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The Origin of the 11D World Membrane As a Pascal Conic Section of a 6D-String in 5D Projective Space
David Hilbert’s biography discusses a debate over whether it was an intellectual mistake to advocate advancing the 2000-year-old Pappus theorem to axiom status. This issue is notable from a number of perspectives, one of which is his 1920 proposal that established the Hilbert Program for formulating mathematics and/or geometry in a more robust and complete manner. logical basis that conforms to inclusively larger “metamathematical principles”.
However, at the time, he proposed that this could be done if: 1. all mathematics follows from a complete or correctly chosen finite system of axiomsand 2. this system of axioms is demonstrably consistent through some means such as its epsilon calculus. Although this formalism has had a successful influence on Hilbert’s work in algebra and functional analysis, it was not committed in the same way to his interests in logic as well as in physics, for not talk about his axiomatization of geometry, given the scheme. question of considering Pappus’ theorem as an axiom. Similarly, a similar problem arose when Bertrand Russell rejected Cantor’s proof that there was no “maximum” cardinal number and defended the “logicism” of his and AN Whitehead’s proposition in Mathematical principles that all mathematics is in some important sense reducible to logic. But both Hilbert’s and Russell’s support for an axiomatized mathematical system of definite principles that could banish theoretical uncertainties “forever” would end in failure in 1931.
Because Kurt Gödel showed that any non-contradictory (self-consistent) formal system complete enough to include at least arithmetic, could not (both) demonstrate its completeness (and/or, conversely, its categorical consistency) by its own axioms . Which means that Hilbert’s program was impossible as stated, since there is no way that the second point can be rationally combined with assumption-1 as long as the system of axioms is actually finite; otherwise you will have to add an endless series of new axioms, starting, I. guess, with Pappus’s! Equally, Gödel’s incompleteness theorem reveals that neither Mathematical principles, nor any other consistent system of recursive arithmetic, could decide whether each proposition, and/or its negation, was provable within that system. However, beyond Hilbert’s misstep over Pappus, it should be noted that Gödel’s theorem itself, in a realist sense, supports Hilbert’s basic idea of a deeper, more inclusive environment, ‘metallurgical’ foundation like a ‘Gödelian cartographywhich “covers” all mathematics and geometry. In fact, it was Hilbert Gentzen’s student who used a Gödel map “orders” of “trans-infinite” number systems to demonstrate Gödel’s theorem: so really metalogically valid ordinary arithmetic. In any case, although this conclusion also fits loosely with Russell’s logistical ideas, it also demonstrates a great improvement over his criticism of Cantor’s proof for an infinite series of cardinal numbers, which, after all, is the point of Cantor’s arguments in the sense that some ‘continuity axiom’ like that of Archimedes is required to generate an infinite field of real numbers. Which makes Hilbert’s Pappian faux pas seem almost trivial by comparison, since I’d like to know how Russell expected to find some “larger cardinal number” as well as how he expected to axiomatically describe continuity for an infinite range of numbers or points. a line; that is, before, let alone after, any infinite axiomatic system became an additional problem!
In any case, if Russell, or Hilbert, had actually taken up Occam’s razor, they probably would have cut their own throats with it before revealing their biased assumptions and inconsistencies for the world to see for eternity. Which simply means why elevate some provable theorem to the status of an axiomatic assumption, or introduce your own inconsistent system of assumptions, when it is clearly better to leave everything as it is. However, I am happy to use this razor properly in order to cut these icons a little posthumously, as if God had torn them from his suicidal hands, just to thank them in return for the indulgent opportunity to show everyone a again why fools seem routinely skewed as absurd fodder for us “lesser” fools or “commoners” in some exclusive or “formal” organizational hierarchy. That’s why the wisest people just say: the higher the monkey climbs the tree, the more it exposes itself to those below! (But also always be careful underneath, before something pops that hole in your face again!!)
In any case, this brings us back to another older and equally pressing issue is directly connected with Pappus’ “hexagon theorem” as generalized by Blaise Pascal in a projective conical sectionor 6-point oval, in 1639, when he was only 16 years old. Naturally impressed by Desargues’s work on conics, he produced, as a means of proof, a short treatise on what he called the “Mystic Hexagram”, better known since then simply as Pascal’s theorem . It basically (as defined by Wikipedia) states that if an arbitrary hexagon is inscribed in any conic section, where opposite sides extend to meet, the three points of intersection will lie on a straight line, called “Pascal line” of this configuration.
Although this simple description verbally suffices, it may fail to convey the fuller and truly “mystical” aspects that give Pascal’s theorem and configuration the distinction of being regarded as the most central fundamental construction of geometry projective And while diagrams would help clear things up, especially the descriptions below, it’s hard enough to reformat the content of these articles from the preferred notebook text to fit the different formats of different e-journals or distribution services. web articles In any case, it is no coincidence that I have not only made Pascal’s conic the cover figure of my text covering the projective and its subgeometries, but include a frontispiece of various 6-element conics relevant to all, including Brianchon’s projective dual to Pascal’s. So any interested reader can go to the resource box and pull out at least the Pascal cover figure, if not the frontispiece.
Anyway, the figure on the cover of the text illustrates Pascal’s theorem represented in a simple hexagon formed by mutually inscribing a full line of 6 points (15 lines) and 6 full lines (15 points) representing the respective plane sections of a complete line of six dimensions. -into a point and a full 6-derivative three-dimensional plane recursively intersecting a full five-dimensional 6-dimensional point it is the simplest representation as a spatially extended maximal projective set of vertices for this object. This description thus underlines its profound importance in terms of the scope of the entire dimensional gamete of the “axioms of incidence” (previously the additional set necessary to establish the meaning and that of continuity is introduced), starting with the simplest dimensional axioms extension and 5D closure, along with its projective dual of six lines on a point, which is then sectioned down to the final incidence ratios corresponding to six full points on a line and six full lines through a point. Similarly, the space of 5 can be added with the dimensions of 6 lines to get an 11D manifold that serves as a coverage space to map what amounts to a finished projecting geometry that is at the same time is both complete i categorically consistent (since it does not refer to infinite ranges of points or numbers, it is not restricted by Gödel’s reasoning, but again it admits). So, for example, it is quite interesting that JW Hirschfeld points out in his text on finite projective groups that there are no six conics of dimension greater than eleven.
Which brings us to the crux of this article as far as math is concerned physics of (super) stringand ‘M’ or membranetheory – which I have yet seen reduced by Occam’s blade to its essence in the basics of geometry, so the summary here is comprehensible to a wider segment of intelligent people. Superstring theory is based on a four-dimensional spacetime or physical metric, which together with a six-dimensional internal (Kauler) manifold (or compact Calabi-Yau space) for what can now be thought of as strings 1D of 6 -line-to-point; forming a total system of 10 dimensions. But by the 1980s it became clear that a promising unification of physics within a theory of quantum gravitation of superstrings was impossible, as they branched off into five 10 different mathematical groups (leading to the situation in which a number of mathematical eggheads, mostly with little interest in physics). per se, began to dominate theoretical physics departments). Which led to a second “superstring revolution” in the mid-1990s, when Ed Witten concluded that each of the 10D superstring theories is a different aspect of what was originally called a single “membrane theory’ (see http://en.wikipedia.org/wiki/Membrane_Theory), the entirety of which is naturally eleven dimensional and establishes interrelationships between the different superchain group theories described by various “dualities”. Because just as 1D strings are more manageable, finite extensions of singular points, groups of strings in a plane form “sheets of the world” as literal “2D membranes”, where these so-called “branes” can be defined of any dimension, starting with a 0-brane or point.
Thus, while the total system may properly be called an “11D world membrane,” Witten prefers generically to call it “M-theory,” where M can stand for membrane, mother, math, matrix, master, mystery, magic, or after , as Pascal would forcefully add: Mystic! In any case, there is little doubt that one day a complete 6-dimensional representation of 1D strings packed into 5D spacetime will fulfill Einstein’s dream of a fully unified physical theory. But personally, I’m much less concerned with “theoretical” unifications than I am with a comprehensive interpretation of physics and cosmology, replete with a host of confirmable data. Because I have developed the first dimensionless or “pure” scale system (Planck) which I call “Mumbers” or “membrane numbers”. and that covers precisely the whole spectrum of particle physics and space-time. And while I don’t have the IQ, inclination, or patience to follow or pursue higher mathematics for theoretical purposes, on the other hand, I’ve tried many, but I’ve yet to find anyone, physicist or mathematician, who can successfully write a pure numerical equation even for a relationship between different physical states. Similarly, standard super-string or M-theory has yet to make any confirmed, or even confirmable, predictions, no more than I, at least, have seen anyone point to the geometric underpinnings of M-theory as a Pascal’s 11-dimensional section. a projective double space of 5 and a six-string 6D at one point. So regardless of my mathematical inadequacies, I can guarantee that no viable “unified M-theory of physics” can be developed until the intellectual community accepts the metalogical tautology of both Pascal’s mysterious 6-conic that underlies the foundations of geometry, as well as the accompanying unified “dimensionless” scale that already represents a proven system that encompasses all of physics.
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