Monday, October 25, 2010

Chugging Along

I must be getting absent minded in my solitary old age. It is a public holiday here today ... but I didn't notice until after I had suffered the weekend bus (that replaces the train), walked through the deserted city, and then passed through a number of locked doors on a deserted campus. Well, I have the place to myself now. Why do the academics all disappear on a holiday? Do they have a life, or something? The main reason for coming into VUW is the wonderful drawing packages on their desktops. Rather than painstakingly typing all diagrams in latex, I can now easily create nice eps files of braid diagrams!

Thanks again to Graham D for continuing his musings at Galaxy Zoo. Only the neutrinos show up with that $\pm \pi /12$ Koide phase. That must be because the neutrinos insist on annihilating with the dark matter sector, whereas electrons prefer to annihilate with ordinary antimatter. The $24$th root of unity is a very nice complex number, denoting for instance the dimension spanned by all three generations of $8$ fundamental leptons: four neutrinos and four charged leptons.

4 comments:

  1. Yes, I know the feelings.

    That 24th root, in terms of geometry, is most interesting to me. Have you associated it with the 4space 24 cell (Euclidean) in any way?

    I am glad I understood some of this in my old age.

    The PeSla

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  2. The PeSla, there are many things to do here. The 24 cell will certainly show up somewhere, as others have noted. But I am not sure it will make it to the top of my list any time soon. The list is vast.

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  3. This is moving along very nicely. I'd get involved trying to understand the beauty but I'm trying to get into grad school right now.

    However, I did think a little more about how to generalize Gibb's proof, i.e. to prove that U(n) = phases + MU(n). Last night I thought I had a hint at a method that, given a random unitary matrix, will more quickly find a magic version of it. But it's one of those things that fades in and out at the back of my mind.

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  4. Well, as usual I am not particularly focused on the ordinary Lie symmetries, but it would be good if you found a nice spot in grad school.

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