**SUMMARY.**

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

**II. ∆±¡:** The elements of Mathematics: Points number and operand.

**III. Evolution of mathematics:** Non-E topology and Non-A logic.

**I. **

**Maths’ 5 disciplines as 5Ð mirrors**

L’algebre n’est qu’une geometrie ecrite; la geometrie n’est qu’une algebre figuree.* Sophie on the ∆§ duality of maths as a topological, social, numerical language of form and scale.*

We translate in this post and subposts mathematics to 5D.

The Universe is a fractal super organism made of…

**Asymmetries**between its 4 components, T, ∆, @, S,which can either annihilate or evolve together, through parallel =**symmetric or Perpendicular/antisymmetric communication**:**S:**space; an ENSEMBLE OF**ternary topologies,****(|+O≈ ø)**… which made up the**3 physiological networks**(|-motion/limbs-potentials + O-particle/heads ≈ Ø-vital energy) of all*simultaneous**super organisms***∆: Planes of size**distributed in ∆±i relative*fractal scales*that come together as**∆º**super organisms, each one sum of smaller**∑∆-1**super organisms… that*trace*in a larger**∆+1 world…****ðime cycles:***a series of timespace actions of survival that integrated as a whole form a sequential cycles of existence with*each one dominated by the activity of one of those 3 networks: motion-youth, or relative past, dominated by the motion systems (limbs, potential); iterative present dominated by the reproductive vital energy (body waves), and informative 3rd age or relative future dominated by the informative systems, whose ‘center’ is:**3 ages**,**@: The Active linguistic mind**that reflects the infinite cycles of the outer world and controls those of its inner world, through its languages of information, which guide its 5 survival actions: 3 simplex,**aei**, finitesimal actions that exchange energy (**e-**ntropy feeding), motion (**a-**celerations) and**i**nformation (perceptions) with other beings, and two complex actions:**o**ffspring reproduction and social evolution from individuals into**U-**niversals that maximize the duration in time and extension in space of the being.

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

In mathematics*, with the duality of **inverse operations, + -, X ÷, √ xª and ∫∂, and the universal ≤≥ symbols that put in relationship two sides of timespace event that connects adjacent, simultaneous parts of a super organism in space, or ‘moves’ and transforms a t.œ in time. So Dimotions are presented by those operand, and functions connected by similarity operand (<=>) express the connection of adjacent topologies in space: |<ø>O.*

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

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

*While the simplest mathematical dynamic ‘Generator Equation’ of all Space-time Systems of the Universe, written in its simplest form as a singularity-mind equation is: 0-mind x ∞ -Universe= C-onstant world, which is therefore the fundamental equation of ‘number theory.*

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

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

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

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

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 is the most important part, as it**studies through operand the different Dimotions, from single S=T steps to larger associations of Dimotions, in more complex ∆+1 structures (Functions) and further on IT DOES SIMULTANEOUS ANALYSIS OF super organisms in space, through the study of its a(nti)symmetries between its space and time dimensions (group theory)… So Algebra is first the science of operands that translate into mathematical mirrors the dimotions of space-time and then build up from them as the Universe does building up from actions, simultaneous organisms in space and worldcycles in time, in different degrees of complexity, mirrors for all those elements of the 5 D¡ universe.**∆t: ∆nalysis**studies ALL forms of time=change, and hence it can be applied to the 5 Dimotions of any space-time being, as long as we study a ‘social structure’, hence susceptible to be simplified with ‘social numbers’. We thus differentiate then 5 general applications of Analysis according to the Dimotion study, and the ‘level’ of analysis, from the minute STeps of a derivative, to larger social gatherings, and changes of entire planes (functionals). It is then not surprising that despite being analysis first derived of algebraic symmetries between numbers, it grew in complexity to study changes in functions (first derivatives/integrals), and then changes of changes of functions, as motions between scales of the fifth dimension (higher degree of ∫∂ functions, called functionals).**@: 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.

So THOSE are the 6 sub-posts we shall slowly complete to translate the mathematical language to 5D.

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

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

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

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

**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.

**II. ∆±¡:** elements of Mathematics

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

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

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

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

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

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

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

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

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

**Points and Numbers**

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

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

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

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

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

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

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

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

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

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

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

That is all. Why?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

** Numbers and constants.**

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

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

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

- 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.*

# Operands reflect 5 D¡

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

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

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

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

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

*The sinusoidal functions. π.*

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

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

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

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

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

*± 2nd Dimotion: Locomotion*

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

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

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

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

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

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

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

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

Yet again perception doesn’t fit in the product.

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

*log a, xª: reproduction*

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

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

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

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

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

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

**Points with parts and pentalogic.**

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

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

So does mathematics, through combinations of:

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

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

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

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

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

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

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

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

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

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

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

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

**The generator of maths**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

# II. BEYOND CLASSIC MATHEMATICS:

# NON-E TOPOLOGY & NON-A LOGIC

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

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

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

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

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

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

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

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

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

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

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

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

Now as we said we have two LEVELS OF DEPTH:

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

**The idealist logic of mathematical physicists vs. ternary reality**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

*Abstract, continuous, one-dimensional point:*

**. ____________**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

** **

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

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

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

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

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

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

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

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

PAST ENTROPY X FUTURE INFORMATION = PRESENT ENERGETIC REALITY

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

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

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

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

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

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

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

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

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

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

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

**Some basic morphologies.**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

First we analyzed its ultimate substances:

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

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

So we accept this simplification and talk of spatial entropy and temporal form and study its inverse properties according to the metrics of the 5th dimension.

Since in practical terms, as we exist in present, through present actions, a combination of past ‘Ðimotions’ and future form, all what we study in fact are energetic/informative combinations of those 2 pure motions.

The perfect cycle does not really exist. Pi is an irrational number and orbits are ellipses with some length; an the perfect line does not exist, the diagonal is a √irrational number that needs some curvature to connect two other lines through the shortest straight diagonal. All yin has some yang, all motion has some energy (mass-particle that moves), all form has some information (translation). And that which is with no form, or infinite gravitational non-local motion is not visible, and that which has no imperfection in tis cynical curvature, with ‘temperature vibration’ is under 0 kelvin degrees. In other words, we do exist in a vibrational imperfect present in terms of physical concepts, we live through present actions and reproductive mixtures of energy and information.

The understanding of those 2 elements, its 3 spatial dimensions and its 3 temporal, dimensional ages, and its bidimensional, topological combinations, S, ST, Ti, entropy, energy action and format, conform the full comprehension of the i-ndividual, I-centered, most important space-time scale of any being, the one in which ‘he lives’, which we have called the ‘5th dimension’, to follow the compact analysis of classic science that studies only the Present most important dimension of time, with ‘instantaneous derivatives’, v=∂s/∂t.

Then we analyzed the combination of both, or the metrics of the 5th dimension

Nest we will analyze the systems built with them, the super organism of reality in which according to those metrics, there are always heads of information and limbs of energy of different size and speed.

The isomorphism of ‘informative heads’ and energetic/reproductive limbs and bodies HAPPENS across multiple world-planes of the 5th dimension, each one studied by a science.

In two coordinates, the height coordinates of information and the X coordinate of space-energy of the main planes of the universe. Notice that paradoxically as we become smaller in space-size upwards in information we increase our fractal information and the perfection of our ‘smooth’, superfluid orderly following of those laws.

Hence we have put on top of the pyramid in a never reached, ideal infinite infinitesimal the ‘seed’ or ‘primary’ encoded ‘non-Euclidean point, Œ, mind of the Universe which encodes all the laws of the 5th dimension and by infinite iteration gave birth to all beings. This would be if it ever existed the particle of god, NOT the higgs, but the ultimate i-logic mind of the Universe.

In the graph above we see the duality of informative smaller heads controlling lineal limbs and reproductive wave-bodies.

A precision: we often simplify bodies and limbs into a single Se system, (see the previous 2 posts for a more rigorous definition).

In strict terms, there are always 3 parts, which correspond to the 3 topologies of bidimensional membranes:

-Pure lineal, hyperbolic space-motion – limbs/fields.

-Pure cyclical, spherical informative motions, heads/particles.

-And its ‘energetic-informative combinations of yin and yang, waves and bodies, since energy is motion with a bit of form (the mass), and information is form with a bit of motion (the wave-particle displacement).

Yet since the ‘present’ body-wave, combination of past-entropic limb/fields and informative pure To forms of future is the dominant element of reality, we do write often Se≈To for the whole system, that is systems of spatial energy and temporal information in perpetual exchange ad transformation through body-waves, ≈.

**¬AE LOGIC**

The next element to innovate in mathematics is to move from Aristotelain causality to duality, ternary logic and pentalogic of 5 Dimotions which we shall not really introduce in this post, though we shall consider some aspects ill-understood of number theory and algebra – its closure with imaginary numbers. As it defined the fundamental theorem of algebra – that all equations have a solution in the Complex numbers. It will also allow us to introduce the proper way to deal with negative numbers and complex equations in terms of its significance for 5 D.

**-¬Æ Logic****: Duality > Trinity**

‘From one comes two yin (form) and yang (motion), from two comes 3 (qi-energy), from 3 come the waves of 10.000 beings’

Cheng-tzu

Just to justify why we use weird symbols of non-Ae logic in this blog. Can we just use the nice mathematical or logic symbols of the axiomatic method? Well, we can’t really.

Consider a simple law of Disomorphic time cycles: 3Ð ∆¡-1 ≈ 4Ð ∆ø

This might sound Chinese to you (: but it has a deep meaning and because we use the symbols of T.œ -Theory of the Organic Everything, it applies to *everything in the Universe* 🙂

So you fully grasp why we had to invent a simple, intuitive new I-logic language, as those are very general laws. Indeed, it means that any system or organism in which there are different scales, the 4th entropic dimensional action of feeding of the larger scale is symbiotic to the 3rd dimension of reproduction of its ∆-1 parts.

It is a law of time clocks synchronized according to the actions they perform in social, organic manner. i.e. your faster cellular time clocks reproduce (a slow action of time-space or 3rd Ðimotion of timespace) to the tune of the larger feeding cycle of one day (faster timespace action). So we can write with our simple symbolism:

Trust me, *this is truly the amazing stuff and ultimate generalization of reality – its laws of exi:st¡ence.*

And they happen in human bodies, animals, plants, crystals, stars and black holes (oh yeah, the black hole ‘eats’ every 11 years, when the activity at saggitarius is maximal and its star cells, like the sun suffer a massive magnetic cycle of black spots or peak of solar activity which in turn determines the weather cycles of reproduction of plants in this planet… believe it or not, there are such cycles ALSO in the organisms of the galaxy).

But the beauty of the symbolism of T.œ is that infinite of such events are resumed with that very simple ‘sub-equation’.

And *all sub-equations of reality can ultimately resumed with the simple ternary terms we have used for ‘time-motions, <≈>, time planes, ∆§±¡ and topologies, O x | = Ø, also expressed to make it a little bit more ‘amenable’ to humans, with the ST, 5 symbols of timespace dimotions: *

- Ði: Informative particles/heads: §ð
- Ð: limbs/potentials: momentum: st.
- Ð: ∑e x ∏i: body waves: ∑∏.
- Ðimotion: entropy: S∂.
- Ðimotion: Organic evolution: ∫T.

The simplicity and beauty of the I-logic equations of the Universe that I hold in my mind-point alone for 30 years is such that all what exists can be synoptically expressed with the ‘world cycle’ of timespace dimensions:

** ∆ð+¡****≈****≥****>****S@<<∆ð-¡**

**∆§±¡:**5D plane§cales of **§**pace **ð**ime **∑≥:** Present-reproduction **<**:Entropy **>**:Information **|≈**:Limb/Potential/Youth **≥:Iterative **Bodywave O@:Old particles-heads: **ΓØœ**:Supœrganism

The universe is a repetitive equation of generation of local ‘Dimotions’, dimensions of space with temporary motions.

Its origin though is a point of space-information. And so creation always departs from seed that emerges after a reproductive, evolutionary process into an organism. And then again fro the head/particle, the mind of the organism.

CREATION thus goes back and forth in chains of steps of existence, Δð>S¡∑>∆º… as systems emerge into super organisms and then die in inverse equations: ∆º<<∆ð, with the caveat that in the entropic death the intermediate existence of ‘minds’ across a relative simultaneous present, S¡∑, is NOT present. This is the reason why is so fast, almost simultaneous, indeed lasting only a quantum of time.

It has to be noticed in the graph thus the existence on the path of life of 3 _≈ symbols of 3 ages, ≥ youth, ≈ reproductive maturity and > collapsing third age, in which there is a deficit to the total universe of two << as the ≈ presents are considered ‘not time consuming’ virtual conservative cycles of existence. S existence is virtual in each ≈≤< present ternary existence and thus explains which death which IS the same travel in the fifth dimension WITHOUT STOPS in the fourth dimension happen.

As if you haven’t noticed a present is a fourth dimension domain, in which present simultaneity is measure as a conceptual definition of an event happen in a superorganism.

So present 4D Space-time of adjacent super organisms which haver a present measure of time in its simultaneous perception by a still languages that commands a nervous informative language of maximal sensorial speed to become the linguistic image we take for still space-time state, will then be divided as we come across its formal reasons of motion between two similar states, to the concept of ternary anti symmetries.

As there are also an antisymmetric future to past fast descent into perpendicular death, a symmetric longing present of a life arrow and an asymmetric state in which that latent present lasts.

So minds evaporate fast into an inverse from symmetry to antisymmetry, but life has many times of present asymmetric missed liquid states. And so we can consider that equation from different perspectives.

WE HAVE highlighted the key ‘logic elements’ of those systems, which are profound laws of structure that define the Universe in its most abstract form.

** As **space and time dimotions are geometric actions, form and function come together in the 5 Dimotions of the Universe. Hence the use of topological methods to study change in the form of beings through time, which we can now widen even further with ¡logic ‘paradoxes’.

Let us briefly consider only one case, of wide use in mathematical physics: the fact that the sum of cyclical motions becomes a lineal open motion and vice versa, all lines when the steps increase become curved into a hyperbolic geometry. The first case is called the Fourier transforms that finally deploys a square ‘wave’.

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

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

**Fourier transform and harmonic functions.**

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

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

And all this could be resumed in a simple definition:

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

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

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

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

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

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

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

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

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

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

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

**Multiple planes in space: **

**COMPLEX negative NUMBERS**

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

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

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

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

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

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

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

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

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

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

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

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

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

Just think of it.

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

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

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

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

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

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

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

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

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

*closing then a single plane.*

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

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

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

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

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

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

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

*The Rashomon truths on complex numbers.*

More generally we can consider the Rashomon effect for complex number and consider its ∆@s=t different perspectives:

**T(s):**As inverse, TEMPORAL numbers OR negative numbers of an inverse direction of motion, already explained.**S(t):**As bidimensional REAL numbers (Bolay) with its own rules of multiplication (a,b) x (c,d) = (ac-bd; ad+bc)**@:**As a self-centred polar frame of reference (r, α)**∆:**As squared coordinates, that is as an ∆-frame of reference. As this is the new solution found by 5D theory we shall consider it first.

# ∆: i²**: Complex plane in scales.**

**The ∆-symmetry of i-numbers.**

The second fundamental role of i-numbers must be related to scalar space-time, hence polynomial structures.

We have also stressed in many paragraphs the duality and differences between polynomials and ∫∂ functions, whose ‘magic’ closeness (as polynomials can be approached by differentials through Taylor binomials), *responds to the social ‘lineal’ herd-like of polynomials, vs. the organic, more complex ‘cyclic’ nature of ∫∂ systems.*

So if we combine the two concepts we can ‘reorganise the complex plane’ in polynomial terms ‘naturally’ by *squaring it, getting rid of the √ elements and its negative complex roots, to reflect a mapping of a fundamental principle of nature:*

The h*olographic 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 since the square of a negative number is positive, the X² main axis of bidimensional space-time units IS mirrored in the positive in both sides. So the proper way to represent the graph is by tumbling it, and making a half positive plane, with the now ± real axis (the i and -i axis) on the X coordinates and the square axis on the Y coordinates, which is much closer to the ‘REAL universe’ of bidimensional T.œs of timespace moving around its 0-identity element in two inverse directions of time (-i²= -1; +i²=1 axis). And suddenly we can start to understand many realist whys of complex numbers and complex spaces.

In the graph we see the immediate application to quantum physics, where ‘probabilities’ are born of the product of the ‘two conjugates’, the positive and negative sides of the imaginary axis, which now looses its √ and so become positive and negative ‘inverse’ arrows/functions/forms, which *combine into a bidimensional holographic real squared element. *

*So the graph is an excellent form of represent, the **neutral present, ST, in the square real line and the ± inverse S and T functions in the positive and negative conjugate axis no longer imaginary.*

This is somehow acknowledge in many equations of physics notably in those related to relativity where we USE square functions (in praxis just to simplify calculus, but now we know in reality they have ‘meaning’).

*So in special relativity we write:*

As this are clearly square metric we just set the time coordinates in the imaginary numbers as bidimensional topologies extended in the imaginary -1 and its parallel – that extends a flat holography through the ‘z axis’ now void of meaning as it is occupied by the ‘folded’ other side of the real square. By this we mean, ‘points in the r² which must represent square numbers can be done into squares but making them ‘holographic clones of the same curve deepening into a plane.

Now the interest of the conjugate pair of ± real solutions to a squared coordinates only positive, is a reduction of information, which still however can be regained returning to √@. In @R² complex numbers simplify some equations.

The complex plane must be understood as a plane that adds two ‘scales’ of the fifth dimension and more generally as a plane that allows to add repetitions in space (square plane) and time (multiple cycles). In the graph, its proper understanding, even if we operate it mostly as a square

While the topological ternary structures and growth of social networks of fractal points can define easily the emergence of a super organism, in strict mathematical terms, the second sub discipline of mathematics, analysis, deals directly with the relationships between finitesimal parts and social, organic wholes. So the specific mathematical discipline that studies the scalar, fractal 5th dimension of space-time Beings in quantitative terms is analysis. And it is specially useful for the study of systems in which the internal organisation is minimal – that is systems of herds displaced in space and of growth and events happening in time.

THE COMPLEX plane will define one plane as specially interesting from the ∆ view of reality; specially when we establish it in square coordinates:

The newest addition is the square plane with ± conjugate planes on a bipolar real axis, closer to the organic ternary topology of t.œs in reality:

ST: As the squared complex plane becomes a topological plane with the real axis, rˆ2 representing the reproductive conjugate ±bilateral plane of dimotion of reproduction.

It does represent in its R² Axis the present bilateral wave state and in the T<S SQUARED imaginary ±asis the particle, polar state and outer world. Ie. Schrodinger & Bohm polar and wave equations of quantum physics.

What is then the main difference between analysis and ∆nalysis. Simple: in the fractal universe, *we take sides with the dispute on the meaning of infinitesimals, which as Leibniz thought are ‘finitesimals’, minimal constant parts of a whole, which do NOT diminish ad infinitum in size, but will always have a minimal number – in planes of ∆, normally on the 10ˆ10 scale.*

So we solve this logical paradox, never fully resolved, stating that the parts of a whole are finitesimals, ‘undistinguishable’ from the perspective of the ∆+1 consciousness – in fact from an ∆+1, the information and perspective of its parts blurs till it seems a continuous. And so all scales below ∆, become increasingly ‘indistinguishable, continuous’ and finally its information erases.

**S<=>T**

Imaginary numbers are thus first as Gauss call them inverse numbers. And next square numbers that represent the holographic principle of ST bidimensionality. Since* 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’.*

**Complex numbers as expressions of the 3 states: potential past <present wave> future particle**

Thus the complex plane IS the mathematical representation of a world cycle of time – not a worldline as physicists want it, because they will NEVER recognise the ‘high, dimension of information’ needed to complete a world cycle. So in the next graph we see first the world cycle expressed in ‘lateral numbers.

Then the world cycle of life in 3 representations – the first one is the same that the complex graph, tumbled; the next one, the best philosophical representation by the Taoist Chinese culture, who understood duality better than western physics 3000 years ago; the 3rd as a representation of a vortex of physical time (charges and masses, whose mathematical unification with cyclical time is one of the first results I obtained in duality 20 years ago, and physicists are still fighting to understand – they call it the ‘Saint Grail of Physics’, and the guy who gets it will be a super-genius homunculus – i have it in my post on cosmology, a work still in progress, as I have been a bit depressed and abandoned this web for a long time):

In the graph, thanks to the ‘serendipitous’ error of earlier mathematicians, which could not conceive negative≈inverse motions, the real line was broken into perpendicular co-ordinates, which are perfect to represent world cycles, where the real line represents Spe (max. size, X-oordiantes) and the negative axis represents information, in as much as its development rests ‘entropy’ to the real numbers; being complex bidimensional numbers the combined expression of TIME-SPACE WAVES.

So positive negative and lateral numbers are time numbers. And again there are 3 types of it. So to fully grasp them we need to explain you the most beautiful cycle of the Universe, the life-death cycle, which also applies to physical ‘big-bangs.

This physicists don’t know and it is a wonder of the ‘automaton’ Universe that they DO use C-numbers to study world cycles, *without knowing what they are and what they study.*

We see indeed, what an i-number does: to rotate from a relative past/future to a relative future/past a function of existence, through a 90° middle angle, that is, the middle ST balanced point, in which the present becomes a bidimensional function, with a REAL, + (relative past-entropic coordinates) and an imaginary, negative (future coordinates) elements.

It is ‘crystal clear’, symmetric and beautiful.

Now, this needs just a couple of clarifications: first the fact that we move ‘backwards’ in the graph from future to past, in as much as most graphs indeed are measuring the ‘motion’ of lineal time which is the *relative Spe Function; so the negative side becomes the time function, something obvious also in relativity where we write S²=x²+y²+z²-c²t²; hence with the warping time-function in negative. The second clarification is even more fascinating.*

Ok, since we are at it, now let us give a hand to the great masters of quantum physics, with this new insights on the meaning of mathematics and its frames of references, explaining what Bohm did to fully grasp what really IS the quantum duality wave-particle, for all to grasp how astounding is the denial of reality by the so-called genius of the military-industrial complex who ‘create’ the Universe with his imaginary lines.

Now, we said that all what exists is a ternary system generated in time and space by a simple fractal generator equation. So are physical systems:

|-Spe (Relative past moving limbs/fields) < Relative Present hyperbolic ST-waves/bodies> Relative future O-informative particles/heads

We see how both biological and physical systems are truly the same structure of 3 time arrows, which give birth to 3 spatial parts. So entropic fields ‘feed’ the motion of ‘hyperbolic waves-bodies’ which feed and guide ahead the particles-heads that do NOT move in its relative stillness of pure informative linguistic view of reality. This is truly fascinating and I could talk to you for hours on the details of it. The proofs are overwhelmingly both in reality – all systems of reality can be model with it; and in languages, which ARE mirrors of those systems.

So for example, in our search for experimental proofs of mathematical mirrors, ALL the topological geometries of the Universe REDUCE to those 3 types: lineal/planar topologies, which are entropic motions as the line is the shortest distance between 2 points; spherical mind/heads, which are n-spheres as the sphere holds maximal information in lesser space and can shrink without deformation to create a 0-mind mirror of an infinite Universe (Poincare Conjeture); and *hyperbolic body-waves, **which combine and hence iterate both, lines and cycles, forming sinusoidal body-waves. *

*And so mathematics again reflects in its 3 only topological varieties, the 3 only organs needed to explain reality. And all what De broglie and bohm did was to ‘intuitively understand this’ for the specific case of a quantum wave, which has again those 3 elements. So they just said: there is a quantum field of pure motion at distance (non-local quantum potential field), over which a wave rides, and over the wave the particle feeding on that motion chooses the best path, to move, as it does a ray of light (my country man Fermat found that too :). *

So he just signalled the 3 elements, and then in a stroke of genius, he *represented the schrodinger hyperbolic wave written in ‘Cartesian coordinates’ in circular Particle coordinates, called ‘Polar coordinates’ and voila! there it appeared ‘magically’ the entropic field that moves the particle. So we could either see the whole system as a ‘present wave’ or as a Past field>Future particle. *

What is then the future direction in the imaginary arrow? Obviously that of a normal clock, down the conjugate is a future moving on a 90 degrees phase faster than the real and in the imaginary side a lag of 90 degrees in the phase of the world cycle – which physically appears in the AC circuit with the forward 90 degrees wave of the capacitive reactance, Xc on the conjugate and the lagging, 90 degrees of Xl the inductive reactance on the Imaginary side.

It is left then to ponder what a 90 degrees, 1/4th of a world cycle of any class which can be represented in the imaginary complex plane means. It is not after all 1/3rd which would make it nicely coincide with the 3 ages of time. But alas! as we know the 3 ages of time in terms of time duration break into 4/4ths, as the youth 1/4th and old age 1/4th last as much as the mature age 2/4ths – in existential algebra we write: Present = past + Future:

So the four parts of unit cycle representing a world cycle can be considered in terms of the 3 ages of time, with 2 quadrants belonging to the present, one to the past and one to the future…

Now we can interpret the positive natural numbers as the future symmetry, which give us the negative as the past antisymmetry, *and the imaginary line as the two sides of the present asymmetry. Or we could consider the present the real number, the past the imaginary and the future the conjugate. *

Both interpretations will render in the kaleidoscopic universe interesting but different results when we operate with existential algebra. Then we shall decide which one is the most promising. And contrast it with quantum physics equations, in which the imaginary element IS NOT as in phasors, a time state that disappears but a p*resent state in the operator momentum embedded within the quantum system. *

# ð

*we stated that the sinusoidal functions, π and its angle of aperture,* becomes the numerical value of the external membrane measured in terms of 3 diameters turning around with 3 apertures to ‘see’, from the self-centered singularity, giving us the general equation of dark matter for all systems (including the Universe): 3’14-3/π=0,14=±4,5%, with 96% of ‘dark matter’ outside the perception of its singularity.

So the angle of the point and sine function is the angle of perception of the central point and hence the function that reflects the 1st Dimotion of existence. This makes the polar coordinates of complex numbers, the best way to deal with informative, perceptive and wave communication between points.

In the graphs a very useful function on the complex plane that mimics the passing of time in world cycles towards an internal i-point. Complex planes are thus better systems of co-ordinates for cyclical times. And its simpler polar form, shows it is indeed, the perfect plane for ∆t analysis. Notice that as X becomes a ‘whole’ of a larger scale, it becomes paradoxically smaller in ‘volume but it speeds up in time’ according to ∆-metric.

Moreover its cycles become so fast that they close into themselves, *converting the whole motion of the being and its world cycle into a relative static present; and in this manner discontinous motion, becomes continuous, static present form of space. A fact which resolves the paradox of Galileo (see above, Satur**n’s rings).*

Other different view of the complex plane related to this perceptive analysis is: §ð: A riemann sphere² in the i²= ±1 axis, sets a dual ð<$t-ate of entropy.