Running

I don't expect anybody to care, but I want to have a record of it. This year I ran 1002.5 miles in 150 runs (6.68 miles per run avg.) totaling 120:41:32 for an average 8.31 miles per hour. Wouldn't mind getting the miles up and the time down next year. We'll see.

Sorry, to all my readers who waited eagerly over the past week or two for a new post. I was home and didn't feel like it. I was busy making origami and TeXing another book. Hopefully I'll have more to say again these days.

One thing I did do was change my google shortcut to use the keyboard shortcuts experimental feature. I love keyboard shortcuts. It was easy, just add '&esrch=BetaShortcuts' to the end of your request. Then I used the Ad-Blocker Plus Firefox extension to hide the message about how I'm currently using the keyboard shortcuts feature. Totally sweet.

Ice Cream Fueled Musings

Back from my ice cream. Since I don't seem to be directing my energies at math today, I thought I'd keeping rambling here. So, I can't decide what to do about charitable donations. I'm sure I should, basically because I can. But how do I know who to give my money to? Is there a poset of charities I can consult, ordered somehow that lets me pick a 'best' (perhaps from some small several of maximal elements) choice? Who set up this poset, and how did they decide? Is there some global cause bank, where all the charity agencies (what qualifies?) can just turn and submit proposals for money? So I could just submit my money to this central hub, and let them decide what to do with it? What's the (is there a?) world bank? What does the UN actually do, and do they have a role in this? If I actually cared, wouldn't I start looking things up? Or am I just a (stereotypically?) self-centered ass hole American? By making this blog, haven't I exhibited my self-centered-ness?

And why do we still have nations? Are they really necessary? Aren't we all members of a global community? Where's Einstein's (didn't he say something about this?) passport as a citizen of the world? Where's mine? Doesn't segregating people based on birth place lead to stereotyping and pride and prejudice (not the book, certainly not the movie)? Or is stereotyping an (necessary?) evolutionary trait that helps us survive our monkeysphere? Even if nations really are that important, instead of just geographic identifiers for somebody's current location, why can't we have a global currency? Or a global language? I'm perfectly happy preserving local flair by making everybody learn their nation's language(s). I'm not asking people to become all the same, that's stupid. But couldn't we also teach our children, while they grow up, some global language, like esperanto or something? [Update 12/21: I'm not against the idea of dividing regions up into nations, states, provinces. I can see that this makes local government, and preservation of culture and such, easier. What I'm against is... raging, unreasoned patriotism I guess. I don't know. I don't think about it that much, honestly.]

Back to charities, in typically stream of thought rambling. Aren't I living on a charity? What are you doing with your life that's so deserving of pay? I mean, why should I get paid to learn about the calculus of functors? More generally, why should mathematicians get paid at all to do "pure math"? What should I be doing to actually earn my living? Maybe I'm getting paid to be a teacher, and need to do research so that I can present my topic better to my students. But if my students follow in my footsteps toward pure math, or never use the math I teach them again, then why should I get paid to teach? If I want to make some difference (if such a thing can actually be made, or we even have time to make it - when's that apocalypse people have been calling for?) shouldn't I give up all my personal interests, and basically give up myself? To who? For what? Why bother?

While I'm talking about teaching, here at the end of the semester, how do I best determine a student's final grade? Take my calculus class for example. I had weekly written homework, daily online homework (using webwork), weakly quizzes, two midterms and a final. There were 250-300ish points for each type of homework, 100ish points for quizzes, 100 for each midterm, and 150 for the final. If quizzes were 5%, written homework 12%, webwork 13%, each midterm 20%, and the final 30% of the final grade, how many decimal places of their final grade is actually meaningful?

Wow. I feel like a philosopher or somebody else I might not respect. All these questions without answers. Probably most of them entirely unanswerable. Maybe I should just pick a cause and move on. Throw a bunch into a hat. I mean look, I just wasted at least the last hour or two or three thinking about and writing these things. Not to mention the 12 hours of sleep I got last night. Shouldn't I have been learning math to get my phd so I can go teach kids who will promptly forget all of the ivory-towerish things I say? Or at the grocery store buying food to donate to some homeless person living under a bridge here in cold and rainy cville? Setting up, or finding, a global fund for charities? Finding somewhere isolated and living as part of nature? Answering some of these damn questions?

Knol

There have already been numerous postings about it (Google's Knol), so I probably don't have much new to say. If you don't feel like reading the above links, its a user-generated knowledge base, similar in spirit to wikipedia (and apparently mahalo and squidoo, which I tried for the first time today (neither turned anything useful up on category theory, so I quit early)). I am excited about it, because it could be fun. As mentioned elsewhere, the project may cut into wikipedia's (which I also like) success. But if google('s algorithm) is fair about deciding quality of articles, it shouldn't be unreasonable. Both systems should be able to coexist, they both have a place and will both contribute to global knowledge. As pointed out in the above links, the two systems are based on slightly different principles. Where wikipedia is focusing on having a single page for a topic, google is encouraging competition - and rewarding winners with ad revenue.

Would I post to it? Sure, if I thought I knew something I could post about. Would I read articles from it? Of course. Hopefully there'll be some good math ones. I've basically been waiting to try getting my math database together until google (or somebody else) beats me to it. They sure are taking their time though. On that note, while I'm here, I was reading the conference proceedings from the third international MKM conference, and the article on c-corn looked like it'd be inspiring. We'll see.

This is certainly an exciting time. We've got applications becoming more and more web based, and hopefully in the process more open. We've got olpc and co. distributing laptops to (hopefully) millions of children worldwide, opening everybody's worldview (maybe?). And this large new set of users mean more big changes are probably right around the corner.

Talked with Sean yesterday, who raised doubts about the olpc mission. I still wonder, like him, if laptops are really the priority. Maybe I should be giving my money to another cause? Which? Is it ok to pick one, make myself believe I'm helping, and keep about my day to day life? Or should I quit everything and sign up for the peace corp? Live escetically so I'm able to donate more? Buy a laptop and try to come up with a program to write for it that kids would benefit from? Buy one and not?

What a mess. I think I'll go have some ice cream.

Thompson v. Dvorak, OLPC

Yesterday's news, but I was tired yesterday from doing calc stuff: Bill Thompson, at BBC, replied to Dvorak's recent remarks about the OLPC program. And Thompson didn't agree with Dvorak; he thinks its a worthwhile program. I also like to think (hope) so. Because I like to think about getting an XO laptop (and therefore giving one). Still debating about it. With the $400 I could also get a nice couch I found at World Market today. The Studio Day Sofa looks to be what I've been thinking I want in some furniture, the next time I think about buying such a thing. If anybody knows of the same shape thing somewhere else for cheaper, I'd be happy to hear about it. Maybe someday I'll peak in an IKEA. Since this summer I'm moving for the 3rd time since getting to grad school, I'm not really looking to buy much in the way of heavy things to lift. Laptops aren't that heavy.

I almost forgot to mention another thought this debate sparked. It illustrates one of the things that draws me to math. In math, there really aren't that many arguments without a winner. If two people are arguing about the correctness of a statement, either they are both wrong, or exactly one is right. Clearly this is not the case in the real world. At least, this is the picture I have of the subject. Perhaps with more experience, I'll learn otherwise. But I certainly hope not. While I'm on the subject of arguments without winners, I'm tempted to touch on religion. But people get more riled up about that than laptops or math, and I don't really feel like (or see the point in) arguing with them.

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?

Putting in Time

Well, I spent most of the afternoon trying to learn things. Might as well have just watched movies though.

Suppose I let R_{k-1}^{k} be the poset of vector subspaces of real k-space whose dimensions are bigger than 0, and no more than k-1 (that is, a point in this poset is a vector space E that is a subspace of real k-space, and 0<dim E<k), ordered by inclusion. This is then a topological category (that is, a category internal in Top), with object space the disjoint union of so many Grassmannians and morphism space the disjoint union of flag manifolds (flags of length 2, I guess you'd say). I've been trying to sort out the realization of this category, because it comes up in a homotopy limit I'd like to calculate. The nerve is a simplicial set whose non-degenerate simplices are flag manifolds (the length gives the dimension of the simplex), and so the largest dimension in which there are non-degenerate simplices is k-1 (those chains E_1<E_2<...<E_{k-1} where dim E_i = i). Anybody have a reference for somebody else's work on this topic? Because I'm not getting anywhere, and it feels like the sort of thing people would have been interested in already. [Update: Found it]

Also finished reading E. T. Bell's "Men of Mathematics" today. I don't remember getting a whole lot out of it, but I guess that'll happen. So now I gotta figure out what to read next. Kinda feel like I should read "Women in Mathematics", which I feel like I've seen in the library. Also just heard about an author Pynchon, sounded like he might be fun.

Guess I should go prepare something to teach LaTeX to high schoolers.

Post the First

Hello World?

I here $\LaTeX$ doesn't work? Nope.