Systems of linear differential equations

We're studying systems of linear differential equations (or vector-valued differential equations) in my class right now. Since linear algebra isn't an official prerequisite for the class, I've had to give a crash course in matrix algebra and eigenvectors during lecture. I think I've succeeded in going in enough detail to bore everybody who's taken linear algebra, but briefly enough that the students who haven't taken linear algebra are still confused. Win-win, baby.

But seriously, I think it's a better idea to leave systems of DEs for a linear algebra class. The time could be spent looking at Laplace transforms or numerical solutions -- these are tools that are more useful to a wider audience, I think. Anybody who needs to know about systems of DEs probably also needs a full course in linear algebra, and it's easier to teach DEs in a linear algebra class than it is to teach linear algebra in a DEs class.



One final note on Larry Summers:

I'm disappointed that Bono didn't fly up from Brazil (where U2 is currently touring) to support a man who worked with him on his campaign to end third world debt. Out of admiration, Bono called Summers "a nutcase and a freak".

One silver lining

One positive outcome from the whole Larry Summers mess is that Derek Bok will be taking over as interim president in July. Bok is perhaps best known for being the father of former Harvard Ultimate Frisbee captain Tom Bok. Tom's Ultimate skill and general sense of style are well depicted in these photos.

With a supporter of Harvard Ultimate at the helm, hopefully the team can secure increased funding for the future and have a say in the planning for the Allston campus. The artists' renditions that I've seen of the future Allston campus show some sort of canal bisecting the intramural sports fields, where the team usually practices. Clearly these plans cannot stand, unless they're planning on giving the team its own indoor FieldTurf practice facility.

Gotta strike while the iron is hot...


A sad day for Harvard

Larry Summers has resigned his position as President of Harvard University.

Personally, I'm very disappointed that the clash between Summers and the Faculty of Arts and Sciences came to this end. Summers had a clear vision for where he wanted to take the University in the 21st century, and he had accomplished many tasks towards this vision:

  • In partnership with MIT, Harvard helped establish the Broad Institute, a new research lab devoted to the application of genomics in medicine.
  • Harvard has established a new lab for stem cell research.
  • Harvard has made it easier for students from poorer families (household income less than $60,000) to attend the College by reducing or doing away with the expected household contributions to tuition and directly inspired a certain university in New Haven to do the same.
  • Summers has expressed to improving the education and overall experience that the College offers. What is surprising is how much Summers himself has directly contributed to this end: he teaches a freshman seminar on issues of globalization, and gives guest lectures and makes appearances at all sorts of campus events.

Alas, for all of Summers' positive accomplishments, he's gotten into a number of dustups with FAS, some small, some bigger:

  • He got into a famous dustup with former University Professor Cornel West over the quality of West's scholarship and some of West's extracurricular pursuits, like recording a spoken-word CD and campaigning for Al Sharpton. West left for Princeton not too long after. Summers probably could have handled that better, if West's account of the private conversation is accurate. To his credit, Summers has refused to give his account of the conversation.
  • He denied tenure to hip-hop scholar Marcyliena Morgan, who had been unanimously approved by her colleagues in the African-American Studies department. Shortly afterward, she and her husband, tenured sociologist Lawrence Bobo, took tenured positions at Stanford. Regardless of the actual merits of Morgan's work, Summers upset a lot of people in the Af-Am department (and possibly elsewhere) with this decision, and he clearly underestimated Morgan's value on the open market.
  • It's clear that Summers believes that basic research in quantitatively-driven disciplines is central to Harvard's success in the future. On the flip side, he's made intemperate private remarks about his estimation of some of the other humanities disciplines to former GSAS dean Peter Ellison.
  • In the aftermath of 9/11 and some of the leftist commentary about the attacks, he proclaimed that Harvard needed to return to patriotic values. Summers, who is Jewish, also said that the whole divestment from Israel campaign was "anti-Semitic in effect, if not in intent". He's entitled to air his views on these matters, of course (and I think he was right), but he probably could have done so using language that wouldn't have immediately upset large numbers of the faculty.
  • He fired Dean of Harvard College Harry Lewis and consolidated the offices of the Dean of the College and the Dean of Undergraduate Education into one office, and handled it rather poorly, I think. It's understandable (even if one disagrees with it) that Summers would want to restructure the administration in this manner in order to emphasize undergraduate education over extracurriculars, but Lewis deserved better.
  • Summers's handling of the forced resignation of former Dean of FAS Bill Kirby was even worse, if he indeed was responsible for leaking the news to the Crimson. The faculty had demanded a much bigger role in the selection of the new dean.
  • Plenty of professors have complained that Summers goes over the heads of the faculty in floating various proposals and has ruled by creating a "climate of fear". Sometimes they cite the incidents above. Other times the complaints are more nebulous, although they may be revealed more concretely now that Summers is out.

It's clear that Larry Summers has stepped on a lot of toes (sometimes intentionally, sometimes inadvertently) during his presidency. It's really too bad that he never mastered the art of picking his battles, as he was really committed to advancing scientific research at Harvard, making faculty more accessible to students and reforming the undergraduate experience at the College. The end of Summers's presidency is a real loss for Harvard.

UPDATE: This opinion piece from Slate is well worth reading.


Guided spam missiles

Apparently some companies hunt you down and spam you if you register for various online amusements and promotions using a throwaway address. Supposedly this is the work of Equifax, the credit bureau, which somehow has been able to build up a database of millions of email address changes. I certainly hope so, because if they managed to accomplish this by tracing IP addresses, that'd be really hideous.

So if you're going to use junk addresses for this purpose, make sure that absolutely nobody knows about them.

Bad beats (or, how Tom Osborne cost me $25)

Okay, so I'm playing in a hold 'em tournament with a few church folks. Nine players, entry fee is $5, prizes are $30-$10-$5.

We start playing at 9:15 pm. I play tight and win some big pots with pocket aces, Aces-Queens and later push some other players out of draws with strong betting. I only make one major mistake all evening, losing a king-high flush to the nuts. At one point, the guy to my right (Kevin M.) says "what happened to all my black chips?". I rustle my stack of black chips in my hand and nonchalantly hold them out for him.

It comes down to a three-person game at around 12:15 am. Like all three-person games, it takes forever. Eventually the hosts (Winnie and Emi) decide to timecap the game at 1 am.

At 12:59 am, the last hand is dealt. I'm the chip leader, 3000-2000-800 or thereabouts. (Don't ask me why we used such a high denomination.) I'm in the small blind and I get dealt A7. Everyone limps into the blinds, and the flop comes: Q68. I make a small bet, and 500 (Leslie, who was subbing for Salome) folds. The button (Larry, subbing for Deborah) then moves all-in, as he had been doing on many hands (stealing blinds) during the three-person game. At this point I can just stall out this hand, fold, and claim 1st place. But instead, I choose to go for the win in regulation and the undisputed title, like Tom Osborne did 22 years ago. Or maybe I was channeling my inner Lindsey Jacobellis.

Larry turns over A5. I'm in good shape.

Turn card comes: 2. He's down to three outs.

River comes: 5. I finish in third place.

Oh well. I still have the best verbal game of anyone there, just like Mike Vanderjagt and Mike Matusow.


Olympic hockey

Goalie Martin Gerber played like a Swiss bank vault in a 2-0 upset over Canada.

Meanwhile, the ridiculously lopsided scores in an eight-team tournament are a pretty good sign that women's ice hockey isn't competitive enough worldwide to belong in the Olympics.

UPDATE: Apolo "don't call me Yoko" Ohno just finished behind two South Korean speed skaters in the 1000m short track event. I can't wait to see the reaction in the motherland; it should be hilarious.


Sadly, nothing over these last few days has inspired a new blog entry.

But while I'm struggling with blogger's block, read this entry by Josh Foust, a gay evangelical Christian and one of my favorite bloggers.


Just as a reminder

De Beers, the international diamond cartel racket distributor, is the most evil corporation in the history of the universe.

Here's a classic article from the Atlantic Monthly back in 1982, and here's one of my favorite blog posts on the subject.

Anti-Valentine's Day playlist

Okay, so I realize the concept of an anti-Valentine's playlist went GP on us years ago. And I realize that some couples are able to genuinely celebrate Valentine's day, free from the pressures foisted upon us by tacky advertisements. Here's the playlist anyway:

1. The Beatles, Run For Your Life. This is the last track on the critically acclaimed album Rubber Soul. After years of writing silly love songs, John Lennon started developing a really dark side around this time. The song opens with "I'd rather see you dead little girl / than to be with another man" and doesn't get much happier. Yow.

2. The Beach Boys, Here Today. Inspired by the sonic genius of Rubber Soul and by massive amounts of THC, Brian Wilson slapped together the album Pet Sounds, on which this song appears. "Right now you think that she's perfection / this time is really an exception / well you know I hate to be a downer / but I'm the guy she left before you found her."

3. Justin Timberlake, Cry Me A River. The Britney Spears-lookalike in the music video was a concidence, really. "So you took a chance / and made other plans / but I bet you didn't think they'd come crashing down."

4. Bob Dylan, Just Like A Woman. This is vintage Dylan: "She takes just like a woman / she makes love just like a woman / and she aches just like a woman / but she breaks just like a little girl."

5. The Cure, Boys Don't Cry. I'll take a break from the rampant misogyny here. "I would break down at your feet / and beg forgiveness, plead with you / but I know that it's too late / and now there's nothing I can do."

6. Billy Joel, Stiletto. Back to misogyny, with a dash of sadomasochism thrown in for flavor. "She cuts you once / she cuts you twice / but still you believe / the wound is so fresh you can taste blood / but you don't have strength to leave."

7. Bob Dylan, If You See Her, Say Hello. "Oh, whatever makes her happy, I won't stand in the way / though the bitter taste lingers on from the night I tried to make her stay." Apparently Dylan was not just divorced, but also emasculated when he wrote this song.

8. Marvin Gaye, When Did You Stop Loving Me, When Did I Stop Loving You. Speaking of divorce albums, this is from Marvin's own divorce album, Here, My Dear. As part of the settlement, he had to fork over part of the proceeds from this album to his ex-wife. "If you ever loved me with all of your heart / you'd never take a million dollars to part." By the way, feel free to ignore the fact that Marvin was a philandering scoundrel who fathered a child out of wedlock and blew his money on Mike Tyson-esque shopping sprees (thus necessitating the record deal) if that bothers you.

9. Prince, When You Were Mine. Speaking of philandering scoundrels... "When you were mine / you were kinda sorta my best friend / so I was blind /I let you fool around / I never cared / I never was the kind to make a fuss / When he was there / Sleeping in between the two of us." Eew. (Cyndi Lauper's cover is worth a listen as well, though the exchange of gender confuses a few things.)

10. Cyndi Lauper, Money Changes Everything. "Oh how could you do it / we swore each other everlasting love / I said yeah I know but when we did / there was one thing we weren't thinking of and that's / money, money changes everything." Not that I'm cynical or anything.

11. Madonna, Material Girl. Same year (1984) as the track above, same theme. "They can beg and they can plead / but they can't see the light / 'cause the boy with the cold hard cash / is always Mister Right."

12. Dave Matthews, Grace Is Gone. "One drink to remember / then another to forget / How could I ever dream to find / sweet love like you again." Nothing chases away the Valentine's day blues like alcohol. The album gets even funnier at the end when Dave Matthews portrays God as a cosmic bartender.

13. Blue Oyster Cult, (Don't Fear) The Reaper. "Valentine is done / here but now they're gone / Romeo and Juliet / are together in eternity / 40,000 men and women everyday." See, this is what happens when two persons love each other. The statistic quoted in this song is one order of magnitude too high, however.

Well, there you go. Happy Valentine's Day.



Just heard a bunch of folks in the White House press corps complaining that they found out about Dick Cheney accidentally shooting a fellow hunter from some local paper in Corpus Christi, who found out from some random friend of Cheney.

It's too bad they didn't find out from a blogger -- the reaction would have been hilarious.


Egregious miscarriagement of taxitude

I hate California.

Califonia taxes income really progressively -- 1% up to $6,320, then 2% up to $14,980, then 4% up to $23,640, then 6% up to $32,820, then 8% up to $41,480, then 9.3% thereafter. By contrast, Taxachusetts collects a flat 5.3% tax. But that's not what really annoys me. (At least it doesn't annoy me now -- it will next year, once I earn an entire calendar year of income here.)

What really annoys me is that they discount your deductions by multiplying by the fraction of the year's income you earned as a CA resident, but then turn around and tax you at the rate you'd pay if your entire year's income was earned as a CA resident. Bastards. (Massachusetts discounts your deductions by multiplying by the fraction of time spent as a resident of the state, but doesn't try to shove you into a higher tax bracket, because it has a flat tax rate.)

Fortunately, my Massachusetts income from last year was fairly low. I graduated in Fall 2004, so I received TA income in spring 2005 but no grad student stipend. But the moral of the story is to move into or out of California only at the beginning or end of the calendar year.



The list of nominees for this year's Grammys was quite underwhelming. U2 swept its awards with an average album (for them) that had only one outstanding song ("City Of Blinding Lights") and one hit that wore out its welcome really quickly ("Vertigo").

The distinction between "song" and "performance" is a false one that dilutes the awards and needs to go. This isn't professional boxing.

Good thing Kanye West win a couple -- after getting jobbed by Maroon 5 for best new artist, I think he'd have gone postal if "Late Registration" had been denied.

Damian Marley's "Welcome To Jamrock" won Best Urban/Alternative Performance. He's good. His best music blends reggae music with hard rap lyrics.

There was something a bit off with a 63-year-old, sober Paul McCartney performing "Helter Skelter" while wearing a suit, but I can't quite put my finger on it.

UPDATE: A conspicuous absence from Kelly Clarkson's list of thank-yous was the crew at American Idol, who are probably more responsible for her Grammy than all of her family, friends and record label personnel put together. Hmm.

UPDATE: I just figured out what was wrong with "Helter Skelter". The drummer didn't scream out "I GOT BLISTERS ON MY FINGERS!" at the end.


Multivariate calc in American high schools? The mind boggles

It's true. And apparently it's not just in these high schools either (though the article does focus on Montgomery County in MD and Fairfax County in VA, the homes of the last two schools I just linked).

Once you get through epsilon-delta limits and the conceptual meaning of the Fundamental Theorem of Calculus, single-variable calc is pretty mechanical -- you just memorize a bunch of derivatives, employ some pattern-matching skills to decipher integrals, get the hang of a few word problems, and so forth. Multivariate calc isn't conceptually much more difficult. Usually the sequence for good students goes like this: algebra in 8th grade, geometry in 9th, algebra II in 10th, trig/pre-calc in 11th, calc in 12th. I'm sure that in the better school districts in the US, there are enough students who are qualified to take algebra in middle school and can ace calc in 11th grade or earlier that a class beyong single-variable calc should be a standard offering. When I was in 6th grade at this private school, there were a bunch of 6th graders taking algebra, and a good number of 10th and 11th-graders taking calc, though they didn't offer anything beyond calc. I think schools could get kids more interested and better prepared for the algebra-through-calculus sequence if they stopped giving it such an aura of mystique.

Of course, the sad fact is that this advanced math track is really quite standard in other countries (scroll down to page 7 of the article). (Actually, the main reason I like this article is because half of the Math 55 class I TA'd last year was interviewed in it.)

And I'll bet none of these kids in the WaPo article reads at a 78th grade level.

If there was any justice, my face would be on a bunch of crappy merchandise

The WaPo has an amusing article on the cottage industry of Che merchandising. They missed this shirt, however.

Considering statistics in a relative context

In the past, I've ranted on about sports announcers and writers using statistics that really don't mean much.

This postseason, NFL fans have been clubbed over the head with the statistic that Bill Cowher is 100-1 or somesuch in games in which the Steelers take a lead of 11 points or more. Now I'm willing to believe that Cowher is good at teaching his teams to sit on a lead, but how good is the average coach with a 11-point lead? 80 percent? 90 percent? 95 percent?

A related gripe is when analysts invariably talk about "keys to victory" for each team. Avoid turnovers. Don't get into foul trouble. And so forth.

Well, duh. Leaving aside correlation vs. causality for now, of course these things are keys to victory. Avoiding turnovers is good (provided your offense doesn't become too conservative). Staying out of foul trouble is good (provided you don't start playing matador D). It's much more important to weigh these things relative to each other. ESPN had a nice couple of articles on these sorts of truisms in football a while back, showing that some factors strongly correlated with winning, others not at all.

Sports media types need to ask, and figure out, which of these factors are more relevant than others. Is it more important to shut down Dwyane Wade or Shaq? (My bet would be on Wade.) How much blitzing is too much, and in which situations? (Blitz more on 1st-and-10, not as much on 3rd down or when the QB is in shotgun, and almost never on 3rd-and-long is my guess.)

Sites like Football Outsiders and 82games do a good job of asking these sorts of questions, and it's unfortunate (if unsurprising) that major media outlets, despite their greater technological and statistical resources, have writers and announcers who can't make use of them.


Philosophy of officiating

I think that not materially penalizing a team for personal conduct infractions that occur while play is dead is a pretty sound principle of officiating. It follows that I believe that the penalty accompanying a technical foul -- one free throw in the NBA, one free throw plus possession (?) in NCAA ball is a terrible penalty, and that counting a technical foul as a personal foul in NCAA ball is an even more unfair penalty still. The purpose of a technical foul should be to censure a player, and nothing more.

(Yes, I know that two technicals result in ejection, which does materially affect a game. Some limit is necessary; the point is that T's should not be treated the same as in-play fouls. And I don't mind if these sorts of fouls are called for in-play infractions, like delay of game or illegal defense in the NBA, or unnecessary roughness in football.)

I bring this up because the ACC recently suspended the officials who refereed the Duke-Florida State contest for one game because they incorrectly called a technical foul on Florida State's Alexander Johnson. Johnson mugged Duke player Shelden Williams on a layup attempt. Johnson was correctly assessed an intentional foul. Williams then shoved Johnson in retaliation while Johnson backed away, and technical fouls were called on both players. The technical foul on Johnson counted as his fifth foul, disqualifying him from the game.

The underlying problem here is not that the referees used poor judgment in assessing a technical on Johnson, as the referees can't really be blamed for acting quickly to defuse a heated situation. The problem is that the accompanying penalty did not just reprimand Johnson; it affected the outcome of the game. The NCAA needs to extricate these three officials from underneath the bus and get rid of these penalties accompanying the technical foul.


Super Bowl XL post-mortem

Bleh. Stevie Wonder and the Stones were competent, but pretty flat in the pregame and halftime shows respectively.

Tom Brady conducted the opening coin flip. Seeing him smirk and cackle as the predominantly Steeler crowd booed him was priceless. Also present at the coin flip, as one of the Seattle Seahawks' 26 captains for the game, was Harvard alum Isaiah Kacyvenski.

Neither team seemed to be at their peak. At the beginning of the game, it looked like Matt Hasselbeck was going to carve up the Steelers secondary, but then made a lot of inaccurate passes and was hurt by a bunch of drops over the last three quarters, with or without pressure. Joey Porter and Troy Polamalu didn't seem to be really big factors on the pass rush; Seattle just made a lot of offensive mistakes. Also, the clock-management on their last drive of the first half made them look like they had taught by Herm Edwards.

Ben Roethlisberger never got into a groove the entire game, after three excellent games in the AFC playoffs. I'll lay part of the blame on the offensive-playcalling. Run on first down, run on second down, throw on third down. Gets predictable after as while. The TD pass of the reverse in the second half was beautiful, even if Pittsburgh runs it several times a season.

I think we can all agree that having two weeks between the conference championship games and the Super Bowl sucks. If people really want to the attend the Super Bowl, they'll find a way to get there within a week.

There were a lot of key calls that went against the Seahawks. I thought most of them were correct except for the pass interference against Darrell Jackson (negating a Seattle TD) and the below-the-waist hit against Matt Hasselbeck (which helped the Steelers on their last TD drive). In particular, I'm pretty sure Ben Roethlisberger's TD was good (he appeared to just sneak the ball over the front edge of the goal line stripe).

Congratulations to Hines Ward for winning the Super Bowl MVP award. Five catches for 123 yards, each of them really important. This is likely the high point of Korean achievments in professional athletics, even if you discount it by 50 percent.

Jerome Bettis, who you may have heard is from Detroit, had a very Bettis-like 14 carries for 43 yards. This includes him getting stuffed from the 1-yard line on consecutive carries, then just barely getting enough of a block to allow Roethlisberger to score the Steelers' first TD. The guy has been so overweight this season it's unbelievable. Still, since he's from Detroit, I'm happy for him. I still haven't completely forgiven him for going to Notre Dame though.

Bettis is going to be tough call for the Hall of Fame. He was a real force in his early years with the Rams and Steelers, but it's hard to vote for a guy with a career yards-per-carry average below 4.0.

Selling out

I just turned on the AdSense feature for this blog. It'll be a day or two before actual ads pop up; Google has to check that this isn't a porn site or whatever.

But really, it's not about the money. I'm mostly curious to see what sorts of ads pop up, given the rather eclectic mishmash of topics that get posted here. As long as I don't start coming up with ads for the Xinhua News Agency or the Korean Central News Agency, I feel fine.

UPDATE: I'd also be unhappy if I started turning up ads for those stupid Ponzi schemes iPod-XBox giveaways like they have on Xanga, but that hasn't happened so far.

Fixing up the house

After Blogger recovered from its unexplained six-hour absence, I fixed up this blog a bit. Header fonts are all sans-serif (Verdana) while text fonts are serif (Palatino). Trackbacks have also been enabled. Not that hordes of other bloggers are linking to any of my posts, but in the event that anybody does, you and I will know about it.

I can't quite figure out why the trash-can logo appears in the pop-up comment window, but not in the individual posting pages. If anyone knows how to fix this, please let me know.


Spawn of Satan, again

So a while ago I lambasted Dick Vitale for being a Duke, Notre Dame and Yankees fan.

Turns out Alex Rodriguez is a Duke fan as well. At least, he was spotted at today's Duke-Florida State game at Cameron Indoor Stadium wearing a Duke t-shirt. Somehow, I'm not all that surprised.

Good thing he's not playing for the USA in the World Baseball Classic. If he were, I might have been forced to root for Cuba.

A question of values

Let me see if I understand the situation: these protestors in Muslim countries want to kill people who publish cartoons depicting Muslims as killers.

In these official statements, the EU and Danish governments have held fast to the freedom of the press to publish offensive statements. Meanwhile, the US's reaction clearly is an attempt to pander to the people in Iraq and other countries, because their support is required for the US's grand ambition of democratizing the Middle East to succeed.

Back when the war in Iraq was launched, I thought the liberals were wrong when they claimed that people in the Middle East wouldn't be able to live in a liberal democracy. I hope that thought is still wrong, but incidents like these protests aren't very reassuring.


Google had a rough week:

Seriously, Google is largely responsible for killing my portfolio this week, as it comprises somewhere around 3% (by value) of this mutual fund in which I am invested.

Analysts have blamed it on a disappointing 4th-quarter earnings report, but I think objective observers from outside of Wall Street, like myself, know the real reason.


The seedy side of hedge funds

Not only do they short-sell massive quantities of stock, scour the markets for arbitrage opportunities and finagle all sorts of complex derivatives -- some of their employees engage in criminal activity:

For instance, on Andor Capital Management LLC's ADV, it says one employee has a criminal record, but without going into detail refers the reader to the brokerage industry's national database, known as the Central Registration Depository, or CRD. A spokesman for Andor indicated that the disclosure relates to an incident involving underage drinking by a junior employee while in college. Andor has been registered with the SEC since the firm's inception in 2001.

Good thing the SEC is watching.