Saturday, June 19, 2010
Kochams (Thoughts in My Moments of Inertia)
Kochams (Thoughts in My Moments of Inertia)
The Reference Frame blogspot of Lubos has an interesting mathematical article on Decartes Kissing circles. Not much on my mind but thinking about these, as they are new to me, I was able to frame some questions and glimpse some possible answers that continues the triviality of the foundations that gives me pause for a deeper look. I thank Lubos for the inspiration here as I was thinking along the lines of some reason that momentum (in the case of neutrinos especially) seems to be discrete. Indeed some suggest and intrinsic positive chirality of them as a possible new extension of the current physics.
Now, did Lubos post this article in answer to my concerns or was it a coincidence? Or perhaps like that MENSA lady said that we can always find a mathematics for anything, so this is just another creative way of arranging notions that are if we have the sensibility to ask about a deeper look?
In any case this all seems part of linear algebra converted in to discrete circular algebra of a sorts. I wonder if it is extended into more spheres in three space and if not why? The quasic ideas do seems to explain to some degree the idea of such touching things as those limits to equations by matrices greater than the fifth degree- Icosahedra and such Equations anyone? Klein seems more relevant to me lately. But in the formalism in describing these "kissing" circles does not some of the formula signs look remarkably like some of the relativistic notations? But we are not far from the Pythagorean theorem in the small to such modifications are we? (Alas, the same cannot be said for integral division of squares in two space for that of three space?) In a sense the fourth dimension can have a negative value such that the distance can be measured as if a distance between such motions.
Generally, the idea of separation and symmetry breaking by complex numbers is a good idea but does this description of the flow of heat really apply as heat to subatomic particles- that is heat and temperature so to define them?
Nevertheless, as a little more than a trivial mathematical recreation I find it quite remarkable (as Lubos suggests non-trivial) of such integer values, and I have this sense of a more grounded and unique idea of space and numbers of which from some frame of reference in thought I can ask way and can find some answer.
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Next day on blog post following mine:
this sort of thing seems most relevant to the coming resolution of these physics.
We in effect have to generalize the generalized concept of topology in ways there are not so obvious. For example the differences of monopole and dipoles in relation to even larger mirror symmetries possible in a fourfold and five fold space- that is essentially what fundamentally are the design and structural differences in the bosons and fermions as things that follow the topology of the design.
In a sense such ideas will not only state the Pythagorean theorem on the microscale but show the reason for it- after all a Bucky ball is really still a relation that is not technically like the geodesics as the microscale is approached. The again these path differences between the square root of two and phi tend to show up where such mirrors (not necessarily supersymmetry as such) as fine variation in the computation of the field strength or matter. This difference too being the aromatic or vanderalls like forces (ie dark energy etc).
It occurs to me also in my musings of last night (not so much into the physics but I did dream new lyrics to my song as if on the spot to make up new lyrics) that there are structures like in Rowlands of the double DNA pentagon stacked. I mean if there is a coherent three axis phi power strut structure it can be so and not be composed of five tetrahedra. On the other hand a tetrahedron analog in four space is composed of five such tetrahedra (the five kissing spheres) so the description of Fuller to the tetrahelix and the unzipping angles by either theory or even by some physical catalyst is the same description. Namely the differences relating to volume of the three space square of two things and the four space golden irrational.
Interestingly, if we restrict structures constructable in three space that involve the phi ratios x y z we get a smashed version of the stella octanga as if the symmetries involve the tree space square root of two. Also the height of such volumes are close shadows if the square root of two and the volume is close to the powers of phi, that is if we are to build solid models of these abstract topologies.