5D Non-Aristotelian, Non-Euclidean Mathematics: Vital Topologic Space-time Organisms

Authors: Luis sancho

We divide the study of Non-Euclidean, Non-Aristotelian 5D Mathematics in 3 parts, Space Geometry, Scalar Algebra & a brief introduction to the foundations of Time calculus. Logic and math are the 2 entangled stiences of spacetime laws. As such in a Universe made of space-time beings, contrary to belief they are the most experimental of all stiences. Mathematics is the main science of vital, scalar Space (represented by spatial points and scalar numbers), in mirror symmetry with the less developed Time focused science of ¡ logic that analyzes the 5 Time dimotions of reality, as humans use only 1 time arrow -entropy- but 'God the seer of time is of a logic higher than man's' Augustine. We dedicate 2 papers to maths main 2 subfields, S@-Geometry & ∆T-Algebra. In this one we upgrade Nº theory & geometry to show mathematics as a logic mirror of the Universe's pentalogic scalar structure made with scalar numbers, Non-E fractal points with inner dimensions and timespace S<≈>T operands that reflect the dynamic symmetries & stœps of its 5 spacetime dimotions. Ænthropic men instead justify math with an ego-trip of digital creationism: Only he & God speak the language, math, that creates reality -not the other way around, and try to prove its truths with an incomplete (Gödel) axiomatic method, as an ideal, perfect absolute 'truth' with NO correspondence with reality (sets as 'imagined' units of math). We shall do the opposite: departing from reality we construct a vital improved mirror of maths, where even the perceived irregularities of mathematics are experimental true symmetries of a vital dynamic Universe: i.e. irrational numbers are required NOT to close a vital pi-cycle and √2 triangle to allow openings into its lower decimal scales to absorb energy and information. So we shouldn't force 'idealist continuity' in a discontinuous Universe. i.e. 3 topologic geometries with motion suffice to mirror the 3 St, sT, ST combinations of an organism because we ARE spacetime'. i.e. numbers are indistinguishable social groups (polytopes) because 5D is 'social'; its Prime, T>S + odd, SB time arrow, into the higher pentalogic of the Universe made of 5 Dimensional motions of space-time (ab. Dimotions), entangled to create reality. Both sciences are immense in scope; but humans have reached a high degree of dexterity in the understanding of mathematics, so we shall study first the science of space in two volumes, this one dedicated to its experimental foundations, fundamental units, points of space and scalar numbers, its symmetry and Non-E Geometry, with a brief introduction to its most extensive Time Algebra. 5D mathematics thus ads to the axiomatic method an experimental view of the discipline as a mirror language of the 5Dimotions of space-time that create all the systems of the Universe, and mathematics reflects from multiple perspectives (sub-disciplines, operands, geometric postulates, pentalogic use of each of its elements, families of numbers, etc. etc.). Weenlarge the foundations of mathematics and illuminate beyond the present 'creationist beliefs' of mathematicians, as the language of God the meaning of its components, as mirrors of the 5 Dimotions and pentalogic, entangled structure of reality. Further more because 5D metric (SxT=K) implies that smaller systems (Min. S) have paradoxically more information (Max. T), as 'seeds' that develop its synoptic form through the immanent program of reality, the enormous synoptic power of mathematical elements, social, scalar numbers and operand makes it the main language of the smallest Timespace beings - particles and atoms, which likely create their local order through 'Existential algebra', the vital mathematical interpretation provided by 5D. Thus we first study the pentalogic of its 5 main sub disciplines, each one based in a pentalogic, slightly different view of the 5 Dimotions of reality: Geometry and its 5D Non-Euclidean fractal points of space; Algebra and its 5 operands expressing each of the 5 Dimotions of time; Number theory and its 5D families of scalar social numbers; self centred in the 5 D main frames of reference of bidimensional space, also corresponding with the 5 Dimotions (2D lineal=cylindrical, 5D Cartesian=flat, entropic, 1D Polar; 3D vectorial and 4D, complex planes), negated by 5D entropic inverse operands. We study in 2 volumes those amazing mirror symmetries between the pentalogic of the Universe and the pentalogic elements of mathematics in all its main sub disciplines. As both reality and its mathematical mirrors are constructed with the 5 dimotions of ¬∆@st , dust of space-time, the substance of which we are all made. Because mirrors are fractal synoptic images of the whole, mathematics also has an internal consistency described by the axiomatic method, but the advance provided by 5 D mathematics is that now we know where the laws of mathematics come from, as a mirror of Scalar time space systems. We shall therefore put mathematics in correspondence with the laws of fractal space and the pentalogic of cyclical time, in 2 parts, given the extension of the discipline ; this first volume will introduce 5D with emphasis in its mathematical mirror images; and then considering the new units of 5D mathematics, the fractal point; its scalar equivalent the number; and its spatial stience, geometry in its 3 ages and 2 forms, mental spaces and vital topology; leaving for a 2nd & 3rd page, the wider fields of Algebra and Analysis. Newton's absolute space-time was proved wrong by quantum physics (space is broken in quanta and organised in 'fractal scales' of different size), and relativity (there are ∞ time clocks in the Universe with different speeds). But if there is not an absolute background space-time we are as Leibniz wanted relational space-time beings that occupy a vital space and last a time duration; and so Space and Time Generate the properties of all systems made of them; which explains why mathematics, the science of space and logic, the science of time, have so many wide applications in all stiences each one studying a relative scale of size of the fifth dimension. We shall thus show math as an experimental science, relate its laws to those of space=geometry and time=algebra and consider some examples on the emergence of those laws in 'higher 'stiences', in this introductory course on 5D math. So we just make an intro to 5D Generational SpaceTime, foundations of mathematics as the language of entangled space, point-S=∆-Number symmetry, Nº theory, mind geometry; translation to 5D of Greek 1st age, bidimensional ST-ill Holographic geometry: Pythagoras, Fermat postulate's Margin Proof, timespace spirals, 1D trigonometry, Euclid's axioms; 2nd age of analytic geometry, mind-graphs and conics, with a brief intro to the huge explosion of mind spaces in its 3rd age (differential geometry, vector spaces, phase spaces, Hilbert spaces, knots, paths & hyperbolic geometry), which deserves a future book of its own . Since if we look at maths as a space-time mirror each LAW reflects 1 ST law. So we improve Einstein's quip: 'I know when mathematics is truth&when is real'. In its 1st young and 2nd mature age almost all maths are ST-reality balanced mirrors though its 3rd inflationary age is filled with idealist distortions, redundancies & language fictions, regardless of its beauty. So the value of 5D mathematics is to return the discipline to its experimental nature, doubling its proofs that must be both consistent within the structure of the mirror (axiomatic method), but also a useful focused image of a general Spacetime law.

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[v1] 2016-05-22 14:15:00
[v2] 2019-08-11 13:50:26

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