Saturday, May 5, 2012
Unususy (Unusual Supersymmetry)
Unususy (Unusual Supersymmetry)
L.Edgar Otto 05 May, 2012
Let us imagine a generalization of the Euclidean plane into the wider reaches of inter-dimensional symmetry,
In the idea that the structure of atoms are intelligible, be it that they accumulate parts or break the symmetry by energetic methods or alternatively there are creative forces at work wherein they actually and not just potential evolve. Presumably they can access energy or structure from the vacuum in some way and this process is intelligible.
It is here that we find the old dream again of some sort of intelligible formula as if algebraic that will generate the pattern of prime numbers or the intuition that there is some reason we imagine doing so. In which case one might theorize that it is a matter of the difference in cubes before it can be solved as merely the difference in squares in a plane. But I vaguely see this as but a possibility of insisting on integer effects that for some reason imply in our continuous thoughts on fields and uncertainty the finite is the result of such higher transfinite or transcendental numbers.
Part of the idea here is that as in natural dimensional Euclidean space we have shadows of higher dimensions that fill some lower dimensional polyhedron, the eutactic vectors that form a star and the assumption an atom has a center and in the ideal is composed of concentric spheres. I suggest that there are other solid like objects of unusual super symmetry when the wider view of at least Euclidean space is flattened to a plane- that in influences or in effect there may be actual materials that act as if such objects that are not clearly in two or three absolute natural dimensions.
What is remarkable and if coincidences of numbers these come up over and over again, they come up in the work of Kea and Pitkanen which in some way the goal is the better unification of topology and arithmetic. It can lead to ideas that we sense are like ideas of dark matter, shadow atoms, or special influences for a deeper understanding of the periodic table including natural limits to the number of atoms as if there are different levels of what we call matter.
I am sorry to say, for want of seeing the number work and missing the idea other than synthetically in crystal clear detail how TGD derives its relation to numbers, the use of primes as a reduction of number theory at least as a given. While I find it easier to critique ideas in the standard use of our methods of analysis (of course I cannot guarantee that I have not missed something in the common literature, or that in fact we all have missed something so it is not there.)
In this respect we encounter again the patterns of five inherent in number theory in that beginning in four space we find the special wide properties of 15. This is obviously a difference in cubes of two primes, 37 and 19, note that twice the latter minus one gives us the 16 minus one. So we find again the fascination with the golden ratio and quasi-crystal tiling of which many theoreticians have found interesting at least as a mathematical puzzle or recreation.
What I suggest here is the idea of the structure of a tiling of pentagons independent even as part of the quasi-xtal for their own internal structure of rhombs in a plane or in space.
Can we not imagine, informally, some sort of super dark like atom composed of 4 24cells of four space in which we have not the 120 vectors of minimum reflections on the surface of a sphere in three space but 384 such reflections in the next set of contiguous dimensions. But there is more, an analog to what we imagine as time-like dimensions. Here we have to add what? we add again 15, which is 111 in binary where we generate such numbers by binary conversions to the ten base and read them literally where they represent such primes.
I mention that the lattice of such decagons seems to have an alternation of colors as if a line of symmetry cuts it and that we could consider it to have 14 edges abstractly, still we are working with structures that at least in the plane are impossible anyway where the angles could destroy the convexity, that is near miss polyhedra. Yet the near misses are important in uncertainty of possible bonding. For me anyway I have not found a standard reason we do not have the natural but usual symmetries of the 18 faced deltahedron at least in matters of general exclusion like that of Pauli as if magnets oriented and repelling on a sphere.
I note also these may be considered half volumes, or that these may be dihedrons but only of one side. There is no good reason in the standard theory to assume that a particle as self dual would have a neutral charge for in some paths or traces an aggregate of these Usususys are not commensurate with their reversals.
But these thoughts would not have occurred to me (and many more when I unrolled my copy of the periodic table- Uuu and Californium comes to mind...) had in my casual and relaxed drawing not particularly intending to find something more and doubting it when I did, had I not drawn the 5 cell with just the right angles such that what can be drawn as four of them in a higher pattern can also be drawn as five of them as if arranged in a pyramid. Then insight of these surprising reductions at the foundation by way of the golden ratio as something I encountered before in making actual models did prepare me to think of this sort of space as real as most any of the abstractions we are already used to in our new experiments and thoughts on math that guides our century of theory and new physics.
OK, I have improved my posting environment to the point I have reached three a day which would be almost a hundred a month so, I will try to slow down now. I find it interesting that the patterns did tend to become snowflake like hexagons. But if this is the sort of experimental facts that Pitkanen is suggesting many do not take seriously then what is to say that such meditations are indeed something like the ordering of theories in our branes by analyses as well the idea of what we intimately know as a truth of intuition?
For the astute reader or the trained one we do have the relations in the complex plain to consider and those sorts of primes and of course elliptic equations and so on of which I quite imagine we can go a little further to shore up our development of such systems. But I am not sure at them moment which direction my thoughts will be heading even if at times it seems like an inexhaustible machine or that in matters of encounters and experience there is some guiding hand one can almost believe in that sets the direction if not the revelation or imagination or discerned hallucinations of our efforts. There is a further level or crack at the foundations of which we think is there and almost can see.
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This morning 8hr later this post does not seem that far fetched but is an obvious extension of the shadow polytopes in eutaxy (see Coxeter) if we regard the faces as tiled on a plane. But this is what I am saying for the depths of how planes are organized (evidently with the idea of branes). In fact it seems all to obvious and may explain the facination some have with the quasi crystals. I am not sure why I did not see these deep connections before hand while working with them informally in a relaxed intuitive enquiry. I do know that in these quasi lattices the holes between such objects can have regular patterns or that in some cases the shadow represention in some given dimension can not be exactly perfect... perhasps this it the crack in the planes that should be investigated in regards to at what level the arithmetic applies...we need such philosophy, we need fresh views.
10:00 am next day...