Monthly Archive for March, 2011

Justice Denied

John Thompson spent 18 years in prison, 14 of them on death row, for a crime that it seems very likely he did not commit. Prosecutors were aware that blood found at the crime scene was not Mr. Thompson’s, but they failed to turn this evidence over to the defense attorneys.

Does Mr. Thompson deserve compensation? A jury thought so, to the tune of $14 million. But five Supreme Court justices disagree, so Thompson gets nothing.

That’s because, according to the majority, it was only a single rogue prosecutor who misbehaved, so it would be wrong to punish the whole district attorney’s office. The dissenting minority argued that in fact there was a pattern of lax training in that office, so the jury award should stand.

But if an innocent man spends 18 years in prison, why should his compensation depend on the nature of the misconduct that sent him there — or even on whether there was any misconduct in the first place?

Look. We’ve pretty much all agreed that we want to have a justice system. Since all justice systems make mistakes, that means we’ve pretty much all agreed that we’re prepared to tolerate a certain number of mistakes. The question, though, is: Who should bear the costs of those mistakes? Should the costs fall entirely on an unlucky few like John Thompson who just happen to have been in the wrong place at the wrong time, or should they be spread more evenly among the populace that is perfectly happy to share in the benefits of the justice system?

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Yesterday’s Puzzle

I didn’t think anyone would get it. I was completely stumped myself until I got help from my friends. But Neil got it.

In his words, “We have onomatopoeaic words for the sounds made by all of the animals on the right.”

Or, as I prefer to think of it, the animals on the right all have vocabularies (consisting, in most cases, of a single word) while those on the left do not.

A donkey brays, and when it brays it says hee-haw. The donkey makes it to the right of the line not by virtue of braying, but by saying hee-haw. Thus the elephant, which trumpets, but thereby merely makes a noise (as opposed to saying a word) is consigned to the left.

Lions, tigers, and jaguars all roar, but to the best of my recollection from extensive reading (mostly at about age 5), lions and tigers, when roaring, actually say the word “roar”, while a jaguar merely roars incoherently. Chickens say “cheep”. Hens say “buck-buck-buck” (the act of saying this is called “clucking”). Roosters can crow in either of two dialects: Some say “rrr-rr-rrr-rr-rrrrr” while others (who my five-year-old self considered unbecomingly pretentious) say “cock-a-doodle-doo”. Pretentious they may be, but as a scientist, I am here to record the facts, not to judge them.

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What Was I Thinking?

It was said of me in graduate school that “He’s never happy unless he’s making a list”.

My compulsion to make lists has abated over the years, but it lasted long enough that I still find occasional relics lying around.

Recently I ran across the list reproduced below, dating, apparently from my zoology phase, when I was making lists that classified animals according to various criteria. But I was completely unable to recall what criterion had governed this particular list. What rule places the giraffe on the left and the dog on the right?

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The Art of Abstraction

enToday is the birthday of the magnificent Emmy Noether, known as the “mother of modern algebra”, and one of my mathematical heroes. She is one of the few mathematicians in history who fundamentally changed what mathematics is about.

It was Emmy (I use her first name in order to distinguish her from her mathematician father Max) who first fully recognized the power of abstraction, which became the driving force of 20th century mathematics. She demonstrated time and again that it can be easier to solve a general problem than a specific one, and therefore the best way to attack a specific problem is often to generalize. Do you want to prove a fact about polynomial functions? First notice that polynomial functions can be added together, and they can be multiplied, and they obey certain laws along the way (like associativity and commutativity). Now prove a theorem that applies to anything that can be added and multiplied subject to those laws. Do it right, and you’ll replace intricate calculations with simple logical deductions. What was hard becomes easy. You get your result for free, and a whole lot of other results as a bonus.

Or, if you that doesn’t quite work, figure out what additional properties you’re using about polynomials, beyond associativity and commutativity, and prove a theorem about everything that has those properties.

To get a sense of how revolutionary this was, consider the Hilbert Basis Theorem, one of the foundational results of modern algebra. Have a look at Hilbert’s original proof — though you might not want to work through every detail in the 62 pages of equations and formulas. By contrast, Noether’s proof of a more general, more powerful and more useful version occupies all of one paragraph on Wikipedia.

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Strategic Reasoning

Senator Jay Rockefeller adds his voice to the chorus calling for the U.S. to deplete the strategic petroleum reserve in order to bring down oil prices.

Put aside the question of whether we should want to bring down oil prices. Put aside the question of whether this is a good use of the strategic reserve. Let’s just ask whether this idea would even work.

Simple economics certainly suggests that the answer is no. Oil, after all, is an exhaustible resource. This means that every barrel sold today is a barrel that can’t be sold tomorrow. Therefore profit-maximizing oil suppliers, of whom there are many, must constantly be asking themselves whether they’d prefer to sell another barrel now or leave it in the ground to sell later. And the key inputs to that decision are the current price and the expected future price.

If the government starts depleting the oil reserve now (with, presumably, the intent to replenish it in the future), they bid down current prices and bid up expected future prices — creating an incentive for all the other suppliers to sell less now and more in the future — pushing current prices right back up again. For a non-exhaustible resource, this would partially offset the government’s action, but for an exhaustible resource (like, for example, oil) there should be a 100% offset, at least on a naive application of Hotelling’s Rule.

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Big Numbers

Sorry to have been uncharacteristically absent all week; I’ve been busy in a good way, though I hope and expect to get back to more regular blogging before long. In the meantime, to keep you busy, let me give you a pointer to a marvelous essay I’ve long been a fan of, and just happened to get reminded of today: Scott Aaronson’s take on the old riddle of who can name the biggest number. Have fun with this, and I’ll see you soon.

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Defici(en)t Thinking

Gerald Seib, in the Wall Street Journal, reports that “There is a cancer eating away at the budget from within, one that steadily drains American wealth, sends much of it overseas and only gets worse over time.”

This is economic illiteracy in spades. The fact is that every single dollar of interest we pay on the national debt comes right back to the pockets of American taxpayers. If you don’t understand that, then you’re not thinking clearly about the national debt.

Suppose the government owes $100 and pays $3 a year in interest. The alternative to paying that interest is to raise current taxes by $100 and pay down the debt. If you do that, taxpayers are going to have $100 less in assets, and will therefore earn less interest on their savings. That costs them (roughly) the same $3 a year.

In other words, the damage was done back when the government spent that $100 in the first place. (Of course, if the $100 was spent wisely, the damage might have been worth doing. Or not.) Once that $100 has been spent, the taxpayers are out $3 a year forever regardless of whether the debt is ever paid off.

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I Bet You Paul Krugman Can’t Do This

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(Larger and more easily viewable version here.)

(My daughter is far more advanced and more graceful than I am. I hope soon to post video proof.)

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How’s That Again?

Paul Krugman’s latest gets my vote for his most incoherent column ever. As I understand his argument, it goes like this:

  1. Computers are good at routine tasks.
  2. Therefore the rewards to performing routine tasks are falling. This is true at all skill levels.
  3. Therefore education does not always make people more productive. It makes people more productive only when it trains them to do tasks that are not better done by computers.
  4. Therefore we need stronger labor unions and universal health care.

Say what?. The basic thesis — that there’s no point in learning to do something difficult if a computer can do it better, and that this is significantly affecting the returns to certain kinds of education — is an interesting one. The moral, of course, is that you can’t imitate your way to prosperity. If we want to be rich, we have to innovate.

So to encourage innovation, you want to strengthen the unions? To encourage innovation, you want to reduce the relative reward to innovation, by insuring that everyone gets the same health care regardless of their social contributions?

Now, you might suppose that Krugman was thinking something along the following lines: Large swaths of American workers are being rendered unproductive by computers. Somehow or another, we have to support those people even though they’re not producing much. Unions and universal health care will keep them afloat.

But that can’t be what Krugman was thinking. I’m sure of this, because I happen to know that Krugman has a Ph.D. in economics. Therefore he must surely be aware that you can’t divorce incomes from productivity. Sure, you can redistribute, but you can’t redistribute more than what gets produced. If the problem is that our old skills are no longer productive, then our incomes must fall unless and until we acquire different — and less computer-replaceable — skills.

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Wisconsin Followup

A couple of followups on yesterday’s post about Wisconsin:

1) Several commenters have pointed out that the conflict in Wisconsin is not (directly) about wages, benefits or working conditions, but rather about collective bargaining. This seems to me to be a distinction without a difference; nobody would care about collective bargaining unless they expected it to affect wages, benefits, and/or working conditions. The point stands that workers who are very upset about losing their collective bargaining rights must expect to use those rights to achieve above-market compensation.

2) Jim from Wisconsin made a comment, and I made a reply, that I think bear highlighting here. Jim from Wisconsin said:

Futhermore, isn’t the idea in private business that if you want the best and the brightest, you pay them well? Don’t we want our Government programs run effectively and efficiently? Seems to work in the private sector, so why can’t this apply to public sector as well?

To which I replied:

The problem with this is that every “best and brightest” who is hired by the public sector is unavailable to the private sector, so it’s not at all clear that we WANT the best and brightest in the public sector. To take an extreme case, I don’t want the best Silicon Valley engineers tempted to work as high school teachers; I’d rather have them pushing the limits of technology. From the point of view of economic efficiency, this is the one and only reason why public sector employees ought NOT be overpaid. (It’s also a reason why private sector employees ought not be overpaid, but there’s generally less threat of that happening because of the private-sector profit motive.) It’s the one and only reason not to overpay public employees — but it is a good and sufficient reason.

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Wisconsin’s Smoking Gun

smokinAre public sector workers overcompensated? A month ago, I’d have said “probably”. Today I think we’ve found the smoking gun.

Here’s what I knew a month ago: Public-sector quit rates are roughly one-third of their private-sector counterparts. The obvious explanation is that public-sector jobs are generally too cushy to walk away from. It seems to me that it would be hard to account for that factor of three in any other way, though you can see some reasonable attempts in the comments here. (To be clear: I think that some of the factors in these comments can reasonably account for part of the difference in quit rates. I find it implausible that those factors are collectively substantial enough to account for a factor of three.)

A month ago, that was the best evidence on the table. Today, thanks to the protestors in Wisconsin, we’ve got something like proof positive.

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