Monday, July 5, 2010
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I do not know if something like this exists in the body of wisdom. But I know it is a much a metaphor for understanding physis as it is a mathematical recreation. I begin to see after the discovery of the notation for he 20 cubes that Rowlands and my 24 units (of thirty cubes)of the algebra are really complimentary of the 64 codons in three space. I may explore further the four space as I have a better handle on the terrain to actually visualize and count such matrices. The twenty cubes I see as some colors hidden internally and these can in a rather particle or charge like metaphor be the corners as a flat circular thing or can describe the inside as linear units that match with the outside implied... again the surface and the core of things. We can also rotate the individual group of 8 making a larger cube individually. I leave to the reader to show how I got the third group of eight (hint: think as if one needed quaternions). The interesting thing is that one can have different external results including hidden (calyptic) colors yet the same relative position of the cubes is invariant. In making these I had a dozen or so such metaphorical thoughts like the quasi magic square of the shapes moving along the main diagonal.
After all, how does the natural design distinguish the amino acid codons from the stops? 1 6 15 20 15 6 1 = 64 even on that level alone in 6D has beautiful symmetries.
Note the Conway matrix in the middle of this- (I was working with this notation from the inversion inside of things on such a matrix so my notation is different than Conway's before publication in Scientific American - I still do not know what he means by non-standard sets or if he followed up on it. I did communicate this sort of thing with Martin Gardner who shared the question among those interested and on the net by Conway so as to "share the fun".
I find some interesting minimal connection structures as if say there is a good way to connect the six of them (opposed to the nine) as if an octahedron where each point is connected to three others. This of course implies a sort of toroidal genus as in the connecting of three and three points that do not intersect. Maybe this sort of programming will make it easier for a computer to recognize patterns, it certainly makes it easier for me to mentally compute and draw them. There are also the sort of five foldness of which Rowlands points out and it does look like the primitive golden ratio a little- that is of the six groups of five, abcde to eilno each of the ten "backdoor gin" or 20-30 cubes use 3 of 5 in the matrix. It is not clear to me either if this can be considered string theory dimensionwise but seems a more foundational principle- as if perhaps color here is a much an idea of charge if not an added dimension or it defined as some property of particles.
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Now the sciencechatforum com physicist are in the last century as to the so called shape of the universe (really from one side of the continuum physics) that one should consider one eight of a sphere! Such is physics from the surface only and not the quantum depths. I suppose the idea of a finite dodecahedron model is beyond their grasp- as is the logic and promise of string theories. But if you want a simple picture of it consider these calyptic cubes- I mean the symmetry is after all a neutral linear one of 20 elements and a chiral positive and chiral negative one (clockwise and anticlockwise) for the 60 elements (and yes one might consider inversions or doubling these if we had overt cube symmetries. But if symmetries is the name of the game then surely these metaphorical ones apply to the physics.