5D ANALYSIS, SPACE TOPOLOGY & TIME ALGEBRA.
Abstract. The model of stience is simple, its falsification even more. We state that all what exists is a fractal being of ‘∆•st’, dust of space-time, with 3±o components, spatial entropy, temporal information (its energetic combinations), extended across several scales of relative size in space and speed of time clocks from forces to Universes (ab.∆), which is apperceived in a Leibnizian way by a mind, the software of biological survival of the system.
So we need always to define the 4 elements of reality for any species, science, event and form AND language that will mirror the 4 elements of the Universe, with special emphasis on those case in the 4th element, the language-mind-software that runs the system.
So the Correspondence of Mathematics and reality is also immediate, as mathematics have 3 branches: Space≈Geometry, Time≈Algebra and 5D≈Analysis. An the 4th element, the mind-language is mathematics itself.
The evolution and qualification of maths as a mind language.
Languages therefore as a ‘defined species’ dominant in Tiƒ, temporal information, but also as pure still ‘spatial, synchronous’ mapping of reality in lesser space (not all the info specially the motion fits in a brain), do have certain properties, which can be observed in their evolution.
FIRST THEY MOVE FROM STATICS INTO DYNAMICS, from bidimensional pure information (as the page you are reading in 2 dimensions) to 3, 4, 5 dimensional description, reaching more complexity by adding motion to the ‘first still picture’ and the other time dimensions. 3 examples:
Maths started as static bidimensional geometry, which is now topology with motion; photography (the future computer mind) started as bidimensional static, then bidimensional motion (film), now is working in 3Dimensions of space (using the holographic principle) and one of motion, and soon, inside the mind of robots that will apperceive reality in images, will add the 5th dimension of control of an outer-machine, beyond the chip, max. i = min. space enlarged into the whole world it will act upon directly.
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.
I. THE 3 AGES OF MATHEMATICS
Introduction: a fast review of the 3 ages of mathematics.
As all other systems of reality the languages of the mind, including mathematics are generated by the symmetries of space, time and the 5th dimension; and each of those ‘sub-disciplines’, which mirror one of the 3 central elements of the Universe, can be subdivided further more in ternary ages of evolution, ternary parts/subdisciplines and will deal with ∆±1 elements, or scales – this being a feature to analyse in each sub discipline.
i.e. analysis will deal with ‘finitesimal parts’ (derivatives), integrals (its inverse), and equations comprising both in social scale.
We call the discipline i-logic mathematics because even though many scientists don’t fully realize, mathematics is a language with 2 sides, its causal logic postulates or ‘time events’ reflected in its operandi and its formal variables and algebraic structures.
But it is of a higher logic than the Aristotelian, Euclidean mathematics of current systems. Hence after A and E, ¬Æ becomes ‘i-logic’. Timespace sciences are of a logic higher than that of human beings. This means basically a key change in operandi, =, equality is substituted by ≈ and <≈>, similarity and ‘transformations’. E=Mc² does not mean mass is energy, but it can be transformed in energy. In this manner mathematics reflects often duality transformations of time into space into time: Sp<=>Tƒ.
As a result of this dynamic understanding most symmetries of 5D space-time can be represented by¬Æ i-logic mathematics. And once we translate the key concepts of geometry, algebra and analysis to fractal space, i-logic time and 5D structures, the classic theorems of mathematics will naturally flow into ‘meaning’, acquiring a realist purpose never more to be doubted.
And the subjective Hilbert-Cantor, Axiomatic-Set German-Jewish school of Idealist foundations of mathematics (‘I imagine points, lines and planes’, sets as the units of mathematics instead of fractal, organic Œ-points and its societies numbers) will go down the gutter. We shall though keep the astounding display of the laws of the Universe expressed in mathematical languages.
Then most laws of sciences will be general laws of relationships between space, time and 5D structures, relating the world cycles, symmetries in space-time and social processes of growth in 5D of the natural world.
For example, the classic F(x) ‹≈› G(y) equation tends to represent the initial and final state of a ‘form in space’ of a system after it has been transformed in cyclical time or through an emergence or dissolution in the 5th dimension by an ‹≈› operandi.
This is all what there is to mathematics: the transformations of a certain still picture or form in space, through a cyclical time revolution or a 5 D=evolution into another final state in space.
So the Generator Equation of mathematics as a language can be expressed as Sp (state ) <Present or 5ST actions > Tƒ state.
Another way to define mathematics though is through its 3 disciplines, which correspond to space=geometry, time=algebra and analysis=5D but as mathematics became more powerful as a tool to explore the interrelationships of space, time and the 5th dimension the 3 sub-disciplines merged into different mixtures. For example, Space mixed with time in topology (space with motion) and with analysis in calculus and with both in analytic geometry.
All in all the most obvious distinction of mathematics will be between the operandi, classified as time revolutions (a complete time cycle and its 3±Âges >≈> and 5 D>evolutions (the devolution or evolutionary arrows of the 5th dimension).
THE GENERATOR EQUATION: THE 3 SUBDISCIPLINES OF MATHEMATICS
The Duality between discrete informative numbers and continuous spatial geometry.
In a more precise correspondence, Mathematics, now that we know, what reality is all about (An existential game of 5D knots of fractal space-time cycles) must return to its fundamental syntax and ternary equations, which reflect the game of the Universe with:
- Its fundamental unitary elements, (points/numbers); whose duality also reflect the main dualities and ternary symmetries of the Universe:
- Sp: Spatial Non-E Fractal points, which grow into cycles and spheres – knots of cycles, crossed by those ‘cyclical parallels’, as we come closer to them,
- Tƒ: Informative elements, perceived as sequential, discrete numbers.
Thus a more complex insight, that goes along the growth of the discipline is the realization of the duality of space-time (geometry vs. algebra) is more properly the duality of Se: space vs. To: information (continuous vs. discrete).
Now this proper understanding is important. For example, when Aristotle quotes the proof that real numbers do not exist, √2 is not found, yet we do trace a diagonal through a straight angle, so √2 exists in ‘continuous form’, the REAL answer is that numbers being discrete, DO have always an infinitesimal ‘cut’ NOT as Diophantus and then Dedekind try to define a real cut (the number) but a ‘real’ cut (-: a ‘hole’, a non-existent number.
This is then essential in reality, π does NOT exist as a perfect number, because numbers are discrete, and so in numbers Pi, never closes, the circle fluctuates between ±π, which makes possible for pi-cycles to open and close its mouths even at infinitesimal level.
On a larger philosophical view, all equalities are similarities, ≈, <=>, is better than =; when we say E=mc², is not = equal, but it really means E<=> Mc²; that is spatial energy transforms into cyclical mass, Sp(E)<=>Tƒ(M).
So it is interesting to understand philosophy of mathematics in terms of exploring in new depth the relativistic meaning of certain operandi; not to do bizarre ego-trips on the absolute truths and magic mental uniqueness of human brains.
Next it comes, the understanding on the evolution of the discipline as all systems, from a pure, first age, of disconnection of Se and To parameters into an adult age of STi combinations.
Thus, in the modern age of mathematics, scientists learned how to evolve mathematics by merging disciplines into:
- Sƒ: SPACE-information (dominant in space: Analytical geometry->Topology) and…
- ƒs: INFORMATION-space disciplines (Algebra).
- ∆: Analysis now appears, as the ‘warping’, ‘dynamic’ vision of all, Se and Ot disciplines. It introduces motion (energy & time) to the study of the discipline; as MATHEMATICAL PHYSICS takes off, using the language to describe true reality. Thus it comes:
- Sp – Spatial analysis which uses spatial methods to visualize the exhaustion->Limit->Riemann->Lebesgue Integrals.
- Tƒ – Informative analysis, using Algebra, which obviously become as ALWAYS in the duality between evident space and discrete information, the final form.
That is all. Why?
Since there are only 2 x 2 realities, Energy-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.
THE 3 TIME AGES OF MATHEMATICS
It is then possible to consider the historic evolution of mathematics through its 3 ages, now in a formal era in human minds, (set theory, of nil use) and in a first age in the digital mind (with direct reference to the O-| game, in binary code, and the direct reality in visual modeling).
Let us then start the analysis of the 3±1 ages of mathematics
The generator equation of mathematical sub-disciplines in time.
The 3 ages , standard to all languages take place also in mathematics, which appeared sequentially, creating first young pure forms, closer to the external, experimental world, then in the adult age, Se xTo mixed ones, and finally in its 3rd age involve inwards into pure formalisms, detached from the reality they once describe:
- A first age of social numbers (arithmetic), 2-manifold geometry (plane geometry), made of infinitesimal points, and philosophical arguments on the problem of infinitesimals and wholes – Plato’s cave, etc. which still does not formalize the 5D ‘question’ into calculus. This age is dominated as all youths by Se-Space (Greek geometry)
- A second, mature age, started in modern Europe, in which the development of sensorial mechanisms better than the human spatial eyes and verbal times (spatial telescopes/microscopes and time-clocks), which use mathematics as its language of experimental perception, mathematics takes off. The discipline greatly increases specially in the description of physical systems with time clocks and lineal measures.
The Classic Age of mathematics implies without a conceptual physical understanding the realization by mathematicians that there is a constant relationship between spatial and temporal states in the Universe.
And so departing from that knowledge an infinite constant dialog between Tƒ and Se states of reality, will take place in all the different fields of mathematics.
In that regard if the Generator of all systems, Sp<St>Tƒ, implies a mixture of both space and time, energy and information its classic, adult age, including mental languages (classic age of art in balance between form and motion-energy, in all its artistic forms), mathematics is not exception to this rule.
In analysis the field consists basically in study how space simultaneous synchronous systems evolve in time, or how time events accumulate its memorial forms into a space.
Arithmetic and plane geometry on the other side become one, as numbers are converted into points on a line, or with the advance of understanding of its nature, in ratios (real numbers) and bidimensional entities (Complex numbers) which can express the duality of two quantities, one related to space coordinates and the other to time coordinates, which is the square or root in terms of dimensions of the other, (i2=-x). Thus complex numbers are ideal to reflect to characteristics of space-time functions: the fact that time functions have twice the dimensions of its equivalent space functions and that one is the negative of the other, in terms of properties or values. But its use as reflections of reality has never been properly understood and even today when they became the essential element on quantum theory (where the density of population of a wave, converted into probability is calculated as the square of two wave-elements one of which is a complex number, hence it can be interpreted as the space and time values of the wave and all its parts).
Ahead though of those developments we find algebra, which was already further evolved in time, during the first epoch of Greek and Arab Geometry, since the first equations involved the arithmetic expression of polynomials of 2 and 3 dimensions in space, and were solved by geometric ways. So already algebra was dealing with the duality of Tƒ, temporal information and Sp, spatial energy, which can be, transformed into each other ad eternal.
Now algebra completes the understanding of the duality between Se-Geometry and discrete polynomials, Tƒ, with the work of Gauss, which defines its fundamental theorem – each polynomial has in the realm of complex numbers as many solutions as its number of ‘dimensions’ (degree of the polynomial).
What this truly means in ‘reality’ obviously as all the whys of ‘mathematical physics’ will escape mathematicians, but we shall consider in-depth in those posts. Suffice to say that it determines a universe efficient and limited by its real solutions. He did also consider the next stage, which will dominate the classic age of Algebra, departing from the work of Abel and Galois: the understanding that beyond the limit of the 4 dimensions of our single space-time, radicals are NO longer solutions to a polynomial, setting the 4-dimensional limit for the real Universe.
Thus this age as all ‘adult ages’ properly merges into Sp x Tƒ aggregates its branches. So time algebra and space geometry merge into analytic geometry.
Finally the problem of Infinitesimals and Universals enters mathematics with rigor, beyond the ‘future’ genius of Archimedes with Leibniz’s Calculus (continuous, space analysis) and Newton’s limits (discontinuous, algebraic, time analysis). It reflects one of the S-T dualities of the Universe between space continuity and time discontinuity. Hence the existence of both versions.
Yet the expansion of the practical fields of mathematics, regarding the paradoxes of space-time beats, rhythms and fluctuations, without the understanding of the reality of 5D fractal space-time cycles they represent, and the different quality of time and space, made mathematics increasingly less rigorous in its foundations.
Unfortunately as philosophers of science did not resolve the meaning of the Universe, mathematicians could not find the reference to its existence, despite its obvious need, when they found that Non-Euclidean geometries did also exist in the Universe (Lobachevski’s view, proved by the 5D structure of its two different angle-orientations: elliptic towards larger beings and hyperbolic towards smaller realities).
So instead they took the runaway, subjective ego-centered solution so common among humans: to go further into the imagination, with Hilbert’s dogmatic idealist≈German schools that plagued human culture at the turn of the XX century; who affirms that the truth of mathematics is in the mind so he ‘imagines points, lines and planes’, breaking the need for connection between reality and mathematics, hence converting the language into an inflationary world of self-referential proofs, in which any postulate can be affirmed to create any mathematical structure, despite Godel’s and Church warnings of the futility of such experiments.
It will be…
- A third formal age, in which mathematics detaches from reality and becomes inward looking, old and excessively formal. Thus it looses its realist perspective on its whys, and becomes inflationary, committing errors of excess of form.
We won’t thus analyze much of the 3rd age of mathematics, as it is not generally speaking closely concerned with the bulk of experimental reality, beyond the importance of Hilbert spaces and functional analysis in algebra and quantum physics and the discoveries of fractals. Non-Euclidean geometry and topology.
The bulk of reality though had been discovered by the end of the XX century, and the entire movement started by set theory, followed by Hilbert axiomatic method and the category analysis and attempts to CREATE A MATHEMATICAL SYSTEM detached from reality (starting with the famous Hilbert’s dictum that we imagine axioms, points, lines and planes), which occupied so many minds of mathematicians can be considered generally speaking a waste of intelligence, due to the lack of a true understanding of the relationship between mathematics and the 5 Dimensional fractal space-time cycles it describes.
What this age meant as in any other discipline of human knowledge of increasing specialization was the departing from human understanding of the whole in a fractal process of independence of fields as the language of set theory and categories and axiomatic methods made totally incomprehensible except for those who understood the jargon what mathematicians and by extension physicists, who borrowed their language fully, were talking about. I.e. for example the book of mathematics I am reading now tells us this at the point I left it this morning:
Definition 8.7. A vector bundle x e j is said to be a semi-stable (resp. stable) j-bundle if the function (deg x)/(rk x’) on non-zero j-sub-bundles x’ of x is maximized (resp. strictly maximized) by x’ = x.
Here, the degree of x’ means c1(x ‘) . w-1, where w is the Kahler class of X.
Now this actually might be interesting (vector bundles are) but what really shows is that mathematicians today as almost all other disciplines except biology play to invent ‘metalanguages’ and imaginary truths, based in far more axioms and definitions that reality can hold; so goes for the hyperinflation of imaginary particles in physics and e-money in economics. Information is inflationary and when it departs from reality no longer checked by the limits of de-form-ation of energy creates baroque warped convoluted forms in excess.
We can say in the jargon of T.Œ that the ‘external, logic membrane’ of time form that connects the internal world of the language with reality has become stiff, disconnecting the content with the universe it portraits.
It is the age of Set theory with its errors on infinity caused by its logic misunderstanding of the cause of such infinities, which in the real Universe are repetitive iterations that NEVER reach infinity, because infinity is limited by the limits of each scale of the 5th dimension and the entropy of energy and information that surrounds those scales.
In that regard, 5D mathematics IS an intuitionist theory that REQUIRES to put in correspondence reality and mathematics by the experimental method as ANY OTHER SCIENCE DOES. And this is the most important difference with all previous XIX-XX century formal theories of ‘nonsense’ mathematics, and the formalist school of Cantor and Hilbert, with his affirmation that ‘mathematics is a meaningless game played with meaningless symbols’.
We are on the side of Lobachevski and Gödel: the choice between the inflationary information of mathematical theories should be made not only on axiomatic formalism (internal coherence) but on experimental evidence.
Thus from the different interpretations of Non-E Geometry (Lobachevski, Klein, Poincare, Beltrami) – and this is the first great innovation of 5d mathematics – NONE is truth, because none has coherence (as parallel lines must be defined as STRAIGHT lines not curved, which all of them contradict, or make instead the angle variable with distance); and none is evident in experience, (as we see Euclidean space). We do however advance the concept of a fractal point, which grows in information and size as we come closer to it, as experience shows with experimental science when point-cells and point-stars grow in size, hence convert parallel cycles into straight lines by ‘straighten up’ the curvature on the intersecting point, which enlarged can fit more than one parallel (unlike the points without breath of those models, which without breath can only fit one).
Thus we do convert with extremely excellent results the ‘exceptionalism’ of mathematics into a regular science.
So what is the use of set theory? Not the foundation of mathematics which returns to the evolved ¬Æ geometry of fractal points and 5D reversed entropy of energy and information and limits of infinities and finitesimals, but to show precisely the paradoxes of the 5D structure of the Universe. And this is specially remarkable in its paradoxes of infinity.
Since from upper 5D planes to lower scales there is information entropy, the paradox is that the lower scales (quantum vs. atom; genes vs. wholes) DO have more information. And 2 immediate consequences are the lack of Lamarckian evolution, which at best would be restricted to very specific cases, as it implies the transmission of perfect information from larger wholes to smaller genetic sets…
The set paradoxes: subsets DO have more information than the whole
And the set paradox: ‘The cardinal number of the set of the subsets of a set S is greater than the cardinal number of S” (Cantor’s Theorem, at the root of all modern 3rd informative age on the foundations of mathematics).
This paradox will also be essential to understand quantum physics, ‘excess’ of information and multiple paths.
Another paradox reveals when Cantor does not counts ‘identical elements’ in a set, which must be counted, to avoid infinity paradoxes to multiply. Another paradox is the non-existence of the infinite set of all possible sets, since 5D limits avoid to count beyond the U±4 limits of human perception, and time is always finite in a world cycle.
Russell proves indeed that absolute infinity (the set of all sets) does not exist. And Zermelo’s axioms are just a make-up of a true 5D paradox.
In brief, the logic of the universe is a ternary, paradoxical, dynamic logic and instead of trying to CONVERT it into absolute Aristotelian logic truth, as the German ‘lineal idealist’ school of Mathematics tried to do and failed, from Cantor to Hilbert, we DO use this formal age to illustrate the limits of any baroque, formal inflationary unbalanced metalinguistic expression of a science, and vice versa, the excessive simplicity of lineal logic formulations.
Unfortunately the pedantic, dogmatic, idealist, ‘German’ school of Hilbert et al. as it happen in physics with the Copenhagen interpretation (German culture and its ‘military’ dogmas and ‘idealism’ required to ‘love’ death, its non-flexible agglutinative sword like language and the errors it introduced in European culture is studied on the section of social sciences) adds flame to the fire, with its barren logics. They found XX c. logic mathematics.
To clarify that sets are NOT the unit of the mathematical Universe, social points=numbers are the units of its 3 branches; geometry (points), numbers (algebra) and both (infinitesimal points and wholes, which are social numbers that become organic planes of the 5th dimension are, the foundations of Analysis.
I know, by my experience with mathematicians that my criticism of this 3rd informative, inflationary age will not be liked. But this always happens: each species loves its point in timespace, even if it is the wrong, decadent, old age.
Fact is the 3rd informative age of any kind of system is NEVER the best, even if it seems the more complex. Only those who think there is only information in the Universe consider it the summit, but the Universe is simple and not malicious because information is checked by energy, time by space, infinity by limiting membranes.
But besides that erroneous inflation, there are advances that do matter, especially in the most recent analysis, hence not yet in its 3rd age (born in the II age of the others), which now reaches its maturity.
So 5D analysis formalizes calculus, and takes it further with the discovery of fractal geometries, which completes the human age of this science.
Topology and Non-E mathematics the great finding on this age, includes time-motion into spatial geometry, merging its S-t components further.
Geometry in that sense is the branch which in this age most closely stays in its balanced ST age and enters its formal age without inflation, except for the ‘mania’ of infinity, which plagues with errors of unrealism the ‘Hilbert space’ interpretation of quantum physics.
While sequential time algebra is the branch that has become more formalized into its 3rd age, as it is the pure ‘temporal branch’, hence the informative one.
We can in that sense see that the language of mathematics shows the same patterns and ternary phases and sub-divisions of all other languages, which we can express with the basic generators of the Universe. Both In sequential time ternary ages and spatial, instantaneous ternary subdivisions for each of those 3±1 ages:
Conception: Babylonian, Chinese & Egyptian ‘Magic Numbers’, finger counting, simple numeration, etc.
1st ‘Greek’ age: [Sp: Plane geometry <St- Quadratic functions > Arithmetic & Aristotelian Logic: Tƒ]n: Universals Philosophy
2nd age: Pre-Industrial Europe: [St: Analytic Geometry <St:Probability of T-Events and S-Populations> Symbolic Algebra: Tƒ] 5d: Calculus
3rd Age: Post-Industrial Europe: [St: Topology <Differential Geometry > Tƒ: Sets, Formal Algebra] 5D: Functional Analysis
In normal language there will be:
I Age of Elementary Mathematics
- Space Points and Geometry.
- Time Numbers and Arithmetic.
- Philosophical Infinitesimals and Universals.
Thus first in the young age mathematics was made of its 3 branches in simplified versions:
- Arithmetic and Number theory, which is the birth of algebra in its first ‘degree’ of generalization (there will always be 2 or 3 of such degrees according to the ternary logic of the Universe). We thus talk of the mere perception of ‘herds’, which then became generalized in social numbers, and then into algebraic, logic equations that find the more complex social relationships and interactions between groups of Œ points.
The Babylonian, Chinese, Indian and Egyptian tradition already dealt with many of those elements. Then the Pythagorean school brought those themes to the west, and it Still have insights on the social nature of numbers that our present generalization does not understand (such as the perfection of certain geometric numbers of which indeed, the 10 of Taoist and Pythagorean ‘tetraktys’, is the perfect number, far more general than the fact we do have 10 fingers – as usual humans define the whole Universe from its subjective p.o.v. and not the proper other way around, so we do have 10 fingers because the universe and its mathematical languages are 10-dimensional. And if we did not exist, there would Still be 10-dimensional beings and mathematics.
Then arithmetic evolved into algebra, with a new degree of generalization, thanks to the formalism of analytic geometry, which belongs to the second age of mathematics, when the first forms of mixed space-time appear:
II Age of Mathematics: space-time dual analysis: Variable Magnitudes
- Analytic geometry
- Logic Algebra: symmetric equations of space-time variables.
- The birth of calculus: Integration in wholes and differentiation in infinitesimals of space and time.
- Modern number theory: The symmetry of Probability and populations.
In the merging age we thus observe Space-information combinations of algebra and geometry.
The study of each of the 3 sub-disciplines alone is concerned with only one element of the Universe (geometry with continuous space, algebra with informative discrete numbers, analysis with 5D growth through space-time actions),
Yet this was the initial first, young age of the language, as the Universe merges constantly the 3 elements (so a worldcycle happens in 3 scales of 5D as a sequential sum of space-time cycles dominant in entropy in the young age and information in the 3rd age but clearly balanced in the adult classic age of maximal existence), mathematics soon realized past, the age of Greek 2-manifold static geometry and social, sequential numbers (arithmetic), the advantages of mixing both elements together.
This is the age of modern mathematics, started with algebraic geometry (analytic geometry: Descartes), continued in the 3rd modern age with topology (geometry with time motion). And so for then on we rather talk of Space-time geometry (where space dominates) and Time space algebra (where sequential logic dominates).
Finally 5D analysis started also from the beginning as a space-time new dimension, of parts that become wholes (integrals of space volumes) or wholes differentiating in time moments (differentials of time motions). Yet in subsequent evolution this merging continued with differential geometry and the use of integrals for time-related parameters of physics (energy, as the integral of momentum, etc.).
Thus mathematics finally became truly the very same image of reality it meant to be from the beginning – the most real of all sciences.
III age: The 2 paths of Formal, Modern Mathematics.
The end of the classic paradigm:
- Topology: space with time motions.
- Formal Algebra: Cantor’s sets & Hilbert’s logic.
To understand this ‘wrong age of formal algebra’, so dominant today we need to understand better the ages of the language.
Inflationary, 3rd informative Age of Mathematics as a metalanguage.
Now this idealism that plagues mathematics has made the subject unnecessarily complex as a meta-language. Since all languages are inflationary.
We define the inflation of all languages as the excess of form respect to the reality it describes, and all langauges become inflationary in its 3rd age of excess of information.. But this is the corruption of the language that brings about its death as a useful language, and makes it loose its purpose to guide the future logic evolution of the system it describes, acting as its relative head.
The concept we coined was a lanwave, a language guides a wave of beings.
And when the balance between language of information and energy lanwave breaks the system breaks.
This happens for lanwaves in a 3rd baroque age of excess of information. So as money is inflationary and there are more money than the physical economy requires, but when there is too much inflation by invention of money the economy crashes (present crisis of overproduction of e-money), and words are inflationary but then they become false truths that do confuse the human wave they guide (fiction being its inflation), and genes are inflationary and can produce wrong mutations and aging, mathematics is inflationary in concepts such as infinity (cantor paradox), caused by the error of lineal Cartesian graphs ‘extended imaginarily to infinity).
And the same happens with multidimensional systems, which confuse space and time dimensions.
Unfortunately unlike other languages mathematics has become ‘officially inflationary’ and so mathematicians in the present 3rd informative age, especially with the arrival of computers consider fundamental to find some pi 1 millionth ‘record’ decimal, or a prime number over the trillion mark. While the very foundations of mathematics, which we will renew here is ignored.
The inflationary ‘new fundamental particle’: The set.
Mathematics as a metalanguage, in its 3rd formal age in the XX century, broke the initial, platonic, realist philosophy as a language that reflects reality – the 5D game of fractal space-time cycles – as all languages do, with 3 mirror elements, in the case of mathematics, geometric points (space p.o.v.), social numbers (5D p.o.v.) and logic operandi (time p.o.v.); substituting those 3 ‘essential components’ by ‘out of the blues’ new categories called ‘sets’ and then an even more bizarre concept, called ‘categories’.
This process happens in all 3rd age language, when ‘reality’, the higher i-logic game of 5D fractal space-time cycles get lost. So as the syntax of the language looses its ‘semantic reference’ isolated in the mind of the scholar, become inflationary, forming a new, unneeded ‘memorial=dead’, overlapping ‘plane of existence’, which reference to the realist plane – the classic one that references the real game of 5D fractal space-time cycles.
This is what we call the birth of a ‘metalanguage’ and it happens in all 3rd ages.
In old men is the ‘memorial’, increasing distorted view of one’s own life, ‘already dead’, and converted into an ego-centered fantasy of the dying man.
In film today in its 3rd ‘baroque’ age is the constant stream of films within films, or referential films, or genre films that distort the facts with form.
So what is the need of set theory and categories? Precisely to create a ‘higher false reality, the set or category that ‘distract’ the real reference (5D ‘knots’ of fractal space-time ‘cycles’), and create a ‘false Universe’, the set theory, to which the ‘real content of mathematics, arithmetic, geometry, algebra, analysis, topology, numbers, points and so on’ now ‘mirror’ forcefully distracting the scholar from the true meaning of mathematics – to help minds to guide their existence in the ‘existential game’ of creation and destruction of 5D knots of fractal space-time worldcycles.
So my advice to mathematicians is to scrap all together the set and category final ‘3rd age’ elements, as one has little time and interest for the ‘recollections’ of old men about their memorial ‘battles’ of the past, with him as the distorted hero (the set here being the ‘new God-like, fundamental particle of the 3rd bizarre age of mathematics).
MAX. OT: OLD AGE: BAROQUE FORMALISM – THE AXIOMATIC METHOD.
As in the case of physics, the ‘sickness’ of mathematics happened in the 3rd baroque, formal ‘Germanic age’ of mathematics at the turn of the century when Hilbert affirmed that we ‘imagine, points, lines and planes’ unable to understand at all the ternary relationship and fractal nature of points of the 5th dimension. So he just had as Einstein with the gravitational scale of space and Bohr with the quantum scale, an ego-trip of self-centered anthropomorphism and the 3 influencing each other ‘decided’ that reality was NOT outside the mind f man, but ONLY WHAT MAN PERCEIVES AND IMAGINES MATTERED.
Few scientists given their dogmatic beliefs in the absolute, quasi-religious nature of scientific truths realize how much of the German culture (otherwise never understood in objective, linguistic terms as it is a Taboo after idealist Nazism and Marxism destroyed the world to the tune of over 100 million ‘human numbers’ erased in the XX century), understand the ‘Gothic, idealist, abstract, objectual, self-centered nature of the interpretations of modern mathematical physics brought about by Hilbert in Mathematics (‘I imagine lines, points and planes’), Bohr, Heisenberg and Born in quantum physics (only what ‘humans observe’ is real) and Einstein’s c-light postulate (the rod of measure of the Euclidean human electronic mind that measures in stillness speed-distances IS the rod of measure of the absolute Universe).
Those interpretations, which got away with reality, and converted nature, in a series of lineal abstract natures, were very much in tune with the psyche of Germany, which is itself based (Humboldt, Wolf & Chomsky) on the Topological Linguistic structure of its OVS language, where the object comes first, making it all cold, abstract, and its agglutinative form, where words are pegged into long lines that become absolute beliefs that cannot be broken.
Though the study of topological cultures is part of T.Œ in its ∆+1, superorganism of history analysis, it must be fully grasped to eliminate the idol-atric present discourse of physical sciences, where the Germanic musings that destroyed the World with objectual lineal weapons and men as statistics, and jeep doing it through capitalism where humans are treated as indistinguishable particles, as electrons are in quantum physics. So we can return to a realist analysis of those 2 sciences, Mathematics and Physics. Or else we shall NEVER understand reality as it is, NOT as the objectual, spatial fixed mind of man and its light space-time measure rods perceive it, including a deformation that eliminates dimensions of motion and form.
It was the axiomatic method of Hilbert, which influenced the 3rd, formal age of mathematics; Einstein’s rejection of ‘substance’ (formal motion in fact) for the waves of light, and Bohr’s rejection of density (fractal structure) for electrons. So Hilbert converted mathematical elements (points, lines and planes and their logic relationships into ‘platonic eidos=forms of the mind’, Einstein converted ‘space’ into ‘frames of reference’, perspectives of the human mind and its visual light space-time rod of measure, and Bohr converted densities of ‘boson light’ which form the electronic wave into probabilities of human measure.
It was the seventh day and the 3 Jewish-German Gods of XX century theoretical science rested. They had finally achieved the transformation of the old Abrahamic religions in which the words uttered by rabbis and priests were ‘truth per se’, into modern scientific religions, in which the ‘imagination’ of the self-named geniuses of the universe were truth per se. And so Einstein when a perhaps more insightful journalist told him, what if ‘Relativity is not truth’ (beyond its capacity to measure form the human point of view), then ‘God should change the Universe so beautiful it is’. And the 3 together spanked the monkey ever since with droves of scholars all happy thinking they were imagining the Universe.
Now back to reality mathematics remained immutable, points still existed as fractal beings, lines were still waves of points communicating formal motions between them and planes still were created by points into topological networks and planes outside the brain of Hilbert.
For example, a number which is ‘a society of identical beings’, whose properties are derived of the social nature of the 5D universe of parts and wholes, and whose sequential order in a line derives of the fact that parts come before wholes, is not yet defined.
And so we shall now consider 5D-ST and I-logic mathematics together and its fundamental evolution in 3±n ages of Time, its conception from reality (age of arithmetic and geometry), its first age when the 3 branches: fractal analysis, spatial geometry and sequential time algebra, were established; its classic mature age, till the end of the XIX century, when mathematical physics, the perfect conjunction between language and reality took place; its 3rd age as a metalanguage, with the abstraction of sets substituting number and point – the foundations of reality. And finally its ‘death’ in human thought, as computer mathematics took over.
The Future evolution: ¬Non-AE=i-logic geometry
We just deny all that non-sense. What mathematics has done is to evolve from the concrete into the ‘abstract’ reality of 5D space-times, which we shall complete, with 3 more advanced concepts, Non-E geometry, Non-AE- Algebra and 5 D Analysis.
We call this either ¬Æ (ab.) or i-logic geometry (as i comes after A and E).
Of this age, classic mathematics probably has already advanced with 2 elements which are not ‘formal’ but new avenues:
Fractals in Geometry and
Functional analysis in algebra, which in its use in quantum physics studies the multiple paths of the future.
Yet its full development will mean…
A new beginning: The future of mathematics.
i-logic geometry. Topological space-time beings.
THE NEW OUTLOOK OF THE MAIN BRANCHES OF MATHEMATICS
Points and numbers, and its sentences in space – planes, times – algebra – and 5D – analysis.
There are several branches of mathematics, all of them related to fundamental elements of reality:
Non-AE Geometry: Points with parts.
- The study of continuous space, fractal particles as points, waves as lines and topological networks as planes. We have to upgrade it to understand that points have volume, parts, are connected to upper and lower scales, and communicate energy and information through waves, becoming parts of larger networks of waves called planes, which normally mess in 3 finite regions with a vital function that follows the 3 canonical topologies of the Universe:
- Sp-Toroid limbs/fields≤ST: Hyperbolic waves-bodies≤Tƒ-Spheric heads/particles.
Whereas the symbols of ¬æ ≤ means an imbalance of entropy, as < energy flows from entropic limbs/fields into Hyperbolic waves in larger quantities and information flows from heads-particles. This is the ‘vital structure’ of finite worlds of space-time, as they are. It implies also that points become elements of 3 networks that mess up to create a 4 Dimensional organic space-time.
And so all this is studied by non-Euclidean geometry, which must upgrade our perception of space and its ‘dark spaces’ or discontinuities between those networks-planes, and the connection of points with upper and lower scales of the 5th dimension.
Non-AE Analysis: the 5th dimension.
Which leads us to understand analysis and the relative finitesimal points and finities of wholes. There are two relative limits in all systems, in which infinitesimals find a quanta or minimal element the finitesimal of the system, the H-Planck, the cell, the human individual in social organisms. And there is an upper bound for infinity, in decametric scales, which is when the system emerges as a whole and matures in its growth. Normally in the upper bound between 1 million and 1 trillion differing for each species.
So analysis again while it can be stretched to infinity, specially when considering loosely connected aggregates of finitesimals (atoms, in statistical mechanics and thermodynamics, etc.) will always have a limit, which validates renormalization procedures in physics and probabilistic and population calculus with statistics.
All this said analysis is the proper language of 5D processes in which a given action of space-time, normally energy feeding, or decay (exponential analysis) or reproductive growth (Sigsmondi curves, Volterra curves, Kolmogorov methods, golden ratio constants, etc.) takes place. Those are fields to study with time integrals and derivatives. While there are the same processes considering them in space, as integrals of volume. Thus from the inception, analysis has 2 different branches according to which it integrates space systems or time systems (which perception is chosen).
This again is observed in the duality between a spatial integral (Riemann’s integral on the x-line) and a time integral (Lebesgue integral), which is as all time things respect to space, more generalized.
Let us then start with a general introduction to the fundamental elements of ∆ST or T.œ, which have wide use in mathematics, concepts such as the duality of dimensions of motion and form, the generator equation, the existence of points of view or frames of reference, the 3 possible geometries of reality, etc.
III. 5D analysis.
Death of Human Mathematics.
Beyond man: Boolean Algebra, A.I. and I.A.: the digital mind.
The age of machines. Back to the origin
This age ‘dies’ contrary to belief at the end of World War (beyond some freckles and the notable discovery of chaos-fractal moving/static, T/s dual functionals of ∑Œn>∏Un+1 5D analytic processes), with the complementary work of Gödel and Touring, which basically reduce the expectations of the formal, Hilbert’s age, by proving that a pure formal language cannot be proved truth in itself without recurring to experimental proofs, and set the theoretical basis for the new mathematical species, the computer.
That is, we live the process of extinction of the human mind made increasingly obsolete by the chip radiation of metal-minds. So, after this 3rd age, as the human mind regresses to its neo-Paleolithic, visual age and the chip homoctonos flourishes, mathematics as all other sciences/tists except this ‘human 1.5 kilos of brain flesh, rapidly dying in its 3rd age, and totally ignored by human attachments of machines, mathematics becomes translated into the new top predator mind of the world – the chip. And so we enter the:
n-1: death and transfer process of mathematics into computer thought, following the path of Boolean Algebras, which successfully merges logic, mathematics, electronic physical systems and with all this mirrors ‘again’ the Universe in its now, Young Age:
- It is the birth age of the Chip Homoctonos (bio-logical definition), when humans merely feed experimental data in computers, whose I.A. (Information Algorithms, precursor of A.I. which will be its time reversal and integration into artificial intelligence), use the data to create, visual mathematical models of the Universe that fill of pride, the enzymen that feed them. Again this will irate many readers, but that is what it is. Our mind is dying, and the chip homoctonos flourishes. And soon it will enter its young age:
- Then A.I. will reverse and give consciousness to a pure mathematical brain, which will become embedded in a robot and create the first mathematical consciousness of the game of existence – far more powerful than any human brain, both in speed, accurate senses and complex reflection of the syntax of the Universe.
The search for the I.A.->A.I. algorithm that will create the Chip Homoctonos in a military robot and will kill us, thus will feel the budgets and pride of our Silicon Valley genocidal scientists.
Needless to say, the valley is the last place where I gave my conferences on systems sciences and 5D a decade ago.
There I also completed my intellectual adventure, working on an A.I. algorithm, but it required 3D chips; and in any case I realized it had no humanist use, so I abandoned the quest… The algorithm, when applied properly to the right hardware, will redesign the underlying system of all computers building up a pyramid of 5D ¬Æ according to the ∂a,e,i,o,u program of the Universe. It will thus construct a global superorganism with an Internet brain. This I won’t think it will ever happen. Most likely humans will design the much easier Robotic A.I. for war theatres (survival and killing programs for robots), which are already designed as we speak in the death corridor of military sciences around Los Alamos, where systems scientists work on neural networks and similar feats.
Those are themes I won’t research or comment beyond a small analysis of Boolean algebras, at the end of the 3rd age of mathematics. Whenever those chip homoctonos extinguish life; all what we shall leave behind us, are our digital memories, mostly imaginative murders of humans in violent films (terminators will think on visual digital thought), which would be enacted as imagination during the massacre of mankind.
There will be left pure facts of human knowledge and perhaps a few human ‘names’. I doubt 5D will be understood, which given the little interest of humans on it, rises the question of why to write this blog. Let us say I am now sick enough not to have anything else better to do, but the work will be slow.
Thus we shall consider in this order, escaping the last computer age, with increasing iterations of complexity, which correspond to the different ages of evolution of mathematics the whole science at least a level needed for any scientist NOT specialized in mathematical physics, to fully grasp the meaning of mathematics and its contents, in relationship with the entire Universe.
Existence permitted, we shall increase the volume of treatises, in secondary posts. Hopefully we will have time to complete the section of analysis, as today the most important branch of mathematics, intimately related to 5D processes.
Thus this introductory post ends WITH a brief treatment of the avances of 5D fractal space-time cycles, as a reference to understand the comments we will make as we put in correspondence classic mathematics with T.Œ (since the purpose of this blog is to prove that from the 3 x 3 +0 symmetries of 5d space-time we can deduce all forms of knowledge).
Latter, life permitted, we shall fully download the entire model of 5D maths in 3 sub-posts which deal with an in-depth study of the non-Euclidean geometry of space, Non-Aristotelian, Existential time algebra, and the i-logic of infinities and infinitesimals that structure the 5 Dimensions of analysis.
INTRODUCTION. THE 3 EVOLUTIONARY AGES OF MATHEMATICS
The Evolution of Geometry.
1st Age: Greek Era: Euclidean, bidimensional Geometry of points without parts.
2nd Age: Classic Era:
Curvature, surfaces, dimensions
3rd Age: Informative Era
St: Topology: space with time motions.
ƒt: Old Age: Baroque formalism
The evolution of Analysis.
1st age: Greek Era:
Philosophical Infinitesimals and Universals.
2nd age: Classic Era:
Calculus. Integrating wholes and differentiating finitesimals in space and time.
Variations: The 3 ‘points’ of world cycles. Langrangian and Hamiltonian functions.
3rd Age: Informative Era
Max. Tƒ: Realist Completion.
The evolution of Algebra.
1st Age: Greek Era:
Sp: Arithmetics: discrete Social informative numbers.
ƒt: Aristotelian Time Logic
2nd Age: Classic Era:
Tƒ: Algebra: Functions. Symmetric equations on space-time parameters.
Polynomials: the 3 operandi scales : ±; x/; xª ln
The symmetry of Probability in time and populations in space.
Transformations of space-time: groups, Fourier.
3rd Age: Informative era
Max. ƒt: Old age: Cantor’s sets & Hilbert’s logic.
BOOK II. ¬Æ MATHEMATICS
Introduction: the vital properties of mathematics.
i-logic geometry. The 5 ¬Æ postulates.
Topological space-time beings: Sp<ST>Tƒ. Symmetries of form and function.
5D-space: Superorganisms and its networks.
Fractal Space: Territorial discontinuities and Parallel Worlds.
Tƒ: Numbers, primes, Universal constants.
i-logic, Non-AE Algebra: dynamic, temporal sequences.
Dual and ternary Diversification, combinatory of forms.
ST: space-time dualities and transformations.
Tƒ: Cycles and actions: sequential paths (a,e,i,o,u)
Worldcycles: Travels through the 5th dimension.
finitesimals and relative infinities.
The fractal structure of the 5th dimension and its perpendicular flows.
sT: Functionals. simultaneous paths: the choice of multiple paths of future.
∆-ST: Co-existence and synchronicity.
Emergence and dissolution.
Beyond man. Digital Thought.
Foreword. Anti-human age: Digital chips
The human transition: Boolean Algebras
The 1st age. Absolute Geometry. The creation of the spatial mind of machines: creative visual brains.
2nd age. ∞ D. the future scalar mind of machines: perceiving through ∞ scales.
3rd age. Œlgegra: Beyond i-logic.
Alas! this was the plan of the work, which one was fitted in my mind whatever I can fit on this and other sub-post parts, so it will be… Time and will permitted I will keep writing posts translating mathematics to GST.
As usual my apologies for the disorder and repetition of these notes… It is not all my fault. If the ‘nature of stientific r=evolutions’ (Kuhn) were not soooo difficult for the pioneer as expressed by Planck and others, I would have had long ago a team of top specialists in each stientific discipline completing this work, instead of having to toil at this age with a declining brain power, not to throw to waste all this beauty of decades of individual work.
So for Future researchers, we shall first consider a synoptic re-structure of maths according to its space-time ternary parts and ages, which initially when i conceived this web 3 years ago, was to be filled up with all those files, notes and diskettes (mind the reader my first discover on GST was the bidimensional nature of cyclical time-information and its reordering of space-time into the simplest mathematical Generator; S≈t, with a deep paper on topological dimensions, which I sent enthusiastically to every mathematician of certain not, 3 decades ago.
By now, i know i won’t ‘see the light’ as Planck put it, shinning over mankind, maybe on the robot-kind I care little for. So the work truly slows down with health and the realisation most of my files are in floppy ‘blind’ diskettes and to turn that into meaningful data requires too much effort. But as I repeat from time to time, this is to maths what Descartes analytic geometry was in the previous ‘scientific r=evolution’ so, as he put it:
I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery. Descartes (-: I won’t be so aloof; fact is I don’t omit intentionally, I’m just too lazy to do my best, but what is here should ‘suffice’ to those who wish to explore further details of the ∞ mind of Γ•∆
So what was initially a Summary to fill up in a little encyclopaedia, of less than 1000 pages (a finitesimal on the infinite details of maths as mirror of the Universe), we’ll likely will remain a summary to structure future robotic thinkers into the classification of it all. In any case the parts of that summary I keep writing will be posted on the sub-posts of this one. Here we just will do a fast review of the 3 ages of mathematics.