The Nuke Kids on the Block

So it seems that North Korea has been developing nuclear arms technology after all, despite swearing up and down back in 1994 that they wouldn't. Is anyone surprised? Frankly, I don't keep up with foreign affairs as much as I should, so if you'd asked me last week if North Korea had nukes, I would have said, "You mean there's a chance they don't? Really?"

In any case, this further confirms my belief that the nuclear genie is out of the bottle, and it's pretty pointless trying to cram it back in. Anyone who wants a nuke will have one, as Tom Lehrer observed decades ago, and there's unfortunately not a heckuva lot we can do about it. Nuclear non-proliferation policy strikes me as being a lot like gun control: it's mostly successful in keeping weapons out of the hands of people (or governments) not terribly inclined to use them anyway.

On a completely unrelated note, I'm wondering if the hit count on this page would increase substantially if I changed the name to "Agora-feel-ya."

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On the Dollar Value of Human Life

In a recent post to the Volokh Conspiracy, Eric Jaffe asks for a means of putting a value on human life: "no matter how crass it may seem, we eventually need some means of valuing lives (or more likely, life-years) and of comparing that value to other disparate values. We do this in any event, and at some point it would aid clear thinking to bring it out into the open a bit more. Society will "spend" lives on lots of things, and it would be nice if we did so with some amount of introspection rather than just by bumbling along."

Exactly right. Some method, even if only a rough-and-ready one, is needed for valuing lives. Saying that a life has infinite value sounds awful nice, but clearly we don't believe it -- for if we did, we would never take even the slightest risk to our own lives. If your death has a value of negative infinity, and there is even the smallest probability of death from whatever activity you'd like to do (driving, riding a roller coaster, eating rare meat, whatever), the expected value of the activity is also negative infinity. Anything multiplied by infinity is infinity, and no finite benefit could possibly be large enough to outweigh an expected loss of infinite magnitude.

So I will humbly suggest the economists' metric for valuing human lives. For any given risk to human life, find out the minimum amount of money it would take to induce the average human being to accept the risk; call this value X. If P is the probability of death from this particular risk, then solve for the value of life (V) using the following equation: PV = X. For example, if the probability of death created by some risky activity is 5%, and it would take $50,000 to persuade the average person to accept this risk, then the value of life is $1,000,000. This value of human life would not work for all purposes, of course; it depends, among other things, on the size of the risk. The dollar value needed to induce the acceptance of risk most likely increases at a greater rate than the size of the risk; the person willing to accept $50,000 for a 5% chance of death would probably need *more* than $100,000 for a 10% chance of death. In effect, the value of life we use in our calculations would be situation-specific, but not arbitrary.

No, I'm not joking. We cannot avoid the problem of weighing lives. Virtually every human activity involves some risk of death to someone, and risk can never be completely eliminated. It can sometimes be reduced (by spending increasing amounts of resources on safety measures, by reducing activity levels, and so on), but eventually our risk-reduction efforts are subject to diminishing returns. We have to spend more and more to achieve smaller and smaller reductions of risk, and it would be infinitely costly to reduce risk to zero. So the question is not whether to have risk or not, but how much to have. Placing an infinite value on human life does nothing to address that question.

(This proposal is certainly not my own idea; see almost anything in the work of Kip Viscusi, among others, for further details on this approach.)

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Federal Department of Being Your Mom

So Health and Human Services Secretary Tommy Thompson is telling fast food restaurants to serve healthier food, as if it were any of his damn business. I suppose he feels entitled by his job title to lecture people about proper eating habits. And to make it worse, he doesn't even respect us enough to lecture us (the eaters of fast food) directly -- instead, he tries to browbeat the producers of fast food into serving us food that we don't want. I doubt Republicans will make a stink about Thompson's audacity, because, well, Thompson is a Republican. But I'll bet they'd raise holy hell if a Democrat in the same office urged restaurants to go vegetarian.

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Occam's Eraser

A colleague of mine suggests a simpler theory of why so many people stink at math: "Math is hard, people are stupid." I don't think this explains everything (such as why so many otherwise intelligent people I know can't deal with math), but it probably explains more than either of the more complicated theories discussed below. There are different forms of intelligence, after all, and perhaps the kind of intelligence needed for math is just more scarce. Of course, the real explanation is probably a combination "all of the above."

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Emoter Voter

Next month, Californians will vote on Proposition 52, which would allow voter registration on election day. This proposal is presumably based on the bogus notion, propagated by journalists and pundits every election year, that maximizing votes cast is the great desideratum of electoral politics. But when it comes to votes, I'm much more concerned about their quality than their quantity. Other things equal, I prefer to be governed by voters who have taken the time to consider the issues and think about them. There's no way to check for a voter's understanding of the issues, of course, but one simple proxy is to see whether she even had the forethought to get registered at least 15 days before the election. It's far from a perfect correlation, but at least it's something.

Lest I be accused of being undemocratic, it's worth noting that advance registration excludes no one from voting except those who *exclude themselves*. Anyone who wants to vote (and meets the other requirements) can do so if she just thinks ahead. Advance registration does not discriminate on the basis of race, gender, or political viewpoint. Yes, it does impose a filter on voters, but what's the matter with that? Age and citizenship requirements also impose filters. We impose them because we think that, on the whole, the pool of voters meeting them will be marginally more informed and thoughtful than would a broader pool. (This does not mean that I fully agree with all existing voting requirements, however. Consider this thoughtful commentary on the voting rights of non-citizens.)

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Money for Puffing

A jury in California recently ordered Philip Morris to pay a whopping $28 billion settlement to a 64-year-old woman with lung cancer. She started smoking 50 years ago, and she blames her choice on the company's failure to warn her of the risk.

I'm not sure when the tobacco companies started putting health warnings on their products, so it might well have been less than 50 years ago. And it's also possible that the companies had internal studies indicating that smoking was even more damaging than was publicly known at the time, so I'll leave that to the jury as well. What really irks me about this and similar cases is the presumption that anyone who starts smoking is utterly incapable of stopping, regardless of what new information emerges. Nicotine addiction is regarded as a force so powerful that it erases all control and responsibility on the part of the addict. Yet there are probably millions of people who have stopped smoking over the last 50 years. No, it's not easy, but the difficulty doesn't erase the responsibility.

There's an old rule of common law known as the "last clear chance" doctrine that would seem to apply here. The paradigmatic case involves a victim who gets hit by a train while walking on the subway tracks. The victim should not have been there, but the train engineer nonetheless has a responsibility to stop the train if he sees the (potential) victim. If the engineer fails to take this "last clear chance" to stop the accident, then he (or his employer) will be held liable for at least part of the resulting damage. Normally, this doctrine is used to limit the contributory negligence of plaintiffs, thereby placing greater liability on defendants. But if you apply the same reasoning in the case of smoking, the doctrine points in the other direction. It seems to me that the smoker is in the position of the train engineer. Even if the tobacco company did something wrong (withholding relevant health information), the smoker herself had the last clear chance to prevent the damage. Shoot, she had the last *one hundred* clear chances to prevent the damage, even if we estimate that you can only try to stop smoking once every six months.

I'm not a lawyer, so perhaps I'm misinterpreting or misapplying the last clear chance doctrine. But my overall point can be made independently: your responsibility to do the intelligent thing, to take action to avoid becoming a victim, does not end just because somebody else has already done something wrong.

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Why Johnny Can't Integrate, By Parts

In her most recent column (Parade magazine, 13 October 2002), Marilyn vos Savant takes up the question of "why more people don't understand math better than they do." Her tentative answer: "I believe that much of the problem lies in the lack of logic and reasoning skills. Math is just logic with numbers and symbols attached, and success with it requires the ability to reason effectively. But children usually are taught *what* to think, not *how* to think." That's a good partial answer (and I don't think Marilyn intended her answer to be exhaustive), but it should be taken with at least a grain of salt. For many years, the fad in pedagogy has been to emphasize understanding rather than outcomes. As Tom Lehrer once put it, "New Math" was based on the notion that "the important thing is to understand what you're doing, rather than to get the right answer." The problem is, math is a field in which understanding and accuracy are bound up together. You can't have one without the other, and accuracy is one (not to say the only) viable indicator of understanding.

In any case, I want to suggest another reason that so many people don't understand math (and this reason is meant as a complement, not a substitute, for Marilyn's). Math is one of those disciplines that builds heavily on itself. If you don't get arithmetic, you won't get algebra; if you don't get algebra, you won't get trig; and so on. Students often learn to hate math because of one really lousy teacher, and after that they never really catch up. If your American history teacher is horrible, that won't cripple your efforts in World history; but if you algebra teacher is horrible, your geometry and trig teachers may never be able to rescue you. The point, then, is that math education is much more sensitive to failure at any point in the learning process.

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