Congruence and Vibration

Congruence and Vibration

Or from a more poetic mood - Rimi and the Spinning Dervishes. Perhaps the search for the windmills of Cervantes and his squire being the realistic one. So this is about spinning things and fixed things. It is the simplest of the congruences, the five fold symmetry. Of course the partition for 4 is 5. The next cases are more difficult and there are more things involved in this internal shifting of numbers as if the quasic plane is a quasi-torus. The important thing is the direction of counting which can go plus or minus... but from zero (or whatever zero) the red squares in this Pesla Quilt add to them the next highest orange not the one that obviously in a positive way precedes it.

Rimi, Spinning Dervishes, and the Cotton Gin That is from the cloud of such a sea of geometric entities and numbers (and yes the logic is the same thing) we sift out the seeds of particles and primes and so on. Of course Rimi the poet (some said on Public Radio yesterday that he was the second most read poet now in the USA.) added the spin to the dance of his mentor merely a Dervish in the distance to regard with love and holiness. I imagine this difference as the B and E forms of vector physics on the electronics description of things. B=0 with a spin. But the congruence of things shows that periodically the patterns can return again fractally over the plane of powers.

The next congruences are rather more difficult to express as partitions. It would involve 16 x16. Apparently, logically, that would involve a 67x67 grid along the lines of a recent link I posted here that links to the logic of this applied to the gray code and its position in Venn like orthogonal diagrams,(by the way the 15 vibrations for the logical 16 show up in this color coded 32x32 Diracan algebraic grid...for there are either 15 or 16 of one color. I did not use the i j k x i j k notation to map these to the quasic grid, but colors.) I suppose this means, if we can look further than mapping things to the eigenvalue diagonals only- that we jump for 5 things to 67 things.

I also tend to think of the wildcards as s sort of complex unit- to which in the higher realms of speculation there may be analogs to i (for now the table of such multiplications the do involve rigid rotations and !!'s ) I use i j k with two dots over the letters. But this is difficult speculation for these numbers are not hypercomplex numbers yet they are easily imagined if we make an analog of Dirac's 32 x32 in a 67 x 67 where it is 64+3 and such i analogs fall almost too naturally into the mystical powers of two at the heart of this number theory. Maybe more beyond this. (three dots). Yet in the edifice of it all we preserve the 12 and 5 of Dirac into such higher topological spaces.

Indeed, just as Euclids work was said to be a hymn to the dodecahedron- in a sense this enquiry has been an hymn to the triacontahedron into more expanded general space. It is as hard to see some of these realms as it is to see beneath what seems so trivial say in the multiplication properties of say the number two and its powers and congruences.

So, we cannot imagine an axiom system of zero and its successors alone but have to imagine (as a consequence of the quadratic plane obviously) that in matters of alternate even and odd dimensions for example, we go forward then back and so on. The idea of the negative of something is in a sense more important than the chirality of its expansion into higher space and logic structures. But in a way it can be reduced to just the positive. This of course is at once a symmetry over some space and a broken symmetry, a centering and yet a shifting of or reading of the flow of centers. It suggests too a natural direction of the flow of ordered things in a bias of time as well as monotonic structures of things like mass...

In the conway matrix of my notation LHC and so on- it is a code to label the colors here I assume like on the triaconway puzzle violet would be the center of it all.

I thought about embedding in the color cells the graph of the totality also... But this was very hard to keep clear to draw in my head and with my eyes.

For those interested in some interesting symmetry and the 15 vibrations here is a listing in my color cube notation (and a proof of sorts showing logic of it all) where A=red orange, B=red yellow and so on in the Conway matrix.




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