Saturday, January 22, 2011
Mass and Moduli
"and Ms. Pacman, and Ms. Frogger... Oh wait, there is no Ms. Frogger but I'm sure the scientists are working on it." Earl's brother in the show My Name is Earl.
Well, I had a spurt of informal exploration and creativity in the cabin fever of the minus 45F windchill. Some of this looks a little less trivial and a little more significant to me today after reading more of the heart of Rowlands with his Dirac representations as quaternions and vectors. I still am not sure what part of his work is original but it does seem to involve a concrete attitude toward three space. Alas, it clearly descends into speculation but shows some interesting paths for judgment on what may appear reasonable doubts. But I tackled this part of the book after the posted illustration of my thoughts, a mind map of sorts in progression, but what I thought made it easier to understand- and today I wikied the terms gamma matrices and gamma functions which seem so well known they were not in the book. All of this seems to relate to the Pascal analogs including the Fibonacci numbers and their interpreted physics as symmetry breaking. But what started this was Kea's post on the trifoil knots which had me look again at cube notations.
One conclusion for me is that there are indeed times when we can assert a priviliged label to some mathematical structure even as potentially or in separate evolving. this thus modifies the core quantum idea of imagining no such privileged labels. In other words, in the clouds of quantum theory intuition we can find crystals and counting as relevant. I am pondering all this in relation to the standard theory (are there attempts to save it as it is along these lines?) as Rowlands considers things like fractional charge or the fraction as fundamental units. Kea asks if perhaps the trifoil knot cube relates to these fractional charge ideas. I do like how Rowlands comments on Dirac's statement of the "if but one monopole it would explain the discreteness of electron charge" and Rowland suggests it is the other way around. From my view too the quark or electron is not fundamental- but that is not to say these are made of strings as such- that theory of field and particle (and of exponentiation) to use the moduli term shows the need for the wedding of string theory and other topological considerations. Yet it still rather seems a matter of trivialities to me when we play with simple Pascal triangles and colored cubes- btw I retain my notations of them in the case of space otherwise we get hung up in the memorization of associated colors which many people like Rucker find excruciating or Conway taking a long time not to see the T tetracube as green (for me it is orange and it is an added burden to translate between our two color notations. (But I get ahead of myself- let us just say I have a more general and logical alphabetical notation on the third illustrated page above- and ABC is also the problem of triality. I understand but am not quite sure Rowlands can suggest in the E8xE8 that one of them is the standard theory so to speak and the other "gravity" or perhaps akin to the 10 of rest mass. Or that this Newton force like property in its inertia and action reaction, all the turns and twists and reductions, describes mass or the differences in mass. Such interpretations also require a "quasic" view and just as Rowlands speculates eventually on genetic structure from this physical model I too had three great epiphanies- Seeing the Beauty of Newton's Laws (5th grade on the way to school then playing hooky and catching fish), The discovery of quasic space and the higher dimensional chess games (of which I can now explain briefly a question asked me on the chat line once as to why I had the board multiples of 4 and not say the three dimensional case 512 cells not just superficially as the need for analogous logic and material of the game as two player, but intrinsic to the structure of math and physics as quasicity. It is a steep learning curve to simplify this- but the quasic grid seems to simplify and summarize everything.) And the dawning of this pattern applying to the genetic code in 74.
The first page concerns knots. I imagine that if we take a band of metal that can be connected into a ring and make a twist on it- string like- we get the moebius strip and so on. A further twist makes a two sided surface again. of course this is half the picture fundamentally but does demonstrate high level physical properties of materials. Of course these are not knots but are so abstractly- that is to say after so many twists the result can be balanced out and centered such that there are lobes that are two, three, even four fold like knots or orbital like things.
In the informational notation I observe again that diagonal upper right to upper left describes the corners of such a cube (is that diagonal called anything so as to name some matrix?) Of course there are such diagonals in other quasized dimensions. These, of course, illustrate specific labels as to if the fourth axes in a pure four space is observed (anticommutative to) the LHC* for my notation in three space for the cube face Conway matrix. I note that before I made such Malhon cube matrices I did it for the game of Sea Dice of 10 (not 15) cubes. Also the 8 cubes in informational notation for the game of Zebra or Piano Dice... and so on but that is a different approach. If I found these problems hard thinking them so trivial I am awakened to how hard this problem seems to be in the description of physics.
The second illustration is where I try to think in the lower level of the complexity of these groups and dimensions in the form of the beta-4 or 4space analog to the hypercube where the informational abstract quasic motions between these as representation on this trifoiled cube can be so interpreted (and colored) into the various interesting sub-symmetries (of which there may be some interesting interpretations and applications- heck, I did not think this informal exploration would lead to much of anything at least when I started it. Usually, I have a good idea where things may lead even if the calculations were a long journey to which the truth of it comes only at the end (much like the models of 4 space that as Coxeter quoted was like digging a tunnel thru a mountain from both end and they meeting perfectly in the middle but we did not know before hand..."
Somehow, I note, when we shift from null or count from zero or one- that these abstract counting structures do indeed suggest what and why of the initiators and terminators in DNA- much as Rowlands investigates as an overview of the 3+1 formalism, but that is merely and bravely just suggestive when we can see it in closer detail- so too this question may have analogs in events of pattern decay. In any case the situation, even in virtual loops, is not all that non-linear in our familiar (and not quantum theory familiar) scale of intuitions.
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I post these which see relevant to various speculations here (water imprinting, creative black hole like things, distinct atomic period system levels...) without comment save we should always keep up with science news...
and this one most interesting from these abstract topological issues in view of other informal speculation on how birds see from a higher dimensional color space:
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