Dec 10 07

Spent another few hours getting nowhere with research today. Interrupted it with x-mas shopping and various other nonsenses, but not too many. Let V_k(Rⁿ) be the Stiefel manifold of k-planes in Rⁿ. Let d be the dimension of the normal bundle for the inclusion V_k(Rⁿ)-->hom(R^k,Rⁿ). For completeness sake, notice d=(1/2)k(k+1). While I'm not entirely sure it makes sense to talk about, I'd also say the dimension of Σ|R_k-1^k|, from yesterday, is this same value. This follows from the dimension of the maximal flag manifold, which is sitting as the k-1-simplex (if any of that is actually true to talk about). Along with not being sure any of this makes sense, I'm not sure how to use any of it.

In actually exciting news, the library had not only the LaTeX graphics companion, but the LaTeX companion and the TeXbook. So I might make the TeXbook my night-time reading. Chances are this week I won't need much reading before I fall asleep.

Only interesting news item I remember from today was Dvorak's rant against the OLPC project. I've been practically giddy about the OLPC project since I heard about it, and the laptop they've come out with. I'm still having a very hard time convincing myself not to participate in the give one get one program (thanks for the extension on that, by the way). But I do wonder how useful the laptop is as a charity sort of thing. Presumably the places they are going are not places where starvation is the main concern? Should money be siphoned away from food for some to go to education for others? What about all the money I spend on myself for things I don't actually need? Like a child's laptop?