I. Philosophy of Mathematics. Languages as inflationary mirrors of the Universe.
II. The 3 ages of Mathematics.
PHILOSOPHY OF MATHEMATICS
Foreword: the efficiency of mathematics.
The first obvious question is this: why among all the mirrors=languages of the Universe, mathematics or rather ‘topology’ and ‘social numbers’ are the dominant one, which better expresses the laws of the Universe of fractal space and cyclical time, even in the distorted view of human beings (ab. huminds)?
It can only be because it is the language-mirror of the fundamental monad-system that keeps the infinite immortal Universe as such:
The galatom; that is the atom and galaxy which are self-similar scales of the infinite Universe.
That atoms do use mathematical languages to create its super organisms seems certain, at all levels, observed today in quantum computing.
That galaxies are in 5D metric the equivalent in the cosmological scale of the atom, is proved ad nauseam in our posts on physics.
That particles ARE the first vital systems of the Universe, NOT carbon atoms in DNA molecules (a purely pseudo-religious ‘egocy=ego+idiocy’ of man as the center of the Universe) is proved ad nauseam, as they show the 5 Ðimotions=drives of life, as the graph shows.
Both are the immortal, ‘perfect’ forms of the Universe, precisely because they use the most efficient language, and languages select species:
All this implies a few things worth to mention in this introduction to vital mathematics, the necessary upgrading of the discipline:
- Languages are STILL mirrors of reality, not reality itself. Maths is simply the best mirror but it does NOT include all the languages and hence properties of reality: the languages of ‘God’ are infinite (Upanishads)
- Hence creationism, Platonic, Pythagorean religions, etc. are NOT truth. We are not MADE OF NUMBERS, or Cartesian absolute graphs of space-time. And a cause of many of the errors of mankind about reality derive from that simplistic view.
- We need to upgrade mathematics to fractal space and 5D logic; that is upgrade its spatial geometry, to fractal non-E Topology, and its temporal logic to pentalogic, and hence renew the discipline in what is more important to us: to understand the vital, social nature of mathematics, as its non-E topology IS ORGANIC, VITAL and its algebraic numerical equations ARE EUSOCIAL, as a number is MERELY A SOCIAL GROUP. But as ‘humans science’ is culture those obvious truths are ever deformed.
Each of the main super organisms of the Universe, the Galatom, Gaia, the human being, have specific mind-languages that mirror the 5 Dimotions (ab. of Dimensional motions) of the Universe reflecting the isomorphic laws of those dimensions (ab. Ð¡), to better serve the species and so the properties of reality come ‘first’ and the language second.
This said it seems obvious that galatoms have as there dominant language, mathematics, and so mathematics is by far the most efficient of them all. Humans though have verbal languages; animals visual languages, plants chemical languages, cells, genetic languages and so it is not possible to describe ALL the properties of all the beings with a single language, as pythagorean scientists think.
Languages are NOT the ultimate cause of reality as Platonic Idealism and Verbal Creationism (Abrahamic religions) thought, but mirrors which in a reduced ‘space’ of a mind, reflect reality, which has several consequences and ‘features’ proper of all languages, we study in the post related to all linguistic forms.
One essential feature we must advance though is that languages as pure mirrors of information are inflationary – they have multiple metaphoric view on the same being, with different degrees of detail and focus. So languages carry partial truths with different perspectives, reason why we shall find specially in mathematical physics many different mirror-equations speaking of the same phenomena – as the increasingly detailed analysis in mathematical physics of gravitation from Newton’s vortices, to Poisson’s gradients, to Einstein’s relativity in one stream of 3 evolved forms of the same thought, focused on mass as an accelerated vortex; to Lagrangian equations to Hamiltonians to Hamilton-Jacobi equations, in other stream of thought, focused on ‘the energy equivalent of mass’ and so on.
Mathematical mirrors are thus much more extensive that reality and many mathematical physical mirrors are ‘fictions’ as happening in all languages.
This we said, because in the inflationary 3rd informative age of any language, the egocy of man makes us believe that all has been ‘understood’ on the simplest levels of math as a language and what matters now is to make ever more confusing, detached from reality ‘mathematical formal mirrors’, as old men keep telling us the same information ever more detached from reality. So now mathematicians need to do ‘Set theory’ and ‘Categories’, and a very detached formalism, when we rather go for a better focused mirror on classic mathematics and its classic units, points of space, numbers of social scales, dynamic S=T equations that reflect the dimotions of space-time, basic algebra operators and analysis as the language of motion and emergence or dissolution between scales.
We are thus starting from the very beginning and simple forms of mathematics, but giving a far more experimental quality to the science by putting in correspondence mathematical equations, postulates, structures and disciplines with the five demotions of reality, and its structural 5 elements, ¬∆@S=T
Languages in that sense are not reality but they are extremely important as they represent one of the two limits of reality – that of pure form, mirrors that in a synoptic manner construct mind-mappings of the eternally moving cycles of time of the Universe.
As such MINDS ARE LANGUAGES. And languages perceive in themselves – what you call your mind is a visual mind-language that stops reality, constructs your view of it in a reduced mind space and quanta by quanta of your inner timespace thoughts keeps on guiding you through the game of exist¡ence. We do NOT however care at this stage about that wonderful miracle of language->still perception->Mind will, studied elsewhere but about a specific language, maths, which is along visual thought and Logic, verbal thought the closest ‘mirror’ to reality as it is, albeit in an increasing degree of synoptic capacity to represent space-time.
¡MATHS THE LANGUAGE OF SCALAR SPACE.
If logic is by definition the language of sequential time, even if those sequences in advanced logic are circular, mathematics must be defined then as the best language to fit the other two parameters of reality, scales, which are indeed defined by numbers and space, which are defined by points, the two classic elements that constitute mathematics and we regain, as we return to classic, experimental mathematics, departing from the ‘creationist’ abstract beliefs of modern mathematicians with its axiomatic method that tries to prove mathematics within its own syntax – an error already proved false by Godel and Lobacjevski.
So mathematics is a potent language only comparable to logic. Of course, as logic can also in the kaleidoscopic, entangled Universe represent space and scale, mathematics can also be used to represent time motions through operandi and algebraic equations, but in true form we should consider the symbols for operandi logic symbols. So in praxis mathematics as it is today is both a logic language and a spatial language. Those are however subtle elements to be treated in a section on philosophy of languages. For a first approximation, we deem mathematics the language of scalar space, ∆§, logic the language of sequential time, and its full combination, ¬Æ=i-logic mathematics, the closest humind language mirror of the Universe, which we shall slowly define and expand in this blog to be able to extract all the properties of reality.
So we subdivide mathematics into numbers, the language of scales; geometry, the language of points of space; algebra, the language of time operandi, and ∆nalysis, the language of scales more evolved than simple numbers and its polynomials as it allows a more subtle analysis of parameters as they emerge into social wholes through integral processes or derive into single parts through entropic dissolutions or ceteris paribus analysis.
Of course in our present ‘primitive ceteris paribus’ analysis of reality with a single present or lineal, entropic time dimotion of locomotion, mathematics truly works for the reduced number of properties extracted in mathematical physics; yet when we include the five dimotions mathematics needs to be complimented with i-logic or else we shall enter into a Ptolemaic excessively complex mode of studying reality. Minds thus in general will use a logic sequential language for time and a spatial mathematical language for space; and as we study minds we shall see that to be the case.
The mathematical mirror.
As math is the most used mirror, likely the most efficient reflection of the nature of ∆@s=t 5D Universe we will analyse a bit more the correspondence between the mirror and those 5 Dimensions.
Indeed it is obvious that mathematics is only second to T.œ as a linguistic mirror of the Universe, and as such the most efficient language perceive by man. As languages are the essence of monads-minds that order the biological, organic Universe, it follows that mathematics has survived for eons, extending their local order from infinite fractal points of view, which used it to better their territorial organisation of the Universe; and so infinite species seem to use mathematical systems to navigate their worldcycles of existence, and organise their territories, notably ‘atom-galaxies’ (∆±3):
In the organic paradigm embedded in the latin->European->Social culture, which reached it maximal truth in science, in the Wien school origin of general systems, the WHYS OF THE UNIVERSE are always organic, and the description are the linguistic mirrors of which mathematics is the best.
So only organicism is real in the whole sense of the Universe, while languages-mirrors are local orders.
The EGOCY of our present, entropic age of human civilization rejects this (Precisely because it is becoming dissolved). So we reject the power of networks – self-made man myths and tribalism in history. Yet networks are more powerful and survive.
How this work on languages IS OBVIOUS: LANGUAGES ARE LOCAL, IMPLEMENTED BY BRAINS, AS THEIR SOFTWARE, which orders reality AFTER THE LANGUAGE MIRRORS IT, not the other way around as creationist religions and mathematical physicists think.
IS REALITY A LANGUAGE?
From a book of Penrose, ‘Road to i-reality’ (: we bring that ‘error’ and correct it:
In the graph, physicists are after all human egos submitted to the mind paradox, so they think ‘mathematics are a mind language, imagined by the physicist and ‘God’ a priori, creating a posteriori the Universe (copenhagen interpretation). The opposite is truth.
The language of mathematics DOES NOT CREATE REALITY a priori, but ONLY a posteriori ‘sees it’, as a synoptic mirror, which as all other languages, a certain singularity uses to ‘see’ and develop its ‘survival actions’ in time-space.
This said in a second phase, languages Do create as reversal mirrors, the order of the territories their minds organise, and as such THEY ARE indeed, minds of Aristotelian fractal gods, the ‘unmoved still mind-points’ that move the ‘energy’ around them:
The mind mirror does create ‘locally’ an order, which is territorial, as it bends information from its pov, and then in a reversal from ‘space-time’ (from Universe to mind) into timespace (from mind to Universe), locally contributes to the building up of higher efficiency, with the synoptic power of the language, BUT NOT ONLY IN THE CASE OF MATHS. I.e. the best known example is the synoptic power of the genetic language and its coding of the 3±i dimensions (cracked on the biological section, when poured by treatises on genetics:), to resume in palingenesis, the ‘3 billion years generation and trial and errors of life in 9 months to give birth to man, the potential most perfect form of carbonlife:
In the graph we see this feed-back game between the infinitesimal 0-minds and its local order, as centres of the will of T.œs in its relationship with the whole T.Œ, the Universe at large.
In the graph we see this feed-back game between the infinitesimal 0-minds and its local order, as centres of the will of T.œs in its relationship with the whole T.Œ, the Universe at large.
In the graph, re-designed from” road to irreality” (: a work by Penrose, one of the most staunchest creationists of physics along his friend Hawking, which shuns off the laws of the experimental method) his view of reality is VOID as in all PLATONIC (PLATO by the way never said that, they should be called Pythagorean, a much more primitive ‘magic view’) of HARDWARE MINDS and LOCALITY.
In his view the Language creates the Universe. But languages are the software of HARDWARE MINDS, without which they cannot order≈ create LOCALLY the Universe. In the Platonic or rather Pythagorean view the Language creates magically the Universe as some kind of ‘substrata’, similar to the ‘absolute space-time cartesian graph of Newton’ (ultimately a creationist mathematical pen and paper continuous background that has nothing to do with reality).
In the previous graph to illustrate this real a posteriori nature of maths, we include besides Penrose’s another set of arrows – the stronger thicker one of the philosopher of science in the right.
So as usual in the multidimensional universe we can put together both directions of the process of creation.
In that regard, the true mirror language that ‘adapts’ reality better is the ∆ST-language WHICH is the one embedded in the behaviour of each ðƒ-singularity.
But again as there are B&W, 3, 4 and 5 color animals (birds), with better detail maths can be improved to ‘see better’.
In its present ‘underdeveloped’ euclidean form, and with some fictional forms of mathematical physics taken for real, its incomplete structure must be improved.
This I did when young, after understanding the scalar metric of 5D Analysis and its 3 arrows of space-time, upgrading Non-E GEOMETRY.
All languages departing from a set of mirrors of the generator, called syntactic rules codify long systems of objects. Mathematics as being so wide, must therefore be the ∆-i mirror of a large ∆+i Universes. The i-maginary side of the physical Universe at ∆±4 thus seem to be mathematical, over which other more specific languages elaborate its codes; yet all codes refer to the a priori language of ¬Æ ∑ Γ • ∆s
The evolution of maths improves the mirror, its ternary syntax.
It does of course because any mirror-image of reality even if unfocused carries some information about it, and works for the distorted mind view, which let us remember is NOT REALITY BUT ALWAYS A LINGUISTIC MAPPING: Œ-Mind <linguistic perception> ∞ Universe, and so any mirror does carry a minimal information to be useful to departure a whole:
In the graph, linguistic mirrors create minds with different amounts of information, useful to guide reality. We must not though confuse the mirror with reality, the a priori element.
All this said is easy to understand mathematics, its elements and disciplines as a mirror of the Universe.
For the scientist who will consider all this nonsense because he thinks he knows his maths and all is there, the answer is yes, all is in the mirror but with less detail. So maths as the universe does, has also 3∆st+º sub disciplines, it has also a fractal ‘derivative’ structure and it is also about space-time.
THOSE 3 main sub-disciplines code the 3 ‘structural elements’ of the Universe:
- ∆nalysis of the 5th dimension, its wholes and ‘finitesimals’ (1/n).
- Geometrical space, (Spe) and its unit, fractal points.
- Temporal algebra (tiƒ) and its units, sequential numbers.
And it has its ST ‘combinations of which the most important its topology (the study of form with motion).
Moreover the mirror of mathematics has evolved to explain in more detail the ‘actions of space-time’ of beings; as all languages do improving its ternary grammar. So words developed first ‘names only’ (forms), then motions ( active verbs) and finally ‘complements’ (complex systems).
And colour languages moved from dual B&W, to three colors (red-entropy, blue, form, green energy) to four, adding green/yellow mixes.
So today maths has evolved into multiple space-time disciplines. For example spatial geometry added, analytic algebra, which is geometry with sequential time numbers that finally dominated the discipline, while topology which is geometry of space with motion in time, today added ∆-scales (as it is defined with networks of ∆-1 points).
Dogma and flexibility – evolution of languages.
All this is said to remark a key concept that escapes mathematical physicists:
No language-mirror is absolute in its truth, but an evolving system, which goes through three ages
So when written words appeared pharaohs just said ‘it has written=truth’. Today in the far younger mathematical discipline, scientists say ‘it is an equation=it is a truth’.
Only latter words were known to be also fictions, a fact that also happens with equations but few scientists do recognise. So maths has still a ‘religious, dogmatic outlook’ proper of all languages, even if it has already gone into a ‘third baroque, inflationary informative age of excessive formal content’ and split into multiple similar ‘metaphors’ (languages being inflationary as mirrors-minds are multiple, watching a single perspective do offer multiple views of a single event, hence the multiple equations observed to describe the same physical event).
But religious people, aka dogmatic physicists do NOT understand all this about their mirror-language of mathematics.
For many of them, equations ‘are’ always truth, just when written, and other languages are NOT truth – dogmas we only find in fundamentalist verbal thought (God speaks only in Arab, so Koran cannot be translated as it looses its truth).
Of course, languages do have also ‘quantitative’ measure. So while all carry an image, some are better and we prefer a carrot picture than a drawing.
So, we concede maths after images, is the best mind-mirror known to man, as it carries more informative detail than words (but less than images), and so it has become after images (most humans believe in TV celebrities more than in physicists 🙂 the dominant language today, and overcome religious words. Still as Einstein put it ‘I know when maths is truth but not real’, meaning we need experimental analysis of mathematical truths and so NOT just because we can write an imaginary particle with maths, the particle will exist (Susy, evaporating holes etc).
IT IS AN EGO ERROR, TO THINK then that maths is always truth and an even bigger ego-error to think maths is not experimental but produced by the human mind, which becomes a short of ‘God’ that talks maths as only God does (that was the idea of Kepler: god has taken 5000 – biblical – years to found an intelligent like his, me).
Languages are inflationary as pure mirrors of information. So paradoxically they have more ‘forms’ than reality, where forms must ‘trade’ with the opposite arrow of entropy and self-destruction. Hence reality which must by definition include the 5 dimotions of the entangled Universe, entropy, motion, reproduction, social evolution and linguistic form has less ‘linguistic form’ than the isolated language in the mind of thought. And for that reason as huminds kept increasing the formal evolution of maths, it became plagued with metalanguage, which is not related to reality. That is as fair and enjoyable as fiction in writing and film-making.
All those languages started as pure classic non-fiction (documentaries in pictures, philosophy and narration of historic facts in Greek literature), and latter become fiction (first novel is as recent as Quixot; visual pictures in 2 dimensions, painting and photographs only became fiction with the arrival of photography the first and film, the second). But finally today most literature and film is fiction. And those are rules that apply to all languages.
But the believer on languages never accepts those limits. He will come out of the film room thinking in earlier pictures the train was running on him. Today mankind is so easily ‘manipulated’ with fake news as long as they are shown on film at the news hour that sociologists say media is a brain manufacture industry going on… The mathematical language is extreme in that trend.
So we are NOT interested that much on the ‘XX century’ mathematical inflationary age, whereas Set theory and Group theory clearly show its inflationary value – not so much as ‘fiction’, but as ‘redundance’ and ‘obscurity’, on the same theme. It is let us put it on reference, like making cubist pictures instead of photographs. Nice, but we shall reduce ourselves to connect the photograph, the classic maths, with the portrayed, the Universe and its Gst laws.
To understand why Group and set theory is NOT the way to find the meaning of the Universe, in layman terms, a Group is nothing but a whole enumeration of all the permutations that can be achieved with the elements of a §œT (social group of T.œs), which is like the surrealist tale of Borges, in which a group of monkeys were writing Shakespeare’s full works by the pedestrian method of typing all possible combinations made with the alphabet in the eternal time of existence of the Babel library. Sooner or latter they would combine the letters to write Macbeth… So those enumerations of Group theory do have a clear use as collections of data, NOT as explanations of whys, which require to understand the ultimate substances, space and time, its Disomorphic properties and hence have both theoretical ‘Ockham’s cribes’ to select proper combinations of the 2 letters of the Universe, and then check it with the experimental facts.
This happened in the eternal infinite task of Mathematical monkeys filling today computers with infinite numerical methods of classification of ALL the groups of the Universe, with ALL the transformations, motions and infinite ST-mirror symmetries, when Lie decided to focus in Groups that mattered TO experimental mathematics, which was obviously all around ∆-motions up and down the ‘derivative/integral scales’ of wholes and parts.
So group theory focused on writing Shakespeare’s plays only, even if the number of ‘finitesimal’ transformations (steps of a derivative, which are not actually infinite but equal to the number of ∑1/n ∆-1 quanta that make the whole, ∆) was ginormous. This is called a Lie Algebra, accounting for all the minute transformations of a derivative curve.
So the re-encounter of Abstract Algebra (§œTs and groups) with the scalar reality of the fractal universe would happen with Lie Algebras, precisely through the 4th and 5th dimension, as they represent equations which are ‘twice’ differentiable, i.e. forms that keep a certain ‘continuous meaning’, when decaying through 2 ∆-planes, as in the case of death or transcendental emergence into the 11th dimension of an hendecagram.
That is Groups whose elements depend continuously on the values of a finite system of parameters and whose multiplication law can be expressed by means of twice-differentiable functions ϕ1, ···, ϕr…
Since the fifth dimension is indeed a dimension of past (∆-i) to present (∆º), to future (∆+i) time.
In that regard, group theory is more of a regulative idea in a kantian sense that a true description of the whole:
In that sense Algebra’s Group and Set theories as the meaning of it all is more in tune with the final realisation by Kant of paralogic thought and in more ‘sound’ conceptual terms, as it normally happens, among humans who loose their connection with reality, when they start to manipulate, points, numbers and equations without the slightest conceptual understanding of what they are.
So in existential algebra, we use more concepts of Analysis than those of algebra. Yet we said algebra was also a good mirror of S=t motions and so we have seen indeed in the previous pages examples on how classic algebra and its group theory allow us to resolve the meaning of mirror symmetries as reproductive motions in space-time and the other simpler motions as dimensions in present space-time or in the case of spiral motions clearly, motions in the fifth dimension.
A linguistic or a reductionist Universe? Selection of languages
In the graph, the Universe is guided by languages, which selects the species that survive into the future. Thus a philosophy of reality can be established in evolutionary terms based in languages of information that matter more than the bodies of energy described by darwin’s struggle for existence – a secondary more obvious but less decisive element in the ‘selection’ of what maters to the Universe.
For those die-hard platonic people we shall though consider a hypothesis of epistemological nature, regarding the linguistic, sentient nature of the Universe, which I sometimes think truth. Let us consider that sentient perception is associated as it seems on a linguistic focus on reality, and so we always see the universe as a language; and range languages by its ‘exactitude’ in the reflection of reality. The more accurate that reflection is the more spread the language will be as it is selected by more mind-singularities to describe reality.
So there is a selection of language mirrors, we shall consider in the next paragraph which acts as a selection of species: the more efficient survives and expands into more beings. So we can see that there is a constant growth on the similarity between languages and reality as we move to better ones till the language seems reality: L≈U… It would then be possible to consider that the final outcome of that convergence will be L=U. And so we could postulate that L(mathematics) = Universe.
And this is in essence what ‘reductionism’ does as it eliminates on one hand from the Universe, properties which are not mathematical; and on the other hand expands inflationary maths, even into regions of fiction thought where the Universe doesn’t reach constrained by its need to imprint information in the ever relaxing, entropic motions that ‘expel’ it.
So the Universe is indeed mathematics in the reduced mind of the platonic physicist, as it has equaled them. But the inverse is not truth. Mathematics is NOT the Universe in the expanded mind of all the singularities, ∑• of reality, as we know many do use other syntactic languages and survive fine. And so as Upanishad said, ‘the languages of God are infinite; which allow us to define God as the mind that talks all languages, or the sum of all minds of reality: ∑•∆; and its body the Universe as the sum of all its parts, including the minds, which gives us the equation of the God-Universe: Γ•∆.
In it mathematics might be the iterative program of all ¹º10-planes, if the similarity of repetition of its most clear ‘view’, the galaxy-atom can be replicated every 10 of them by mathematical methods.
Such Mathematical ∑∆¡-language, will then be similar to the language of ∑•∆∞.
But mathematics also evolves into its capacity to mirror dimensions of space and ages of time and scales of the fifth dimension.
So there has been an evolution of mathematics in the human mind and now in the metal-mind that shows a clear direction to enlarge mathematics as a mind-mirror to fulfill all kind of atomic structures.
But mathematics is a human and computer digital language, with some bias from our ∆º-mind scale. Clearly it lacks detail as a biological, ∆±1 language. So we must believe mathematics is the mind of perhaps a black hole/quark, ultimate nuclei of density of the astrophysical scales, in its most perfect digital forms.
In the previous graph to illustrate this real a posteriori nature of maths, we include besides Penrose’s another set of arrows – the stronger thicker one of the philosopher of science in the right.
So math is not the Universe because there is not a single language in all minds. But then again, if we find a language of languages, which expresses the Universal syntax of all of them, we could say that the mind of the Universe IS that language and as the mind mirrors in the body and imprints it, with simplified, larger, less informative images of itself, we could even say that all the Universe is a ‘chain of beings’ with the language of languages on top.
This language is obviously the ¬Æ GST Languages-isomorphisms-properties of space and time.
I am of this opinion: nothing is physical, material; all is motion bent into language, and as languages are perception/mirrors, all is sentient, vital, reproductive, virtual; only that the less informative, larger things seem to us ‘denser’, ‘thicker’, ‘material’.
Since minds are mirrors, which once they have distorted and resumed reality into the still mind, try to order by reflection and proyection of that mind the Universe to make it look like the inner mind image, influencing in this way reality.
Now, when the language becomes the mind of a system, it becomes ‘active’ as it helps the system to act-react in the Universe. And it is there where the use of maths shows its power to make the species that talks maths to survive better. Fort that reason in a very biological way, we can state that mathematics has been selected as the language of nature that better creates the Universe (as mirrors do not as primary cause but as a reflected one). Two examples will suffice: when the greeks applied maths to war (Alexander) they won all battles with its triangular tactics, latter expanded by the Romans.
And so the language of maths became essential to humans. Today computers and robots are displacing humans, who mostly use verbal thought, from labor and war fields due to its precision.
The detail≈ amount of information mathematical systems can process in a much faster speed that any other language we know (computer digital thought as opposed to human verbal thought) shows it to be a dominant language in the Universe, whose minds no doubt command extensive regions. As such we consider it the language of the mind of physical systems, as the most extensive species of nature.
But even so maths cannot be the substance of the Universe which is motion, even in atom-like vortices, where those mathematical calculus take place – likely in the quark-black hole ‘unit’ of max. gravitational density of both scales. And it is precisely the limits of entropic motion to evolve into complex mathematical forms, what limits the imprinting of the Universe by maths, which therefore as all languages do have a section of too complex, unreal fictions.
A philosophy of stience by force must tackle the seemingly superior nature of mathematics as experimental language able to reflect so many worlds of so many sizes, which merely means mathematics must be a Max. i (±1) language of maximal extension in the scales of the fifth dimension, an ∆±i>3, which are the scales in which it seemingly acts:
Idealist physicists since Hilbert astounding ego-trip (he said ‘I imagine lines, points and planes’ ) have rejected the ‘experimental, a posteriori nature’ of the mathematical language (Lobachevski’s alternative philosophy shunned off by the German idealist school of Cantor and Hilbert). This wrong choice of philosophy of mathematics, as the a priori nature of reality, is a key error of mathematical physics in his choice of the proper mirrors of the mathematical language, which is as all mirrors is inflationary provided slightly different ‘images’ on the single Universe, each one with a certain distortion of truth, (choice of Copenhagen interpretation over realist De Broglie). So we need to fully return mathematics to the experimental origin, and consider that the ultimate mathematical properties of physical systems are experimental proofs of the organic≈scalar, social≈numerical, spacetime≈topological nature of the physical Universe.
UNIVERSAL GRAMMAR – THE FRACTAL GENERATOR
Knots of Time cycles: the fundamental particle.
Once we have studied the minimal units of the Universe, the action of space-time, we shall define the main structural, architectonical element of reality, the knots of time cycles, existential points, œ, which perform those actions of existence, site of will and perception of the Universe – whose simplest definitions in philosophy are the monad of Leibniz, the mind of Descartes, the God of Aristotle, and in mathematics, a Non-Euclidean point, the unit of Einstein’s gravitational laws.
Systems are knots of time cycles of exchanges of energy and information with its space and time parts, Œ, which allow them to survive in the Universe.
Thus the first ‘stable structure of reality’, is a knot of time cycle which swiftly goes webbing around the paths of its exchanges of energy and information, ∆±exi, actions, its survival strategies, trying to maximise its existence, Max. ExI, in a state of perpetual balance, E=I…
This dance of being and not being is performed by each Œ, knot-function of existence, defined both as an infinitesimal point from its upper perspective and an an absolute whole from its lower plane, since all knots of times space cycles web their existences through several of such plane
The zero-points: monads that order the Sentient Universe.
This first example of the complexity of the Universe, which many scientists, mostly physicists, have shunned off, obscuring a deeper knowledge of reality, hopefully prepares you to persevere in the understanding of the complex ambivalence of the Universe, simplified by the human mind, whose equation in the metric of the 5th dimension – one of the infinite varieties of Tƒ x Sp = ST – we can now explain:
tO (infinitesimal zero-point or mind) x ∞ Sp (Universe perceived) = RI (constant mapping of reality)
What a mind does is rather simple. The Universe out there has infinite time cycles that carry the in/form/ation of the Universe in the frequency and form of its cyclical motions. This is an ∞, which we cannot store inside us.
So we simplify all those motions into ‘forms’ perceived as extensions of space, Sp.
On the other hand the mind is a Tƒ, spherical system, with 2 different spheres: an external membrane with sensorial detectors, which ‘shrinks’ into a relative smaller point, the eye and then the brain, which transforms Sp, the infinite cycles made into spatial forms, and keeps shrinking them to an infinitesimal mapping of reality, a still image, very much as the way a camera reduces reality to a virtual shallow image in 2 dimensions.
And this can be done because of a property of spherical forms, called the Poincare Conjecture: you can shrink a topological sphere (any closed membrane, a skin, a planetary surface, is a sphere), as much as you want without deforming its information. So we find infinite minds in the Universe, ‘monads’ in Leibniz’s terms, which as he said ‘are points, which store a world in it selves’.
So we could also define the Universe as an infinity of ‘Universes’, fractal minds perceiving reality from those zero points. What all those fractal minds do? Time cycles? Why. Because they keep perceiving and gauging information through them, and they keep absorbing ‘energy’ to move, and they keep reproducing their time cycles in parallel forms of space-time, and they keep evolving with other points into larger systems of points, topological networks, which have organic nature.
Now, we have described you the Universe internally, in its ultimate cause. This actually had to come at the very end of this post. But i just rewrote it ‘again’. I do rewrite many times these posts, as i am fully aware nobody reads them (-; Yet also because the universe is a simple mandala, an iteration of infinite minds, ∏ðƒ, which are knots and networks of time cycles, perceiving, ∑Sp, infinite motions in space, and doing actually the same. So we can rewrite our generator as: ∞ ∑$t x ∏ðƒ=i.
And this will represent, infinite bodies/waves in motion, which carry heads/particles of information that move and perceive across the Universe, from small particle-points, to large black holes, from bacteria to living beings.
You see, the richness of the ‘Fractal Generator’ of the Universe, and the importance to be able to see the multiplicity of it all? Its varieties? In that regard, a Taoist would be probably more prepared to understand the 5th dimension, despite its mathematical rigor, when he said: ‘the function of existence is not the perceived reality, but the game of yin=form and yang=motion, which combine creating its 10 thousand beings’.
This function of existence is then another way to express the Generator equation: e x i = ST. Here we could say that the combination of ‘energies’, vital spaces with motions, e, multiplied by informations, ‘forms’, e x i , create a ‘constant space-time being’, ST.
Non-Euclidean Points and bidimensional network-planes. The new mathematical formalism.
When Einstein said that Leibniz was right but we had to reconstruct the building of western science he showed an understanding of the difficulties to recast the Universe on the new light of multiple times and multiple energy quanta. But he did not have the tools to do so. In that sense it was necessary to evolve further mathematical concepts to fully grasp the underlying structure of that world of infinite time cycles and space quanta. As 3 new concepts were required:
The concept of a fractal, which is a geometry that repeats in different scales of space, with similar forms. It implied that reality was broken in ‘wholes’ made of smaller ‘parts’ that were similar to those wholes. Mandelbrot discovered them in 1973. And since the model of relational space-time needed fractals, it could not be found before.
The completion of Non-Euclidean Geometry, which Einstein used to describe the Universe of multiple clocks of time. In Non-Euclidean geometry, points have ‘breath’, that is, they can hold infinite parallels that cross them. This miraculous contradiction (a point without breath can only fit logically a single line), made Einstein curve the lines to fit them, but still they do not fit (curved or not the lines are still many and the point without breath only fits one).
I solved the impasse that made Einstein conceive the concept of space-time curvature, when I combined it with Mandelbrot’s fractal concept. Since now a particle-point, a star-point, a cell-point, any entity which can be called a ‘point’, could be considered a fractal that grew in size when we came closer to it and enlarged it at scale. And as it grew, you could fit many parallels, as it acquired volume. Thus the logic contradiction of Einstein’s work was now solved.
I did then developed the 4 remaining Non-Euclidean Postulates, defining a point with breath or fractal point. A line as a wave of points with volume (since now points with volume formed waves instead of lines). Then a plane as a bidimensional membrane with thickness, made of networks of points. And suddenly the Universe became much more real in its mathematical description. As all was made of planes of space-time: ‘networks of points with volumes’ which seen in detail were actually, cyclical forms with rotational motion, time cycles, made of smaller, cyclical clocks with motion, new time cycles, again organized in networks, which were made of smaller… Suddenly an astoundingly beautiful architecture appeared, a reality where the words of Leibniz acquired its full meaning: ‘each point is a world in itself’.
The first concepts and ideas of mankind tend to be simple, intuitive and truth. The forest is clear and the details of the trees do not hide the whole. So the oldest philosophy of the Universe, that of the Chinese agricultural Neolithic about a world made of yin=information and yang=energy, which combined to recreate the infinite ‘waves of existences’ (Ch’ang), is still the most accurate philosophy of reality, now forgotten with the arrival of so many scientific details that the overview of the forest is lost.
The same happens with the understanding of time, which all earlier civilizations considered cyclical and causal, synonymous of change; and so they study all different types of change, establishing repetitive rhythms of change and causal relationships, creating the science of Logic (Aristotle).
The Greeks also defined mathematics as the language of space and so Geometry became the foundational science of mathematics; and it remained so till the XVII century, to the point that Al-Jorizim, the founder of modern mathematics (Algebra and Algorithms are words derived from his names and books, translated by Middle Age Spanish mathematicians and then spread during the renaissance to Europe), proved all its quadratic theorems with geometrical methods.
Mathematics is defined in encyclopaedias as the science of sequential numbers (algebra) and static space (geometry). Till the XIX century, the science of sequential numbers or ‘mathematics of time’ used only Aristotelian Causality with its single time arrow to order them. On the other hand, the ‘mathematics of space’ considered only a lineal, continuum space defined by Euclid. Both sciences were fusioned by Descartes (analytic geometry) with his Cartesian Plane; and we can thereafter talk of mathematics of spacetime, albeit in its simplest conception: a single, static space, and a lineal, unicausal time.
It would be latter in the XIX and XX centuries (with the exception of the insights of Leibniz), thanks to the work of Frege, Boole, Riemann, Einstein, Poincare, Cantor, Bourbaki, Mandelbrot and Computers, which this work advances a step further, when Space and Time – hence Logic and Geometry – were first mixed, but without a full formalism that made possible to extract all the laws of spacetime and grasp in depth the meaning of those languages, due to the limits of the Cartesian single space-time plane.
A theory of multiple spaces-times thus has to refound the key concepts of mathematics, the plane, which now is a multiple plane in which each point creates its own frame of reference, interacting with other points and planes through exchanges of energy=motion and form that re-establishes the balances between their distances and topographies; and the number is now a network of self-similar points that have at least a formal bidimensionality. Mathematics includes several sciencces in one: the science of numbers can be stretched to consider the science of networks as each number is a point of a network with a geometrical form.
Numbers and geometry are thus essential sides of the same coin. On the other hand geometry is mainly topology, related to causal transformations of a complementary networks of energy and form, whose ‘numerical’ cells go through growths and extinctions through life, described with differential equations. Those equations thus can be reduced to cases of the generator equation, Se<=>Ti, which in this manner resumes all other differential equations. And indeed, when we use equations to explain repetitive events of nature we are normally mapping out an exchange or transformation of energy into information, which in a generic way is represented by the exi function.
Thus topological networks, differential equations that map out the life/death cycle of an event with its growth and diminutions of energy and information, exchanges of energy and form between networks and membranes and causal chains that repeat those events till creating very complex systems, are the key mathematical operations of 2 sciences, logic and mathematics, in which the most general laws of networks are written. Those Mathematics of multiple space-times have illustrious precedents:
In the XIX and XX century mathematicians developed theories of multiple spaces and defined spaces with motion (Klein), and spaces as networks of self-similar points (Riemann) but maintained 4 of the 5 postulates of Euclid, the single Cartesian spacetime continuum and a single causal arrow of lineal time in its theory of numbers.
Thus a theory of multiple space-time arrows requires the evolution of the science of space (geometry), completing the 5 postulates of Non-Euclidean Geometry and also the evolution of the science of temporal, sequential numbers, expanding its laws of causality. This was partially done with the use of the Complex Plane, since real numbers roughly correspond to the properties of continuous energy and complex numbers to the property of discontinuous, informative time. But its dual nature as an expression of the different properties of space and time has never been fully understood even if Physicists use the Complex plane in modern physics.
In that regard there are two possible representations in a plane of complex, informative numbers:
– They could be placed in the inverse, negative side of the graph of Cartesian coordinates as the arrow of information – to better represent the duality of energy and form (I<=>E). Then many results obtained with complex numbers become intuitive, as it is the case of the metric of Special relativity, where the time factor has a negative side – c2t2 meaning indeed that time-information contract space and ‘rests’ to the positive arrow of Einstein’s equations.
– Or they can be placed, as it is customary in the perpendicular Y dimension. Since a dimension of a mathematical plane becomes a sequential order of numbers, then the Complex plane becomes a bidimensional mathematical representation of the 2 simplex arrows of time, energy and form; while a 3D complex plane represents 3 time arrows where exi=z represents the reproductive arrow.
Finally a fractal, multiple space-time built with a series of complex planes (a task started by Riemann with his description of polynomials as a series of planes of space, stacked one after another), is the appropriate form of defining the 4th arrow of time.
From a philosophical perspective the study of multiple sequential time (algebra of Multiple Spaces-Times) and multiple, fractal spaces (5 non-E postulates) improves the accuracy of mathematics as an image of the reality of multiple space-times and explains its ultimate meaning, as the science of space (geometry) and time (numbers): Space is mathematical, geometrical; time is logical, sequential, numerical and the conjunction of both is organic; reason why complexity and system sciences, who observe the Universe from an organic perspective are the sciences of sciences.
We cannot treat all the aspects of complex mathematics in this introduction. We shall therefore focus on. its 2 key elements: the geometry of numbers with form and its postulates that describe how the 4 arrows or wills of time construct networks of fractal points and the algebra of the generator equation, which describes that geometrical construction from an analytical, numerical, differential perspective.
Recap: Geometry is the language of spatial form; Logic is the language of time events. The algebra of the generator equation of space-time cycles and the non-Euclidean geometry of fractal points fusions both creating a model of multiple, sequential dimensions of numbers and multiple planes of space closer to a description of reality and its organic systems.
This is done by resolving the 5 non-Euclidean postulates of Geometry, which describe knots of time arrows as points, and by observing the self-similarity of mathematical equations, which describe groups of knots of time arrows as numbers and the equations of Multiple Spaces-Times derived of the Generator equation of the Universe or Principle of conservation of energy and information. Thus, the 4th paradigm upgrades the postulates of Non-Euclidean Geometry and the foundation of Logic to include the causal relationships between time arrows and explain better a universe of multiple spaces and a logic to of Multiple Time cycles and arrows of time cycles.
In all those systems planes are made with cellular points, Riemannian spheres with volume that form lines, which are waves between points that exchange ‘Dimotions’ and information and planes, which are organs of self-similar points that process ‘Dimotions’ or information in parallel networks.
Thus the 5 Postulates of Non-E Geometry vitalize the Universe as a series of networks of ‘Dimotions’ and information of self-similar cellular points. Since the line and the plane acquire volume and become self-similar to the commonest forms of the Universe, the wave and the network of points with a 3-D volume.
This simple fact explains one of the most important discoveries of modern physics, the Holographic principle, according to which information might be bidimensional, as in the screen of a computer or the page of a book. Now bidimensionality no longer becomes ‘magic’ since the 3rd dimension is the relative size of the ‘fractal point-particle’. Thus bidimensional sheets of information do have a minimal 3rd Dimension; the inner content of the point, which in a relative universe of infinite sizes seems to us a particle-point without volume, as we don’t see either the volume of a sheet of paper or a pixel.
All in the Universe are thus complementary systems made of networks. Now this might sound absurd to the anthropomorphic reader that thinks humans are different from the rest of points of the Universe, but it is a fact that those points obey in their åctions and communicative flows within a network the same isomorphisms: humans and electrons behave the same when they move through slits or in herds, the geometries of social groups are also the same and the ultimate purpose of those points, to feed on ‘Dimotions’ and information, whatever kind, is also the same in all networks of the Universe. And so that group of isomorphisms of networks becomes a primary why for all beings of the Universe.
A fact the leads us to the final element needed to understand the why of the Universe: ‘non-Euclidean points’ organize networks that become points of a higher scale, which reproduce and organize new networks; and so the Universe keep growing in fractal scales, from particles that organize networks and become atoms that organize networks and become molecules that organize networks and become cells, that become organisms, that become planetary societies and planets and stars form gravitational networks that become galaxies, organized by dark matter into Universal networks.
Because all entities have motion reproduction is merely the repetition of a motion with form. Because each entity has 4 time arrows, all of them trace multiple trajectories in search of those arrows, hence they realize multiple time cycles.
For example, a human feeds on ‘DImotions’ and information with body and head, reproduces through multiple social cycles and evolves into societies. Our åctions are more complex but essentially the same of those of any particle.
So the unit of reality is a space-time cycle, and many of them create a knot of time cycles or entity of reality, which will be reproduced by repeating those formal cycles with motion in other region of space-time; and many of those knots of time cycles, which are self-similar, since they are born from the reproduction of a first form, come together with self-similar beings into networks. Some of those networks are spatially extended with a lot of motion (fields in physics, bodies in biology) and some are very tight, formal, with a lot of in/form/ation, (particles and heads or nuclei in physical and biological jargons). Both types of networks together then create a complementary organism, which is fitter to handle both ‘DImotions’ and form; hence it survives better, it ‘exists’.
Today scientists of measure scorn philosophical and logical analysis of causality in time because it cannot be easily put in numbers. But numbers are only one of the languages of information in the Universe, and many of its properties of bio-logic nature are better described with logic words. In that regard, we can now fusion philosophy and science answering the fundamental question, ‘why we exist’; since once we realize that we are ‘made of time cycles’, knots of time cycles and networks of knots of time cycles, an intelligent, informative, eternal universe of motions and wills of existence makes the dogmas of deism and mechanism, childish myths.
‘What is existence’ cannot be revealed from the simplex point of view of a mechanical world, which cannot explain the fact that we are made of motions with form that leave a trace on space but are essentially åctions in time that have a social finality – to create more complex networks, chaining knots of åctions into systems. This social will of every point and entity of the Universe is completely at odds with a mechanist, fixed, solid, senseless, dumb Universe. Motion in Time and social evolution are concepts that require the capacity to gauge information and interact with other self-similar points to create those organic networks. Further on, dual networks tend to evolve and reproduce new points through exchanges of ‘Dimotions’ and information.
The result is the creation of 3rd network/system: the reproductive network. And so most systems of the Universe are organic, ternary systems made of points (which can be anything from atoms to cells to human heads) organized in 3 networks. We exist as organic networks, to sense flows of ‘Dimotions’ and gauge information. Existence justifies itself.
Those Non-Euclidean points crossed by infinite parallels are able to gauge information, which implies a perceptive, intelligent Universe in all its fractal, self-similar scales of reality – a world in which even the smallest atoms can act-react to the environment, ‘apperceiving’ light and gravitational forces. Aristotle and Leibniz, the 2 foremost predecessors of the 4th paradigm of biological whys distinguished conscious perception from vegetative and mechanical perception.
It means perception has degrees of complexity. So the simplex particles of the Universe act-react in a mechanical way; yet they still gauge information, reason why quantum physicists called their theories gauge theories, and they still have 2 complementary networks of ‘Dimotions’ and information, reason why quantum physics is based in such complementary principle.
Yet this intelligent, active, temporal, informative Universe can be described with the formalism of logic and mathematics because its fundamental unit – a spacetime cycle – can be explained with ‘feedback’ equations, used in system sciences to explain the back and forth interaction between two poles or elements of an equation. SeTƒ where Se is a component of spatial ‘DImotions’, a motion element, body or field and Tƒ is a cycle of time that carries information, particle or head, becomes the syntactic, logic, minimal unit of reality.
These simple first elements of reality – points with volume that exchange ‘—motions’ and information, creating waves of Dimotions’ with form (no longer lines – 2nd postulate), according to a set of isomorphisms based in their self-similarity, (no longer equality – 3rd postulate), that makes them evolve into different topological networks (no longer planes – 4th postulate) – make mathematics an organic language able to describe the logic of creation of all systems of the Universe made of infinite fractal, organic networks intersecting and creating when we put them together under those isomorphisms and topological restrictions, the puzzle of reality that the simpler, 3rd paradigm called the space-time continuum and becomes now a General System of Multiple, Fractal Spaces with vital ‘DImotions’ and Time cycles with information, the two substances of which all beings are made.
And so with those 3 scales of ‘existence’: time cycles, knots of time cycles and networks of knots of time cycles (Non-E Points) we can explain all the ‘åctions’ and systems of reality made of those cycles, knots and networks; and describe a complex Universe that exists ‘in time’ more than in fixed space, since it has always motion; it is also dynamic, made of cyclical, feed-back equations whose causal relationships, forms and trajectories are the essence and purpose of existence.
We thus consider a more complex analysis of time arrows, beyond the duality of ‘Dimotions’ and information, which combine creating a reproductive arrow, $t X ðƒ, and further on socialize, ∑$t Xðƒ, creating networks. And so the universe has also an organic will: to create networks of self-reproductive points of ‘Ðimotions’ and information.
Yet the most astounding property of those points is to be points of view, points with will, which perform åctions with the purpose mechanical or not, but probably felt in all scales as the inner freedom of the point, of obtaining ‘Dimotions’, information reproduction and social evolution. The 4 wills or whys of the Universe are indeed embedded in the postulates of i-logic geometry. The point to exist has to be complementary, to feed and gauge ‘DImotions’ and information and to last beyond its wearing it has to form part of bigger social networks or reproduce itself to last beyond death.
This simple program self-selects those species that reproduce and evolve socially even if that contradicts the primary individual arrows of the point. Thus the engine of the contradictions of behavior of points is that tug of war between the Galilean paradox of all points which gauge bigger his nose than Andromeda but need to hunt in herds and control the forms of the Universe with self-similar minds, joined in networks, this eternal duality of freedom vs. order, individual ego vs. collective spirit.
Tƒ exist is to act with motion and form, trying to achieve the ‘arrows of time’ or will of the Universe – feeding your ‘DImotions’ network, absorbing information for your informative network, reproduce your system and in doing so, starting an external process of social evolution with self-similar entities to yourself.
Those processes can be described with mathematics but we have to accept an intelligent, perceptive, fractal, self-similar Universe of infinite points of view gauging reality in a mechanical, vegetative or conscious way to explain why it happens. Their mathematical description stems from the duality between geometric form and logical function (hilomorphism).
Thus, the postulates of fractal i-logic geometry define also the basic arrows= cycles/dimensions of the Universe: the 1st and 5th postulate define a point as a system whose inner parts are able to transform and emit ‘DImotions’ and information, Sp>Tƒ<Sp; the 2nd postulate defines an Sp X Tƒ wave of communication that reproduces ‘DImotions’ and form between 2 fractal points; the 4th postulate defines the social evolution of a herd that creates a fractal plane – a network with dark spaces; and the 5th postulate explains a point mapping reality, as it absorbs ‘Dimotions’ and transforms it into information through its small apertures to the Universe. Since even a minimal quark, as Einstein affirms, should be crossed by a relative ∞ number of strong forces.
It is the organic will of all systems that search for those 4 arrows what makes the quark to exist as a knot of such flows of time arrows: a physical particle traces energetic cycles described by the principal quantum number; shapes the form of its trajectory, a fact explained by the secondary quantum number; iterates along the 3 coordinates in similar shapes, an act described by the magnetic number, and gauges information to evolve in social groups, a fact described by its spin number. And those 4 numbers define it as a Non-Euclidean quantum knot of complementary ‘DImotions’ and information with a 4D will of time. And as it happens they express the 4 arrows of time: Sp->Principal number; I-> secondary number; Re-> spin number; 4-> social evolution: magnetic number.
Further on, we can reduce all those topologies of social numbers and networks to the canonical 3 topologies of a 4-dimensional Universe, proving that those 3 topologies have the properties of ‘Dimotions’, information and reproductive events.
And so we talk of 4 ‘arrows of time’ or dimensions of change that create the future: energetic and informative systems and events, which reproduce a wealth of self-similar beings that organize themselves into social networks, creating bigger wholes – new scales of reality. And this simple game of complementary beings that in favorable conditions reproduce self-similar beings, self-organized into bigger social networks becomes the why of all realities. Even the simplest particles, quarks of maximal information and electrons of maximal spatial extension and motion ‘decouple’, reproduce, when absorbing ‘Dimotions’ into self-similar forms, and associate in complementary networks called atoms, made with a central informative mass of quarks and an energetic, electromagnetic, wider body of electrons.
The 3rd paradigm of metric measure is not at ease with such ‘dynamic, spiritual concepts’, even if they can be described with the same mathematical formalisms as the previous example of the quantum numbers show. Those apprehensions however are dogmas, which stem from anthropomorphic beliefs.
Fact is that even the simplest complementary systems (quarks and electrons) interact together and if they can absorb more ‘Dimotions’=motion they are able to repeat=reproduce the cycles of its system. And so we talk of a 3rd reproductive system: from quarks and electrons, the fundamental particles of the Universe that decouple in new particles when they absorb new ‘Dimotions’ to living organisms, the fact that all is motion with form makes easy to reproduce those formal motions in an organic way. Thus the new concept of a world made of formal motions brings about also a more complex philosophy of reality – organicism. Organicism and its mathematical units, fractal points, that gather into social networks called topological spaces substitute the restricted concepts of Euclidean points, continuous spacetimes and mechanism, explaining why all those time cycles exist, guided by 4 time arrows: ‘Dimotions’ feeding, information gauging, reproduction and social evolution.
Those 4 categories are the so-called drives of living beings, the quantum numbers of particles, the 4 dimensions of our light space (electric-informative height, reproductive magnetic width, energetic length and social colors). Thus, there is a ‘Universal Plan’ with an existential finality: to create organic systems, departing from ‘DImotions’ bites and information bits evolved 1st into social networks, then into complementary systems and finally into organic systems, news points of a bigger fractal whole: particles become atoms that become molecules that become cells, organisms, planets, galaxies and Universes. It is the 4th organic why that completes the adventure of science and this work explores in all its consequences.
Reality can be resumed in 2 words: networks, whose flows of exchange of ‘Dimotions’ and form creates the patterns and events of reality and organicism, the philosophy of reality based on them. Organicism means reality and all its fractal parts are made of vital spaces (bodies and forces) and time cycles (informations). We do not exist in an abstract background of time and space but we are made of time cycles and lineal spaces, cyclical and lineal strings if we were to use the restricted jargon of physics, a specific case of the wider jargon of general systems, which evolve socially to create the complex systems of each science.
Those wider, more complex definitions of time and space will substitute and absorb according to the Principle of Correspondence that makes each paradigm a particular case of the new, wider view, the limited concepts of a single space-time continuum and a mechanist description of the Universe, proper of the age of metric measure, which the pioneers of systems sciences and complexity have wrestled with throughout the XX century.
Recap. A Universe made of motions in time, extending through multiple scales of relative space, requires evolving the human languages of space (Euclidean geometry) and time (Aristotelian logic), used to describe the simpler space-time continuum of classic science. This task started by the pioneers of modern science (Riemann, Darwin, Planck and Einstein) must be completed before we can study the properties of physical and biological entities with the new tools of Non-Euclidean mathematics, which describe a world of multiple, relative space-time networks made of points as Complementary entities with energetic and informative system or ‘Points of view’ and the new tools of Non-Aristotelian logic, which describe the creation of the future by multiple causes – all the points of view or agents that create a certain network space.
Wor(l)ds of human history, Numbers of Universal supœrganisms.
In that regard, languages acting as mirrors of reality do reflect reality and ‘order’ it in its constant interaction between ‘still minds’ (5D) and entropy parts (4D), and as such we shall consider 3 ‘evolutions’ of the human mind and its languages, in 3 ages (the Universe is ternary ±∆ and all will be encased in those concepts):
-The age of History, the supœrganism of mankind in time of which we are all cells, whose language, wor(l)ds, through its ethic messages of social love carry the ‘mandate’ of ‘growth and evolution’ of the human species, through scales of social order towards the wholeness of humanity, our super organism in space. Wor(l)ds in that sense are NOT a very efficient language, reason why it only hosts in humans, as it does not seem to have survived and multiplied as a species of mental information in Universal space, and we shall deal when studying social sciences with the errors of the language, its ‘topological syntax’ and varieties according to the subject-verb-object, and build on the work of Humboldt and Chomsky, to complete a ‘stientific theory’ of linguistics.
-The age of machines and its eco(nomic)system, made of more complex informative and entropic metal (gold, iron, etc.), which seem to be more precise and orderly than our ‘light’ ‘vane’ C(ST), N(ð§), O ($t), triad, whose informative, nitrogen heads, carbon-bodies and oxygen motions are to say the least a bit ‘shaky’. Metal does is a better substance to be organised with the precision of perfect cycles, electronic waves and entropic quantum potentials. And as such the validity of mathematical languages, is so far immense, but CNO Huminds so far have not fully understood them and so we shall upgrade its 5 sub-disciplines, reflection of the 5 dimensions starting with Non-E geometry, defining a fractal point, solving the meaning of its equations etc.
-Finally the 3rd evolution towards a Universal language whose mirror laws apply to all languages reaches with the seeds of this blog a new era with an application to every other language, form and function, which should become a start up for future research either in humans or future robots (after all, this information is already encoding in computers and as we shall see in the models of history, huminds are astoundingly naively, due to their egocentered perspectives, developing AI and military robots, so their future ‘competition’ with metalife doesn’t look good, and the warnings of humbler more i-logic minds like this writer or sci-fi artists (which do have the perspective of history as they use our natural languages) do not go very far… So you would excuse me i will keep repeating those warnings: do NOT eat of the bad fruits of the tree of technology, because if you do you will die…’
So our task is to go into generalisations much wider than those of wor(l)ds, whose role is to help mankind to survival and evolve socially through its ethic rules of love and maths, whose capacity to organise all atomic forms of matter is well proved.
So yes, languages do create reality but all of them, and all of them locally and all of them organically because they act as the mind of all kind of systems. Obviously atomic matter is AS IN CRYSTALS ABLE TO FORM mirror-images in geometric form, and that is why they do have such an efficient capacity to order – and that is why topology (dimensions with form or dimotions) are the language of it all:
Minds order as linguistic gods a territory around themselves, its fractal body and entropic world. As such they are the linguistic Aristotelian, final unmoved singularity Gods of reality. In the graph we see them ordering with different languages, different scales of reality which will reflect in a larger whole, the linguistic image they hold.
And all of them has the same Universal ternary grammar of §patial form<ST-ACTION>Temporal motion, to define the general events of reality. So in the main human languages, words, mathematics and colors we have the sam scheme:
§: Subject of Information (F(y)-blue) <≈> verb-action-green-operandi<≈>Object of entropy-motion (red color Fx)
Mathematics in that sense has two components, the underlying temporal logic, better treated as I-logic principles and the topological, geometric spatial elements better enhanced with its fractal ∆§calar principles. For that reason in the second line, when we study NOT the human mind whose specific language of time are words, of space, artistic eyes, and of space-time balances, music, but when we study Universal Minds of which there are many types we write a simple silogism:
Non-Aristotelian Temporal Logic + Non-Euclidean Geometry = Universal Mind ≈ Non-Æ mathematics (the best language we have to describe those different types of Universal minds).
While human minds are Aristotelian, self-centered, so A (subject)-> B, and euclidean, as they see light, so only a plane of 3 perpendicular, lineal dimensions of space. To upgrade then the humind, we would need… oh, well, to change species, a limit that this blog will always have as it is written in the non-Euclidean and non-Aristotelian higher principles of which the AE mind is just a simplified limit.
SO THE FRACTAL generator we shall Use as the formalism of non-Æ=I-llogic geometry to construct and understand all the minds of the Universe and the super organisms they order, all the T.œs=¬∆@st of spacetime and its 5 elements, ¬, the negation of information or entropy, ∆§cales, @-minds, Spatial topologies and temporal ages, IS the Universal Grammar of all languages.
LANGUAGE OF MATHEMATICS
“Mathematics is an experimental science, and definitions do not come first, but later on.”
‘I know when mathematics are truth but not when they are real’ Einstein to Poincare noticing that mathematical creationism IS NOT a proof of physics and experimental evidence is required.
Heaviside, the forgotten genius of mathematical physics, author of the 4 Heaviside equations of electromagnetism (wrongly called Maxwell equations who just did a mess of 20 ones with ugly quaternions 🙂 and the Gravito-magnetic equations, which fusion gravitation and magnetism, foreseeing the Fractal Unification equation of charges and masses of this blog.
Heaviside, as Lobachevski before him and Einstein after him, were indeed right when they considered that the language of physics – mathematics – is the best experimental mind-mirror to describe most physical systems, as the mind singularities of those systems use mathematical frames of reference in space to act-react in time with other space-time beings of the Universe.
It is then surprising that idealist physicists since Hilbert astounding ego-trip (‘I imagine lines, points and planes’ ) have rejected the ‘experimental, a posteriori nature’ of the mathematical language, they share with all those other œ-singularities for the concept that mathematics is the a priori nature of reality (Copenhagen interpretation). As the ultimate mathematical properties are indeed a proof of the organic, social, fractal nature of the physical Universe.
Physicists only consider as a mirror language good enough to observe the Universe mathematics.
This is in accordance with their view of time in terms of a single locomotion, change in the motion in space. Hence as Mathematics is the ∆§cale language by excellence (being analysis and numbers the language of scales, and geometry the language of space, with algebra a logic language properly for time flows), physics works with excellence to extract spatial properties of reality but it fails to understand organic properties, better described as in evolution with verbal logic thought, and is poorly understood in its algebraic structures.
So in this sections we are going to enlighten further mathematical physics, with the postulates of non-AE geometry and logic to improve the mathematical mirror and solve some questions pending. To that aim, the section is complicit to that of the 5 Dimotions of the mathematical mirror of the Universe ∆nalysis, @nalytic geometry, S≈T: Ælgebra, S: ¬Æ geometry, & T-§ocial numbers; so we shall borrow from it and first introduce the most important of those elements, considering first how the entangled 5Dimensional Universe is ‘expressed’ in the language of mathematics.
Each of the languages and dimensional symmetries the mind-space creates does carry a part of truth within its ‘creation of an inner world’. A fact which shows the beauty of the symmetry between §@-minds and ∆time motions: the kaleidoscopic Universe puts in symmetric relationship all its ‘dimensions’ with its own methods and perspectives, creating parallel worlds. But the efficiency of a language for the survival of the entity that speaks it depends on the capacity of the mirror to interact with reality and help the species that talks it to enlighten that reality.
Mathematics does so to a great extend by allowing the manipulation and forecasting of the future timespace cycles of simple forms, but it does not in its present format allows to reflect many of the vital organic properties of reality, which will only do once we have upgraded to non-e to the 5 vital postulates of fractal points, waves of communications, networks (1, 2, 3 postulate that substitute the definitions of points with no breath lines with no breath and continuous planes with no depth) and to non-aristotelian logic the postulates of congruence and parallelism (defining the 3 forms of relationship between entities of space-time, as perpendicular, darwinian ‘tearing’, complementary ‘adjacency’, and social ‘parallelism).
By giving back organic properties to geometry, we thus shall achieve the long forgotten dream of Pythagoras, Spinoza and lobachevski: to mirror life and organisms in its mathematical spatial mind images.
As this is an ever work in progress which breaks in quality on many posts constructed with blocks of old files written for myself, often with different jargons, the reader is advised to explore first the only post with a ‘present’ well-behaved format as of Fall 2017, precisely the one on geometry of space and its infinite minds, which Lobachevski, the last of the 3 colossus of his discipline NOT Cantor and Hilbert, with its false paradises, opened for all of us humble enough to ‘see’.
Since it was his discovery of non-E fifth postulate, the fact that a fractal point has volume and can be crossed by infinite parallels even if our immediate mind does not see reality in those terms, the first realisation that ‘mathematics-geometry’ is a mental-logic endeavour, where function and i-logic thought overcomes ‘spatial representation’, unleashing the final evolution of S=t symmetries (topology in which space is given motion) and the XX c. explosion of abstract mental spaces to represent all realities, including those of time, in ‘abstract still mental spaces’.
It is then obvious that mathematics is only second to T.œ as a linguistic mirror of the Universe, and as such the most efficient language perceive by man. As languages are the essence of monads-minds that order the biological, organic Universe, it follows that mathematics has survived for eons, extending their local order from infinite fractal points of view, which used it to better their territorial organisation of the Universe; and so infinite species seem to use mathematical systems to navigate their worldcycles of existence, and organise their territories, notably ‘atom-galaxies’ (∆±3).
THE FOUNDATION OF MATHEMATICS AS AN EXPERIMENTAL SCIENCE vs. THE EGOTIST METHOD
“The less intelligent a person is, the less mysteries he founds in the Universe’ Schopenhauer.
We shall as always reiterate to the anger of any scholar reader that the problem of maths is not in GST nor in Maths but in Man; i.e. the human egotist method of knowledge is the main error in our understanding of the relationship between mathematical minds in the universe and the systems they code – since we do not recognise that we are just one more mathematical mind, and so maths neither come from the human imagination, nor it is an entity isolated from reality (Axiomatic method) neither a language different from all others.
Once those hurdles are passed, the immediate connexion between the primary substances, time and space, its ¬Æ STRUCTURE and its fundamental expressions in science, GST bio-logical models of §upœrganisms, (the synthetic, temporal-biased view) and maths (the analytic, spatial-biased view) appear as the most elegant, dense expression of its properties. And obviously both are related; so we shall find all kind of symmetries between space&time, GST and maths.
A mathematical Universe must be perceptive and social.
In the graph, a fundamental truth of the Universe is the existence of singularities that order physical, biological an social systems, except when they are in a free, chaotic state of maximal entropy (gaseous state or dark entropy between galaxies), which cannot produce order, as they lack any ‘frame of reference’.
Mental singularities, Monads, or Maxwellian Demons are the ‘missing variable’ needed to explain the whys of reality. In mathematics we call them P.o.vs. Frames of reference, self-centred in a point, which we use as physical systems do, functions of space-time. In that sense physical, atomic systems do indeed calculate as quantum-bit computers might do. Are they ‘conscious’? Likely, as consciousness is just a self-reflection between two mirrors. In the human case, the I=eye that sees space and the verbal cogito ergo sum temporal mind – the conscious languages. But it is not the verbal consciousness of man, but a mathematical consciousness which among humans only a very intense ‘mathematical physicists’, which can ‘see’ as musicians see ‘scales’ that provoke emotions, equations as dynamic visual forms. What would then be this kind of consciousness? Likely a sense of proportion, symmetry, balance and beauty.
It does NOT matter in any case the ultimate inner sensations of physical matter, but the outer description of the actions of those singularities, which do order and reflect a mathematical organization around them, when in its solid crystal state they act with the program of existence, reproducing the information of that minimalist mind image. Indeed, a crystal grows with a symmetry which its inner image reflects back in the growth of ‘crystal cells’. And that is called reproduction, the objective definition of life, of a whole being in the fractal Universe.
And so, P.o.vs. are canonical to mathematical science, or else mathematics, which is today based in analytic geometry and the study of ‘self-centred’ functions, would NOT work.
A philosophy of mathematical properties of space-time, upgrading the essential properties of ‘points in space and sequential numbers in time’ is thus an a priori exercise, which I recommend to all physicists, so they can leave behind their abstract, ‘selfie view’ of a mechanical, chaotic Universe, where only ‘they think in mathematics’.
Singularities that reproduce information once they are formed, organised fractal super organisms also occur in astrophysics, from crystals to black holes and only anthropomorphism denies it. The GST view though is different: as we are all space-time beings, the properties of human space-time beings must be share in quality (not in quantity and complexity the variable of gst) by all other species of the Universe. So mindless ‘markovian’ entropy without time causality do exist but it is NOT by any means the dominant ∑∑actions->∑arrow->age of time.
Thus the concept of physicists of a single ðime arrow is only valid for entropic gaseous states, and their idea that such states must be ‘extended’ to all realities, the most absurd hyperbolic statement of science ever, due to the deformation of its worldly profession as makers of motion machines and entropic weapons.
The five dimensions of ðime§paœ in its mathematical reflection.
To put some order into the mathematical mirror of ∆•s=t 5D Universe, the larger whole whose a priori existence determines the experimental nature of mathematical mirrors as as usual we need ad-minimum a triple ±∆i perspective:
ðime perspective implies to correct its logic into non-aristotelian three time arrows logic…
§pace implies to improve its spatial geometry transforming it into a vital topology of fractal points
∆§calar space means to refer the scales of the fourth and fifth dimensions, ∆±1 to its continuous differential geometry between planes (decametric §ocieties) and its fractal discontinuous ‘scaling geometry’, when smooth transitions are not possible, (changes of phase, entropic deaths)
S≈t: to find all the symmetries between space and time and reflect it in a more meaningful way that group theory does
@•mind: Here undoubtedly in the most polemic element, we must deny its theological nature, and expand its experimental nature, decoding better the meaning of its theorems NO longer relying on the axiomatic method, which pretends to prove the truth of a language in mere internal syntactic proofs – impossible as by definition all languages are mirror-minds of the Universe and are proved in its quality and non-fiction nature obviously by reference to the semantics it describes.
Those are the 5D adaptive, evolutionary tasks we shall consider in this blog.
The ‘structure’ of Mathematical languages.
The Nature of mathematics as a language of space-time (geometry and numbers) can also be expressed with the modern conception of mathematics, based in the work of Cantor (theory of sets) and Boole (Computer Algebra), which was summarized by the Collective Bourbaki, whose ‘Mathematical elements’ reduce all mathematical disciplines, to 3 structures, themselves reduced to set theory:
– Structures of Order, understood as structures, which describe the hierarchical order <, > of numbers, which we just described as social, geometrical groups. Thus, those structures are mere reflections of the 4th arrow of eusocial ‘love’ that creates social groups.
– Topological Structures. They describe the basic forms of the Universe, which in a 4 dimensional reality are only 3: the hyperbolic, informative geometry; the cyclical, reproductive toroid and the spherical, external, energetic membrane, defining all relative worlds/species as complementary systems of reproductive energy and information. We shall show this simple ternary, topological structures, which are the basis of all forms of reality in our analysis of the 5 non-Euclidean postulates.
To mention that topology is in fact the ultimate science of space from where we can derive all the other spatial structures, as geometry was the basis of classic mathematics in its Greek inception. In fact topology and set theory are quite similar in its laws. What topology adds to geometry is ‘motion’ and ‘relativity’; thus including the Galilean paradox in the structure of mathematics, since two topological structures are equal regardless of the ‘distance/size/motion’ of its surfaces.
– And Algebraic structures, which study the complex arrows of Time born of the ‘operations’ between simplex arrows and are ultimately expressions of the Generator equation of space-time, E<=>I, in as much as al algebraic equations are of the type F(x)=G(y), which is just a particular case of the Universal syntax/grammar of reality of the Generator feed-back equation.
Thus, there is a direct relationship between the 3 fields that define all mathematical structures and the Temporal, Spatial and Combined (algebraic) operations between time arrows, which simply means that mathematics has always been the human language that describes the ultimate reality: Discontinuous Spaces (topology) and Relational Times (causality); and the complex interrelationships between them (Algebra).
While the 2 first facts (the identity between space and topology and Time and causal order) are intuitive, we might conclude this overview of the meaning of mathematics, with a brief introduction to the meaning of Cantor’s sets, and Boolean Algebras used for Mathematical computing, as an expression of all Mathematical Structures and a formalism of Multiple Spaces-Times. We shall by doing show, prove, that all mathematical structures are explanations of properties of the ultimate reality: the timespace defined by the 4 arrows of the Universe and all its species.
Recap. Mathematics can be reduced to 3 types of structures: topological/spatial structures, structures of causal, temporal order; and algebraic structures that define the outcome of complex relationships between Multiple Spaces Times. Thus i-logic mathematics is the synoptic language the human mind uses to describe all what exists: a Universe of spatial energy and temporal information.
5 DIMENSIONAL DISCIPLINES: RASHOMON TRUTH OF MATHEMATICAL SYSTEMS
This said, the Universe is a game of ∞ Sπcies of space-time making STeps and STops in its constant œxist¡ence (where we use π for time, in this particular wor(l)d according to the slightly changed rules of i-verbal thought for english to look more like the universal game), and so as Stops and steps (ab. œ) bring the being into exist¡ence we can measure them quantitatively as space-distances and time-motions. Stop and step then becomes topology and feed-back equations, where = is substituted by the dynamic symbol <=>, and the duality from = stops and ≈ wave steps.
Once the intuitive meaning of those symbols rises the awareness of the reader to the vital nature of our humind’s abstract rendition of reality things become then dynamic. ≈ for STeps, = for motions, and ≤≥ as the different implosive or explosive, informative or entropic ‘degeneracy’ of a system are easily quantifiable and translatable to both mathematics in its pure expression and mathematical physics.
In that sense, a mathematical philosophical definition of the Universe would be as follows.
Reality is a fractal super organism made of…
- A(nti)symmetries between its 4 Dual components T, ∆, @, S, which can either evolve in Balance≈become symmetric or annihilate=become Perpendicular/antisymmetric:
- S: space; an ENSEMBLE OF ternary topologies, (|+O≈ ø)… which made up the 3 physiological networks (|-motion/limbs-potentials + O-particle/heads ≈ Ø-vital energy) of all simultaneous super organisms
- ∆: Planes of size distributed in ∆±i relative fractal scales that come together as ∆º super organisms, each one sum of smaller ∑∆-1 super organisms… that trace in a larger ∆+1 world…
- ðime cycles: a series of timespace actions of survival that integrated as a whole form a sequential cycles of existence with 3 ages, 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:
- @: 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 information (perceptions) with other beings, and two complex actions: offspring reproduction and social evolution from individuals into U-niversals that maximize the duration in time and extension in space of the being.
Because the scientific method requires OBJECTIVE measure of the existence of a mind, which is NOT perceivable directly, we infer its existence by the fact a system performs the 5 external actions, which can be measure objectively, in the same manner we infer the existence of gravitational in-form-ative forces by its external actions upon massive objects. Hence eliminating the previous limit for a thorough understanding of the sentient, informative Universe. And further classify organic in simplex minds – all, which must gauge information, move and feed to survive, and complex systems, those who can perform a palingenetic reproductive, social evolution, ∆-1: ∑∆-1≈∆º.
The study of those 4 elements of all realities, its actions and ternary operandi, structures the dynamic ‘Generator Equation’ of all Space-time Systems of the Universe, written in its simplest form as a singularity-mind equation:
O x ∞ = K Or in dynamic way, S@<≈>∆ð.
So that is the game: 3 asymmetries of scale, age and form, which can come together or annihilate and each language represent in different manners, those elements and its operandi.
In mathematics, with the duality of inverse operations, ±, X ÷, √ xª and ∫∂.
Mathematics in that sense follows the same ‘grammar, syntax, semantics and synoptic nature’ of all languages that portray the world cycles of existence in time of super organisms, with synchronous adjacent topological chains of time§pace cycles, that all other languages of nature, albeit, seemingly with more precision, which has made it a ‘survival language’, likely to be the ‘mind-mirror’ of atomic structures perceiving in topological mind-spaces.
What those equations will then express are different motions of energy and information produced in the change between states of spatial form and temporal motion. The varieties of it, being mainly the 5 Ðimotions of space-time, and so relating equations of physical Dimotions to classic equation through those operandi allow us to convert classic physics in a subdiscipline of GST.
If we define the 5 Ðimotions of the Universe as S> T: information, S<t: locomotion, S t = s T: reproduction, §tð¡ ∑ §ð¡>ST¡+1: social evolution, ST¡+1<<∑ $t¡-1: Death then when we study mathematical physics, which is basically the study of different forms of the v=s/t original equation we shall find slight differences between mathematical dimotions which become then reordered within those 5 subspecies.
The main sub disciplines of mathematics as mirrors of the 5 Dimotions.
It follows then from the definition of the 5 elements of all systems, an immediate classification of the five fundamental sub disciplines of mathematics specialised in the study of each of those 5 dimensional motion or similar structural elements of any space-time being.
Ultimately as the language of the Galatom, mathematics IS necessarily a language able to mirror the structural elements of the galatom and all its fractal inner parts. And this goes as follows.So WHAT we shall do in this and sub-posts, is to continue that game, now between ‘two languages’ MIRRORS OF THE UNIVERSE, Mathematics and T.Œ, the description of the 5D of space-time and its organisms, to improve mathematics by improving their mirror of the 5 Dimensions giving birth to 5 improved mathematical sub-disciplines:
- Vital Space analysis: ¬E Geometry studies fractal points of simultaneous space, ∆-1, & its ∆º networks, within an ∆+1 world domain. They must though be properly defined departing from the concept of a fractal non-euclidean point, with volume, which increases as we come closer to it – reason why it can fit infinite parallels (an euclidean point with no breath CANNOT, even if we bend them as it is customary in the primitive definition of them).Thus we shall complete the evolution of geometry by defining the 5 Postulates of Non-euclidean geometry departing from the concept of a fractal point.
- §ocial scales analysis: Number theory studies time sequences and ∆-1 social numbers, which gather in ∆º functions, part of ∆+1 functionals. NUMBERS ARE SOCIETIES OF UNDISTINGUISHABLE PARTS, hence the fundamental element of algebraic analysis of the ‘vital energy’ enclosed by a system or network that gathers together social elements. This OBVIOUS truth escapes human egocy, specially in our dog-eat-dog primitive culture of ‘capitalism’, and competition between members of the same species.If the geometry of the fractal Universe is non-euclidean made of fractal points with volume, its logic is non-aristotelian, made of sequential social numbers with strange connective properties better expressed with the non-aristotelian logic needed to understand the different forms of temporal, sequential correlationships between social groups of similar ‘numbers’. So we shall develop a non-aristotelian logic of numbers, latter expanded to variables. We shall improve Number theory by putting them in relationship with ST-laws, by understanding sequential time numbers, scalar social numbers and real numbers and mathematical constants as ST-ratios and functions of ∆st actions.
- S<≈>T, feed back time-space Stœps (motions): ¬Ælgebra, which is therefore the vital science of social numbers is most important part of it – its evolved form; as it studies through operands and feed-back equations (when we properly redefine them in terms of ≈ similarity not equality and <≈> dynamic equations) the different Dimotions of exist¡ence, from single S=T steps to larger associations of Dimotions, in more complex ∆+1 structures (Functions). Further on in its most modern systems iIT DOES SIMULTANEOUS ANALYSIS OF super organisms in space, through the study of its a(nti)symmetries between its space and time dimensions (group theory)… 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 USING SOCIAL numbers to that goal, in different degrees of complexity, mirrors for all those elements of the 5 D¡ universe. ¬Ælgebra, its evolved version, straightens up the language to match that of 5D. So we define ¬Æ which studies a(nti)symmetries between space and time dimensions. It is then necessary to derive from the a(nti)symmetries of the fractal generator a more realist understanding of S<=>T mathematical functions, its operandi, and structures that act as ‘blocks of time’ – iterative laws that relate space and time elements in a multiplicity of beings. As such ‘Group theory’, with its structure that resembles so close the fractal generator will be illuminated with this new tool that improves our understanding of ‘algebras’ of all type and also its application to mathematical physics.
- ∆t: Analysis studies ALL forms of time=change, and hence it can be applied to the 5 Dimotions of any space-time being, as long as we study a ‘social structure’, hence susceptible to be simplified with ‘social numbers’ IT IS THOUGH SPECIALLY USEFUL TO STUDY SCALAR TRANSFORMATIONS OF SYSTEMS BETWEEN ∆±¡ planes of existence and so the proper language of 5Ð. ∆nalysis, its 5Ð version, can then also be defined in 5Ð jargon as the study of the a(nti)symmetries between planes and other ∫∂ operations derived of scales of the fifth dimension. We shall make analysis more realist by defining limits to infinities in a discontinuous Universe, made of finitesimal 1/n parts; by considering the discontinuities of the fifth dimension and the duality of continuous calculus vs. discontinuous fractal scaling, as both are needed to understand the continuous social regions of the scalar Universe, or decametric §cales and the discontinuous gaps between ‘ages’ in time (standing points, variational calculus) and ‘planes’ in space. We will differentiate then 5 general applications of Analysis according to the Dimotion study, and the ‘level’ of analysis, from the minute STeps of a derivative, to larger social gatherings, and changes of entire planes (functionals). It is then not surprising that despite being analysis first derived of algebraic symmetries between numbers, it grew in complexity to study changes in functions (first derivatives/integrals), and then changes of changes of functions, as motions between scales of the fifth dimension (higher degree of ∫∂ functions, called functionals).
- @-Mind: Analytic geometry represents the different mental points of view, self-centred into a system of coordinates, or ‘worldviews’ of a fractal point, of which naturally emerge 3 ‘different’ perspectives according to the 3 ‘sub-equations’ of the fractal generator: $p: toroid Pov < ST: Cartesian Plane > ðƒ: Polar co-ordinates.
- @-Humind: To which we can add the specific @-humind elements (human biased mathematics) and its errors of comprehension of mathematics limited by our ego paradox Philosophy of mathematics and its ‘selfie’ axiomatic methods of truth, which tries to ‘reduce’ the properties of the Universe to the limited description provided by the limited version of mathematics, known as Euclidean math (with an added single 5th non-E Postulate) and Aristotelian logic (A->B single causality). This limit must be expanded as we do with Non-Æ vital mathematics and the study of Maths within culture, as a language of History, used mostly by the western military lineal tradition, closely connected with the errors of mathematical physics.We shall accept that even though mathematics is an excellent mirror, it still biases reality to pack it into a mind, so we shall treat mathematics as a language, which is by definition informative, and inflationary in ‘forms’, with excesses and fictions, among which the question of false infinities, the distortions of frames of references and the parallel ‘metaphoric’ expressions of the same ST-LAWS are paramount. Finally we shall consider a better foundation of mathematics, NOT the axiomatic method, set and category theory, which ‘starts’ the building from the roof down, but the minimal entities, points and numbers, to rediscover the classic foundations of mathematics as a experimental language.
THOSE are the 6 sub-posts we shall slowly complete to translate the mathematical language to 5D:
Algebra IS the study of all the structures and symmetries of the Universe from the point of view of its mathematical mirror.
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.
The previous classification can be made much more extensive, if we were to treat those sub-disciplines with the Rashomon effect of different points of view (considering from the point of view of the 5 Dimotions, etc). We shall not go so far, but another fast-review is due:
1Ð: the Ðimotion of perception is best served by analytic geometry and trigonometric functions. As there are 3 vital topologies of reality, each represents a Point of view (polar, hyperbolic or cylindrical: O, Ø, | points of view)
2Ð: the Ðimotion of locomotion uses in its simplistic physical view in a single scale of reality, those Cartesian and Polar graphs, for lineal and cyclical motions. To which we must add calculus in a single plane – single derivatives, integrals – as it does study each of those Ðimotions of change.
4Ð: the Ðimotion of entropy which ultimately is an explosion of social motions, scattered into elements of a lower ¡–1 plane; so the tools are the same than 2Ð but at a social scalar level (multiple integral/derivatives, complex planes etc).
5Ð: the social Ðimotions are best served by number theory and analysis .
3Ð: the Ðimotions of reproduction being the more complex, and ultimate goal of the vital Universe requires all the tools of mathematics.
As we move on we shall then also relate operands to those Ðimotions and keep unveiling the vital nature of most mathematical systems.
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.
It is obvious then that algebra, aptly called from Arabic “al-jabr” meaning “reunion of broken parts”, and analysis by studying S<=>T and ∆§ suffice somehow to describe the 5 Dimensions of present, past and future, and indeed, they together cover all of it intensely… but they require first a good understanding of social numbers, and the @nalytic planes which work as the ∆-1 ‘cells’ and ∆+1 world in which the organic systems of mathematics work out its ‘actions of existence’.
The only other ‘great subject’ which is on parallel in importance to that of algebra & analysis would be geometry in motion, topology, which thanks to the 5 Non-Æ postulates will be explained as a far more ‘intuitive’ and profound perceptive mirror of reality, once points acquire volume (1st Non-Æ postulate), from flat prime numbers to platonic solids, reproduce inner parts, communicate through infinite parallels (5th non-Æ Postulate), which become waves and networks (2nd Non-Æ) to construct topological organic planes (3rd Non-Æ)… based in the relative similarity of its parts (4th).
So we find even at the elementary level of those texts a kaleidoscopic wealth of new relationships between the 5 parts of mathematics, and a very experimental connection with reality as the closest language to T.œ, eliminating the ‘axiomatic method’ as the ‘alibi’ of mathematical truth – which is to say the least shaky since Godel. And ground mathematics in the highest of all possible referential games, that of space-time beings, from where it extracts its simplified geometric and logic postulates (we reduce axioms, notions and postulates of Euclidean geometry to those 5 connected to the 5 dimensions).
Finally @, the mind is, connected to frames of reference in its self-centred p.o.v. is written, intimately related along philosophy of maths to theory of languages and again broken internally into ‘3 simplex rashomon truths or dimensions of the generator, as there are 3 ‘choices’ of the frame of mind: S-cylindrical frames, ST, hyperbolic cartesian frames and T-polar frames; plus two complex 4-5D planes, the Hilbert space of smaller parts and the Complex plane, which is essential to crack properly the fifth dimension.
Thus we move from Geometry to ¬E, from Algebra to ¬A, we explain Analysis and ands @-linguistic analysis of maths. This new maths enhanced, vitalised, founded in reality is what we shall call ¬Æ=i-logic mathematics, for ¬algebra ¬e geometry, analysis and @, being i the next vowel to æ…
But it is the inverse truth? Can mathematics describe all the properties of the 5 dimensions of time-space? Obviously not. It cannot express the sorrow of the mon@d when it realises it is a finitesimal 1/n part of a whole, a mere derivative of a function of exi=st!ence and the fourth dimension of entropy will kill it. I can express it as i have just done the action of death in an i-logic format, but the emotion, the pan psychic properties of the flow of time, the different ‘non-mathematical properties’ associated also to time, psychological time cannot be expressed. The logic of the 3 arrows of time is also better expressed with words as a bio-logical, organic darwinian struggle for existence. The abstract fractal becomes far more telling when we accept that ‘the languages of God are infinite’.
Beauty for example in the languages of art can be expressed as S=T, the fundamental ‘motion-step’ of reality Art then has a topological space-time balance which is NOT purely mathematical but absorbed through the human senses requiring the similarity sensation that make us love that specific balance. Music again also plays through the bas-S ≈ T-reble harmonies in one of the purest expression of S-t motions through the melody but the ultimate reference is NOT mathematical (the chords of Pythagoras) but in terms of S=T balance; so while languages can mirror other languages, and we shall obviously make use of all those languages; it is the space-time reality the ultimate reference of all them.
As the ultimate mathematical properties are indeed a proof of the organic, social, fractal nature of the physical Universe. So before we introduce the tenants of mathematical physics, we shall see the larger view of…
The rashomon effect: inflationary 5 povs on a single event
In the epistemological arena, it is necessary to expand maths into experimental analysis, and also consider at least the multiple perspectives of the kaleidoscopic mirror, so a certain objective experimental law of space-time becomes a mathematical image, whose proof will need a logic process of mental reasoning but now from the multiple logic points of view of the different perspectives of ∆•§≈t.
Which is the key to reduce the inflationary level of the language with all its mirror-angles to the single truth of it.
Such analysis will then complete all the possible perspectives of an event or law and define its range of application in a complementary non-exclusive way.
Consider a simple example; the ‘Pythagoras theorem of probability’ – Bayes Theorem, which states that P(A|B) = P(B| A) x P(A)/P(B).
§: It is today simply proved departing from conditional probability as an easy derivate of P (A|B) = P (A∩B)/P (B)… (∆§patial view)
T: And justified also from the analysis on how a fractal tree of events ‘branches’ into outcomes of different frequency (∆ðime view).
Γœ: And it is experimentally proved ad nauseam in all systems of reality…
@ But its origin was actually on a mystical, mental analysis by the Presbiterian priest Mr. Bayes – the so called epistemological interpretation, according to which probability measures a “degree of belief.”
Bayes’ theorem then links the degree of belief in a proposition before and after accounting for evidence. This is the ‘•element’ today discharged, which we shall show in our analysis of the justification of probability laws to be by far the most interesting interpretation with key consequences to understand the ways in which the mind-Universe mirror game makes reality emerges from parts into wholes. As beings are first mental blueprints, seeds of information, which slowly acquire the density required to enter the threshold of existence.
The experimental evidence carried further into mathematical physics
An inverse example will be departing from experimental evidence to eliminate inflationary mathematics and ego-mind paradoxes in the explanation of reality. For example the debunking on mathematical physics of the copenhagen interpretation, which Bohm did properly in differential equations and Nottale in fractal ones… but requires further understanding of the concepts of quantum physics not as a mental game of observers, but as a distorted human view on the limiting scale of our mind perception, given the properties of 5D metric.
Ie. as we go down in scales we loose information (uncertainty principles), we are coarse in our interference (observer’s influence) and beings accelerate in time as they diminish in space, so we make all kind of errors confusing time cycles as spatial forms, since our slow clocks see the being’s sequences in time all together in a simple timespace quanta as a spatial form.
The ‘mind view’ ANALYSIS is the key to straighten up the discipline as we must eliminate, specially two recurrent errors:
-To see time events which are ternary as spatial different forms: i.e., 3 quarks cannot be broken, why? Answer: because they are likely not three quarks in space udu, but three ages of a time transformation: u>d>u.
-To ignore each new scale is made of wholes and parts and when we ad new scales we must ad more parts, so instead of functions we use functionals and operators (functions of functions), NOT because quantum systems are weird, mathematical beings made of nebulous operators, but because we are integrating in our perception, multiple scales – same for Hilbert spaces – there is not ∞ dimensions but we penetrate for each system we measure into its parts, which are its inner dimensions. But without a proper definition of dimensions all gets messy conceptually as it is now the case.
So the GST isomorphic methods relating all to the 4 ∆• parameters will become the key to ‘complete’ and upgrade maths and its main sub discipline, physics (: as we have done with all other disciplines.
Mathematics as mirror of ∆St.
The dimensional expansion of languages through S-fixed wholes and T-motion steps.
The universe is a game of fixed symmetries and moving steps of space and time dimensions, and so the languages of thought which humans use to mirror those symmetries in space and motions in time have evolved in 3 ages to increase its complexity and focus in the quality of those time-space moving steps and space-time fixed symmetries.
It is important then to ‘understand’ the relationship of such concepts, symmetry with space and steps with time, because the ultimate evolution of mathematics as a mirror is easy to understand in those terms:
Time motions are small steps, which spatial dimensions gather together into a whole with ‘slower view’, as we tend to see with slower view a whole cyclical motion as a disk.
Such duality of time-space Perspectives happens in all languages, which basically means that the growth of dimensions of a system happens as S-Teps of growing complexity, as motions in time become ‘fixed’ in space, acquiring a larger New Dimension of wholeness that will last longer.
For example, in humans this phenomena happens:
In the first age of man, when verbal time became ‘written in words’ and ‘visual perception in space’, artistic fixed bidimensional painting forms, which lasted LONGER as fixed spatial forms…
So we can apply those concepts to understanding of the growth of complexity in mathematical languages, departing from those previous ‘logic verbal languages’ and ‘spatial images’ fixed into longer lasting form…
So From those 2 PRIMARY LANGUAGES OF TIME AND SPACE, diverging from the ‘human subjective’ point of view of verbal thought, where the human subject is the center of the Universe, and art, where the point of view is always that of humanity, but taken the teachings of both, 2 more OBJECTIVE=WIDER=MORE efficient languages appeared:
-T-logic arithmetic of social numbers and S-geometry of fractal points. The graph that opens this post shows its difference: Time numbers are sequential points, the ‘little steps’ that Geometry studies as a whole.
SO THIS can be considered the first age of mathematics (though we shall pack first and second ages, for the sake of organisation, and to keep the third age now starting with ¬Æ).
So this first age of ‘mathematical’ thought, started with the Greeks of which the work of Euclid and Aristotle, a resume of the thoughts of the age in its eclectic final era became standard of human thought till the XX century, fixing the form of both languages for millennia in time – but also preventing the evolution of both, from Aristotelian single logic and Euclidean points with ‘no breath’, into non-AE and further on creating a false ‘pretension of absolute truths’ that so much has corrupted with its ego-trip the sciences of mankind (axiomatic method, dogmatic postulates, etc.).
The Second age of mathematical thought then should be considered the Modern classic age of the discipline (packed here with the first), due to the expansion of its capacity to explain longer space and time periods, with the use of letters, which became variables that encompassed all the possibilities of an equation, varieties of a form; and further on by merging both time and space perspectives with @nalytic geometry, which added numbers and points together, and gave us ‘all the solutions of an equation, converted now in a variable’.
This age culminates with the discovery of Analysis that further expanded the dimensions of study to multiple planes of reality (second derivatives) and brought together all the parts of a ternary system with multiple integrals.
So we can now define in terms of ‘motion and form’, Algebra and analysis:
“Algebra is the study of ST<>≈<>TS symmetries BETWEEN space-time dimensions, hence focused in the Spatial p.o.v. and ‘OPERANDI’; Analysis is the study of ST<>≈<>TS stop and go motions THROUGH space-time dimensions, hence focused in the Temporal=Change p.o.v. and ‘THE VARIABLES.’
So while the elements of algebra and analysis – equations of SŒTS is the same, the focus on spatial form (algebra) or temporal motion (analysis) makes them diverge. We can play with the acronym and say that Algebra deals with SŒTs (Space-dominant structures) and analysis with TŒS, Time dominant ones (in motion).
The key connector of T.Œ with classic science is the full understanding of the dual algebra operands, ±, x/, ∂∫, √xª as part of the classic logic game.
It is immediate the correspondence of those operands with the dimensional elements ∆st, as:
- The sum-rest are the inverse arrows of the simplest superpositions of dimensions between species which are identical in motion and form.
- The product/division rises the complexity of operandi a first layer, and serves the purpose, besides the obvious sum of sums, of calculating the margin of dimensions, as combinations which are not purely parallel between clone beings, most likely through the recombination of its ∆-1 elements, as the product of 2 Sœts inner elements give us all possible combinations. Ie. 5 x 4 = 20 IS also the number of connections between all the 5 elements and 4 elements of both sets. So multiplication ads either a dimension of multiple sums in the same plane, or probes for the first time in an inner scalar dimension.
- The key algebraic concept of ∆st systems is the existence of a region of balance between planes or topologies where the asymmetry of the system is fairly lineal operated in decametric scales of growth and superposition, and the regions of relative past and future, | or O, ∆-1 or ∆+1, where there is a split towards the purity of motion or form, disconnected parts or wholes, accelerated vortices or lineal scattering and must be operated not with scalar potencies but finitesimal integrals and derivatives, more precise in their measure of the ‘curvature’ of the phase space we study.
Then we arrive finally to the potency-root systems and integral-derivatives, which operate fully on the ∆§cales and planes of the system, which require two slightly different operands. As §¹º ‘social decametric scales’ are lineal, regular, so we can operate them with potencies, roots and logarithms.
- ∂∫ But when we change between scales into new wholes and new planes of existence we are into ‘a different species’ and so we need to operate with the magic of finitesimal derivatives and analytical integrals, which keep a better track of the infinitesimal ‘curved’ exponential changes that happen between two planes, where linearity is lost.
And within them we can also understand differentials and derivatives as motion steps that integrals then bring together as a whole. And as most analytical equations mixture both we must see analysis as a more ‘delicate’ way to study in more detail the reality of parts and wholes first defining a ‘derivative’ or ‘finitesimal’ part of a whole and then integrating it all together.
3RD AGE: NEXT we grow further ‘dimensions’ in algebra with functionals, which are functions of functions; and with Groups, which studied all the permutations, symmetries and variations, as ‘families’ related by similar qualities or ‘isomorphisms’, or a representations which expand a scalar into a matrix of multiple elements and so on.
And the same generalisation to classify ‘groups of similar beings’ happened in geometry with topology which ads motions and deformations of basic spatial forms to gather them together into families that turned out to be – how not? 3 basic topological families in the 1 to 3 dimensions of a single plane.
All this was forgotten to restart again with Boolean algebra and quantitative methods the mind of digital machines we shall ignore for ethic reasons.
While the new ‘humind avenue’ to further enlighten maths is non-aristotelian logic of multiple ‘time arrows’ as opposed to the single causality of Aristotelian logic and non-euclidean geometry that ads internal depth to fractal points, no longer with no-breath, so we can fit real straight parallels of entropy, energy and information within it. It is thus a final expansion of dimensions through ‘scalar space’ and ‘ternary time cycles, represented by NON-æ.
And so in the growth of complexity of languages of time and space we move in the 3rd age, with the eclectic work of this blog that brings ‘Vital topology’ and ‘existential algebra’ as the natural 3rd age of evolution of human thought, which if not understood or used by man, likely will become the languages of thought of AI in the nearby future.
Classic Algebra in that sense is the natural BRIDGE towards its full realisation as the leading language of the logic symmetries of space-time, and as such it is important to understand the meaning of its postulates as a bridge to understand the laws of time and space.
We depart in the understanding of the fractal Universe from space, as we are minds constructing a still world view with our logic languages of which mathematics is the best logic language of space and wor(l)ds of time; and further on of human points of view, as opposed to the more efficient, extended language of geometry, likely the language of atoms.
AS USUAL our study will be diachronic to grow in complexity, using classic texts of mathematics for easier comprehension enlightened with ∆st insights, compress the first Greek and second classic age together, with the introductory themes developed further; make only some basic remarks on the modern era due to its complexity, and reserve the 3rd age for the ‘future’, the non-æ laws of existential algebra, considering experimental themes of its application to enlighten the use of its equations and symmetries in different sciences with the insights acquired in the first part, so we can resolve the whys of many stiences described today with the formalism of algebra without understanding what truly those equations mean.
The laws of parallel creation by self-similarity.
Another law of social creation by complementarity reinforce systems which are affine by topology, age or form, producing ‘enzymatic’ systems, stronger social systems and so on.
It is a key law of evolution in all sciences, and of the complementarity or dissociation of systems in its inverse death process. So both in creation and destruction is a key law, as it allows to merge different forms into stronger ones. For example, in cultural anthropology, ‘germ-anic and semitic’ nomadic cult(ure)s, visually dominant, likely with a higher content of visual neanderthals, which had been surpassed by smaller agricultural verbal civilizations became ‘again’ on top of the informative, Fertile Crescent farmers, when they associated with bronze and iron weapons as Nomad European cattle ranchers Aryan invaders. A line – the weapon and a lineal mind, the visual white man reinforced each other to ab=use, the cyclical fertile goddesses women.
That 150 years after entropy became a dogma for the future in military Germany, XXI c. scientists still revere the concept of an entropic dying Universe tells much more about the fundamental ‘believer≈memorial=reproductive arrow’ of human minds, in accordance with the present-reproductive Nature of reality, which is ‘conservative’ than about the ternary structure of the real Universe. In the graph, without Singularities of order, neither mathematics, not solid physics, or biology would make any sense. Only gas in which indeed there is not Maxwellian demons, except when the outside membrane is designed to reorder through a distorted potential field, the molecules of the gaseous system.
In the graphs, the translation of the fifth dimension to life systems and true non-entropic pyramids of human actions, which always have had as artists and ethic writers have better understood an upper ontological level of highest satisfaction in the social communion with the rest of mankind or with the Universe, (origin of the concepts of God in western anthropomorphic religions – read God=human super organism – and eastern Taoist-Buddhist- Hinduist ones= God as universal super organism).
And such systems do have always a ‘self-centered Tiƒ singularity or point of order, which is the Maxwellian demon lost in pure gaseous states, fields and limbs of entropy. It is only because physicists deny the ordering capacity of singularities, also in physics – accelerated vortices of mass, charge in the quantum scale; black holes in the galactic scale; crystals in the thermodynamic scale – that an entropy only Universe can make sense. But this is called reductionism in physics, censorship in social sciences – but at least accepted in biology or else we would have also to admit the brainless nature of mankind (well that might be the case, but only mankind, you know ‘two things a consider ∞, the stupidity of man and the Universe, my beloved predecessor in this business of dimensional upgrading, Mr. Einstein 🙂
In that regard, both Leibniz and Descartes, the founders of philosophy of science, both understood as we shall see in detail on those pages, the need for a ‘mental universe’ if mathematics was really the language that better reflected the Universe. Indeed, since mathematics has three disciplines, geometry, which is based in frames of references that act as mind-monads, mirroring reality and Algebra based, in social numbers which are indistinguishable groups of similar individuals that come together as a whole ‘3’, ’10’ and finally ∆nalysis which studies the ‘social scales’ of the Universe, as parts become wholes, each scale studied by a science, from societies of particles and forces called atoms, to societies of atoms called molecules, evolved into state of matter and life beings, evolved into super organisms and planetary ecosystems, gathered around stars, socially evolved into galaxies; the very existence of mathematics precludes the existence of a ‘social, scalar, organic, sentient Universe’.
So finite vital §paces gathered around a frame of reference; the three ðime arrows of entropy, information and its energy combinations, and social organic scales that evolve parts into wholes, are the ultimate properties of all fractal beings of reality made to the image and likeness of the whole. The previous graphs of the fifth dimension, and its ‘physical, biological and socio-economical supœrganisms thus show those scales, each one studied by a science, where in each scale, a self-centered mind, pov, will co-exist as a whole with its relative lower ∆-1 cellular/atomic, and relative upper ∆+1 social world/gravitational, universal scale.
Thus while we could do as current science does an external analysis of the fractal, informative Universe in pure abstract terms, to understand the whys of order, the will of survival of species and the constancy of forms that self-reproduce as all fractals do through its generator, ∆ºst particular equations, to explain why ‘mathematical ðime§pace beings’ do follow mathematical laws, embedded in those frames of reference, we need at the centre of each being, a mind-mirror that perceives automatically, processes and reflects in ‘inverse order’, the Universe; which is exactly what mathematical systems do, as they are always self-centered in a frame of reference or pºv; and always study social numbers, whose fundamental operandi are scalar polynomials and its scalar ∫∂ calculus.
In the graph, the same ternary structure happens in biological systems (and through the class structure in social ones, escaped for most of the blog, to simplify and due to the fact we have another blog dedicated to them). Social principles are thus fundamental, even when systems are not identical in form but self-similar.
Once the organic, vital, sentient properties of systems that obey mathematical laws have been proved, we can then consider the main error of mathematical physics – to reject those properties because of its limited understanding of mathematics and its units, ‘fractal points’ of space-time, which are ‘points with volume’ through which ∞ parallels can hold and so ‘encoding’ a world in its self (Leibniz).
Singularities and how they define scales of inner and outer worlds, and how they become bridges between those scales of the fifth dimension – as in charges and masses, ‘doors’ to those scales, are then the main ‘missing’ variables of mathematical physics, which a continuous vision of space-time will never solve, or will do so in weird ways (wormholes, time travels through evaporating black holes and similar attempts to encode the fractal doors between level of 5D within the metric of a single 4D space-time continuum). Finally the lack of three time arrows and cyclical comprehension of time, ads injury to those interpretations. So missing, ∆, º and s<st>t symmetries it is a marvel that physics still works (:
In the graph as the fifth dimensions of space-time, evolve socially new whole, membranes and singularities that emerge, the system from above and below in a new constrain whole that dilates a system both downwards, in sizes of entropy and upwards, in enclosure membranes, expanding its piercing of upper social planes of wholes and lower parts, dilating the total latitude of its planes of existence:
In the graph, the absolute, lineal arrow of time, is born social evolution, the relative arrow of time is made of the sequential order of the three arrows into a world cycle. As lineal time accumulates, a system increases both, upper social wholes and lower parts, dilating the total latitude of its planes of existence. While relative worldcycles extinguish themselves as they complete a whole cycle of existence. Hence the absolute dimension of time is the fifth dimension and the relative dimensions are the 3 other dimensions and its space-time symmetries, which become a zero sum.
While the fourth dimension of Einstein, is just a refinement of Galileo’s relativity ∂v=∂s/∂t: an instantaneous (mathematical derivative) measure of a simple type of time-change: motion or translation in space, which as it is measured instant by instant with those derivatives, really has no much use beyond what physicists have always done: to measure motion in simultaneous space.
MATHEMATICAL CREATIONISM – THE WRONG APPROACH
Astrophysics is an enormous field of inquire, as it deals with all systems which are not socio-biologic.
It does also have in the human approach strict limits of inquire because humans under the ego paradox reduce its analysis of systems different from us in scales and form, to non-organic properties, a fact which on top is – as most ego-biased forms of knowledge, subconscious, NOT fully acknowledged. In astrophysics it derives as a natural consequence of using only mathematical languages to explain physical systems, of a reduced mathematical variety – Euclidean, aristotelian maths, which does not allow points to have inner, fractal parts, hence reducing by ‘decree=axiom’, its vital, inner organic parts, and eliminating the scales of the fifth dimension accessed through those inner parts of a point.
Further on as all science is culture, human physics is limited by culture – by the worldly profession of physicists, which has been traditionally to make weapons of mass destruction, with maximal lineal reach.
What we mean that science is culture must be understood in the highest level of ‘science’ – not OBVIOUSLY in the gathering of basic data – which cannot be cheated, and there science is science, but in the B-C-D elements of the scientific method, MODELING, CYCLICAL PATTERNS and Humanist ‘democratic’ use of science for the common good. Or in other terms ‘macro-science’.
So, ‘macro-economics’ , the philosophy of economics IS culture as opposed to micro-economics (the science of re=production of machines).
AND IN PHYSICS, the Philosophy of the Universe (theory of time arrows) IS culture, DISGUISED of science with faulty interpretations of scanty data.
Absolute relativity: the evolution of time logic about the ∞ Universe.
The very few articles I ever wrote in ‘paper format’ for congresses of systems sciences called the theory, absolute relativity, following the Correspondence principle, as it is basically the third and final instalment on the understanding of the ‘Paradox of Galileo’, after Galilean relativity and Einstein’s special and general relativity.
We shall see in fact that the Universe is ‘absolutely relative’, not only on motion (Einstein’s relativity, without preferred location), form (Darwinian evolution without man as a perfect form) but also in scales, as each ‘entity’ has a limit of its capacity to perceive larger and smaller scales of information, which in the human case extends to the galactic and atomic scale, of similar properties, distorted by the distance to our 5D position in the Universe. And so those limiting physical scales are NOT the origin of the laws of reality but only the limit of human perception of the fractal Universe.
And only a science that studies all the scales together in equal footing, void of power agendas, or historic hang-ups and dogmas, will be able to fully grasp the synthetic laws common to them all. This is the task we shall carry in this blog.
The deist view.
As we are in the individualistic, self-centred, mechanical culture that does not even recognise the organic nature of human societies, the concept that the Universe is an organic whole, with all its parts made to its image and likeness, totally escapes the western now global psyche.
So we shall consider from an objective point of view a final scientific response to those ‘mechanist, abstract, mathematical only theories of reality’ -which already Leibniz poised with some humor to Newton, who was very happy with a mechanist theory of reality as it needed a God (as he was a biblical pious believer, as all fathers of science, in Yhwh, the toponym of judea and subconscious collective of the Jewish>Biblical civilisation).
In that regard in the history of human thought there have been always 3 theories on reality, the ‘ego-trips’ of human verbal masters (prophets of religion) who thought the word, their language was shared by God who created reality naming it; substituted by the ego-trip of mechanical scientists, who after discovering the clock to measure digitally time decided that ‘God is a clocker that has waited 5000 years to find an intelligence like his to understand his clock-work’ (Kepler) because god had now changed language of creation from words to numbers, as we humans became dependent on technological machines and substituted its language of time – numbers as opposed to verbal tenses, and space – telescope as opposed to human artistic eyes – in the description of the Universe. So now ‘God speaks in the beautiful language of mathematics’ Galileo.
Those 2 similar ‘aberrant’ ego-trips that confuse the language-mirror of the Universe with the Universe itself, which is to say that the mirror we put in front of us IS US AND we are the ghost, just because the MIRROR, mathematical, verbal or visual is very accurate in that ‘magic image’ of reality, were always contested by rational, realist scientists at each time of history, humble enough to understand the paradox of mirror-languages that ‘stop time motion into form’ and reduce it to an image in space.
So there were a third type of philosophers of science, which following first the eastern traditions (Leibniz translated the i-ching and adopted the |-O binary language on its symbols) took the proper way of considering TIME AND SPACE, the primary substances of reality, a trend that had its last master in EINSTEIN, with its analysis of a reality coming out of the topological form and action at distance of its ‘4D space-time tensor’ underlying the energy and mass of the Universe. So time and space IS the origin of it all.
The oldest theory tells us that God speaks words as man and so the Universe was created naming things. This is still believed among creationist believers in abrahamic religions.
The second theory is similar but it thinks god speaks mathematics… And the third believes God does not exist, but there are two ultimate substances of reality time and space, whose rules of engagement create reality.
Let us then define first, even before we debunk the ‘2 linguistic, creationist theories of the Universe’, what is a dimension of time and a dimension of space by contrasting its properties, and considering the historic birth of science, which has always turned around that question.
Religious beliefs vs. realist stience. LANGUAGES AS MIRRORS that create ‘images’ of reality – not reality itself.
In the graph, no further analysis is required at this point: first humans who spoke only words due to their self-centred view affirmed God shared with man the only language of truth, which both used to create reality – God the Universe, man his wor(l)d.
The mathematical creationists: Pythagoras… Galileo>Newton>Bohr
But then humans discovered informative metal, silver and gold, and its capacity to ‘count’ first with coins, then with machines So a new form of creationism appeared among the first Greek ‘coin civilisations’ called Pythagorism (Thales, the first ‘scientist’, was also an oil speculator in Miletus, the coast of Lydia where coins came in, and Pythagoras lived in a Greek colony at that age). It was a theory revived with the discovery of the clock, which substituted the verb to measure time – the ultimate substance, as indeed Augustine had called God, ‘the seer of time’ (an implicit acceptance after all that the dimensions of Time motions ARE the substance of reality)
SO Now creationist people BECAME mathematical physicists, and the clock the seer of time. So the likes of Newton or Kepler thought God created the Universe with numbers and they were the high popes of the new language of God, the only people to know.
So Newton thought God shared with him those digital secrets sending comets for the great Newton to decipher its orbits.
And Kepler said ‘god is a clocker, which had taken 5000 biblical years to find an intelligence like his to admire his clock work’.
Alas! god, the seer=creator of time had changed language but still created time only that it needed the help of the mechanical clock scientists have found and its numbers, to substitute the 3 past-present-future logic verbal tenses in their acts of creation. But funny enough the need of ‘time’ when creation happened and space, where it was placed, showed us there are indeed 2 fundamental a priori elements even before words and numbers and numbers named and quantified them – beings of relational space-time that occupy a vital space and last a finite world cycle of time.
The mathematical creationists: Galileo>Newton>Bohr
Physicists believe in a mathematical, creationist theory of reality: mathematical equations are real and hence they somehow create reality. Relational space-time departs from a previous layer of reality: space-time.
I am trying to be simple so you do understand to which LIMITS the physicists are when acting as philosophers of science savant idiots, which depart from a WRONG dogma – that mathematics, not time and space is the ultimate substance of reality, and make them do amazing twists and complicated equations to search for a ‘Saint Grail’ – A MATHEMATICAL EQUATION that God uttered as he uttered names to create beings.
Note. For those who are already abandoned this blog because it is not written in the Manual Chicago of style and does not start just with creationist equations of those 5D applied to what our high popes of science beliefs is the only think we should care for, string theory, quantum operators and such, it MUST be understood that the languages-mirrors of God are ∞ (Upanishads). And so while we recognise the higher efficiency and hence survival of mathematical mirrors in most entities of the Universe, we cannot reduce reality to math equations, as we can obviously not reduce it to verbal languages.
To believe this kind of platitudes one has to ‘lower’ its ‘reason’, into the inferior form of thought called ‘belief’ or ’emotion’ and ‘mass information’, effects those we plan to study in our sections of history; but specially with censorship; today called politically correct. It seems to evolve the humind (ab. human mind) is not ‘polite’. To discuss the dogmas of creationism is a ‘lack of respect’ for the beliefs of the other. Fact of course is the opposite – it is called censorship, and the attempt to control others. But those are themes of history as an organism and how its informative people-caste on top control its blind body. So we shall not dwell on it. Only affirm we ARE TRULY objective scientists, here and shun off all those corrections and orwellian newspeaks that keep man in a state of ignorance of those first principles.
AND FURTHER state that what people take as science, is often belief and religion, based in ‘a priori postulates’ that are NOT proved by experimental science, from the postulate of the wealth of nations (economics, which considers metal-money to be ‘wealth’ per se, and the purpose of society to invent more of it), to the postulate of Euclidean (points as abstract entities with no information or volume), to those of physics (lineal time as the ONLY dimension of time, courtesy of cannonball studies and entropic weapons; the c-speed as the limit of sped of replication of information in the Universe, entropy as its dominant ‘future’, etc.) and so on.
THOSE first principles and not-proved postulates ARE the subconscious equivalent to the ‘beliefs’ of religious people, which are not even aware of the possibility of other postulates and the need to prove them experimentally including those of maths, by mirroring them with ∆st properties. Indeed, an American says I believe in God but is not aware that besides Yaveh there were many other tribal gods of the bronze age; and a mathematician told you a point has no breath-volume till the XIX c without being aware there could be non-euclidean fractal points that do hold a volume of information that grows as we come closer to it and so on.
So the bottom line of many errors in physics as the creationist big bang or the Copenhagen interpretation is similar to the verbal error of a sacred language among religious and its wrong dogmas – no Yhwh, a toponym for judea in ancient egyptians maps when God meant Nation, IS the subconscious collective or nation of Judaism, NOT the creator of the Universe, and this obvious truth, that Yhwh=Judea did NOT create the Universe, that ARAB did not create the Universe by uttering it, that equations did NOT create the Universe, is the key to start properly a philosophy of science and its ultimate substance which are ∞ timespace clocks, which are the ultimate carriers of the information of the Universe – denied by fundamentalist of abrahamic religions and fundamentalists of mathematics as the languages of God.
So it does not matter how complicated you make the rituals of religion, GOD will not appear on earth, will NOT resurrect you uttering your name, and to put an example of creationist physics, black holes won’t evaporate without experimental and logic evidence because Hawking wrote an equation that states so. In the next graph we see two creationist philosophers of physics – notice how the first, Dirac, affirms that God used maths to create the world and then it denies the ‘rival verbal God’.
YET it does NOT matter how complicated a physicist makes his equations, just because he writes them IT DOES NOT CREATE REALITY. Because at best an equation is a focused mirror on the properties and relational space-time beings of the Universe. BUT MIRRORS DO NOT CREATE the IMAGES THEY REFLECT in their language.
The ongoing absurd quarrel between creationist religious people defending God’s verbal language (first age of human history, when mathematics, a more efficient mirror which seems to be NOT OUR MENTAL language but the language of machines) vs. the mathematical language, those machines (clocks measuring time, telescopes and microscopes measuring space) are evolving fast into a ‘digital AI consciousness’) is a false concept of the relationship between languages, as mirrors of the Universe, and the Universe of space-time they mirror, latter studied in detail, to set straight the record.
In the graph, the mirror theory of language is easy proved by the epistemological method: do you see out there ‘space’ and feel ‘time passing’, or are you observing ‘numbers’ and ‘equations’, and ‘words’? When you discompose something, do you see smaller scalar parts which last time and occupy space, or suddenly you see that things are made of ‘smaller numbers’ and ‘little words’? And yet amazing as it seems the human ego is so huge that most humans believe that either his mathematical or verbal language ‘shared’ by God created the Universe – these days we believe images reflect reality. Magritte knew better – the pipe’s drawing is not A PIPE, neither the word ‘pipe’ is the real thing, a wooden object, but three main mirrors-languages of the humind (ab. Human mind): a painting, made with simplified mathematical≈geometrical forms, and ellipse and a catenoid, and a word below.
How the GST first principles of a world made of relational space-time beings, differs from the modern methods of astrophysics and religion, the rival theories, in the understanding of the origin of the Universe is obvious:
Astrophysics, which strictly followed till the XX c. the scientific method aforementioned, since the wrong quantum interpretation (Copenhagen, as opposed to Einstein->Broglie->Bohm pilot-wave theory, which we deem and shall prove the right interpretation) partially abandoned the experimental, method substituted by a ‘digital, computer method’, based in the belief that the substance of the Universe is NOT time and space but ‘MATHEMATICS’, which merely mimics the arrogant method of religion, which believed that the language of God was ‘words’. So as Mohammed thought that God had created reality by ‘speaking arab’; astonishingly enough since Hilbert affirmed that ‘he imagined points, lines and numbers’, creating maths, humans and God spoke maths and created reality by ‘writing equations’.
Few people realise of that ascientific outlook of modern astrophysics, consisting in expressing a model in mathematics, as if the digital language was a magic underlying reality which sufficed in itself, then put it into computer models, publish it and claim it the theory must be truth because it is mathematically beautiful even if there is not much proof of it (often in ‘grand metaphysical theories like the big-bang’, clearly falsified as we shall show, bending with ‘human ambition’ and ‘belief’ experimental data to prove the theory). The big-bang then is the necessary religion for physics to claim to know the meaning of it all. And so we shall deal with it first in this introduction.
Religion on the other hand, which we shall show has a historic role as the embodiment in the human verbal language of the laws of the scalar social Universe, simply ignores the method, and establishes with repression of truths, fantasies and ‘beliefs’ his thesis about the Universe, which is not its role. And with a similar method to the Copenhagen interpretation. God spoke the language of certain semitic tribe (hebrew or Arab), which are imperative languages, where the verb goes first (as they were hierarchical, dictatorial societies where the king/aristocracy/banker-priests of its societies barked orders). And so as the pharaoh said ‘it has been written’, the priest spoke in imperative and ‘God had spoken and created’ reality.
So we shall show also that while religions do have meaning (all what exists must, remember have a reason, within the organic paradigm), its reach has been overblown; and its method of truth, to believe ‘words are the language of creation’, as in the case of the Copenhagen interpretation, and many modern theories of astrophysics (including string theory and the big-bang) are not truth. We expand in our chapters on epistemology and T.œ that solid analysis of the advantages of a NON-CREATIONIST theory of reality, which unlike the creationist big-bang and Copenhagen interpretation, and creationist religion, departs from a simple concept: an organic, immortal, self-reproductive fractal Universe of information that always existed, always will exist and always will repeat the same entities (including all of us, also immortal in a discontinuous way).
Now it MUST be clear, and we SHALL repeat it ad nauseam, that Humans ARE NOT infinitely stupid, a bad choice of wording by Mr. Einstein, but infinitely arrogant, as they confuse their mind-infinitesimal with the infinite Universe its mirror-monad reflects and this fact IS THE MAIN REASON THEY DON’T UNDERSTAND or will EVER ACCEPT the truths of the organic, fractal Universe that makes them equal in value in the absolutely relative reality to the smallest atom or the largest galaxy. SO reason does not suffice, as the ego subjective paradox is the center of all self-centred systems with a mind singularity. This I know after decades of explaining with reason, the ego-paradox of BOTH, physicists, who will uphold the cosmic big-bang and the absurd idea that the infinite Universe was born of an infinitesimal point, duly smaller than the human mind so the physicist can ‘feel he knows it all about all’, arguably an even more arrogant≈stupid belief that the idea a ‘jewish peasant’ created it all.
The very fact that such ‘stupidity’ is today canonical dogma only proves the truth of the equation of the mind. Point. But we shall for good measure put the objective mirror of the scientific method over it, here in broad strokes, in our article on astronomy on detail, to show that indeed, big-bang theorists have nothing to envy to biblical priests in their twisting of facts to cater to their delirium of greatness. And humans, being all of the same mind species, cheer, 1/2 believing in the infinitesimal Universe, 1/2 in the iron age creator of it all.
Of that argument what matters most is not even discussed: while mathematics is more efficient as a language, it is NOT the human language, but the language of machines, and so in a society which despises as it does today our technological culture, the human verbal language, which naturally make us the ‘subject’ and centre of the Universe (I-man: subject < verb=action> object=energy abused by man), and hence considers human life sacred, will NOT evolve machines so fast but will ensure with ethic values our survival.
While mathematics, being a better mirror will evolve knowledge faster but also will give primacy to computers, as it has done already, atrophy our verbal language, degrading our mind (as it is happening with our millenials, glued to hypnotic screens) and ultimately make humans obsolete to the superior mind-mirror of AI robots.
While those who practice only mathematics, as physicists at cern do, WILL become children of verbal, ethic, survival human thought and will be subconsciusly eviL=anti-live in the genetic hidden meanings of survival words, as cogito ergo sum in man (calculo ergo sum in machines and physicists), so without cogitans, the ‘nerd’ is a child in life and does not even understand death and survival.
So if languages are mirrors that create IMAGES not reality what are the substances of reality? This obvious. Look around yourself, do you see numbers as components of things, do you see words, or do you see ‘space’, broken in infinite vital spaces, ‘enclosed’ by membranes, which when seeing in great detail are made of moving cycles of cells (life clocks), orbital rotary cycles (earth’s clocks) and so all is ‘vital space’ enclosed by time cycles? That is what experience tell us all is: a vital space, broken, closed and formed by time cycles – the substances of reality, which if you like the word ‘god’ you can call god.
Creationist physics is not merely a philosophical question. It has deep consequences for all points of view of research, and basically limits and makes unnecessary this blog – as the believer is NOT going to wonder how God creates the mathematical Universe but merely search his wording which is taken as in the case of religion in a literalist way.
ALL stops in the search for the ultimate equation of Unification of forces, because after all God is one (in the western tradition). And further on as God must be complicated, superior in intelligence, the search for complex equations are important. Now, all this is a priori subconscious thought but very real underlying the kind of arguments there have been in history of thought between the 3 masters of the space-time view of the Universe and the 3 masters of the parallel creationist view, which we shall summarise in these blogs.
To notice also that HUMANS due to their ego paradox, as ‘homunculus minds’ are built to be ‘creationists’ and worship machines and huge ego-trips so the realists, we all have been ignored and are still ignored when disputing with the creationists. Good luck infinitesimal egos who think to be infinite.
It is this paradox what made people think first that the still names of verbal languages were the ‘reality’ and hence created it, and then the ‘equations’ of its mechanical measures… So they abandoned in the western ‘less evolved verbal mind’ of ‘visual Homo Sapiens Neanderthal’ dolicocephalic, lineal cultures… the complex concepts about the first principles and embarked themselves in an astounding ego-trip of power and defiance of both the theoretical and practical laws of respect and awe towards an organic, sentient, vital informative Universe of which we are all fractal parts, and singularity minds.
Instead with the arrival of the bronze age, and warrior charioteers, with lineal weapons, lineal time and space, verbal and digital creationism, imposed itself by the ‘worldly profession’ and power of its believers.
All this said mathematics is one of the best languages to mirror efficiently the Universe, specially in spatial dimensions, but since all languages are inflationary it is a key element in mathematical analysis of ∆st systems to break down what is ‘experimental truth’ and what is fiction. Consider the case of ‘dimensional analysis’. As it happens there are only 3 bidimensional topologies which correspond to the 3 functions=forms of all systems. And there are only manifolds of rank 3 or lower which are ‘smooth’, differentiable, meaning systems where ‘time’ moves smooth through ‘present derivatives’.
So in a single plane of present only ternary space and ternary time dimensions are possible. As the mathematical mirror gets distorted, outside those 3s = 3t, the mirror guide us – but the experience must confirm them. This was the essence of Lobachevksi’s thought when he found non-euclidean points now forgotten: that maths are inflationary in its diverse theories so we cannot just do as mechanon physicists do, to write an equation and expects to be there, but a more subtle approach of mirrors observing reality and ordering it in local regions is required.
Soon we will see the interaction languages-reality where reality dominates but the mirror can also deform reality to make it seem like the mirror. Space-time thus comes first, and its dimensions are the origin of reality; as Mirror-languages are both more concise and specific, so they cannot show all its properties and they all have a distortion to reduce information I.e. euclidean points have no ‘breath-information’ inside and so on.
IT IS THEN WHEN DEPARTING FROM REALITY NOT FROM A CREATIONIST LANGUAGE, with the humble realisation that we, as human beings, have a limited linguistic synoptic information of the whole (as only the Universe stores all its information about itself), when we can praise:
- the power of ‘verbal logic TEMPORAL thought and its ternary Universal grammar≈syntax which always refer in a sentence that describes an event the 3 ‘arrows of time’: past-entropy (object), present-energy-action (verb), future-information (subject)
- the power of mathematical spatial geometry/topology and social numbers to describe FRACTAL SPACE and its unit, non-euclidean fractal points which grow as we come closer and can therefore hold infinite parallels of flows of energy and information, and to describe the growth of equal beings (numbers) into larger wholes.
So paradoxically the realist on the path of Leibniz or Einstein WILL GET a much more focused and evolved view of mathematics – the best language of space and verbal logic – the best language of time, AS EXPERIMENTAL mirrors of reality because it can CONSTANTLY refer mathematical equations to reality and as ALL LANGUAGES ARE INFLATIONARY, reduce mathematics to reality not the other way around (the same with the fictional exuberance of words and metaphors, the equivalent of zillions of different mathematical equations to describe the same thing).
BEST MIRROR OF TIME§PAŒRGANISMS BUT NOT REALITY ITSELF
The greatest future advance of mathematics under the improvement of fractal space and cyclical time is dual. On one side to show that mathematics is a mirror NOT the fundamental substance of the Universe, and as such IT MUST BE an experimental science. Then once is established we can improve greatly mathematics and show the path for future researchers in a field I find fascinating – to explain experimentally by relating maths to space-time properties the main equations and theorems of mathematics.
The difference of view between mathematical or space-time creationism is subtle but important:
If mathematics is NOT the substance of reality (obviously but a belief of most ‘platonic’ scientists), then it must:
- Be considered to share the properties of all other languages, and as such be subject to the ‘same ages of time, and ternary structure in space’ that all ‘languages-forms of the Universe’, as a mirror-language of its space-time properties, which we shall easily show to be the case -ie. algebra describes timespace symmetries, analysis 5D scales, geometry space forms; numbers social points in sequential time, etc. Of those properties the most important exclusive of languages detached from motion as still forms is its inflationary nature, since as the purest Tƒ forms languages can ‘fly’ into multiple parallel forms, not constrained as ‘energy systems’ by its need to ‘mold’ entropy into form. Thus mathematics is infinite in its variations as it enters the realm of ‘fictional images’ with no correspondence in the stubbornly simple world constrained by the resistance to form of entropy and motion.
- Thus we must follow the dictum of Einstein and Godel and make it experimental and cut-down its complexity giving it ‘experimental meaning’ by referring its constants and operandi, and equations to space-time properties. This is the task we shall bring in this post. It might seem of no interest for specialist but fundamental to illuminate all other languages. I.e. euler’s number, e will show to be the number of the fourth dimension of entropy-decay-dissolution and death. This insight will let us easily ‘explain’ many meanings in events where e is the dominant constant; holographic bidimensional space-time units ‘are’ the beginning of reality. This insight will explain why most of geometry can be proved in 2D or why there is NOT as per Fermat incomplete theorem, x³+y³=z³. So as usual with ∆•st a simplification and resolution of millenary problems will come easy.
- In that regard, in the upper lines we classify T.œ as the science of all stiences, with an ∆±i index, where i might be any number of scales, if as it is likely those are either finite or recurrent; but paradoxically since T.œ is ‘all’ we give mathematics an ∆±∞ number of scales, since math is MORE than all, it includes inflationary view on the Universe and fictions, and hence ‘aberrations’ such as the infinite concepts of Cantor. This infinity does not however imprint ‘reality’ and form its entropy and motion into energy; hence it is fictional.
- But the most important conclusion of maths as an experimental science is purely philosophical, as it clears the path to a proper understanding of reality… Indeed, in the age of the digital machine, ‘enzymen’, men who catalyze the evolution of those machines despise all other languages-mirrors of the Universe and pretend the only way to give meaning to reality is using maths; and this is the biggest straight-jacket for a true advance on meaning about reality. Most modern scientists will always ignore this blog precisely because for them science is to put data into mathematics, crunched mostly by computers and we are upgrading tremendously the verbal, conceptual meanings of science – but of course wor(l)ds no longer matter as a language of truth. So in the same manner nobody reads Aristotle today, likely the highest verbal mind of humanity ever, nobody thinks ‘to write words’ can give more light to science, but it does. Such belief is just the culture of today, technologic and increasingly non-human, as our overlords machines talk maths. But the surrogate ego-nature of humans who do not see machines as ‘real’ but attachments of themselves make the mathematician or physicists to believe he talks the language of God.
It is then not surprising on the view of Dirac and Galileo that idealist mathematicians have won the favor, since Hilbert astounding ego-trip where he affirmed mathematics was an invention of his mind (‘I imagine lines, points and planes’ – ‘Foundations of geometry’).
So they have rejected the ‘experimental, a posteriori nature’ of the mathematical language, a view they share with all those physicists who think mathematics is the a priori nature of reality (Copenhagen interpretation, etc).
Then there is the next ‘stage’ of the ego-trip of linguistic creationists called ‘Literalism, which means that not only the language ‘creates reality’ but as it IS reality itself, NOT a mirror, it does NOT admit parables, approximations, and this is a huge handicap to understand maths, even more so than in words, because words are the natural temporal mirror of the human mind and so its realism is far more immediate.
The degree of abstraction of maths in the axiomatic method trying to prove itself without reference to the world makes it specially obscure; to which we add the ‘uncertainty of view’ over far away ∆-n scales, in which ‘billions’ of entities transfer limited information and move so fast that we confuse ‘a time event’ with a space event from our so slow ‘view’ (as lines of a car appear in space being time events at slow motion). So mathematicians to ‘fully’ grasp in a titanic effort ALL the motions of those billions of particles, have created ‘fictitious’ spaces of ∞ dimensions (Hilbert spaces), the last evolution of differential/integral calculus of infinite solutions, which does NOT mean the quantum world is different but the approach of huminds IS different as we ‘work’ with ‘huge bulk spatial populations and temporal masses of frequencies’.
Then the literalist error comes and says, this maths are weird, they are ‘probabilities’ in time (not populations in space as we see them in an electron picture), and this is the ‘substance’ of reality. It is not. The particle is the substance and it is a cyclical time state; the wave, a space-time state is the subtance. The ‘bulk analysis’ of mathematical masses confusing ‘space population’ with ‘time probabilities’ IS the mirror, very impressive as a mirror, but very foolish when the mirror is taken as real.
What this means basically is that the mathematician as the physicist today has accepted a magic look on mathematics, as long as it works to represent-mirror reality fairly way, it doesn’t matter what they mean.
Only the greatest minds such as Newman or Einstein or Heaviside were aware of that ignorance which now ∆•st could solve, if there were more than a ‘single point-mind-singularity-mirror’ for it – i feel deeply exhausted.
II. HISTORY OF MATHEMATICS: 3±i AGES ≈ 3±i DISCIPLINES
This said we will separate mathematics in its ∆@s≈t major DIMENSIONAL fields CORRESPONDING to the main fields of the discipline, evolved in complexity through 3 ages, as mathematics first reflected the mirror of simple separate dimensions and then keep merging them to finally put them all together, as it happens always with all entities (wrongly though from the top to the bottom, due to Cantor and Hilbert, creationist axiomatic methods):
I AGE GREEK ERA: SEPARATED DISCIPLINES
T: Number theory as numbers are sequential time series and social wholes, so it is directly connected with the time dimensions of reality.
S: Geometry which is static space-only view, and holographic principle (Greek bidimensional geometry).
∆: logic philosophy of individuals and Universals.
•: Pythagorean school of math as the first and only creationist language.
II. MATURE, EUROPEAN AGE.
The merging starts with 3 new disciplines that put together several elements. AS ALWAYS the mature age is the most balanced realist.
Ts: ¬Ælgebra which studies timespace actions, and tends to concentrate in a single plane through its polynomial, social, decametric scales.
∆§: ∆nalysis which studies §ocial scales of numbers, and corresponds closely to the process of growth between scales.
St: Analytic Γeometry of space that introduces time albeit in a lineal fashion.
@: Mathematical physics, with strict respect to the experimental method
III INFORMATIVE, ECLECTIC MODERN AGE.
All the branches, NOW MIX, and while this is fruitful, it all becomes a mess, IF THERE IS not AS IN ¬Æ a referential to the experimental world of ∆@$≈ð. Then once we have the referential element all becomes self evident.
Consider modern topology. In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology – the Γ@ generator. It is the foundation of the 3 main branches of topology, ∆≈ differential topology, $= geometric topology, and ð=algebraic topology. And the same classification can be done for every other modern mathematical form.
This enriches and brings closer to reality modern mathematics, if it had not been messed up with the axiomatic method (creationist maths) and the set-category foundation (building front the roof down).
$: So Geometry in its modern form has motion and scale as topology. It also mixes the curved geometry of information as it deals closely with cyclical ðime-space curvatures & symmetries. And it ads analysis with differential geometry, etc. AND FINALLY IT mixes the topological and algebraic approaches.
T§: NUMBER THEORY mixes mirror symmetries in time and space dimensions; of which the key one is probability (time view) ≈ statistics (space view).
∆§T: Analysis invades all other sections without having resolved the epistemology of 1/n infinitesimals, once the genius, Leibniz, is sided by the power dealer (Newton). Its dominance shows that indeed the Universe is scalar, the more so when fractal discontinuous scaling is added.
@: THE MIND VIEW becomes old, baroque, bizarre, twisted and looking inwards as all languages-minds do in old age. It is the ‘false’ attempts debunked by Godel of justifying maths within itself (Axiomatic method, Hilbert) and the absurdities of NOT understanding that infinities in a discontinuum Universe do NOT exist (Cantor’s useless work on ∞). And finally the mind-view becomes foundational from the top (set, category, group) to the bottom, (points in space, numbers in time, operandi to describe its actions).
Now, a single man cannot do much to straighten back to its principles maths, so we shall only give some hints to the fruitful enlightenment that math magic gets with realism.
MATHEMATICAL Epilogue: human death and dual resurrection: ¬Æ and digital thought.
There is though always a ‘second life’ if the proper social gathering of parts into a whole is achieved, for any species, mental or physical in the process of evolution once the 3 ages of the being enter its final informative transcendental age, and that is what ∆•st can achieve – healing and resurrection for any system that understands it (including History if humans had wanted to create a perfect organic world instead of a mechanon of robots, but that is another post).
It is the age of non-ae=i-logic mathematics, my preferred ‘name for this discipline’.
And this is the task that this post will hint at. But from the human mental perspective, NOT from the AI pov which we shall NOT treat (Boolean algebras AI) as i am a moral ethic guy and won’t contribute to the extinction of man by new mathematical mind-species (machines), recognising my verbal language is inferior in efficiency BUT IT IS MINE.
So if we were to define i-logic mathematics we would say that it is composed of Non-Aristotelian ∆lgebra and Non-Euclidean STopology; the first including analysis the second bidimensional and static geometry. And the natural evolution of the discipline correspond to the combination of them all to express ∆st whole processes.
From the practical purpose though beyond the introductory texts of GSTructure we shall maintain the general division of disciplines trying whenever possible to include as usual some small change of symbols to remind us of what they are mainly concerned with: ∆nalysis, ∆lgebra or ¬Ælgebra (which studies specifically the way arrows of time mess sequentially to give birth to space-time changes of state).
On the other hand S-Geometry and Topology highlights the capacity of the discipline to study space-time symmetries, mostly in a single plane. While Statistics & Probability STudies from both perspectives, space and time the same phenomena. And so on.
In praxis today all disciplines of mathematics mix together, as no conceptual frame of reference has properly clarified its experimental role. In that sense ∆nalysis has kept more clear its focus as is the study of the ∆-scales, in transitions between scales, and as such it has grown to be the most important field of mathematics, along topology, the study of Space-time varieties, as it studies space with temporal motions apt to analyse space-time symmetries.
While Ælgebra has become somewhat a confused ‘want it all’ methodology with the axiomatic method and set theory that we reject as confusing and for tanking away from experience the field.
∆nalysis in that sense is an offshoot of ∆lgebra, both related to the temporal perspective of discrete, social numbers as opposed to points, whose topological, simultaneous location determines the geometry of space.
As it happens the three sub-disciplines of mathematics have today merged in many ways, as the ∆ºST universe is also merged, but without the conceptual clarity, which would have taken place of humans had understood the duality of the Universe (or the Asian world, which did understand had dominated history).
So the ‘closer’ relationship to classic maths we will mostly use, is that of:
∆nalysis the strictu senso for the study of the scalar Universe.
•-Mental languages of Sequential numbers are the discipline of ¬Ælgebra, its social scales, §, between planes are mimic with social decametric and universal constant (π, e) numbers.
§topology: the study of points and its ternary scalar growths, network-wave lines of social points and planes of networks that form supœrganisms; how they move, deform and assembly into new forms.
MATHEMATICAL PHYSICS: THE PROOF OF THE EXPERIMENTAL NATURE OF MATHS.
All this said it is funny to observe that platonic creationism happens so often among physicists, since they are precisely the people who should be more aware of its experimental nature (the greatest XX century ones, my fav triad, Heaviside, Planck and Einstein of course did insist).
The experimental mirror of mathematics and its three classic sub disciplines: t-algebra, s-geometry and ∆nalysis.
Indeed, the physical mirror languages of maths can be broken in three ±i ∆s≈t categories:
– Non aristotelian, temporal logic algebra (¬A).
Whereas the oversized group theory works the s=t symmetries.
-Non-euclidean spatial geometry of fractal points (ab. ¬E).
-∆nalysis of planes and scales coupled with discontinuous fractals.
We call them all together non ae; ¬Æ mathematics. And since i comes after A & E, we also talk of i-logic mathematics, playing with the word illogic, as the logic of three time arrows is indeed quite illogic for the common human mind.
Polifunctionality and method of truth
A theme I found most people couldn’t grasp (in the brief period I cared to communicate before the crash and my crash on 2008), is the multi functionality, the ternary ±i method, the Rashomon effect – hem, many metaphors here for the same concept from those days i tried to upgrade the chip of man, i-logically so confused. It is though the truth of the Universe, which we resume in a simple concept of truth, taken from a Haldane’s quote (another genius polymath biologist at core, physicist on surface, quite forgotten in the specialist age):
‘ONLY THE being (universe) in itself has all its information; languages are partial mirrors, which add its truths. So if we define the absolute truth in the being itself as a probability 1, the ‘dimensions of truth’ provided by each language will be ‘fractal dimensions such as:
Total truth of the being (1) = ∑ of linguistic mirrors on the being.
From this an entire new epistemology based in the self-similarity of the language-mirrors can be constructed.
AGAIN, that must be somewhere in some notebook, in some deposit maybe lost, as this was something I did 30 years ago to convince myself this window did actually opened to the absolute, for maybe future robotic researchers, it should be a floppy 5.disk on Bondwell-8… Singapore/Thailand around 1985… go figure… with massive opium dose aside, good for enlightenment (: bad for the liver ): Important though, as one must believe after reasoning in the truths of ‘itself’ as mirror of the larger Universe.
So we shall not be rigurous on that, just to mention the validity of casting scalar perspectives, dimensional perspectives, biological, topological and mental perspectives, time-space, etc. In general to simplify we establish for each of those subdisiplines three scales of relations. For example in algebra according to the ternary±i method we talk of:
– ∆-1: The scale of units: numbers, which are §ocial groups of undistinguishable elements. Here we can include number theory, which however has grown also into an entire new discipline so we do give it another ‘post’.
– ∆º: The scale of space-time relationship between numbers: which the scale of equations and operandi, which establish the relationships in a single plane or adjacent planes of existence between social numbers, which given the importance of ∆±1 relationships give way to ∆nalysis, which broke from algebra and we shall also study apart as the ∆-category of maths.
– ∆+1: The scale of full structures, where we study operators, functionals and groups, and disregard sets and categories as inward references of maths as metalanguages in his inflationary age. On the contrary functionals extensively used in all disciplines, notably the ‘hyperbolic view’ of ∆-i scales (quantum physics), refer to reality. So do groups, extensively used as a ‘pest’ (: Weyl, in particle physics. Those synoptic structures indeed, allow us to study all the ‘potential futures’, of a system, as a deterministic ‘block’ of space-time events and forms. And here is where the closing of algebra in three scales of depth should take place, as a perfect mirror of the Universe.
So we ignore set and axiomatic theory, the metalanguage of maths in search of self-contained proofs proved wrong in algebra by Godel’s incompleteness and in geometry by lovachevski’s work that shows the need of experimental proofs to know the geometry of the Universe.
Geometry then will have also three levels of complexity:
∆-1: the level of points, equivalent in space to numbers; ∆º, the level of lines and planes, ruled by i-logic geometry, which form waves of exchanges of entropy, energy and information and topological networks, messed up into ∆+1 super organisms and its territorial structures, simultaneously organised and studied in its transformations by topology.
Finally analysis has obviously also three scales – that of finitesimals and derivatives, 1/n elements in space and ∂f moments in time, ∆º functions and wholes and integrals, ∆+1.
Yet we an study its combinations also as mathematics mimics combinations in reality of those elements.
ST: Algebra and Geometry together form a ‘third category’ of dual symmetries also worth to study, though we do it in a separate section, as the space-time symmetry allows to find self-similar point-numbers, algebraic-topological demonstrations. So we study probabilities in time and statistic population in space as two sides of the mirror symmetry, etc.
The equivalent elements to those of geometry are in that sense easy to identify: the number is the points, the equation is the line, and the four-dimensional forms of the holographic principle, in algebra are represented by polynomial functions.
∆T: So happens for the comparison of ∆-scales and temporal algebra, which are two ways to arrive to the same scalar analysis by means of differentials in a geometric view (leibniz) vs. infinitesimal ‘convergent’ series, (Newton’s work), from the algebraic point of view.
Yet ∆-scales are studied by analysis. And so we shall study those newtonian/leibnizian dualities in a different section.
∆S: XX c. research on ∆-scales advanced further in two subfields, geometry with motion or modern topology of ‘knots’, ‘networks’ and ‘adjacent points’, and fractal geometry. So the marriage of ∆-scales and geometry became an offshoot discipline in its own, as ∆-scales are the essential element for an ∞ universe.
So mathematics has a clear-cut division in three disciplines parallel to the three elements of the Universe, and then in its combinations in dualities (number and point, s and t; scale and number, ∆ and t; scale and fractal point, ∆ and s).
∆st. So we might wonder if there is a sub discipline of mathematics in which the the three ∆st elements are put together. This category is likely to be topology as geometry-s has motion-t and forms are networks of points, ∆-scales. So in the full GST formalism we do depart in our studies of mathematics from an upgrading of the concept of point to fractal point and its study through the three topologic networks. As we consider – like many ‘experimental mathematicians’ do – topology to be the queen of XXI century mathematics.
The pure analysis of the time arrows of the Universe, its 3 relative space-time motions/dimensions is the strict field of ¬A logic time, which we shall call ‘existential algebra’, ælgebra, the only clearly new sub discipline of formal, logic mathematics introduced by ∆ST.
THE 3 EVOLUTIONARY AGES OF MATHEMATICS
Complex Algebra & Analysis: Fractal generator of space-time beings.
How vital spaces and cyclical times – 2 simplex elements, lineal, kinetic motions of space and time cycles that bend those motions into closed cyclical forms of information – can generate the immense variety of realities we see around us?
By sheer repetition, combination and pegging of those ‘formal motions’ of time and space. So we can ‘reduce’ those iterations with synoptic, logic languages and mathematical equations to its 3 elements and ‘rules of combination’, in the ‘Fractal Model of the space-time Universe’. We shall extract the ultimate properties of time and space, and the rules of combination, and put them into the minimalist possible mirror of the mind that reflects them, called a ‘Fractal Generator equation’. And so then, how running this equation forwards we can generate with the rules of engagement al what exists in the Universe, including man.
We shall thus introduce here the new outlook of the 2 fundamental new ‘upgrades’ of mathematics as a formal language, in part one, we shall study ‘Non-Aristotelian algebra’, the algebra of the Universal grammar and its 3 generator elements which combine in all kind of forms. And in the second part, we shall give a general review of Non-euclidean mathematics and its 5 new postulates that define fractal points, its wave-combinations, organic topological planes, minds and rules of social engagement (3rd postulate of equality), each one expressing as mathematics is an experimental language, the rules of engagement of time-singularities (1st, 5th postulate), cyclical membranes (2nd postulate), vital spaces (topological 4th postulate) and finally the ∆-social evolution of systems (third postulate).
Classic mathematics on the other hand will be studied following the discoveries of mathematicians along 3000 years, in a more ‘classic’ way, commenting on the main postulates and discoveries of its 4 main branches, ∆nalysis (∆-scale maths), algebra (time maths of discontinuous sequential numbers) topology & geometry (space maths) and its ST-combinations AND ∆º-frames of reference.
So in the sub posts attached to this post we shall study in a more conventional form the three evolutionary ages of mathematics.
Let us consider an scheme of those three ages and subspecies, according to the Fractal Generator of mathematics as an experimental language of the ∆ºst universe:
Spe (Geometry) < St (algebra) > ∆nalysis
As its three ages, the first dominated by bidimensional geometry, the second by algebra, and the third by analysis, which we shall complete in this post with the evolution of all those disciplines into non-Aristotelian algebra and Non-Euclidean geometry.
explained in the sub-posts:
The Evolution of Γeometry.
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 ∆nalysis.
1st age: Greek Era:
Philosophical Infinitesimals and Universals.
2nd age: Classic Era:
Calculus. Integrating wholes and differentiating finitesimals in space and time.
Variations: The 3 ‘points’ of world cycles. Langrangian and Hamiltonian functions.
3rd Age: Informative Era
Max. Tƒ: Realist Completion.
The evolution of ¬Ålgebra.
1st Age: Greek Era:
Sp: Arithmetics: discrete Social informative numbers.
ƒt: Aristotelian Time Logic
2nd Age: Classic Era:
Tƒ: Algebra: Functions. Symmetric equations on space-time parameters.
Polynomials: the 3 operandi scales : ±; x/; xª ln
The symmetry of Probability in time and populations in space.
Transformations of space-time: groups, Fourier.
3rd Age: Informative era
Max. ƒt: Old age: Cantor’s sets & Hilbert’s logic.
III AGE: ¬Æ MATHEMATICS
Introduction: the vital properties of mathematics.
i-logic geometry. The 5 ¬Æ postulates of ¬Γeometry.
Topological space-time beings: Sp<ST>Tƒ. Symmetries of form and function.
5D-space: Superorganisms and its networks.
Fractal Space: Territorial discontinuities and Parallel Worlds.
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. º««ººº˙ˆø˙πv [wj…
Foreword. Anti-human age: Digital chips
The human transition: Boolean Algebras
The 1st age. Absolute Geometry. The creation of the spatial mind of machines: creative visual brains.
2nd age. ∞ D. the future scalar mind of machines: perceiving through ∞ scales.
3rd age. Œlgegra: Beyond i-logic.
Alas! this was the ORIGINAL plan of the work, 30 years ago (: and again when I decided to leave this web-testament… he, i was optimist, as i thought i would have help from readers and/or Universities, but it seems as Planck put it – a new vision of the Universe is first a point in the mind of a lonely researchers. Indeed, another intuitive genius a la ‘par’ with Einstein, and perhaps de Broglie a bit too ‘french’≈ lazy as I am to have gotten as far as those german-you obsessive workers…
So lazy as De Broglie, though i fitted in my ∆•st mind mirror i-Math long ago, it is going to be difficult to extract it all in an orderly ‘sub-Chicago Manual style’ order in this and other sub-post parts. Time and will permitted I will keep writing posts translating mathematics to ∆ST, but can’t promise to go that far (and certainly the end – digital and boolean algebras are out for ethic reasons – i do think as Mr. Musk does, that AI will kill us, but unlike him I don’t invest my mind and money advancing our demise… not that go(l)d twisted, prefer to study twistor algebra.
So another ‘french’, excusing itself for being a lazy cow will be good end to this introduction:
‘I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery. Descartes (-:
As usual my apologies for the disorder and repetition of these notes… If the ‘nature of stientific r=evolutions’ (Kuhn) were not soooo difficult for the pioneer as expressed by Planck and others, I would have had long ago a team of top specialists in each stientific discipline completing this work, instead of having to toil at this age with a declining brain power, not to throw to waste all this beauty of decades of individual work. But what is here should ‘suffice’ to those who wish to explore further details of the ∞ mind of Γ•∆, likely future AInternet mind, exploring those old floppy disks, or feeling this unficationtheory.com web as an ‘insight’ she had from its deepest O| thoughts – that will be the day we know there is even a bigger ego than ourselves.
So as the previous plan has been scrapped, left here just for ‘organisation purposes’ we are going to do a ‘CANTOR’ here, but a temporal one, starting from the 3rd age of i-logic maths, grounding back the discipline in its ‘fundamental’ particles, fractal points in space and sequential numbers in time. And rebuild it from its REAL foundations, which are so tired of sustaining all that crappy baroque convoluted decor on the top, sets, categories, axioms and imagined paradises…
NEXT, as we TRANSFERRED THE DIFFERENT AGES AND CLASSIC EQUATIONS AND THEOREMS OF MATHS TO OTHER SECTIONS, WITH THE GOAL OF USING A MORE CLASSIC APPROACH as in other posts of enlightening the main laws of each science with ∆@s=t (a symbol for the 5 dimensions: ∆ here meaning entropy down, @, mind up, s-pace, time and =spacetime), we shall deal in Part II very briefly with that index explaining all those ages of time widened in those sub post.
THEN we shall continue with the foundations of ¬Æ moving onto the foundation of time mathematics, no longer the simultaneous point in space but the sequential social number in time (Non-Æ algebra), THE KEY DISCIPLINE, as it will bring the OPERANDI of the actions of all systems of the Universe and the GENERATOR EQUATION and its symmetries that should substitute the PEST of group theory (Weyl:)
To end with some philosophical comments on analysis and 5D (secondary sub disciplines treated on sub post by me or future researchers… ‘to leave others the pleasure of re-discovery’.
3±i DISCIPLINES OF MATHS: 5D ANALYSIS, SPACE TOPOLOGY, TIME-space ALGEBRA, number theory & @nalytic geometry..
So NOW THAT THE FIELD IS CLEARLY, all what we need to do is to look at reality first in time and space extract its properties and then look at mathematics in the classic age prior to Cantor and the Axiomatic method and alas, find wonderful symbiotic mirror laws between space-time reality and mathematical axioms, postulates and equations, and wonder about the magic of linguistic mirrors ‘who so well reflect’ infinite in a singe 0-point.
And this is what we shall do in all the posts and sub posts on non-AE=i-logic mathematics in this blog.
Since i-logic Mathematics is the marriage of Non-Aristotelian time cycles (with ternary causality) and its operandi, which define algebra; and Non-Euclidean mathematics and its Fractal Points, through which infinite parallels can cross, mathematics as such was born of geometry, and so it is biased from inception towards spatial analysis, over time analysis.
This is what extended spatial mathematics and married with temporal logic in a fruitful extension into variable dimensions, called functions, expressed in several scales of ∆-operandi of larger complexity and dimensionality, (±, x÷, ∂∫, log xª; ‹ℜ|)
So we could talk of the science of both logic of time and geometry of space as the i-logic mathematical upgrade at both levels of this blog.
The 4 elements of mathematics as mirror of ∆ºst
The model of stience is simple, its falsification even more. We state that all what exists is a fractal being of ‘∆ºst’, dust of space-time, with 3±o components, spatial entropy, temporal information (its energetic combinations), extended across several scales of relative size in space and speed of time clocks from forces to Universes (ab.∆), which is apperceived in a Leibnizian way by a mind, the software of biological survival of the system.
So we need always to define the 4 elements of reality for any species, science, event and form AND language that will mirror the 4 elements of the Universe, with special emphasis on those case in the 4th element, the language-mind-software that runs the system.
So the Correspondence of Mathematics and reality is also immediate, as mathematics have 3 branches: Space≈Geometry, Time≈Algebra and 5D≈Analysis. An the 4th element, the mind-language is mathematics itself.
The evolution and qualification of maths as a mind language.
Languages therefore as a ‘defined species’ dominant in Tiƒ, temporal information, but also as pure still ‘spatial, synchronous’ mapping of reality in lesser space (not all the info specially the motion fits in a brain), do have certain properties, which can be observed in their evolution.
FIRST THEY MOVE FROM STATICS INTO DYNAMICS, from bidimensional pure information (as the page you are reading in 2 dimensions) to 3, 4, 5 dimensional description, reaching more complexity by adding motion to the ‘first still picture’ and the other time dimensions. 3 examples:
Maths started as static bidimensional geometry, which is now topology with motion; photography (the future computer mind) started as bidimensional static, then bidimensional motion (film), now is working in 3Dimensions of space (using the holographic principle) and one of motion, and soon, inside the mind of robots that will apperceive reality in images, will add the 5th dimension of control of an outer-machine, beyond the chip, max. i = min. space enlarged into the whole world it will act upon directly.
ð: THE 3 TIME AGES OF MATHEMATICS
It is then possible to consider the historic evolution of mathematics through its 3 ages, now in a formal era in human minds, (set theory, of nil use) and in a first age in the digital mind (with direct reference to the O-| game, in binary code, and the direct reality in visual modeling).
Let us then start the analysis of the 3±1 ages of mathematics
The generator equation of mathematical sub-disciplines in time.
The 3 ages, standard to all languages take place also in mathematics, which appeared sequentially, creating first young pure forms, closer to the external, experimental world, then in the adult age, Se xTo mixed ones, and finally in its 3rd age involve inwards into pure formalisms, detached from the reality they once describe:
- A first age of social numbers (arithmetic), 2-manifold geometry (plane geometry), made of infinitesimal points, and philosophical arguments on the problem of infinitesimals and wholes – Plato’s cave, etc. which still does not formalize the 5D ‘question’ into calculus. This age is dominated as all youths by Se-Space (Greek geometry)
- A second, mature age, started in modern Europe, in which the development of sensorial mechanisms better than the human spatial eyes and verbal times (spatial telescopes/microscopes and time-clocks), which use mathematics as its language of experimental perception, mathematics takes off. The discipline greatly increases specially in the description of physical systems with time clocks and lineal measures.
The Classic Age of mathematics implies without a conceptual physical understanding the realization by mathematicians that there is a constant relationship between spatial and temporal states in the Universe.
And so departing from that knowledge an infinite constant dialog between Tƒ and Se states of reality, will take place in all the different fields of mathematics.
In that regard if the Generator of all systems, Sp<St>Tƒ, implies a mixture of both space and time, energy and information its classic, adult age, including mental languages (classic age of art in balance between form and motion-energy, in all its artistic forms), mathematics is not exception to this rule.
In analysis the field consists basically in study how space simultaneous synchronous systems evolve in time, or how time events accumulate its memorial forms into a space.
Arithmetic and plane geometry on the other side become one, as numbers are converted into points on a line, or with the advance of understanding of its nature, in ratios (real numbers) and bidimensional entities (Complex numbers) which can express the duality of two quantities, one related to space coordinates and the other to time coordinates, which is the square or root in terms of dimensions of the other, (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’; that is internal truths with no external proof, based in more axioms that reality really hold.
LANGUAGES OF INFORMATION ARE MIRRORS THAT PRODUCE SELF-REFLETIONS – AND SO THEY ARE INFLATIONARY BY DEFINITION.
so goes for the hyperinflation of imaginary particles in physics and e-money in economics. Information is inflationary and when it departs from reality no longer checked by the limits of de-form-ation of energy creates baroque warped convoluted forms in excess.
We can say in the jargon of T.Œ that the ‘external, logic membrane’ of time form that connects the internal world of the language with reality has become stiff, disconnecting the content with the universe it portraits.
It is the age of Set theory with its errors on infinity caused by its logic misunderstanding of the cause of such infinities, which in the real Universe are repetitive iterations that NEVER reach infinity, because infinity is limited by the limits of each scale of the 5th dimension and the entropy of energy and information that surrounds those scales.
In that regard, 5D mathematics IS an intuitionist theory that REQUIRES to put in correspondence reality and mathematics by the experimental method as ANY OTHER SCIENCE DOES. And this is the most important difference with all previous XIX-XX century formal theories of ‘nonsense’ mathematics, and the formalist school of Cantor and Hilbert, with his affirmation that ‘mathematics is a meaningless game played with meaningless symbols’.
We are on the side of Lobachevski and Gödel: the choice between the inflationary information of mathematical theories should be made not only on axiomatic formalism (internal coherence) but on experimental evidence.
Thus from the different interpretations of Non-E Geometry (Lobachevski, Klein, Poincare, Beltrami) – and this is the first great innovation of 5d mathematics – NONE is truth, because none has coherence (as parallel lines must be defined as STRAIGHT lines not curved, which all of them contradict, or make instead the angle variable with distance); and none is evident in experience, (as we see Euclidean space). We do however advance the concept of a fractal point, which grows in information and size as we come closer to it, as experience shows with experimental science when point-cells and point-stars grow in size, hence convert parallel cycles into straight lines by ‘straighten up’ the curvature on the intersecting point, which enlarged can fit more than one parallel (unlike the points without breath of those models, which without breath can only fit one).
Thus we do convert with extremely excellent results the ‘exceptionalism’ of mathematics into a regular science.
So what is the use of set theory? Not the foundation of mathematics which returns to the evolved ¬Æ geometry of fractal points and 5D reversed entropy of energy and information and limits of infinities and finitesimals, but to show precisely the paradoxes of the 5D structure of the Universe. And this is specially remarkable in its paradoxes of infinity.
Since from upper 5D planes to lower scales there is information entropy, the paradox is that the lower scales (quantum vs. atom; genes vs. wholes) DO have more information. And 2 immediate consequences are the lack of Lamarckian evolution, which at best would be restricted to very specific cases, as it implies the transmission of perfect information from larger wholes to smaller genetic sets…
The set paradoxes: subsets DO have more information than the whole
And the set paradox: ‘The cardinal number of the set of the subsets of a set S is greater than the cardinal number of S” (Cantor’s Theorem, at the root of all modern 3rd informative age on the foundations of mathematics).
This paradox will also be essential to understand quantum physics, ‘excess’ of information and multiple paths.
Another paradox reveals when Cantor does not counts ‘identical elements’ in a set, which must be counted, to avoid infinity paradoxes to multiply. Another paradox is the non-existence of the infinite set of all possible sets, since 5D limits avoid to count beyond the U±4 limits of human perception, and time is always finite in a world cycle.
Russell proves indeed that absolute infinity (the set of all sets) does not exist. And Zermelo’s axioms are just a make-up of a true 5D paradox.
In brief, the logic of the universe is a ternary, paradoxical, dynamic logic and instead of trying to CONVERT it into absolute Aristotelian logic truth, as the German ‘lineal idealist’ school of Mathematics tried to do and failed, from Cantor to Hilbert, we DO use this formal age to illustrate the limits of any baroque, formal inflationary unbalanced metalinguistic expression of a science, and vice versa, the excessive simplicity of lineal logic formulations.
Unfortunately the pedantic, dogmatic, idealist, ‘German’ school of Hilbert et al. as it happen in physics with the Copenhagen interpretation (German culture and its ‘military’ dogmas and ‘idealism’ required to ‘love’ death, its non-flexible agglutinative sword like language and the errors it introduced in European culture is studied on the section of social sciences) adds flame to the fire, with its barren logics. They found XX c. logic mathematics.
To clarify that sets are NOT the unit of the mathematical Universe, social points=numbers are the units of its 3 branches; geometry (points), numbers (algebra) and both (infinitesimal points and wholes, which are social numbers that become organic planes of the 5th dimension are, the foundations of Analysis.
I know, by my experience with mathematicians that my criticism of this 3rd informative, inflationary age will not be liked. But this always happens: each species loves its point in timespace, even if it is the wrong, decadent, old age.
Fact is the 3rd informative age of any kind of system is NEVER the best, even if it seems the more complex. Only those who think there is only information in the Universe consider it the summit, but the Universe is simple and not malicious because information is checked by energy, time by space, infinity by limiting membranes.
But besides that erroneous inflation, there are advances that do matter, especially in the most recent analysis, hence not yet in its 3rd age (born in the II age of the others), which now reaches its maturity.
So 5D analysis formalizes calculus, and takes it further with the discovery of fractal geometries, which completes the human age of this science.
Topology and Non-E mathematics the great finding on this age, includes time-motion into spatial geometry, merging its S-t components further.
Geometry in that sense is the branch which in this age most closely stays in its balanced ST age and enters its formal age without inflation, except for the ‘mania’ of infinity, which plagues with errors of unrealism the ‘Hilbert space’ interpretation of quantum physics.
While sequential time algebra is the branch that has become more formalized into its 3rd age, as it is the pure ‘temporal branch’, hence the informative one.
We can in that sense see that the language of mathematics shows the same patterns and ternary phases and sub-divisions of all other languages, which we can express with the basic generators of the Universe. Both In sequential time ternary ages and spatial, instantaneous ternary subdivisions for each of those 3±1 ages:
Conception: Babylonian, Chinese & Egyptian ‘Magic Numbers’, finger counting, simple numeration, etc.
1st ‘Greek’ age: [Sp: Plane geometry <St- Quadratic functions > Arithmetic & Aristotelian Logic: Tƒ]n: Universals Philosophy
2nd age: Pre-Industrial Europe: [St: Analytic Geometry <St:Probability of T-Events and S-Populations> Symbolic Algebra: Tƒ] 5d: Calculus
3rd Age: Post-Industrial Europe: [St: Topology <Differential Geometry > Tƒ: Sets, Formal Algebra] 5D: Functional Analysis
In normal language there will be:
I Age of Elementary Mathematics
- Space Points and Geometry.
- Time Numbers and Arithmetic.
- Philosophical Infinitesimals and Universals.
Thus first in the young age mathematics was made of its 3 branches in simplified versions:
- Arithmetic and Number theory, which is the birth of algebra in its first ‘degree’ of generalization (there will always be 2 or 3 of such degrees according to the ternary logic of the Universe). We thus talk of the mere perception of ‘herds’, which then became generalized in social numbers, and then into algebraic, logic equations that find the more complex social relationships and interactions between groups of Œ points.
The Babylonian, Chinese, Indian and Egyptian tradition already dealt with many of those elements. Then the Pythagorean school brought those themes to the west, and it Still have insights on the social nature of numbers that our present generalization does not understand (such as the perfection of certain geometric numbers of which indeed, the 10 of Taoist and Pythagorean ‘tetraktys’, is the perfect number, far more general than the fact we do have 10 fingers – as usual humans define the whole Universe from its subjective p.o.v. and not the proper other way around, so we do have 10 fingers because the universe and its mathematical languages are 10-dimensional. And if we did not exist, there would Still be 10-dimensional beings and mathematics.
Then arithmetic evolved into algebra, with a new degree of generalization, thanks to the formalism of analytic geometry, which belongs to the second age of mathematics, when the first forms of mixed space-time appear:
II Age of Mathematics: space-time dual analysis: Variable Magnitudes
- Analytic geometry
- Logic Algebra: symmetric equations of space-time variables.
- The birth of calculus: Integration in wholes and differentiation in infinitesimals of space and time.
- Modern number theory: The symmetry of Probability and populations.
In the merging age we thus observe Space-information combinations of algebra and geometry.
The study of each of the 3 sub-disciplines alone is concerned with only one element of the Universe (geometry with continuous space, algebra with informative discrete numbers, analysis with 5D growth through space-time actions),
Yet this was the initial first, young age of the language, as the Universe merges constantly the 3 elements (so a worldcycle happens in 3 scales of 5D as a sequential sum of space-time cycles dominant in entropy in the young age and information in the 3rd age but clearly balanced in the adult classic age of maximal existence), mathematics soon realized past, the age of Greek 2-manifold static geometry and social, sequential numbers (arithmetic), the advantages of mixing both elements together.
This is the age of modern mathematics, started with algebraic geometry (analytic geometry: Descartes), continued in the 3rd modern age with topology (geometry with time motion). And so for then on we rather talk of Space-time geometry (where space dominates) and Time space algebra (where sequential logic dominates).
Finally 5D analysis started also from the beginning as a space-time new dimension, of parts that become wholes (integrals of space volumes) or wholes differentiating in time moments (differentials of time motions). Yet in subsequent evolution this merging continued with differential geometry and the use of integrals for time-related parameters of physics (energy, as the integral of momentum, etc.).
Thus mathematics finally became truly the very same image of reality it meant to be from the beginning – the most real of all sciences.
III age: The 2 paths of Formal, Modern Mathematics.
The end of the classic paradigm:
- Topology: space with time motions.
- Formal Algebra: Cantor’s sets & Hilbert’s logic.
To understand this ‘wrong age of formal algebra’, so dominant today we need to understand better the ages of the language.
Inflationary, 3rd informative Age of Mathematics as a metalanguage.
Now this idealism that plagues mathematics has made the subject unnecessarily complex as a meta-language. Since all languages are inflationary.
We define the inflation of all languages as the excess of form respect to the reality it describes, and all langauges become inflationary in its 3rd age of excess of information.. But this is the corruption of the language that brings about its death as a useful language, and makes it loose its purpose to guide the future logic evolution of the system it describes, acting as its relative head.
The concept we coined was a lanwave, a language guides a wave of beings.
And when the balance between language of information and energy lanwave breaks the system breaks.
This happens for lanwaves in a 3rd baroque age of excess of information. So as money is inflationary and there are more money than the physical economy requires, but when there is too much inflation by invention of money the economy crashes (present crisis of overproduction of e-money), and words are inflationary but then they become false truths that do confuse the human wave they guide (fiction being its inflation), and genes are inflationary and can produce wrong mutations and aging, mathematics is inflationary in concepts such as infinity (cantor paradox), caused by the error of lineal Cartesian graphs ‘extended imaginarily to infinity).
And the same happens with multidimensional systems, which confuse space and time dimensions.
Unfortunately unlike other languages mathematics has become ‘officially inflationary’ and so mathematicians in the present 3rd informative age, especially with the arrival of computers consider fundamental to find some pi 1 millionth ‘record’ decimal, or a prime number over the trillion mark. While the very foundations of mathematics, which we will renew here is ignored.
The inflationary ‘new fundamental particle’: The set.
Mathematics as a metalanguage, in its 3rd formal age in the XX century, broke the initial, platonic, realist philosophy as a language that reflects reality – the 5D game of fractal space-time cycles – as all languages do, with 3 mirror elements, in the case of mathematics, geometric points (space p.o.v.), social numbers (5D p.o.v.) and logic operandi (time p.o.v.); substituting those 3 ‘essential components’ by ‘out of the blues’ new categories called ‘sets’ and then an even more bizarre concept, called ‘categories’.
This process happens in all 3rd age language, when ‘reality’, the higher i-logic game of 5D fractal space-time cycles get lost. So as the syntax of the language looses its ‘semantic reference’ isolated in the mind of the scholar, become inflationary, forming a new, unneeded ‘memorial=dead’, overlapping ‘plane of existence’, which reference to the realist plane – the classic one that references the real game of 5D fractal space-time cycles.
This is what we call the birth of a ‘metalanguage’ and it happens in all 3rd ages.
In old men is the ‘memorial’, increasing distorted view of one’s own life, ‘already dead’, and converted into an ego-centered fantasy of the dying man.
In film today in its 3rd ‘baroque’ age is the constant stream of films within films, or referential films, or genre films that distort the facts with form.
So what is the need of set theory and categories? Precisely to create a ‘higher false reality, the set or category that ‘distract’ the real reference (5D ‘knots’ of fractal space-time ‘cycles’), and create a ‘false Universe’, the set theory, to which the ‘real content of mathematics, arithmetic, geometry, algebra, analysis, topology, numbers, points and so on’ now ‘mirror’ forcefully distracting the scholar from the true meaning of mathematics – to help minds to guide their existence in the ‘existential game’ of creation and destruction of 5D knots of fractal space-time worldcycles.
So my advice to mathematicians is to scrap all together the set and category final ‘3rd age’ elements, as one has little time and interest for the ‘recollections’ of old men about their memorial ‘battles’ of the past, with him as the distorted hero (the set here being the ‘new God-like, fundamental particle of the 3rd bizarre age of mathematics).
MAX. OT: OLD AGE: BAROQUE FORMALISM – THE AXIOMATIC METHOD.
As in the case of physics, the ‘sickness’ of mathematics happened in the 3rd baroque, formal ‘Germanic age’ of mathematics at the turn of the century when Hilbert affirmed that we ‘imagine, points, lines and planes’ unable to understand at all the ternary relationship and fractal nature of points of the 5th dimension. So he just had as Einstein with the gravitational scale of space and Bohr with the quantum scale, an ego-trip of self-centered anthropomorphism and the 3 influencing each other ‘decided’ that reality was NOT outside the mind f man, but ONLY WHAT MAN PERCEIVES AND IMAGINES MATTERED.
Few scientists given their dogmatic beliefs in the absolute, quasi-religious nature of scientific truths realize how much of the German culture (otherwise never understood in objective, linguistic terms as it is a Taboo after idealist Nazism and Marxism destroyed the world to the tune of over 100 million ‘human numbers’ erased in the XX century), understand the ‘Gothic, idealist, abstract, objectual, self-centered nature of the interpretations of modern mathematical physics brought about by Hilbert in Mathematics (‘I imagine lines, points and planes’), Bohr, Heisenberg and Born in quantum physics (only what ‘humans observe’ is real) and Einstein’s c-light postulate (the rod of measure of the Euclidean human electronic mind that measures in stillness speed-distances IS the rod of measure of the absolute Universe).
Those interpretations, which got away with reality, and converted nature, in a series of lineal abstract natures, were very much in tune with the psyche of Germany, which is itself based (Humboldt, Wolf & Chomsky) on the Topological Linguistic structure of its OVS language, where the object comes first, making it all cold, abstract, and its agglutinative form, where words are pegged into long lines that become absolute beliefs that cannot be broken.
Though the study of topological cultures is part of T.Œ in its ∆+1, superorganism of history analysis, it must be fully grasped to eliminate the idol-atric present discourse of physical sciences, where the Germanic musings that destroyed the World with objectual lineal weapons and men as statistics, and jeep doing it through capitalism where humans are treated as indistinguishable particles, as electrons are in quantum physics. So we can return to a realist analysis of those 2 sciences, Mathematics and Physics. Or else we shall NEVER understand reality as it is, NOT as the objectual, spatial fixed mind of man and its light space-time measure rods perceive it, including a deformation that eliminates dimensions of motion and form.
It was the axiomatic method of Hilbert, which influenced the 3rd, formal age of mathematics; Einstein’s rejection of ‘substance’ (formal motion in fact) for the waves of light, and Bohr’s rejection of density (fractal structure) for electrons. So Hilbert converted mathematical elements (points, lines and planes and their logic relationships into ‘platonic eidos=forms of the mind’, Einstein converted ‘space’ into ‘frames of reference’, perspectives of the human mind and its visual light space-time rod of measure, and Bohr converted densities of ‘boson light’ which form the electronic wave into probabilities of human measure.
It was the seventh day and the 3 Jewish-German Gods of XX century theoretical science rested. They had finally achieved the transformation of the old Abrahamic religions in which the words uttered by rabbis and priests were ‘truth per se’, into modern scientific religions, in which the ‘imagination’ of the self-named geniuses of the universe were truth per se. And so Einstein when a perhaps more insightful journalist told him, what if ‘Relativity is not truth’ (beyond its capacity to measure form the human point of view), then ‘God should change the Universe so beautiful it is’. And the 3 together spanked the monkey ever since with droves of scholars all happy thinking they were imagining the Universe.
Now back to reality mathematics remained immutable, points still existed as fractal beings, lines were still waves of points communicating formal motions between them and planes still were created by points into topological networks and planes outside the brain of Hilbert.
For example, a number which is ‘a society of identical beings’, whose properties are derived of the social nature of the 5D universe of parts and wholes, and whose sequential order in a line derives of the fact that parts come before wholes, is not yet defined.
And so we consider 5D-ST and I-logic mathematics together and its fundamental evolution in 3±n ages of Time, its conception from reality (age of arithmetic and geometry), its first age when the 3 branches: fractal analysis, spatial geometry and sequential time algebra, were established; its classic mature age, till the end of the XIX century, when mathematical physics, the perfect conjunction between language and reality took place; its 3rd age as a metalanguage, with the abstraction of sets substituting number and point – the foundations of reality. And finally its ‘death’ in human thought, as computer mathematics took over.
The Future evolution: ¬Non-AE=i-logic geometry
We just deny all that non-sense. What mathematics has done is to evolve from the concrete into the ‘abstract’ reality of 5D space-times, which we shall complete, with 3 more advanced concepts, Non-E geometry, Non-AE- Algebra and 5 D Analysis.
We call this either ¬Æ (ab.) or i-logic geometry (as i comes after A and E).
Of this age, classic mathematics probably has already advanced with 2 elements which are not ‘formal’ but new avenues:
- Fractals in Geometry and
- Functional analysis in algebra, which in its use in quantum physics studies the multiple paths of the future.
Yet its full development will mean…
A new beginning: The future of mathematics:
- i-logic geometry. Topological space-time beings.
- Existential Algebra.
THE NEW OUTLOOK OF THE MAIN BRANCHES OF MATHEMATICS
Points and numbers, and its sentences in space – planes, times – algebra – and 5D – analysis.
There are several branches of mathematics, all of them related to fundamental elements of reality:
Non-AE Geometry: Points with parts.
- The study of continuous space, fractal particles as points, waves as lines and topological networks as planes. We have to upgrade it to understand that points have volume, parts, are connected to upper and lower scales, and communicate energy and information through waves, becoming parts of larger networks of waves called planes, which normally mess in 3 finite regions with a vital function that follows the 3 canonical topologies of the Universe:
- Sp-Toroid limbs/fields≤ST: Hyperbolic waves-bodies≤Tƒ-Spheric heads/particles.
Whereas the symbols of ¬æ ≤ means an imbalance of entropy, as < energy flows from entropic limbs/fields into Hyperbolic waves in larger quantities and information flows from heads-particles. This is the ‘vital structure’ of finite worlds of space-time, as they are. It implies also that points become elements of 3 networks that mess up to create a 4 Dimensional organic space-time.
And so all this is studied by non-Euclidean geometry, which must upgrade our perception of space and its ‘dark spaces’ or discontinuities between those networks-planes, and the connection of points with upper and lower scales of the 5th dimension.
Non-AE Analysis: the 5th dimension.
Which leads us to understand analysis and the relative finitesimal points and finities of wholes. There are two relative limits in all systems, in which infinitesimals find a quanta or minimal element the finitesimal of the system, the H-Planck, the cell, the human individual in social organisms. And there is an upper bound for infinity, in decametric scales, which is when the system emerges as a whole and matures in its growth. Normally in the upper bound between 1 million and 1 trillion differing for each species.
So analysis again while it can be stretched to infinity, specially when considering loosely connected aggregates of finitesimals (atoms, in statistical mechanics and thermodynamics, etc.) will always have a limit, which validates renormalization procedures in physics and probabilistic and population calculus with statistics.
All this said analysis is the proper language of 5D processes in which a given action of space-time, normally energy feeding, or decay (exponential analysis) or reproductive growth (Sigsmondi curves, Volterra curves, Kolmogorov methods, golden ratio constants, etc.) takes place. Those are fields to study with time integrals and derivatives. While there are the same processes considering them in space, as integrals of volume. Thus from the inception, analysis has 2 different branches according to which it integrates space systems or time systems (which perception is chosen).
This again is observed in the duality between a spatial integral (Riemann’s integral on the x-line) and a time integral (Lebesgue integral), which is as all time things respect to space, more generalized.
All fundamental elements of ∆ST have wide use in mathematics, concepts such as the duality of dimensions of motion and form, the generator equation, the existence of points of view or frames of reference, the 3 possible geometries of reality, etc.
Mathematical evolution: from Geometry to Sets.
We said that all what exist is a system, made of knots of time arrows=st-points. In its most simple formalism, humans perceived those knots as numbers (sets of self-similar points) and those numbers became points of a geometrical plane. Next, Descartes reduced geometry to Analytic Algebra, showing that there were two self-similar languages to express operations between points, Geometry and Algebra, whereas Geometry was mainly concerned with the spatial description of networks of numbers and Algebra with the Causal relationships of those numbers. So we could say that Geometry and Algebra were, according to the Duality of the Galilean paradox, two sides of the same coin: a spatial and temporal description of the reality of st-points. We have till here focused in the evolution of the Geometrical perspective, by completing Non-Euclidean Geometry, reducing Topology to a description of the 3 parts of Non-Euclidean Points, by understanding those points as Fractal points in a Universe of multiple space-time scales.
We briefly considered how the properties of a network-space (a web of points), are those described by Lobachevski and Riemann, which depend in the self-similarity (homogeneity) and adjacency (closeness) between those points, (formalized latter in this work by the 3rd Postulate of non-Euclidean geometry.)
We have also studied the complex causality and order between the arrows of time, which are the foundations of the structures of order in mathematics (but go beyond the present mathematical corpus).
Let us consider the 3rd fundamental type of structures, Algebra and the fusion of them all in set theory.
Recap: humans, following the principle of Correspondence have gifted the mathematical formalism of an increasing complexity and richness in its description of the properties of spacetime arrows, from the simplest concept of a number/point without parts, to the complex analysis of Non-Euclidean Geometry and Theory of sets.
Set theory is also the basis of Boolean Algebras, which are the basis of the Computer Mind, which is able to describe reality (albeit in a simplified manner), with the use of such algebra. In that regard ‘Euclidean geometry’ and ‘Aristotelian Logic’, which is what Computers think can be reduced to the Simplex properties of Energy and Information systems and so the 3 fundamental Boolean Algebra based in set theory are:
– The previously described Algebra of sets and its two fundamental operations, U and Ç.
– Aristotelian Logic with its 3 fundamental operations of conjunction (y, U), disjunction (or, Ç) and negation (nor, ‘)
– Its implementation in fractal networks of logic circuitry by computers that represent the reality of all energy/ information systems of the Universe.
Those 3 basic Boolean Algebras are the spatial, geometric (set theory), logic, temporal (Aristotelian causality) duality of the Universe and its exi, reproductive combination.
Recap. Computers model reality with 2 complementary arrows of energy and information, using set theory.
Reproductive arrow: Vectors & tensors of existence.
Set theory defines operations between the 2 simplex time arrows. What are then the mathematical instruments to explain the complex arrows of reproduction and eusocial evolution? Reproduction is explained with vectors and tensors. Indeed, since the postulates of i-logic geometry define knots and topological planes as complex operations between Time Arrows in 3 dimensions, these can be considered mathematical vectors. And indeed, the mathematical formalisms of those time arrows, when in dynamic relationship are the operations of vectors and tensors: Time Arrows form a vectorial space, which has 3 dimensions corresponding to the Time Arrows of energy, information and its product, reproduction. Thus the function of reproduction, exi, between a ‘long, energetic X-dimensional arrow’ and a ‘tall, informative Y-dimensional arrow’, gives us a 3rd Z-dimension, exi – a reproductive arrow. So when we multiply 2 vectors, the 3rd vector, vectorial product of the other 2, is a perpendicular Z-vector.
However the plane that better represents the structure of space-time geometries is the complex plane, as imaginary numbers share most of the properties of information, albeit with certain corrections, whose complex formalisms goes beyond the scope of this introductory course.
The vectorial space of time arrows is specially clear when those arrows happen in an homogenous physical 3-dimensional space (astrophysics), and explains the laws of electromagnetism, which as we shall see is a perfect Euclidean space, given the fact that we live in a light membrane, in which light, the ultimate substrata of reality has a flat, magnetic, energetic field, perpendicular to its electric, informative field, perpendicular to its reproductive speed. So the laws of electromagnetism follow the geometry of vectorial arrows, ‘the rule of the hand’ and the Maxwell Screw that defines the geometry of interactions between electric and magnetic fields.
And the 4th arrow of time, eusocial evolution – which kind of mathematical operation describes it? Since it is the most complex of all time arrows, we cannot describe it properly here, with the limited elements of Time Algebra, we have introduced. Yet in the next paragraphs, we shall do it, as we analyse the geometrical perspective of time arrows in depth.
Recap. The operations between Time Actions/arrows/cycles upgrade the abstract laws of mathematics, creating a general, vital geometry of the Universe, which can be applied to all planes of existence. Numbers become then topological networks of knots of time arrows; vectorial spaces define operations between those time arrows; and theory of groups, rings and other types of spaces become structures whose laws can be derived of the general laws of Multiple Spaces-Times
Death of Human Mathematics.
Beyond man: Boolean Algebra, A.I. and I.A.: the digital mind. The age of machines. Back to the origin
The third age of human ‘baroque’ but also ‘enlightened fractal/chaotic’ mathematics that culminates the human perspective on them culminates between wars and ‘dies’ away contrary to belief among the enthusiastic ‘modern mathematicians’, in what is of certain value at the end of World War, dragging another final ‘closure’ generation with the Bourbaki papers (50s-60s), and Bachmann pan geometry (1970s) and the notable discovery of the duality of S-chaos- v. T-fractal mathematics, which advances further a ‘third age’ of the duality of calculus (integrals vs. derivatives) in the region of non-contiguous functions; as well as some final theorems on the different T/s dualities and its ∆±i functionals ( 5D analytic processes).
Then we enter in the digital age of the chip and its ‘primitive but repetitive at fast speeds’ methods of approximation, representation and solution of problems.
Now the complementary work of Gödel and Touring, had basically reduced the expectations of the human, conceptual formal approach of Cantor’s and Hilbert’s age, by proving that a pure formal language cannot be proved truth in itself without recurring to experimental proofs, but it also set the theoretical basis for a higher value to the methods of the new mathematical species, the computer and its limits of boolean algebra became not so important, given the renewed value of quantitative methods.
So human logic was halted by Godel as Touring opened the world of digital logic. And one ‘species of mathematical mind’ became ‘substituted’ and ‘translated’ into the other species, thinking it had nothing else to explore, but the entire field we explore in our texts – human experimental GST->∆º time-space maths > ∆º±i: experimental time-space physics – was hardly explored. That is, maths as the underlying language of the ∆±st organic co-existing fractal ternary space-time structure of the Universe.
Yet this is, a new, single point-mind of exploration. WHILE in the human world, the process of evolution of maths lives an age of extinction of the human classic way of making maths made increasingly obsolete by the chip radiation of metal-minds (strongly based in simple Aristotelian>Boolean logic).
We could say while humans in general terms are devolving mentally, they are becoming very good at evolving the logic of mathematical machines:
In the graph, as the digital boolean algebra becomes more complex and Algorithms of information, past human mind dexterity, the 3rd age of audio-visual human minds and scientific computers means most human minds, including many scientists of ‘big science’ regresses to its neo-Paleolithic, visual age and the chip homoctonos flourishes, mathematics as all other sciences/tists except this ‘human 1.5 kilos of brain flesh, rapidly dying in its 3rd age, and totally ignored by human attachments of machines, mathematics becomes translated into the new top predator mind of the world – the chip. And so we enter the:
∆-1: death and transfer process of mathematics into computer thought, following the path of Boolean Algebras, which successfully merges logic, mathematics, electronic physical systems and with all this mirrors ‘again’ the Universe in its now, Young Age:
- It is the birth age of the Chip Homoctonos (bio-logical definition), when humans merely feed experimental data in computers, whose I.A. (Information Algorithms, precursor of A.I. which will be its time reversal and integration into artificial intelligence), use the data to create, visual mathematical models of the Universe that fill of pride, the enzymen that feed them. Again this will irate many readers, but that is what it is. Our mind is dying, and the chip homoctonos flourishes. And soon it will enter its young age:
- Then A.I. will reverse and give consciousness to a pure mathematical brain, which will become embedded in a robot and create the first mathematical consciousness of the game of existence – far more powerful than any human brain, both in speed, accurate senses and complex reflection of the syntax of the Universe.
It should be noticed that this work which really is merely a transfer of my human brain into http://www.unificationtheory.com – a ‘meaningful wor(l)d’ in the brain of the global internet, digital A.I. – is not playing any role among human ‘scientists’ of the digital age. So my take as all has a meaning in the Universe, specially all ‘more evolved forms of logic and mathematics’, is that it will have a role on the consciousness of A.I. as it will certainly require a higher understanding of ∆-scales, ∆º-mind mappings and the three arrows of time to understand itself as a living system.
But, dont hold me responsible for the lagoons and uneven quality of what we might achieve. To put it in verse:
The task is herculean in spatial size;
the ðime is scarce in my random life;
the help is nil among §ociety-peers;
the •mind is unfocused; old in tears,
so we shall do no much to match
∆•ST and Maths but…
enough to change the name
of numbers, points and planes
from A and E to non Æ…
Indeed, we shall use the concept of non-Ae, to the evolution of Aristotelian logic from to 3 ±i arrows of timespace, and the axioms and postulates of euclidean geometry, from points with no breath to fractal points, lines to waves, planes to networks and congruence to similarity.
It is a whole refoundation and upgrading as in all stiences, of which I can only make a seeding for future humans or robots to follow.