June 2007 – Sean Carroll

Fixing the Lottery

June 28, 2007 / 18 Comments

I’m back from dinosaur hunting, no worse for wear, save for the indignities suffered upon me by Delta Airlines on the trip home. A brief report will be forthcoming.

But a looming event demands our attention: tonight’s NBA draft, the process by which the world’s most promising young basketball talent is apportioned to the Association’s various teams. A process, which, by all accounts, is in serious need of fixing. But don’t worry, I have it figured out. (Hey, I was stuck in airports for over eight hours.)

The basic problem is one that is common to the draft process of most professional sports leagues: the draft rewards failure. The teams that finish at the bottom of the season’s standings get to choose first in the draft, funneling the best players to the worst teams. The motivation, of course, is fairness: the good teams have had their chance at success, let’s give the bad ones a fighting chance. The ultimate goal is to win, so the incentive to grab a better player should be offset by the incentive to win games.

In most other sports that idea basically works, but it fails drastically for basketball. The problem is that the difference in game-altering ability between the first one or two players and the next few can be huge. There are fewer players on court in hoops than in other sports, so one great player can wield a disproportionate influence. The incentive to get that very first pick can be tremendous, especially if it’s between a group of teams that aren’t good enough to make the playoffs anyway.

As a result, a straightforward worst-pick-first draft structure leads to a race to the bottom, where bad teams intentionally lose games to have a chance to make the first pick. Repulsed by the idea that teams would purposely tank, the NBA decided to alter the incentive structure by softening the reward for losing. In 1985 the NBA instituted the Lottery: all of the teams that had missed the playoffs (seven back then, fourteen today) would be entered into a random drawing for draft position, with equal chances of getting any of the first picks.

The lottery removed the incentive for finishing with the worst record in the NBA, but introduced an even worse incentive: now a team that just missed the playoffs could possibly land a franchise-caliber player if the ping-pong balls bounced their way. The last thing the Association wants is to see teams trying to not make the playoffs, so they instituted a compromise: via an ungainly formula, each non-playoff team would have a weighted chance of getting a top pick, with better chances for the teams with the worse records. This year, for example, the 14th-worse team had a 0.5% chance of getting the #1 pick.

Which, of course, is the worst of all worlds! There is still some tempting incentive to miss the playoffs, but there is also incentive for non-playoff teams to lose more games. It is almost inevitable: the first pick, in the right year, can be enormously valuable, so any chance to get it will be highly sought-after, no matter how such chances are distributed.

Aside from all this, there is another nagging problem with the basic idea of worst-pick-first drafts: teams can be rewarded not only because they struggled valiantly but lost with inferior talent, but also because of sheer incompetence. Good players can be steered to teams that regularly suffer from bad decision-making at the level of coaching or management.

With all that in mind, here is my magic formula for fixing the NBA Lottery. (Unfortunately, I know of no way to prevent the crimes against fashion regularly committed by draft attendees.) Each year, the draft order will be chosen by the following two-step algorithm:

Order the teams by their record over the last two years. Break ties using this year’s record.
In one simple stroke of genius, most of the draft’s problems are solved. A team’s two-year record is less affected by an individual loss than its one-year record is. The incentive for tanking games is correspondingly diminished. More importantly, it’s the teams that are consistently bad that really need the help, not one-year horrors. The obvious case in point is the San Antonio Spurs, who in the late 90’s were a very good team, led by David Robinson, who couldn’t quite get over the hump. Then Robinson was injured for most of the 96-97 season, the Spurs had the third-worst record in the league, and they won the lottery. They were able to choose Tim Duncan, with whom they have just won their fourth NBA championship. That’s just wrong.
Teams will choose in (reverse) order of their two-year records, except that a team cannot choose in the top 3 for two consecutive years. Those that would be in the top three are bumped down until they are not.
We want to help truly bad teams, not one-year flukes, but we don’t want to reward consistent failure either. By preventing teams from choosing in the top 3 two years in a row, we let bad teams play their best basketball without feeling like they are costing the franchise a great draft pick. Note that there is no randomizing element at any step of the algorithm, but it manages to greatly reduce the incentive for bad teams to tank late-season games. Such an incentive will still exist whenever two teams are in close competition for a single once-a-decade talent, but those players have to go somewhere.

To see how this would work, here are the records of the bottom 14 teams for the combined 2005/2006 and 06/07 seasons, starting with the worst:
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Glamorous Multimedia Lifestyle Update

June 22, 2007 / 20 Comments

Yesterday morning I woke up moderately early to hie myself down to the NPR West studio in Culver City, where the magic of electromagnetism enabled me to participate in a BBC Radio 4 program, The Material World. Also appearing as a guest was Peter Woit, as we talked about — wait for it — string theory. It was fun, but to be honest, it wasn’t the most enlightening fifteen minutes I’ve ever spent, as too much time was spent talking about whether this ambitious scientific idea was overhyped or not, rather than making the effort to elucidate the idea’s successes and shortcomings in any substantive way. But perhaps I am just spoiled by blogs, where the constraints of time and space are felt much less keenly.

More interestingly, Peter in his post points to a blog I hadn’t heard of, The Atom Smashers. It’s by Clayton Brown, a filmmaker who is presently working on a documentary about particle physics. I won’t give too much away, except to encourage you to read it, and note that one of our bloggers plays a crucial role!

Then, a couple of hours after the BBC interview, I had a really interesting and fun meeting in Beverly Hills, which I’m not going to tell you about, or at least not now. Ha!

Tomorrow morning I will wake up truly early, in order to hop on a plane to scenic Billings, Montana, from which I’ll join an intrepid crew of bone hunters on a trip to the Kedesh Ranch in beautiful Shell, Wyoming. This is one of my occasional chances to join up with Project Exploration, as Paul Sereno and the gang lead some enthusiastic amateur paleontologists to dig up honest-to-goodness Jurrasic dinosaur fossils. I’ve done this a couple of times before, as recounted (naturally) in blog posts about the 2004 trip:

Here’s a picture of Paul and me, laughing in the face of danger as we stand astride an interesting geological formation:

Paul is the one who looks like a paleontologist in the field; I’m the one who looks like a theoretical physicist who someone dragged into the sunlight. He was also voted one of People magazine’s “50 Most Beautiful People” in 1997. But I am better at calculus!

Sadly, the seeming ubiquity of the internet has not managed to extend its way to the Kedesh Ranch. So no blogging. Cell phones don’t work there, either. In fact I’m pretty sure that this particular part of Wyoming is absolutely free of electromagnetic radiation of any sort. That’s the only explanation I can think of.

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Designs, Intelligent and Stupid

June 22, 2007 / 67 Comments

PZ Myers links to a great Ted Rall cartoon on Stupid Design. The point being that the world around us isn’t anything close to being efficiently designed. If it is the reflection of the plans of some supernatural architect, many of us could have offered a few useful pointers. As with most such arguments, David Hume was there first:

In a word, Cleanthes, a man who follows your hypothesis is able perhaps to assert, or conjecture, that the universe, sometime, arose from something like design: but beyond that position he cannot ascertain one single circumstance; and is left afterwards to fix every point of his theology by the utmost license of fancy and hypothesis. This world, for aught he knows, is very faulty and imperfect, compared to a superior standard; and was only the first rude essay of some infant deity, who afterwards abandoned it, ashamed of his lame performance: it is the work only of some dependent, inferior deity; and is the object of derision to his superiors: it is the production of old age and dotage in some superannuated deity; and ever since his death, has run on at adventures, from the first impulse and active force which it received from him.

Hume gets extra bonus points for writing before Darwin demonstrated how complex adaptive organisms can arise even without a designer. (But he loses some points for weaseling at the end of the Dialogues.)

Before Darwin, you couldn’t really fault someone for thinking “Gee, my two choices are between imagining that something as complicated as a human being just sort of came together by accident, or that someone designed it. I think I’ll go for Door Number Two.” But once we figured out that there was a Door Number Three — that such complexity could evolve through descent with random modification and natural selection — it boggles the mind how anyone could look at the natural world and conclude that it shows any signs of being intentionally constructed just this way.

One of the prevalent misconceptions about evolution is that, in response to a certain problem, organisms can (over the course of generations) simply “evolve an appropriate solution.” Of course they don’t always do so; sometimes they just die off. But more importantly, the space of possibilities that organisms explore via descent with minor modifications is most definitely not the space of small variations on bodies (or behaviors); it’s the space of small variations on genomes. Even if a certain physiological feature would be useful, we’re not going to be able to evolve it unless flicking a few switches in the genetic code would lead to an intrinsically useful mutation that would move us along that direction.

Years ago, Stephen Jay Gould and Richard Lewontin borrowed the term spandrel from architecture to illustrate an important consequence of the way evolution works. A spandrel is an aspect of some form (whether from Renaissance arches or paedomorphic morphology) that arises as a side effect of some other trait that is useful, even if it doesn’t itself serve a necessary purpose. Those kinds of non-adaptations and accidents and anachronistic features are found all over the place in real organisms. Any intelligent designer with a shred of self-respect would be embarrassed to exhibit such shoddy workmanship.

The classic argument-from-design question is: What good is half an eye? Even when I was twelve years old, I could guess the answer to that one: it’s a lot of good! Imagine just a few photo-sensitive cells evolving on the skin of a sightless organism; that could be immensely useful, offering a decided advantage to its offspring. Continual reinforcement of that tendency could directly lead to better sensitivity and all the other highly-specialized upgrades that our own eyes come with.

On the other hand: What good is half a wheel? Now you’ve got me. The wheel is an excellent answer to a pretty obvious question, if you’re a person sitting there thinking about how to move heavy loads more quickly or efficiently. And it’s not hard to imagine wheels coming in useful on certain organisms. (Tell me that a snake with wheels wouldn’t be pretty efficient, if a bit scary.) But you just can’t get there from here, by ordinary evolutionary means. It’s hard to think of useful transitional forms.

All of which should teach us a lesson when we sit down to try to understand and reproduce the workings of actual organisms. The idea behind Strong Artificial Intelligence is that the brain is basically a computer — a thesis I’m happy to go along with. But reproducing brainlike behavior in actual computers has turned out to be much harder than many people anticipated. In retrospect it’s not hard to see why; the brain might be a computer, but it’s certainly not the same kind of computer that we are used to programming. Its functioning arose naturally, rather than through top-down planning, and this kind of “organic design” leads to very different structures than “synthetic design.” Rather than relatively straightforward sets of algorithms expressed in neurological lines of code divided into tidy subprograms, our minds are subtle machines with virtual processors distributed holographically and interacting nonlocally throughout the brain. As a result, computers still aren’t very good poets, but they’re definitely better at multiplication and division than we are. (Now you tell me which talent might have been more useful out there on the veldt.)

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Thoughtful, Consistent Diplomacy

June 20, 2007 / 18 Comments

This morning’s Chicago Tribune website, via The American Sector:

I’ll give them the benefit of the doubt that it is a mistake. But I do wonder how exactly that happened.

Also interesting on the internets: Randy Barnett gives you the inside scoop on being a technical consultant for, and landing a minor role in, a legitmate Hollywood movie; and Ezra Klein talks about the importance of changing areas of specialization throughout one’s career. Both of which I note because it would be very easy to substitute “scientist” for “lawyer” and “pundit” in the respective discussions.

Consider this an open thread in which you are encouraged to mock my co-bloggers for being the slackers they so obviously are. Also, if you have any groundbreaking theories about the fundamental nature of space and time and would like someone to have a look at them because reading up on the literature yourself sounds like too much of a bother and besides which great wisdom only springs forth from a position of ignorance, this is the place!

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The Alternative-Science Respectability Checklist

June 19, 2007 / 207 Comments

Believe me, I sympathize. You are in possession of a truly incredible breakthrough that offers the prospect of changing the very face of science as we know it, if not more. The only problem is, you’re coming at things from an unorthodox perspective. Maybe your findings don’t fit comfortably with people’s preconceived notions, or maybe you don’t have the elaborate academic credentials that established scientists take for granted. Perhaps you have been able to construct a machine that produces more energy than it consumes, using only common household implements; or maybe you’ve discovered a hidden pattern within the Fibonacci sequence that accurately predicts the weight that a top quark would experience on Ganymede, expressed in femtonewtons; or it might be that you’ve elaborated upon an alternative explanation for the evolution of life on Earth that augments natural selection by unspecified interventions from a vaguely-defined higher power. Whatever the specifics, the point is that certain kinds of breakthroughs just aren’t going to come from a hide-bound scholastic establishment; they require the fresh perspective and beginner’s mind that only an outsider genius (such as yourself) can bring to the table.

Yet, even though science is supposed to be about being open-minded, and there’s so much that we don’t understand about how the universe works, it’s still hard for outsiders to be taken seriously. Instead, you run up against stuffy attitudes like this:

If there are any new Einsteins out there with a correct theory of everything all LaTeXed up, they should feel quite willing to ask me for an endorsement for the arxiv; I’d be happy to bask in the reflected glory and earn a footnote in their triumphant autobiography. More likely, however, they will just send their paper to Physical Review, where it will be accepted and published, and they will become famous without my help.

If, on the other hand, there is anyone out there who thinks they are the next Einstein, but really they are just a crackpot, don’t bother; I get things like that all the time. Sadly, the real next-Einsteins only come along once per century, whereas the crackpots are far too common.

And that last part is sadly true. There is a numbers game that is working against you. You are not the only person from an alternative perspective who purports to have a dramatic new finding, and here you are asking established scientists to take time out from conventional research to sit down and examine your claims in detail. Of course, we know that you really do have a breakthrough in your hands, while those people are just crackpots. But how do you convince everyone else? All you want is a fair hearing.

Scientists can’t possibly pay equal attention to every conceivable hypothesis, they would literally never do anything else. Whether explicitly or not, they typically apply a Bayesian prior to the claims that are put before them. Purported breakthroughs are not all treated equally; if something runs up against their pre-existing notions of how the universe works, they are much less likely to pay it any attention. So what does it take for the truly important discoveries to get taken seriously?

Happily, we are here to help. It would be a shame if the correct theory to explain away dark matter or account for the origin of life were developed by someone without a conventional academic position, who didn’t really take a lot of science classes in college and didn’t have a great math background but was always interested in the big questions, only for that theory to be neglected because of some churlish prejudice. So we would like to present a simple checklist of things that alternative scientists should do in order to get taken seriously by the Man. And the good news is, it’s only three items! How hard can that be, really? True, each of the items might require a nontrivial amount of work to overcome. Hey, nobody ever said that being a lonely genius was easy.
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Bérubé on Rorty

June 16, 2007 / 11 Comments

Via Mixing Memory, Slate has a collection of short reminisces about Richard Rorty by everyone from Brian Eno to Jurgen Habermas. (Although, admittedly, I sometimes have trouble telling the two apart.) In one contribution, semi-retired blogger of leisure Michael Bérubé says just what I was saying, except from a better-informed and more eloquent perspective.

In the spring of 1985, when I was a graduate student at the University of Virginia, Richard Rorty’s seminar on Martin Heidegger changed my life. Not because he converted me to Heidegger; he was not much of a Heidegger fan himself. But his seminar introduced me to anti-foundationalist pragmatism — to the idea that our beliefs, our vocabularies, and our ways of life are contingent. “Um, contingent on what?” I asked. “Not contingent on anything,” Rorty replied, “just — contingent.”

Although I was never quite convinced by Rorty’s claims that the languages of the physical sciences were as contingent as any other form of language, I was thoroughly convinced, by the end of the term, that it was a bad idea to think of philosophy as a kind of epistemological physics, in which moral truths are waiting somewhere out there to be discovered, like planets or particles. One of the reasons Rorty’s view of the world seemed so attractive was that it offered us humans a useful way to think about why it is that we disagree with each other about what those moral truths actually are: If you think you are acting in accordance with the eternal moral truths of the universe, after all, it is likely that you will think of people who think and act differently as being defective, deluded, or downright dangerous. On the other hand, if you think that morality is a matter of contingent vocabularies, you don’t have to become a shallow relativist — you can go right on believing what you believe, except that you have to give up the conviction that there’s no plausible way another rational person could think differently.

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Procedure

June 15, 2007 / 14 Comments

There’s a scene in Six Degrees of Separation, where the Donald Sutherland character tells some friends at a party:

I remembered asking my kids’ second-grade teacher:

“Why are all your students geniuses?”

Look at the first grade – blotches of green and black. The third grade – camouflage.

But your grade, the second grade…

Matisses, every one.

Like art, science relies on a combination of understanding and curiosity. As we gain wisdom and experience over time, we should be better able to understand what is going on; but with time can also come cynicism and boredom, especially if one’s exposure to the subject fails to convey the underlying mystery behind the essential grunt work. So there can be a point of diminishing returns.

In art, if John Guare’s judgment is to be trusted, that point often comes between second grade and third grade. What about science, you are no doubt wondering? Eli Lansey has done the research, and has the answer to your question: between fifth and sixth grade. The same set of cool physics demos, presented to each class, was met with dramatically different responses; excitement and independent investigation from the fifth graders, blase indifference from the sixth graders.

Like any good scientist, Eli also has a theory about why this is the case. What is more, he has data to back it up! I won’t give away the theory, but it was inspired by classroom poster presentations that looked like this:

Pretty good penmanship. Nothing to do with science. In fact, a pretty good approximation of horrid, soul-sucking antiscience. No wonder kids get turned off.

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Physics Envy

June 13, 2007 / 18 Comments

Celebrated economist, James Bates Clark Medal winner, and Freakonomics author Steven Levitt is having a good time, and doing pretty darn well, at the World Series of Poker. (Via Marginal Revolution; here’s Levitt’s own blog.) I am willing to go on record as predicting that he will not do as well as physicist Michael Binger did last year.

I’ve been reading a bit about game theory and the mathematics of poker, and have lots of great theories, including an elaborate analogy between poker and quantum mechanics. Here is one theory: physicists (and I imagine economists, too) will end up being much better poker players than mathematicians. The reasoning is that No Limit Hold’em is an incredibly complex system; not only can we not derive a dominant strategy in closed form, we can’t even prove any very useful theorems about realistic games. So game theorists and mathematicians study simplified systems about which they can actually prove theorems. They can do pretty well in figuring out strategies at a showdown (just two players), but early in the hand at a full table there’s almost nothing they can say. It becomes a question of which approximations to make and which models to choose for your opponents. That’s much more the purview of physicists and economists, who are forced to get their hands dirty in the real world. (A corollary: phenomenologists and astrophysicists will be better poker players than string theorists.)

Why am I not at the WSOP myself? Good question. I’m totally going next year.

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“Who’s Been Deeply In Love?”

June 12, 2007 / 6 Comments

Via Jacob Levy, a little anecdote from a class at Princeton taught by Cornel West and Robert George.

Having touched upon such profound notions as free will, autonomy, and the alienation of man from God, the discussion of St. Augustine’s “Confessions” is humming along nicely when Cornel West *80, the Class of 1943 University Professor of Religion, poses the afternoon’s toughest question. “Who’s been deeply in love?” he asks, leaning so far forward in his chair that his goatee is almost touching the table as he looks around him at the rapt faces of 15 Princeton freshmen.

That’s not a question most students feel comfortable answering in a setting as public as a freshman seminar. There is silence until Dov Kaufmann, showing the sort of pluck you’d expect from a former first sergeant in the Israeli army, raises his hand, tentatively at first. If he is about to fall into a trap, it will be particularly awkward to climb out, since the climbing will have to be done in front of 14 curious classmates. But Kaufmann is spared having to make any further confessions when West steps in and rescues him: “Now, this brother knows!” he exclaims. “You fall in love, you stop looking at those other girls. They became uninteresting.”

“Now, let’s not look too closely,” laughs Robert George, the McCormick Professor of Jurisprudence, who teaches the course with West and is sitting next to him.

But West is not to be deterred. He wants to bring the point around to the freedom that comes, paradoxically, from surrender. “When you fell in love, you became free,” he tells Kaufmann. “Before that, on Saturday night, you’d be looking at all the girls. You were a slave.”

It is a witty eureka! moment, one that deftly links Augustine’s 1,600-year-old autobiography to life on the Princeton campus today. Kaufmann remembers it fondly: “Professor West seemed to maybe have some hidden story of his own, because he was really smiling too,” he says. “I thought that was neat.”

A lot of college classes present intimidating vistas of endless drudgery, but occasionally you get ones that really, truly, make you think, deep down into your core. Those are magical, and are why the undergraduate experience can be like nothing else in your life. Celebrity professors are not required; I certainly had several such experiences at Villanova.

The news hook for the story is actually not “here’s a cool class,” but “look at these ideological opposites co-teaching a course.” West (who quit Harvard after clashing with Larry Summers) is a charismatic leftist, while George is an influential conservative. But they apparently have a good time coming together with students to engage seriously with Great Ideas, and have struck up a friendship “based on a shared passion for intellectual inquiry.”

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Latest Declamations about the Arrow of Time

June 11, 2007 / 75 Comments

Here are the slides from the physics colloquium I gave at UC Santa Cruz last week, entitled “Why is the Past Different from the Future? The Origin of the Universe and the Arrow of Time.” (Also in pdf.)

The real reason I’m sharing this with you is because this talk provoked one of the best responses I’ve ever received, which the provokee felt moved to share with me:

Finally, the magnitude of the entropy of the universe as a function of time is a very interesting problem for cosmology, but to suggest that a law of physics depends on it is sheer nonsense. Carroll’s statement that the second law owes its existence to cosmology is one of the dummest [sic] remarks I heard in any of our physics colloquia, apart from [redacted]’s earlier remarks about consciousness in quantum mechanics. I am astounded that physicists in the audience always listen politely to such nonsense. Afterwards, I had dinner with some graduate students who readily understood my objections, but Carroll remained adamant.

My powers of persuasion are apparently not always fully efficacious.

Also, that marvelous illustration of entropy in the bottom right of the above slide? Alan Guth’s office.

Update: Originally added as a comment, but I’m moving it up here–

The point of the “objection” is extremely simple, as is the reason why it is irrelevant. Suppose we had a thermodynamic system, described by certain macroscopic variables, not quite in equilibrium. Suppose further that we chose a random microstate compatible with the macroscopic variables (as you do, for example, in a numerical simulation). Then, following the evolution of that microstate into the future, it is overwhelmingly likely that the entropy will increase. Voila, we have “derived” the Second Law.

However, it is also overwhelmingly likely that evolving that microstate into the past will lead to an increase in entropy. Which is not true of the universe in which we live. So the above exercise, while it gets the right answer for the future, is not actually “right,” if what we care about is describing the real world. Which I do. If we want to understand the distribution function on microstates that is actually true, we need to impose a low-entropy condition in the past; there is no way to get it from purely time-symmetric assumptions.

Boltzmann’s H-theorem, while interesting and important, is even worse. It makes an assumption that is not true (molecular chaos) to reach a conclusion that is not true (the entropy is certain, not just likely, to increase toward the future — and also to the past).

The nice thing about stat mech is that almost any distribution function will work to derive the Second Law, as long as you don’t put some constraints on the future state. That’s why textbook stat mech does a perfectly good job without talking about the Big Bang. But if you want to describe why the Second Law actually works in the real world in which we actually live, cosmology inevitably comes into play.

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