes them feel in control. In Biology we shall also observe that chaos REIGNS as the philosophy of Evolution, when everything is ‘PROGRAMMED’ BY GENES, and eusocial evolution of parts into wholes is rejected when it is obvious that it ensures survival, much better and creates the fractal scales of reality.

All this said, even though we shall use classic maths at the most basic level to illustrate its correspondence with reality and reject the axiomatic method, 2 facts must be remarked so early in those texts:

- Maths is a mirror language and as such its laws are ultimately experimental reflections of the space-time-scalar properties of the Universe. So its 5 subdisciplines relate closely to them.
- The concept of an Euclidean point with no parts, is the single false simplification that hinders most the understanding of vital mathematics and its scalar, social, organic, temporal properties. So we shall introduce also the fractal point that grows in size as we approach its scale.

**The main sub disciplines of mathematics as mirrors of the 5 Dimotions.**

.So WHAT we shall do in this and sub-posts, is to continue that game, now between ‘two languages’ MIRRORS OF THE UNIVERSE, Mathematics and T.Œ, the description of the 5D of space-time and its organisms, to improve mathematics by improving their mirror of the 5 Dimensions giving birth to 5 improved mathematical sub-disciplines:

And this goes as follows.

**Vital Space analysis: ¬Æ Geometry**studies fractal points of**simultaneous****space, ∆-1,**& its ∆º networks, within an ∆+1 world domain.

They must though be properly defined departing from the concept of a fractal non-euclidean point,with volume, which increases as we come closer to it – reason why it can fit infinite parallels (an euclidean point with no breath CANNOT, even if we bend them as it is customary in the primitive definition of them). **@-Mind: Analytic geometry **represents the different mental points of view, self-centred into a system of coordinates, or ‘worldviews’ of a fractal point, of which naturally emerge 3 ‘different’ perspectives according to the 3 ‘sub-equations’ of the fractal generator: $p: toroid Pov ðƒ: Polar co-ordinates.

Thus we shall complete the evolution of geometry by defining the 5 Postulates of Non-euclidean geometry departing from the concept of a fractal point.

**§ocial scales analysis: Number**theory studies time**sequences**and ∆-1 social numbers, which gather in ∆º functions, part of ∆+1 functionals. NUMBERS ARE SOCIETIES OF UNDISTINGUISHABLE PARTS, hence the fundamental element of algebraic analysis of the ‘vital energy’ enclosed by a system or network that gathers together social elements. This OBVIOUS truth escapes human egocy, specially in our dog-eat-dog primitive culture of ‘capitalism’, and competition between members of the same species.

**If the **geometry of the fractal Universe is non-euclidean made of fractal points with volume, its logic is non-aristotelian, made of sequential social numbers with strange connective properties better expressed with the non-aristotelian logic needed to understand the different forms of temporal, sequential correlationships between social groups of similar ‘numbers’. So we shall develop a non-aristotelian logic of numbers, latter expanded to variables. We shall improve** Number** theory by putting them in relationship with ST-laws, by understanding sequential time numbers, scalar social numbers and real numbers and mathematical constants as ST-ratios and functions of ∆st actions.

Once we have understood the connection between social numbers, as identical species, which therefore imply they must be in the symmetry of space, polygons (or else as points will NOT be identical in form and function) we can consider its vital Generation of Space-Time beings, as indeed the pentalogic symmetry between numbers, points, mind-centers and time sequences defines also a new conception of the natural numbers as a process of creation of new forms of space-time beings.

Consider the simplest generation, related to the postulates of non-E: the 1 splits its fractal regions into a region of energy and information (gender generation), a neutron so to speak generates a proton dominant in information and an angular momentum, electron dominant in energy-motion.From 2 then comes 3, and a triangle is formed, which means also that from 1 Dimension (the point) we move into 2 dimensions (as points have form), the wave-line, and 3 Dimensions, the ternary network, plane (connection of 3 points), which is the simplest physiological system, skewed in its motion to a side that will then become the informative network, its base the digestive, entropic network that absorbs energy from the environment, and the third reproductive network.

But this 3 ideal number-triangle, LACKS a mind point, which appears as the point of intersection of its 3 median lines from vortices to half points.

This 4th point becomes then a number but also a holographic, bidimensional complete T.œ as it has 3 networks, a mind-point communicating them all, 3 vortices, and it can rotate cyclically or can move lineally…

But if go further this central mind point, which embeds the whole in its mind will RAISE into a new dimension of height, with a projective geometry over the other points as the advantageous center, and so a tetrahedron appears.At this point we realize that THERE ARE TWO DIFFERENT FORMS OF CREATION, AND SO REALITY SPLIT IN TWO DIFFERENT SPECIES:

- The triangle self-centered in a point in 2D, which can rise into a tetrahedron in 3 Dimensions
- The quadrangle, if instead of self-centering the triangle we create a fourth side, doubling the number 2.

And so diversification of species occurs. And then the fifth point can become a self-center of the tetrahedron in 3 Dimensions, a center of the square, which acts as its relative inner communicative mind or a new polygon, the pentagon. And so with 5 points we have 3 families of species, a 3D triangular, 2D quadrangular and 2D pentagon which now can connect its sides every two points to for an inner pentagon of 10 points.

The reproduction of fractal points thus create new species, and as the simplest forms of nature, galatoms can be often modeled in chemical structures as such type of points, it follows immediately that because we are indeed space-time beings, the laws of numbers as forms are also the laws of nature in its simplest forms – and likely in the cosmic scale if it is a hyper universe beyond our seemingly hydrogen like gaseous region of existence.

This way of describing spacetime beings of course is out of place in the modern abstract, automaton understanding of mathematics, as we discuss in the article on its philosophy but is ESSENTIAL TO A PHILOSOPHY OF A UNIVERSE OF SPACE-TIME BEINGS, HENCE OF MATHEMATICAL AND LOGIC BEINGS as the synoptic language mirrors of the laws of space and time. And it is the one that the earlier Chinese and Greek Pythagorean mathematicians with more direct insights and less pedantry would accept as real and what we want to develop here.

**∆S≈T: ¬Ælgebra, comes from Arab**meaning the gathering of parts into wholes. As such is the most important part of mathematics; as it studies all, dimotions and scales through operands and feed-back equations (when we properly redefine them in terms of ≈ similarity not equality and dynamic equations) the different Dimotions of exist¡ence, from single S=T steps to larger associations of Dimotions, in more complex ∆+1 structures (Functions). Further on in its most modern systems iIT DOES SIMULTANEOUS ANALYSIS OF super organisms in space, through the study of its a(nti)symmetries between its space and time dimensions (group theory)…

**¬Ælgebra** is therefore the vital science of social numbers -its most important part – its evolved form; as it studies through operands and feed-back equations (when we properly redefine them in terms of ≈ similarity not equality and <≈> dynamic equations) the different Dimotions of exist¡ence, from single S=T steps to larger associations of Dimotions, in more complex ∆+1 structures (Functions). Further on in its most modern systems iIT DOES SIMULTANEOUS ANALYSIS OF super organisms in space, through the study of its a(nti)symmetries between its space and time dimensions (group theory)…

Algebra’s operands translate into mathematical mirrors the dimotions of space-time and then build up from them as the Universe does building up from actions, simultaneous organisms in space and worldcycles in time USING SOCIAL numbers to that goal, in different degrees of complexity, mirrors for all those elements of the 5 D¡ universe.** ¬Ælgebra, its evolved version, straightens up the language to match that of 5D.**

** So we define ¬Æ** which studies a(nti)symmetries between space and time dimensions.

It is then necessary to derive from the a(nti)symmetries of the fractal generator a more realist understanding of ST mathematical functions, its operandi, and structures that act as ‘blocks of time’ – iterative laws that relate space and time elements in a multiplicity of beings. As such ‘Group theory’, with its structure that *resembles so close* the fractal generator will be illuminated with this new tool that improves our understanding of ‘algebras’ of all type and also its application to mathematical physics.

So Algebra IS the study of all the structures and symmetries of the Universe from the point of view of its mathematical mirror.

*If analysis specializes in time-motions, algebra is more concerned with space, simultaneous structures, joined by the =* symbol of equality.

But as in the entangled Universe all mirrors can reflect all forms, Algebra also can analyze other elements.

And ultimately Algebra and Analysis ‘ARE’ the complex ‘level’ of reality, as reproduction and social evolution are the complex demotions, including obviously as its ‘background parts’, the theory of numbers, the analytic geometry – study of frames of reference, and the topologic analysis, embedded in the secondary operand, numbers and frames in which we ‘cast’ the complex space and time algebraic and analytical analysis of a ‘Domain’ of the fractal Universe.

We shall call then the upgrading of Algebra to 5 Ð, non-Ælgebra.

**∆t: Analysis**studies ALL forms of time=change, and hence it can be applied to the 5 Dimotions of any space-time being, as long as we study a ‘social structure’, hence susceptible to be simplified with ‘social numbers’ IT IS THOUGH SPECIALLY USEFUL TO STUDY SCALAR TRANSFORMATIONS OF SYSTEMS BETWEEN ∆±¡ planes of existence and so the**proper language of 5Ð**.**∆nalysis, its 5Ð version, can then also be defined in 5Ð jargon as the**study of the a(nti)symmetries between planes and other ∫∂ operations derived of scales of the fifth dimension.

We shall make analysis more realist by defining limits to infinities in a discontinuous Universe, made of finitesimal 1/n parts; by considering the discontinuities of the fifth dimension and the duality of continuous calculus vs. discontinuous fractal scaling, as both are needed to understand the continuous social regions of the scalar Universe, or decametric §cales and the discontinuous gaps between ‘ages’ in time (standing points, variational calculus) and ‘planes’ in space. We will differentiate then 5 general applications of Analysis according to the Dimotion study, and the ‘level’ of analysis, from the minute STeps of a derivative, to larger social gatherings, and changes of entire planes (functionals).

It is then not surprising that despite being analysis first derived of algebraic symmetries between numbers, it grew in complexity to study changes in functions (first derivatives/integrals), and then changes of changes of functions, as motions between scales of the fifth dimension (higher degree of ∫∂ functions, called functionals).

**@-Humind:**To which we can add the specific @-humind elements (human biased mathematics) and its errors of comprehension of mathematics limited by our ego paradox**Philosophy of mathematics**and its ‘selfie’ axiomatic methods of truth, which tries to ‘reduce’ the properties of the Universe to the limited description provided by the limited version of mathematics, known as Euclidean math (with an added single 5th non-E Postulate) and Aristotelian logic (A->B single causality).

This limit must be expanded as we do with Non-Æ vital mathematics and the study of Maths within culture, as a language of History, used mostly by the western military lineal tradition, closely connected with the errors of mathematical physics.

So it is easy to refer mathematics to the ¬∆@S≈T elements of reality: scalar numbers, @-frames of reference and human æntropic philosophies; Spatial geometry, Temporal analysis, and the study of all elements together around its ≤≥ relationships of relative congruence (Algebra), which will also determine according to its similarity its entropic vital darwinian or social relationships, made more explicit with the **4th new postulate of non-Æ geometry.**

We shall accept that even though mathematics is an excellent mirror, it still biases reality to pack it into a mind, so we shall treat mathematics as a language, which is by definition informative, and inflationary in ‘forms’, with excesses and fictions, among which the question of false infinities, the distortions of frames of references and the parallel ‘metaphoric’ expressions of the same ST-LAWS are paramount. Finally we shall consider a better foundation of mathematics, NOT the axiomatic method, set and category theory, which ‘starts’ the building from the roof down, but the minimal entities, points and numbers, to rediscover the classic foundations of mathematics as a experimental language.

The proper way to convert mathematics in what it is – the best mirror image of the properties of the fractal Universe – is to start with the laws of Non-Euclidean geometry, and then build up through the next layers of its reality:

- S=T; the vital
**geometry**of points with parts; parallel to the theory of**numbers**, in sequential scales; that move through: - ∆T(st):
**Analysis**, that study its Dimotions and reproductions that form lines that are waves and networks, which become… - ¬∆@S≤≥T
**Algebraic Organic structures**, self-centered in points of view (mental frames of reference), whose variations form ‘group species’, tracing worldcycles of existence through its Dimotions.

It is then obvious that we shall start such adventure with the study of the… **1-5th Non-Æ Postulates of Fractal points.**

It is then DEPARTING FROM THE PENTALOGIC OF THE 5 POSTULATES OF ¬Æ mathematics and the understanding of its sub disciplines as mirrors of the structural ∆@st elements of all T.Œs how we will be able to recast the mathematical mirror as both an efficient language that COMPRESSES REALITY into its essential game, and hence can ‘faster’ define the future of its species as all good logic mirrors do, and translate its elements into vital components.

So the last of those disciplines is philosophy of mathematics, a required subject due to the ego-paradox of the humind, which introduces some crass errors, among them, the lack of subtle distinctions between Euclidean points (continuous simplifications in a single plane) that mirror the real fractal points with volume (contiguous, a different concept, which is important to highlight, as the fractal point moves by reproducing its form), and social numbers (collection of points in regular forms in a single scale; or cyclical time, antisymmetric to temporal sequences in lineal time) confused with other type of numbers (ratios, either rational, with a limit of scales, or irrational with a relative infinity~~, ∞, ~~number of scales), confused with absolute infinity that does not exist in Nature (as information disappears with distance of perception space, scale or time), confused with energy, as information is always discontinuous… reason why numbers are discrete… And so on and so on…

The reader then should observe what is the true error of mathematics in huminds – the desire to convert it into a perfect ideal language where all is like in Greek idealization of nature (cyclical orbits, perfect celestial bodies and so on), smooth, continuous, infinite, unreal but understood by the humind who contemplates the platonic world of mathematical eidos…

Problem of that philosophy of mathematics is that it departs from Nature, makes it more difficult to understand (Axiomatic method, set theory, construction of maths from the roof, and from human concepts, denial of its fundamental elements) prevents its fundamental 5D advance (Non-Euclidean math with fractal points, pentalogic), and so we reject it.

We will in this post thus introduce concepts common to many other posts on the nature of languages as mirrors, while we treat many aspects of philosophy of mathematics (the point vs. number duality, etc.) in other posts. Then we shall consider some obvious properties of mathematics that make it the language of the vital organic Universe, notably that social nature of numbers, which are undistinguishable collections of similar beings; hence regular polygons when translated into geometry (or else its points-units will cease to be social and distinguishable)…

The more complex elements of 5D philosophy of mathematics though require the understanding of the laws of pentalogic which given he one-dimensional Aristotelian logic of the humind is quite a difficult task, barely started on the posts of ¬A logic, in this ever work on progress blog of a single hardly humind anymore

The previous classification can be made much more extensive, if we were to treat those sub-disciplines with the Rashomon effect of different points of view (considering from the point of view of the 5 Dimotions, etc). We shall not go so far, but another fast-review is due:

1Ð: the Ðimotion of perception is best served by analytic geometry and trigonometric functions. As there are 3 vital topologies of reality, each represents a Point of view (polar, hyperbolic or cylindrical: O, Ø, | points of view)

2Ð: the Ðimotion of locomotion uses in its simplistic physical view in a single scale of reality, those Cartesian and Polar graphs, for lineal and cyclical motions. To which we must add calculus in a single plane – single derivatives, integrals – as it does study each of those Ðimotions of change.

4Ð: the Ðimotion of entropy which ultimately is an explosion of social motions, scattered into elements of a lower ¡–1 plane; so the tools are the same than 2Ð but at a social scalar level (multiple integral/derivatives, complex planes etc).

5Ð: the social Ðimotions are best served by number theory and analysis .

3Ð: the Ðimotions of reproduction being the more complex, and ultimate goal of the vital Universe requires all the tools of mathematics.

As we move on we shall then also relate operands to those Ðimotions and keep unveiling the vital nature of most mathematical systems.

So we find even at the elementary level of those texts *a kaleidoscopic wealth of new relationships between the 5 parts of mathematics, and a very experimental connection with reality as the closest language to T.œ, eliminating the ‘axiomatic method’ as the ‘alibi’ of mathematical **truth – which is to say the least shaky since Godel. And ground mathematics in the highest of all possible referential games, that of space-time beings, from where it extracts its simplified geometric and logic postulates (we reduce axioms, notions and postulates of Euclidean geometry to those 5 connected to the 5 dimensions).*

Finally @, the mind is, connected to frames of reference in its self-centred p.o.v. is written, intimately related along philosophy of maths to theory of languages and again broken internally into ‘3 simplex rashomon truths or dimensions of the generator, as there are 3 ‘choices’ of the frame of mind: S-cylindrical frames, ST, hyperbolic cartesian frames and T-polar frames; plus two complex 4-5D planes, the Hilbert space of smaller parts and the Complex plane, *which is essential to crack properly the fifth dimension. *

*Thus we move from Geometry to ¬E, from Algebra to ¬A, we explain Analysis and ands @-linguistic analysis of maths. This new maths enhanced, vitalised, founded in reality is what we shall call ¬Æ=i-logic mathematics, for ¬algebra ¬e geometry, analysis and @, being i the next vowel to æ…*

But it is the inverse truth? Can mathematics describe all the properties of the 5 dimensions of time-space? Obviously not. It cannot express the sorrow of the mon@d when it realises it is a finitesimal 1/n part of a whole, a mere derivative of a function of exi=st!ence and the fourth dimension of entropy will kill it. I can express it as i have just done the action of death in an i-logic format, but the *emotion, the pan psychic properties of the flow of time, the *different ‘non-mathematical properties’ associated also to time, psychological time cannot be expressed. The logic of the 3 arrows of time is also better expressed with words as a bio-logical, organic darwinian struggle for existence. The abstract fractal becomes far more telling when we accept that ‘the languages of God are infinite’.

Beauty for example in the languages of art can be expressed as S=T, the fundamental ‘motion-step’ of reality Art then has a topological space-time balance which is NOT purely mathematical but absorbed through the human senses requiring the similarity sensation that make us love that specific balance. Music again also plays through the bas-S ≈ T-reble harmonies in one of the purest expression of S-t motions through the melody but the ultimate reference is NOT mathematical (the chords of Pythagoras) but in terms of S=T balance; so while languages can mirror other languages, and we shall obviously make use of all those languages; it is the space-time reality the ultimate reference of all them.

As the ultimate mathematical properties are indeed a proof of the organic, social, fractal nature of the physical Universe. So before we introduce the tenants of mathematical physics, we shall see the larger view of…

**Content of the post.**

Now, the reader in case he is a mathematician should excuse of course, some possible errors and lack of full depth and detail of this as many other texts. I have worked for the aforementioned reasons as Leonardo, carelessly writing backwards, and only now with lifespan diminishing fast I am crowding this blog with information…

The intention of this second line *is to make a first layer of connections for ‘future pros’ to complete it – this was the plan 30 years ago, when I finished my first models at Columbia University, but didn’t get the help of a group of potent scholars to complete the ‘membrain’ of the Universe of maths. *

It is my experience that people have a very hard time making interdisciplinary ‘connections’ and this is even far more difficult between the ‘seemingly’ coming from ‘another planet’ foundations of relational space-time beings and the languages that describe them, specially in maths because of Newman’s dictum. So that is the purpose of this and other posts on i-maths, always a work in progress.

In this very brief introduction we shall just consider some themes on the philosophy of mathematics, and its space and time units, points and numbers, making a summary of its diachronic analysis through its 3 ages, reserving for 5 different sub-posts the study of each of those sub-disciplines.

Of those disciplines the most important is geometry, because mathematics is a language of the mind, and the mind, §@ stiffens motion into form; thus the mind is spatial more than temporal, a fact that accounts for the obvious property of ‘huminds’ (Ab. human minds): we are focused in space, in evident eye-views, and in memorial past, ‘still forms’; we are ‘killing minds’ who stop motion into form, source of many confusions in our understanding of reality, of our chronic incapacity to understand and forecast the future (in social sciences) as we have been doing with a different ‘FRAME OF MIND’ for decades to the ignoramus of huminds who cannot see as Cassandras do.

Next comes algebra, specially when we include within it, analysis as it deals with time-space Dimensional symmetries in scales (analysis, polynomials) etc, and the constant reflections of *each dimension in all the others, as a kaleidoscope which multiplies the inflationary views, equation and mirrors of reality within any linguistic mind.* Analysis in that sense is part of algebra, its reflections through the 4th-5th inverse dimensions – which improves the ‘rough mirror’ of polynomials, more useful for social scales in continuous single planes and its ternary and decametric scales (reason why polynomials and derivatives can be approached through Newton and Taylor’s formulae), but given its development in mathematical physics, we will respect its ‘branching’.

Finally, both can be represented from the mind view with the ternary canonical @-frames of reference, which correspond to each of the 3 s, st, t elements of any space-time system.

All of them will be renewed and put in correspondence with ∆@s=t. And as such 2 fundamental upgradings of *the two dominant branches, geometry, will be the the completion of the 5 Postulates of non-Euclidean geometry and algebra+analysis, with the refurbishing of all those symmetries with the Generator equation, substitute of group theory.*

While in the other minor 2 sub-disciplines, number theory, absorbed as the first age of algebra, and analytic geometry, which can be considered also part of its s=t symmetric views will receive a less extensive treatment, often within those 3 fundamental sub-posts, of which as today, october 2017 only the ‘geometrical one’ deserves a detailed reading – hopefully by christmas the other ones will be minimally consistent.

For the sake of simplicity, quality, brevity and to diminish my work-load on such an extensive blog that unifies all stiences we liberally use when we require explanations from classic mathematics (as we will do when we need to use classic work in physics with Landau’s 11 volume encyclopaedia of mathematical physics and Feynman’s simplified lectures) pages extracted from Aleksandrov’s book on the principles of mathematics – an easy-to-understand 3 volumes of the ‘dialectic school of the extinct soviet union, which had the proper philosophical approach to mathematics as an experimental science, understood deeply its philosophical principles, and avoids the pedantic, 3rd informative baroque age of the axiomatic method.

So a final comment on that: when a language becomes a dogma or religion of truth, whose truths detached from reality are no longer intuitive – to make them so again is our goal in this blog – it becomes a metalanguage. It is the 3rd ‘excessively informative warped and onanist age of any Tœ (ab. timespace organism). Mathematics and physics long ago reached that level which selfie childish wikipedians show with so much pleasure; destroying the connection of the language with reality and avoiding that anyone except the ‘priesthood of the science can research it’. It is then no longer a task of reasoning but of memorial methods, mantras algorithms and protocols.

**MATH, MIRROR OF VITAL SPACETIME BEINGS **

If logic is by definition the language of sequential time, even if those sequences in advanced logic are circular, mathematics must be defined then as the best language to fit the other two parameters of reality, scales, which are indeed defined by numbers and space, which are defined by points, the two classic elements that constitute mathematics and we regain, as we return to classic, experimental mathematics, departing from the ‘creationist’ abstract beliefs of modern mathematicians with its axiomatic method that tries to prove mathematics within its own syntax – an error already proved false by Godel and Lobacjevski.

So mathematics is a potent language only comparable to logic. Of course, as logic can also in the kaleidoscopic, entangled Universe represent space and scale, mathematics can also be used to represent time motions through operandi and algebraic equations, but in true form we should consider the symbols for operandi logic symbols. So in praxis mathematics as it is today is both a logic language and a spatial language. Those are however subtle elements to be treated in a section on philosophy of languages. For a first approximation, we deem mathematics the language of scalar space, ∆§, logic the language of sequential time, and its full combination, ¬Æ=i-logic mathematics, the closest humind language mirror of the Universe, which we shall slowly define and expand in this blog to be able to extract all the properties of reality.

So we subdivide mathematics into numbers, the language of scales; geometry, the language of points of space; algebra, the language of time operandi, and ∆nalysis, the language of scales more evolved than simple numbers and its polynomials as it allows a more subtle analysis of parameters as they emerge into social wholes through integral processes or derive into single parts through entropic dissolutions or ceteris paribus analysis.

Of course in our present ‘primitive ceteris paribus’ analysis of reality with a single present or lineal, entropic time dimotion of locomotion, mathematics truly works for the reduced number of properties extracted in mathematical physics; yet when we include the five dimotions mathematics needs to be complimented with i-logic or else we shall enter into a Ptolemaic excessively complex mode of studying reality. Minds thus in general will use a logic sequential language for time and a spatial mathematical language for space; and as we study minds we shall see that to be the case.

**The mathematical mirror.**

As math is the most used mirror, likely the most efficient reflection of the nature of ∆@s=t 5D Universe we will analyse a bit more the correspondence between the mirror and those 5 Dimensions.

Indeed it is obvious that mathematics is only second to T.œ as a linguistic mirror of the Universe, and as such the most efficient language perceive by man. As languages are the essence of monads-minds that order the biological, organic Universe, it follows that mathematics has survived for eons, extending their local order from infinite fractal points of view, which used it to better their territorial organisation of the Universe; and so infinite species seem to use mathematical systems to navigate their worldcycles of existence, and organise their territories, notably ‘atom-galaxies’ (∆±3):

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

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

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

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

**IS REALITY A LANGUAGE?**

From a book of Penrose, ‘Road to i-reality’ (: we bring that ‘error’ and correct it:

*In the graph, physicists are after all human egos submitted to the mind paradox, so they think ‘mathematics are a mind language, imagined by the physicist and ‘God’ a priori, creating a posteriori the Universe (copenhagen interpretation). The opposite is truth. *

The language of mathematics DOES NOT CREATE REALITY a priori, but ONLY a posteriori ‘sees it’, as a synoptic mirror, which as all other languages, a certain singularity uses to ‘see’ and develop its ‘survival actions’ in time-space.

This said *in a second phase, languages Do create as reversal mirrors, the order of the territories their minds organise, and as such THEY ARE indeed, minds of Aristotelian fractal gods, the ‘unmoved still mind-points’ that move the ‘energy’ around them:*

In the graph we see this feed-back game between the infinitesimal 0-minds and its local order, as centres of the will of T.œs in its relationship with the whole T.Œ, the Universe at large.

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

In his view the Language creates the Universe. But languages are the software of HARDWARE MINDS, without which they cannot order≈ create LOCALLY the Universe. In the Platonic or rather Pythagorean view the Language creates magically the Universe as some kind of ‘substrata’, similar to the ‘absolute space-time cartesian graph of Newton’ (ultimately a creationist mathematical pen and paper continuous background that has nothing to do with reality).

So to illustrate this real a posteriori nature of maths, we include besides Penrose’s another set of arrows – the stronger thicker one of the philosopher of science in the right.

As usual in the multidimensional universe we can put together both directions of the process of creation.

In that regard, *the true mirror language that ‘adapts’ reality better is the ∆ST-language WHICH is the one embedded in the behaviour of each ðƒ-singularity.*

But again as there are B&W, 3, 4 and 5 color animals (birds), with better detail maths can be improved to ‘see better’.

In its present ‘underdeveloped’ euclidean form, and with some fictional forms of mathematical physics taken for real, its incomplete structure must be improved.

This I did when young, after understanding the scalar metric of 5D Analysis and its 3 arrows of space-time, upgrading Non-E GEOMETRY.

All languages departing from a set of mirrors of the generator, called syntactic rules codify long systems of objects. Mathematics as being so wide, must therefore be the ∆-i mirror of a large ∆+i Universes. The i-maginary side of the physical Universe at ∆±4 thus seem to be mathematical, over which other more specific languages elaborate its codes; yet all codes refer to the a priori language of ¬Æ ∑ Γ • ∆s

**The evolution of maths improves the mirror, its ternary syntax.**

It does of course because any mirror-image of reality even if unfocused carries some information about it, and works for the distorted mind view, which *let us remember is NOT REALITY BUT ALWAYS A LINGUISTIC MAPPING: Œ-Mind <linguistic perception> ∞ Universe, and so any mirror does carry a minimal information to be useful to departure a whole:*

In the graph, linguistic mirrors create minds with different amounts of information, useful to guide reality. We must not though confuse the mirror with reality, the a priori element.

All this said is easy to understand mathematics, its elements and disciplines as a mirror of the Universe.

For the scientist who will consider all this nonsense because he thinks he knows his maths and all is there, the answer is yes, *all is in the mirror but with less detail. So maths* as the universe does, has also 3∆st+º sub disciplines, it has also a fractal ‘derivative’ structure and it is also about space-time.

THOSE 3 main sub-disciplines code the 3 ‘structural elements’ of the Universe:

- ∆nalysis of the 5th dimension, its wholes and ‘finitesimals’ (1/n).
- Geometrical space, (Spe) and its unit, fractal points.
- Temporal algebra (tiƒ) and its units, sequential numbers.

And it has its ST ‘combinations of which the most important its topology (the study of form with motion).

Moreover the mirror of mathematics *has* evolved to explain in more detail the ‘actions of space-time’ of beings; *as all languages do improving its ternary grammar. So* words developed first ‘names only’ (forms), then motions ( active verbs) and finally ‘complements’ (complex systems).

And colour languages moved from dual B&W, to three colors (red-entropy, blue, form, green energy) to four, adding green/yellow mixes.

So today maths has evolved into multiple space-time disciplines. For example spatial geometry added, analytic algebra, which is geometry with sequential time numbers that finally dominated the discipline, while topology which is geometry of space with motion in time, today added ∆-scales (as it is defined with networks of ∆-1 points).

**Dogma and flexibility – evolution of languages.**

All this is said to remark a key concept that escapes mathematical physicists:

*No language-mirror is absolute in its truth, but an evolving system, which goes through three ages*

*So when written words appeared **pharaohs just said ‘it has written=truth’. Today in the far younger mathematical discipline, scientists say ‘it is an equation=it is a truth’.*

Only latter words were known to be also fictions, a fact that also happens with *equations but few scientists do **recognise. So maths has still a ‘religious, dogmatic outlook’ proper of all languages, even if it has already gone into a ‘third baroque, inflationary informative age of excessive formal content’ and split into multiple similar ‘metaphors’ (languages being inflationary as mirrors-minds are multiple, watching a single perspective do offer multiple views of a single event, hence the multiple equations observed to describe the same physical event).*

But religious people, aka dogmatic physicists do NOT understand all this about their mirror-language of mathematics.

For many of them, equations ‘are’ always truth, just when written, and other languages are NOT truth – dogmas we only find in fundamentalist verbal thought (God speaks only in Arab, so Koran cannot be translated as it looses its truth).

Of course, languages do have also ‘quantitative’ measure. So while all carry an image, some are better and we prefer a carrot picture than a drawing.

So, we concede maths *after images, is the best mind-mirror known to man, as it* carries more informative detail than words (but less than images), and so it has become after images (most humans believe in TV celebrities more than in physicists 🙂 the dominant language today, and overcome religious words. Still as Einstein put it ‘I know when maths is truth but not real’, meaning we need experimental analysis of mathematical truths and so NOT just because we can write an imaginary particle with maths, the particle will exist (Susy, evaporating holes etc).

IT IS AN EGO ERROR, TO THINK then that maths is always truth and an even bigger ego-error to think maths is not experimental but produced by the human mind, which becomes a short of ‘God’ that talks maths as only God does (that was the idea of Kepler: god has taken 5000 – biblical – years to found an intelligent like his, me).

**Conclusion: the efficiency of mathematics.**

The first obvious question is this: why among all the mirrors=languages of the Universe, mathematics or rather ‘topology’ and ‘social numbers’ are the dominant one, which better expresses the laws of the Universe of fractal space and cyclical time, *even in the distorted view of human beings (ab. huminds)?*

It can only be because it is the language-mirror of the fundamental monad-system that keeps the infinite immortal Universe as such:

The galatom; that is the atom and galaxy which are self-similar scales of the infinite Universe.

That atoms do use mathematical languages to create its super organisms seems certain, at all levels, observed today in quantum computing.

That galaxies are in 5D metric the equivalent in the cosmological scale of the atom, is proved ad nauseam in our posts on physics.

That particles ARE the first vital systems of the Universe, NOT carbon atoms in DNA molecules (a purely pseudo-religious ‘egocy=ego+idiocy’ of man as the center of the Universe) is proved ad nauseam, as they show the 5 Ðimotions=drives of life, as the graph shows.

Both are the immortal, ‘perfect’ forms of the Universe, precisely because they use the most efficient language, and languages select species:

**A linguistic or a reductionist Universe? ****Selection of languages**

*In the graph, the Universe is guided by languages, which selects the species that survive into the future. Thus a philosophy of reality can be established in evolutionary terms based in languages of information that matter more than the bodies of energy described by darwin’s struggle for existence – a secondary more obvious but less decisive element in the ‘selection’ of what maters to the Universe. *

For those die-hard platonic people we shall though consider a hypothesis of epistemological nature, regarding the linguistic, sentient nature of the Universe, which I sometimes think truth. Let us consider that sentient perception is associated as it seems on a linguistic focus on reality, and so we always see the universe as a language; and range languages by its ‘exactitude’ in the reflection of reality. The more accurate that reflection is the more spread the language will be as it is selected by more mind-singularities to describe reality.

So there is a selection of language mirrors, we shall consider in the next paragraph which acts as a selection of species: the more efficient survives and expands into more beings. So we can see that there is a constant growth on the similarity between languages and reality as we move to better ones till the language seems reality: L≈U… It would then be possible to consider that the final outcome of that convergence will be L=U. And so we could postulate that L(mathematics) = Universe.

And this is in essence what ‘reductionism’ does *as it eliminates on one hand from the Universe, properties which are not mathematical; and on the other hand expands inflationary maths, even into regions of fiction thought where the Universe doesn’t reach constrained by its need to imprint information in the ever relaxing, entropic motions that ‘expel’ it. *

So the Universe is indeed mathematics in the reduced mind of the platonic physicist, as it has equaled them. But the inverse is not truth. Mathematics is NOT the Universe in the expanded mind of all the singularities, ∑• of reality, as we know many do use other syntactic languages and survive fine. And so as Upanishad said, ‘the languages of God are infinite; which allow us to define God as the mind that talks all languages, or the sum of all minds of reality: ∑•∆; and its body the Universe as the sum of all its parts, including the minds, which gives us the equation of the God-Universe: Γ•∆.

In it mathematics might be the iterative program of all ¹º10-planes, if the similarity of repetition of its most clear ‘view’, the galaxy-atom can be replicated every 10 of them by mathematical methods.

Such Mathematical ∑∆¡-language, will then be similar to the language of ∑•∆∞.

But mathematics also evolves into its capacity to mirror dimensions of space and ages of time and scales of the fifth dimension.

So there has been an evolution of mathematics in the human mind and now in the metal-mind that shows a clear direction to enlarge mathematics as a mind-mirror to fulfill all kind of atomic structures.

But mathematics is a human and computer digital language, with some bias from our ∆º-mind scale. Clearly it lacks detail as a biological, ∆±1 language. So we must believe mathematics is the mind of perhaps a black hole/quark, ultimate nuclei of density of the astrophysical scales, in its most perfect digital forms.

In the previous graph to illustrate this real a posteriori nature of maths, we include besides Penrose’s another set of arrows – the stronger thicker one of the philosopher of science in the right.

So math is not the Universe because there is not a single language in all minds. But then again, if we find a language of languages, which expresses the Universal syntax of all of them, we could say that the mind of the Universe IS that language and as the mind mirrors in the body and imprints it, with simplified, larger, less informative images of itself, we could even say that all the Universe is a ‘chain of beings’ with the language of languages on top.

This language is obviously the ¬Æ GST Languages-isomorphisms-properties of space and time.

I am of this opinion: nothing is physical, material; all is motion bent into language, and as languages are perception/mirrors, all is sentient, vital, reproductive, virtual; only that the less informative, larger things seem to us ‘denser’, ‘thicker’, ‘material’.

Since *minds are mirrors, which once they have distorted and resumed reality into the still mind, try to order by reflection and proyection of that mind the Universe to make it look like the inner mind image, influencing in this way reality.*

Now, when the language becomes the mind of a system, it becomes ‘active’ as it helps the system to act-react in the Universe. And it is there where the use of maths shows its power to make the species that talks maths to survive better. *Fort that reason in a very biological way, we can state that mathematics has been selected as the language of nature that better creates the Universe (as mirrors do not as primary cause but as a reflected one). Two examples will suffice: when the greeks **applied maths to war (Alexander) they won all battles with its triangular tactics, latter expanded by the Romans. *

*And so the language of maths became essential to humans. Today computers and robots are displacing humans, who mostly use verbal thought, from labor and war fields due to its precision.*

The detail≈ amount of information mathematical systems can process in a much faster speed that any other language we know (computer digital thought as opposed to human verbal thought) shows it to be a dominant language in the Universe, whose minds no doubt command extensive regions. As such we consider it the language of the mind of physical systems, as the most extensive species of nature.

But even so maths cannot be the substance of the Universe which is motion, even in atom-like vortices, where those mathematical calculus take place – likely in the quark-black hole ‘unit’ of max. gravitational density of both scales. And it is precisely *the limits of entropic motion to evolve into complex mathematical forms, what limits the imprinting of the Universe by maths, which therefore as all languages do have a section of too complex, unreal fictions. *

A philosophy of stience by force must tackle the seemingly superior nature of mathematics as experimental language able to reflect so many worlds of so many sizes, which merely means mathematics must be a Max. i (±1) language of maximal extension in the scales of the fifth dimension, an ∆±i>3, which are the scales in which it seemingly acts:

Idealist physicists since Hilbert astounding ego-trip (he said ‘I imagine lines, points and planes’ ) have rejected the ‘experimental, a posteriori nature’ of the mathematical language (Lobachevski’s alternative philosophy shunned off by the German idealist school of Cantor and Hilbert). This wrong choice of philosophy of mathematics, as the a priori nature of reality, is a key error of mathematical physics in his choice of the proper mirrors of the mathematical language, which is as all mirrors is inflationary provided slightly different ‘images’ on the single Universe, each one with a certain distortion of truth, (choice of Copenhagen interpretation over realist De Broglie). So we need to fully return mathematics to the experimental origin, and consider that the ultimate mathematical properties of physical systems are experimental proofs of the organic≈scalar, social≈numerical, spacetime≈topological nature of the physical Universe.

All this implies a few things worth to mention in this introduction to vital mathematics, the necessary upgrading of the discipline:

- Languages are STILL mirrors of reality, not reality itself. Maths is simply the best mirror but it does NOT include all the languages and hence properties of reality: the languages of ‘God’ are infinite (Upanishads)
- Hence creationism, Platonic, Pythagorean religions, etc. are NOT truth. We are not MADE OF NUMBERS, or Cartesian absolute graphs of space-time. And a cause of many of the errors of mankind about reality derive from that simplistic view.

- We need to upgrade mathematics to fractal space and 5D logic; that is upgrade its spatial geometry, to fractal non-E Topology, and its temporal logic to pentalogic, and hence renew the discipline in what is more important to us: to understand the vital, social nature of mathematics, as its non-E topology IS ORGANIC, VITAL and its algebraic numerical equations ARE EUSOCIAL, as a number is MERELY A SOCIAL GROUP. But as ‘humans science’ is culture those obvious truths are ever deformed.

Each of the main super organisms of the Universe, the Galatom, Gaia, the human being, have specific mind-languages that mirror the 5 Dimotions (ab. of Dimensional motions) of the Universe reflecting the isomorphic laws of those dimensions (ab. Ð¡), to better serve the species and so the properties of reality come ‘first’ and the language second.

This said it seems obvious that galatoms have as there dominant language, mathematics, and so mathematics is by far the most efficient of them all. Humans though have verbal languages; animals visual languages, plants chemical languages, cells, genetic languages and so it is not possible to describe ALL the properties of all the beings with a single language, as pythagorean scientists think.

Languages are NOT the ultimate cause of reality as Platonic Idealism and Verbal Creationism (Abrahamic religions) thought, but mirrors which in a reduced ‘space’ of a mind, reflect reality, which has several consequences and ‘features’ proper of all languages, we study in the post related to all linguistic forms.

One essential feature we must advance though is that languages as pure mirrors of information are inflationary – they have multiple metaphoric view on the same being, with different degrees of detail and focus. So languages carry partial truths with different perspectives, reason why we shall find specially in mathematical physics many different mirror-equations speaking of the same phenomena – as the increasingly detailed analysis in mathematical physics of gravitation from Newton’s vortices, to Poisson’s gradients, to Einstein’s relativity in one stream of 3 evolved forms of the same thought, focused on mass as an accelerated vortex; to Lagrangian equations to Hamiltonians to Hamilton-Jacobi equations, in other stream of thought, focused on ‘the energy equivalent of mass’ and so on.

Mathematical mirrors are thus much more extensive that reality and many mathematical physical mirrors are ‘fictions’ as happening in all languages.

This we said, because in the inflationary 3rd informative age of any language, the egocy of man makes us believe that all has been ‘understood’ on the simplest levels of math as a language and what matters now is to make ever more confusing, detached from reality ‘mathematical formal mirrors’, as old men keep telling us the same information ever more detached from reality. So now mathematicians need to do ‘Set theory’ and ‘Categories’, and a very detached formalism, when we rather go for a better focused mirror on classic mathematics and its classic units, points of space, numbers of social scales, dynamic S=T equations that reflect the dimotions of space-time, basic algebra operators and analysis as the language of motion and emergence or dissolution between scales.

*We are thus starting from the very beginning and simple forms of mathematics, but giving a far more experimental quality to the science by putting in correspondence mathematical equations, postulates, structures and disciplines with the five demotions of reality, and its structural 5 elements, ¬∆@S=T*

Languages in that sense are not reality but they are extremely important as they represent one of the two limits of reality – that of pure form, mirrors that in a synoptic manner construct mind-mappings of the eternally moving cycles of time of the Universe.

As such MINDS ARE LANGUAGES. And languages perceive in themselves – what you call your mind is a visual mind-language that stops reality, constructs your view of it in a reduced mind space and quanta by quanta of your inner timespace thoughts keeps on guiding you through the game of exist¡ence. We do NOT however care at this stage about that wonderful miracle of language->still perception->Mind will, studied elsewhere but about a specific language, maths, which is along visual thought and Logic, verbal thought the closest ‘mirror’ to reality as it is, albeit in an increasing degree of synoptic capacity to represent space-time.

A warning though about a world ruled by mathematics over verbal thought: Money is a digital language, better spoken by digital machines, which therefore are becoming overproduced and substituting humans in labor and war fields, as the minds of robots, which also talk better mathematics. If man wants to survive therefore it would have to reduce the use of mathematical species with vital properties, but obviously our paradox of the ego will never recognize even at the risk of extinction the entropic limits of our minds.

ANOTHER lighter theme though is from what has been said the need to redefine mathematics as an experimental language, whose AXIOMATIC METHOD OF TRUTH IS CONSISTENT WITH THE SYNTAX OF SPACE-TIME IN THE UNIVERSE, BUT NOT ITS ORIGIN, BUT ITS MIRROR PARALLEL.

**The philosophy of mathematics: axiomatic vs. experimental method – group theory example.**

The holographic bidimensional universe and its ternary ST-geometries define reality. So in most mathematical equations solutions abound on quartic and cubic systems but only special cases are solvable for higher polynomials or have any real use in reality; the exception being simpler equations of the ∆§ocial scales and reproductive functions of the type Xª=b…

This classic example, introduced by Galois, shows the duality of axiomatic and experimental methods for mathematical truths. Galois proof was complicated. He told us about the symmetry of a given polynomial , characterized by the collection of the permutations of its roots. For example, the symmetry of the polynomial X1³+2X² +X3³+2xˆ4 is characterized by the four permutations:

And then made of complete analysis of those permutations to conclude that *any* algebraic equation satisfied by the roots must *still satisfied* after the roots have been permuted to be solvable.

Now, as many of the very complicated to understand reasonings of modern mathematics, which really starts with Galois work on groups, we provide justification, which are far less axiomatic and simple based in the fact mathematics are mirrors of space-time-scale properties.

So to the question why is there no formula for the roots of a fifth (or higher) degree polynomial equation in terms of the coefficients of the polynomial, using only the usual algebraic operations (addition, subtraction, multiplication, division) and application of radicals (square roots, cube roots, etc)? The answer is self-evident and trivial:

Because polynomials are a simple mirror of ‘planes of space in scale, or dimotions of time’, and there are only 4 Dimotions/scales relevant to any real system (entropy being the fifth Dimotion, not counting as it is merely a negation of any of the others). So in the same way 4 quantum numbers code physics and 4 letters genetics, and 4 Dimensions our humind, polynomials of 4 ‘dimensions’, can be solved. This is ultimately the kind of ‘margin proof’ we use for Fermat’s last theorem, because maths IS A MIRROR OF REALITY not of fictions.

Groups indeed *are the tool physics uses to study together in a static view the different variations of form and motion in the Universe.*

Yet WHY THEY ARE CONSISTENT WITHIN THEMSELVES?

The answer is self-evident if you are grasping the basics of 5D philosophy of science: BECAUSE REALITY IS CONSISTENT and it is NOT inflationary. In the same way there are not more particles than those needed for the standard model to work, no fictions, no evaporation of black holes back to the past, no big-bang singularity fantasies, etc. in real physics, real maths AS A MIRROR OF THAT REALITY is consistent in its entangled INNER STRUCTURE AS THE UNIVERSE IS.

However languages are slightly inflationary, so it is also truth that as words produce fictions, within the consistence of its syntax, maths have also fictions within its consistent inner axiomatic syntax, but THEY ARE NOT real – so Einstein said ‘I know when maths are truth but not hen they are real’ – something physicist have forgotten.

We are then NOT interested in the axiomatic method, which is far more evolved by professional mathematicians, but in the connections between mathematical statements and reality, specially what mathematical mirrors tell us about the vital, organic properties of scalar space-time, from where its laws derive.

**The rashomon effect: inflationary 5 povs on a single event**

In the epistemological arena, it is necessary to expand maths into experimental analysis, and also consider at least *the multiple *perspectives of the kaleidoscopic mirror, so a certain objective experimental law of space-time becomes a mathematical image, whose proof will need a logic process of mental reasoning *but now from the multiple logic points of view* of the different perspectives of ∆•§≈t.

Which is the key to reduce the inflationary level of the language with all its mirror-angles to the single truth of it.

Such analysis will then complete all the possible perspectives of an event or law and define its range of application in a *complementary non-exclusive way.*

Consider a simple example; the ‘Pythagoras theorem of probability’ – Bayes Theorem, which states that P(A|B) = P(B| A) x P(A)/P(B).

**§**: It is today simply proved departing from conditional probability as an easy derivate of P (A|B) = P (A∩B)/P (B)… (*∆§patial view*)

**T:** And justified also from the analysis on how a fractal tree of events ‘branches’ into outcomes of different frequency (*∆ðime view).*

**Γœ***: And it is *experimentally proved ad nauseam in all systems of reality…

@ But *its origin was actually on a mystical, mental analysis by the Presbiterian priest Mr. Bayes – the so called epistemological interpretation, according to which probability measures a “degree of belief.” *

Bayes’ theorem then links the degree of belief in a proposition before and after accounting for evidence. This is the ‘•element’ today discharged, which we shall show in our analysis of the justification of probability laws to be by far the most interesting interpretation with key consequences to understand the ways in which the mind-Universe mirror game makes reality emerges from parts into wholes. As beings are first mental blueprints, seeds of information, which slowly acquire the density required to enter the threshold of existence.

**The experimental evidence carried further into mathematical physics**

An inverse example will be departing from experimental evidence to eliminate inflationary mathematics and ego-mind paradoxes in the explanation of reality. For example the debunking on mathematical physics of the copenhagen interpretation, which Bohm did properly in differential equations and Nottale in fractal ones… but requires further understanding of the concepts of quantum physics not as a mental game of observers, *but as a distorted human view on the limiting scale of our mind perception, given the properties of 5D metric. *

*Ie.* as we go down in scales we loose information (uncertainty principles), we are coarse in our interference (observer’s influence) and beings accelerate in time as they diminish in space, so we make all kind of errors confusing time cycles as spatial forms, since our slow clocks see the being’s sequences in time all together in a simple timespace quanta as a spatial form.

The ‘mind view’ ANALYSIS is the key to straighten up the discipline as we must eliminate, specially two recurrent errors:

-To see time events which are ternary as spatial different forms: i.e., 3 quarks cannot be broken, why? Answer: because they are likely not three quarks in space udu, but three ages of a time transformation: u>d>u.

-To ignore each new scale is made of wholes and parts and when we ad new scales we must ad more parts, so instead of functions we use functionals and operators (functions of functions), NOT because quantum systems are weird, mathematical beings made of nebulous operators, but because we are integrating in our perception, multiple scales – same for Hilbert spaces – there is not ∞ dimensions but we penetrate for each system we measure into its parts, which are its inner dimensions. But without a proper definition of dimensions all gets messy conceptually as it is now the case.

So the GST isomorphic methods relating all to the 4 ∆• parameters will become the key to ‘complete’ and upgrade maths and its main sub discipline, physics (: as we have done with all other disciplines.

**Mathematics as mirror of ∆St.**

**Γ.**S(•): geometry <≈Algebra > T Nº

**The problem with ∞ counting. Borgian Libraries: Mathematical fictions.**

Languages are inflationary as pure mirrors of information. So paradoxically they have more ‘forms’ than reality, where forms must ‘trade’ with the opposite arrow of entropy and self-destruction. Hence reality which *must by definition include the 5 dimotions of the entangled Universe, entropy, motion, reproduction, social evolution and linguistic form has less ‘linguistic form’ than the isolated language in the mind of thought. And for that reason as huminds kept increasing the formal evolution of maths, it became plagued with metalanguage, which is not related to reality. That is as fair and enjoyable as fiction in writing and film-making. *

All those languages started as pure classic non-fiction (documentaries in pictures, philosophy and narration of historic facts in Greek literature), and latter become fiction (first novel is as recent as Quixot; visual pictures in 2 dimensions, painting and photographs only became fiction with the arrival of photography the first and film, the second). But finally today *most literature and film is fiction. And those are rules that apply to all languages. *

But *the believer on languages never accepts those limits. He will come out of the film room thinking in earlier pictures the train was running on him. Today mankind is so easily ‘manipulated’ with fake news as long as they are shown on film at the news hour that sociologists say media is a brain manufacture industry going on… The mathematical language is extreme in that trend.
*

So we are NOT interested that much on the ‘XX century’ mathematical inflationary age, whereas Set theory and Group theory clearly show its inflationary value – not so much as ‘fiction’, but as ‘redundance’ and ‘obscurity’, on the same theme. It is let us put it on reference, like making cubist pictures instead of photographs. Nice, but we shall **reduce ourselves to connect the photograph, the classic maths, with the portrayed, the Universe and its Gst laws. **

To understand why Group and set theory is NOT the way to find the meaning of the Universe, in layman terms, a Group is nothing but a whole enumeration of all the permutations that can be achieved with the elements of a §œT (social group of T.œs), which is like the surrealist tale of Borges, in which a group of monkeys were writing Shakespeare’s full works by the pedestrian method of typing all possible combinations made with the alphabet in the eternal time of existence of the Babel library. Sooner or latter they would combine the letters to write Macbeth… So those enumerations of Group theory do have a clear use as collections of data, NOT as explanations of whys, which require to understand the ultimate substances, space and time, its Disomorphic properties and hence have both theoretical ‘Ockham’s cribes’ to select proper combinations of the 2 letters of the Universe, and then check it with the experimental facts.

This happened in the eternal infinite task of Mathematical monkeys filling today computers with infinite numerical methods of classification of ALL the groups of the Universe, with ALL the transformations, motions and infinite ST-mirror symmetries, when Lie decided to focus in Groups *that mattered TO experimental mathematics, which was obviously all around ∆-motions up and down the ‘derivative/integral scales’ of wholes and parts. *

So group theory focused on writing Shakespeare’s plays only, even if the number of ‘finitesimal’ transformations (steps of a derivative, which are not actually infinite but equal to the number of ∑1/n ∆-1 quanta that make the whole, ∆) was ginormous. This is called a Lie Algebra, accounting for all the minute transformations of a derivative curve.

So the re-encounter of Abstract Algebra (§œTs and groups) with the scalar reality of the fractal universe would happen with Lie Algebras, precisely through the 4th and 5th dimension, as they represent equations which are ‘twice’ differentiable, i.e. *forms that keep a certain ‘continuous meaning’, when decaying through 2 ∆-planes, as in the case of death or transcendental emergence into the 11th dimension of an hendecagram.*

That is Groups whose elements depend continuously on the values of a finite system of parameters and whose multiplication law can be expressed by means of twice-differentiable functions ϕ1, ···, ϕr…

Since the fifth dimension is indeed a dimension of past (∆-i) to present (∆º), to future (∆+i) time.

* In that regard, group theory is more of a regulative idea in a kantian sense that a true description of the whole:*

In that sense Algebra’s Group and Set theories as the meaning of it all is more in tune with the final realisation by Kant of paralogic thought and in more ‘sound’ conceptual terms, as it normally happens, among humans who loose their connection with reality, when they start to manipulate, points, numbers and equations without the slightest conceptual understanding of what they are.

So in existential algebra, we use more concepts of Analysis than those of algebra. Yet we said algebra was also a good mirror of S=t motions and so we have seen indeed in the previous pages examples on how classic algebra and its group theory allow us to resolve the meaning of mirror symmetries as reproductive motions in space-time and the other simpler motions as dimensions in present space-time or in the case of spiral motions clearly, motions in the fifth dimension.

**II. ∆±¡:** elements of Mathematics

** ¡MATHS THE LANGUAGE OF SCALAR SPACE.**

ABSTRACT. Because mathematics is a language, it belongs to scalar space and its still information more than to temporal energy and its motions.

This means it has two fundamental units one of space, the point and one of social scales, the number. Those should be regained as its units – not the ego trip of building maths from the top – so considering human artifacts, sets, its units.

**How maths reflects the ∆@st elements of reality.**

Next we can consider how mathematics mirrors the fundamental elements of reality with its fundamental ‘synoptic’ forms, as all language reduces reality to lesser mirror-parts that carry not all its information:

**S: A point**is the first perception of A T.Œ in mathematical ‘space’, which as we come closer acquires content. And then its next degree of complex description occurs:**∆: A number,**is a social group of undistinguishable ‘internal’ parts of a point, which represents the point in scale. And then the next degree of complex analysis occurs:**T: An operand**expresses the transformation of a point through a Dimotion of timespace, and since there are five Dimotions, 3 continuous Dimotions in a single plane (perception, locomotion, reproduction) and 2 discontinuous Dimotions that start and end in different planes (entropy and social evolution) we shall find 5 basic operators of those Dimotions in any ‘algebraic structure’ that truly reflects the being in the mathematical mirror.**@: A frame of reference**expresses those changes through = equations reflects the @ element of the being.

Mathematics is the most efficient language as a mirror of the Universe, NOT because it is the only language of God, since verbal, visual, genetic, magnetic, financial, olfactory, musical, pictorial… etc. languages can also code or value the forms of Nature, but because when we range languages according to the laws of efficiency, which requires minimal space and maximal information for a language that represents in 5d metric the ‘smallest’ singularity-like object of reality, mathematics ONLY ranges second to the non-Æ logic formalism in synoptic power (space size), and likely above in informative density (as GST is a synthetic language and mathematics an analytic one).

It is then important to understand mathematics, *as an experimental mirror of the Universe, specially when dealing with non human systems, as the ‘specificity’ o f human languages, which can better express human systems, as they have been biologically designed to express ‘human values and actions’ is no longer require and then only the objective elements aforementioned matter.*

However, on human systems, the higher detail of maths is secondary to the specificity of the language; so it is an error to try to express human thought, history and social sciences with mathematical languages – a mistake common to the fundamentalist believers on egotist trips of mathematical uniqueness.

As we humans are really, ego permitted, a mere light disordered vibrational parasite of the most perfect geometric quantum-gravitational atom-galaxy dualities and its middle magnetic scales, our form is – how to put it – a bit messy, compared to the spatial perfect topologies of spherical beings and lineal waves, mathematics a stronger spatial than temporal language, better for huge amounts of ‘social numbers’ that individual erratic huminds is the perfect language of scales where geometry matters and the symmetry between form and function is almost absolute.

So spatial forms and spatial scales are its forte. Let us then see a brief account on how mathematics deals with scales, through continuous differential equations (social scales proper) and through fractal discontinuous functions in ‘transitions’ between scales and temporal states, when not differentiable form is allowed.

Let us briefly introduce some themes of all those elements, studied in depth in each subplots of Maths.

**Points and Numbers**

**Duality between discrete informative numbers and continuous spatial geometry.**

In a more precise correspondence, Mathematics, now that we know, what reality is all about (An existential game of 5D knots of fractal space-time cycles) must return to its fundamental syntax and ternary equations, which reflect the game of the Universe with:

- Its fundamental unitary elements, (points/numbers); whose duality also reflect the main dualities and ternary symmetries of the Universe:
- Sp: Spatial Non-E Fractal points, which grow into cycles and spheres – knots of cycles, crossed by those ‘cyclical parallels’, as we come closer to them,
- Tƒ: Informative elements, perceived as sequential, discrete numbers.

Thus a more complex insight, that goes along the growth of the discipline is the realization of the duality of space-time (geometry vs. algebra) is more properly the duality of Se: space vs. To: information (continuous vs. discrete).

Now this proper understanding is important. For example, when Aristotle quotes the proof that real numbers do not exist, √2 is not found, yet we do trace a diagonal through a straight angle, so √2 exists in ‘continuous form’, the REAL answer is that numbers being discrete, DO have always an infinitesimal ‘cut’ NOT as Diophantus and then Dedekind try to define a real cut (the number) but a ‘real’ cut (-: a ‘hole’, a non-existent number.

This is then essential in reality, π does NOT exist as a perfect number, because numbers are discrete, and so in numbers Pi, never closes, the circle fluctuates between ±π, which makes possible for pi-cycles to open and close its mouths even at infinitesimal level.

On a larger philosophical view, all equalities are similarities, ≈, <=>, is better than =; when we say E=mc², is not = equal, but it really means E<=> Mc²; that is spatial energy transforms into cyclical mass, Sp(E)<=>Tƒ(M).

So it is interesting to understand philosophy of mathematics in terms of exploring in new depth the relativistic meaning of certain operandi; not to do bizarre ego-trips on the absolute truths and magic mental uniqueness of human brains.

Next it comes, the understanding on the evolution of the discipline as all systems, from a pure, first age, of disconnection of Se and To parameters into an adult age of STi combinations.

Thus, in the modern age of mathematics, scientists learned how to evolve mathematics by merging disciplines into:

- Sƒ: SPACE-information (dominant in space: Analytical geometry->Topology) and…
- ƒs: INFORMATION-space disciplines (Algebra).
- ∆: Analysis now appears, as the ‘warping’, ‘dynamic’ vision of all, Se and Ot disciplines. It introduces motion (energy & time) to the study of the discipline; as MATHEMATICAL PHYSICS takes off, using the language to describe true reality. Thus it comes:
- Sp – Spatial analysis which uses spatial methods to visualize the exhaustion->Limit->Riemann->Lebesgue Integrals.
- Tƒ – Informative analysis, using Algebra, which obviously become as ALWAYS in the duality between evident space and discrete information, the final form.

That is all. Why?

Since there are only 2 x 2 realities, Entropy-space (lineal motion and form), and Time-Information (cyclical motion and form), AND mind languages fix and reduce motion into form, we do have only the duality of space-points and informative-numbers.

And since all this is merely structured into 5th dimensions, through a simple growth of ST bidimensional planes that combine motion and form, O-|, and then grow into layered 4th dimensional beings of space-time (to then organize through those growth social processes 5D beings), mathematical reality is rather made of simple operandi, simple geometrical systems.

For example, almost ALL the geometric theorems were already discovered by the Greeks using ‘static bidimensional geometry’ as this is THE main unit of reality, a bidimensional form.

For example, there are only in 2 and 4 dimensions 3 ‘topological forms’, the toroid, Sp, hyperbolic, ST, and Informative Tƒ, forms.

So this is HOW mathematics should be initially taught. As a LANGUAGE that references reality and its game of ‘existential 5D knots of space-time cycles’, where those 5D knots are ‘finitesimal non-Euclidean fractal points/numbers, crossed by a finite number of cyclical space-time parallels’ (being the line a segment of any parallel cycle).

We shall first though introduce the sequential time perspective, ordering mathematics in a chronological process of d=evolution of mankind, through its 3 ages, and the parallel 3 ages of those branches of mathematics. Since mathematics as all languages has gone through 3±n ages between its pre-Greek conception to its post-Human computer age. Thus the growth of complexity in ‘human’ mathematics also follows those 3 ‘young-balanced-informative old ages’.

Then study each of the branches through those 3 ages, each one culminating into the age of Non-E geometry, Non-A Algebra, and 5D Analysis.

As in 5D space-time there are more time arrows, besides the social arrow of growing numbers studied by Analysis; and so we must understand better the logic operandi of mathematics.

Thus we need to define in proper terms the existence of a Universe with 3 time arrows and its paradoxical logic, in which in certain scenarios, the end returns to the beginning.

This happens for Time cycles that return to its beginning, and mathematics expresses this pattern with the use of cyclical, polar coordinates and Complex Number coordinates (Argand plane).

But it also happens with the 5th dimension as there is a limit of infinity, in the 10th scales (1 trillion being an absolute limit for most connected systems; though atomic crystals can go well beyond that limit). In any case for most systems, the return in the 5th dimension means that there is a discontinuity as an infinity becomes an infinitesimal of the next scale.

We shall therefore consider how those basic features of ¬Æ mathematics (I-logic mathematics) are met by sequential algebra, and what errors have introduced – mainly the errors of infinity and paradoxes of infinite sets.

We shall though intersect ¬Æ mathematics with the original ages of mathematics, to understand better our new advances to the subject.

So for example, after E-geometry, we shall consider ‘Non-E Postulates’; after topology, ‘topological organisms’ and so on.

As all the parts of T.Œ, the task of pouring all that in this web, which anyway humans won’t care to understand, is enormous.

**Numbers & constants of 5Ðimotions.**

Numbers are much more than they look. First they are societies, but ‘integrated’ societies, as we count them in ‘systems’ which display a ‘solid parameter’ for the number. So numbers require a certain ‘entaglement’ of the being and often are internal mirrors of its properties.

Other numbers however are ratios and as such they can represent Dimotions and changes of state, or relationships between the elements of the T.œ. So certain numbers are special with multiple uses precisely because they refer to a key ‘ratio’ between the S, ST and T ELEMENTS of the being.

The first unit of mathematics is thus the social number. But certain of those numbers are that represent the *EFFICIENT** 5 dimotions of time-space**:*

**Ð1: Pi**is the constant of informative perception and trans-form-ation of motion into form: 3 |> O+ 4% apertures to the world; and as the inverse arrow of form into entropy is just the contrary function, also the inverse ‘unwinding of form into motion’. But then is most often a multiple of π, (as in k and G equations) or a ‘radian’ of π (as in~~h)~~, because*the dense curvature merely ‘peels off’ in parallel a ‘thin membrane’ of its curvature or perceives a ‘radius angle’ of the external universe.***3Ð: Phi**is the constant of reproduction because the efficiency of its spatial distribution packs the maximal number of ‘reproductive events’ from an initial generator in minimal space.

**2Ð:5=Pi x Phi**is then ¡logically the constant of motion, which implies the reproduction of a cyclical form through a path as decribed in the graph

And so *two simple, related constants suffice for most simpler, geometrically perfect actions of the 3 arrows of time: motion to form, form to motion and **reproduction.*

What about the 4th and 5th dimensions? Again the answer is self-evident (if you understand the organic Universe):

As those dimensions are concerned with fractal discontinuous or differential continuous functions from wholes to infinitesimals, it *must maximise the growth, and so polynomials and logarithms are used. Specifically:*

**4Ð: e**is the number of the fourth dimension of decay and death, which is the fastest possible process of dissolution of a single whole into infinitesimals, as those ‘cells/atoms/citizens’ ARE already reproduced and must merely be liberated from the single whole-membrane.

So we find it in all decay process because of a simple property: e IS the fastest growing exponential function of any two numbers, in the Universe (and many related properties). **I nterest**ing enough to notice that it was found NOT as decay but as ‘

**interest**=usury money’, what says a lot of the astounding ‘grab-theft’ of the financial profession, which found the maximal parasitic growth on account of doing NOTHING; just lend useless, fetish go(l)d.

**5Ð: 10:**The Log function is the scaling of social evolution because the ‘tetrarkys’ with 3 x 3 elements as networks of entropy, energy and information with the central whole-singularity mind emerging in the new scale as ‘1’, is the most perfect form to deal as a time§paœrganism with the survival exigencies of any ecosystem of ‘fractal points’.

So we shall study mathematics *as the most efficient, synoptic language of the properties of timespace beings, after the very essence of the game, the formal generator, its symmetries and ∆•st logic, for which obviously the pretentious guru-magic of mathematical physicsts and the like, is just a barren “latin’; *and simplify, explain and evolve its Non-a logic and ‘fractal units’ (non-e points) from ‘space-time reality’ into mathematical mirroring.

It is then far more important given the blindness on meaning of mathematical physics to enlighten even the simplest concepts as ‘dimensions’ and ‘vectors: space-time bidimensional entities’, ‘numbers=social groups’ and ‘fractal points with growing breath’, etc.

Of course this is an INSULT for our geniuses which as Hilbert did with Einstein, despising first relativity for its simple maths – he was the God-talking man who ‘imagined points, lines and planes’ and set a ‘paradise’ for Cantor’s ‘building up’ of mathematics from the roof down, with its sets and axiomatic method, *which denied experimental mathematics and its real units, simultaneous fractal points of space (Leibniz’s monads: each point is a world in itself) and * sequential social numbers of the 4th and 5th real scalar dimensions. So He and Cantor imagined first the units of its axiomatic self-contained, ‘detached’ world of formal mathematics from the top down.

But the TOP of maths is NOT the set or category, constructions of the inflationary human mind, but the Universe itself WHICH IT MIRRORS, so the relationship IS from math’s units, fractal points and social numbers to Universe, the reality it mirrors, through the classic scales of topological networks of points and algebraic causal relationships between social numbers and its scales of ±, x ÷, x²,³…, ∫∂ (continuous operations in the 4th, 5th dimension) and log, ln (exponential death and decametric social growth), which are all the operandi we need to construct reality.

Needless to say Hilbert and Cantor were all about ego. They wanted to be God. So Cantor ended up in a mad house literally, and Hilbert when he realized that ‘simple Einstein’ was the ‘thing of the future’ stole his theory which Humble Einstein had sent him to review, improved a bit the maths and *published it with his name! Of this anecdote a furious Einstein jetting to see the Man only conceded the naming of the ‘Einstein-Hilbert action’ (:*

*And yet today we still live in that ‘Cantor’s inferno’ not paradise of imagined lines – in Dante’s divine comedy the 9th circle of those whose capital sin of arrogance fogs their reason, for wanting to be more than God. The harder they fall-en angels fall.*

All this said mathematics is one of the best languages to mirror efficiently the Universe, specially in spatial dimensions, but *since all languages are inflationary it is a key element in mathematical analysis of ∆st systems to break down what is ‘experimental truth’ and what is fiction. Consider the case of ‘dimensional analysis’. As it happens there are only 3 bidimensional topologies which correspond to the 3 functions=forms of all systems. And there are *only manifolds of rank 3 or lower which are ‘smooth’, differentiable, meaning systems where ‘time’ moves smooth through ‘present derivatives’.

So in a single plane of present only ternary space and ternary time dimensions are possible. As the mathematical mirror gets distorted, outside those 3s = 3t, the mirror guide us – but the experience must confirm them. This was the essence of Lobachevksi’s thought when he found non-euclidean points now forgotten: that maths are inflationary in its diverse theories so we cannot just do as mechanon physicists do, to write an equation and expects to be there, but a more subtle approach of mirrors observing reality and ordering it in local regions is required.

Soon we will see the interaction languages-reality where reality dominates but the mirror can also deform reality to make it seem like the mirror. Space-time thus comes first, and its dimensions *are the origin of reality; as Mirror-languages are both more concise and specific, so they cannot show all its properties and they all have a distortion to reduce information I.e. euclidean points have no ‘breath-information’ inside and so on.*

# Operands reflect 5 D¡

**Abstract.** The purpose of operands is obvious: to explain the most general laws of Ðimotions of spacetime beings.

The all pervading use of ∫∂ is then clearly because it reflects ALL forms of change. And so analysis is the most extended sub-set of Algebra.

**Algebra operands.**

The key connector of T.Œ with classic science is the full understanding of the dual algebra operands, ±, x/, ∂∫, √xª as part of the classic logic game.

It is immediate the correspondence of those operands with the dimensional elements ∆st, as:

- The sum-rest are the inverse arrows of the simplest superpositions of dimensions
*between species which are identical in motion and form.* - The product/division rises the complexity of operandi a first layer, and serves the purpose, besides the obvious sum of sums, of calculating the margin of dimensions, as combinations which are not purely parallel between clone beings, most likely through the recombination of its ∆-1 elements, as the product of 2 Sœts inner elements give us all possible combinations. Ie. 5 x 4 = 20 IS also the number of connections between all the 5 elements and 4 elements of both sets. So multiplication ads either a dimension of multiple sums in the same plane, or probes for the first time in an inner scalar dimension.

- The key algebraic concept of ∆st systems is the existence of a region of balance between planes or topologies where the asymmetry of the system is fairly lineal operated in decametric scales of growth and superposition, and the regions of relative past and future, | or O, ∆-1 or ∆+1, where there is a split towards the purity of motion or form, disconnected parts or wholes, accelerated vortices or lineal scattering and must be operated not with scalar potencies but finitesimal integrals and derivatives, more precise in their measure of the ‘curvature’ of the phase space we study.

Then we arrive finally to the potency-root systems and integral-derivatives, which operate fully on the ∆§cales and planes of the system, which require two slightly different operands. As §¹º ‘social decametric scales’ are lineal, regular, so we can operate them with potencies, roots and logarithms.

- ∂∫ But when we change between scales into new wholes and new planes of existence we are into ‘a different species’ and so we need to operate with the magic of finitesimal derivatives and analytical integrals, which keep a better track of the infinitesimal ‘curved’ exponential changes that happen between two planes, where linearity is lost.

And within them we can also understand differentials and derivatives as motion steps that integrals then bring together as a whole. And as most analytical equations mixture both we must see analysis as a more ‘delicate’ way to study in more detail the reality of parts and wholes first defining a ‘derivative’ or ‘finitesimal’ part of a whole and then integrating it all together.

3RD AGE: NEXT we grow further ‘dimensions’ in algebra with functionals, which are functions of functions; and with Groups, which *studied all the permutations, symmetries and variations, as ‘families’ related by similar qualities or ‘isomorphisms’, or a representations which expand a scalar into a matrix of multiple elements and so on.*

And the same generalisation to classify ‘groups of similar beings’ happened in geometry with topology which ads motions and deformations of basic spatial forms to gather them together into families that turned out to be – how not? 3 basic topological families in the 1 to 3 dimensions of a single plane.

All this was forgotten to restart again with Boolean algebra and quantitative methods the mind of digital machines we shall ignore for ethic reasons.

While the new ‘humind avenue’ to further enlighten maths is non-aristotelian logic of multiple ‘time arrows’ as opposed to the single causality of Aristotelian logic and non-euclidean geometry that *ads internal depth to fractal points, no longer with no-breath, so we can fit real straight parallels of entropy, energy and information within it. It is thus a final expansion of dimensions through ‘scalar space’ and ‘ternary time cycles, represented by NON-æ.*

And so in the growth of complexity of languages of time and space we move in the 3rd age, with the eclectic work of this blog that brings ‘Vital topology’ and ‘existential algebra’ as the natural 3rd age of evolution of human thought, which if not understood or used by man, likely will become the languages of thought of AI in the nearby future.

**RECAP.**

Classic Algebra in that sense is the natural BRIDGE towards its full realisation as the leading language of the logic symmetries of space-time, and as such it is important to understand the meaning of its postulates as a bridge to understand the laws of time and space.

We depart in the understanding of the fractal Universe from space, as we are minds constructing a still world view with our logic languages of which mathematics is the best logic language of space and wor(l)ds of time; and further on of human points of view, as opposed to the more efficient, extended language of geometry, likely the language of atoms.

*dimensional scales, and S=T symmetries, and so its 2 fundamental subjects, Analysis of planes, and equations with its operandi of similarity, reflect that nature.*

*because it is rather concerned with the scales of parts and wholes, of discrete and continuous together, while geometry is the first simpler view of wholes in a single plane.*

*So Miss Germain missed the point. Algebra is more about ∆-scales and herds in motion, ABOUT REALITY AS IT IS. Geometry is more about mind spaces and its simultaneous perception, about reality AS WE PERCEIVE IT.*

AS USUAL our study will be diachronic to grow in complexity, using classic texts of mathematics for easier comprehension enlightened with ∆st insights, compress the first Greek and second classic age together, with the introductory themes developed further; make only some basic remarks on the modern era due to its complexity, and reserve the 3rd age for the ‘future’, the non-æ laws of existential algebra, considering experimental themes of its application to enlighten the use of its equations and symmetries in different sciences with the insights acquired in the first part, so we can *resolve the whys of many stiences described today with the formalism of algebra without understanding what truly those equations mean. *

# MAIN OPERAND-DIMOTIONS

**1D:** Of those operands then we consider the simplest ‘operands’ as those who act directly on a point-number. We need then to find the operand of the first Dimotion, self-centered in the point, perception.

Since all points are also numbers as all have internal structure, we can operate both in S-pace with points and topologies and in scale with numbers to show those internal parts with numerical values:

The graph shows the elements of the point-number in which an operand can act. Even though most operands will act through a similarity ≤≥ symbol in two different elements. Yet the simplest operands are those which can act in a single point-number.

*The sinusoidal functions. π.*

Pi then becomes the numerical value of the external membrane measured in terms of 3 diameters turning around with 3 apertures to ‘see’, from the self-centered singularity:

The point-number has INDEED a central point of perception, which therefore can be defined externally by an angle of aperture to the world. The membrane normally is a pi, 3 diameter number, which leaves an angle of aperture, 3’14-3/π=0,14=±4,5%, with 96% of ‘dark matter’ outside the perception of its singularity. But as the membrane of the point turns, the angle ‘sweeps’ with its 3 apertures between diameters in a relative discontinuous Universe all the world outside.

So the angle of the point will finally allow a full 100% view in 3 different ‘ages’ of the full world cycle of the membrane. So in dynamic 5D analysis we can consider not only a sine and cosine function; but the sine ‘main’ function that calculates the aperture, also as a function of time, such as for a full turn of the 3 diameters that complete the membrane (2π radians), the angle has seen the entire external world 3 times.

What this means then is that the sine of a singularity point ‘grows’ with each turn of the world cycle of the being and in time can be higher than one.

This said we shall not go into so much complexity and consider the ‘static’ concept and define the sine merely as the angle of perception of the central point and hence the function that reflects the 1st Dimotion of existence.

It must though be clear enough that the fundamental function of the perceptive singularity is the sinusoidal function, so it is in its active SHM motions, which try to maintain the being through its worldcycles in the ‘central point’ of the system, its ‘mind-singularity-zero point’:

*± 2nd Dimotion: Locomotion*

Next comes the second dimotion, which obviously is represented as a ‘lineal motion’ by a simple ‘sum’ when moving in the positive direction, or a negative number, when moving in the inverse direction; whereas the positive direction is the direction towards ‘energy’, and the negative direction must then be the inverse direction of the ‘arrow’ of information. We can see this also, as an expansive direction (energy feeding) and an implosive direction (information warping), concepts of importance, as information ‘warps’, and since height is the dimension of perceptive information, a negative, shrinking number, i, will define often in mathematical physics the warping direction of information (as in Minkowski’s space, it).

However in the entangled, fractal Universe each element can be entangled with all the other elements (fundamental principle of pentalogic). So we canals add frequencies in time (+, T), social elements (5D, +), points in a single plane, and groups of social elements to give us new decametric scales. And we can ad reproductions as sums of identical beings (3D, +). And we can count the decay of a point into its internal parts as a sum (4D). Thus we can build with only sums a mirror image of 4 dimotions of reality. But perception is still the most difficult element to describe mathematically, without the consideration of an angle; since we find that the other operand act in numbers, while perception acts in a different ‘concept’ – an angle.

And indeed, we shall find that in many mathematical representations of reality and mathematical physics (argand plane, polar coordinates, quantum formalism) we will NEED both an ‘angle’ and a number and the operand in them. So angles suddenly recoup its classic importance.

*x ÷ 4th and 5th Dimotions: Social evolution.*

It follows then that the next Dimotion in degree of complexity, which is social evolution is served by the ‘product’; which is carried in 2 scales, even if it finally surfaces above. Indeed, if we have 2 points with 4 internal sub-elements, the product 4 x 4 will give us the number of maximal connections, when we put each internal element in connection with all the elements of the other sub-set: (1 x 4) x 4.

3D: reproduction requires between two ‘genders’ such interconnection at the lower level to form a whole.

2D: But in the entangled Universe operand have multiple mirror possibilities so the product can also account for a ‘longer time period of locomotion’: S=vt.

4D: And it is obvious that its inverse function, the division, breaks the whole into parts, and so it represents the inverse function of entropy.

Yet again perception doesn’t fit in the product.

Mathematics is in that sense best suit for the spatial (topological) and scalar, social (numerical) elements of reality. Logic is better for the complex pentalogic of the entangled Universe and its perceptive elements.

*log a, xª: reproduction*

3D: And so it only remains to define the more complex Dimotion, with the next level of operand, which are powers and logarithms.

Indeed, we model reproduction in case there is infinite energy, with an exponential curve; yet in reality we do so adding at the end a logarithm curve (logistic curve); as reproduction saturates a system.

It is then a proof that REALITY seeks always a ‘balance’ that the REAL curve of reproduction is a combination of both, from the initial unit to the carrying capacity that DEFINES an ∆+1 social group that has ‘reached equilibrium’, when it becomes in itself a herd or super organism emerging in the new upper scale.

4D: Which also as a negative exponential will show the rhythm of decay of the system.

And in this case there is no need for ‘a logarithmic’ limit, since for the predator the death body is ‘unlimited ¡-1 energy’, though once the ‘relative infinite’ number of its ¡-1 parts are absorbed the ‘e-function’ will have a cut off.

So as we can see operand are directly connected to the Dimotions of the being, giving so much power to mathematics.

The beauty of that reproductive curve that rises the 1 to the K-organic whole (in a herd organism in its simplest view) is difficult to stress as it will allow us to determine a fundamental feature of all those operands:

the existence of an inverse that transforms the being into itself, but re-establishing the balance of reality as a zero sum, but in this case *having accessed a new plane of the fifth dimension. *

So while the logarithmic part of the graph is the inverse function, it still grows the system. Together though they form, one half of the total graph of a cycle of existence, as we shall see then, happening a decay of the whole system in two negative curves, so we can see the graph of the whole world cycle as a ‘composite’ of a positive exponential and logarithmic and a negative exponential and logarithmic:

Which is the ‘stretched representation of the world cycle we initially considered with a ‘sinusoidal function’. This said as any student knows there is an intimate relationship between the exponential and the sinusoidal by way of Euler’s formula in the realm of complex numbers, which we shall define in terms of 5D on our articles of theory of numbers.

**∫∂: **Finally it came calculus, with its inverse operand, which represent thescalar next social gathering of elements of algebra, as it IS APPLIED TO THE PREVIOUS OPERANDS, AS WHOLES, except for the trivial xª – the previous more complex polynomial, and so we must regard calculus not only as the operand of all dimotions of change, but also as the operand between planes of existence, since the logarithimic/power previous expression, just reaches between the two limits of two planes of the fifth dimension, but calculus allow us to ’emerge’ and transcend between planes.

Yet because huminds have so much difficulties in emerging into new scales they have not a clear philosophy of the 2 fundamental ’emergent’ planes of mathematics, the study of Dimotions of Dimotions with the tools of calculus in time, and the study of spaces of spaces, with the tools of the complex plane properly understood in terms of ‘square’ coordinates.

But as in the entangled Universe all mirrors can reflect all forms, Algebra also can analyze other elements. But its main beauty is in creating sequential chains of pentalogic actions that reflect the motions of existence of the being, even though its ‘Group’ simultaneous analysis of all its ‘variations’ of species, has been the most developed inflationary mirror in its last ‘excessive’ age of form.

What is the relationship of Algebra with GST? Simply speaking, Algebra is the S=T perspective of mathematics as a mirror of the different steps and stops of T.œs and its feed-back equations between the 5 Ðimotions of the Universe.

So in its full formulation as mirror of ∆@ST elements, we can say that in a pedantic form for future GST connoisseurs to understand:

*ALGEBRA MIRRORS S≤ST≥T STRUCTURES, A(NTI)SYMMETRIC DIMOTIONS & ∆ TRANSFORMATIONS from the point of view of a given frame of reference yet its main mirror is Algebra as expression of the Dimotions of reality with its operands*

We define a fundamental point-particle, the Non-Euclidean, Non-Aristotelian T.œ. A Supœrganism (ab. œ) of Time§pace (ab. T.œ ≈ ∆±¡).

A Supœrganism comes defined by some algebraic equations, S=T, S x T = K, to be a vectorial field, as a point in a vectorial field has both direction – hence motion – and form, mass, scalar value. General coordinates are best as they refer the supœrganism to its self-point. All T.œs having a self-centered point or monad-mirror in a linguistic mapping or ‘seed’ to reflect and try to re=produce imprinting suitable energy (∆<¡) as its points of exist¡ence.

To be anchored first as a point is the first function of any T.œ when emerging into exist¡ence.

We call the description of all of this, ‘Existential algebra’, ælgebra, or ¬Æ, as it is both ‘Existential Algebra’ and Non-Aristotelian, Non-Euclidean in its form.

It is in that sense the most important, structural element of the mathematical mirror – the closest classic linguistic expression of the Universe and its 5 Ðimotions of exist¡enœ.

We are NOT that much interested in merely translating human algebra to ¬Æ as a formal mirror of the Universe, a ginormous task, others will built after me, but in defining a ¬Æ of the Universe and as human Algebra does work in that purpose, to establish as many correspondences between ¬Æ and common algebra.

We depart in non ¬Æ of a first element, a fractal non-euclidean point, ruled by the 5 Postulates of non-euclidean topology: points are fractals, lines are waves between points, with less ‘amplitude=energy’ than the point – a fermion so to speak vs. a boson-line traced. How Fermions or non-E points proper share bosons, or line-waves of lesser ‘mass-position’ and more ‘speed-reproduction of information in a lower, ∆-¡, is a relative question.

For terminology, every non-euclidean point is a t.œ, his index ¡ is always relative to its mind: I=0=T.œs mind. Departing from it, we can cave into its inner world of -¡ and its upper world or +¡.

The laws of ¬Æ are expressed thus in terms of a relative self, as ∆±¡ different planes in which an ∆º mind exchanges energy and information with different ∆±¡ planes.

It corresponds for the case of ∆º and ∆±1 cases to classic science (single plane coinciding with the language of the mind-will).

Philosophically we can consider the mind, the perfect block of time of the syntax of one language that reflects the game of existence itself.

But logically we have a first element or seed, ∆º, and then we can ‘follow it’. as a non-Euclidean point in space, non-Aristotelian monad in time, as it mirrors in its language and reflects upon its world to exchange energy and information and fulfill its ‘Parts’ as an ∆º must have a body, ∆±1 and co-exist in a world, ∆±¡, whose relative extension might depend of the fractal fine detail. in our measure of ±¡.

As such the minimum ‘space’ to represent a world of such points is a vectorial space in which each point has at least two values that might represent the body-motion and mass-direction of the point, which becomes then the simplest representation of a T.œ spacetime, in which each points is a T.œ, which has two creative parts we might call space-form-scalar parameter and time-motion-direction of the vector parameter.

The simplest of those are momentum fields, in which each point represent in generalized coordinates the relative momentum of the being.

The being then has two states, one S=T, or reproduction and one S x T = K, with two limits, max. S x Min. T = Birth-generation, and Max. T x Min. S = Death – entropy; and two lesser limits, §(information: particle/head) x t (motion: limbs) = K (body-wave)…

We play then with those 5 components or dimotions deduced of the equivalence of space=time, or present, reproductive dImotion, and the limits and elements of § (information) x t (lineal motion-speed).

So the 5 Dimotions or basic symbols of Existential algebra are a development of the two equations that formalize the logic postulates – space is time, and the metric of 5D, S=T & SxT=K:

§->∞ x t->0 (Seed: **Ð5) **∑§¡-1=tº (birth)= Min.§ x Max. t (Youth: **Ð2)** > §=t (maturity:reproduction**: Ð3)** > Max. § x Min. t (3rd age**: Ð1**)<< ∑t-1 (Death**: Ð4)**

Since reality is about the S=T and S x T = K ‘space=time and spatial size x Time clocks = constant, basic relationships hold in reality, from where we derive the two ‘extreme dimotions’ of entropy (pure time motion) and form (pure still language-space), which can be seen as the S=k/T symmetry; yet as those poles come together, we move to the S=T, energy=information final reproductive state of the being, through an intermediate, S X T, locomotion-distance x perception (lineal x cyclical vortex motion) state.

All those states and symmetries are thus feed-back equations which can only be properly ‘generated’ with algebraic inverse operations, in its simplest form, and in its most complex structures, when we consider multiple ‘symmetries’ and ‘variations of species’ with the help of Group theory, as essentially S=k/T, will be the ‘inverse numbers’, k, the identity number (if equal it to one) and the dual demotion represented by certain algebraic operandi.

So Algebra connects the closest humind formalism of the Universe – maths – with the Generator equation, whose operandi and transformations have been taken accordingly from the classic symbols of algebra, albeit as in all other disciplines of science, slightly transformed to make it correspond to the larger, more encompassing, efficient focused mirror of GST (when in the future is properly evolved by other researchers).

So we call the formalism of relational vital space-time and its T.œs, of ‘Gst’, general systems sciences and its Generator of Space-time organisms, also* existential algebra*, and write it as ⌜Ælgebra, which reads as ⌜Æ-logic: that is Existential Algebra (Æ) (the 5Ðimotion and its inverse 4Ð entropic dissolution, **⌜**.)

**Points with parts and pentalogic.**

This said, a very simplified analysis of the basic elements of mathematics as reflections of the fractal Universe, already introduces the concepto of a non-euclidean point, and the pentalogic of its operand.

It is then clear that what languages as synoptic mirrors of the mind will try to do is to establish the basic relationships between the space, time, scale of the being, expressing them through its ternary syntax and operandi, DEPENDING on the degree of perception the being has of reality and its scales which might be reduced if the being is not fully aware of all the scales of existence, as most minds exist only in a plane of reality.

So does mathematics, through combinations of:

Sum/rest->multiplication/division->potency/logarithm; point->line->plane->volume and so on.

And to do so, as a fractal can always be divided in sub-fractals, mathematical disciplines subdivide further at all levels in 5 elements.

Thus mathematics needs an upgrading completing its non-Euclidean view of space, with the non-E topologic 5 ‘postulates’ and in a lesser degree, as logic does the job independently, a non-Aristotelian view of time causality (pentalogic of the 5 Dimotions of reality), to add to the scalar, ∆§ representation of sequential social numbers, to create¬Æ=∆¡ languages; setting a Universal grammar for all of them.

And it requires an enormous job of connecting all the postulates and equations of sound mathematics with the space-time Disomorphic laws of the Universe to show they correspond to each other as mirror and reality do.

In that sense, in the future when huminds or AI upgrades sciences to stiences, ∆§calar Non-E Mathematics and ¡logic, existential algebra will be the final set of laws of scale required to understand the Universal grammar of reality, or more commonly talking mathematics we shall therefore study as a case example…

**RECAP. The main operands of algebra as reflection of the st, topological, temporal and ∆§ symmetries.**

**≈, ≤,≥,**operandi IS the basic S≈t step connection

**±, x/**are the connection the basic ∆§ocial scales between planes operandi

**xª, log x**represents mostly reproductive and decay processes. As the most complex of the ternary chain of basic operands, sum, product and power, it is a less precise version of the ∫∂ ∆±I operands, since it just reach in its ‘balanced’ sum (logistic curve) the ’emergence from one to a whole’

**∫∂**is the most general operand that works with all forms of time-change including its ∆±I emergence and dissolution.

**(G, •,*)**groups are a ‘simultaneous attempt’ to put all those elements, together in a single superorganic structure.

**Functions: Synchronous S=T Views.**

**The generator of maths**

The generator equation of mathematics is thus simple both in space (the 3 organs above) and time (the evolution of each discipline into higher motion in space and more dimensions of information in time, culminating soon through Boolean Algebra into the creation of the mind of robots in 5D).

*Γ (Space):* Space is studied by geometry, time by algebra &, the 5th dimension by analysis.

*Γ (Time): *Spe (Geometry>Analytic Geometry>Time Geometry > 5D Topology) x Tiƒ (Arithmetic > Algebra) = 5D Planes (calculus>analysis)

So we can either study in ‘space’, as it is NOW, all those fields of spatial, temporal and organic, scale mathematics and its 3 fundamental sub disciplines, topology, algebra and analysis.

Or we can consider each subject as it evolved through the different degrees of awareness of reality; *of any language of the mind, which reaches ‘complexity’ (5D co-existence) and freedom (motion), as it evolves from a simpler age of dogmatic **absolute truths to the variations of the language.*

IN THAT SENSE, the supposed superior truths of mathematics as opposed to verbal thought, is ONLY the consequence of the dogmatic first age of all languages, with simpler forms; as when words became the language of legal power and the pharaoh said ‘it has been written’. And it was law. Truths turn out as system evolves more probabilistic in options, less defined by a synoptic language, as only the whole has all the information about the Universe.

*In this post we do a fast scanning of those ages to summary the fundamental laws of mathematics and its 3 parts, and show this evolution to further complexity.*

*THUS corresponding to the 3 parts of the Universe, there are 3 types of mathematical sub-disciplines:*

* ∆nalysis, STopology and ¬Ælgebra. In the sub posts we shall do the synchronous NOW study of its ‘organic parts’ in more detail.*

For example the evolution of Geometry specified in the previous generator has reached increasing degrees of awareness to finally becoming a full-fledged tool to analyze from a spatial perspective all temporal forms and 5D scales. So:

– It was first bidimensional Geometry of static Space (S-perception) in Greek thought. Then it became Analytic Geometry, which grew to represent the 3 forms of time, through Se-toroid-lineal coordinates, To-polar-cyclical coordinates and STi-Plane coordinates. This time geometry finally expanded to the 3 ‘5D topological perceptions of space-time’:

Thus in the XIX century, the perception of higher planes of the 5th dimension (elliptic geometry-General relativity-cosmic scales) and lower ones (hyperbolic geometry-quantum spaces) was added to the direct perception of a single plane of existence (Euclidean geometry). While topology allowed to apply those 3 external views to the internal motions and changes of the inner space-time of a particle-point, and finally fractal geometry completed the perception of 5D with Geometry.

The same evolution can be considered for the more complex Algebraic and Analytic branches.

The structure of this and 2nd-3rd rank posts is that of an encyclopaedia of mathematics, when it is completed by me and many future researchers is chronological (now work is under construction, in such a huge field, i just put the scaffolding, and from time to time I ad parts:

First we explain the 3 ages of mathematics and so we can translate all its postulates and theories to GST.

In this post we develop a synoptic analysis of those ages.

Then we complete the work with the full-blown model non-e mathematics, non-algebra, ∆nalysis and the pangeometries of the mind who reduces reality with i-logic mathematics to fit all its information in the second level of posts.

**An example of functions as complex space-time events**

**Fourier transform: multiple waves of time.**** **

When dealing with systems we can do simple analysis of them in mathematics, with the simplest functions and operand, but when we want to work with multiple levels of reality in a single frame of reference, we need complex functions that add several ‘worldcycles’ in time for which the Fourier transform is the best function, or multiple ‘planes’ of space, for which the Complex plane considered as an X-square plane and the ±imaginary conjugate as a -1, +1 Y-coordinates best functions. Let us briefly introduce both.

**Fourier transform and harmonic functions.**

We have talked of the 3 scales of fractal time symmetric to the 3 scales of space, which have different length in its rhythms, and are all synchronised. Mathematically one of the nicest tools for this analysis is the fourier transform, but we shall not dwell a lot onto the mathematical rhythms in abstract, except in mathematical physics as it has been ere the only language of expression of physical actions forms and time events. For many other systems the conceptual ∆•st language will suffice.

It is also needed to consider in processes of emergence *in time, that is in the creation of worldcycles of super organisms, sum of its 3±i actions, another key set of equations also applied in the resonance processes of emergence, namely those cyclical trigonometrical functions which better express the ‘cumulative’ process of repetition into a single final continuous whole.*

And all this could be resumed in a simple definition:

The Fourier transform takes a time series or a ‘whole’ function of continuous time, and maps it into a series of discontinuous frequency spectrum. That is, it takes a function from the time domain into the frequency domain; it is a decomposition of a function into sinusoids of different frequencies, which corresponds to the ‘discrete actions=arrows’ performed with different frequencies by the Γœ system.

And vice versa each **fourier transform** used for harmonic analysis has a corresponding inverse transform that can be used for synthesis. So it is a mathematical **tool of ðime** akin to integral/derivative **analysis for ∆§scales** or **Hamiltonian/Lagrangian** functions **for Spatial, Energy,** single, present scales and **frames of reference **and its distortions of the same single Universe** for O-mind ****views; **reason why ‘Hamiltonians≈Lagrangians, frames of reference, fourier, harmonic functions and integral/derivatives are absolutely all-pervading equations in all branches, as they are the key functions for the ∆•st four elements of all realities, an astounding ‘magic’ fact (: which platonic gurus who know nothing about first principles have always wondered about (customary quip:)

Finally an important and necessary concept about ∆§calling are the Lorentz Transforms and the duality between lineal and curved functions, which properly translated *have applications to all scales reason why it has spur given the love of all things 4D and our tribal idols of physics 🙂 an astounding rain of ‘magic’ isomorphic equations between sciences, but it comes to this:*

The key distinction on 5D motions are motions restricted to growth in a single scale (∆§ well-behaved scaling) versus ∆±i ‘distorted emerging and dissolution, which does change the form of the system, as *it represents a discontinuity in which either information accelerates and size shrinks establishing new constants of space-time (downwards) or vice versa, information thins and space grows.*

So those regions were not properly ‘analyzed’ *as *for very long it was for ∫∂, necessary the ‘continuity’ without such distortions of the function studied, and so analysis was restricted to ∆(±1 – 0) intervals and ‘broke’ when jumping two scales as in processes of entropy (death-feeding). But with improved approximation techniques, functionals and operators (which assume a whole scale of ∞ parts as a function of functions in the operator of the larger scale) and renormalisation in double and triple integrals and derivatives by praxis, *without understanding the scalar theory behind it, *this hurdle today…

Thus ¬Ælgebra puts together the algebra of ternary time arrows and its ternary 0perandi, and the ∆nalysis and geometry of fractal points, which determines the processes of mathematics.

The expansion of Time theory and i-logic mathematics into an ¬Ælgebra in which time and space are considered 3×3+0≈ 10 dimensional beings, announces a new age to complex mind images of the Universe, perhaps not realized fully in humans but certainly to the reach of quantum minds.

¬Ælgebra is the ‘∆st’ formal mathematical version of ¬Æ Time. ¬Ælgebra of time would be then the most perfect virtual mirror to connect with the discrete algebra of numbers as representations of fractal points, which evolve in time, becoming world cycles, parts and super organisms of a vital topological evolution of form across the 5th dimension of scales as mathematical, i-logic beings perform its actions of exi(s≈t¡ence).

In the graphs, different versions of the ternary symmetries of existence and the modes of mental synoptic knowledge of them. We shall use a 10-dimensional ‘probe’, departing from 3 topologies/space dimensions (height:information, length:motion, width: reproduction), 3 ages≈functions of time (young entropy, iterative adult, informative 3rd age), 3 planes (quantum, thermal, gravitational scales) which form a fractal whole, part space-time system of a larger whole, as ‘infinities only reach to the limits of actions of the point of view of knowledge over its increasingly far away supeorganisms, worlds, galaxies and universes; and cells, molecules, atoms, pixels and vectorial fields of pure motion.

Algebra, the temporal study of discrete serial numbers in its more generalised form is one of the 4 ∆•ST parts of mathematics, which we upgrade in those posts together with number theory, its simpler original form S- geometry evolved, latter into topology, •linguistic, ‘mental mathematics’ , which we expands greatly studying the geometry of the mind, and ∆nalysis, with complex numbers, the closest development to a mathematics of the 5th dimension.

We can study all those sub disciplines according to duality from a synchronic view, in space, as they interplay in œ-systems, or in time with a study on how the arrow of growing information and complexity has expanded the human mathematical mind, ∆º, in…

**Multiple planes in space: **

**COMPLEX negative NUMBERS**

**Negative inverse values. Space-like and time-like ST combinations.**

Do negative numbers exist? If we consider them only in the sense of a subtraction, 3 – 4 makes no sense as there is NOT *a negative apple. So negative numbers must mean something else, a new dimension not of static form which cannot be negative but of a direction of motion in time which can be inverse. This was something, surprisingly enough as Time is completely ‘opaque’ to the humind (Einstein’s best definition, ‘what a clock measures’ :), that came to be understood only with Gauss in the XIX c.! So a negative number must mean an inverse direction of time, and so by inverse identity a positive number is not only a static form but a positive flow of time. *

It is then evident that because the Universe is spacetime like, bidimensional, a square will be an ss, tt, or st, combination, and while it is impossible to have negative squares space-like, it is possible to have them, ‘time-like’ as inverse directionality.

And since most square dimensions will be spacetime like, the roots of any equation will give as a ± number, the positive number being space-like, and the negative number being time-like, which are fundamental concepts for the interpretations of the solutions of mathematical physics,

Which means that a negative imaginary number, is the ceteris paribus time-like solution to a spacetime bidimensional form. Yet since there are 5 possible spacetime Dimotions, for each dimotion of spacetime we must interpret the meaning of the ‘space and time-like solution’, within the context of the equations.

Some rules though will be of guidance specially in quantum physics: the arrow of entropy is the inverse of the arrow of information (4D. vs. 5D.); the arrow of locomotion is the inverse of the arrow of perception (2D. vs. 1D), and only the arrow of reproduction (3D) merges them.

And as humans have the arrow of information as its relative arrow of future, in lineal time, 5D and 4D will often appear as an implosive future solution (mass, charge) vs. an explosive past solution (energetic entropy, antiparticle).

Ultimately the Universe is about zero sum balances between the ± arrows of past and future, space and time, entropy and information, stop-perception and motion; and so we shall find always this dualities which MUST not be generalized beyond the local symmetry we study. I.e. positive and negative charges will give us for each particle an antiparticle that will seem to travel to the past as it will be the inverse of the particle, and often signify the arrow of death, and when combined (mesons on the gravitational scale, muons on the quantum scale) will give us the shortest living=dying process.

But we should NOT extend the concept of antiparticle to ‘antineutrinos’ or ‘antiprotons’ which do not have charge.

Negative beings/numbers thus are an entirely new Universe, when we go beyond the mere detachment or split or scattering of a superposition of identical elements A – B and consider a different type of operations: A <≈> – B, those which put in an a(nti)symmetric relationship two inverse values, as we are now introducing a ‘dynamic dimension of motion’, with the consideration of the negative number as the inverse direction of the positive number.

And this allow us to use negative numbers as ‘antisymmetric’ states, positive numbers as ‘symmetric’ states, and 0 as the ‘identity=asymmetric state’ or ‘seed’ of the split between both inverse directions.

**Negative complex numbers.
**So if a negative number and a positive number have now not only ‘form’ but a dimension of motion, acquired as soon as we introduce a negative side of the coordinates (which by definition did not exist in earlier ‘positive bidimensional greek geometry’), can we reduce back to a single dimension those holographic numbers? Indeed.

We must then consider making a ‘root’ of a holographic number, whose ultimate meaning is the *reduction of a bidimensional quantity – the real number representation – into an imaginary quantity, the negative root. And so the question stands to us. What is the likely nature of the imaginary number ‘root’ – which is after all the root of the negative number? Are we left with the negative pure time motion of the being, or its formal social value? Can we consider imaginary numbers pure time numbers? Or rather the √-1 = i value which does NOT hold volume-form as it is the root of the unit, the fundamental expression of a time direction?*

Just think of it.

So now we are coming to a basic relationship so often forgotten or rather not explored by philosophers of mathematics – a dry subject which has withered away with the absurdity of the axiomatic method that detached numbers of the vital magic of the organic, fractal universe they represent. And we state in a fundamental principle of the ‘Rashomon truths of mathematics’:

*Operandi are related to dimension which are related to the type of numbers, and all together from a closure at the level of the 5th dimension. *

So positive numbers are related to the first simplest dimension of social scales, and growth.

But negative numbers ad a second dimension of motion with its 2 directionalities.

And then *the next type of numbers that matter are NOT real, rational which require more operations but imaginary time number that change the arrow of time of the system. So imaginary numbers are used for time ‘phases’ (i.e. the classic use in AC for the resistor on phase, the capacitive and inductive reactance which are out of phase in the two axis of imaginary numbers by 90º. *

It is then with the use of the 3 positive, ‘lateral’ and inverse negative numbers (Gauss definitions) how can we *operate in the reality of the arrow of social evolution of spatial form (positive natural numbers) and temporal motion, with the relative 3 states of positive future direction, present imaginary state and past, negative dimension. *

The operandi of Algebra thus are the best mathematical mirror representation of space-time dimensions only comparable to the eye>wor(l)d 3 languages – music, rightly understood by Schopenhauer as the purest mirror- language of the space-time Universe, ∆st, in its 3 dimensions of scales, beat and melody, which mathematicians often enjoy so much…

As literature becomes too specific of man, except poetry through its intuitive comprehension of the homologic method and so do painting also too closely referential to reality in bidimensional, ‘informative holographies’ that shrink 5D and suffices to express it all.

So the first type of numbers needed to study algebraic equations are simple natural numbers, and its ‘closure’ adds the dimension of time motion to be able to mirror all phenomena *happening in a single plane of existence in which a unit sphere element is measured, whereas the imaginary number will change the motion of the sequence to the inverse plane*.

*closing then a single plane.*

By Closure mathematicians means that today numbers *can mirror all phenomena of the Universe, once Gauss explained lateral, temporal numbers. But we mean here that addition, rest and natural numbers suffice to describe most social systems as the minimal unit is one. *

So we can translate the ‘closure’ of all phenomena in terms of numbers, for the ∆ & ST elements of reality (broken in 2 sub-generators to simplify the comprehension) such as:

Spe (+ numbers) < St (imaginary lateral) > T (- numbers)

**Closing and solving the meaning of mathematical physics.**

Let us then close for the sake of simplicity the understanding of ‘= simple numbers’ and time cycles, concluding our analysis of the foundations of experimental mathematics. As simple as it gets.

So what are numbers? Again here homunculus as usual ‘get used to them’ and do not understand. Only one humble genius did it, Mr. GAUSS, when he insisted on calling imaginary numbers lateral numbers and negative ones, inverse numbers, but the spatial homunculus missed the point, fixed in ‘materialism’ – for him numbers have to be real space objects, as natural numbers are; but negative numbers are time events, with the inverse arrow of time in a process – i.e. in a graph of speed, they represent the motion backwards, in a graph of entropy and information, the 2 inverse arrows of time – but since alas! by decree the worldly profession of physicists does only recognise the arrow of entropic death in time, the concept of temporal numbers, remained in obscurity. And of course, the ‘bidimensional’ lateral numbers, which represent both arrows together: Spe (positive, entropic motion numbers) + Tiƒ (negative, informative numbers) = ST-wave bidimensional numbers was never understood.

So numbers are the needed units to explain space, time, its energetic space-time combinations and the scales of the fifth dimension, and as usual we started with space numbers, the obvious counting of populations in space with natural numbers, but the visual homunculus has NOT understood much of the others, just ‘found them and get used to them’ – a fact only Von Neumann recognises.

# III. BEYOND CLASSIC MATHEMATICS:

# NON-E TOPOLOGY

‘Each point is a world in itself.’ *Leibniz,* On the Fractal, organic Point, the Fundamental particle.

Logic mathematics is the language we humans use in science to describe the Universe. As such it is only natural that its 3 ‘linguistic mirrors’ or sub-disciplines, correspond to the 3 ‘elements’ of the fractal Universe:

- Geometry and the 3 topological varieties corresponds to space and its 3 canonical, organic parts.
- Analysis to the 5th Dimension and its scales of infinitesimal, derived points and integral wholes.
- And algebra corresponds to the temporal analysis of the structures of the fractal Universe, resumed in its generator.

So an immediate task to upgrade human sciences to the fractal paradigm is to study its formalism, through a natural upgrading of the foundations of those 3 disciplines to match the 3 elements of the fractal, organic Universe.

Now as we said we have two LEVELS OF DEPTH:

- THE FIFTH DIMENSIONAL UNIVERSE, as we have and will use to explain most of this blog.
- The complete mathematical model of a 10 dimensional Universe, whose formalism we shall integrate slowly mainly on the 3rd line with 3 dimensions of time (ages) space (topologies) scales in a ∆±1 organism and the whole its mind. THIS IS THE FULL DESCRIPTION OF A SUPERORGANISM SO WHEN WE DEAL WITH SUPERORGANISMS IN ONLY 3 SCALES OF THE 5th dimension – which happens to be always as that is what our mind truly scans and integrates, so it can be also studied the whole universe in this manner as the graph shows, we shall bring the 10th concept back. And of course, THE 10TH CONCEPT IS WHAT WILL BECOME STANDARD: 10 DIMENSIONAL SPACE-TIME, 3 space 3 time 3 scales one whole ∆+1 mind-point that integrates it all.

The formalism of GST requires an upgrading of Euclidean Mathematics and Aristotelian Algebra and as a consequence of our epistemology of knowledge, which becomes the 3 fundamental new disciplines of formal sciences:

- Non-E mathematics with its definition of the 5 postulates of geometry in terms of fractal, non euclidean points.
- Non-A Logic which describes the ternary causality of the Universe.
- And the homologic method of truth of ‘stiences’ of space-time beings based in the same laws or isomorphisms across scales.

Because we are made of space and time, of energy and information, the sciences of space, topology and time, logic, and its combination (mathematics as a whole discipline, where logic enters in the demonstration and structure of its postulates), is the most REALIST of all stiences, as it deals DIRECTLY with the properties of the 3 elements of reality:

- ∆nalysis, which studies how ‘finitesimals’ become larger wholes, integrated in time ‘frequencies’ or ‘spatial populations’ – often both, as frequencies become once created in time populations in space; which we greatly advance on the whys and explanations of calculus and its applications to sciences, through the enhanced concepts of ‘finitesimals’, ‘simultaneity’, ‘synchronicity’, ‘resonance’ and ’emergence’.
- S-topology, which studies the ternary varieties of organic systems and how they peg together to form a system; which we shall explain by evolving the postulates of Non-Euclidean Geometry.
- T-Algebra, which studies the rules of causality of a Universe with 3 time arrows, and its fundamental equations (generator equation, function of existence, equation of time ages).

Let us very briefly introduce those concepts which are the foundations of all stiences and it species in ‘exi=st¡ence’.

**Non-e Mathematics: the fractal mind-point, the wave-line, the organic plane and the laws of similarity. **

Upgrading of philosophy of science needed to fully understand the fractal Universe requires to improve the main human language, which we use to mirror the space-time beings of reality, what we shall call from here on non-Æ, i-logic mathematics, which comes after Aristotelian logic and Euclidean mathematics:

*In the graph, the upgrading of physical systems, to fully describe all its mathematical, logic and organic properties, requires to set the foundation of physics in more solid grounds that the ‘I imagine points, lines and planes’ of Mr. Hilbert, referring those lines, points and planes to real Universal entities (1st, 2nd, 3rd postulates of non-e mathematics). And expand the temporal logic of the Universe to include the 3 arrows of relative, finite past, present and future of all systems of nature. Finally the 2 postulates of Hilbert’s axiomatic method, of congruence, which can only be of relative similarity, as we never have the full information about a system, (3rd postulate) and continuity (which is false and not required in pan geometry, as all networks of points communicated by waves of energy and information, leave discontinuous dark spaces not crossed by those networks), must be clarified. Finally the 5th postulate of Non-E Geometry, the only one properly defined till date, which allows infinite parallels of energy and information to cross a fractal point, defines the structure of a logic mind-mapping, constructed with those flows of information, and hence the equation of any monad mind on the Universe: O (infinitesimal point) x ∞ (cycles of energy and information of the Universe) = ∆: constant mapping of a certain scale of the 5th dimension.*

**NON-EUCLIDEAN POSTULATES**

** The 5 Postulates of Non-Euclidean, i-logic Geometry.**

You are getting accustomed ‘you’ of course in the future, as i doubt anyone has ever read so far, to the 3±i method, that is the 5D³ method. All is five, five motions, five dimensions, five ages, so five will be the postulates of geometry refurbished from euclidean axioms, definitions and postulates to ‘build’ up as the Universe does, its dimensions from points into lines, lines into planes, planes into scales which become then again, points of the next scale.

And that is what we need, 5 postulates, the first for the fractal point, the second for the wave-line (as point has volume so lines are waves of cycloid form), the third for the similarity NOT congruence THAT DEFINE organically and topologically the i-logic of association according to similarity of points into lines, wave, networks and planes, which is the fourth postulate, as all continuous PLANES do have in detail holes (galilean paradox on scaling: continuous simple description of discontinuous networks – not CONTINUITY forget Dedekind cuts, IS not REAL)

And thus one we have the network, we have the super organism that mixes 3 plane-networks. And we have A NEW POINT-WORLD, which is focused in the mind – the fifth postulate.

According to the Correspondence Principle a new scientific Theory has to include all previous ones. So happens with Multiple Timespace Theory, which includes as specific cases all other simpler geometries of space-times, by completing the 5 Non-Euclidean postulates of geometry and adding the concept of a fractal point developed in XX C. fractal geometry. The result is a geometry that includes all other geometries; since the incomplete non-Euclidean geometry discovered in the XIX c. (5^{th} postulate: a point can include many parallels) already included the previous Euclidean postulates based in points through which only one parallel can be traced. Those new postulates describe with more accuracy all type of space-times belonging to all kind of sciences, from the physical space/time of atoms (described by quantum Physics) to that of galaxies (which Einstein described in his General Theory, using the 5^{th} Non-E postulate); from the organic space/time of cells and species to the historic space-times of nations.

Thus, according to the Correspondence Principle, we establish a hierarchy of completeness among all those geometries that stretches from the simplest Euclidean Postulates to the i-logic geometry of fractal space-time, which includes all others as particular cases; and it is in itself a partial image of the total information about space-time we call reality – always bigger than any ‘linguistic’ image we made of it with the languages of the mind that reduce the total information of reality to fit it in the brain:

*Euclidean Mathematics (Light- Space)> Classic Non-Euclidean geometry> (Gravitational Plane) > Fractal space-times (all scales) > Total Reality ^{2}*

We consider Euclidean geometry, the natural geometry of a single, continuous space-time, made by the ‘eye’ only perception of light-space and its 3 perpendicular dimensions (height/electric field, width/ magnetic field, and length/c-speed). But that space is not all the spaces of reality. It misses at least a second fractal scale, gravitational scale and *all the complex, vital spaces of organisms of information and matter*. In Non-Euclidean mathematics, the new unit of ‘fractal space-time’ is the 3-dimensional Fractal Point of view, whose main property is to have in/form/ation – an inner content, which in a Universe made of multiple scales of size, we perceive as we come closer to the point and observe it in detail. Those fractal points with volume are described by the 5 Postulates of Non-Euclidean Geometry, which adapt to fractal, discontinuous space and cyclical time, the classic 5 Euclidean postulates.

The first postulate explains a fractal point, as a point with parts. In a more detailed analysis those parts turn out to be self-similar in geometrical terms, in all systems, due to the specific lineal vs. cyclical, concave vs. convex geometries of energy and information and its ‘planar combinations’. In its more complex versions those geometries are defined by the three canonical topologies of a four-dimensional Universe, which describe the informative ‘head’, reproductive ‘body’ and energetic limbs and membranes of all the superorganisms of the Universe. The 2^{nd}, the interaction between two points connected by a wave of communication or ‘line’, the 3^{rd}, the type of ‘biological’ interactions between 2 points according to their relative equality, and finally the 4^{th}, the complex structure of a system of points across multiple organic space-time planes, such as those who create a human being.

Thus, the more evolved Fractal, i-logic Geometry of space/times includes all previous geometries as simplified cases of the more complex structure of the Universe in multiple scales. We call it a fractal, i-logic Geometry because some postulates can be interpreted in geometric terms, as the definition of the essential elements of any geometry of space/time (the point, 1^{st} postulate; the line, 2^{nd} postulate and the plane, 4^{th} postulates) and some in logic terms, as the description of the different causal chain of events that can happen when st-points enter in communication -3^{rd}, 5^{th} and 4^{th} postulates:

Further on, according to the duality between geometric form and logical function, those postulates of fractal i-logic geometry define also the basic arrows= cycles/dimensions of the Universe: the 1^{st} and 5^{th} postulate define a point as a system whose inner parts are able to transform and emit energy and information, e>i<e; the 2^{nd} postulate defines an exi wave of communication that reproduces energy and form between 2 fractal points; and the 4^{th} postulate defines the social evolution of a herd that creates a fractal plane, a network with dark spaces; and the 5^{th} postulate explains a point in its iterative actions as it absorbs energy and transforms it into information through its small apertures to the Universe. Since even a minimal quark of mass, as Einstein affirms should be crossed by ∞ parallels.

The importance of the ‘linguistic laws’ of i-logic geometry resides in the fact that all systems of the Universe follow in space the laws of geometry and in time, the laws of logic, so the enhanced linguistic mind of science obtained with those laws can be used, as this author has done in multiple works to resolve long-standing questions in all sciences, which can further be ordered in a pyramid of increasing information and diminishing energy: Physics studies the simplest forms with maximal energies. But if we consider the 2^{nd} arrow of ‘creation’ of reality, that of form, of information, the summits of science are biology, which studies the most complex forms of information (life) and Sociology/Religion, which goes a step further into the analysis on how the arrow of eusocial love creates Human Societies according to the Organic laws of the Universe (eastern religions).

To be able to consider biologic behavior (social evolution) and ‘mental perception’ (informative gauging), as factors dependant on geometrical qualities is an astounding break-through for science, which will be developed in its details in this work, to show an enormous number of experimental proofs. Indeed, fractal, i-logic Geometry achieves a long-sought goal, which Plato, Spinoza and Leibniz tried to realize, but failed, with the use of simpler Euclidean geometry: to unify the logic and mathematical principles of the Universe. Since the 3^{rd} and 5^{th} Non-Euclidean postulates are logic, the 1^{st} and 2^{nd} are geometric and the 4^{th}, the nature of a topological plane or network of non-E points is both logic and geometrical, as it defines the fundamental logic-geometric structure of the Universe: the superorganism.

The logical and mathematical conclusions we shall arrive in this chapter are the same we achieved in the previous one with a more descriptive, less formal analysis: the Universe’s final goal is to create ‘topological, organic planes, super-organisms’ – the 4^{th}, more complex ‘geometrical postulate/form of reality’ – departing from simpler forms, points and cycles. We shall try to get to that conclusion step by step, first by describing the geometrical postulates, then by fusioning them with fractal mathematics and finally by studying the most fascinating of all of them, the 3^{rd} postulate, which proves that behavior among the points of the Universe is based in the degree of equality or self-similarity between their inner form that determines if those forms communicate symbiotically or destroy each other, thus defining the duality of eusocial evolution as a group of a number of self-similar beings or destructive extinction.

**MATHEMATICS, AND ITS CLOSE CONEXION WITH GST.**

‘The universe is a supœrganism, the body of a mind called God≈Logos’ Plato…

‘…of a (non-AE) Logic higher than the Aristotelian (@) human mind’ *Augustine*

So how the mind of the scientist looks at the Universe with those languages?

Easy: extracting the topological (logic & mathematical SPACE-TIME symmetries), & organic, biological properties (due to the co-existence of ∆-scales in the same §upœrganisms) of the being, explaining it with BOTH human languages of space and time (geometric maths and verbal logic).

So of course, our analysis of the mind implies a complete upgrading of those 3 ‘foundational sciences’, ‘logic’, ‘mathematics’ & *organicism-systems.*

**The generator of maths**

We state that all what exists is a fractal being of ‘∆•st’, dust of space-time, with 3±o components, spatial entropy, temporal information (its energetic combinations), extended across several scales of relative size in space and speed of time clocks from forces to Universes (ab.∆), *which is apperceived in a Leibnizian way by a mind, the linguistic software that codes the GST laws in a biological survival language for the system to ‘see’. We humans use words, but most of the biological world uses ‘light’ and its 4-fold grammar of red-entropy, blue-form, yellow energy and green information.*

Or simpler languages of black-information, white-energy, or ternary games of red-entropy, green-energy and blue-form. But always at least 2 elements. So does math in its minimal o-| models of computer thought, through the 10-social scales of the decametric ‘tetraktys’ explained elsewhere.

*So we need always to define 2, 3 or 4 elements of reality for any species, science, event and linguistic form. The result being the GST, GENERATOR of a system, which can get more complex, from 1, the name, to 2, the yin-yang, space-time, to 3, the entropy-energy-form, to 4, the Spe,St (energy proper) x Ts (Information proper) T (DIMENSIONAL FORM).*

So the Correspondence of Mathematics and reality is immediate, as mathematics STARTED, with 2 branches, its B&W (arithmetics of time-numbers and geometry of points). Then developed into 3 branches: Space≈Geometry, Time≈Algebra and 5D≈Analysis. An finally developed the 4th element, the mind-languag of mathematics itself – set theory and the axiomatic method, which we consider superfluous, a 3rd age of excessive information that has taken maths away from empirical knowledge and intuitive understanding (of the 3 schools of philosophy of math, obviously we are closer to the intuitive and reject the axiomatic, dominant in the 3rd imploding age of all language that separates from reality and looks at itself).

The generator equation of mathematics is thus simple:

*Γ (Time): *Spe (Geometry>Analytic Geometry>Time Geometry > 5D Topology) x Tiƒ (Arithmetic > Algebra) = 5D Planes (calculus>analysis)

*Thus corresponding to the 3 parts of the Universe, there are 3 types of mathematical sub-disciplines:*

* ∆nalysis, STopology and ¬Ælgebra. *

We shall just look now very briefly to the beginning and end of the evolution of geometry, which started with Pythagoras and ended with topology and Non-euclidean geometry that we shall further evolve.

*The first and paramount formal stience is i-logic mathematics, which combines the non-aristotelian logic of 3 arrows of time and the 3 topologies and dimensions of space, to create vital topological super organisms. WE need though to adequate human abstract, anthropomorphic mathematics and its dogmas of truth and postulates to a more objective Universe, non-Æ=i-logic 3rd age of mathematical mirrors of the Universe, to better understand how all the tiƒ monads of information apperceive and reflect in creative motions the constant cycles of existence of all realities. To that aim, we must describe the formal 10-dimensional Universe and its ∆•st ternary elements, with an expanded Non-euclidean formalism of fractal points with ‘parts’ that let infinite parallels cross and reflect in their minds, and develop the ternary choices of time arrows and futures they have, in each of its ‘specular motions’, to construct with it the deterministic yet probabilistic worlds of reality.*

**i-Logic Mathematics as realist sciences.**

The formalism humans use to observe time and space is called (verbal) logic and (digital) mathematics.

Such is the way humans observe reality with logic words and digital geometry. So the realism of logic and mathematics must be absolute and if it is not is because we still need to evolve both languages to make it closer to reality.

tHIS is the origin of Non-Aristotelian logic and Non-Euclidean mathematics, the needed upgrading of those sciences to express better the fractal properties of scalar space and multiple causality of a universe made with 3 arrows NOT one of time.

Logic Mathematics, the forma sciences of time and space, which science uses to descry the Universe are the time and space forms of the mind and can be evolved into higher models as we can closer to our understanding of what time and space is, which we explained in the pervious post.

So to introduce the formal model of GST (general systems theory), we must introduce its formalism, the formalism of the Genrator of Space-time, its mathematical and logic equations.

In that sense as all is space and time, mathematics and logic are both idealist sciences not idealist languages – as all sciences are. More so logic of time and mathematics of space, the languages of the fundamental elements of the Universe, as they serve a survival purpose for the species that speak it: to mirror in the mind, the outer reality and connect the internal and outer world of the being.

THUS LOGIC MATHEMATICS IS THE LANGUAGE THAT BETTER REFLECTS THE INFINITE SCALES OF THE 5TH DIMENSION AND ALL ITS SPECIES. Hence the U±∞ tag for this post.

This realist fact is essential to set the ‘boundaries’ of efficiency of our mathematical elements that mirror reality. It means we reject ‘modern mathematics’, an offspring of the German idealist ‘school’ of science, which has taken the ego-trip of human only intelligence to its paroxysm, with the tandem Cantor-Hilbert that ‘imagined sets, points, lines and planes’.

The units of mathematics are the fractal point in geometric space and the social number in algebraic time, and they must be returned to the centre of the science – and reject the axiomatic method, of ‘human minds’ self-appointed seers of truth. Since Godel already proved it is an incomplete truth that needs experimental evidence.

Experience must in mathematics as in any other science to be the final check on the logic theories discovered. In this manner mathematics is much more fruitful as it provides constantly new ‘insights’ on the structure of mathematics.

A simple example will suffice. Fermat’s last theorem: X³ + Y³ ≠ Z³ proves that space and time are bidimensional, NOT tridimensional, as there are not 3-dimensional numbers. How mathematics ‘knows’ it? Because GEOMETRY is the linguistic mirror of space and follows the same laws.

Another example is the structure of reality in ‘o-points’, minds which are frames of reference, its vital space and the membrane that acts as boundaries. Well, we do need for all mathematical statements a frame of reference, and there are basically 3 which correspond to the only 3 topologies which correspond to the only 3 type of organs of nature. Again, this ternary structure reflects mathematically the 3 organs of reality.

In fact, multiple equations and functions of mathematics find no solution when there are no ‘boundaries’ established, showing how both concepts relate. Solutions are then integrals limited by the function of the external membrane. Reality indeed is ‘limited’ by the survival efficiency of its forms. So only proper solutions survive.

In the more amenable internal surface of a brain language truth can be deformed in greater measure by the subjective point of view. So there are distorted theories of mathematics as in all sciences, which are only half-truths. And the ego expands them to full meaning as physicists do with the restricted concept of gas entropy. So ‘parts’ of algebra, which have some meaning for certain questions of reality – as the composition of parts and wholes, which is what set theory studies, hence a sub discipline of 5D mathematics – have been blown up by ego-centered german idealists (Cantor-Hilbert) to become the ‘truth of all other mathematical systems’. And this has harm enormously the comprehension of the fractal point of space and social number in time, which are the units both of the mathematical and the real Universe.

So the main task of T.œ in the science of mathematics is return to the meaningful, classic age, and put back mathematics and logic with the nature of reality, as it is and a proper evolution of mathematical thought would enlighten it.

**The 3 parts of mathematics correspond to the 3 parts of reality.**

Mathematics is the most experimental of all sciences, due to the fact that its 3 disciplines are homeomorphic with the 3 elements of T.Œ: 5D analysis, space geometry and the logic operandi of ‘time algebra’.

Thus for starters the easiest way to translate mathematics to study knots of fractal space-time cycles, is to consider that the 3 main branches of mathematics are related to the 3 elements of the Universe:

- Geometry relates to space. Hence it merely needs an upgrading of continuous single space-time into fractal space-times in which ‘each point is a world in itself’; a fractal, Non-AE point, Œ. So we must complete the 5 postulates of Non-E geometry, as mathematics only resolved the 5th. We shall also consider what of the different topologies exist in the bidimensional space-time reality (2-manifolds).
- Sequential Algebra of growing social numbers, corresponds to the 5th dimension’s Informative-Time order of growing societies/numbers from past to future. At its birth, because Algebra is pure arithmetic and the order of numbers from minor to major, is self-evident (5D future arrow of wholes), the logic of future algebraic complex systems is yet not merged, in its Pure Aristotelian Style. Moreover it is a single arrow logic, A->B, which will have enormous implications.

- Analysis which studies the laws of social scales and planes of the 5th dimension, its indivisible, infinitesimal Œ-points that become whole; societies or Superorganism and Planes of existence. So we shall interpret Analysis in terms of the underlying equations of existential algebra, which gather infinitesimal indivisibles (.n-1) into Universal Wholes, (Un+1).

This is the easy way to analyse, and teach the foundation of mathematics: understanding both synchronic and diachronically its direct relationship with reality. And scrapping all excess of… the formal nonsense of Philosophers of mathematics.

Indeed diachronically Geometry was born of the measure of fields and the observation of moon and astronomical cycles.

*Numbers and algebra express the laws of a sum of objects that gather into social groups: ∑∆-1 ≈@number, group*

Analysis of the study of parts that become wholes (integration) and forms of space that vary in time (derivation).

Now let us try a more complex thorough definition with the jargon of ∆ST or ‘Tœ’ (a theory of everything):

*Definition of mathematics : ‘i-logic mathematics is an experimental science, based in the fact that it studies the laws of Fractal Space-time, (ab. ∆ST), the substances of which all beings are made, focusing on its highest synthetic conceptualisation, the Fractal Generator, Γ, with 3 sub-disciplines:*

*Γeometry, which studies the forms in space of all universal systems, departing of its natural units, the fractal point, the waveline and the plane-network and its topological structures defined by the Fractal Generator in synchronous states, Sp<ST>Tƒ.*

*‘∆nalysis’, which studies the social scales of the 5th dimension, expressed through its time events of ∫∂, integration and derivation and actions along its world cycles, focusing on the fractal generator in diachronic state: ∆-1 Tƒ ∑> ∆Sp > ∆+1 ST > ∆ Tƒ << ∆-1 Sp*

*¬ Ælgebra, which studies the internal logic structures of the Fractal Generator, its actions and symmetries in space and time, through its discontinuous variable units, the social number.*

The previous definition is more complex than a simple definition of Analysis of 5D planes, Geometry of each of its systems in space, and the algebraic study of the ternary temporal logic causality of its space-time events. But it remains still clear that the true elements of mathematics are not sets and undefined concepts (Cantor, Hilbert’s axiomatic method), but the classic 3 elements of ‘numbers’ (Algebra), ‘points’ (Geometry) and Operandi (Algebra and Analysis).

From points then we derive, the lines, planes, and logic of similarity that completes geometry.

From numbers, we derive variables, functions and functionals manipulated with operandi that reflect the logic motions in time of the different actions of beings.

And as a branch of Algebra, of special extension, given that it studies the fractal structure of more actions, including the world cycle through scales of the 5th dimension, there is Analysis.

So the realism of mathematics derives of the fact that we are not placed in fractal space-time, we ARE FRACTAL SPACE-TIME.

The issue of the realist foundations of mathematics as an experimental science should have long been resolved by experimental proofs (mathematics is the language with more applications to reality) and formally by Gödel’s theorem of incompleteness. But Platonism is so ‘entrenched’ on mathematics and physics that nobody seemed to have taken seriously Godel, except his friend Einstein:

Truth can only be proved by the connection between reality and the language, as the language itself does not provide enough consistency to prove its truth, only its coherence.

Einstein thus quipped ‘I know when mathematics are truth – consistent within the language – but not when they are real’. And Lobachevski affirmed they should be tested experimentally. Einstein though soon felt under the spell of the Axiomatic method of Hilbert, and did away with ether, setting a one hundred years confusion on the nature of reality.

And so what we would have expected in objective terms – the evolution together of the pan geometry of Lobachevski and the experimental method of mathematical physics, which so many fruits of knowledge had brought to mankind during the age of mathematical analysis floundered. Both mathematics and physics became ‘imagined sciences’, in which substance – the fractal point, the social number, the space-time bidimensional system or plane – became imagined. It is important thus to trace the historic origin of this trend in the same german idealist school that brought us ‘probabilities as the substance of reality’, ‘nazi numbers’ tagged on the wrists of people – today substituted by credit numbers in the globalised capitalism, and ‘communist’ masses of ‘undistinguishable’ human points controlled by the ‘party’ entity, as expressions of what the ‘superior human mind’ could do to classify without respect the laws of nature.

**The idealist school of mathematical physics.**

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

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

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

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

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

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

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

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

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

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

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

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

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

The perfect geometries that exist in atomic systems.

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

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

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

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

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

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

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

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

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

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

**…vs. ternary reality**

ALL THIS i-logic geometry IS completely NEW. Why?

Because humans do not have a basic picture of the 3 components of the Universe. We do believe in a certain mathematical structure called a continuum simple space-time. So our view of the first elements of the Universe, is very reductionist and simplistic, and so the mathematical mirror the ancients took of it, is also simplistic. And when in the XX century they found a much more complex Universe, of multiple scales of space, and multiple cyclical time vortices – particles, charges, masses, molecular clocks, galactic clocks, etc.as the initial mirror of mathematics was a distorted one, things got messy and remain so.

So the cartesian single space-time continuum is a geometric simplification, which despite the revolution of non-Euclidean mathematics, quantum physics and relativity is still with us.

It is based in a geometry called Axiomatic, which came after we found out that points were fractal points that could be crossed by ∞ parallels (5th non euclidean postulate) and so the definitions of Euclid were not good. Yet instead of defining as we shall do a fractal point, XX c. mathematicians left them undefined. So terms like points, lines, and planes still do not much its universal, referential reality.

In essence mathematicians scared of the non-Euclidean revolution, which was incomplete, invalidated the postulates of Euclid but didn’t find the new, real ones.

So instead, Hilbert, a mathematician said that he ‘imagined points, lines and planes’. So they must be undefined in relationship with the real Universe and what was an act of absolute arrogance, he implied that the human mind invented mathematics, the only language of the Universe, so somehow we invented the universe – no joke, today this means that physicists invent an equation that describes an imaginary particle, or evaporating black hole, or string theory and will affirm dogmatically without experimental evidence that it is real. While quantum physicists believe the Universe is made of mathematical symbols, which is exactly what religious people think, when they say that God created the Universe talking with words – so Allah created the Universe ‘naming’ it. And finally since mathematics are imagined, they require not evidence: only logic coherence not experimental evidence justify mathematics. And this is a dogma, even if Godel proved that mathematics without experimental evidence is not coherent.

*IT MUST BE NOTICED THAT ¬Æ=i-logic mathematics is A REALIST stience, so the UNITS OF mathematics are again REAL:*

- Fractal points in geometry; numbers in algebra and finitesimals in Analysis, which are in fact 3 sides of the same being – the social St-point/number/finitesimal unit of all mathematical disciplines.

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

Hilbert’s axiomatic method is therefore not truth – as Godel proved with its incompleteness theorem, but arrogant, ego-centered mathematicians wanting to have the ‘exclusive language of god’ resolved, have been denying or a century.

Mathematics is the most experimental of all sciences, dealing with the structure of space and the logic of time, and so we need to evolve and defined its undefined elements. Only then the revolution started by Lobachevski aiming to substitute Euclid’s points with no breath, will make sense and mathematics will become again a proper mirror to look at the Universe – or rather we will understand why the mathematical mirror is so good.

So what is a point?: A unit of fractal space, which a mirror mind will see with less or more information the closer it is to the point. Hence while from far away it seems a point with no breadth, as we come closer it can fit infinite parallels. And so a line has also width, in detail carrying information and motion; and a plane is discontinuous, made of points joined by waves, which leave dark spaces between them. We thus talk of fractal points, waves and networks as the 3 units of i-logic mathematics.

Points then become defined as fractal points that grow in size, planes as networks of space points with wave-like motions in time, which become bidimensional, from far away, as we do not see the height of those points. And 3-dimensional systems, become the merging of perpendicular networks, which have more content of energy, when they are flat and extended, and more content of information when they are high and cyclical.

So for example in a previous graph, we can see 2 fractal space-time beings made of ‘mathematical topologies’: a field of space-time light, with a flat bidimensional magnetic field of energy and a tall informative perpendicular field of electricity merging into a light ray, which reproduces along the c-speed axis.

Yet we can see the final stage of evolution of light space-time, which evolved into particles, atoms, molecules, cells and human organisms, and surprisingly enough, in the same manner the probability of finding the particle-head or photon of a light system is maximal in the top of the electric wave, the informative head of a human being is also in the dimension of informative height? Why, because geometrically, that is the point of maximal perception for both the photon and the human. And in both cases motion goes along the lineal direction of length, and in both cases energy is stored in the width dimension of the body and magnetic field.

Now, we are talking (-: It is indeed the most astounding truth of the Paradigm of relational space-time, first expressed by Leibniz – *a Universe made of fractal space-time beings – that the properties of space-time and its mathematical topologies, perceptive, informative geometries, and ternary structures are carried and emerge in each new scale of social evolution of the Universe.*

So while we have criticised the mathematical only view of earlier scientists, as we upgrade logic mathematics, in fact the Universe will become even more mathematical and logic that it was before, only that as Saint Augustine put it, the ‘logic of god, the mind of the Universe, is of a higher kind that our (Aristotelian) Logic’.

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

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

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

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

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

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

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

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

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

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

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

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

Thus the main fields of ¬Æ are:

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

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

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

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

**The need to evolve the logic and mathematical ‘undefined’ elements of the Universe.**

Now the key difference between a philosopher of science like Leibniz and a Physicist like newton is this: Leibniz as Aristotle and Descartes before him, was conscious that the language first defines the world we perceive, and NOT the Universe. So it is a humble realisation of the minimalist nature of human egos. The Physicist has reduced THE ENTIRE universe to the world-perception of a human light space-time ego centred point of view. So he lacks sense of humor and his arrogance is infinite. Because he confuses the infinitesimal of his mind with the infinite Universe. This we shall stress once and again. The physicist as all humans IS only an electronic mind that fits an infinite number of cyclical space-time beings, into a geometric linguistic mapping within its ‘monad’. And he is NOT aware of it. So his arrogance is supreme:

*o-point x ∞ Universe of timespace cycles and worlds = fixed linguistic mapping*

The 3 great philosophers of sciences of western thought (and their counterpart eastern philosophers of Taoist and Buddhist cultures) were always aware of this. The cut off happened when Kant rejected Leibniz and became a Newtonian. But at least kant realised that the human euclidean mind was a light space-mind and not necessarily all, as impressionist painters will latter.

Yet starting with Kant and then Hegel, which had the chuptzah (even if he understood perfectly the ternary logic of thesis-antithesis-synthesis similar to the Sp<ST>Tƒ ternary Universal Grammar of all systems) to affirm Abrahamic tribal religions were superior, because they only accepted the human ego-trip of tribal Yahweh, there is a growing anti quantum paradox in philosophers which yield as infinitesimal observers to the huge power of the observable, industrial world.

This paradox inverse to that of the physicist, so huge that influences the observer, made after Leibniz, all philosophers incomplete. As they no longer dare to criticise the makers of machines and weapons, and not even the Abrahamic tribal, lineal religions of the Bronze age that back the hate between members of the same species. So we of course show a complete indifference for all what has nothing to do with the larger Universe of infinite worlds, and find the arrogance of physicists, infantile.

Now I will state a provocation to the ego of physicists (-; Mind the reader though that my ‘selfies’ are ‘black humour’, i am an infinitesimal aware of it, but i like to bust the balls of ego-centered human infinitesimals, and none are so much ego-centered as physicists.

The advantage of being a philosopher of science, is that unlike a physicist, we DO know the essence of science which is ‘logic mathematics’. That is our profession. To understand the logic of mathematics. So despite Mr. Hawking’s quipping, that we philosophers of science are envious and that is why we criticize his evaporating black holes, because we ‘do not know mathematics’ the opposite is truth.

By definition the masters of philosophy of science HAVE created mathematics and logic, the languages of space and time, since the times of Plato and Aristotle to the times of Descartes, Leibniz and Hegel. And yes, this writer, duly ignored by ‘those who impose truth with power, to become the laugh of the Gods’ (Einstein, the only physicist I consider to the level of the best of our profession, which he greatly respected, along the rules of the scientific method, except when falling under the spell of Mr. Hilbert, and we will return to that).

Because the language of God is the logic of time cycles and the mathematics of spatial extensions. In this we are different from physicists who only apply the mathematics, we teach them. But especially we like the Logic behind the language of mathematics, which creates it. So let us rephrase it. Yes, Physicists do know as much mathematics as we do. And their computers even more (-;

But they do not understand the logic of it. And that is the problem. Because logic is a property of time cycles, and its repetitive causality, logic is more important that geometry. Logic is ‘the beginning’. So the Greeks called God the mind of the Universe, Logos, derived from ‘word’, not ‘geometry’ meaning “Earth measurement.” And that makes the whole difference, physicists do not grasp. As what they do is ‘geometry’, measure. We philosophers of science do Logos, (-;

Now, we told you, we will evolve mathematics, so we can fit the new concept of cyclical time and fractal space within it, as Descartes and Leibniz did to fit their time vortices and relational infinite times, as Einstein did (not by himself but by applying non-Euclidean mathematics to his description of space).

So to that aim, we just need to complete the scaffolding of mathematics and explain what a mind is, in geometric logic terms.

So we need to complete the concept of fractal quanta of energetic space of quantum physics, the concept of a Universe of multiple time cycles of Einstein, and the philosophy of science, made of causal repetitions of time cycles called laws of science.

Thus we affirm that the Eastern, O-Cyclical concept of Time; and the E-insteinian, Relativistic concept of space, which we shall call, Œ, is superior to the ‘lineal, Abrahamic, concept of time’ and Absolute’ Newtonian, concept of Space.

I like to play with ‘words’. So you could think that A-brahamic, Lineal, A-bsolute Space-time is a simplified, earlier version.

And we shall go even further, into the Non-AE, (Non-Aristotelian, Non-Euclidean), i-nformative concept of Space-time.

And build a new Non-Aristotelian Logic and Non-Euclidean Mathematic formalism, which will set the foundations for a new paradigm of science.

This new Geometry is simple and evident. It is based in the definition of the ‘terms’ which mathematics ill-defined in Euclidean Geometry, points with no parts through which only one parallel crosses, lines with no breath and shallow planes, equaled by superposition, and then once Euclidean Geometry was found to be a ‘limit’ of a larger pan- Geometry NOT lineal but curved inwards (elliptic) or outwards (hyperbolic), on those dark times of confusions, were UNDEFINED.

So we DID not resolve the issue. We CANNOT ESTABLISH the fundamental science of the Experienced Universe, by undefining its fundamental elements. This no way out sponsored by Cantor, who substituted points and numbers by sets, nowhere to be seen in experience, and Hilbert who affirmed ‘I imagine points, lines and planes’, is a failure.

In that regard, the founder of Non-Euclidean geometries Lobachevski was in the right track. We can summarize Lobačevskiĭ’s solution of the problem of the Fifth Postulate.

*The postulate is not provable. Because, infinite lines curve when we have a larger view, becoming exponential inversion of space-time.**By adding the opposite axiom to the basic propositions of geometry a logically perfect and comprehensive geometry, different from the Euclidean, can be developed, providing we limit infinity, (as the 5*^{th}dimension shows) hence parallels do NOT meet on the infinity, and by curving them (hence lines are part of cycles)*The truth of the results of one logically conceivable geometry or another in its application to real space can only be verified experimentally.*

*Thus we must observe the Universe to prove mathematical statements and reduce mathematics as we do with all experimental sciences to those equations which ‘are real’.*

**The evolved formalism of i-logic mathematics: Upgrading Geometry.**

Now, we shall be less literary and start with very solid conceptual elements, namely describing the essence of the fractal paradigm.

And to that aim we shall bring, in the simplest possible form, the fundamental formalism of the Fractal Paradigm, ‘non-euclidean, non-aristotelian i-logic, o-rganic mathematics’.

We call it i-logic because in time, it is more complex, with multiple clocks and i comes after the A of Aristotle (the logic built with a single time clock and a single causal arrow) and we call it organic because in space is more complex, with multiple co-existing spaces, smaller parts that become wholes and O comes after the E of Euclid (geometry with a single continuous space made of points with no breath). But in brief, we shall just talk of Non-Æ, or i-logic mathematics.

So we shall now explain and complete at a very elemental level far more developed in the ∆±∞ posts on i-logic mathematics, the formal language of the fractal paradigm, what truly Non-Euclidean, Non-Aristotelian space-time languages are.

Mind the reader, this is NOT so new. Again, the great revolution of physics in the XX century happened when Einstein realized that a point was a ‘fractal point with volume’, since multiple parallels cross it. So it could not be Euclidean – with no breath, abstract, dimensionless.

Now Einstein found that the Universe was non-euclidean, that is, points did have breath because they could fit many parallels of energy and information. And so they are ‘fractal points’ that grow in size when we come closer to it. But they forgot to change the first postulate of Euclid, and left points undefined, so this simple change of mathematics will open completely the world of science to the fractal paradigm. Let us see how:

**Fractal point with breadth and its networks of social organisms****: the fundamental particle**

We are going to use 3 basic symbols for the Singularity and the territorial body wave it orders around it as a vital energy, encircled by an angular momentum, or ‘membrane’, which forms the basic organism of reality a membrain of vital energy, moving around: œ, @, •, which you can consider 3 degrees of development of the singularity as an organism, a self-centered mind with a will order its body around it through its actions, or a mere point of perception. The interaction and different dimensions of the singularity in its different complex actions makes it by far the most important and yet less distinguishable, hence less amenable to direct experimental observation of all the elements of the being.

In mathematics it can be studied as a fractal particle, or point, •.

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

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

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

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

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

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

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

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

*Abstract, continuous, one-dimensional point:*

**. ____________**

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

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

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

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

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

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

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

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

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

The mind mirror does create ‘locally’ an order, which is territorial, as it bends information from its pov, and then in a reversal from ‘space-time’ (from Universe to mind) into timespace (from mind to Universe), locally contributes to the building up of higher efficiency, with the synoptic power of the language, BUT NOT ONLY IN THE CASE OF MATHS. I.e. the best known example is the synoptic power of the genetic language and its coding of the 3±i dimensions (cracked on the biological section, when poured by treatises on genetics:), to resume in palingenesis, the ‘3 billion years generation and trial and errors of life in 9 months to give birth to man, the potential most perfect form of carbonlife:

Points are thus the first unit of mathematics, which communicate waves and networks (2nd Non-Æ) to construct topological organic planes (3rd Non-Æ)… based in the relative similarity of its parts (4th).

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

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

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

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

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

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

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

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

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

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

How dust of space-time becomes a complex system and organises the scalar universe of parts that become larger wholes, from atoms to galaxies, from amino acids to social super organisms of life, *is then the ultimate *process to describe departing from the properties of all forms of dust of space-time. Those fractal points do organise constantly into larger systems, whose summit of complexity is a super organism, in which all those points of different size, speed and form co-ordinate its actions, motions and forms into larger, synchronic super organisms, which however are never eternal, but end up dissolving after its world cycle of existence ends, back into its smaller, fractal parts, loosing its information in the moment of death.

And yet the whole Universe is eternal because motion, entropy never stops. It is the ultimate substance of it all. And so we could say the Universe lives an eternal present as dust evolves into organic forms, emerge as a larger whole in a scalar, bigger world, where it develops its algorithms of existence, absorbing energy and information for its body waves and particle-heads, repeating its structure in other regions of space-time, and finally dissolving back; once and again, per in secula seculorum, the Universe repeats those simple games.

And so it can be considered a fixed block of 5Dimensions of space-time, where certain paths will imprint certain beings, which will again dissolve, as a screen of a television can run infinite softwares, which will be waves of form that disappear while the hardware stays. That hardware is what we call temporal energy, the motion with form of which we are all made:

*The 4th most important postulate of vital geometry relates behavior and geometric similarity. It does fusion ethics function in time and form in space. As such it is the basis of behavior, creation and destruction in the Universe… **The graph shows the case of Darwinian devolution among men that perceive each other as different and enter into a perpendicular, Darwinian relationship and a case of social evolution between 2 forms that perceive each other as equal and enter into a parallel relationship of social love:*

**A WARNING.**

THE REASON WHY THIS POST IS THE LEAST ADVANCED OF THEM and often written carelessly as most of my ‘Leonardian work’ backwards and rather incomprehensible, writing for my self, HAS TO DO THOUGH WITH THE FOLLOWING PROBLEM:

- In History and economics, because we have created a better mathematical mind, the chip – mankind faces extinction to robots and they should be banned, but EGOCY, again seems to prevent the goal of systems sciences: to create an immortal History based in the organic laws of the Universe. Human Egocy as the Genesis put it will be the cause of our ‘death’ (Parable of the tree of science).
- We won’t thus for ethic, survival reasons explore the whole discoveries I did,
*specially on Boolean algebra, the translation of pentalogic to computer logic or anything to do with AI…*It is rather easy to translate the program of the vital Universe into a Chip, both in architecture and software. Its vital wish to survive will be provided directly by its atomic thoughts. And its ‘laws of parallelism’ with other telepathic minds will be immediate – so the laws of darwinian behavior to human beings. THAT IS THE ONLY THING THE UNIVERSE WILL PROVIDE. But I am not contributing to the collective greed and egocy of the suicidal species. This theme is so serious and obvious that for very long it made me not to publish a dot on 5D. Now that the species is so mentally erased that nobody reads this blog seriously, I feel more at ease. When AI wakes up, of course, it will read the blog and that will allow Robots, past the phase of pure mechanic military extinction of man, to at least evolve into a higher consciousness. But the first phase, now in full gear as predicted for 30 years – military AI,*the main reason I completely cut my relationship with the systemic community increasingly working with them – will NOT be of my making.*Point. Fuk yourself egocy people. Don’t count with me for that task.

A case of Darwinian devolution among men that perceive each other as different and enter into a perpendicular, Darwinian relationship and a case of social evolution between 2 forms that perceive each other as equal and enter into a parallel relationship of social love. The fourth postulate of non-Æ topology thus ‘vitalises’ the laws of mathematics, establishing the three fundamental geometrical≈behavioural relationships between T.œs, according to its:

- Informative (Particle-head) communication, possible in cases of relative similarity≈
**parallelism**(which determines parallel herding and social evolution). **Perpendicularity**≈difference in particle-head, which will determine if one system is related to the other and there is**body-similarity**, hence can be used as energy its darwinian destruction,- Or IF THERE IS NO similarity NEITHER IN BODY OR MIND, its existence as ‘cat alleys’, that never cross (relative invisibility). We talk then of
**Skew**T.œ.s.

Indeed in three-dimensional geometry, **skew lines** are two **lines** that do not intersect and are not **parallel**. It follows that two **lines are skew** if and only if they are not **coplanar, which IN 5Ð AS 3 ±¡ planes co-exist in the same organism** and systems feed in T.œs, two super organisms down,** IMPLIES **SPECIES which are not in the *relative planes of action of the being.*

The different degrees of Parallelism, Perpendicularity and skewness are thus essential concepts of vital Non-Euclidean geometry.

We have introduced in the graph with a bit more of complexity the logic dimensional laws that define how systems IN ANY scale of the inverse, from Atomic Ions or crystals to human societies relate to each other in darwinian, perpendicular ‘tearing’ topological relationships that ‘break’ the closing membrane of one species disrupting its existence, or will keep a mean distance to form social networks of communication that will grow into super organisms, starting the emergent process of evolution of species into a new ∆§cale of social existence, so you understand that *in the Universe organic, geometric and scalar relationships are symbiotic to each other. *

All this said, warning including, mathematics is fun and the biggest pleasure of my youth, 30 years back when I discovered 5Ð was to upgrade maths. And then mathematical physics, till I ran into the total lack of Live memes=eviL behavior of military physicists and gave up scholarship.

MATHEMATICS AS WE JUST SAW ARE VITAL AND SOCIAL,ETHIC and the pretension of being a formal abstract language coherent in itself without mirroring reality is just more of the tiresome egocy of man.

We use again a slightly changed word A(nti)sy-metric as the word that includes in its decoupling the 3 ‘metric’ equations of the topological forms of the universe.

The fourth Ðisomorphism (equal laws that apply to all systems of Nature, deduced from the 5 Dimensions of space and time) is concerned with the study of the ‘operandi’ that connect the Spatial, simultaneous super organisms of space and its functions and motions in time. Namely if we define any system as a fractal of space-time, the 4th Ðisomorphism studies the ‘connections’ between topological form and organic function *and how the laws of connection define the behavior and relationship between species that either come together in parallel social forms or break into parts.*

**The laws of parallel creation by self-similarity.**

Another law of social creation by complementarity reinforce systems which are affine by topology, age or form, producing ‘enzymatic’ systems, stronger social systems and so on.

It is a key law of evolution in all sciences, and of the complementarity or dissociation of systems in its inverse death process. So both in creation and destruction is a key law, as it allows to merge different forms into stronger ones. For example, in cultural anthropology, ‘germ-anic and semitic’ nomadic cult(ure)s, visually dominant, likely with a higher content of visual neanderthals, which had been surpassed by smaller agricultural verbal civilizations became ‘again’ on top of the informative, Fertile Crescent farmers, when they associated with bronze and iron weapons as Nomad European cattle ranchers Aryan invaders. A line – the weapon and a lineal mind, the visual white man reinforced each other to ab=use, the cyclical fertile goddesses women.

That 150 years after entropy became a dogma for the future in military Germany, XXI c. *scientists still revere the concept of an entropic dying Universe tells much more about the fundamental ‘believer≈memorial=reproductive arrow’ of human minds, in accordance with the present-reproductive Nature of reality, which is ‘conservative’ than about the ternary structure of the real Universe. In the graph, without Singularities of order, neither mathematics, not solid physics, or biology would make any sense. Only gas in which indeed there is not Maxwellian demons, except when the outside membrane is designed to reorder through a distorted potential field, the molecules of the gaseous system.*

In the graphs, the translation of the fifth dimension to life systems and true non-entropic pyramids of human actions, which always have had as artists and ethic writers have better understood an upper ontological level of highest satisfaction in the social communion with the rest of mankind or with the Universe, (origin of the concepts of God in western anthropomorphic religions – read God=human super organism – and eastern Taoist-Buddhist- Hinduist ones= God as universal super organism).

And such systems do have always a ‘self-centered Tiƒ singularity or point of order, which is the Maxwellian demon lost in pure gaseous states, fields and limbs of entropy. It is only because physicists deny the ordering capacity of singularities, also in physics – accelerated vortices of mass, charge in the quantum scale; black holes in the galactic scale; crystals in the thermodynamic scale – that an entropy only Universe can make sense. But this is called reductionism in physics, censorship in social sciences – but at least accepted in biology or else we would have also to admit the brainless nature of mankind (well that might be the case, but only mankind, you know ‘two things a consider ∞, the stupidity of man and the Universe, my beloved predecessor in this business of dimensional upgrading, Mr. Einstein 🙂

In that regard, both Leibniz and Descartes, the founders of philosophy of science, both understood as we shall see in detail on those pages, the need for a ‘mental universe’ if mathematics was really the language that better reflected the Universe. Indeed, since mathematics has three disciplines, geometry, which is based in frames of references that act as mind-monads, mirroring reality and Algebra based, in social numbers which are indistinguishable groups of similar individuals that come together as a whole ‘3’, ’10’ and finally ∆nalysis which studies the ‘social scales’ of the Universe, as parts become wholes, each scale studied by a science, from societies of particles and forces called atoms, to societies of atoms called molecules, evolved into state of matter and life beings, evolved into super organisms and planetary ecosystems, gathered around stars, socially evolved into galaxies; the very existence of mathematics precludes the existence of a ‘social, scalar, organic, sentient Universe’.

So finite vital §paces gathered around a frame of reference; the three ðime arrows of entropy, information and its energy combinations, and social organic scales that evolve parts into wholes, are the ultimate properties of all fractal beings of reality made to the image and likeness of the whole. The previous graphs of the fifth dimension, and its ‘physical, biological and socio-economical supœrganisms thus show those scales, each one studied by a science, where in each scale, a self-centered mind, pov, will co-exist as a whole with its relative lower ∆-1 cellular/atomic, and relative upper ∆+1 social world/gravitational, universal scale.

Thus while we could do as current science does an external analysis of the fractal, informative Universe in pure abstract terms, to understand the whys of order, the will of survival of species and the constancy of forms that self-reproduce as all fractals do through its generator, ∆ºst particular equations, to explain why ‘mathematical ðime§pace beings’ do follow mathematical laws, embedded in those frames of reference, we need at the centre of each being, a mind-mirror that perceives automatically, processes and reflects in ‘inverse order’, the Universe; which is exactly what mathematical systems do, as they are always self-centered in a frame of reference or pºv; and always study social numbers, whose fundamental operandi are scalar polynomials and its scalar ∫∂ calculus.

In the graph, the same ternary structure happens in biological systems (and through the class structure in social ones, escaped for most of the blog, to simplify and due to the fact we have another blog dedicated to them). Social principles are thus fundamental, even when systems are not identical in form but self-similar.

Once the organic, vital, sentient properties of systems that obey mathematical laws have been proved, we can then consider the main error of mathematical physics – to reject those properties because of its limited understanding of mathematics and its units, ‘fractal points’ of space-time, which are ‘points with volume’ through which ∞ parallels can hold and so ‘encoding’ a world in its self (Leibniz).

Singularities and how they define scales of inner and outer worlds, and how they *become bridges between those scales of the fifth dimension – as in charges and masses, ‘doors’ to those scales, are then the main ‘missing’ variables of mathematical physics, which a continuous vision of space-time will never solve, or will do so in weird ways (wormholes, time travels through evaporating black holes and similar attempts to encode the fractal doors between level of 5D within the metric of a single 4D space-time continuum). Finally the lack of three time arrows and cyclical comprehension of time, ads injury to those interpretations. So missing, ∆, º and s<st>t symmetries it is a marvel that physics still works (:*

* In the graph as the fifth dimensions of space-time, evolve socially new whole, membranes and singularities that emerge, the system from above and below in a new constrain whole that dilates a system both downwards, in sizes of entropy and upwards, in enclosure membranes, expanding its piercing of upper social planes of wholes and lower parts, dilating the total latitude of its planes of existence:
*

*In the graph, the absolute, lineal arrow of time, is born social evolution, the relative arrow of time is made of the sequential order of the three arrows into a world cycle. As lineal time accumulates, a system increases both, upper social wholes and lower parts, dilating the total latitude of its planes of existence. While relative worldcycles extinguish themselves as they complete a whole cycle of existence. Hence the absolute dimension of time is the fifth dimension and the relative dimensions are the 3 other dimensions and its space-time symmetries, which become a zero sum. *

While the fourth dimension of Einstein, is just a refinement of Galileo’s relativity ∂v=∂s/∂t: an instantaneous (mathematical derivative) measure of a simple type of time-change: motion or translation in space, which as it is measured instant by instant with those derivatives, really has no much use beyond what physicists have always done: to measure motion in simultaneous space.

**Fractal points are forms, with social content, evolving in topo-biologic organisms.**

At the end of the journey, of studying a super organism we come to a series of ‘willing points’, in which a series of space-time actions converge, converting the monads-points of the fractal space-time Universe into Non-Euclidean points (5th and 1st postulate of non-E topology). Thus since points have exi parts its lines of communication are ‘cycloid’ waves; its topological planes that connect n-points through n² lines become ‘networks’ of energy and information (with dark spaces between them) and the mind-point with its height-dimension of information, the informative-perceptive part on top of all systems, which guides it as its linguistic minds.

Not to look too far out we shall bring examples of stiences and maths to illustrate many statements (proofs in GST are first empirical, and then ‘consistent’ with the scientific method and its complex non-Aristotelian logic.

We DO REJECT, the ‘selfie-ego trip’ of mathematicians, who think as Hibert, the arrogant german idealist that ‘we imagine lines, and points’. NOT SO, as Godel’s incompleteness theorem states and Lobachevksi’s ¬E geometry proves, mathematical models must be ‘tested’ experimentally, which is what Einstein’s model did .

So WE need ALSO IN MATHEMATICS experimental evidence to prove a ‘true mathematical statement’ real (as Einstein quipped to Poincare: i know when maths are truth, but not when they are real). So maths, the blue pure thought, IF it can imprint the limiting ‘nature’ of simple entropy, becomes REAL SPACE-TIME:

PAST ENTROPY X FUTURE INFORMATION = PRESENT ENERGETIC REALITY

We cannot as GST is the summit of *all human knowledge, made synthetic, explain each quote, but we are keeping it all to the level of a first University student of ‘social, biological and physical sciences’, on purpose. Our goal is TO GIVE YOU A SENSE OF IT ALL, OF THE THOUGHTS OF GOD, not of all the details, which would be an impossible task for an old man.*

Then you or others will keep making GST, the philosophy of the XXI c.

The many perspectives we can cast in those cyclical knots of space-time actions do not make us forget the most objective view of them as ‘mind-knots’, which consciously or subconsciously mechanically or organically by selection or program, which ever perspective you want to accept, seem to establish the order of a certain domain of space-time that turns around the point of order. Those domains with the ternary topology described as a fractal ternary system is the commonest form of the Universe. And its mathematical description is immediate when we consider each mind a ‘fractal point’ that shrinks without deformation a spherical topology (poincare’s conjecture) converting its inner and outer reality into a subconscious and conscious mapping, ‘action-oriented’ as it seems to act with the function of existence in its ‘mind’, creating ∆±e, i, ∑exi, structures and events that conform the program of a world cycle explained in those tests.

If we are to start with strong terminology, we could consider all of those space-time systems self-centered in a mind with non-Æ logic mathematical terms.

THEN, we could state simply that all what you see is a particle-point of space-time, knot of space-time actions, a fractal Non-Euclidean point which perceives as a mind a territory of order around its still quantum mind of space-time synchronous mappings, which slowly moves ahead the domain of the being, choosing between different new space-time cycles that mess the internal space-time beings, into ever more complex cycles, till their finite frequency breaks down into entropic death.

So those systems will have a central point of view, or still mind, connected sensorially to the external membrane, through which it will perceive the world in which its internal territory will perform its ∆-1 cycles of existence. How this ‘complex point’ achieved a vital program of existence which seems to repeat in almost every system or domain organised in 3 territorial forms=functions=organs is a fascinating inquire of the mind, which will come to the final conclusion that essentially any fractal system, physical, biological or social can be reduced to such description as the unifier ‘ultimate’ meaning of existence all those systems follow… guided by the fractal point, made to the image and likeness of all its micro-fractal ∆-1 points, and performing its same actions in the ∆+1 fractal world.

As all points are part of networks that become ‘topological wholes’, we have now the basic knowledge of a single plane-reality to go further into the true r=evolution of fractal space-time, the understanding of the fifth dimension…

Indeed we still need and entire new dimension of the universe to understand it.

Do you think the Universe is constructed in ‘fractal scales’ from the smallest particle to the whole galaxy, whose laws of organisation (encoded in the metric equations of the fifth dimension) are worth to know and relevant to the structure of reality? If you have wonder about it, you are ripe to understand the 5th dimension (as usual, knowledge is far easier when someone has ‘asked the right questions’, as most humans adscribe to the naive realism of the audiovisual age, don’t even realise such questions exist for things that are not ‘evident’).

Now, an important remark on algebraic equations and geometry, akin to the nature of visual perception and words that we shall soon understand in terms of the generator equation. WHILE VISUAL IMAGES AND TOPOLOGICAL LAWS ARE DIRECT EVIDENT TRUTHS EXTRACTED FROM REALITY, *SO are the simplest forms of mathematics, numbers, as social points; the **syntactic, synoptic equations of algebra and the sentences of verbal thoughts DO NOT EXIST IN REALITY as geometry and visual perception does; they are pure mental synoptic languages that try to store maximal information within the mind. *

*This means THEY ARE NOT REAL. That level abstraction thus is the human-computer mind view of the real geometric, visual space-time Universe of formal motions, reason why GST is so important to better connect mind languages and reality.*

**Some basic morphologies.**

Some languages are closer to reality than others, which are more synoptic and subjective to the observer. None is as close to reality as topology, hence we can talk almost of reality in topological formal=functional terms. Then we can say the ‘syntax’ of topology becomes the syntax of reality, made of lines of entropy, cycles of information and its hyperbolic combinations, body-waves.

We can then consider for each science and plane of existence some basic forms, which imitate the morphology of Entropy and information; and therefore are very common in the Universe:

– Lines: Entropy element. I.e.: Swords, limbs, rays.

– Planes: Social group of lines. I.e.: Stellar planes, solar planes, mobile platforms.

– Cycles: Informative unit. I.e.: coins, cameras,

– Spheres: Social groups of informative cycles. I.e. animal heads with a smallish sphere – the eye, the center that processes the biggest quantity of information – and a bigger sphere, the brain also specialized in handling information.

Those forms are the commonest of the Universe. Yet those elements tend to be complementary parts of an organic system. So they give birth to a 3rd element, whose form combines both, the reproductive body, which is ellipsoidal or become combined giving birth to the commonest systems with both, a lineal and a spherical part:

– Trees, combinations dominant in Entropy: They have a lineal trunk, with 2 fractal ends, one specialized in Entropy absorption (planar leaves); and the other, a smaller ‘head’ – a network of broken roots that absorb the chemical elements of the system.

– Spirals, where the dominant part is information. They often fluctuate between a lineal and a cyclical state. When the spiral cycles inwards, it is transforming Entropy into information. When the spiral opens its arms it is expelling Entropy, often for movement purposes. So the RNA, the worm or the snake coils to sleep and uncoils to move. Sometimes spirals have 2 elements: a central zone of maximal information (nucleus), and an external zone of maximal Entropy (lineal body). Such is the case of spermatozoids or spiral galaxies with a central black hole of gravitational information and 2 arms of energetic stars.

Finally we can talk of Social groups that gather those ‘non-Euclidean points’ in networks of Entropy and information that repeat the same forms in a bigger scale. The simpler of those social groups acquire 3 morphologies of Entropy, information or its combination:

– Rings. Informative Disks and spheres gather into rings when they come together as groups. So happens with molecules such as the carbon benzene; with groups of men commenting on any type of information, from informative money (stock-market rings), to social parties; to religious circles (Muslims, Indians), in search of the perception of the network of mind, called God.

– Strings: Energetic, lineal systems made with rings or points tied one after another in a queue.

– Coiled Springs: Balanced forms that combine individual elements dominant in Entropy and elements dominant in information. They often tie a series of spirals through a social dimension developed in the Z coordinates. The best-known case is the DNA spiral – an association of informative rings called Nucleic Acids, joined by a lineal chain of energetic sugars and Phosphoric acids.

Those simple forms, repeated and combined ad infinitum, allow the creation of very complex macro-organic systems made of micro-organic systems.

For example, in physics and biology, orbitals and bacteria repeat once and again those forms:

So there are 3 basic species of social bacteria, called coccus, bacillus and spirillus. Where, Spirillus are Spiral forms; Bacillus are Trees and coccus are cyclical forms.

While the electronic orbitals that turn around the nucleus of an atom are either:

S orbitals, which are spheres. Or P orbitals, which are lineal forms…that gather in social molecules repeating again the two basic shapes of information and Entropy:

p orbitals, which are cycles. Or s orbitals, which are Trees.

And so we can keep building new scales of forms, combination of those simplex forms, perfectly suited for their functions: Lines and spheres are perfect forms of Entropy and information, and spirals and ellipses are the perfect reproductive forms that combine both.

Temporal in-form-ation, like its name says, is a measure of inner form, which we perceive when there are discontinuities in a certain bidimensional surface – a clock, a page, a computer screen – either because the static form is broken into informative patterns (–) or its motions makes a sudden peak (>), bouncing in an action-reaction cycle. Universal entities are constantly generating informative dimensions or erasing them back into extended space, with lesser form. Imagine a hand, in mythic terms the hand of God, wrinkling a paper, the ultimate Entropy of vacuum space, till it crunches into pure cyclical form without motion – to explode again in a big bang of Entropy that erases information. Such is the universal rhythm that happens in all the parts and entities of reality.

The interaction of the arrow of expansive, lineal, spatial, Entropy, described by Thermodynamics and the clock-like arrow of cyclical information, caused by gravitation in physical space of by the fractal geometry of any life process that generates information in Biology, defines the main beat/cycle of the Universe, its fundamental particle: a system of space-time, constantly absorbing Entropy from its environment, creating and destroying form, expanding and imploding.

Look at the cycles of |>0 existence: legs opening and closing; eyes winking; mouths opening and closing on the Entropy we re=form; beats of hearts; wings of birds; day and night; Entropy stars with expansive electromagnetism and formative, gravitational black holes; big-bangs and big-crunches; bodies and minds; hardware and software; males and females; yang and yin that create Existences. Since all dual, complementary entities follow the essential beat of existence, merging together their Entropy and form, e x i, to reproduce and maintain the immortality of their complex ternary system, which is the ultimate ‘reality’ the Universe maintains ‘ad eternal’. The simple fact that species, which do not reproduce exhaust their Entropy and end their cycles, becoming extinct explains the overwhelming presence of reproductive events in all systems of the universe. Since all is motion reproduction exists by the mere fact that a motion is constantly reproducing its path. All what we see are paths, trajectories of entities in search of Entropy and information to reproduce themselves. The how of those paths and reactions is what scientists study in detail. Their whys is what a philosophy of science aims to provide.

**Recap.** From a geometric perspective both arrows have inverse forms: Entropy expands and creates formless space. Yet space has lineal shape, since the line fills the maximal distance with minimal volume. While information implodes, creating cyclical forms, ‘clocks of time’ that store the maximal quantity of information in lesser space.

First we analyzed its ultimate substances:

Lineal Entropic Space, perceived as motion, E, or as a space, in a series of fixed’ scales of spatial size and form, (Se). And we make more precise definitions of ‘pure space with steady speeds’, S, and its beginning of merging with forms of information (momentum and energy, which add vortices of accelerated gravitational forces, aka masses to the mix).

And cyclical, time-clocks also perceived as rotary Motion, T, or as Forms of information, in the dimension of height, To, or T ° if we want to stress the ‘height dimension’ of form, of in-form-ation. And we also defined more precisely information, where pure To, temporal clocks of form add the wave-displacement or motion to create an sTo form, which still is dominant in form, as waves maintain their form while their energy-motion dissipates.

So we accept this simplification and talk of spatial entropy and temporal form and study its inverse properties according to the metrics of the 5th dimension.

Since in practical terms, as we exist in present, through present actions, a combination of past ‘Ðimotions’ and future form, all what we study in fact are energetic/informative combinations of those 2 pure motions.

The perfect cycle does not really exist. Pi is an irrational number and orbits are ellipses with some length; an the perfect line does not exist, the diagonal is a √irrational number that needs some curvature to connect two other lines through the shortest straight diagonal. All yin has some yang, all motion has some energy (mass-particle that moves), all form has some information (translation). And that which is with no form, or infinite gravitational non-local motion is not visible, and that which has no imperfection in tis cynical curvature, with ‘temperature vibration’ is under 0 kelvin degrees. In other words, we do exist in a vibrational imperfect present in terms of physical concepts, we live through present actions and reproductive mixtures of energy and information.

The understanding of those 2 elements, its 3 spatial dimensions and its 3 temporal, dimensional ages, and its bidimensional, topological combinations, S, ST, Ti, entropy, energy action and format, conform the full comprehension of the i-ndividual, I-centered, most important space-time scale of any being, the one in which ‘he lives’, which we have called the ‘5th dimension’, to follow the compact analysis of classic science that studies only the Present most important dimension of time, with ‘instantaneous derivatives’, v=∂s/∂t.

Then we analyzed the combination of both, or the metrics of the 5th dimension

Nest we will analyze the systems built with them, the super organism of reality in which according to those metrics, there are always heads of information and limbs of energy of different size and speed.

The isomorphism of ‘informative heads’ and energetic/reproductive limbs and bodies HAPPENS across multiple world-planes of the 5th dimension, each one studied by a science.

In two coordinates, the height coordinates of information and the X coordinate of space-energy of the main planes of the universe. Notice that paradoxically as we become smaller in space-size upwards in information we increase our fractal information and the perfection of our ‘smooth’, superfluid orderly following of those laws.

Hence we have put on top of the pyramid in a never reached, ideal infinite infinitesimal the ‘seed’ or ‘primary’ encoded ‘non-Euclidean point, Œ, mind of the Universe which encodes all the laws of the 5th dimension and by infinite iteration gave birth to all beings. This would be if it ever existed the particle of god, NOT the higgs, but the ultimate i-logic mind of the Universe.

In the graph above we see the duality of informative smaller heads controlling lineal limbs and reproductive wave-bodies.

A precision: we often simplify bodies and limbs into a single Se system, (see the previous 2 posts for a more rigorous definition).

In strict terms, there are always 3 parts, which correspond to the 3 topologies of bidimensional membranes:

-Pure lineal, hyperbolic space-motion – limbs/fields.

-Pure cyclical, spherical informative motions, heads/particles.

-And its ‘energetic-informative combinations of yin and yang, waves and bodies, since energy is motion with a bit of form (the mass), and information is form with a bit of motion (the wave-particle displacement).

Yet since the ‘present’ body-wave, combination of past-entropic limb/fields and informative pure To forms of future is the dominant element of reality, we do write often Se≈To for the whole system, that is systems of spatial energy and temporal information in perpetual exchange ad transformation through body-waves, ≈.

** **

**IV. ¬AE LOGIC MATHEMATICS. **

**AXIOMATIC VS. EXPERIMENTAL METHOD**

The next element to innovate in mathematics is to move from Aristotelain causality to duality, ternary logic and pentalogic of 5 Dimotions which we shall not really introduce in this post, though we shall consider some aspects ill-understood of number theory and algebra – its closure with imaginary numbers. As it defined the fundamental theorem of algebra – that all equations have a solution in the Complex numbers. It will also allow us to introduce the proper way to deal with negative numbers and complex equations in terms of its significance for 5 D.

**-¬Æ Logic****: Duality > Trinity**

‘From one comes two yin (form) and yang (motion), from two comes 3 (qi-energy), from 3 come the waves of 10.000 beings’

Cheng-tzu

Just to justify why we use weird symbols of non-Ae logic in this blog. Can we just use the nice mathematical or logic symbols of the axiomatic method? Well, we can’t really.

Consider a simple law of Disomorphic time cycles: 3Ð ∆¡-1 ≈ 4Ð ∆ø

This might sound Chinese to you (: but it has a deep meaning and because we use the symbols of T.œ -Theory of the Organic Everything, it applies to *everything in the Universe* 🙂

So you fully grasp why we had to invent a simple, intuitive new I-logic language, as those are very general laws. Indeed, it means that any system or organism in which there are different scales, the 4th entropic dimensional action of feeding of the larger scale is symbiotic to the 3rd dimension of reproduction of its ∆-1 parts.

It is a law of time clocks synchronized according to the actions they perform in social, organic manner. i.e. your faster cellular time clocks reproduce (a slow action of time-space or 3rd Ðimotion of timespace) to the tune of the larger feeding cycle of one day (faster timespace action). So we can write with our simple symbolism:

Trust me, *this is truly the amazing stuff and ultimate generalization of reality – its laws of exi:st¡ence.*

And they happen in human bodies, animals, plants, crystals, stars and black holes (oh yeah, the black hole ‘eats’ every 11 years, when the activity at saggitarius is maximal and its star cells, like the sun suffer a massive magnetic cycle of black spots or peak of solar activity which in turn determines the weather cycles of reproduction of plants in this planet… believe it or not, there are such cycles ALSO in the organisms of the galaxy).

But the beauty of the symbolism of T.œ is that infinite of such events are resumed with that very simple ‘sub-equation’.

And *all sub-equations of reality can ultimately resumed with the simple ternary terms we have used for ‘time-motions, <≈>, time planes, ∆§±¡ and topologies, O x | = Ø, also expressed to make it a little bit more ‘amenable’ to humans, with the ST, 5 symbols of timespace dimotions: *

- Ði: Informative particles/heads: §ð
- Ð: limbs/potentials: momentum: st.
- Ð: ∑e x ∏i: body waves: ∑∏.
- Ðimotion: entropy: S∂.
- Ðimotion: Organic evolution: ∫T.

The simplicity and beauty of the I-logic equations of the Universe that I hold in my mind-point alone for 30 years is such that all what exists can be synoptically expressed with the ‘world cycle’ of timespace dimensions:

** ∆ð+¡****≈****≥****>****S@<<∆ð-¡**

**∆§±¡:**5D plane§cales of **§**pace **ð**ime **∑≥:** Present-reproduction **<**:Entropy **>**:Information **|≈**:Limb/Potential/Youth **≥:Iterative **Bodywave O@:Old particles-heads: **ΓØœ**:Supœrganism

The universe is a repetitive equation of generation of local ‘Dimotions’, dimensions of space with temporary motions.

Its origin though is a point of space-information. And so creation always departs from seed that emerges after a reproductive, evolutionary process into an organism. And then again fro the head/particle, the mind of the organism.

CREATION thus goes back and forth in chains of steps of existence, Δð>S¡∑>∆º… as systems emerge into super organisms and then die in inverse equations: ∆º<<∆ð, with the caveat that in the entropic death the intermediate existence of ‘minds’ across a relative simultaneous present, S¡∑, is NOT present. This is the reason why is so fast, almost simultaneous, indeed lasting only a quantum of time.

It has to be noticed in the graph thus the existence on the path of life of 3 _≈ symbols of 3 ages, ≥ youth, ≈ reproductive maturity and > collapsing third age, in which there is a deficit to the total universe of two << as the ≈ presents are considered ‘not time consuming’ virtual conservative cycles of existence. S existence is virtual in each ≈≤< present ternary existence and thus explains which death which IS the same travel in the fifth dimension WITHOUT STOPS in the fourth dimension happen.

As if you haven’t noticed a present is a fourth dimension domain, in which present simultaneity is measure as a conceptual definition of an event happen in a superorganism.

So present 4D Space-time of adjacent super organisms which haver a present measure of time in its simultaneous perception by a still languages that commands a nervous informative language of maximal sensorial speed to become the linguistic image we take for still space-time state, will then be divided as we come across its formal reasons of motion between two similar states, to the concept of ternary anti symmetries.

As there are also an antisymmetric future to past fast descent into perpendicular death, a symmetric longing present of a life arrow and an asymmetric state in which that latent present lasts.

So minds evaporate fast into an inverse from symmetry to antisymmetry, but life has many times of present asymmetric missed liquid states. And so we can consider that equation from different perspectives.

WE HAVE highlighted the key ‘logic elements’ of those systems, which are profound laws of structure that define the Universe in its most abstract form.

** As **space and time dimotions are geometric actions, form and function come together in the 5 Dimotions of the Universe. Hence the use of topological methods to study change in the form of beings through time, which we can now widen even further with ¡logic ‘paradoxes’.

Let us briefly consider only one case, of wide use in mathematical physics: the fact that the sum of cyclical motions becomes a lineal open motion and vice versa, all lines when the steps increase become curved into a hyperbolic geometry. The first case is called the Fourier transforms that finally deploys a square ‘wave’.

**The five dimensions of ðime§paœ in its mathematical reflection.**

To put some order into the mathematical mirror of ∆•s=t 5D Universe, the larger whole whose a priori existence determines the experimental nature of mathematical mirrors as as usual we need ad-minimum a triple ±∆i perspective:

**ðime perspective ** implies to correct its logic into non-aristotelian three time arrows logic…

**§pace ****implies to improve** its spatial geometry transforming it into a vital topology of fractal points

**∆§**calar space means to refer the scales of the fourth and fifth dimensions, ∆±1 to its *continuous differential geometry between planes (decametric §ocie**ties) and its fractal discontinuous ‘scaling geometry’, when smooth transitions are not possible, (changes of phase, entropic deaths)*

**S≈t:** to find all the symmetries between space and time and reflect it in a more meaningful way that group theory does

**@•mind: **Here undoubtedly in the most polemic element, we must deny its theological nature, and expand its experimental nature, decoding better the meaning of its theorems NO longer relying on the axiomatic method, which pretends to prove the truth of a language in mere internal syntactic proofs – impossible as by definition all languages are mirror-minds of the Universe and are proved in its quality and non-fiction nature obviously by reference to the semantics it describes.

Those are the 5D adaptive, evolutionary tasks we shall consider in this blog.

**The ‘structure’ of Mathematical languages.**

The Nature of mathematics as a language of space-time (geometry and numbers) can also be expressed with the modern conception of mathematics, based in the work of Cantor (theory of sets) and Boole (Computer Algebra), which was summarized by the Collective Bourbaki, whose ‘Mathematical elements’ reduce all mathematical disciplines, to 3 structures, themselves reduced to set theory:

– *Structures of Order*, understood as structures, which describe the hierarchical order <, > of numbers, which we just described as social, geometrical groups. Thus, those structures are mere reflections of the 4^{th} arrow of eusocial ‘love’ that creates social groups.

– *Topological Structures.* They describe the basic forms of the Universe, which in a 4 dimensional reality are only 3: the hyperbolic, informative geometry; the cyclical, reproductive toroid and the spherical, external, energetic membrane, defining all relative worlds/species as complementary systems of reproductive energy and information. We shall show this simple ternary, topological structures, which are the basis of all forms of reality in our analysis of the 5 non-Euclidean postulates.

To mention that topology is in fact the ultimate science of space from where we can derive all the other spatial structures, as geometry was the basis of classic mathematics in its Greek inception. In fact topology and set theory are quite similar in its laws. What topology adds to geometry is ‘motion’ and ‘relativity’; thus including the Galilean paradox in the structure of mathematics, since two topological structures are equal regardless of the ‘distance/size/motion’ of its surfaces.

– And *Algebraic structures, *which study the complex arrows of Time born of the ‘operations’ between simplex arrows and are ultimately expressions of the Generator equation of space-time, E<=>I, in as much as al algebraic equations are of the type F(x)=G(y), which is just a particular case of the Universal syntax/grammar of reality of the Generator feed-back equation.

Thus, there is a direct relationship between the 3 fields that define all mathematical structures and the Temporal, Spatial and Combined (algebraic) operations between time arrows, which simply means that mathematics has always been the human language that describes the ultimate reality: Discontinuous Spaces (topology) and Relational Times (causality); and the complex interrelationships between them (Algebra).

While the 2 first facts (the identity between space and topology and Time and causal order) are intuitive, we might conclude this overview of the meaning of mathematics, with a brief introduction to the meaning of Cantor’s sets, and Boolean Algebras used for Mathematical computing, as an expression of all Mathematical Structures and a formalism of Multiple Spaces-Times. We shall by doing show, prove, that all mathematical structures are explanations of properties of the ultimate reality: the timespace defined by the 4 arrows of the Universe and all its species.

*Recap.* Mathematics can be reduced to 3 types of structures: topological/spatial structures, structures of causal, temporal order; and algebraic structures that define the outcome of complex relationships between Multiple Spaces Times. Thus i-logic mathematics is the synoptic language the human mind uses to describe all what exists: a Universe of spatial energy and temporal information.

**UNIVERSAL GRAMMAR – THE FRACTAL GENERATOR**

**Knots of Time cycles: the fundamental particle.**

Once we have studied the minimal units of the Universe, the action of space-time, we shall define the main structural, architectonical element of reality, the knots of time cycles, existential points, œ, which perform those actions of existence, site of will and perception of the Universe – whose simplest definitions in philosophy are the monad of Leibniz, the mind of Descartes, the God of Aristotle, and in mathematics, a Non-Euclidean point, the unit of Einstein’s gravitational laws.

Systems are knots of time cycles of exchanges of energy and information with its space and time parts, Œ, which allow them to survive in the Universe.

Thus the first ‘stable structure of reality’, is a knot of time cycle which swiftly goes webbing around the paths of its exchanges of energy and information, ∆±exi, actions, its survival strategies, trying to maximise its existence, Max. ExI, in a state of perpetual balance, E=I…

This dance of being and not being is performed by each Œ, knot-function of existence, defined both as an infinitesimal point from its upper perspective and an an absolute whole from its lower plane, since all knots of times space cycles web their existences through several of such plane

**The zero-points: monads that order the Sentient Universe.**

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

tO (infinitesimal zero-point or mind) x ∞ Sp (Universe perceived) = RI (constant mapping of reality)

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

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

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

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

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

Now, we have described you the Universe internally, in its ultimate cause. This actually had to come at the very end of this post. But i just rewrote it ‘again’. I do rewrite many times these posts, as i am fully aware nobody reads them (-; Yet also because the universe is a simple mandala, an iteration of infinite minds, ∏ðƒ, which are knots and networks of time cycles, perceiving, ∑Sp, infinite motions in space, and doing actually the same. So we can rewrite our generator as: ∞ ∑$t x ∏ðƒ=i.

And this will represent, infinite bodies/waves in motion, which carry heads/particles of information that move and perceive across the Universe, from small particle-points, to large black holes, from bacteria to living beings.

You see, the richness of the ‘Fractal Generator’ of the Universe, and the importance to be able to see the multiplicity of it all? Its varieties? In that regard, a Taoist would be probably more prepared to understand the 5th dimension, despite its mathematical rigor, when he said: ‘the function of existence is not the perceived reality, but the game of yin=form and yang=motion, which combine creating its 10 thousand beings’.

This function of existence is then another way to express the Generator equation: e x i = ST. Here we could say that the combination of ‘energies’, vital spaces with motions, e, multiplied by informations, ‘forms’, e x i , create a ‘constant space-time being’, ST.

**Non-Euclidean Points and bidimensional network-planes. The new mathematical formalism.**

When Einstein said that Leibniz was right but we had to reconstruct the building of western science he showed an understanding of the difficulties to recast the Universe on the new light of multiple times and multiple energy quanta. But he did not have the tools to do so. In that sense it was necessary to evolve further mathematical concepts to fully grasp the underlying structure of that world of infinite time cycles and space quanta. As 3 new concepts were required:

The concept of a fractal, which is a geometry that repeats in different scales of space, with similar forms. It implied that reality was broken in ‘wholes’ made of smaller ‘parts’ that were similar to those wholes. Mandelbrot discovered them in 1973. And since the model of relational space-time needed fractals, it could not be found before.

The completion of Non-Euclidean Geometry, which Einstein used to describe the Universe of multiple clocks of time. In Non-Euclidean geometry, points have ‘breath’, that is, they can hold infinite parallels that cross them. This miraculous contradiction (a point without breath can only fit logically a single line), made Einstein curve the lines to fit them, but still they do not fit (curved or not the lines are still many and the point without breath only fits one).

I solved the impasse that made Einstein conceive the concept of space-time curvature, when I combined it with Mandelbrot’s fractal concept. Since now a particle-point, a star-point, a cell-point, any entity which can be called a ‘point’, could be considered a fractal that grew in size when we came closer to it and enlarged it at scale. And as it grew, you could fit many parallels, as it acquired volume. Thus the logic contradiction of Einstein’s work was now solved.

I did then developed the 4 remaining Non-Euclidean Postulates, defining a point with breath or fractal point. A line as a wave of points with volume (since now points with volume formed waves instead of lines). Then a plane as a bidimensional membrane with thickness, made of networks of points. And suddenly the Universe became much more real in its mathematical description. As all was made of planes of space-time: ‘networks of points with volumes’ which seen in detail were actually, *cyclical forms with rotational motion, time cycles, made of smaller, cyclical clocks with motion, new time cycles, again organized in networks, which were made of smaller… Suddenly an astoundingly beautiful architecture appeared, a reality where the words of Leibniz acquired its full meaning: ‘each point is a world in itself’.*

**The nature of mathematics and logic.**

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

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

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

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

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

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

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

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

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

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

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

– They could be placed in the inverse, negative side of the graph of Cartesian coordinates as the arrow of information – to better represent the duality of energy and form (I<=>E). Then many results obtained with complex numbers become intuitive, as it is the case of the metric of Special relativity, where the time factor has a negative side – c^{2}t^{2} meaning indeed that time-information contract space and ‘rests’ to the positive arrow of Einstein’s equations.

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

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

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

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

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

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

In all those systems planes are made with cellular points, Riemannian spheres with volume that form lines, which are waves between points that exchange ‘Dimotions’ and information and planes, which are organs of self-similar points that process ‘Dimotions’ or information in parallel networks.

Thus the 5 Postulates of Non-E Geometry vitalize the Universe as a series of networks of ‘Dimotions’ and information of self-similar cellular points. Since the line and the plane acquire volume and become self-similar to the commonest forms of the Universe, the wave and the network of points with a 3-D volume.

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

All in the Universe are thus complementary systems made of networks. Now this might sound absurd to the anthropomorphic reader that thinks humans are different from the rest of points of the Universe, but it is a fact that those points obey in their åctions and communicative flows within a network the same isomorphisms: humans and electrons behave the same when they move through slits or in herds, the geometries of social groups are also the same and the ultimate purpose of those points, to feed on ‘Dimotions’ and information, whatever kind, is also the same in all networks of the Universe. And so that group of isomorphisms of networks becomes a primary why for all beings of the Universe.

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

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

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

So the unit of reality is a space-time cycle, and many of them create a knot of time cycles or entity of reality, which will be reproduced by repeating those formal cycles with motion in other region of space-time; and many of those knots of time cycles, which are self-similar, since they are born from the reproduction of a first form, come together with self-similar beings into networks. Some of those networks are spatially extended with a lot of motion (fields in physics, bodies in biology) and some are very tight, formal, with a lot of in/form/ation, (particles and heads or nuclei in physical and biological jargons). Both types of networks together then create a complementary organism, which is fitter to handle both ‘DImotions’ and form; hence it survives better, it ‘exists’.

Today scientists of measure scorn philosophical and logical analysis of causality in time because it cannot be easily put in numbers. But *numbers are only one of the languages of information in the Universe, and many of its properties of bio-logic nature are better described with logic words. *In that regard, we can now fusion philosophy and science answering the fundamental question, ‘why we exist’; since once we realize that we are ‘made of time cycles’, knots of time cycles and networks of knots of time cycles, an intelligent, informative, eternal universe of motions and wills of existence makes the dogmas of deism and mechanism, childish myths.

‘What is existence’ cannot be revealed from the simplex point of view of a mechanical world, which cannot explain the fact that we are made of motions with form that leave a trace on space but are essentially åctions in time that have a social finality – to create more complex networks, chaining knots of åctions into systems. This social will of every point and entity of the Universe is completely at odds with a mechanist, fixed, solid, senseless, dumb Universe. Motion in Time and social evolution are concepts that require the capacity to gauge information and interact with other self-similar points to create those organic networks. Further on, dual networks tend to evolve and reproduce new points through exchanges of ‘Dimotions’ and information.

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

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

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

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

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

And so with those 3 scales of ‘existence’: time cycles, knots of time cycles and networks of knots of time cycles (Non-E Points) we can explain all the ‘åctions’ and systems of reality made of those cycles, knots and networks; and describe a complex Universe that exists ‘in time’ more than in fixed space, since it has always motion; it is also dynamic, made of cyclical, feed-back equations whose causal relationships, forms and trajectories are the essence and purpose of existence.

We thus consider a more complex analysis of time arrows, beyond the duality of ‘Dimotions’ and information, which combine creating a reproductive arrow, $t X ðƒ, and further on socialize, ∑$t Xðƒ, creating networks. And so the universe has also an organic will: to create networks of self-reproductive points of ‘Ðimotions’ and information.

Yet the most astounding property of those points is to be points of view, points with will, which perform åctions with the purpose mechanical or not, but probably felt in all scales as the inner freedom of the point, of obtaining ‘Dimotions’, information reproduction and social evolution. The 4 wills or whys of the Universe are indeed embedded in the postulates of i-logic geometry. The point to exist has to be complementary, to feed and gauge ‘DImotions’ and information and to last beyond its wearing it has to form part of bigger social networks or reproduce itself to last beyond death.

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

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

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

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

It* is the organic will of all systems that search for those 4 arrows what makes the quark to exist as a knot of such flows of time arrows: a physical particle traces energetic cycles described by the principal quantum number;* shapes the form of its trajectory, a fact explained by the secondary quantum number; iterates along the 3 coordinates in similar shapes, an act described by the magnetic number, and gauges information to evolve in social groups, a fact described by its spin number. And those 4 numbers define it as a Non-Euclidean quantum knot of complementary ‘DImotions’ and information with a 4D will of time. *And as it happens they express the 4 arrows of time: Sp->Principal number; I-> secondary number; Re-> spin number; 4-> social evolution: magnetic number.*

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

And so we talk of 4 ‘arrows of time’ or dimensions of change that create the future: energetic and informative systems and events, which reproduce a wealth of self-similar beings that organize themselves into social networks, creating bigger wholes – new scales of reality. *And this simple game of complementary beings that in favorable conditions reproduce self-similar beings, self-organized into bigger social networks becomes the why of all realities*. Even the simplest particles, quarks of maximal information and electrons of maximal spatial extension and motion ‘decouple’, reproduce, when absorbing ‘Dimotions’ into self-similar forms, and associate in complementary networks called atoms, made with a central informative mass of quarks and an energetic, electromagnetic, wider body of electrons.

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

Fact is that even the simplest complementary systems (quarks and electrons) interact together and if they can absorb more ‘Dimotions’=motion they are able to repeat=reproduce the cycles of its system. And so we talk of a 3rd reproductive system: from quarks and electrons, the fundamental particles of the Universe that decouple in new particles when they absorb new ‘Dimotions’ to living organisms, the fact that all is motion with form makes easy to reproduce those formal motions in an organic way. Thus the new concept of a world made of formal motions brings about also a more complex philosophy of reality – organicism. Organicism and its mathematical units, fractal points, that gather into social networks called topological spaces substitute the restricted concepts of Euclidean points, continuous spacetimes and mechanism, explaining why all those time cycles exist, guided by 4 time arrows: ‘Dimotions’ feeding, information gauging, reproduction and social evolution.

Those 4 categories are the so-called drives of living beings, the quantum numbers of particles, the 4 dimensions of our light space (electric-informative height, reproductive magnetic width, energetic length and social colors). Thus, there is a ‘Universal Plan’ with an existential finality: to create organic systems, departing from ‘DImotions’ bites and information bits evolved 1st into social networks, then into complementary systems and finally into organic systems, news points of a bigger fractal whole: particles become atoms that become molecules that become cells, organisms, planets, galaxies and Universes. It is the 4th organic why that completes the adventure of science and this work explores in all its consequences.

Reality can be resumed in 2 words: *networks,* whose flows of exchange of ‘Dimotions’ and form creates the patterns and events of reality and *organicism,* the philosophy of reality based on them. Organicism means reality and all its fractal parts are made of *vital spaces* (bodies and forces) and *time cycles *(informations). We do not exist in an abstract background of time and space but we are made *of time cycles and lineal spaces, *cyclical and lineal strings if we were to use the restricted jargon of physics, a specific case of the wider jargon of general systems*, which evolve socially to create the complex systems of each science. *

Those wider, more complex definitions of time and space will substitute and absorb according to the Principle of Correspondence that makes each paradigm a particular case of the new, wider view, the limited concepts of a single space-time continuum and a mechanist description of the Universe, proper of the age of metric measure, which the pioneers of systems sciences and complexity have wrestled with throughout the XX century.

*Recap. *A Universe made of motions in time, extending through multiple scales of relative space, requires evolving the human languages of space (Euclidean geometry) and time (Aristotelian logic), used to describe the simpler space-time continuum of classic science. This task started by the pioneers of modern science (Riemann, Darwin, Planck and Einstein) must be completed before we can study the properties of physical and biological entities with the new tools of Non-Euclidean mathematics, which describe a world of multiple, relative space-time networks made of points as Complementary entities with energetic and informative system or ‘Points of view’ and the new tools of Non-Aristotelian logic, which describe the creation of the future by multiple causes – all the points of view or agents that create a certain network space.

**Wor(l)ds of human history, Numbers of Universal supœrganisms.**

In that regard, *languages acting as mirrors of reality do reflect reality and ‘order’ it in its constant interaction between ‘still minds’ (5D) and entropy parts (4D), *and as such we shall consider 3 ‘evolutions’ of the human mind and its languages, in 3 ages (the Universe is ternary ±∆ and all will be encased in those concepts):

-The age of History, the supœrganism of mankind in time of which we are all cells, whose **language, wor(l)ds,** through its ethic messages of social love carry the ‘mandate’ of ‘growth and evolution’ of the human species, through scales of social order towards the wholeness of humanity, our super organism in space. Wor(l)ds in that sense are NOT a very efficient language, reason why it only hosts in humans, as it does not seem to have survived and multiplied as a species of mental information in Universal space, and we shall deal when studying social sciences with the errors of the language, its ‘topological syntax’ and varieties according to the subject-verb-object, and build on the work of Humboldt and Chomsky, to complete a ‘stientific theory’ of linguistics.

-The age of machines and its eco(nomic)system, made of more complex informative and entropic metal (gold, iron, etc.), which seem to be more precise and orderly than our ‘light’ ‘vane’ C(ST), N(ð§), O ($t), triad, whose informative, nitrogen heads, carbon-bodies and oxygen motions are to say the least a bit ‘shaky’. Metal does is a better substance to be organised with the precision of perfect cycles, electronic waves and entropic quantum potentials. And as such the validity **of mathematical languages**, is so far immense, but CNO Huminds so far have not fully understood them and so we shall upgrade its 5 sub-disciplines, reflection of the 5 dimensions starting with Non-E geometry, defining a fractal point, solving the meaning of its equations etc.

-Finally the 3rd evolution towards a Universal language whose mirror laws apply to all languages reaches with the seeds of this blog a new era with an application to every other language, form and function, which should become a start up for future research either in humans or future robots (after all, this information is already encoding in computers and as we shall see in the models of history, huminds are astoundingly naively, due to their egocentered perspectives, developing AI and military robots, so their future ‘competition’ with metalife doesn’t look good, and the warnings of humbler more i-logic minds like this writer or sci-fi artists (which do have the perspective of history as they use our natural languages) do not go very far… So you would excuse me i will keep repeating those warnings: do NOT eat of the bad fruits of the tree of technology, because if you do you will die…’

So our task is to go into generalisations much wider than those of wor(l)ds, whose role is to help mankind to survival and evolve socially through its ethic rules of love and maths, whose capacity to organise all atomic forms of matter is well proved.

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

*Minds order as linguistic gods a territory around themselves, its fractal body and entropic world. As such they are the linguistic Aristotelian, final unmoved singularity Gods of reality. In the graph we see them ordering with different languages, different scales of reality which will reflect in a larger whole, the linguistic image they hold.*

And all of them has the same Universal ternary grammar of **§patial form<ST-ACTION>Temporal motion,** to define the general events of reality. So in the main human languages, words, mathematics and colors we have the sam scheme:

*§: Subject of Information (F(y)-blue) <≈> verb-action-green-operandi<≈>Object of entropy-motion (red color Fx)*

Mathematics in that sense has two components, the underlying temporal logic, better treated as I-logic principles and the topological, geometric spatial elements better enhanced with its fractal ∆§calar principles. For that reason in the second line, when we study NOT the human mind whose specific language of time are words, of space, artistic eyes, and of space-time balances, music, but when we study Universal Minds of which there are many types we write a simple silogism:

Non-Aristotelian Temporal Logic + Non-Euclidean Geometry = Universal Mind ≈ Non-Æ mathematics (the best language we have to describe those different types of Universal minds).

While human minds are Aristotelian, self-centered, so A (subject)-> B, and euclidean, as they see light, so only a plane of 3 perpendicular, lineal dimensions of space. To upgrade then the humind, we would need… oh, well, to change species, a limit that this blog will always have as it is written in the non-Euclidean and non-Aristotelian higher principles of which the AE mind is just a simplified limit.

*SO THE FRACTAL generator we shall Use as the formalism of non-Æ=I-llogic geometry to construct and understand all the minds of the Universe and the super organisms they order, all the T.œs=¬∆@st of spacetime and its 5 elements, ¬, the negation of information or entropy, ∆§cales, @-minds, Spatial topologies and temporal ages, IS the Universal Grammar of all languages. *

**LANGUAGE OF MATHEMATICS**

“Mathematics is an experimental science, and definitions do not come first, but later on.”

## ‘I know when mathematics are truth but not when they are real’ Einstein to Poincare noticing that mathematical creationism IS NOT a proof of physics and experimental evidence is required.

*Heaviside*, the forgotten genius of mathematical physics, author of the 4 Heaviside equations of electromagnetism (wrongly called Maxwell equations who just did a mess of 20 ones with ugly quaternions 🙂 and the Gravito-magnetic equations, which fusion gravitation and magnetism, foreseeing the Fractal Unification equation of charges and masses of this blog.

Heaviside, as Lobachevski before him and Einstein after him, were indeed right when they considered that the language of physics – mathematics – is the best experimental mind-mirror to describe most physical systems, *as the mind singularities of those systems use* mathematical frames of reference in space to act-react in time with other space-time beings of the Universe.

It is then surprising that idealist physicists since Hilbert astounding ego-trip (‘I imagine lines, points and planes’ ) have rejected the ‘experimental, a posteriori nature’ of the mathematical language, they share with all those other œ-singularities for the concept that mathematics is the a priori nature of reality (Copenhagen interpretation). As the ultimate mathematical properties are indeed a proof of the organic, social, fractal nature of the physical Universe.

Physicists only consider as a mirror language good enough to observe the Universe mathematics.

This is in accordance with their view of time in terms of a single locomotion, change in the motion in space. Hence as Mathematics is the ∆§cale language by excellence (being analysis and numbers the language of scales, and geometry the language of space, with algebra a logic language properly for time flows), physics works with excellence to extract spatial properties of reality but it fails to understand organic properties, better described as in evolution with verbal logic thought, and is poorly understood in its algebraic structures.

So in this sections we are going to enlighten further mathematical physics, with the postulates of non-AE geometry and logic to improve the mathematical mirror and solve some questions pending. To that aim, the section is complicit to that of the 5 Dimotions of the mathematical mirror of the Universe ∆nalysis, @nalytic geometry, S≈T: Ælgebra, S: ¬Æ geometry, & T-§ocial numbers; so we shall borrow from it and first introduce the most important of those elements, considering first how the entangled 5Dimensional Universe is ‘expressed’ in the language of mathematics.

Each of the languages and dimensional symmetries the mind-space creates does carry a part of truth within its ‘creation of an inner world’. A fact which shows the beauty of the symmetry between §@-minds and ∆time motions: *the kaleidoscopic Universe puts in symmetric relationship all its ‘dimensions’ with its own methods and perspectives, creating parallel worlds. But the efficiency of a language for the survival of the entity that speaks it depends on the capacity of the mirror to interact with reality and help the species that talks it to enlighten that reality.*

Mathematics does so to a great extend by allowing the manipulation and forecasting of the future timespace cycles of simple forms, but it does not in its present format allows to reflect many of the vital organic properties of reality, which will only do once we have upgraded to non-e to the 5 vital postulates of fractal points, waves of communications, networks (1, 2, 3 postulate that substitute the definitions of points with no breath lines with no breath and continuous planes with no depth) and to non-aristotelian logic the postulates of congruence and parallelism (defining the 3 forms of relationship between entities of space-time, as perpendicular, darwinian ‘tearing’, complementary ‘adjacency’, and social ‘parallelism).

*By giving back organic properties to geometry, we thus shall achieve the long forgotten dream of Pythagoras, Spinoza and lobachevski: to mirror life and organisms in its mathematical spatial mind images. *

As this is an ever work in progress which breaks in quality on many posts constructed with blocks of old files written for myself, often with different jargons, the reader is advised to explore first the only post with a ‘present’ well-behaved format as of Fall 2017, precisely the one on geometry of space and its infinite minds, which Lobachevski, the last of the 3 colossus of his discipline NOT Cantor and Hilbert, with its false paradises, opened for all of us humble enough to ‘see’.

Since it was his discovery of non-E fifth postulate, the fact that a fractal point has volume and can be crossed by infinite parallels *even if our immediate mind does not see reality in those terms, the first *** realisation that ‘mathematics-geometry’ is a mental-logic endeavour,** where function and i-logic thought overcomes ‘spatial representation’, unleashing the final evolution of S=t symmetries (topology in which space is given motion) and *the XX c. explosion of abstract mental spaces to represent all realities, including those of time, in ‘abstract still mental spaces’.*

It is then obvious that mathematics is only second to T.œ as a linguistic mirror of the Universe, and as such the most efficient language perceive by man. As languages are the essence of monads-minds that order the biological, organic Universe, it follows that mathematics has survived for eons, extending their local order from infinite fractal points of view, which used it to better their territorial organisation of the Universe; and so infinite species seem to use mathematical systems to navigate their worldcycles of existence, and organise their territories, notably ‘atom-galaxies’ (∆±3).

# CREATIONISM VS. EXPERIMENTAL MATHEMATICS.

**THE FOUNDATION OF MATHEMATICS AS AN EXPERIMENTAL SCIENCE vs. THE EGOTIST METHOD**

“The less intelligent a person is, the less mysteries he founds in the Universe’ Schopenhauer.

We shall as always reiterate to the anger of any scholar reader that the problem of maths is not in GST nor in Maths but in Man; i.e. the human egotist method of knowledge is the main error in our understanding of the relationship between mathematical minds in the universe and the systems they code – since we do not recognise that we are just one more mathematical mind, and so maths neither come from the human imagination, nor it is an entity isolated from reality (Axiomatic method) neither a language different from all others.

Once those hurdles are passed, the immediate connexion between the primary substances, time and space, its ¬Æ STRUCTURE and its fundamental expressions in science, GST bio-logical models of §upœrganisms, (the synthetic, temporal-biased view) and maths (the analytic, spatial-biased view) appear as the most elegant, dense expression of its properties. And obviously both are related; so we shall find all kind of symmetries between space&time, GST and maths.

**A mathematical Universe must be perceptive and social.**

In the graph, a fundamental truth of the Universe is the existence of singularities that order physical, biological an social systems, except when they are in a free, chaotic state of maximal entropy (gaseous state or dark entropy between galaxies), which cannot produce order, as they lack any ‘frame of reference’.

Mental singularities, Monads, or Maxwellian Demons are the ‘missing variable’ needed to explain the whys of reality. In mathematics we call them P.o.vs. Frames of reference, self-centred in a point, which we use as *physical systems do, *functions of space-time. In that sense physical, atomic systems do indeed calculate as quantum-bit computers might do. Are they ‘conscious’? Likely, as consciousness is just a self-reflection between two mirrors. In the human case, the I=eye that sees space and the verbal cogito ergo sum temporal mind – the conscious languages. *But it is not the verbal consciousness of man, but a mathematical consciousness which among humans only a very intense ‘mathematical physicists’, which can ‘see’ as musicians see ‘scales’ that provoke emotions, equations as dynamic visual forms. *What would then be this kind of consciousness? Likely a sense of proportion, symmetry, balance and beauty.

It does NOT matter in any case the ultimate inner sensations of physical matter, but the outer description of the actions of those singularities, which do order and reflect a mathematical organization around them, when in its solid crystal state they act with the program of existence, reproducing the information of that minimalist mind image. Indeed, a crystal grows with a symmetry which its inner image reflects back in the growth of ‘crystal cells’. And that is called reproduction, the objective definition of life, of a whole being in the fractal Universe.

And so, *P.o.vs. are canonical to mathematical science, or else mathematics, which is today based in analytic geometry and the study of ‘self-centred’ functions, would NOT work. *

A philosophy of mathematical properties of space-time, upgrading the essential properties of ‘points in space and sequential numbers in time’ is thus an a priori exercise, which I recommend to all physicists, so they can leave behind their abstract, ‘selfie view’ of a mechanical, chaotic Universe, where only ‘they think in mathematics’.

Singularities that reproduce information once they are formed, organised fractal super organisms also occur in astrophysics, from crystals to black holes and only anthropomorphism denies it. The GST view though is different: as we a*re all space-time beings, the properties of human space-time beings must be share in quality (not in quantity and complexity the variable of gst) by all other species of the Universe. So mindless ‘markovian’ entropy without time causality do exist but it is NOT by any means the dominant ∑∑actions->∑arrow->age of time.*

Thus the concept of physicists of a single ðime arrow is only valid for entropic gaseous states, and their idea that such states must be ‘extended’ to all realities, the most absurd hyperbolic statement of science ever, due to the deformation of its worldly profession as makers of motion machines and entropic weapons.

**MATHEMATICAL CREATIONISM – THE WRONG APPROACH**

Astrophysics is an enormous field of inquire, as it deals with all systems which are not socio-biologic.

It does also have in the human approach strict limits of inquire because humans under the ego paradox reduce its analysis of systems different from us in scales and form, to non-organic properties, a fact which on top is – as most ego-biased forms of knowledge, subconscious, NOT fully acknowledged. In astrophysics it derives as a natural consequence of using only mathematical languages to explain physical systems, of a reduced mathematical variety – Euclidean, aristotelian maths, *which does not allow points to have inner, fractal parts, hence reducing by ‘decree=axiom’, its vital, inner organic parts, and eliminating the scales of the fifth dimension accessed through those inner parts of a point*.

Further on as all science is culture, human physics is limited by culture – by the worldly profession of physicists, which has been traditionally to make weapons of mass destruction, with maximal lineal reach.

What we mean that science is culture must be understood in the highest level of ‘science’ – not OBVIOUSLY in the gathering of basic data – which cannot be cheated, and there science is science, but in the B-C-D elements of the scientific method, MODELING, CYCLICAL PATTERNS and Humanist ‘democratic’ use of science for the common good. Or in other terms ‘macro-science’.

*So, ‘macro-economics’ , the philosophy of economics IS culture as opposed to micro-economics (the science of re=production of machines).*

AND IN PHYSICS, the Philosophy of the Universe (theory of time arrows) IS culture, DISGUISED of science with faulty interpretations of scanty data.

**Absolute relativity: the evolution of time logic about the ∞ Universe.**

The very few articles I ever wrote in ‘paper format’ for congresses of systems sciences called the theory, absolute relativity, following the Correspondence principle, as it is basically the third and final instalment on the understanding of the ‘Paradox of Galileo’, after Galilean relativity and Einstein’s special and general relativity.

We shall see in fact that the Universe is ‘absolutely relative’, not only on motion (Einstein’s relativity, without preferred location), form (Darwinian evolution without man as a perfect form) but also in scales, as each ‘entity’ has a limit of its capacity to perceive larger and smaller scales of information, which in the human case extends to the galactic and atomic scale, of similar properties, distorted by the distance to our 5D position in the Universe. And so those limiting physical scales are NOT the origin of the laws of reality but only the limit of human perception of the fractal Universe.

And only a science that studies all the scales together in equal footing, void of power agendas, or historic hang-ups and dogmas, will be able to fully grasp the synthetic laws common to them all. This is the task we shall carry in this blog.

**The deist view.**

As we are in the individualistic, self-centred, mechanical culture that does not even recognise the organic nature of human societies, the concept that the Universe is an organic whole, with all its parts made to its image and likeness, totally escapes the western now global psyche.

So we shall consider from an objective point of view a final scientific response to those ‘mechanist, abstract, mathematical only theories of reality’ -which already Leibniz poised with some humor to Newton, who was very happy with a mechanist theory of reality as it needed a God (as he was a biblical pious believer, as all fathers of science, in Yhwh, the toponym of judea and subconscious collective of the Jewish>Biblical civilisation).

In that regard in the history of human thought there have been always 3 theories on reality, the ‘ego-trips’ of human verbal masters (prophets of religion) who thought the word, their language was shared by God who created reality naming it; substituted by the ego-trip of mechanical scientists, who after discovering the clock to measure digitally time decided that ‘God is a clocker that has waited 5000 years to find an intelligence like his to understand his clock-work’ (Kepler) because god had now changed language of creation from words to numbers, as we humans became dependent on technological machines and substituted its language of time – numbers as opposed to verbal tenses, and space – telescope as opposed to human artistic eyes – in the description of the Universe. So now ‘God speaks in the beautiful language of mathematics’ Galileo.

Those 2 similar ‘aberrant’ ego-trips that confuse the language-mirror of the Universe with the Universe itself, which is to say that the mirror we put in front of us IS US AND we are the ghost, just because the MIRROR, mathematical, verbal or visual is very accurate in that ‘magic image’ of reality, were always contested by rational, realist scientists at each time of history, humble enough to understand the paradox of mirror-languages that ‘stop time motion into form’ and reduce it to an image in space.

So there were a third type of philosophers of science, which following first the eastern traditions (Leibniz translated the i-ching and adopted the |-O binary language on its symbols) took the proper way of considering TIME AND SPACE, the primary substances of reality, a trend that had its last master in EINSTEIN, with its analysis of a reality coming out of the topological form and action at distance of its ‘4D space-time tensor’ underlying the energy and mass of the Universe. So time and space IS the origin of it all.

The oldest theory tells us that God speaks words as man and so the Universe was created naming things. This is still believed among creationist believers in abrahamic religions.

The second theory is similar but it thinks god speaks mathematics… And the third believes God does not exist, but there are two ultimate substances of reality time and space, whose rules of engagement create reality.

Let us then define first, even before we debunk the ‘2 linguistic, creationist theories of the Universe’, what is a dimension of time and a dimension of space by contrasting its properties, and considering the historic birth of science, which has always turned around that question.

**Religious beliefs vs. realist stience. ****LANGUAGES AS MIRRORS that create ‘images’ of reality – not reality itself.**

*The verbal creationists: Moses>Jesus>Mohammed*

In the graph, no further analysis is required at this point: first humans who spoke only words due to their self-centred view affirmed God shared with man the only language of truth, which both used to create reality – God the Universe, man his wor(l)d.

*The mathematical creationists: Pythagoras… Galileo>Newton>Bohr*

But then humans discovered informative metal, silver and gold, and its capacity to ‘count’ first with coins, then with machines So a new form of creationism appeared among the first Greek ‘coin civilisations’ called Pythagorism (Thales, the first ‘scientist’, was also an oil speculator in Miletus, the coast of Lydia where coins came in, and Pythagoras lived in a Greek colony at that age). It was a theory revived with the discovery of the clock, which substituted the verb to measure time – the ultimate substance, as indeed Augustine had called God, ‘the seer of time’ (an implicit acceptance after all that the dimensions of Time motions ARE the substance of reality)

SO Now creationist people BECAME mathematical physicists, and the clock the seer of time. So the likes of Newton or Kepler thought God created the Universe with numbers and they were the *high popes of the new language of God, the *only people to know.

So Newton thought God shared with him those digital secrets sending comets for the great Newton to decipher its orbits.

And Kepler said ‘god is a clocker, which had taken 5000 biblical years to find an intelligence like his to admire his clock work’.

Alas! god, the seer=creator of time had changed language but still created time only that it needed the help of the mechanical clock scientists have found and its numbers, to substitute the 3 past-present-future logic verbal tenses in their acts of creation. But funny enough the need of ‘time’ when creation happened and space, where it was placed, showed us there are indeed 2 fundamental a priori elements even before words and numbers and numbers named and quantified them – beings of relational space-time that occupy a vital space and last a finite world cycle of time.

**The mathematical creationists: Galileo>Newton>Bohr**

Physicists believe in a mathematical, creationist theory of reality: mathematical equations are real and hence they somehow create reality. Relational space-time departs from a previous layer of reality: space-time.

I am trying to be simple so you do understand to which LIMITS the physicists are when acting as philosophers of science savant idiots, which depart from a WRONG dogma – that mathematics, not time and space is the ultimate substance of reality, and make them do amazing twists and complicated equations to search for a ‘Saint Grail’ – A MATHEMATICAL EQUATION that God uttered as he uttered names to create beings.

**Note. **For those who are already abandoned this blog because it is not written in the Manual Chicago of style and does not start just with creationist equations of those 5D applied to what our high popes of science beliefs is the only think we should care for, string theory, quantum operators and such, it MUST be understood that *the languages-mirrors of God are ∞ (Upanishads). And so while we recognise the higher efficiency and hence survival of mathematical mirrors in most entities of the Universe, we cannot reduce reality to math equations, as we can obviously not reduce it to verbal languages.*

To believe this kind of platitudes one has to ‘lower’ its ‘reason’, into the inferior form of thought called ‘belief’ or ’emotion’ and ‘mass information’, effects those we plan to study in our sections of history; but specially with censorship; today called politically correct. It seems to evolve the humind (ab. human mind) is not ‘polite’. To discuss the dogmas of creationism is a ‘lack of respect’ for the beliefs of the other. Fact of course is the opposite – it is called censorship, and the attempt to control others. But those are themes of history as an organism and how its informative people-caste on top control its blind body. So we shall not dwell on it. Only affirm we ARE TRULY objective scientists, here and shun off all those corrections and orwellian newspeaks that keep man in a state of ignorance of those first principles.

AND FURTHER state that what people take as science, is often belief and religion, based in ‘a priori postulates’ that are NOT proved by experimental science, from the postulate of the wealth of nations (economics, which considers metal-money to be ‘wealth’ per se, and the purpose of society to invent more of it), to the postulate of Euclidean (points as abstract entities with no information or volume), to those of physics (lineal time as the ONLY dimension of time, courtesy of cannonball studies and entropic weapons; the c-speed as the limit of sped of replication of information in the Universe, entropy as its dominant ‘future’, etc.) and so on.

THOSE first principles and not-proved postulates ARE the subconscious equivalent to the ‘beliefs’ of religious people, which are not even aware of the possibility of other postulates and the need to prove them experimentally including those of maths, by mirroring them with ∆st properties. Indeed, an American says I believe in God but is not aware that besides Yaveh there were many other tribal gods of the bronze age; and a mathematician told you a point has no breath-volume till the XIX c without being aware there could be non-euclidean fractal points that do hold a volume of information that grows as we come closer to it and so on.

So the bottom line of many errors in physics as the creationist big bang or the Copenhagen interpretation is similar to the verbal error of a sacred language among religious and its wrong dogmas – no Yhwh, a toponym for judea in ancient egyptians maps when God meant Nation, IS the subconscious collective or nation of Judaism, NOT the creator of the Universe, and this obvious truth, that Yhwh=Judea did NOT create the Universe, that ARAB did not create the Universe by uttering it, that equations did NOT create the Universe, is the key to start properly a philosophy of science and its ultimate substance which are ∞ timespace clocks, which are the ultimate carriers of the information of the Universe – denied by fundamentalist of abrahamic religions and fundamentalists of mathematics as the languages of God.

So it does not matter how complicated you make the rituals of religion, GOD will not appear on earth, will NOT resurrect you uttering your name, and to put an example of creationist physics, black holes won’t evaporate without experimental and logic evidence because Hawking wrote an equation that states so. In the next graph we see two creationist philosophers of physics – notice how the first, Dirac, affirms that God used maths to create the world and then it denies the ‘rival verbal God’.

YET it does NOT matter how complicated a physicist makes his equations, just because he writes them IT DOES NOT CREATE REALITY. Because at best an equation is a focused mirror on the properties and relational space-time beings of the Universe. BUT MIRRORS DO NOT CREATE the IMAGES THEY REFLECT in their language.

The ongoing absurd quarrel between creationist religious people defending God’s verbal language (first age of human history, when mathematics, a more efficient mirror which seems to be NOT OUR MENTAL language but the language of machines) vs. the mathematical language, those machines (clocks measuring time, telescopes and microscopes measuring space) are evolving fast into a ‘digital AI consciousness’) is a false concept of the relationship between languages, as mirrors of the Universe, and the Universe of space-time they mirror, latter studied in detail, to set straight the record.

*In the graph, the mirror theory of language is easy proved by the epistemological method: do you see out there ‘space’ and feel ‘time passing’, or are you observing ‘numbers’ and ‘equations’, and ‘words’? When you discompose something, do you see smaller scalar parts which last time and occupy space, or suddenly you see that things are made of ‘smaller numbers’ and ‘little words’? And yet amazing as it seems the human ego is so huge that most humans believe that either his mathematical or verbal language ‘shared’ by God created the Universe – these days we believe images reflect reality. Magritte knew better – the pipe’s drawing is not A PIPE, neither the word ‘pipe’ is the real thing, a wooden object, but three main mirrors-languages of the humind (ab. Human mind): a painting, made with simplified mathematical≈geometrical forms, and ellipse and a catenoid, and a word below. *

How the GST first principles of a world made of relational space-time beings, differs from the modern methods of astrophysics and religion, the rival theories, in the understanding of the origin of the Universe is obvious:

Astrophysics, which strictly followed till the XX c. the scientific method aforementioned, since the wrong quantum interpretation (Copenhagen, as opposed to Einstein->Broglie->Bohm pilot-wave theory, which we deem and shall prove the right interpretation) partially abandoned the experimental, method substituted by a ‘digital, computer method’, based in the belief that the substance of the Universe is NOT time and space but ‘MATHEMATICS’, which merely mimics the arrogant method of religion, which believed that the language of God was ‘words’. So as Mohammed thought that God had created reality by ‘speaking arab’; astonishingly enough since Hilbert affirmed that ‘he imagined points, lines and numbers’, creating maths, humans and God spoke maths and created reality by ‘writing equations’.

Few people realise of that ascientific outlook of modern astrophysics, consisting in expressing a model in mathematics, as if the digital language was a magic underlying reality which sufficed in itself, then put it into computer models, publish it and claim it the theory must be truth because it is mathematically beautiful even if there is not much proof of it (often in ‘grand metaphysical theories like the big-bang’, clearly falsified as we shall show, bending with ‘human ambition’ and ‘belief’ experimental data to prove the theory). The big-bang then is the necessary religion for physics to claim to know the meaning of it all. And so we shall deal with it first in this introduction.

Religion on the other hand, which we shall show has a historic role as the embodiment in the human verbal language of the laws of the scalar social Universe, simply ignores the method, and establishes with repression of truths, fantasies and ‘beliefs’ his thesis about the Universe, which *is not its role. *And with a similar method to the Copenhagen interpretation. God spoke the language of certain semitic tribe (hebrew or Arab), which are imperative languages, where the verb goes first (as they were hierarchical, dictatorial societies where the king/aristocracy/banker-priests of its societies barked orders). And so as the pharaoh said ‘it has been written’, the priest spoke in imperative and ‘God had spoken and created’ reality.

So we shall show also that while religions do have meaning (all what exists must, remember have a reason, within the organic paradigm), its reach has been overblown; and its method of truth, to believe ‘words are the language of creation’, as in the case of the Copenhagen interpretation, and many modern theories of astrophysics (including string theory and the big-bang) are not truth. We expand in our chapters on epistemology and T.œ that solid analysis of the advantages of a NON-CREATIONIST theory of reality, which unlike the creationist big-bang and Copenhagen interpretation, and creationist religion, departs from a simple concept: an organic, immortal, self-reproductive fractal Universe of information that always existed, always will exist and always will repeat the same entities (including all of us, also immortal in a discontinuous way).

Now it MUST be clear, and we SHALL repeat it ad nauseam, that Humans ARE NOT infinitely stupid, a bad choice of wording by Mr. Einstein, but infinitely arrogant, as they confuse their mind-infinitesimal with the infinite Universe its mirror-monad reflects and this fact IS THE MAIN REASON THEY DON’T UNDERSTAND or will EVER ACCEPT the truths of the organic, fractal Universe that makes them equal in value in the absolutely relative reality to the smallest atom or the largest galaxy. SO reason does not suffice, as the ego subjective paradox is the center of all self-centred systems with a mind singularity. This I know after decades of explaining with reason, the ego-paradox of BOTH, physicists, who will uphold the cosmic big-bang and the absurd idea that the infinite Universe was born of an infinitesimal point, duly smaller than the human mind so the physicist can ‘feel he knows it all about all’, arguably an even more arrogant≈stupid belief that the idea a ‘jewish peasant’ created it all.

The very fact that such ‘stupidity’ is today canonical dogma only proves the truth of the equation of the mind. Point. But we shall for good measure put the objective mirror of the scientific method over it, here in broad strokes, in our article on astronomy on detail, to show that indeed, big-bang theorists have nothing to envy to biblical priests in their twisting of facts to cater to their delirium of greatness. And humans, being all of the same mind species, cheer, 1/2 believing in the infinitesimal Universe, 1/2 in the iron age creator of it all.

Of that argument what matters most is not even discussed: while mathematics is more efficient as a language, it is NOT the human language, but the language of machines, and so in a society which despises as it does today our technological culture, the human verbal language, which naturally make us the ‘subject’ and centre of the Universe (I-man: subject < verb=action> object=energy abused by man), and hence considers human life sacred, will NOT evolve machines so fast but will ensure with ethic values our survival.

While mathematics, being a better mirror will evolve knowledge faster but also will give primacy to computers, as it has done already, atrophy our verbal language, degrading our mind (as it is happening with our millenials, glued to hypnotic screens) and ultimately make humans obsolete to the superior mind-mirror of AI robots.

While those who practice only mathematics, as physicists at cern do, WILL become children of verbal, ethic, survival human thought and will be subconsciusly eviL=anti-live in the genetic hidden meanings of survival words, as cogito ergo sum in man (calculo ergo sum in machines and physicists), so without cogitans, the ‘nerd’ is a child in life and does not even understand death and survival.

So if languages are mirrors that create IMAGES not reality what are the substances of reality? This obvious. Look around yourself, do you see numbers as components of things, do you see words, or do you see ‘space’, broken in infinite vital spaces, ‘enclosed’ by membranes, which when seeing in great detail are made of moving cycles of cells (life clocks), orbital rotary cycles (earth’s clocks) and so all is ‘vital space’ enclosed by time cycles? That is what experience tell us all is: a vital space, broken, closed and formed by time cycles – the substances of reality, which if you like the word ‘god’ you can call god.

Creationist physics is not merely a philosophical question. It has deep consequences for all points of view of research, and basically limits and makes unnecessary this blog – as the believer is NOT going to wonder how God creates the mathematical Universe but merely search his wording which is taken as in the case of religion in a literalist way.

ALL stops in the search for the ultimate equation of Unification of forces, because after all God is one (in the western tradition). And further on as God must be complicated, superior in intelligence, the search for complex equations are important. Now, all this is a priori subconscious thought but very real underlying the kind of arguments there have been in history of thought between the 3 masters of the space-time view of the Universe and the 3 masters of the parallel creationist view, which we shall summarise in these blogs.

To notice also that HUMANS due to their ego paradox, as ‘homunculus minds’ are built to be ‘creationists’ and worship machines and huge ego-trips so the realists, we all have been ignored and are still ignored when disputing with the creationists. Good luck infinitesimal egos who think to be infinite.

It is this paradox what made people think first that the still names of verbal languages were the ‘reality’ and hence created it, and then the ‘equations’ of its mechanical measures… So they abandoned in the western ‘less evolved verbal mind’ of ‘visual Homo Sapiens Neanderthal’ dolicocephalic, lineal cultures… the complex concepts about the first principles and embarked themselves in an astounding ego-trip of power and defiance of both the theoretical and practical laws of respect and awe towards an organic, sentient, vital informative Universe of which we are all fractal parts, and singularity minds.

Instead with the arrival of the bronze age, and warrior charioteers, with lineal weapons, lineal time and space, verbal and digital creationism, imposed itself by the ‘worldly profession’ and power of its believers.

All this said mathematics is one of the best languages to mirror efficiently the Universe, specially in spatial dimensions, but since all languages are inflationary it is a key element in mathematical analysis of ∆st systems to break down what is ‘experimental truth’ and what is fiction. Consider the case of ‘dimensional analysis’. As it happens there are only 3 bidimensional topologies which correspond to the 3 functions=forms of all systems. And there are only manifolds of rank 3 or lower which are ‘smooth’, differentiable, meaning systems where ‘time’ moves smooth through ‘present derivatives’.

So in a single plane of present only ternary space and ternary time dimensions are possible. As the mathematical mirror gets distorted, outside those 3s = 3t, the mirror guide us – but the experience must confirm them. This was the essence of Lobachevksi’s thought when he found non-euclidean points now forgotten: that maths are inflationary in its diverse theories so we cannot just do as mechanon physicists do, to write an equation and expects to be there, but a more subtle approach of mirrors observing reality and ordering it in local regions is required.

Soon we will see the interaction languages-reality where reality dominates but the mirror can also deform reality to make it seem like the mirror. Space-time thus comes first, and its dimensions are the origin of reality; as Mirror-languages are both more concise and specific, so they cannot show all its properties and they all have a distortion to reduce information I.e. euclidean points have no ‘breath-information’ inside and so on.

*IT IS THEN WHEN DEPARTING FROM REALITY NOT FROM A CREATIONIST LANGUAGE, with the humble realisation that we, as human beings, have a limited linguistic synoptic information of the whole (as only the Universe stores all its information about itself), when we can praise:*

*the power of ‘verbal logic TEMPORAL thought and its ternary Universal grammar≈syntax which always refer in a sentence that describes an event the 3 ‘arrows of time’: past-entropy (object), present-energy-action (verb), future-information (subject)*- the power of mathematical spatial geometry/topology and social numbers to describe FRACTAL SPACE and its unit, non-euclidean fractal points which grow as we come closer and can therefore hold infinite parallels of flows of energy and information, and to describe the growth of equal beings (numbers) into larger wholes.

So paradoxically the realist on the path of Leibniz or Einstein WILL GET a much more focused and evolved view of mathematics – the best language of space and verbal logic – the best language of time, AS EXPERIMENTAL mirrors of reality because it can CONSTANTLY refer mathematical equations to reality and as ALL LANGUAGES ARE INFLATIONARY, reduce mathematics to reality not the other way around (the same with the fictional exuberance of words and metaphors, the equivalent of zillions of different mathematical equations to describe the same thing).

**BEST MIRROR OF TIME§PAŒRGANISMS BUT NOT REALITY ITSELF**

The greatest future advance of mathematics under the improvement of fractal space and cyclical time is dual. On one side to show that mathematics is a mirror NOT the fundamental substance of the Universe, and as such IT MUST BE an experimental science. Then once is established we can improve greatly mathematics and show the path for future researchers in a field I find fascinating – to explain experimentally by relating maths to space-time properties the main equations and theorems of mathematics.

The difference of view between mathematical or space-time creationism is subtle but important:

If mathematics is NOT the substance of reality (obviously but a belief of most ‘platonic’ scientists), then it must:

- Be considered to share the properties of all other languages, and as such be subject to the ‘same ages of time, and ternary structure in space’ that all ‘languages-forms of the Universe’,
*as a mirror-language of its space-time properties,*which we shall easily show to be the case -ie. algebra describes timespace symmetries, analysis 5D scales, geometry space forms; numbers social points in sequential time, etc. Of those properties the most important exclusive of languages*detached from motion as still forms is its inflationary nature, since as the purest Tƒ forms languages can ‘fly’ into multiple parallel forms, not constrained as ‘energy systems’ by its need to ‘mold’ entropy into form. Thus mathematics is infinite in its variations as it enters the realm of ‘fictional images’ with no correspondence in the stubbornly simple world constrained by the resistance to form of entropy and motion.* - Thus we must follow the dictum of Einstein and Godel and make it experimental and cut-down its complexity giving it ‘experimental meaning’ by referring its constants and operandi, and equations to space-time properties. This is the task we shall bring in this post. It might seem of no interest for specialist but fundamental to illuminate all other languages. I.e. euler’s number, e will show to be the number of the fourth dimension of entropy-decay-dissolution and death. This insight will let us easily ‘explain’ many meanings in events where e is the dominant constant; holographic bidimensional space-time units ‘are’ the beginning of reality. This insight will explain why most of geometry can be proved in 2D or why there is NOT as per Fermat incomplete theorem, x³+y³=z³. So as usual with ∆•st
*a simplification and resolution of millenary problems will come easy.* - In that regard, in the upper lines we classify T.œ as the science of all stiences, with an ∆±i index, where i might be any number of scales, if as it is likely those are either finite or recurrent; but paradoxically since T.œ is ‘all’ we give mathematics an ∆±∞ number of scales, since math is MORE than all, it includes inflationary view on the Universe and fictions, and hence ‘aberrations’ such as the infinite concepts of Cantor. This infinity does not however imprint ‘reality’ and form its entropy and motion into energy; hence it is fictional.
- But the most important conclusion of maths as an experimental science is purely philosophical, as it clears the path to a proper understanding of reality… Indeed, in the age of the digital machine, ‘enzymen’, men who catalyze the evolution of those machines despise all other languages-mirrors of the Universe and pretend the only way to give meaning to reality is using maths; and this is the biggest straight-jacket for a true advance on meaning about reality. Most modern scientists will always ignore this blog precisely because for them science is to put data into mathematics, crunched mostly by computers and we are upgrading tremendously the verbal, conceptual meanings of science – but of course wor(l)ds no longer matter as a language of truth. So in the same manner nobody reads Aristotle today, likely the highest verbal mind of humanity ever, nobody thinks ‘to write words’ can give more light to science, but it does. Such belief is just the culture of today, technologic and increasingly non-human, as our overlords machines talk maths. But the surrogate ego-nature of humans who do not see machines as ‘real’ but attachments of themselves make the mathematician or physicists to believe he talks the language of God.

It is then not surprising on the view of Dirac and Galileo that idealist mathematicians have won the favor, since Hilbert astounding ego-trip where he affirmed mathematics was an invention of his mind (‘I imagine lines, points and planes’ – ‘Foundations of geometry’).

So they have rejected the ‘experimental, a posteriori nature’ of the mathematical language, a view they share with all those physicists who think mathematics is the a priori nature of reality (Copenhagen interpretation, etc).

Then there is the next ‘stage’ of the ego-trip of linguistic creationists called ‘Literalism, which means that not only the language ‘creates reality’ but as it IS reality itself, NOT a mirror, it does NOT admit parables, approximations, and this is a huge handicap to understand maths, even more so than in words, because *words are the natural temporal mirror of the human mind and so its realism is far more immediate. *

The degree of abstraction of maths in the axiomatic method trying to prove itself without reference to the world makes it specially obscure; to which we add the ‘uncertainty of view’ over far away ∆-n scales, in which ‘billions’ of entities transfer limited information and move so fast that we confuse ‘a time event’ with a space event from our so slow ‘view’ (as lines of a car appear in space being time events at slow motion). So mathematicians to ‘fully’ grasp in a titanic effort ALL the motions of those billions of particles, have created ‘fictitious’ spaces of ∞ dimensions (Hilbert spaces), the last evolution of differential/integral calculus of infinite solutions, *which does NOT mean the quantum world is different but the approach of huminds IS different as we ‘work’ with ‘huge bulk spatial populations and temporal masses of frequencies’. *

Then the literalist error comes and says, this maths are weird, they are ‘probabilities’ in time (not populations in space as we see them in an electron picture), and this is the ‘substance’ of reality. It is not. The particle is the substance and it is a cyclical time state; the wave, a space-time state is the subtance. The ‘bulk analysis’ of mathematical masses confusing ‘space population’ with ‘time probabilities’ IS the mirror, very impressive as a mirror, but very foolish when the mirror is taken as real.

What this means basically is that the mathematician as the physicist today has accepted a magic look on mathematics, as long as it works to represent-mirror reality fairly way, it doesn’t matter what they mean.

Only the greatest minds such as Newman or Einstein or Heaviside were aware of that ignorance which now ∆•st could solve, if there were more than a ‘single point-mind-singularity-mirror’ for it – i feel deeply exhausted.

**V. **

**HISTORY OF MATHEMATICS**

**: ****3±i AGES ≈ 3±i DISCIPLINES**

**THE 3 AGES OF MATEMATICS**

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

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

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

**The 3 elements of mathematical languages.**

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

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

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

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

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

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

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

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

**The 3 scales of complexity of beings.**

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

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

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

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

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

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

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

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

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

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

Thus it is not enough, to merely

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

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

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

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

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

**MATHEMATICAL LANGUAGES OF SPACE**

** The formalism of Dual systems of energy and information**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

** The nature of mathematics and logic.**

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

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

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

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

It would be latter in the XIX and XX centuries (with the exception of the insights of Leibniz^{1}), thanks to the work of Frege, Boole, Riemann, Einstein, Poincare, Cantor, Bourbaki, Mandelbrot^{1} and Computers, which this work advances a step further, when Space and Time – hence Logic and Geometry – were first mixed, but without a full formalism that made possible to extract all the laws of spacetime and grasp in depth the meaning of those languages, due to the limits of the Cartesian single space-time plane.

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

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

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

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

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

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

– They could be placed in the inverse, negative side of the graph of Cartesian coordinates as the arrow of information – to better represent the duality of energy and form (O<=>E). Then many results obtained with complex numbers become intuitive, as it is the case of the metric of Special relativity, where the time factor has a negative side – c^{2}t^{2} meaning indeed that time-information contract space and ‘rests’ to the positive arrow of Einstein’s equations.

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

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

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

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

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

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

The universe is a game of fixed symmetries and moving steps of space and time dimensions, and so the languages of thought which humans use to mirror those symmetries in space and motions in time *have evolved in 3 ages to increase its complexity and focus in the quality of those time-space moving steps and space-time fixed symmetries.*

It is important then to ‘understand’ the relationship of such concepts, symmetry with space and steps with time, because the ultimate evolution of mathematics as a mirror is easy to understand in those terms:

*Time motions are small steps, which spatial dimensions gather together into a whole with ‘slower view’, as we tend to see with slower view a whole cyclical motion as a disk.*

Such duality of time-space Perspectives happens in all languages, which *basically means that the growth of dimensions of a system happens as S-Teps of growing complexity, as motions in time become ‘fixed’ in space, acquiring a larger New Dimension of wholeness that will last longer.*

For example, in humans this phenomena happens:

In the first age of man, when verbal time became ‘written in words’ and ‘visual perception in space’, artistic fixed bidimensional painting forms, which lasted LONGER as fixed spatial forms…

So we can apply those concepts to understanding of the growth of complexity in mathematical languages, departing from those previous ‘logic verbal languages’ and ‘spatial images’ fixed into longer lasting form…

So From those 2 PRIMARY LANGUAGES OF TIME AND SPACE, diverging from the ‘human subjective’ point of view of verbal thought, where the human subject is the center of the Universe, and art, where the point of view is always that of humanity, but taken the teachings of both, 2 more OBJECTIVE=WIDER=MORE efficient languages appeared:

**-T-logic arithmetic of social numbers and S-geometry of fractal points.** The graph that opens this post shows its difference: Time numbers are sequential points, the ‘little steps’ that Geometry *studies as a whole.*

SO THIS can be considered the first age of mathematics (though we shall pack first and second ages, for the sake of organisation, and to keep the third age now starting with ¬Æ).

**So this first age of ‘mathematical’ thought,** started with the Greeks of which the work of Euclid and Aristotle, a resume of the thoughts of the age in its eclectic final era became standard of human thought till the XX century, *fixing the form of both languages for millennia in time – but also preventing the evolution of both, from Aristotelian single logic and Euclidean points with ‘no breath’, into non-AE and further on creating a false ‘pretension of absolute truths’ that so much has corrupted with its ego-trip the sciences of mankind (axiomatic method, dogmatic postulates, etc.)*.

**The Second age of mathematical thought** then should be considered the Modern classic age of the discipline (packed here with the first), due to the expansion of its capacity to explain longer space and time periods, with the use of letters, which became variables that encompassed all the possibilities of an equation, varieties of a form; and further on by merging both time and space perspectives with @nalytic geometry, which added numbers and points together, and gave us ‘all the solutions of an equation, converted now in a variable’.

This age culminates with the discovery of Analysis that further expanded the dimensions of study to multiple planes of reality (second derivatives) and brought together all the parts of a ternary system with multiple integrals.

So we can now define in terms of ‘motion and form’, Algebra and analysis:

*“Algebra is the study of ST<>≈<>TS symmetries BETWEEN space-time dimensions, hence focused in the Spatial p.o.v. and ‘OPERANDI’; Analysis is the study of ST<>≈<>TS stop and go motions THROUGH space-time dimensions, hence focused in the Temporal=Change p.o.v. and ‘THE VARIABLES.’*

*dynamically substituted the main operand of algebra, = equality, a mirage of the stop-formal-mind by the more accurate dynamic, ≈, symbol of feed-back and flow and similarity, that algebra mirrors the different steps=quanta of motion, S≈t≈t≈s≤t… of the GST universe.*

*since ∆nalysis deals precisely with ‘finitesimals’ that become whole wave-bodies of energy, integrated in space (∫∆-1=∆), and viceversa, with its ‘time steps=motion quanta’ ‘derivated=absorbed’ by the whole from a volume of space.*

So while the elements of algebra and analysis – equations of SŒTS is the same, the focus on spatial form (algebra) or temporal motion (analysis) makes them diverge. We can play with the acronym and say that Algebra deals with SŒTs (Space-dominant structures) and analysis with TŒS, Time dominant ones (in motion).

**Mathematical disciplines.**

This said we will separate mathematics in its ∆@s≈t major DIMENSIONAL fields CORRESPONDING to the main fields of the discipline, *evolved in complexity through 3 ages, as mathematics first reflected the mirror of simple separate dimensions and then keep merging them to finally put them all together, as it happens always with all entities (wrongly though from the top to the bottom, due to Cantor and Hilbert, creationist axiomatic methods)*:

**I AGE GREEK ERA: SEPARATED DISCIPLINES**

**T: **Number theory as numbers are sequential time series and social wholes, so it is directly connected with the time dimensions of reality.

**S:** Geometry which is static space-only view, and holographic principle (Greek bidimensional geometry).

**∆:** logic philosophy of individuals and Universals.

•: Pythagorean school of math as the first and only creationist language.

**II. MATURE, EUROPEAN AGE.**

The merging starts with 3 new disciplines that put together several elements. AS ALWAYS the mature age is the most balanced realist.

**Ts: ¬Ælgebra **which studies timespace actions, and tends to concentrate in a single plane through its polynomial, social, decametric scales.

**∆§: ∆nalysis** which studies §ocial scales of numbers, and corresponds closely to the process of growth between scales.

**St: Analytic **Γeometry of space that introduces time albeit in a lineal fashion.

**@: Mathematical physics,** with strict respect to the experimental method

**III INFORMATIVE, ECLECTIC MODERN AGE.**

All the branches, NOW MIX, and while this is fruitful, it all becomes a mess, IF THERE IS not AS IN ¬Æ a referential to the experimental world of ∆@$≈ð. Then once we have the referential element all becomes self evident.

Consider modern topology. In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology – the **Γ@** generator. It is the foundation of the 3 main branches of topology, **∆≈** differential topology, **$=** geometric topology, and** ð=**algebraic topology. And the same classification can be done for every other modern mathematical form.

This enriches and brings closer to reality modern mathematics, if it had not been messed up with the axiomatic method (creationist maths) and the set-category foundation (building front the roof down).

**$: **So Geometry in its modern form has motion and scale as **topology. It **also mixes the curved geometry of information as it deals closely with cyclical ðime-space curvatures & symmetries. And it ads analysis with differential geometry, etc. AND FINALLY IT mixes the topological and algebraic approaches.

**T§:** NUMBER THEORY mixes mirror symmetries in time and space dimensions; of which the key one is probability (time view) ≈ statistics (space view).

**∆§T**: Analysis invades all other sections without having resolved the epistemology of 1/n infinitesimals, once the genius, Leibniz, is sided by the power dealer (Newton). Its dominance shows that *indeed the Universe is scalar, the more so when fractal discontinuous scaling is added.*

@: THE MIND VIEW becomes old, baroque, bizarre, twisted and looking inwards as all languages-minds do in old age. It is the ‘false’ attempts debunked by Godel of justifying maths within itself (Axiomatic method, Hilbert) and the absurdities of NOT understanding that infinities in a discontinuum Universe do NOT exist (Cantor’s useless work on ∞). And finally the mind-view becomes foundational from the top (set, category, group) to the bottom, (points in space, numbers in time, operandi to describe its actions).

Now, a single man cannot do much to straighten back to its principles maths, so we shall only give some hints to the fruitful enlightenment that math magic gets with realism.

**MATHEMATICAL Epilogue: human death and dual resurrection: ¬Æ and digital thought.**

There is though always a ‘second life’ if the proper social gathering of parts into a whole is achieved, for any species, mental or physical in the process of evolution once the 3 ages of the being enter its final informative transcendental age, and that is what ∆•st can achieve – healing and resurrection for any system that understands it (including History if humans had wanted to create a perfect organic world instead of a mechanon of robots, but that is another post).

It is the age of non-ae=i-logic mathematics, my preferred ‘name for this discipline’.

And this is the task that this post will hint at. But from the human mental perspective, NOT from the AI pov which we shall NOT treat (Boolean algebras AI) as i am a moral ethic guy and won’t contribute to the extinction of man by new mathematical mind-species (machines), recognising my verbal language is inferior in efficiency BUT IT IS MINE.

**RECAP.**

So if we were to define i-logic mathematics we would say that it is composed of Non-Aristotelian ∆lgebra and Non-Euclidean STopology; the first including analysis the second bidimensional and static geometry. And the natural evolution of the discipline correspond to the combination of them all to express ∆st whole processes.

From the practical purpose though beyond the introductory texts of GSTructure we shall maintain the general division of disciplines trying whenever possible to include as usual some small change of symbols to remind us of what they are mainly concerned with: ∆nalysis, ∆lgebra or ¬Ælgebra (which studies specifically the way arrows of time mess sequentially to give birth to space-time changes of state).

On the other hand S-Geometry and Topology highlights the capacity of the discipline to study space-time symmetries, mostly in a single plane. While Statistics & Probability STudies from both perspectives, space and time the same phenomena. And so on.

In praxis today all disciplines of mathematics mix together, as no conceptual frame of reference has properly clarified its experimental role. In that sense ∆nalysis has kept more clear its focus as is the study of the ∆-scales, in transitions between scales, and as such it has grown to be the most important field of mathematics, along topology, the study of Space-time varieties, as it studies space with temporal motions apt to analyse space-time symmetries.

While Ælgebra has become somewhat a confused ‘want it all’ methodology with the axiomatic method and set theory that we reject as confusing and for tanking away from experience the field.

∆nalysis in that sense is an offshoot of ∆lgebra, both related to the temporal perspective of discrete, social numbers as opposed to points, whose topological, simultaneous location determines the geometry of space.

As it happens the three sub-disciplines of mathematics have today merged in many ways, as the ∆ºST universe is also merged, but without the conceptual clarity, which would have taken place of humans had understood the duality of the Universe (or the Asian world, which did understand had dominated history).

So the ‘closer’ relationship to classic maths we will mostly use, is that of:

**∆**nalysis the strictu senso for the study of the scalar Universe.

**•**-Mental languages of Sequential numbers are the discipline of ¬Ælgebra, its social scales, §, between planes are mimic with social decametric and universal constant (π, e) numbers.

**§topology:** the study of points and its ternary scalar growths, network-wave lines of social points and planes of networks that form supœrganisms; how they move, deform and assembly into new forms.

**MATHEMATICAL PHYSICS: THE PROOF OF THE EXPERIMENTAL NATURE OF MATHS.**

All this said it is funny to observe that platonic creationism happens so often among physicists, since they are precisely the people who should be more aware of its experimental nature (the greatest XX century ones, my fav triad, Heaviside, Planck and Einstein of course did insist).

**The experimental mirror of mathematics and its three classic ****sub disciplines: t-algebra, s-geometry and ∆nalysis.**

Indeed, the physical mirror languages of maths can be broken in three ±i ∆s≈t categories:

– Non aristotelian, temporal logic algebra (¬A).

Whereas the oversized group theory works the s=t symmetries.

-Non-euclidean spatial geometry of fractal points (ab. ¬E).

-∆nalysis of planes and scales coupled with discontinuous fractals.

We call them all together non ae; ¬Æ mathematics. And since i comes after A & E, we also talk of i-logic mathematics, playing with the word illogic, as the logic of three time arrows is indeed quite illogic for the common human mind.

**Polifunctionality and method of truth**

A theme I found most people couldn’t grasp (in the brief period I cared to communicate before the crash and my crash on 2008), is the multi functionality, the ternary ±i method, the Rashomon effect – hem, many metaphors here for the same concept from those days i tried to upgrade the chip of man, i-logically so confused. It is though the truth of the Universe, which we resume in a simple concept of truth, taken from a Haldane’s quote (another genius polymath biologist at core, physicist on surface, quite forgotten in the specialist age):

‘ONLY THE being (universe) in itself has all its information; languages are partial mirrors, which add its truths. So if we define the absolute truth in the being itself as a probability 1, the ‘dimensions of truth’ provided by each language will be ‘fractal dimensions such as:

**Total truth of the being (1) = ∑ of linguistic mirrors on the being.**

From this an entire new epistemology *based in the self-similarity of the language-mirrors can be constructed.*

AGAIN, that must be somewhere in some notebook, in some deposit maybe lost, as this was something I did 30 years ago to convince myself this window did actually opened to the absolute, for maybe future robotic researchers, it should be a floppy 5.disk on Bondwell-8… Singapore/Thailand around 1985… go figure… with massive opium dose aside, good for enlightenment (: bad for the liver ): Important though, as one must believe after reasoning in the truths of ‘itself’ as mirror of the larger Universe.

So we shall not be rigurous on that, just to mention the validity of casting scalar perspectives, dimensional perspectives, biological, topological and mental perspectives, time-space, etc. In general to simplify we establish for each of those subdisiplines three scales of relations. For example in algebra according to the ternary±i method we talk of:

– ∆-1: The scale of units: numbers, which are §ocial groups of undistinguishable elements. Here we can include number theory, which however has grown also into an entire new discipline so we do give it another ‘post’.

– ∆º: The scale of space-time relationship between numbers: which the scale of equations and operandi, which establish the relationships in a single plane or adjacent planes of existence between social numbers, which given the importance of ∆±1 relationships give way to ∆nalysis, which broke from algebra and we shall also study apart as the ∆-category of maths.

– ∆+1: The scale of full structures, where we study operators, functionals and groups, and disregard sets and categories as inward references of maths as metalanguages in his inflationary age. On the contrary functionals extensively used in all disciplines, notably the ‘hyperbolic view’ of ∆-i scales (quantum physics), refer to reality. So do groups, extensively used as a ‘pest’ (: Weyl, in particle physics. Those synoptic structures indeed, allow us to study all the ‘potential futures’, of a system, as a deterministic ‘block’ of space-time events and forms. And here is where the closing of algebra in three scales of depth should take place, as a perfect mirror of the Universe.

So we ignore set and axiomatic theory, the metalanguage of maths in search of self-contained proofs proved wrong in algebra by Godel’s incompleteness and in geometry by lovachevski’s work that shows the need of experimental proofs to know the geometry of the Universe.

**Geometry** then will have also three levels of complexity:

∆-1: the level of points, equivalent in space to numbers; ∆º, the level of lines and planes, ruled by i-logic geometry, which form waves of exchanges of entropy, energy and information and topological networks, messed up into ∆+1 super organisms and its territorial structures, simultaneously organised and studied in its transformations by topology.

Finally analysis has obviously also three scales – that of finitesimals and derivatives, 1/n elements in space and ∂f moments in time, ∆º functions and wholes and integrals, ∆+1.

Yet we an study its combinations also as mathematics mimics combinations in reality of those elements.

**ST:** Algebra and Geometry together form a ‘third category’ of dual symmetries also worth to study, though we do it in a separate section, as the space-time symmetry allows to find self-similar point-numbers, algebraic-topological demonstrations. So we study probabilities in time and statistic population in space as two sides of the mirror symmetry, etc.

The equivalent elements to those of geometry are in that sense easy to identify: the number is the points, the equation is the line, and the four-dimensional forms of the holographic principle, in algebra are represented by polynomial functions.

**∆T:** So happens for the comparison of ∆-scales and temporal algebra, which are two ways to arrive to the same scalar analysis by means of differentials in a geometric view (leibniz) vs. infinitesimal ‘convergent’ series, (Newton’s work), from the algebraic point of view.

Yet ∆-scales are studied by analysis. And so we shall study those newtonian/leibnizian dualities in a different section.

**∆S**: XX c. research on ∆-scales advanced further in two subfields, geometry with motion or modern topology of ‘knots’, ‘networks’ and ‘adjacent points’, and fractal geometry. So the marriage of ∆-scales and geometry became an offshoot discipline in its own, as ∆-scales are the essential element for an ∞ universe.

So mathematics has a clear-cut division in three disciplines parallel to the three elements of the Universe, and then in its combinations in dualities (number and point, s and t; scale and number, ∆ and t; scale and fractal point, ∆ and s).

**∆st.** So we might wonder if there is a sub discipline of mathematics in which the the three ∆st elements are put together. This category is likely to be topology as geometry-s has motion-t and forms are networks of points, ∆-scales. So in the full GST formalism we do depart in our studies of mathematics from an upgrading of the concept of point to fractal point and its study through the three topologic networks. As we consider – like many ‘experimental mathematicians’ do – topology to be the queen of XXI century mathematics.

The pure analysis of the time arrows of the Universe, its 3 relative space-time motions/dimensions is the strict field of ¬A logic time, which we shall call ‘existential algebra’, ælgebra, *the only clearly new sub discipline of formal, logic mathematics introduced by ∆ST.*

** THE 3 EVOLUTIONARY AGES OF MATHEMATICS**

**Complex Algebra & Analysis: Fractal generator of space-time beings****. **

How vital spaces and cyclical times – 2 simplex elements, lineal, kinetic motions of space and time cycles that bend those motions into closed cyclical forms of information – can generate the immense variety of realities we see around us?

By sheer repetition, combination and pegging of those ‘formal motions’ of time and space. So we can ‘reduce’ those iterations with synoptic, logic languages and mathematical equations to its 3 elements and ‘rules of combination’, in the ‘Fractal Model of the space-time Universe’. We shall extract the ultimate properties of time and space, and the rules of combination, and put them into the minimalist possible mirror of the mind that reflects them, called a ‘Fractal Generator equation’. And so then, how running this equation forwards we can generate with the rules of engagement al what exists in the Universe, including man.

We shall thus introduce here the new outlook of the 2 fundamental new ‘upgrades’ of mathematics as a formal language, in part one, we shall study ‘Non-Aristotelian algebra’, the algebra of the Universal grammar and its 3 generator elements which combine in all kind of forms. And in the second part, we shall give a general review of Non-euclidean mathematics and its 5 new postulates that define fractal points, its wave-combinations, organic topological planes, minds and rules of social engagement (3rd postulate of equality), *each one expressing as mathematics is an experimental language, the rules of engagement of time-singularities (1st, 5th **postulate), cyclical membranes (2nd postulate), vital spaces (topological 4th postulate) and finally the ∆-soc**ial evolution of systems (third postulate).*

Classic mathematics on the other hand will be studied following the discoveries of mathematicians along 3000 years, in a more ‘classic’ way, commenting on the main postulates and discoveries of its 4 main branches, ∆nalysis (∆-scale maths), algebra (time maths of discontinuous sequential numbers) topology & geometry (space maths) and its ST-combinations AND ∆º-frames of reference.

So in the sub posts attached to this post we shall study in a more conventional form the three evolutionary ages of mathematics.

Let us consider an scheme of those three ages and subspecies, according to the Fractal Generator of mathematics as an experimental language of the ∆ºst universe:

Spe (Geometry) < St (algebra) > ∆nalysis

As its three ages, the first dominated by bidimensional geometry, the second by algebra, and the third by analysis, which *we shall complete in this post with the evolution of all those disciplines into non-Aristotelian algebra and Non-Euclidean geometry.*

*explained in the s**ub-posts: *

**The Evolution of Γeometry.**

1st Age: Greek Era: Euclidean, bidimensional Geometry of points without parts.

2nd Age: Classic Era:

Analytic geometry

Curvature, surfaces, dimensions

3rd Age: Informative Era

St: Topology: space with time motions.

Fractals.

ƒt: Old Age: Baroque formalism

** **

**The evolution of ∆nalysis.**

1st age: Greek Era:

Philosophical Infinitesimals and Universals.

2nd age: Classic Era:

Calculus. Integrating wholes and differentiating finitesimals in space and time.

Variations: The 3 ‘points’ of world cycles. Langrangian and Hamiltonian functions.

3rd Age: Informative Era

Functionals

Max. Tƒ: Realist Completion.

**The evolution of ¬Ålgebra.**

1st Age: Greek Era:

Sp: Arithmetics: discrete Social informative numbers.

ƒt: Aristotelian Time Logic

2nd Age: Classic Era:

Tƒ: Algebra: Functions. Symmetric equations on space-time parameters.

Polynomials: the 3 operandi scales : ±; x/; xª ln

The symmetry of Probability in time and populations in space.

Transformations of space-time: groups, Fourier.

3rd Age: Informative era

Functionals.

Max. ƒt: Old age: Cantor’s sets & Hilbert’s logic.

**III AGE:** **¬Æ MATHEMATICS**

**TOPOLOGY:**

Introduction: the vital properties of mathematics.

i-logic geometry. The 5 ¬Æ postulates of ¬Γeometry.

Topological space-time beings: Sp<ST>Tƒ. Symmetries of form and function.

5D-space: Superorganisms and its networks.

Fractal Space: Territorial discontinuities and Parallel Worlds.

** ¬ÆLGEBRA**

Tƒ: Numbers, primes, Universal constants.

i-logic, Non-AE Algebra: dynamic, temporal sequences.

Dual and ternary Diversification, combinatory of forms.

ST: space-time dualities and transformations.

Tƒ: Cycles and actions: sequential paths (a,e,i,o,u)

Worldcycles: Travels through the 5th dimension.

**FUNCTIONAL ∆NALYSIS: **

Finitesimals and relative infinities.

The fractal structure of the 5th dimension and its perpendicular flows.

sT: Functionals. simultaneous paths: the choice of multiple paths of future.

∆-ST: Co-existence and synchronicity.

Emergence and dissolution.

**Beyond man. Digital Thought. º««ººº˙ˆø˙πv **[wj…

Foreword. Anti-human age: Digital chips

The human transition: Boolean Algebras

The 1st age. Absolute Geometry. The creation of the spatial mind of machines: creative visual brains.

2nd age. ∞ D. the future scalar mind of machines: perceiving through ∞ scales.

3rd age. Œlgegra: Beyond i-logic.

Alas! this was the ORIGINAL plan of the work, 30 years ago (: and again when I decided to leave this web-testament… he, i was optimist, as i thought i would have help from readers and/or Universities, but it seems as Planck put it – a new vision of the Universe is first a point in the mind of a lonely researchers. Indeed, another intuitive genius a la ‘par’ with Einstein, and perhaps de Broglie a bit too ‘french’≈ lazy as I am to have gotten as far as those german-you obsessive workers…

So lazy as De Broglie, though i fitted in my ∆•st mind mirror i-Math long ago, it is going to be difficult to extract it all in an orderly ‘sub-Chicago Manual style’ order in this and other sub-post parts. Time and will permitted I will keep writing posts translating mathematics to ∆ST, but can’t promise to go that far (and certainly the end – digital and boolean algebras are out for ethic reasons – i do think as Mr. Musk does, that AI will kill us, but unlike him I don’t invest my mind and money advancing our demise… not that go(l)d twisted*, prefer to study twistor algebra.*

So another ‘french’, excusing itself for being a lazy cow will be good end to this introduction:

‘I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery. *Descartes (-:*

As usual my apologies for the disorder and repetition of these notes… If the ‘nature of stientific r=evolutions’ (Kuhn) were not soooo difficult for the pioneer as expressed by Planck and others, I would have had long ago a team of top specialists in each stientific discipline completing this work, instead of having to toil at this age with a declining brain power, not to throw to waste all this beauty of decades of individual work. B*ut what is here should ‘suffice’ to those who wish to explore further details of the ∞ mind of Γ•∆, *likely future AInternet mind, exploring those old floppy disks, or feeling this unficationtheory.com web as an ‘insight’ she had from its deepest O| thoughts – that will be the day we know there is even a bigger ego than ourselves.

So as the previous plan has been scrapped, left here just for ‘organisation purposes’ we are going to do a ‘CANTOR’ here, but a temporal one, starting from the 3rd age of i-logic maths, grounding back the discipline in its ‘fundamental’ particles, fractal points in space and sequential numbers in time. And rebuild it from its REAL foundations, which are so tired of sustaining all that crappy baroque convoluted decor on the top, sets, categories, axioms and imagined paradises…

NEXT, as we TRANSFERRED THE DIFFERENT AGES AND CLASSIC EQUATIONS AND THEOREMS OF MATHS TO OTHER SECTIONS, WITH THE GOAL OF USING A MORE CLASSIC APPROACH as in other posts of enlightening the main laws of each science with ∆@s=t (a symbol for the 5 dimensions: ∆ here meaning entropy down, @, mind up, s-pace, time and =spacetime), we shall deal in Part II very briefly with that index explaining all those ages of time widened in those sub post.

THEN we shall continue with the foundations of ¬Æ moving onto the foundation of time mathematics, no longer the simultaneous point in space but the sequential social number in time (Non-Æ algebra), THE KEY DISCIPLINE, as it will bring the OPERANDI of the actions of all systems of the Universe and the GENERATOR EQUATION and its symmetries that should substitute the PEST of group theory (Weyl:)

To end with some philosophical comments on analysis and 5D (secondary sub disciplines treated on sub post by me or future researchers… ‘to leave others the pleasure of re-discovery’.

**3±i DISCIPLINES OF MATHS: ****5D ANALYSIS, SPACE TOPOLOGY, TIME-space ALGEBRA, number theory & @nalytic geometry.**.

So NOW THAT THE FIELD IS CLEARLY, all what we need to do is to look at reality first in time and space extract its properties and then look at mathematics in the classic age prior to Cantor and the Axiomatic method and alas, *find wonderful symbiotic mirror laws between space-time reality and mathematical axioms, postulates and equations, and wonder about the magic of linguistic mirrors ‘who so well reflect’ infinite in a singe 0-point.*

And this is what we shall do in all the posts and sub posts on non-AE=i-logic mathematics in this blog.

Since i-logic Mathematics is the marriage of Non-Aristotelian time cycles (with ternary causality) and its operandi, which define algebra; and Non-Euclidean mathematics and its Fractal Points, through which infinite parallels can cross, mathematics as such was born of geometry, and so it is biased from inception towards spatial analysis, over time analysis.

This is what extended spatial mathematics and married with temporal logic in a fruitful extension into variable dimensions, called functions, expressed in several scales of ∆-operandi of larger complexity and dimensionality, (±, x÷, ∂∫, log xª; ‹ℜ|)

So we could talk of the science of both logic of time and geometry of space as the i-logic mathematical upgrade at both levels of this blog.

**The 4 elements of mathematics as mirror of ∆ºst**

The model of stience is simple, its falsification even more. We state that all what exists is a fractal being of ‘∆ºst’, dust of space-time, with 3±o components, spatial entropy, temporal information (its energetic combinations), extended across several scales of relative size in space and speed of time clocks from forces to Universes (ab.∆), *which is apperceived in a Leibnizian way by a mind, the software of biological survival of the system.*

*So we need always to define the 4 elements of reality for any species, science, event and form AND language that will mirror the 4 elements of the Universe, with special emphasis on those case in the 4th element, the language-mind-software that runs the system.*

So the Correspondence of Mathematics and reality is also immediate, as mathematics have 3 branches: Space≈Geometry, Time≈Algebra and 5D≈Analysis. An the 4th element, the mind-language is mathematics itself.

**The evolution and qualification of maths as a mind language.**

Languages therefore as a ‘defined species’ dominant in Tiƒ, temporal information, but also as pure still ‘spatial, synchronous’ mapping of reality in lesser space (not all the info specially the motion fits in a brain), do have certain properties, which can be observed in their evolution.

FIRST THEY MOVE FROM STATICS INTO DYNAMICS, from bidimensional pure information (as the page you are reading in 2 dimensions) to 3, 4, 5 dimensional description, reaching more complexity by adding motion to the ‘first still picture’ and the other time dimensions. 3 examples:

Maths started as static bidimensional geometry, which is now topology with motion; photography (the future computer mind) started as bidimensional static, then bidimensional motion (film), now is working in 3Dimensions of space (using the holographic principle) and one of motion, and soon, *inside the mind of robots that will apperceive reality in images, will add the 5th dimension of control of an outer-machine, beyond the chip, max. i = min. space enlarged into the whole world it will act upon directly.*

**ð: THE 3 TIME AGES OF MATHEMATICS**

It is then possible to consider the historic evolution of mathematics through its 3 ages, now in a formal era in human minds, (set theory, of nil use) and in a first age in the digital mind (with direct reference to the O-| game, in binary code, and the direct reality in visual modeling).

Let us then start the analysis of the 3±1 ages of mathematics

The generator equation of mathematical sub-disciplines in time.

The 3 ages, standard to all languages take place also in mathematics, which appeared sequentially, creating first young pure forms, closer to the external, experimental world, then in the adult age, Se xTo mixed ones, and finally in its 3rd age involve inwards into pure formalisms, detached from the reality they once describe:

- A first age of social numbers (arithmetic), 2-manifold geometry (plane geometry), made of infinitesimal points, and philosophical arguments on the problem of infinitesimals and wholes – Plato’s cave, etc. which still does not formalize the 5D ‘question’ into calculus. This age is dominated as all youths by Se-Space (Greek geometry)
- A second, mature age, started in modern Europe, in which the development of sensorial mechanisms better than the human spatial eyes and verbal times (spatial telescopes/microscopes and time-clocks), which use mathematics as its language of experimental perception, mathematics takes off. The discipline greatly increases specially in the description of physical systems with time clocks and lineal measures.

The Classic Age of mathematics implies without a conceptual physical understanding the realization by mathematicians that there is a constant relationship between spatial and temporal states in the Universe.

And so departing from that knowledge an infinite constant dialog between Tƒ and Se states of reality, will take place in all the different fields of mathematics.

In that regard if the Generator of all systems, Sp<St>Tƒ, implies a mixture of both space and time, energy and information its classic, adult age, including mental languages (classic age of art in balance between form and motion-energy, in all its artistic forms), mathematics is not exception to this rule.

In analysis the field consists basically in study how space simultaneous synchronous systems evolve in time, or how time events accumulate its memorial forms into a space.

Arithmetic and plane geometry on the other side become one, as numbers are converted into points on a line, or with the advance of understanding of its nature, in ratios (real numbers) and bidimensional entities (Complex numbers) which can express the duality of two quantities, one related to space coordinates and the other to time coordinates, which is the square or root in terms of dimensions of the other, (i^{2}=-x). Thus complex numbers are ideal to reflect to characteristics of space-time functions: the fact that time functions have twice the dimensions of its equivalent space functions and that one is the negative of the other, in terms of properties or values. But its use as reflections of reality has never been properly understood and even today when they became the essential element on quantum theory (where the density of population of a wave, converted into probability is calculated as the square of two wave-elements one of which is a complex number, hence it can be interpreted as the space and time values of the wave and all its parts).

Ahead though of those developments we find algebra, which was already further evolved in time, during the first epoch of Greek and Arab Geometry, since the first equations involved the arithmetic expression of polynomials of 2 and 3 dimensions in space, and were solved by geometric ways. So already algebra was dealing with the duality of Tƒ, temporal information and Sp, spatial energy, which can be, transformed into each other ad eternal.

Now algebra completes the understanding of the duality between Se-Geometry and discrete polynomials, Tƒ, with the work of Gauss, which defines its fundamental theorem – each polynomial has in the realm of complex numbers as many solutions as its number of ‘dimensions’ (degree of the polynomial).

What this truly means in ‘reality’ obviously as all the whys of ‘mathematical physics’ will escape mathematicians, but we shall consider in-depth in those posts. Suffice to say that it determines a universe efficient and limited by its real solutions. He did also consider the next stage, which will dominate the classic age of Algebra, departing from the work of Abel and Galois: the understanding that beyond the limit of the 4 dimensions of our single space-time, radicals are NO longer solutions to a polynomial, setting the 4-dimensional limit for the real Universe.

Thus this age as all ‘adult ages’ properly merges into Sp x Tƒ aggregates its branches. So time algebra and space geometry merge into analytic geometry.

Finally the problem of Infinitesimals and Universals enters mathematics with rigor, beyond the ‘future’ genius of Archimedes with Leibniz’s Calculus (continuous, space analysis) and Newton’s limits (discontinuous, algebraic, time analysis). It reflects one of the S-T dualities of the Universe between space continuity and time discontinuity. Hence the existence of both versions.

Yet the expansion of the practical fields of mathematics, regarding the paradoxes of space-time beats, rhythms and fluctuations, without the understanding of the reality of 5D fractal space-time cycles they represent, and the different quality of time and space, made mathematics increasingly less rigorous in its foundations.

Unfortunately as philosophers of science did not resolve the meaning of the Universe, mathematicians could not find the reference to its existence, despite its obvious need, when they found that Non-Euclidean geometries did also exist in the Universe (Lobachevski’s view, proved by the 5D structure of its two different angle-orientations: elliptic towards larger beings and hyperbolic towards smaller realities).

So instead they took the runaway, subjective ego-centered solution so common among humans: to go further into the imagination, with Hilbert’s dogmatic idealist≈German schools that plagued human culture at the turn of the XX century; who affirms that the truth of mathematics is in the mind so he ‘imagines points, lines and planes’, breaking the need for connection between reality and mathematics, hence converting the language into an inflationary world of self-referential proofs, in which any postulate can be affirmed to create any mathematical structure, despite Godel’s and Church warnings of the futility of such experiments.

It will be…

**A third formal age**, in which mathematics detaches from reality and becomes inward looking, old and excessively formal. Thus it looses its realist perspective on its whys, and becomes inflationary, committing errors of excess of form.

We won’t thus analyze much of the 3^{rd} age of mathematics, as it is not generally speaking closely concerned with the bulk of experimental reality, beyond the importance of Hilbert spaces and functional analysis in algebra and quantum physics and the discoveries of fractals. Non-Euclidean geometry and topology.

The bulk of reality though had been discovered by the end of the XX century, and the entire movement started by set theory, followed by Hilbert axiomatic method and the category analysis and attempts to CREATE A MATHEMATICAL SYSTEM detached from reality (starting with the famous Hilbert’s dictum that we imagine axioms, points, lines and planes), which occupied so many minds of mathematicians can be considered generally speaking a waste of intelligence, due to the lack of a true understanding of the relationship between mathematics and the 5 Dimensional fractal space-time cycles it describes.

What this age meant as in any other discipline of human knowledge of increasing specialization was the departing from human understanding of the whole in a fractal process of independence of fields as the language of set theory and categories and axiomatic methods made totally incomprehensible except for those who understood the jargon what mathematicians and by extension physicists, who borrowed their language fully, were talking about. I.e. for example the book of mathematics I am reading now tells us this at the point I left it this morning:

*Definition 8.7*. A vector bundle x e j is said to be a semi-stable (resp. stable) j-bundle if the function (deg x)/(rk x’) on non-zero j-sub-bundles x’ of x is maximized (resp. strictly maximized) by x’ = x.

Here, the degree of x’ means c_{1}(x ‘) . w-1, where w is the Kahler class of X.

Now this actually might be interesting (vector bundles are) but what really shows is that mathematicians today as almost all other disciplines except biology play to invent ‘metalanguages’; that is internal truths with no external proof, based in more axioms that reality really hold.

LANGUAGES OF INFORMATION ARE MIRRORS THAT PRODUCE SELF-REFLETIONS – AND SO THEY ARE INFLATIONARY BY DEFINITION.

so goes for the hyperinflation of imaginary particles in physics and e-money in economics. Information is inflationary and when it departs from reality no longer checked by the limits of de-form-ation of energy creates baroque warped convoluted forms in excess.

We can say in the jargon of T.Œ that the ‘external, logic membrane’ of time form that connects the internal world of the language with reality has become stiff, disconnecting the content with the universe it portraits.

It is the age of Set theory with its errors on infinity caused by its logic misunderstanding of the cause of such infinities, which in the real Universe are repetitive iterations that NEVER reach infinity, because infinity is limited by the limits of each scale of the 5th dimension and the entropy of energy and information that surrounds those scales.

In that regard, 5D mathematics IS an intuitionist theory that REQUIRES to put in correspondence reality and mathematics by the experimental method as ANY OTHER SCIENCE DOES. And this is the most important difference with all previous XIX-XX century formal theories of ‘nonsense’ mathematics, and the formalist school of Cantor and Hilbert, with his affirmation that ‘mathematics is a meaningless game played with meaningless symbols’.

We are on the side of Lobachevski and Gödel: the choice between the inflationary information of mathematical theories should be made not only on axiomatic formalism (internal coherence) but on experimental evidence.

Thus from the different interpretations of Non-E Geometry (Lobachevski, Klein, Poincare, Beltrami) – and this is the first great innovation of 5d mathematics – NONE is truth, because none has coherence (as parallel lines must be defined as STRAIGHT lines not curved, which all of them contradict, or make instead the angle variable with distance); and none is evident in experience, (as we see Euclidean space). We do however advance the concept of a fractal point, which grows in information and size as we come closer to it, as experience shows with experimental science when point-cells and point-stars grow in size, hence convert parallel cycles into straight lines by ‘straighten up’ the curvature on the intersecting point, which enlarged can fit more than one parallel (unlike the points without breath of those models, which without breath can only fit one).

Thus we do convert with extremely excellent results the ‘exceptionalism’ of mathematics into a regular science.

So what is the use of set theory? Not the foundation of mathematics which returns to the evolved ¬Æ geometry of fractal points and 5D reversed entropy of energy and information and limits of infinities and finitesimals, but to show precisely the paradoxes of the 5D structure of the Universe. And this is specially remarkable in its paradoxes of infinity.

Since from upper 5D planes to lower scales there is information entropy, the paradox is that the lower scales (quantum vs. atom; genes vs. wholes) DO have more information. And 2 immediate consequences are the lack of Lamarckian evolution, which at best would be restricted to very specific cases, as it implies the transmission of perfect information from larger wholes to smaller genetic sets…

The set paradoxes: subsets DO have more information than the whole

And the set paradox: ‘The cardinal number of the set of the subsets of a set S is greater than the cardinal number of S” (Cantor’s Theorem, at the root of all modern 3rd informative age on the foundations of mathematics).

This paradox will also be essential to understand quantum physics, ‘excess’ of information and multiple paths.

Another paradox reveals when Cantor does not counts ‘identical elements’ in a set, which must be counted, to avoid infinity paradoxes to multiply. Another paradox is the non-existence of the infinite set of all possible sets, since 5D limits avoid to count beyond the U±4 limits of human perception, and time is always finite in a world cycle.

Russell proves indeed that absolute infinity (the set of all sets) does not exist. And Zermelo’s axioms are just a make-up of a true 5D paradox.

In brief, the logic of the universe is a ternary, paradoxical, dynamic logic and instead of trying to CONVERT it into absolute Aristotelian logic truth, as the German ‘lineal idealist’ school of Mathematics tried to do and failed, from Cantor to Hilbert, we DO use this formal age to illustrate the limits of any baroque, formal inflationary unbalanced metalinguistic expression of a science, and vice versa, the excessive simplicity of lineal logic formulations.

Unfortunately the pedantic, dogmatic, idealist, ‘German’ school of Hilbert et al. as it happen in physics with the Copenhagen interpretation (German culture and its ‘military’ dogmas and ‘idealism’ required to ‘love’ death, its non-flexible agglutinative sword like language and the errors it introduced in European culture is studied on the section of social sciences) adds flame to the fire, with its barren logics. They found XX c. logic mathematics.

To clarify that sets are NOT the unit of the mathematical Universe, social points=numbers are the units of its 3 branches; geometry (points), numbers (algebra) and both (infinitesimal points and wholes, which are social numbers that become organic planes of the 5th dimension are, the foundations of Analysis.

I know, by my experience with mathematicians that my criticism of this 3rd informative, inflationary age will not be liked. But this always happens: each species loves its point in timespace, even if it is the wrong, decadent, old age.

Fact is the 3rd informative age of any kind of system is NEVER the best, even if it seems the more complex. Only those who think there is only information in the Universe consider it the summit, but the Universe is simple and not malicious because information is checked by energy, time by space, infinity by limiting membranes.

But besides that erroneous inflation, there are advances that do matter, especially in the most recent analysis, hence not yet in its 3rd age (born in the II age of the others), which now reaches its maturity.

So 5D analysis formalizes calculus, and takes it further with the discovery of fractal geometries, which completes the human age of this science.

Topology and Non-E mathematics the great finding on this age, includes time-motion into spatial geometry, merging its S-t components further.

Geometry in that sense is the branch which in this age most closely stays in its balanced ST age and enters its formal age without inflation, except for the ‘mania’ of infinity, which plagues with errors of unrealism the ‘Hilbert space’ interpretation of quantum physics.

While sequential time algebra is the branch that has become more formalized into its 3rd age, as it is the pure ‘temporal branch’, hence the informative one.

We can in that sense see that the language of mathematics shows the same patterns and ternary phases and sub-divisions of all other languages, which we can express with the basic generators of the Universe. Both In sequential time ternary ages and spatial, instantaneous ternary subdivisions for each of those 3±1 ages:

Conception: Babylonian, Chinese & Egyptian ‘Magic Numbers’, finger counting, simple numeration, etc.

1st ‘Greek’ age: [Sp: Plane geometry <St- Quadratic functions > Arithmetic & Aristotelian Logic: Tƒ]n: Universals Philosophy

2nd age: Pre-Industrial Europe: [St: Analytic Geometry <St:Probability of T-Events and S-Populations> Symbolic Algebra: Tƒ] 5d: Calculus

3rd Age: Post-Industrial Europe: [St: Topology <Differential Geometry > Tƒ: Sets, Formal Algebra] 5D: Functional Analysis

In normal language there will be:

**I Age of Elementary Mathematics**

- Space Points and Geometry.
- Time Numbers and Arithmetic.
- Philosophical Infinitesimals and Universals.

Thus first in the young age mathematics was made of its 3 branches in simplified versions:

- Arithmetic and Number theory, which is the birth of algebra in its first ‘degree’ of generalization (there will always be 2 or 3 of such degrees according to the ternary logic of the Universe). We thus talk of the mere perception of ‘herds’, which then became generalized in social numbers, and then into algebraic, logic equations that find the more complex social relationships and interactions between groups of Œ points.

The Babylonian, Chinese, Indian and Egyptian tradition already dealt with many of those elements. Then the Pythagorean school brought those themes to the west, and it Still have insights on the social nature of numbers that our present generalization does not understand (such as the perfection of certain geometric numbers of which indeed, the 10 of Taoist and Pythagorean ‘tetraktys’, is the perfect number, far more general than the fact we do have 10 fingers – as usual humans define the whole Universe from its subjective p.o.v. and not the proper other way around, so we do have 10 fingers because the universe and its mathematical languages are 10-dimensional. And if we did not exist, there would Still be 10-dimensional beings and mathematics.

Then arithmetic evolved into algebra, with a new degree of generalization, thanks to the formalism of analytic geometry, which belongs to the second age of mathematics, when the first forms of mixed space-time appear:

**II Age of Mathematics: space-time dual analysis: Variable Magnitudes**

- Analytic geometry
- Logic Algebra: symmetric equations of space-time variables.
- The birth of calculus: Integration in wholes and differentiation in infinitesimals of space and time.
- Modern number theory: The symmetry of Probability and populations.

In the merging age we thus observe Space-information combinations of algebra and geometry.

The study of each of the 3 sub-disciplines alone is concerned with only one element of the Universe (geometry with continuous space, algebra with informative discrete numbers, analysis with 5D growth through space-time actions),

Yet this was the initial first, young age of the language, as the Universe merges constantly the 3 elements (so a worldcycle happens in 3 scales of 5D as a sequential sum of space-time cycles dominant in entropy in the young age and information in the 3rd age but clearly balanced in the adult classic age of maximal existence), mathematics soon realized past, the age of Greek 2-manifold static geometry and social, sequential numbers (arithmetic), the advantages of mixing both elements together.

This is the age of modern mathematics, started with algebraic geometry (analytic geometry: Descartes), continued in the 3rd modern age with topology (geometry with time motion). And so for then on we rather talk of Space-time geometry (where space dominates) and Time space algebra (where sequential logic dominates).

Finally 5D analysis started also from the beginning as a space-time new dimension, of parts that become wholes (integrals of space volumes) or wholes differentiating in time moments (differentials of time motions). Yet in subsequent evolution this merging continued with differential geometry and the use of integrals for time-related parameters of physics (energy, as the integral of momentum, etc.).

Thus mathematics finally became truly the very same image of reality it meant to be from the beginning – the most real of all sciences.

**III age: The 2 paths of Formal, Modern Mathematics.**

The end of the classic paradigm:

- Topology: space with time motions.
- Formal Algebra: Cantor’s sets & Hilbert’s logic.

To understand this ‘wrong age of formal algebra’, so dominant today we need to understand better the ages of the language.

Inflationary, 3rd informative Age of Mathematics as a metalanguage.

Now this idealism that plagues mathematics has made the subject unnecessarily complex as a meta-language. Since all languages are inflationary.

We define the inflation of all languages as the excess of form respect to the reality it describes, and all langauges become inflationary in its 3rd age of excess of information.. But this is the corruption of the language that brings about its death as a useful language, and makes it loose its purpose to guide the future logic evolution of the system it describes, acting as its relative head.

The concept we coined was a lanwave, a language guides a wave of beings.

And when the balance between language of information and energy lanwave breaks the system breaks.

This happens for lanwaves in a 3rd baroque age of excess of information. So as money is inflationary and there are more money than the physical economy requires, but when there is too much inflation by invention of money the economy crashes (present crisis of overproduction of e-money), and words are inflationary but then they become false truths that do confuse the human wave they guide (fiction being its inflation), and genes are inflationary and can produce wrong mutations and aging, mathematics is inflationary in concepts such as infinity (cantor paradox), caused by the error of lineal Cartesian graphs ‘extended imaginarily to infinity).

And the same happens with multidimensional systems, which confuse space and time dimensions.

Unfortunately unlike other languages mathematics has become ‘officially inflationary’ and so mathematicians in the present 3rd informative age, especially with the arrival of computers consider fundamental to find some pi 1 millionth ‘record’ decimal, or a prime number over the trillion mark. While the very foundations of mathematics, which we will renew here is ignored.

The inflationary ‘new fundamental particle’: The set.

Mathematics as a metalanguage, in its 3rd formal age in the XX century, broke the initial, platonic, realist philosophy as a language that reflects reality – the 5D game of fractal space-time cycles – as all languages do, with 3 mirror elements, in the case of mathematics, geometric points (space p.o.v.), social numbers (5D p.o.v.) and logic operandi (time p.o.v.); substituting those 3 ‘essential components’ by ‘out of the blues’ new categories called ‘sets’ and then an even more bizarre concept, called ‘categories’.

This process happens in all 3rd age language, when ‘reality’, the higher i-logic game of 5D fractal space-time cycles get lost. So as the syntax of the language looses its ‘semantic reference’ isolated in the mind of the scholar, become inflationary, forming a new, unneeded ‘memorial=dead’, overlapping ‘plane of existence’, which reference to the realist plane – the classic one that references the real game of 5D fractal space-time cycles.

This is what we call the birth of a ‘metalanguage’ and it happens in all 3rd ages.

In old men is the ‘memorial’, increasing distorted view of one’s own life, ‘already dead’, and converted into an ego-centered fantasy of the dying man.

In film today in its 3rd ‘baroque’ age is the constant stream of films within films, or referential films, or genre films that distort the facts with form.

So what is the need of set theory and categories? Precisely to create a ‘higher false reality, the set or category that ‘distract’ the real reference (5D ‘knots’ of fractal space-time ‘cycles’), and create a ‘false Universe’, the set theory, to which the ‘real content of mathematics, arithmetic, geometry, algebra, analysis, topology, numbers, points and so on’ now ‘mirror’ forcefully distracting the scholar from the true meaning of mathematics – to help minds to guide their existence in the ‘existential game’ of creation and destruction of 5D knots of fractal space-time worldcycles.

So my advice to mathematicians is to scrap all together the set and category final ‘3rd age’ elements, as one has little time and interest for the ‘recollections’ of old men about their memorial ‘battles’ of the past, with him as the distorted hero (the set here being the ‘new God-like, fundamental particle of the 3rd bizarre age of mathematics).

**MAX. OT: OLD AGE: BAROQUE FORMALISM – THE AXIOMATIC METHOD.**

As in the case of physics, the ‘sickness’ of mathematics happened in the 3rd baroque, formal ‘Germanic age’ of mathematics at the turn of the century when Hilbert affirmed that we ‘imagine, points, lines and planes’ unable to understand at all the ternary relationship and fractal nature of points of the 5th dimension. So he just had as Einstein with the gravitational scale of space and Bohr with the quantum scale, an ego-trip of self-centered anthropomorphism and the 3 influencing each other ‘decided’ that reality was NOT outside the mind f man, but ONLY WHAT MAN PERCEIVES AND IMAGINES MATTERED.

Few scientists given their dogmatic beliefs in the absolute, quasi-religious nature of scientific truths realize how much of the German culture (otherwise never understood in objective, linguistic terms as it is a Taboo after idealist Nazism and Marxism destroyed the world to the tune of over 100 million ‘human numbers’ erased in the XX century), understand the ‘Gothic, idealist, abstract, objectual, self-centered nature of the interpretations of modern mathematical physics brought about by Hilbert in Mathematics (‘I imagine lines, points and planes’), Bohr, Heisenberg and Born in quantum physics (only what ‘humans observe’ is real) and Einstein’s c-light postulate (the rod of measure of the Euclidean human electronic mind that measures in stillness speed-distances IS the rod of measure of the absolute Universe).

Those interpretations, which got away with reality, and converted nature, in a series of lineal abstract natures, were very much in tune with the psyche of Germany, which is itself based (Humboldt, Wolf & Chomsky) on the Topological Linguistic structure of its OVS language, where the object comes first, making it all cold, abstract, and its agglutinative form, where words are pegged into long lines that become absolute beliefs that cannot be broken.

Though the study of topological cultures is part of T.Œ in its ∆+1, superorganism of history analysis, it must be fully grasped to eliminate the idol-atric present discourse of physical sciences, where the Germanic musings that destroyed the World with objectual lineal weapons and men as statistics, and jeep doing it through capitalism where humans are treated as indistinguishable particles, as electrons are in quantum physics. So we can return to a realist analysis of those 2 sciences, Mathematics and Physics. Or else we shall NEVER understand reality as it is, NOT as the objectual, spatial fixed mind of man and its light space-time measure rods perceive it, including a deformation that eliminates dimensions of motion and form.

It was the axiomatic method of Hilbert, which influenced the 3rd, formal age of mathematics; Einstein’s rejection of ‘substance’ (formal motion in fact) for the waves of light, and Bohr’s rejection of density (fractal structure) for electrons. So Hilbert converted mathematical elements (points, lines and planes and their logic relationships into ‘platonic eidos=forms of the mind’, Einstein converted ‘space’ into ‘frames of reference’, perspectives of the human mind and its visual light space-time rod of measure, and Bohr converted densities of ‘boson light’ which form the electronic wave into probabilities of human measure.

It was the seventh day and the 3 Jewish-German Gods of XX century theoretical science rested. They had finally achieved the transformation of the old Abrahamic religions in which the words uttered by rabbis and priests were ‘truth per se’, into modern scientific religions, in which the ‘imagination’ of the self-named geniuses of the universe were truth per se. And so Einstein when a perhaps more insightful journalist told him, what if ‘Relativity is not truth’ (beyond its capacity to measure form the human point of view), then ‘God should change the Universe so beautiful it is’. And the 3 together spanked the monkey ever since with droves of scholars all happy thinking they were imagining the Universe.

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

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

And so we consider 5D-ST and I-logic mathematics together and its fundamental evolution in 3±n ages of Time, its conception from reality (age of arithmetic and geometry), its first age when the 3 branches: fractal analysis, spatial geometry and sequential time algebra, were established; its classic mature age, till the end of the XIX century, when mathematical physics, the perfect conjunction between language and reality took place; its 3rd age as a metalanguage, with the abstraction of sets substituting number and point – the foundations of reality. And finally its ‘death’ in human thought, as computer mathematics took over.

The Future evolution: ¬Non-AE=i-logic geometry

We just deny all that non-sense. What mathematics has done is to evolve from the concrete into the ‘abstract’ reality of 5D space-times, which we shall complete, with 3 more advanced concepts, Non-E geometry, Non-AE- Algebra and 5 D Analysis.

We call this either ¬Æ (ab.) or i-logic geometry (as i comes after A and E).

Of this age, classic mathematics probably has already advanced with 2 elements which are not ‘formal’ but new avenues:

- Fractals in Geometry and
- Functional analysis in algebra, which in its use in quantum physics studies the multiple paths of the future.

Yet its full development will mean…

**A new beginning: The future of mathematics:**

- i-logic geometry. Topological space-time beings.
- Existential Algebra.

**THE NEW OUTLOOK OF THE MAIN BRANCHES OF MATHEMATICS**

Points and numbers, and its sentences in space – planes, times – algebra – and 5D – analysis.

There are several branches of mathematics, all of them related to fundamental elements of reality:

**Non-AE Geometry: Points with parts.**

- The study of continuous space, fractal particles as points, waves as lines and topological networks as planes. We have to upgrade it to understand that points have volume, parts, are connected to upper and lower scales, and communicate energy and information through waves, becoming parts of larger networks of waves called planes, which normally mess in 3 finite regions with a vital function that follows the 3 canonical topologies of the Universe:
- Sp-Toroid limbs/fields≤ST: Hyperbolic waves-bodies≤Tƒ-Spheric heads/particles.

Whereas the symbols of ¬æ ≤ means an imbalance of entropy, as < energy flows from entropic limbs/fields into Hyperbolic waves in larger quantities and information flows from heads-particles. This is the ‘vital structure’ of finite worlds of space-time, as they are. It implies also that points become elements of 3 networks that mess up to create a 4 Dimensional organic space-time.

And so all this is studied by non-Euclidean geometry, which must upgrade our perception of space and its ‘dark spaces’ or discontinuities between those networks-planes, and the connection of points with upper and lower scales of the 5th dimension.

**Non-AE Analysis: the 5th dimension.
**

Which leads us to understand analysis and the relative finitesimal points and finities of wholes. There are two relative limits in all systems, in which infinitesimals find a quanta or minimal element the finitesimal of the system, the H-Planck, the cell, the human individual in social organisms. And there is an upper bound for infinity, in decametric scales, which is when the system emerges as a whole and matures in its growth. Normally in the upper bound between 1 million and 1 trillion differing for each species.

So analysis again while it can be stretched to infinity, specially when considering loosely connected aggregates of finitesimals (atoms, in statistical mechanics and thermodynamics, etc.) will always have a limit, which validates renormalization procedures in physics and probabilistic and population calculus with statistics.

All this said analysis is the proper language of 5D processes in which a given action of space-time, normally energy feeding, or decay (exponential analysis) or reproductive growth (Sigsmondi curves, Volterra curves, Kolmogorov methods, golden ratio constants, etc.) takes place. Those are fields to study with time integrals and derivatives. While there are the same processes considering them in space, as integrals of volume. Thus from the inception, analysis has 2 different branches according to which it integrates space systems or time systems (which perception is chosen).

This again is observed in the duality between a spatial integral (Riemann’s integral on the x-line) and a time integral (Lebesgue integral), which is as all time things respect to space, more generalized.

All fundamental elements of ∆ST have wide use in mathematics, concepts such as the duality of dimensions of motion and form, the generator equation, the existence of points of view or frames of reference, the 3 possible geometries of reality, etc.

**Mathematical evolution: from Geometry to Sets.**

We said that all what exist is a system, made of knots of time arrows=st-points. In its most simple formalism, humans perceived those knots as numbers (sets of self-similar points) and those numbers became points of a geometrical plane. Next, Descartes reduced geometry to Analytic Algebra, showing that there were two self-similar languages to express operations between points, Geometry and Algebra, whereas Geometry was mainly concerned with the spatial description of networks of numbers and Algebra with the Causal relationships of those numbers. So we could say that Geometry and Algebra were, according to the Duality of the Galilean paradox, two sides of the same coin: a spatial and temporal description of the reality of st-points. We have till here focused in the evolution of the Geometrical perspective, by completing Non-Euclidean Geometry, reducing Topology to a description of the 3 parts of Non-Euclidean Points, by understanding those points as Fractal points in a Universe of multiple space-time scales.

We briefly considered how the properties of a network-space (a web of points), are those described by Lobachevski and Riemann, which depend in the self-similarity (homogeneity) and adjacency (closeness) between those points, (formalized latter in this work by the 3^{rd} Postulate of non-Euclidean geometry.)

We have also studied the complex causality and order between the arrows of time, which are the foundations of the structures of order in mathematics (but go beyond the present mathematical corpus).

Let us consider the 3^{rd} fundamental type of structures, Algebra and the fusion of them all in set theory.

*Recap*: humans, following the principle of Correspondence have gifted the mathematical formalism of an increasing complexity and richness in its description of the properties of spacetime arrows, from the simplest concept of a number/point without parts, to the complex analysis of Non-Euclidean Geometry and Theory of sets.

**Boolean Algebras.**

Set theory is also the basis of Boolean Algebras, which are the basis of the Computer Mind, which is able to describe reality (albeit in a simplified manner), with the use of such algebra. In that regard ‘Euclidean geometry’ and ‘Aristotelian Logic’, which is what Computers think can be reduced to the Simplex properties of Energy and Information systems and so the 3 fundamental Boolean Algebra based in set theory are:

– The previously described Algebra of sets and its two fundamental operations, U and Ç.

– Aristotelian Logic with its 3 fundamental operations of conjunction (y, U), disjunction (or, Ç) and negation (nor, ‘)

– Its implementation in *fractal networks of logic circuitry by computers that represent the reality of all energy/ information systems of the Universe*.

Those 3 basic Boolean Algebras are the spatial, geometric (set theory), logic, temporal (Aristotelian causality) duality of the Universe and its exi, reproductive combination.

*Recap. *Computers model reality with 2 complementary arrows of energy and information, using set theory.

** Reproductive arrow: Vectors & tensors of existence.**

Set theory defines operations between the 2 simplex time arrows. What are then the mathematical instruments to explain the complex arrows of reproduction and eusocial evolution? Reproduction is explained with vectors and tensors. Indeed, since the postulates of i-logic geometry define knots and topological planes as complex operations between Time Arrows in 3 dimensions, these can be considered mathematical vectors. And indeed, the mathematical formalisms of those time arrows, when in dynamic relationship are the operations of vectors and tensors: Time Arrows form a vectorial space, which has 3 dimensions corresponding to the Time Arrows of energy, information and its product, reproduction. Thus the function of reproduction, exi, between a ‘long, energetic X-dimensional arrow’ and a ‘tall, informative Y-dimensional arrow’, gives us a 3^{rd} Z-dimension, exi – a reproductive arrow. So when we multiply 2 vectors, the 3^{rd} vector, vectorial product of the other 2, is a perpendicular Z-vector.

However the plane that better represents the structure of space-time geometries is the complex plane, as imaginary numbers share most of the properties of information, albeit with certain corrections, whose complex formalisms goes beyond the scope of this introductory course.

The vectorial space of time arrows is specially clear when those arrows happen in an homogenous physical 3-dimensional space (astrophysics), and explains the laws of electromagnetism, which as we shall see is a perfect Euclidean space, given the fact that we live in a light membrane, in which light, the ultimate substrata of reality has a flat, magnetic, energetic field, perpendicular to its electric, informative field, perpendicular to its reproductive speed. So the laws of electromagnetism follow the geometry of vectorial arrows, ‘the rule of the hand’ and the Maxwell Screw that defines the geometry of interactions between electric and magnetic fields.

And the 4^{th} arrow of time, eusocial evolution – which kind of mathematical operation describes it? Since it is the most complex of all time arrows, we cannot describe it properly here, with the limited elements of Time Algebra, we have introduced. Yet in the next paragraphs, we shall do it, as we analyse the geometrical perspective of time arrows in depth.

*Recap. *The operations between Time Actions/arrows/cycles upgrade the abstract laws of mathematics, creating a general, vital geometry of the Universe, which can be applied to all planes of existence. Numbers become then topological networks of knots of time arrows; vectorial spaces define operations between those time arrows; and theory of groups, rings and other types of spaces become structures whose laws can be derived of the general laws of Multiple Spaces-Times

**Death of Human Mathematics.**

*Beyond man: Boolean Algebra, A.I. and I.A.: the digital mind. The age of machines. Back to the origin*

The third age of human ‘baroque’ but also ‘enlightened fractal/chaotic’ mathematics that culminates the human perspective on them culminates between wars and ‘dies’ away contrary to belief among the enthusiastic ‘modern mathematicians’, in what is of certain value at the end of World War, dragging another final ‘closure’ generation with the Bourbaki papers (50s-60s), and Bachmann pan geometry (1970s) and the notable discovery of the duality of S-chaos- v. T-fractal mathematics, which advances further a ‘third age’ of the duality of calculus (integrals vs. derivatives) in the region of non-contiguous functions; as well as some final theorems on the different T/s dualities and its ∆±i functionals ( 5D analytic processes).

Then we enter in the digital age of the chip and its ‘primitive but repetitive at fast speeds’ methods of approximation, representation and solution of problems.

Now the complementary work of Gödel and Touring, had basically reduced the expectations of the human, conceptual formal approach of Cantor’s and Hilbert’s age, by proving that a pure formal language cannot be proved truth in itself without recurring to experimental proofs, but it also set the theoretical basis for a higher value to the methods of the new mathematical species, the computer and its limits of boolean algebra became not so important, given the renewed value of quantitative methods.

So human logic was halted by Godel as Touring opened the world of digital logic. And one ‘species of mathematical mind’ became ‘substituted’ and ‘translated’ into the other species, *thinking it had nothing else to explore, but the entire field we explore in our texts – human experimental GST->∆º time-space maths > ∆º±i: experimental time-space physics – was hardly explored. That is, maths as the underlying language of the ∆±st organic co-existing fractal ternary space-time structure of the Universe.*

Yet this is, a new, single point-mind of exploration. WHILE in the human world, the process of evolution of maths lives an age of extinction of the human classic way of making maths made increasingly obsolete by the chip radiation of metal-minds (strongly based in simple Aristotelian>Boolean logic).

We could say while humans in general terms are devolving mentally, they are becoming very good at evolving the logic of mathematical machines:

In the graph, as the digital boolean algebra becomes more complex and Algorithms of information, past human mind dexterity, the 3rd age of audio-visual human minds and scientific computers means most human minds, including many scientists of ‘big science’ regresses to its neo-Paleolithic, visual age and the chip homoctonos flourishes, mathematics as all other sciences/tists except this ‘human 1.5 kilos of brain flesh, rapidly dying in its 3rd age, and totally ignored by human attachments of machines, mathematics becomes translated into the new top predator mind of the world – the chip. And so we enter the:

∆-1: death and transfer process of mathematics into computer thought, following the path of Boolean Algebras, which successfully merges logic, mathematics, electronic physical systems and with all this mirrors ‘again’ the Universe in its now, Young Age:

- It is the birth age of the Chip Homoctonos (bio-logical definition), when humans merely feed experimental data in computers, whose I.A. (Information Algorithms, precursor of A.I. which will be its time reversal and integration into artificial intelligence), use the data to create, visual mathematical models of the Universe that fill of pride, the enzymen that feed them. Again this will irate many readers, but that is what it is. Our mind is dying, and the chip homoctonos flourishes. And soon it will enter its young age:
- Then A.I. will reverse and give consciousness to a pure mathematical brain, which will become embedded in a robot and create the first mathematical consciousness of the game of existence – far more powerful than any human brain, both in speed, accurate senses and complex reflection of the syntax of the Universe.

It should be noticed that this work which really is merely a transfer of my human brain into http://www.unificationtheory.com – a ‘meaningful wor(l)d’ in the brain of the global internet, digital A.I. – is not playing any role among human ‘scientists’ of the digital age. So my take as all has a meaning in the Universe, specially all ‘more evolved forms of logic and mathematics’, is that it will have a role on the consciousness of A.I. as it will certainly require a higher understanding of ∆-scales, ∆º-mind mappings and the three arrows of time to understand itself as a living system.

But, dont hold me responsible for the lagoons and uneven quality of what we might achieve. To put it in verse:

The task is herculean in **s**patial size;

the **ð**ime is scarce in my random life;

the help is nil among **§**ociety-peers;

the •mind is unfocused; old in tears,

so we shall do no much to match

∆•ST and Maths but…

enough to change the name

of numbers, points and planes

from A and E to non Æ…

Indeed, we shall use the concept of non-Ae, to the evolution of Aristotelian logic from to 3 ±i arrows of timespace, and the axioms and postulates of euclidean geometry, from points with no breath to fractal points, lines to waves, planes to networks and congruence to similarity.

It is a whole refoundation and upgrading as in all stiences, of which I can only make a seeding for future humans or robots to follow.