Tuesday, January 18, 2011

Torus Genus

Torus Genus

[Judging from the lack of comments lately I hope my work is readable and I have not stepped on anyone's TOEs.]

I have stumbled on a realization that these topological and information ideas as simple as their conception is, including the simplified illustration above, may be powerful enough to describe by paths of abstract motions certain structures like those of particle decay. I feel asleep after a glass of wine to see if it kept its strength after a week and pondered a question and pictured moving in such space in a much more detailed picture than the one above. The question is "Does the epsilon n honeycomb a needed concept from the view of more general and continuous space for abstract invariant and accusal, even probabilistic, particle description. But this is after all things on a lower level of the conception of cosmology than even wider systems and descriptions, in the face of that metaphysical edifice the idea of simple particles and their self reduction and evolving seems rather concrete and the case- one at least to stay close to in exploring speculations. I did not mean to include the fox,chicken,corn idea yesterday but it seems part of the dreaming.

*1 By shift between dimensions of the context of the informational coordinates in a quasic space even as a bonding by duality oscillations in a natural dimensional space, I do not necessarily mean an extension of complexity as entanglement. We can partially realize the totality of numbers at some distant diffuse view of the Riemann sphere.

*2 The (abstract) motion from cell to cell constitutes a linear quasic distance of sorts, discretely invariant and the "particle" in motion as complex as it is on this level I assume it as an ad hoc yet variably given (a being).

*3 The non-crossing over (knot theory) of such paths in a given dimensional representation and genus may evolve particle collision, creation (energetic) or annihilation when the genus in such dimensions is reduced.

The fox, chicken and corn puzzle (and boatman) is thus intimately tied up to the connecting of three things to three other things (as in the gas, water, electricity problem for three dwellings where lines cannot cross over and solved on a torus. [this section left out yesterday- did I mention these methods can divide the torus volume into so many parts too- 13?]

*4 We can decided by these methods the minimum slicing of such tori.

*5 The idea of Klein's bottle intersection in three space as a singularity (another example of my spherical singularity) [see Rowlands] applies to tori of higher benus as if point-like simply connected singularities.

*6 A particle as singularity does not know which genus or dimension it may be in; nor if its context space is one or more sided.

*7 A given particle may be assumed to have both and averaging of mass or a generational progression of masses and that these intelligibly changes or its state persists. (Again, asymmetry and non-association descriptions count.)

*8 A persisting particle in a strictly orthogonal motion existentially in a given dimension does not know which universal dimension its motion is in (nor if it may be in but one such place in that or other dimensions- a QM idea). Thus topological uncertainty meets topological asymptotic (freedom?) boundries.

*9 Changes of states of abstract motion, analogous trivially to the abstract inertia principle require input of energy to the dimension threshold where motions are concrete. Yet not recognized or are independent from action at a distance contexts. (that is all concrete changes are intrinsic to the general quasic state matrix).

*10 The rare and nearly infinitesimal region of exceptions to some persistence (QM jumps and so on) can be an initial point of chaos for the structure where global system paths break loops or enfolding's of symmetrical systems intelligibly. Even over infinite time thus averaging, these shunting's may occur irreversibly. In a given QS field there is a least one exceptional cell that initiates such, but may shift - say 12, 13, 14 as in a 4D representation of a hypercube some cell centered, or for that matter the new improved tropical constellation of Lubos- in the case of a second order quasic constellation of abstract dynamic generally self evolving cells.

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