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.

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

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.

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.

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.