Arcadian Elegant Matrix

Arcadian Elegant Matrix

I came back at night to post for this afternoon I was thinking about how 36 comes up so much lately in the simple arithmetic so I played with the matrix thinking it was a page I probably would not post. But the results seemed to give me better understanding of some of the more intuitive things I have done over the years with the color cubes as recreational math. I am very good at the design of such puzzles but not as good with the solutions, that is I usually allow those who are very good at the solution of such puzzles to solve them faster than I can. The arrangement of all 30 cubes for example in a row for plus or minus labels on the three axes. A lady made a set for this solution of the 15 cubes, but 30 were needed when we consider the sign of the axes. I immediately saw there were five other alphabetical solutions merely by permutations of the three letters and alphabetizing them.

After a meal and a nap I awoke from the chair and recalled how two other of my puzzles related to all this. One important one is the Calyptic Cubes, 6 cubes of 9 color patterns each used four times on one of the faces. But I do not have time to discuss that yet, and it seems to lead to some interesting speculation in general. But seeing the reduction of the four quadrants it dawned on me that when I exclude the diagonals of the conway label matrix it looks a lot like Kea's transforms. So I reread the one paper of hers I have in hard copy Quark Lepton Braids and Heterotic Supersymmetry. Now the amazing thing is that I understand a lot more than my first reading and surely this is because the patterns are universal although in different languages. This elegant matrix is thus a PeSla to Kea translator. I can see a couple of points not understood nor balanced where she suggests things I am sure she worked out in further papers- and those errors could be my own.

In my Backdoor Gin post of last year I made a six color cube of only three colors per cube which proves more than a mathematical recreation after all. For to understand the structure where in a sense particles are real, as real as the actual physical turning and twisting of cubes, the 15 three letter labels are so and the BKDGIN seems to match her sets of other types of particle numbers.

In fact I am impressed such a structure can be seen by such a different method. I am not sure by what she meant by cosmological factors unless that means gravity. I understand the accumulation of charge idea, a Machian and Diracian idea. Are we doing some sort of string theory here? I mean are there gluons in the end as we interpret them? I saw also that I have been using the terms generation and flavor interchangeably which is a good thing because there are after all two distinct ideas to which I have interpreted generation. Flavor and Color I do not use the same way nor as just a matter of partitions. Yet, I do use the general ideas presented in the paper in cases where recently she has posted on some methods of flattened topological objects. I wonder also what this paper may say about a Z' idea.

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Next Morning- footnote: I had to revise the illustration twice for typos. Notice in particular H and -H seem to cancel out a neutral, a center, with small degree sign over it in the three fold axes letter combination's.

I tried again to extend this to the super-elegant level of a matrix of 4 x 4 but I will have to find the general formulas or perhaps just list them the hard way- maybe a color map of them. I should check Kea's later work on such matrix transforms too.
Why not the z' idea (in the future notation I will use the repeater pennant system with four numbers 1 2 3 4 each with a degree sign rather than st nd rd th for some listings of such cubes. Interestingly, we find the 1 8 28 56 70 56 28 8 1 here again and in a real sense of a sort of positive duplication of elements we add the two wildcards to make 72 and so on- but in general we need to work out this informational and binary numerology better where there are useful but different possibilities to consider when they are so close. We can extend the flat representations also in real space- something I dub tetrahelication or in some ways of combining singularities with inversions metatronication. Which are words that will probably not survive in my pantheon- yet, as I said some of my terms like quasic and calyptic are easy to use, hard to represent otherwise, and are indispensable for the notions they carry with no need for disambiguation- let's face it in my next post quasi-physical is not a clear and is a cumbersome word.

The idea of "flagelation" the flare or rim comes up in the intuition mentioned in Kea's paper that in these structures and matters higher space functions do seem to have effects or observations in the lower particle space- the idea that our ability to see pure n-dimensional spaces reflects how nature herself would do so. I cannot say that matter and antimatter are not an important distinction ultimately without the reason for this of some structures if viewed from the outside (as we seem to be viewing the atom.) I suspect like that result of the last face of a hypercube that there are a few more surprises when we combine these matrix label elements in higher space as if they in a sense were particles or classes of them.

Happy Earthday, everyone!