Thursday, February 24, 2005

In Defense of the Core

I try to follow the blogospheric wars about my esteemed alma mater, and some comments about the core disturbed me. So, a defense.

First, I come to bury the core, not to praise it, and unlike Marc Antony I mean it. The modern core has many, many problems -- large classes, sometimes a lack of intellectual rigor, appearance of being about nothing (a linguistic proof: many a student describing their schedule will list off a bunch of titles, ending with "...and a core."), and I think scrapping it and starting over is a great idea. The trouble is that, on paper, the core makes plenty of sense, which is why it was implemented in the first place. If a student is going to take one course in your discipline and forget most of the material after the fact, what do you want them to get out of it? Most likely an introduction to your methods, approaches to problems, and so on -- you want them to be able to think about things your way rather than name all the characters in some book. And you want the classes taught by good senior professors, so the students get exposure to top faculty rather than whichever postdoc drew the short straw, so you let them talk about whatever interests them while they try to make students understand how to tackle their problems. And yes, there are better and worse works to introduce to people, but who better to judge that than the professor of the class anyhow? Unless you particularly believe in a fairly specific curriculum that everybody should learn, the core is a much better way to go. In theory.

The real trouble, in my opinion, is that there's too little effort to teach students the methods of thinking that are the purported purpose of the core -- some classes do, others just assume that everyone can do it when they come into the class. If I could make just one change to reform the core, it would be to try to do this more formally: every area has to figure out what methods of analysis they're trying to teach, then actually teach them in some way rather than merely hope the students can osmose it from their TFs. It's the mismatch of this idea to actual core areas (the core is split by vague topic-area division rather than reasoning method) that seems to breed the trouble. And it's a lot of trouble. The core in the real world is horrible, but that doesn't mean the philosophy is broken.

Tuesday, February 22, 2005

Leftovers

I've been thinking politics, god, complexity, probability, and other abstractions all day, some with a mind for a blog post. But will I post on any of them? Nope. Time for food.

So I've finally decided to start roasting chickens seriously, figured it all out, and now do it fairly regularly; I try to pick up a roaster every time I go to the store. It's way too easy to not, and has the benefit of producing a mountain of leftovers when I do it for just me and Kara. On the other hand, now I have to figure out what to do with a mountain of leftovers.

I recognize this should be easy. Cooked chicken in little bits is in a million dishes and is half the point of roasting a bird for two people to begin with (the other half is that it's great to have the carcass around for stock and I'm kinda ashamed of buying parts), but I feel I'm coming up short of ideas. With spring break coming fast, I need answers soon. Soup, hash, quiche -- what else?

Two caveats though: my roommate likes neither Asian cuisines of any type or any dish involving rice. Don't ask, just believe. Second, I have a longstanding visceral dislike of chicken salad -- it's a ridiculous prejudice, but I think it's slimy. Tuna's fine, but no chicken.

PS: Joy of Cooking's recipe for "Turned Roast Chicken" is the best I've found -- you get a whole, well-cooked bird at the end with a bunch of pan drippings for gravy (their recipe plus a shallot works surprising wonders) for about 1:15 roasting time.

Monday, February 14, 2005

Recruitment

My stoop is filled with packages, seemingly mostly flowers and chocolate, for occupants of other apartments.

Anybody want to help me promote fertility and the civic good by running through the streets naked, whipping the young maidens with bits of wolfhide?

Sunday, February 13, 2005

Memeing

Trying in my vain way to help produce the college-prof-thanking meme that Brad DeLong's been talking about, shoutouts to (in no particular order; non-me-in-college profs not on the list):

Leslie Valiant, Noam Elkies, Salil Vadhan, Michael Rabin, Lisa Carbone, Nathan Dunfield, Steve Rosen, my amazing history of technology prof whose name I have utterly forgot (crying shame because I think she's here now), Andreea Nicoara, John Boller, Andy Engleward, Gerald Sacks, and many more.

Doing the math

There's a part of me that wants to devote lots of time and energy to rebutting Ross Douthat's ridiculous articles and books about Harvard; he's a huge liar, he knows it, and he should be ashamed. There's another part of me that, unlike any part of him, is doing something constructive with its time, and it's this part that complains about me arguing too hard. So on the off chance he reads this, let me simply say that just because you're a dumbfuck doesn't mean Harvard was bad in any of the ways you describe.

The thing that pisses me off today though is misuse of math. Supply-siders like to claim that since a tax rate of 100% would yield no government revenue, lower taxes must always increase revenue, because people will work harder if they can keep some money. However, a tax rate of zero also produces no revenue; what we can conclude (if everything is smooth) is only that there are points where higher taxes mean more income and points where higher taxes mean less. So we can argue about where the changeover point is (or how many there are), but in reality both of these things must be true. Conservatives can't really debate this because it would lead to the obvious truth that current tax rates are on the wrong side of the local maximum for supply-side arguments (nobody fails to start new projects because they're taxed at 39% rather than 36%); all I'm saying to people is do the damn math, draw the conclusions, then argue from there.

Thursday, February 10, 2005

Unsubstantiated Thoughts

It occurs to me that I miss Douglas Adams. Perhaps this sensation of missing will be enough to make me dive through the giant stack of boxes of books that now takes up the better part of my bedroom.

Many topics seem to have, at least in terms of public debate, a fairly constrained space of tropes that can be invoked in favor of or opposed to any position on them (foreign policy, Social Security); moreover, some of these are clearly better than others and once one side uses a given trope it stops being available to the other side. That said, since there are currently no repercussions for using rhetoric bearing no relation to the policy actually being advocated, it seems like a strong strategy for many political arguments is simply to grab up the good tropes before anybody else gets to them.

Reductions are like homotopies. Hrm.

The current crop of AI contenders have absolutely no ability to learn lyrics. No brain whatsoever. Hrm again.

Tuesday, February 08, 2005

I'm guessing

... that my hypothetical readers don't care to hear me muse about spectral sequences (a chunk of math which is basic but of technical complexity high enough that the only way to understand is to work it out for yourself); if this isn't the case, let me know. Otherwise, I'll keep my mouth shut.

On the other hand, they are an example of a kind of intellectual phenomenon I have seen rarely outside of math: machinery. Within math, this term refers to a theory not a priori interesting in its own right, but potentially very enlightening for dealing with other stuff, usually connoting a high degree of internal technical complexity that may not be necessary for the use of the theory for its desired purpose. I suppose math itself may function this way in other fields, but somehow that seems too conceptual to count (though of course I would say that in any case); machinery is characterized by being somehow un-conceptual, while math used in other fields is usually used because it makes sense in that context. Hrmph.

Inevitably, of course, I can't elucidate the concept via example without explaining something non-mathematicians haven't even heard of. So hrmph.

By the way, "musing" would be a written record (presumably half in pseudo-tex) of me trying to figure out spectral sequences, i.e. many sentences filled with strange symbols and stranger attempts to write them in ascii. Just be aware.

Sunday, February 06, 2005

Current Reading

A friend gave me "What's the Matter with Kansas" for my birthday; I'm pretty sure that all actual contents of this book are seriously old hat, so it's not worth mentioning the obvious conclusions (Dems need to link capitalism and mass-produced culture better, intellectuals need to grab some victimhood), but I did have one thought not entirely implied by the book -- the larger an organization gets, the worse it is at complex optimization strategies. In particular I was thinking about the way that bigger corporations get worse at worrying about things that aren't the bottom line, particularly things that seem like they ought to be constraints like the law or treating people like humans. And it seems to me that in general bad corporate behavior, when not orchestrated from the top, can be completely emergent since more layers of management make it harder to explain why a particular action is the best permitted by constraints. If anybody knows about anybody I could read on this point I'd be gratified.

In the meantime, I went to the supermarket today and saw low-fat butter. Aaaaarrrrggggghhh.

I'm still waiting for low-meat steak.

Thursday, February 03, 2005

State of the Union

I would like to let it be known that I have a plan to solve our {social security, foreign policy, terrorism, tort, medical, energy, budget} crisis. It will make us all healthy, wealthy, and wise, not to mention better people. Also, it will ensure that our children will all be all of these things too, not to mention attractive and tall. But we must not content ourselves with these victories; I will give every child in America a puppy, wish away everyone's extra pounds, and supply every man with a pliant supermodel for a girlfriend, and anybody who questions any of this must hate America.

So whose job is it to make sure statements agree with some semblance of reality? The disinterested public? Right.

Wednesday, February 02, 2005

Fun with math

So I was pondering life today and thinking about the joy of mathematics and about how life works, politics, the whole bit, which inevitably led into one of my favorite facts about probability: the Chernoff bound. I fairly regularly bemoan the general public ignorance of probability, so I explain as a service, but hopefully also 'cause other people will think it's cool too.

Of course, like most cool things, it's both simple and complex; the complex version is all jazzy with symbols and precision and generality (in fact, so much that there are many different statements called Chernoff bounds for different situations), but the simple one just has a few words: if you flip n coins, the chance that you'll get more than a fixed bit off from n/2 heads decreases exponentially as n gets bigger. Another version: the longer you play, the more likely you get closer to expectation. If the coin is biased, it just changes that last fraction. It's a little subtle to get properly, but explanation won't help, so some exercises for the reader:

1) Why does polling work?
2) How do you explain why casinos make crazy profits, but backing a roulette game is a crappy thing to do with your life savings?
3) Why is social security privitazation bad?

I'll post my answers some other time if anyone cares. In the meantime, it's cool to ponder...