Monday, February 19, 2007

It's time.

In the great tradition of academia, I am taking a sabbatical from the Blog-o-Tubes. No comment on any connection this hiatus has to "Lent". I'll still be around on e-mail, but that's it.

It's too bad that I won't have time for a post that was on my mind- the relation of virtue and willpower. After watching Letters from Iwo Jima, I had some issues with its de-mythologizing of the World War II drama (in much the way that Unforgiven de-mythologized the Western). In great measure, Iwo Jima undermined the Japanese sense of honor and heroism in favor of delusion and hypocrisy; the only two Japanese characters portrayed as admirable are the Americanized ones, while the 'true believers' in Japanese honor are shown to be frauds, maniacs and fools.

What this movie offers in place of the old heroism is willpower- fighting on when it does no more good. But persevering in utter futility is mere stubbornness (a la Camus' Myth of Sisyphus), not courage. The courageous man will not throw his life away for nothing, but will give his life for something worthy of it. (Yeah, I'm still reading Aquinas and Pieper on fortitude. THEY ARE ROCK STARS.) In particular, courage implies hope, not always in temporal victory, but always the hope that one's act is meaningful.

But that's all I'll try and write about it now- I don't want to spend any more of my weekend than I've already wasted. I wanted to use this as a starting point to talk about my deepening understanding of the virtues, and why Aristotle did not count a tremendous interior struggle as a sign of virtue. But I'm still as disorganized a thinker as I was when I began this blog- if I'm a little more aware of it now, thank God for that at least. It beats going crazy.

Have a splendid feast on the morrow, and may the Lord grant us His peace throughout this Lent!

P.S. I couldn't think of a decent self-description for this blog, so I'm holding a contest on that theme- see the upper right-hand corner! Er, I'm lazy. You might want to include that in your submission.

P.P.S. I don't normally bring partisan politics into ONB, but feel free to actually make these bumper stickers I came up with:

Wednesday, February 14, 2007

I accidentally touched my head,

and noticed that I had been bleeding,
for how long I didn't know.

No, really. There was an unexplained scar on my head this morning. One of my students noticed the bandage; after I explained that I had no idea how I'd cut myself, another student suggested that I must have been drunk last night. I replied that I always got drunk on Tuesdays, to help me write the quizzes.

But in reality, there was no reaction.

Saturday, February 10, 2007

Quotidian Post!

This is one of THREE posts this evening (and probably the weakest of the three)! I just felt a tad inspired, that's all.

Life has been all right. I have this semester to either become an actual mathematician or die trying; I'm planning to take my qualifying exam (contents: me, 4 professors, a chalkboard, and three hours) in late May. After that, it will be time to start making math of my own and working towards a thesis. If I don't screw up too badly, I might have a PhD by 2010.

I've finally gone and started learning how to swing dance, and the first class was excellent; I can't recall the last time I've had so much fun for 90 minutes. At the very beginning, I must confess to a minor bout of totally irrational chorophobia (or perhaps venustraphobia), but the joy of dancing soon overcame that.

Last night was the "Evening with G.K. Chesterton", which lived up to its billing: though I have no way of knowing how thorough was Dr. Chalberg's imitation of Chesterton's manner, it was impressive to hear such a deft synthesis of his famous works- every word was Gilbert's. The food was excellent; Erik prepared an amazing haggis risotto (much better than I'm sure it sounds), a juicy pot roast and more. (Incidentally, you ought to stop by and wish Mr. Keilholtz a happy 'Ducebruary' if you haven't already.)

The company was excellent, too; St. Margaret Mary's has truly become a home for me, and I'm rapidly finding how interconnected is the local community of Catholics wacky enough to consider that the Church might be exactly what She's always claimed to be. Arturo, a.k.a. the Sarabite, is even more erudite and interesting in person than on his blog (which I highly recommend).

From the past to the future- this spring break, I'll be heading out for the East Coast (Lord knows I've paid some dues, getting through...) to see sister Katie in New York and a couple of friends in Boston (i.e. University of Chicago, East Campus). A duel awaits me on the banks of the Charles, and my foe shall be humbled! Oh, and if you'll be in NYC or Boston for the last week of March, dear Reader, don't hesitate to let me know; perhaps there may be a lunch in it for you...

Well, that about sums it up for the time being. Seek the good!

P.S. I finally got a new cell phone, since the old one lost the ability to receive calls. Now people can call me anytime!

Just to Scare Off the Non-Mathematicians

It's been a while since I posted anything about mathematics that wasn't a protracted whimper on my part. In the spirit of improvement, here are two interesting problems I've solved for HW this semester. (Incidentally, I'm not asking you to try these at home; the solutions turn out to be applications of some relatively hefty theorems, not methods you'd arrive at starting from scratch. I just thought it was interesting to show some concrete examples of what I've been up to.)

1. Given any string of digits (say, 1-2-3), there exists a power of 2 which begins with those digits (in this case, 2^90 ≈ 1.23794 x 10^27, 2^379 is approximately 1.23131 x 10^114, etc). (Actually, the exercise proves that there are infinitely many such powers of 2.)

2. If a knight starts on a corner of an ordinary chessboard and moves randomly thereafter (choosing with equal probability from each of its legal moves), how long on average will it take for the knight to return to its original space? (More precisely, if I were to pay you $1 for every move it took before returning to that corner, what sum would you have to pay me in advance to make it a fair gamble?)

oh man, you missed out
For those interested, the first problem can be put into a better context by taking the base 10 log of powers of 2 and always dropping the part before the decimal point (because that doesn't affect the digits, only the power of 10); then it's a question of whether these points are dense in [0,1), and an 'ergodic' theorem (proved with a little Fourier analysis) proves that they are.

And the second problem is from my Probability Theory class, which is now covering Markov chains (situations in which the future doesn't depend on the past, only the current situation). There's a neat theorem that shows that the expected time of return can be derived from a stationary probability measure on the space (in this case, we put positive weights on each square that correspond to the number of ways to arrive at that square).

Looking back, I didn't really do much of a job removing/explaining jargon, but I can't think of a better way at the moment. Anyhow, I think this stuff is pretty excellent, and I do it so you don't have to!

St. Thomas, you win again.

Even pusillanimity may in some way be the result of pride: when, to wit, a man clings too much to his own opinion, whereby he thinks himself incompetent for those things for which he is competent. Hence it is written (Proverbs 26:16): "The sluggard is wiser in his own conceit than seven men that speak sentences." For nothing hinders him from depreciating himself in some things, and having a high opinion of himself in others. Wherefore Gregory says (Pastoral. i) of Moses that "perchance he would have been proud, had he undertaken the leadership of a numerous people without misgiving: and again he would have been proud, had he refused to obey the command of his Creator."

Summa II-II 133, 1 ad 3.
I've been pondering the virtues of late, particularly fortitude, and especially in the context of the Catholic faith and its critics. At Chicago, I was an awful beast of conceit, convinced of my own arguments (more so than convinced of the thing itself) and certain that I could convince the Other after a few more rounds. But at Berkeley, I've transformed into something quite different; I've begun to instinctively retreat from any controversy involving the hard sayings of the Church. (Worse, I've become embarrassed by those who do publicly defend the Church, because I fear being lumped together with them. For that there's simply no excuse.)

As you might have witnessed, the objective content of this blog has declined accordingly. I've ceased to make the naive pronouncements and quasi-aphoristic claims that were my Intertubes raison d'etre; instead, this has become excusively a domain of personal worries, webcomic links and threatened arson (OK, I don't regret that post).

For a while, I've wanted to go back and recapture that feeling of glory and confidence in debate. But that's not what's asked of me, any more than is my retreat into silence and triviality. What's asked of me, insofar as I have anything at all to say, is to look to the truth and leave behind both these extremes of pride: the pride of presumption and the pride of despair.

Of course, dear Reader, you know well just how diligent I've been in keeping prior resolutions of life and mind- particularly the qualitative ones.

Thursday, February 01, 2007

Dammit, Feynman!

I've just realized that in my style of lecturing, I'm turning into my high school chemistry/physics teacher, Mr. Koz. This is actually pretty awesome.

I hope that everybody's had at least one clever and enthusiastic science teacher. I hope that a few of you have had the added bonus of a teacher with awful puns ("What's nu?" "C over lambda!") and self-deprecating humor about his personal life1. And trebuchet-building contests.

What really occasioned this wasn't my spate of awful jokes and cheesy references (though I have realized that the best mental image for teaching determinants involves the game Super Bomberman), but the experience of dealing with students who start to remind me of myself in high school. You know, the student who already knows a lot and is blithely unaware of social norms, so he asks a bunch of questions which either aim to impress the teacher, or draw the class off on a tangent that doesn't help the other 29 students.

It's my responses to these students that start to remind me of Mr. Koz, all those times of "We don't have time to go into this, Patrick!" and "Anybody but Patrick have a question?". Now the shoe's on the other foot. I've evaded, I've swept under the rug, I've answered a "Does this have anything to do with the Gram-Schmidt process?" with a brusque "No!"

It's not that these students make me angry, but it's just going to be tough to teach to the greater number and leave Those Kids' enthusiasm intact at the same time. Sometimes you have to be cruel to be kind.

Perhaps these students fall into everybody's class. Perhaps it's just sweet justice for my own tormenting ways. Either way, I'm going to be very careful that I don't pick up other Koz tics and start ranting hilariously about Valentine's Day (Mr. Koz's advice was, "Only get girlfriends after Valentine's Day, and break up with them before Christmas and New Years- you'll save yourselves a world of trouble") or cubic zirconium ("a guy's best friend").

1. Great Googly Moogly, how did I not realize this at the time? I have heard two different and uproarious tales of romance ruined by rampaging raccoons, and there's no way that either was the source for the other. Maybe they really do know too much...