Friday, December 31, 2010

Theory Update 28

The PeSla discusses how the six quarks fit onto a categorical cube, with charge represented by path length. The zero charge source stands for neutrinos and the charge $3$ target for the charged leptons. Edges are directed by the addition of one twisted ribbon piece to a three strand particle diagram.

Happy New Year.


  1. I'm getting tired of people telling me things that I discussed on the blog some years ago. Have you people not heard of Google?

  2. P.S. That comment was not directed at you, The PleSa.

  3. Actually, the innovation of PleSa is the need of some diagonals of the cube (the W boson, guess). The cube itself has been rediscovered in the last 20 years two or three times.

  4. Now I look at it again, it seems to me that PleSa organisation really puts the quarks in the corners of the cube, while most presentations just do 1 3 3 1: 1 point, three lines, three surfaces, 1 volume. In these presentations, the t quark should be drawn as the square 0std in the drawing above.

  5. Alejandro, the diagonals do matter, as you can see in the diagram above. These are the chords of hexagons, as in the associahedron labels. This tricategorical cube comes in many forms, as I have discussed since long before blogging began but without managing to get any attention ...

  6. Kea,

    I am quite honored you quoted my diagrams. Sorry, I just try to google my brain and forget there is so much is now on the internet.

    In fact I knew the problem was difficult but I did not think my math recreations applied to these sorts of theories.

    From my view this amounts to writing matrices in at three space notation. My labels help keep things strait. What of the other possibilities of the Vn's of which there are 15? and in the Conway matrix there are two others that form such a cube? Now I have to wonder how much of the codes apply.

    On some level the assumption that generations have increasing mass is after all an assumption that at first approximation does seem like a linear method.

    I wrote to Gardner about the cubes and it was discussed all over the bulletin boards long before I had a computer (as he replied that we could all share in the fun) and Conway's was published in Scientific American shortly thereafter. But I do not want to take any credit for anything someone else has achieved, sorry if somehow I stepped on your toes.

    I found another solution of one form instead of three for one of Conway's puzzles he said was very "elegant". And Coxeter, my mentor, said Conway thought in 24 dimensions (he only 8). I see you can think in high dimensions judging from your next posts.

    I am really nobody at all. Now I have a keen interest in seeing what you have done :-)

    Thank You, The PeSla

  7. The PeSla, wow. Thanks for those fascinating anecdotes about some great mathematicians. I assure you that I cannot think in more than 3 or 4 dimensions! That's why I am an algebraist more than a geometer. Lol, so Coxeter is a complex number man while Conway can do octonions! I met Conway briefly at a conference in New Zealand a few years back, but never really had the chance to talk to him. He was an excellent lecturer.


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