Quasi-discrete ( Lie and Klein Dividing Labors)

Quasi-discrete
( Lie and Klein Dividing Theoretical Labors)

I posted these comments on Pitkanen's blog today:


http://matpitka.blogspot.com/2011/06/categorification-and-finite-measurement.html



ThePeSla said...

Matti,

The symplectification of science was an interesting article which cleared up the term for me- it is not talking about simplexes or such. Any triangular structures as a grounding.

I understand the need for a different and new look at the plane which for me has no problem being n-dimensional or even complex. Well, anything exploring such a space as the article said the complex plane did would lead to an explosion in new mathematics.

But such a plane must include the odd dimensions and can include them. And in the end this model of higher spaces merges with the others.

But where Riemann explains they are ultimately flat- if you can approach the very small, these are part of the mass measure problem in that 128 is the key deeper than say 135 where the measure has a finite mass and so on...

Of course he sees 5 space as adding nothing important from his viewpoint.

The PeSla

At 9:01 AM, Blogger ThePeSla said...

Oh,

I find it interesting that some of the same mass values in the current discussions and debate occur around this level of say a Planck unit as in the case of the string theory.

But these internal values in such a shielded sympletic space would have what appears a hierarchy of Planck values. Light in such a space, or maybe even the gravity would be if we could see it at least a warp ten the velocity of light as if we see a particle or say a quasar through a fog of simpler space.

Such things when they focus out as in the article on a black hole violently consuming a sun with supposed tidal forces can have this hidden structure explanation and in a sense goes beyond quantum theory as we imagine it.

The Pe Sla

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Because of the nature of dimensions we miss each others points as to what is doable in the newer physics. I doubt for example that there is only one form of association possible in any dimension, not as the articles suggest. We can explore as some do much deeper in the foundations than that.

A simple explanation and history of category theory seems to suggest it as trivial or long developed by this or that author. If the K-circuits in Coxeter has anything to do with it then there is very little on the basic treatments of the applications I see that he has not covered. (surely the correspondence of cubes and associhedra can have much wider implications than the statement as a simple theorem) Such a flatland would seem the barrier or great divide to how we diverge into a more advanced treatment of such abstract concepts. Otherwise, it seems ridiculous to me that in our emphasized view we cannot see our own and the general contradictions. In a sense the closer to a fundamental theory the more trivial it seems if it reaches the foundation. Even then there is great freedom and diversity in our styles of understanding and interpretations.

On the other hand numbers are not as simple a ground to start with as we think, the concept of unity while universally applied is not a simple concept to start with (as Rowlands who studied the foundations points out) let alone something that seems outside of a certain focus as infinite primes. What sort of space indeed would be braids within braids and so on- always the corresponding trees of energy transfer in nature- how can this be resolved with a hierarchy of echoed resonances and not be a possibility that in its own way has a fractal FX -like framework? But to do so even if the raw number for a vertex coordinate includes say the integer 6 would be to undermine the certainty or intelligibility of any Yang-like compactified spaces. One must show where we can make exceptions as they cannot be both maintained as we braid in our notions the contradictory but corresponding theories on steroids to that of the simpler problem of unifying the two physics.

The odd dimensions, that is at the heart of what is evenness and oddness, in that it can be represented as -1 or plus 1 to 2n is more than just a mathematical coincidence in even sympletic planes. Particles, quasi-discrete, can of course exhibit this idea of 0 spin as 2n or 1 spin as 2n+1 dimensions. But this is Coxeter Euclidean 101. Nature where she is true is no respecter of whom discovers what first or if it is an individual effort- in any case all will be forgotten anyway while the general ideas, hardly new after all, outlive us for today.

There is a certain measure of time as if a chronological arrow we may or may not experience or touch. One way to compare our progress in theory is to see just where we were along the way individually at some era or age and if we have thought about things long enough, lived long enough, we will look back an see exactly where others where along the way in ways they cannot. We will come a little closer and maybe pass some new and beautiful boundary- and you will know it was good. A poet is he who sees the beauty and chooses or is compelled to write it down no differently than anybody else- But those who seek the truth in physics are those who have not given up the quest, fallen out of the race, despaired of dead ends for their cherished seeds of wisdom. In an infinite universe we imagine we can see all at once in its complexity and continuity the paths to wasted efforts are infinitely more probable then the few motes of cottonwood who find fertile ground and solid roots and who command the evolution of the future in a sustainable way. But the Bible says this as with any book worth its poetry.

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