Dimensions and Algebra Dialog with David Chako on Goole Plus
L. Edgar Otto September 25, 2013
David, thanks for the dialog - I certainly and not making judgments or assertions of personal attributes such as perverse or mystical an so on - again, I have no formal training. When you bring things down to this level you certainly do make it precise. It show me just exactly where a difference in my understanding or misconceptions may be then I can bring back these math and physics issues to a less precise in a sense issue of philosophy.
Geometry, such as Coxeter, has many interesting ideas... each line of his book faces at first exposure connections to the 1150 or so branches of mathematics so it took me long to read. Why given a box bounded by six square mirrors is the sixth one not needed in the reflection descriptions?
I doubt, in you description of what is an algebra that nature makes the distinction between such addition and multiplication on some level. A number is a class of things even if an integer, even if they take on the aspect of scalars. Sure, even Dirac used the 2 rather than 4 formulism but he felt home in both. Apparently, the symmetries involved did not make a difference to the abstract structures they believed. Numbers can be a slice or small part of a continuum (erected like lines on points like in Conway) or in what may be a deeper sense a number is a singularity or if viewed deeper a complex of singularities. A super black hole object that emits a lot of power periodically (see the recent article) can be seen as a system that materializes into clusters of stars or galaxies.
By convention the null polytope is subscripted as minus one... in an abstract sense null is not quite the same as zero.
So, in this sort of intelligible fantasy even if we were to understand the symmetries completely in 3D, we can certainly see a range of possible color encoding of higher symmetry (I just saw art at the Guggenheim of color effects without a cue in the landscape that as eyes readjust can induce hallucination or readjusting have residual color effects. I will post a rather simplified graph of such symmetry of the 81 subcells of a hypercuble in my bicolor letter notation. I can crudely imagine such an algebra if that is what it is describing possible particle paths and decay products but in a much more complicated detail as if unseen symmetries if we merely see the apparent asymmetry of these letters or numbers as point like objects. I do not mean the usual representing of molecules each of which has six degrees of freedom... I mean the logic of these twenty objects made from pairs of 24... Now why is the 15 bicolors, the minimum school children need to memorize for addition... not 16 logically... do we think a four lobed molecule like NH4 vibrating in microwaves in 15 states have two of them superimposed of the 16? But for all I know this mystery was solved since I read of it 30 years ago.
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Let me add, that if there is an unseen and possibly wide range of such hidden algebras that amount to the same answer in what we see in natural three space say for the "quantum measurement paradox" then that question is a non issue across many dimensions... so why the one superimposition of the 16... even if extended to QCD. After all between the quantum and classical worlds we have the same results in different mathematics and styles of statistics.... and between them with the local diversity we see of random paths we have Brownian motion... yet a random walk in 2D eventually returns to its starting space - it is thought not so in 3D. So in a region of physical effects of contiguity the state of a system may exhibit hidden choices of discrete and continuous or issues of algebras of consecutive effects casual and causal. Is there a greater unity of physics or in some sense actually and conceptually bound?
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Seems related to the idea in a plane of paths that exclude or do not cross over zero and a negative x axis as in Riemann- not a clearly established idea really...sort of stacked complex sheets, I have thought of things like this for decades (perhaps wrong), but things on Astronomy Picture of the Day looks to me it interprets things backwards. Truth perhaps in between, In 4D we can find asymmetry too in distribution over equal points in a 3 volume. Now yesterday this shell like idea suggested the black hole at the center of our galaxy was active in cycles, not just of the usual dimensions... science daily. For me this is evidence of higher symmetries and dimensions, but there is always an equivalent way to describe such processes as some model of particles. Is the complex plane iy not perpendicular to x and y planes? we can cling to the idea of three dimensions and a fourth abstract one as physicality but this is not dependent on but one choice of abstract algebra unless there is a general one choice. A 1 dimensional object from some view contains information that describes it as a higher dimensional one as well.... fractals and holography both important in more modern terms. A path around a hypercuble as two space can cover each vertex twice... the essential formula is 2D - 2D = 0D that is 2+2 is 4D as in whereever such doubling or halving appears in formulas, viriality. But is 1 plus 1 = 2 in this question of even or odd dimensions? Thus perhaps right angle rays and so on as part of the general picture.
I thought I would add more snippets of the dialog I sent to David on Google plus but I really should put it all synced here... as far as the theme under which we started this dialog I also on facebook saw a link to Sabines arXiv submission of a decade or so ago on the quasi-stability of black holes of which I commented this was still relavant and someone missed an opportunity for origninal and fundamental predictions as in todays new substance of the interaction as if molecular of zero mass photons (see science daily com).
I will certainly check out your link and some of what I just wrote in comments I posted at http://www.pesla.blogspot.com for something to accompany the example for you to ponder. Yes, 64 discrete is most likely the unifying idea (if perhaps things can so be unified in physics if we cannot have it both ways). As a discrete view Eddingtons model fits better than Dirac or my quason idea which looks deeper into the 256 elements.
Fuller's guru was Coxeter's. what you posted earlier on icosahedral symmetry is correct. Of the two greats, Lie and Klein I found "The Icosahedron and Equations of the Fifth Degree" a most influential book. Is it a numerological concidence the 240 soma cube solutions involve that 120 faces of the symmetries of the dodecahedron or that 120 plus 16 equals 136 and like Dirac a concern with the fine structure dimensionless constant... an but it is not exactly 136 not is the tetrahedral volume of a sphere Bucky's 5. Yet in this sense would you not say there is some definition of the ten Euclidean dimensions involved here. In my drawing A is red orange of six colors, black and white too in that representation of dimensions if we have four axes.
Oh, it is early Fuller... let us not but stand amazed at the fullerenes and buckyballs as a reality... still, from his view three can be only 92 elements instead of the 120 that may be the limit of elements as we know them. Do you have a site for your take on the 64 as in the Exceptional group perhaps. Also we can dispense with the complexity of consideration of a mixture we may call gray groups... there are no gray groups that way. While Fuller saw a down to earth omnidirectional 4D Coxeter say 8D and in a note he said... on the contrary Conway saw 24D... so independently I found the Conway matrix of color matching cubes for my alphanumeric labels a the time just before he posted it to Scientific American.
Reminds me of that Yang-Mills Compactification concept which we can slice thru and clearly draw--- but as Kierkegaard said... to the corkscrew the knife is crooked. Where are the other four in a 64 shadow polytope or eutatic star representation... perhaps it is like the I ching where for of the hexigrams correspond to the 4 seasons but in any case all the lines count as 384 for the days of the Chinese calendar and the full rotation group of a hypercube. discretely. In any case two of the 8 not 6 compaction dimensions may be not observable or time-like hidden, or perhaps half hidden *thus a ray"
to qm the posted topic itself more directly
Note on the article above on QM gravity.... we see there may be some evidence, not so much just a collapsing into hyper-black holes but an hierarchy of these in a super black hole regime. So 4+1 I will use hyper- and n+1 n=5 or greater super- for now. http://www.sciencedaily.com/releases/2013/09/130924091317.htm . but as I have imagined it such a range of objects as if mirrored or inverted can be creative in the sense of quasar like ones making stars over a range of densities. If this very low dimensional physics images or concludes, that is the gist of it, in the abstract field baby universe may be created and so on (again there is no reason to deny the universe may be at its solid base as flat in these matters... intrinsic rectitude. If that is the case, and some numbers like Fullers 2, 3, and 5 or say the p-adic Mersenne Primes, the fact of it would be rather far beyond these lower dimensions. In this view we should really sort out what we mean by mass itself as well as how it applies to gravity. since 63 or so I imagined quasars were evidence of this more fractal crystalline world in the ideal. Imagine a form of matter which would have analogs to graphine and its Casmir dark-like matter properties and so on...
OK the wxyz formula does look like it is promising (for awhile solid geometry was not taught at any university but higher geometry is back in force again.) It shares a lot of my arithmetic ideas by my counting things in my so called quasic grid to visualize some of these things and focus on the suggested principles and interpretation. Of course in the vast world of number theory these could be put into algebrac forms as well I imagine. My system in such complicated but reduced dimensions has a position of initial cells and or terminator cells as in the 64 codon 4base DNA system. Your exclusion of a pole for technical reasons like 8 instead of 9 gluons as a principle extends to this discrete formula where of the 384 entrys we exclude one of the cells to make 383... that is the initial point of that left constant in rotations and inversions of the 4D cube analog... which is written as 2^4(4!) for that general group. that is for each dimension 2^n(n!). The issue is just how closely does this apply to our models of existing physics. The old model of what was also called Partons, three layers with the central one full or not of one electron thus proton or neutron or not... and this sort of inverse division does indeed result in what look inverted in the counting of things in an atom.... this principle seemed very profound to me in 74 or so and made me feel I understood mass at last... but this came a decade or so after a similar corpuscular (discrete) idea of muons and other particles having such structures. (like Matti Pitkanen's model on blogspot TGDdiary who had the same sort of model of such an object)....that said, in 64 I concluded that what we thought was fundamental or irreducible for things like electrons were composed of what I called "iotas" and that in a way is something slowly being suggested in today's speculations. The spirit of quarks is OK but does not quite capture the general case of such supersymmetry issues in the geometry, not easily to see anyway, One theoreticians sense of a profound model may seem absolutely trivial to another's and vice versa. Even when we conclude the same sort of things or similar things of nature our debates may miss each other's point and together the very point of possible results of inquiry.
for Sabines posts on fb:
L. Edgar Otto Everyone complains about the weather (global warming?) but nobody does anything about it. (sorry for the terse smart phone typing Sabine... I was quite impressed by that earlier and I think still relevant paper.) Steve, our natural love of science even if childhood couriosity... I myself took my mother's concave makeup mirror and invented a new for of telescope- yeah, a little let down Newton did it first :-)
L. Edgar Otto Behaviorism as the second revolution in psychology did not work without deeper science and funding for it... national or international socialism failed as a scientific stance other than setting the race for technology. A third expected revolution was derailed by partial understanding of brain chemistry so as to avoid the problem or keep the people in opiates. Physics turns out to be harder than economics (reported remark of Einstein reversed here). Statistical and top down micromanagement of the human spirit will tell us less than what is needed to intelligently understand or implement models of society. The nations that invest in basic research will be the leaders knowing why from knowing how things are in reality for the near future.
L. Edgar Otto All bh 0 spin recursive leptons. 1 cloaked quasi mass vacuum complex force molecular shell brane particle.
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L. Edgar Otto They dropped. Ball for an original and fundimintal. Prediction.
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L. Edgar Otto Nature is loop "quabi" stable. Otherwise 1st. Reactor. U238 would have blown up University of Chicago.
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L. Edgar Otto Which among others was along the lines of this: http://www.sciencedaily.com/.../2013/09/130925132323.htm
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