Uncertain Principles

One of my students is giving a fifteen-minute talk at a conference in Salt Lake City this afternoon. At least, as far as I know, he's speaking there this afternoon-- I'm in Schenectady.

This is sort of a new position for me-- I've given lots of talks, occasionally on behalf of other people (I'm listed in one or two meeting programs under the name of my post-doc advisor, who sent me in his stead...), but I've never sent someone else to a conference. I've had other people speak at conferences about my work, but they were always co-workers, not students. I've also had research students give talks before, but in those cases, I was actually in the room, to provide a bail-out answer if they got stuck during the question period. It's a little weird knowing that someone several hundred miles away will be giving a talk in a few hours that will (somewhat indirectly) reflect on me and my work, and there's nothing that I can do about it.

It also reminds me that I really enjoy going to conferences (which in turn reminds me that I should sign up for this year's Gordon Conference), and giving conference talks. It wasn't always thus, of course-- after the first ten-minute talk I gave, some colleagues commented on the fact that I kept walking around in the presentation area, from the projector to the screen, and back and forth, which they said was a good idea. In fact, I was walking around because I was afraid that if I stood still, my knees would buckle. That wasn't a whole lot of fun-- not during the talk, anyway. After I got through it, though, it was quite a rush.

The first invited talk I gave was at the Centennial Meeting of the American Physical Society, which was sort of a double-whammy of nerves. It was the first time I'd ever been in an invited session, and looking at the list of speakers for the session was one a "One of these things is not like the others..." sort of moment. I half expected everyone to get up and leave when I started speaking, thinking that my presence was some sort of horrible mistake. On top of that, I was planning to use the same talk for my PhD defense a few weeks farther down the road, and the stress over that whole thing was just beginning to peak up.

When I came into the room before the session, though, I discovered that they'd set up a platform at the front of the cavernous room set aside for invited sessions, to lift the speakers and projector a good five or six feet above the level of the seats. Unfortunately, they'd apparently built the platform out of balsa wood and duct tape. When I walked in, the first speaker in the session was up there testing things out, and when he walked, the projector vibrated so violently, his slides were almost unreadable. And I outweigh him by a good hundred pounds.

We eventually figured out that there was one safe spot on the platform, over by the podium that they had inexplicably set up (scientists don't usually talk from a podium). This turned out to be a godsend-- I'd walk over to the projector, setting the whole platform slewing crazily, change the slide, and then walk back to the podium. When I was changing slides, everything was shaking so violently that nobody would be able to see that my hands were shaking, and by the time I got back to the podium, the slides would be legible again, and I could talk.

A funny thing happened there, though. When I started out, my hands were shaking, my mouth was dry, my knees were wobbly, and the whole nine yards. But somewhere halfway through the talk, I had the sudden realization that I just wasn't nervous any more. I knew the material cold (pardon the pun), the data were great, I had the talk down, and once I was actually up there talking, I had nothing else to worry about. At that point, it became fun.

I'd like to say that I was never nervous again, but, of course, my thesis defense came a month later, which pretty much blew any chance of that happening. My pre-defense case of nerves was enough to dwarf all the others put together, and didn't really let go until the end of the question period (though it lightened dramatically after the "Who discovered xenon?" question). And, of course, when I opened the celebratory bottle of champagne somebody had brought, I sprayed it all over my official advisor's coat (one of his other students said later "I wondered why John came back to the lab smelling like a whorehouse...").

Anyway, what started as a comment about one of my students has turned into a long personal reminiscence, which goes to show what an egotistical bastard I am. The point is, one of my students is speaking this afternoon at a conference, and there's really not anything I can do to influence events from here. He's got a good project, has made excellent progress, and his practice talk went well. Barring some sort of freakish occurrence (and I think we got that out of the way when we moved his talk out of the education research session, where "Computer Based Frequency Control of a Diode Laser" had been scheduled to follow "Perception of African-American Women in Rap Videos"...), he should do well, but I won't find out until Monday. Which leads to nervousness of an entirely different sort...

Not that you'll read this, but good luck, Colin.

Posted at 8:30 AM | link | follow-ups | 14 comments

We run on a trimester system at Union-- three ten-week terms-- and the Winter term is now drawing to a close. This means all the usual end-of-term hassles: students seeking a way to boost themselves two letter grades in the last week of class; trying to arrange make-ups for people who missed labs, and track down all the work that hasn't been handed in yet; actually having to grade those papers I collected a month ago and hand them back. It also means numerous requests for a quick recap of the entire course. Preferably in one class period or less.

In response, I've started giving an end-of-term lecture that I mentally call "Fifteen-Minute Mechanics" (in reality, it takes something closer to half an hour). It's about as close as I can come to distilling the whole ten weeks of freshman mechanics down to a single lecture, and basically consists of listing off the bedrock principles of physics that are covered in the course of the term-- the important rules and concepts that future professors will count on them having at least seen, if not completely grasped. There are four of these in regular classical mechanics.

The first important principle is actually three things: Newton's Laws of Motion.

• Newton I: Inertia. A body at rest tends to remain at rest unless acted on by an external force. A body in motion tends to remain in motion at constant speed in a straight line unless acted on by an external force.
• Newton II: F = ma. The sum of all forces acting on a body is equal to the mass of the body times the acceleration.
• Newton III: Action-Reaction. For every action, there is an equal and opposite reaction. If you exert a force on some object, that object will exert a reaction force on you that is equal in magnitude and opposite in direction to the initial force.

There are three laws, of course, because three is the magic number, though, really, if you look closely at them, there are actually only two, the Second Law being little more than the quantification of the First. The first law says that things don't move unless you push them, while the second tells you how hard you need to push something in order to move it.

It's interesting to note the degree to which these have become common sense (not that I remember when they weren't)-- everybody's at least heard the catchphrases, and nobody really blinks when you rattle these off. When Newton first wrote these down (in a slightly different form), though, they were revolutionary. It's mind-boggling to think that several hundred years went by without anyone doing the really simple experiments you would need to do to see that Aristotle was full of crap. In a way, though, it's a nice reminder of just how recent and fragile scientific thought is.

Once you've got these, in one sense, you're done. Anything you need to know about the motion of everyday objects can be worked out using Newton's Laws and a little bit of calculus. If you know the forces that act on a body, you know its acceleration. If you know its acceleration, you can find the velocity, and when you know the velocity, you can predict the position.

OK, you actually need a fair bit of calculus. While in principle you don't need anything beyond Newton's Laws to describe motion, in practice, it can be fiendishly difficult to work through the math. In general, you probably want a computer to deal with the problems, or some better tools. Which is why there are three more principles to come...

The second core principle of physics introduced in mechanics is the Law of Conservation of Energy. This is a little harder to nail down, just because "energy" isn't something you can really measure. This is also one of the prime examples for the whole "why is it that mathematics is so successful at describing the universe?" debate.

At a deep and formal level, conservation of energy, like all conservation laws is a consequence of fundamental symmetry. This isn't especially illuminating to me, and I spent six years in physics grad school, so for freshman mechanics, I stick with explaining that energy is a mathematical quantity that you can associate with things that are moving, or might start moving. Something that's moving has kinetic energy, something that might start moving has potential energy, and there are a handful of other forms. The key thing is that the total amount of energy (of all kinds) in a system can't change-- you've got the same total energy at the end of the problem as at the beginning. You can change energy from one form into another, but you can't create it or destroy it.

The beauty of this, from a practical standpoint, is that it dramatically simplifies problem solving, reducing a huge number of physics problems from exercises in calculus to mere bookkeeping. Rather than using Newton's Laws to calculate the position, velocity, and acceleration of some object, and following those quantities through time, you can just calculate the energy at the beginning (from the initial position and velocity), then again at the end, and find out what you need to know. It's a way to get quick answers to problems where you don't care about how something gets where it's going, just what it's doing when it gets there.

A colleague is fond of describing conservation of energy as accounting, and I've cribbed the analogy from him. Energy is like money: kinetic energy is money you have in your pocket, potential energy is money you have in the bank, and energy lost to friction and the like is money that you spend, and don't get back. You can shuffle money back and forth between different accounts, spend some of it, withdraw a big fat roll of bills to wave around and impress people, whatever you like, but at the end of the day, the total amount of money is the same as when you started-- it's just changed hands.

(Turning the analogy around, of course, this means that Ken Lay is the financial equivalent of one of those "Free Energy" loons who try to patent perpetual motion machines...)

The fascinating and important thing about conservation of energy is that it extends well beyond mechanics-- if you can find an energy associated with some quantity, you can include that energy in conservation of energy. And conservation of energy works on all levels, from the very big to the very small (save for the occasional little transitory quantum blip, such as, oh, the entire universe, according to some theories...). From people, to atoms, to galaxies, conservation of energy holds everywhere.

Next on the list is Conservation of Momentum. In many ways, it would make sense to cover this much earlier than we do, as it's really just another way of looking at Newton's Laws (and, indeed, Newton originally phrased his rules in terms of momentum). Momentum is the product of mass and velocity, and force is just a way of changing momentum. Given that the mass of most ordinary objects is constant, this gives you F = ma (acceleration being change in velocity).

In the absence of forces, of course, momentum is conserved-- things keep moving in straight lines at constant velocity, and all that. And, as with conservation of energy, this reduces a large class of problems to exercises in bookkeeping. Any time you have collisions between two or more objects (so the only forces in the problem are forces between the objects, which by Newton's third law are equal and opposite), you can use conservation of momentum: the total momentum of all the objects involved at the beginning of the problem is the same as the total momentum of all the objects involved at the end of the problem. This lets you prove mathematically that being hit by a 1000-kg car is a good deal less traumatic than getting hit by a half-kilogram basketball, and saves you a lot of hassle with insurance agents and policemen.

(OBDemo: Get a basketball and a racquetball. If you drop either one on the floor from chest level, it will bounce back up to about waist level. If you hold them with the racquetball on top of the basketball, and then drop them, the racquetball will kick way up in the air-- if you get it to go straight, it will probably hit the ceiling, otherwise, it will fly out into the middle of the class. There's an elegant way to explain this using conservation of momentum, but there isn't enough space in this post to contain it...)

The final principle covered in introductory mechanics is the Conservation of Angular Momentum. This works just like the other two conservation laws, but applies only to things that are spinning (or behave as if they were spinning, in the case of electrons). Once you've got some angular momentum, unless some external force acts to change the rotation rate, you keep the same angular momentum throughout the problem.

Angular momentum lends itself to the coolest demos of anything in the class. Conservation of angular momentum is the reason why spinning tops remain upright, and gyroscopes point in a constant direction-- gravity isn't aligned in the right way to change their angular momentum. It's also why ice skaters can change their rate of rotation by moving their arms-- angular momentum depends not just on the mass, but also on the distribution of mass, so a wide, slowly spinning object (a skater with her arms outstretched) has the same angular momentum as a narrow, rapidly spinning one (the same skater with her arms pulled in).

As with conservation of energy, both momentum conservation laws are absolute, on all scales (quantum fluctuations aside). The angular momentum of a single spinning electron is conserved, as is the angular momentum of a giant star collapsing to form a black hole. Linear momentum is conserved in all collisions, whether the colliding objects are slow-moving atoms, or asteroids weighing millions of tons.

There's a whole lot of mathematical apparatus surrounding all of this, of course, that I'm leaving out for the purposes of this post. But these four ideas are absolutely central to all of physics, and as long as a student can rattle them off, and sketch what they mean, the rest is gravy.

Posted at 8:01 PM | link | follow-ups | 3 comments

I wrote a huge post last night about physics, that I failed to upload to Blogger's servers. Predictably enough, Blogger was all screwed up this morning, and I couldn't post it before work. I'll put it up later tonight.

In the meantime, I just want to say that while the current administration has a deplorable tendency to make me feel like a nutbar conspiracy theorist, I'm glad that I have Electrolite comment threads to restore my sense of perspective. In reading the comments to that one article alone, I've learned that there are people who believe that even if all 100,000 of the Floridians who had voted for Nader had voted for Gore, Jeb Bush and Katherine Harris still would've stolen the election, and that Graydon Saunders appears to believe that nothing short of civil war will remove the current administration from power.

Yikes.

As for the endless Nader-Gore catfight, satisfying as it may feel to blame Nader for throwing the election to Bush, this never should've been close. Gore was a sitting Vice President, coming off the greatest economic boom in memory, and running against a smirking halfwit with a platform built on outright lies and dangerous economic lunacy. The election never should've been close enough for Nader's paltry support to have a serious chance of tipping it one way or the other. The fact that it was close enough for Ralph to screw things up was entirely the fault of the Gore camp for running a miserable campaign. Nader is nothing more than the cherry on top of the shit sundae the Democrats served themselves.

Posted at 11:59 AM | link | follow-ups | 12 comments

Regular commenter and weasel lover Mike Kozlowski joins the ranks of general-interest bloggers with Unmistakable Marks. Among other interesting things, he has a post with a different slant on the tax code:

The rich really aren't getting screwed by the poor paying low tax rates, because the rich pay those exact same rates. If we were to further lower the tax rates on income below, say, $30,000, Bill Gates would benefit from that reduction in exactly the same amount that the poor would, and that I would. And yes, Bill pays more on his income over $300,000 than he does on his income under $30,000. This is not punishment for being wealthy, though -- it's just the realization that those fabulous sums of wealth are of less importance to Bill than that initial $30,000; the tax code takes advantage of the law of diminishing returns to draw its revenue where it hurts the least, without ever unfairly punishing one person at expense of another. It's utilitarian and egalitarian at the same time.

The problem with this is that I don't really believe that "those fabulous sums of wealth are of less importance to Bill than that initial $30,000." Or, to be more precise, while that may be true in terms of material comfort, I don't think it's true psychologically. I don't think you get to be Bill Gates without caring just as much about the last nickel of your gazillion-dollar income as the first. If the last few zeroes of his salary didn't matter as much as the first, he'd be Paul Allen, not Bill Gates.

This psychological picture explains a lot of the most irritating features modern America. It's why the vast majority of the whining about the tax code comes from the wealthy-- they're being taxed sums that are insignificant when compared with their actual income, but they begrudge every last nickel of it, whether they have a use for the money or not. It's also why you get ridiculous spectacles like the various insider trading scandals-- the difference between doing things legally and breaking the law is the difference between making millions and making tens of millions. Most ordinary people would be happy to follow the rules and take the millions, but the people who have the proper psychological make-up to get those sums of money are more likely to roll the dice for the tens of millions-- the way you get to be rich is by being obsessed with getting every single dollar you can lay your grubby little hands on. And it's why Microsoft resorts to illegal strong-arm tactics to maintain and expand its monopoly on crap software-- someone who was in the business for the sake of actually making computer software would do the job right, but people who are in it for the money behave like, well, Microsoft.

I also think this is why the tax debate gets to be so acrimonious. Well-meaning, middle-class liberals don't understand that there really isn't a threshold above which the ultra-rich don't care about further income, and so are baffled and offended by their unwillingness to chip in to aid various social projects. The rich, meanwhile, view any attempt to tax their income as an attempt by jealous poor people to line their own pockets because, well, it's what they would do if the roles were reversed.

Posted at 8:14 PM | link | follow-ups | 4 comments

Matthew Yglesias has another in a long series of posts about early handicapping of the 2004 Presidential election, which reminded me of a luncheon a few weeks ago where the students in a local honors program got together with the Political Science department to discuss electoral politics. There was a lot of the same sort of "X will carry this state, and Y will carry that state" wonkery seen (or, rather, corrected) in Matt's post, but also a good deal of bemoaning of the fact that foregin policy issues don't really favor the Democrats at the moment. The handful of Republican students there were more or less openly gloating, and the hard-core Democrats seemed on the verge of despair. One or two people even suggested that it would be a good idea to throw up a sacrificial lamb from the hard left as a sop to the "base," and essentially punt until 2008, an idea which has also been floated in comments to this Electrolite post.

I have a hard time really getting worked up about this stuff at this stage of the campaign, mostly because (unlike most of the students at lunch that day), I remember the first Bush presidency. In early 1991, the Democrats were in more or less the same position they are now-- worse, even. Bush the Elder was riding stratospheric job approval ratings in the wake of the first Gulf War (or the beginning of the 12-year intermission in the ongoing Gulf War, depending on your perspective). He looked unbeatable, and most of the people touted as potential Democratic candidates-- remember Mario Cuomo?-- bowed out of the race early, in what seemed like essentially a concession to the Republicans. There was a Saturday Night Live skit at the time in which prominent Democrats on a "Meet the Press" type show spent all their time confessing to outrageous sins that would disqualify them from having to run.

Bill Clinton was not anybody's first choice as a Democratic candidate. It's easy to forget that now, after he proved to be a great campaigner and a two-term President, but the Democratic field going into the primary season was jokingly dubbed the "Seven Dwarves," and Clinton wasn't even thought to be the tallest Dwarf-- most of what people remembered about Bill Clinton was the absolutely dreadful speech he gave at the convention in 1988. And heading into the campaign season, people were talking about the race in terms of throwing up a sacrificial candidate who would get pasted, but set the stage for a better run in 1996.

Things changed pretty drastically between the days of the "Seven Dwarves" and the actual election, of course. The post-Gulf-War wave of Bush-a-mania that drove all the Big Name Democrats out of the field crested and broke while the economy stagnated. Clinton was able to re-focus attention on economic matters (this in the days when people could say with a straight face that the Republican party was on solid economic ground), and win the actual election.

Am I claiming that something similar will happen in 2004? Not directly, no, but a year and a half is an absolute eternity in American politics. There's basically no point it making really detailed election plans right now, because it's hard to say what the leading issues will even be. The ongoing "War on Terror" is likely to figure prominently, but there's a good teal of terror-war to come between now and then, and given the dangerous lunacy passing for economic policy these days, the war might even be eclipsed by economic issues.

There's also really no telling, at this stage, whether any of the Democratic candidates will actually turn out to be good campaigners, the way Clinton did. There really aren't any other elections that work in quite the same way as a presidential election, and there's no way to say for sure how a candidate will do until they're on the actual campaign trail.

It's important to think about the issues-- particularly the "War on Terror" issue-- and it's important to come up with a general plan. After all, as Patrick Nielsen Hayden reminds us, we're presently led by "knaves, criminals, and morons," and the sooner they're driven back into the outer darkness, the better. At the same time, though, it's not worth hyperventilating about the lack of a perfect candidate and the perfect strategy (or even a perfect health care plan) eighteen months before the actual election. A lot's going to happen between now and November of 2004.

Posted at 4:02 PM | link | follow-ups | 5 comments

The Library of Babel has been updated, and also moved to steelypips. If you link to it from your site, first of all, thanks. Also, please change your links/ bookmarks/ whatever. The Earthlink site will remain up for another month or so, but won't be updated any more.

Also, if you have any problems with the new page, please let me know, and I'll see if I can get Kate to fix it...

Posted at 9:46 AM | link | follow-ups | no comments

I'm not feeling any great blogging inspiration at the moment, and most of my screwing-around-with-the-computer effort today will be put into updating the book log and moving it to steelypips.org. I will, however, note this article from the Cairo Times by my friend Paul, describing the current situation in America to an Egyptian audience. Commentary-wise, it's nothing all that shocking-- anyone who read political blogs has probably already seen most of the main ideas-- but it is amusing to see Vermont described as "a small north- eastern state with a quarter the population of Shoubra."

Speaking of Cairo, I should probably ask Paul about the Arabic pop ditty described in this morning's Post. Titled "The Attack on Iraq," with lyrics like:

"Enough!" demands the singer, an Egyptian named Shaaban Abdel-Rahim. "Chechnya! Afghanistan! Palestine! Southern Lebanon! The Golan Heights! And now Iraq, too? And now Iraq, too? It's too much for people. Shame on you! Enough, enough, enough!"

this would seem to be a nice demonstration that the rule "Excessively topical pop songs suck" knows no borders. But then, maybe there's just something lost in translation.

Posted at 7:53 AM | link | follow-ups | 7 comments

We call them "hero shots" in pick-up. They're the plays when it's 14-all in a game to fifteen, and the next basket wins, and the guy with the ball inexplicably shoots a thirty-footer, despite a well-demonstrated inability to put the ball in the basket from more than six feet away. Or a guy who's a fairly decent player runs down into the lane, and flings it up with four defenders on him, and nary a rebounder in sight. They're attempts to end the game quickly and decisively, and stick it to the losing team in the process.

To really count as a "hero shot," it has to be spectacularly ill-advised-- long shots with defenders right in your face are prime "hero shots." It also needs to be quick-- ideally, you should take about three dribbles after crossing half-court, then let fly.

Oh, yeah, and they have to miss. Badly.

Drew Nicholas had no fewer than four "hero shots" in the closing minutes and overtime of Maryland's loss to Virginia last night, and Steve Blake had two (he took a third long shot, but hit it, disqualifying it from "hero shot" consideration). Nicholas's final attempt, a thirty-foot bomb with about ten seconds left was the very epitome of a "hero shot"-- he looked like he'd spent the whole week re-reading his press clippings from last weekend.

What made it even worse was that Maryland was utterly incapable of getting a rebound for the entire game, so it's not like taking the quick, long shot was going to give them time for a second attempt. According to the box score, Maryland was outrebounded 59-36, which is just a pathetic showing for a team with a vaunted veteran front line.

To some degree, this was a game the Terps were just fated to lose-- a little-used senior reserve for Virginia torched them in the first half, despite having played a total of 14 minutes in the year to date. He also had three blocked shots (aided somewhat by the senior day gift of immunity from foul calls), and altered quite a few more. Clearly, the Woof Gods were on the side of the Cavaliers.

At the same time, though, Maryland's inside players were thoroughly awful. They wandered around as if in a daze, failing to box out, failing to rebound, failing to play anything approaching effective defense. If Virginia hadn't turned the ball over 21 times, mostly on bad passes bring the ball up the floor, they would've blown the Terps out in regulation.

Feh. Not the way you want to end the regular season. Two more sorry efforts like this, and the season's over.

Posted at 3:50 PM | link | follow-ups | no comments