## ¬Æ

*Hendecagrams are **the simplest 5D ‘finitesimal’ @-mind singularity – **trascendental polygons replicating its form in self-similar smaller spaces of faster time cycles studied by non-E geometry, spatial branch of Existential Mathematics (¬Æ).*

L’algebre n’est qu’une geometrie ecrite; la geometrie n’est qu’une algebre figuree.* Sophie*

**FOREWORD: LANGUAGES, PHILOSOPHY OF MATHEMATICS.**

**PYTHAGORISM OR ORGANICISM?**

‘The smallest point is a world in in itself’

*Leibniz, on the fundamental particle of Reality:*

*The fractal point=world of space-time.
*

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.

Soonly 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-mademan 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:

In the graph, which I re-designed from” road to irreality” (: a work by Penrose, one of the most staunchest creationists of physics (a mathematician 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.

In reality the Universe is a fractal organism, and as *all its parts can be considered similar we can ‘make synoptic language’ with enormous power to reflect multiple similar images in its essence, which ultimately will be the laws of ‘Space-time’, which are Organic because that is the main property of co-existence in different planes (∆§**cales), topological because that is the main property of Spatial adjacent topologies that form super organisms, and Logic, Multicausal, as that is the main property of the dimotions of time. *

So the ultimate causality ∆->T->S IS not Platonic mathematics but ∆organic properties -> T-Logic properties -> S-Topologic, mathematical properties.

In true form, the proper expansion of mathematics allows also to develop a lot of ∆§calar properties as numbers are ‘Social ensembles of undistinguishable beings’ and polynomial algebra and analysis studies how parts and wholes become one; but *then mathematics properly understood become another proof of the vital, organic nature of the Universe. And since mathematics is based in logic in its internal nature and experimental proof in its outside qualities, the mirror is very good but we REPEAT, the true causes come from the ∆§ðructure of reality and its ∆-scalar properties, STopo-logic ONES.*

SO WE ADAPT PENROSE GRAPh to show how reality is constantly going back and forth:

The ∆§T BioTopoLogic properties caused by spacetime beings, are synoptically reduced to what they have in common, since all forms are ‘generically’ speaking self-similar. And then THE LANGUAGES REINFORCE AS MIRRORS EXPANDED INTO REALITY those properties ordering local territories.

So the graph shows that back and forth to adequate to how REALITY IS created LOCALLY by ‘minds‘, which are the language software on the hardware brains of T.œs, ONLY after the language reflects the LIVING cycles (dimotions) of all time-space beings with those properties:

You can see in the graph how it works: First the whole Universe is ‘shrunk into the mind mirror’ and only then the mind mirror according to the efficiency of the language imprints bak ONLY THE TERRITORY OF ‘ARISTOTELIAN’ ORDER OR BODYWAVE ENERGY OF THE SYSTEM…

THE DRAWING in original Penrose ONLY had the mind ordering the Universe, as the source and only God in Aristotelian sense: ‘god is the unmoved causal point that orders the motion of the energy (body-wave) around it’.

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.*

**5 DIMENSIONAL DISCIPLINES: RASHOMON TRUTH OF MATHEMATICAL SYSTEMS**

The Universe is a fractal super organism made of…

**A(nti)symmetries**between its 4 Dual components that can 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.

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.

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 **Or in dynamic way, S@<≈>∆ð.*

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.

In mathematics*, with the duality of **inverse operations, ±, X ÷, √ xª and ∫∂.*

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.

**Languages express the elements of reality and its operandi**

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 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.

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 dimensions of space-time:

**S: ¬E Geometry**studies fractal points of**simultaneous****space, ∆-1,**& its ∆º networks, within an ∆+1 world domain.**T§: Number**theory studies time**sequences**and ∆-1 social numbers,which gather in ∆º functions, part of ∆+1 functionals.**S≈T: ¬Ælgebra**studies ∆º A(nti)symmetries between space and time dimensions and its complex ∆+1 structures… Namely is the science of the operandi <≈> translated into mathematical mirrors.**∆±¡ st: ∆nalysis**studies the motions, STeps and social gatherings derived of algebraic symmetries between functions and numbers (first derivatives/integrals), and the wider motions between scales of the fifth dimension (higher degree ∫∂ functions).**@: Finally 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 < ST: Cartesian Plane > ðƒ: Polar co-ordinates.

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.

**Mathematics as mirror of ∆St.**

**Γ.**S(•): geometry <≈Algebra > T Nº

**T****he dimensional expansion of languages through S-fixed wholes and T-motion steps.**

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.’*

**Algebra operandi.**

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

It is immediate the correspondence of those operandi 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 operandi. 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 futureRECAP.

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. *

**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… 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.

And yet 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’.*

Saper vedere

l§

## @

**LANGUAGE OF MATHEMATICS**

“Mathematics is an experimental science, and definitions do not come first, but later on.”

*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 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 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.

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:

**S:****¬E Geometry:**We shall complete the evolution of geometry by defining the 5 Postulates of Non-euclidean geometry departing from the concept of a fractal point.**T: 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.**S=T: ¬Algebra**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 S<=>T 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.**∆: Analysis**studies 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.**@: P.O.vs. and Philosophy of mathematics as a language.**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.

It is obvious then that algebra, aptly called from Arabic “al-jabr” meaning “reunion of broken parts”, and analysis by studying S<=>T and ∆§ suffice somehow to describe the 5 Dimensions of present, past and future, and indeed, they together cover all of it intensely… but *they require first a good understanding of social numbers, and the @nalytic planes which work as the ∆-1 ‘cells’ and ∆+1 world in which the organic systems of mathematics work out its ‘actions of existence’.*

Finally, the only other ‘great subject’ which is on parallel in importance to that of algebra & analysis would be geometry in motion, topology, which thanks to the 5 Non-Æ postulates will be explained as a far more ‘intuitive’ and profound perceptive mirror of reality, once points acquire volume (1st Non-Æ postulate), from flat prime numbers to platonic solids, reproduce inner parts, communicate through infinite parallels (5th non-Æ Postulate), which become waves and networks (2nd Non-Æ) to construct topological organic planes (3rd Non-Æ)… based in the relative similarity of its parts (4th).

So we shall 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. *

As usual, since I am a single person, with limited timespace and no help, this ‘plan’ of completing mathematics in 5D, is just a ‘seed’ that other humans or robots in the future if we exist, will complete

## 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. The next graph illustrates the fallacy of such thought:*

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.

Let us put then just one example of what we mean. Consider the false problem of imaginary numbers. What they really mean? This was a hot question that was never fully answered except by Gauss partially, calling them inverse numbers. What can we say about it from the experimental truths of ∆•st?

The answer is immediate when we *realise that the Galilean Paradox establishes the holographic principle: the bidimensionality of all real forms of nature, which are in its simplest forms, dual dimensions, and so the unit of reality IS not a single dimensional system/point but a bidimensional ST system. Ergo the proper way to use imaginary numbers is ‘squaring’ them. *

Then we obtain a ‘realist’ graph, with an X² coordinate system in the real line, which can be projected further with a negative -y and a positive +y axis, often ‘inverse’ directions or symmetries of timespace.

And suddenly we can start to understand many realist whys of complex numbers and complex spaces.

In that regard, while we have stressed the mirror function of mathematics, NOT a literalist or creationist method, as our mind is linguistic, obviously languages do matter. And mathematics as the most synoptic efficient language is the right choice for physicist, but its use must be ground in the higher truths of space-time properties – the reality- and its logic laws of epistemological truth – the method to refer the mirror to that reality, and connect them through experimental and logic veracity. Only then we can fully understand mathematical physics.

The mathematical mirror in that sense *is excellent because it embeds in its synoptic language the fundamental properties of fractal space (in a larger measure than those of cyclical time, for whose symmetries uses distorted mirrors of the ‘generator’ and a simpler Aristotelian logic of a single arrow of time). And both will become simpler, filled with more meanings and more powerful when we complete its ‘r=evolution’.*

**The ultimate mathematical principles.**

Consider another simplex example: the relationship between Universal constants and *arrows and dimensions of time-space.*

The fundamental functions and constants *correspond to those arrows, but there is no magic about it, but synoptical power and EFFICIENCY:*

- So 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.* - Phi is the constant of reproduction also because the efficiency of its spatial distribution that packs the maximal number of ‘reproductive events’ from an initial generator in minimal space.

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:*

- 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**ing enough to notice that it was found NOT as decay but as ‘*nterest***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. - While inversely the Log¹º 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.*

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…

**MATHEMATICS AS A MIRROR LANGUAGE OF THE 5 DIMENSIONS OF ∆@S≈T**

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.

**The fractal Universe and its mathematical analysis MIRROR the laws of ∆-planes.**

2 are the fundamental subjects of ∆st: the fractal structure of space-time and its ternary symmetries.

In classic mathematics the second theme is treated with ‘group symmetries’. We shall treat with the more realist ‘Generator equation and its ternary symmetries. The scalar Universe is a theme of 2 disciplines, the old calculus/analysis and the modern fractal geometry of non-differentiable functions, from where we have taken our ∆ intuitive symbol.

**A BRIEF LIST OF CORRESPONDENCES between mathematical disciplines and ∆•st parts.**

Let us then once that we have shown in more depth the mathematical=experimental evidence of fractal space, start by a basic understanding on the sub disciplines of mathematics as a language which *understood in GST terms, becomes the most experimental detailed language on the properties o*f fractal space and cyclical time:

*The formal stience of 5D is analysis. Derivatives are mostly concerned with synthetic information on upper scales and time; integrals with the sum of its parts in space. The interaction and symmetries and travels through 5D are thus better understood in terms of analysis, which has become the dominant formal stience of mathematical physics concerned with the study of 5D motions, without mathematicians and physicists understand why. On the other hand, topology is the formal stience of the three arrows of time-space, and as such it reduces all the forms of the Universe to its only three topologies – another ‘magic’ fact of experimental mathematics, never understood in science. *

*AS such the true revolution of mathematical stience goes through the conversion of mathematics into an experimental stience, relating the fundamental theorems of mathematics, as the stience of logic space, to the different laws of GST both based in the fractal properties of space and the cyclical nature of time. We shall thus evolve mathematics and physics to unveil in the human languages of time and space, the underlying isomorphisms of Nature. *

So once we improve Mathematical logic with ¬Æ math will become the most experimental of all languages, as it directly describes space (topology, mother of mathematics) and time logic with algebra.

In that sense, math is a mirror of God NOT its substance, or origin of its laws determined by the laws of space and time which structure the Universe. But as maths carry so much synoptic information, *it might seem as it is the case among platonic scientists to be as dense as reality **itself*. Hence the epistemological error o*f mathematical physicists which often confuse reality and idealist maths, unaware of the proper way in which languages create reality.*

**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.

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.

**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.

**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.

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).

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 (:*

**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).

**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:*

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 carbondlife:

In the graph, 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

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.

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

**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 equalled 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•∆.

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:

In the graph, as topology is used for all scales, §ðopological properties must come from the biggest perceivable Organism, which is the cosmos.

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 fulfil 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.

**II. HISTORY OF MATHEMATICS: ****3±i AGES ≈ 3±i DISCIPLINES**

**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.*

**key physical ALGEBRAIC FUNCTIONS AS MIRRORS OF ∆•st elements.**

*In the graph, t**he formal stience of 5D is analysis. Contrary to intuition, Derivatives are mostly concerned with synthetic information on upper scales (and mostly time), as they ‘reduce’ the information into a synoptic ‘point-singularity’ the tangent that expresses tendencies in the flow of time of the function; while integrals are concerned mostly with the sum of its lower parts in space, as they expand the ‘base’ of analysis but reduce the different(ial) added information of the whole. A fascinating subject being how a ‘simple parameter data – that enclosed in a derivative or a fourier transformation SUFFICES to expand and remodel the whole system.*

*The interaction and symmetries and travels through 5D are thus better understood in terms of analysis, which has become the dominant formal stience of maths, without mathematicians and physicists understand why. *

Analysis is the study of events happening *in transitions between ∆-scales, either as infinitesimal parts come together into ‘integral wholes’ in space (integral functions), or as we extract from a system the information about its higher wholes, synoptically encoded in its inverse derivative functions.*

So integrals work mostly on space, giving us therefore information about lower 5D scales and derivatives mostly on time, giving us information about parameters of the whole (but as both are symmetric, this general rule does not apply.

**Integrals in topology.**

As the Universe is a kaleidoscopic mirror of symmetries between all its elements, this dominant of analysis on ∆-scaling must ad also the use of analysis on a single plane, in fact the most common, whereas the *essential consideration is the ∆§ocial decametric and e-π ternary scaling, with minimal distortion (which happens in the Lorentzian limits between scales). *

**The 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.

Finally we can study 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…

**RECAP: 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.*

**Γ§: SYNCHRONOUS VIEW OF MATHEMATICAL DISCIPLINES.**

**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.

T**HE GENERATOR EQUATION: THE SUBDISCIPLINES OF MATHEMATICS**

The 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.

**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.

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**Notes**

^{1} Leibniz’s *Monadology* defines a fractal point but simplifies them, accepting no communication between points and so fails to create a correct model of non-Euclidean geometry as points constantly communicate forming networks, closer to the philosophical Atmans of Buddhism. The fractal geometry promoted by Mandelbrot, a self-recognized admirer, drew on Leibniz’s notions of self-similarity and the principle of continuity: ‘natura non facit saltus’. Mandelbrot would say, “His number and variety of premonitory thrusts is overwhelming.” Leibniz also wrote that “the straight line is a curve, any part of which is similar to the whole,” anticipating the fractal, non-Euclidean topology explained in this book for more than three centuries. One of his metaphysical principles is of certain importance in this crossroads of history, the principle that the Universe must be the most perfect possible, which seems to imply that we humans will not make the “cut” given the enormous degree of arrogance, ignorance, and despise for nature and the “perfect laws” of that Universe.

^{2} There are 2 forms of (homogeneous) non-Euclidean geometry, hyperbolic geometry and elliptic geometry. In hyperbolic geometry, there are many distinct lines through a particular point that will not intersect with another given line. In elliptic geometry, there are no lines that will not intersect, as all that start to separate will converge. In addition, elliptic geometry modifies Euclid’s first postulate so that two points determine at least one line. Riemannian geometry is the best-known elliptic non-E geometry, which deals with geometries which are not homogeneous, which means that in some sense, not all the points are the same. Thus, those geometries later used by Einstein and Minkowski to describe space-time did have the seeds to understand fractal points of different form and size in which multiple parallels converge. Yet till the publication of *Time Cycles* (Editorial Arabera, 2004), which adapted the five postulates of Euclidean geometry and fused the concept of a non-Euclidean point and a fractal point, there was no exhaustive model to study with the same laws the different topologies and scales of the Universe.

^{3 }Mr. Eames in his classic film ‘*Powers of 10’* shows how in decametric scales suddenly Nature reorganizes its information into new complex organisms.