Wednesday, June 30, 2010

The 4D 24 (octahedra) cell as Abstract Particle

The 4D 24 (octahedra) cell as Abstract Particle

Today there is an article on thereferenceframe, a blog I follow. I did not know the 24 cell was a representation of the F exceptional group but it does make sense from my rather finite counting of things. Here I speculate on the 24 cell being some sort of particle and breaking down into others topologically and from a three space perspective. Trying to solve these things for puzzle making mathematical recreations I had no idea it was hard because it was the frontier of our current thinking on string theory and so on. In the letter notation LHC means yellow-violet orange-blue and red-green axes. It seems to me the 24 cell is in a way a higher space analog of the rhombic cubohedron in space and that the ground plan of honeycomb cells. If we have a sort of invariant virtual dimensional continuous space why not particles that break from it in a discrete and more quantum-like manner?

The PeSla
Thanks Lubos,

This is just the sort of world view I feel comfortable with- I liked the 248 dimensional idea and the exceptional groups as part of it all long ago,

I am not sure it can be only about continuous groups alone, say the gravino making a smooth transition over a string- points are in a sense important too. I suppose that is some sort of Non-cantorian basis for a particle idea.

Here maybe the mapping of infinity into zero to one should be expanded and it certainly seems to be if we consider multiverse ideas- In a sense the idea of such branes as parallel is after all just a version of the parallel postulate on steroids!

Cheers, The PeSla

By the way this sort of thing sounds a lot like I have been saying. So you may want to see my june 30 blog. I have heard of the saying that a theory is so beautiful it must be true- for those of us who have chills run up our spine over the symmetry of it all and can see it- I think the truth of this is true because of exceptional beauty. You are on the right track!

The PeSla

* These numbers keep coming up as in 15 x 16 bicolors = 240 the eight dimensional close packing around a central 8-sphere. In the discrete sense we have to count on our fingers too and labeling can be essential not just an aid where color adds a dimension to the problem. The 24 breaks into mirrors of the 15... consider the 248 dimensional group, consider the number of soma cubes or ways to unfold a hypercube as near this number. Things look much more symmetric when we understand we can view them in a higher space when in a lower dimension they do not seem so. I suspect the privilege labeling of some axes by color has evolving uses for things like cell differentiation- and maybe in some some sense atoms themselves evolve at least to the Z= 120 element limit in four space.

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