Some years back, I wrote a Facebook post with this tl;dr (“too long, didn’t read”) about a professor in the St Olaf College math department. Yesterday I learned that he died a few weeks ago. May his memory be a blessing.
tl;dr for Rebecca Boardman: you don’t lose points for what you get wrong—you gain points for what you get right.
Most of my friends know me either as a musician, a horn player, or as a tech nerd, but I’m both. My degrees are both in music performance, but my Bachelor of Music in horn performance also had a math major—and music history, too, but that was an accident caused by Alice Hanson being the best professor on the planet, and that’s another story entirely. Today’s story is about math.
I got a math major because math is fun. I did give some thought to the possibility that I’d need to earn a living somehow someday, and playing horn is a notoriously poor way to do that, but that was just a bonus. The real value for me of studying math, and the reason I worked really hard long before I arrived on campus my freshman year figuring out how to cram a math major into my schedule, was that I enjoyed it. All those math classes brought incidental benefits, too, including some of my best friendships, having a second home on campus, and getting out of the music building with all its gossip and jealousy. But the best part was the math itself. So fun.
St Olaf had and still has a great math department, and I got incredibly lucky with my choices of profs. My brother Kevin Vang was also a math (and art) major there, three years ahead of me, and he got me off to a good start. He wisely told me that I should take the honors calc section taught by Cliff Corzatt even though it was someone else’s section that made sense for my schedule. Cliff was fabulous, so I ended up taking my first three semesters of math from him. I then took three semesters from Ted Vessey, had an interim and a semester with Loren Larson, another semester with Cliff, and an unforgettable semester with Laura Chihara. There was one awful semester of probability with a prof better forgotten, and I must be forgetting a couple more semesters (and maybe an interim?), because I’m pretty sure I ended up with 13 math credits. The probability class was the only math class I ever hated, I think in my life… so yeah, kind of a cruel twist of fate that I’ve ended up spending 30 years and counting in statistical software. All the other classes, and those professors, were variations on wonderful.
And it’s Ted Vessey who is the hero of today’s story. He was an excellent math prof. His lectures were always free-ranging demonstrations of several interrelated concepts, and watching him wing it through 3-4 chalkboards of math in an hour was just a hoot. Like my other math profs, he was known for supremely funny asides, and I became known for collecting them and publishing the best ones at the end of each semester of math. “The Wit and Witticisms of Uncle Ted Vessey” had three well-loved volumes, and I should probably go dig those up to give you a few examples, but I’m not going to.
I don’t think Ted worked out well as a math prof for everybody. Those wild, improvisatory lectures that accomplished several different ideas at once got some people more confused than enlightened, and sometimes I found that I had to go back over all the material again myself before I could figure out the homework, because the key method for the day had gotten a little lost in fun.
A lot of the time, even I felt like I was hopelessly lost. Sometimes I’d be so stuck and paralyzed with cluelessness about the homework that I couldn’t even start it. One time I gave up and went to the music library to work on Alice’s latest listening assignments, and it was somewhere in the second of many sides of the “Einstein on the Beach” (Phillip Glass) recording that I got so bored, I took my Vessey homework out and magically was able to crank right through it. Something about the hypnotic monotony of Glass’s minimalist phase-shifting and nonsensical lyrics shifted my math brain into gear. I ended up checking out “Einstein on the Beach” to get through math homework quite a few more times before I graduated.
For the record, I’m not sure I even like “Einstein on the Beach,” or much else of his music, but I quite literally find it good for my brain. Steve Reich’s “Tehillim” also proved useful for math homework, for similar reasons I think, during Laura Chihara’s combinatorics class.
Worst, and best, Vessey’s tests were hard. I mean HARD.
Sure, there’d always be a few pages of stuff you could more or less rip off, if you’d been keeping up on the homework and had a decent memory (or studied, I guess—that was a skill I never quite acquired). But there’d also be a few pages of stuff that was baffling. Problems of a type you’d never seen before, or a need to prove something new, or an essay question on a new concept. To get those questions right, you’d need to let go of knowing and surrender yourself to discovering. You’d have to sort of poke at them with some of the tools you’d learned, or do pages and pages of brute-force algebra, or just keep drawing stuff until you could finally start to see something you could nibble away at. If you managed to get somewhere with those problems, though, something magical happened. You’d be integrating previously unrelated concepts, or deriving the method for something new, or discovering a whole new thing.
It was exhausting. I’d leave those tests in a sweaty, tired fog. I could barely even remember what I’d just done, and a few times when I got the papers back, I couldn’t follow my own scratchwork—but I’d always gotten full or nearly full credit for those problems, so I must have been on the right track, even if I couldn’t understand it later. A few hours after the test, though—usually over pizza and beer—my friends and I would talk about the tests we’d just survived, and that’s when I’d suddenly click on what we’d been doing for the last six or eight weeks of class.
His final exams were grueling. I think they lasted 2-3 hours, and other than reviewing a few things I should have memorized, I never did figure out any useful way to study for them on my own. Glenn Elliott and I would often study together, though, and he’d explain to me the things I hadn’t quite figured out, and I’d explain to him the things he hadn’t quite figured out, and teaching each other like that was the closest I ever came to “preparing” effectively. Even so, arrivng at the final having secured our ability to do anything and everything from that semester’s homework did not mean that we’d have any clue what to do with most of the test. Nope, we’d have to flail away at it and just do what we could, and like I mentioned, it would be later that night over pizza and beer before either of us ever understood any of what we’d scribbled on the impossible problems.
A few weeks after each final, though, I’d suddenly have a mathematical insight that would make me realize I had, in fact, learned a whole bunch of math from Ted Vessey.
It was eerie, how learning from Ted always took place later, somehow. Not during. I’ve experienced that seldom in life other than from Ted.
So now we come to the point of my story.
The first time I was taking a Ted Vessey test, I along with probably just about everyone else in my class was sitting in a cold sweat, panicking about how few of the problems on the test made any kind of sense to me. I was torn between going back to the few I’d done and slowly triple-checking them to be sure I at least got those right, and forcing myself to find some kind of way into one of the many impossible problems that sat empty before me.
I started to do the thing that in computer science we called “thrashing,” back in the day before we each had a self-contained desktop or laptop to ourselves. Thrashing is when a big time-sharing system, such as UNIX running on a VAX that serves hundreds of students sitting at terminals around campus, gets itself all tied up. It speneds so many of its cycles trying to assign the next cycles to a process (essentially deciding which user’s command to execute next) that it doesn’t have any cycles left to do the process. It’s trying so hard to decide which work to do that it can’t do any work. The only cure is to reboot the whole thing.
That’s when Ted came back into the room.
(At St Olaf, all tests are administered on an honor system, without proctors. The prof comes in a few times during the test period to take questions, and occasionally they end up fixing a typo or a thinko that that had slipped past them when they were writing the test, but for the most part it’s a courtesy that they check in, just in case. Otherwise, it’s just the students in the room, and you police yourselves. The last thing you do before you hand your test in is sign “the pledge,” which states, “I pledge my honor as a lady/gentleman that during this examination I have neither given nor received assistance and that I have seen no dishonest work.” Violations of the honor code are taken quite seriously. If any test’s pledge is not signed, it’s a whole Megillah for the prestigious student honor council to sort it all out. We took it so seriously that once, when I was stuck and panicking in a music history test, I spent a long moment considering the possibility of glancing over at someone else’s blue book, which I could see quite easily, and then rebuking myself with the fact that I wouldn’t be able to sign the pledge if I did. I thought that was just me being a nutjob, but it turns out a lot of StO students have stories like that.)
When Ted came back into the classroom and saw us panicking, instead of following the usual script and asking if there were any questions, Ted launched into a rant that made very little sense at the time.
“Friends, you’ve got it all wrong. You think you’ve got a hundred points and anything you mess up, you’re going to lose points over it.”
Well, duh. That’s exactly the situation.
“But you’ve got it wrong. You all have zero points right now.”
Gee, thanks. We’re already sitting here white with terror because we know that, you jerk!
“You don’t have any points at all right now. Your job isn’t to lose points from a hundred, it’s to start earning points, because you’re at zero.”
Again, not helpful to be reminded we’re failing this test, dude.
“You all have nothing. So start earning points. Do what you can. Double-check what you’ve done to be sure you get all the points for it. And then start tackling the stuff you don’t know how to do, so you can try to get at least SOME points for it.
“You’re not here to avoid losing points. You’re here to do as much as you can and get as many points as you can, and every little thing you manage to do is better than the zero you started with.
“I’ll be back again in about ten minutes.”
I only barely understood this at the time—just like most of the math I learned from Ted, it came later.
I was on stage with the St Olaf Orchestra. I think we were on tour, and I think it was the year we did ”Till Eulenspiegel” and Tchaikovsky 5, both huge huge works for principal horn, my seat. I was getting nervous about how many things could go wrong on the concert, and how many notes I’d miss, and how much I’d disappoint my colleagues and our extraordinary conductor, Steven Amundson, also known as “SMA” because of the way he initialed memos on the orchestra bulletin board.
Friends, I had it all wrong. I thought I had a perfect concert ahead of me, which I was going to screw up. I was going to be losing points left and right.
But I had it wrong. I had zero points.
There was no concert ahead of me, waiting for me to screw it up. There was nothing at all happening.
There was NO SOUND. We had to start making some sound.
Every sound we made was a sound that didn’t exist until we made it. We were starting with silence.
We weren’t there to avoid missing notes. We were there to play as many notes as we could, as well as we could, and to listen as hard as we could to everyone else, and to play with them better and to hold it all together tighter, and to watch SMA as closely as we could, to try to play it as much in the way he was leading it as we could.
And that, my friends, has made all the difference. We don’t avoid screwing concerts up. That’s inevitable. We are going to mess them up, all over the place. But that’s not what we’re doing. What we’re doing is creating as much beautiful sound as we can, and giving the audience as much music as we can, because otherwise it’s just silence.
That’s the most important thing I ever learned about performing music. And it’s not just about music, or math tests.
Thanks, Uncle Ted.