Elsewhere on the web (link omitted because the source is the invitation-only blog of a personal friend), I read the following:

In the former case, you’re a danger to the person who wronged you. In the latter, you’re a danger to tens of millions of people, and that’s just in the US.

Hate crimes are different because the perp’s target list is vastly larger, with the built-in implication of recidivism.

There’s so much wrong with this I’m not sure where to begin. First of all, when a guy kills another guy for cutting him off in traffic, I’m inclined to think the likelihood of recidivism is pretty high. It’s not like nobody’s ever going to piss him off again. Second of all, I’d think that severity of punishment should be tied primarily to its effectiveness as a deterrent to others, not as a deterrent to recidivism. We can deal with recidivism partly by keeping an eye on past offenders, but when it comes to deterring unknown others, punishment is all we’ve got.

But I mention those issues only in passing on my way to what I think is the really interesting question, namely: Which is more harmful? Targeting a specific individual for death or targeting a randomly chosen representative of some race?

And while we’re at it: Which is more harmful? Targeting someone for being black, or for being white?

Some thoughts:

1. Generally speaking, people will pay more than a million times as much to avoid certain death as they will to avoid a one-in-a-million chance of death. By that measure, targeting a specific individual is more harmful than targeting a randomly chosen Albanian. And indeed, we allow this fact to guide public policy all the time. We are willing to spend, typically, maybe 5 or 10 million dollars for a guard rail that we expect to save a single randomly chosen life, but we’re willing to spend far more than that to save a particular miner trapped underground. I’ve argued (for example, in Chapter 15 of More Sex is Safer Sex that we ought to rethink those policies, but most people (unlike me) seem to be entirely comfortable with them. If you’re one of those people, then you ought to be willing to spend more to deter the death of one specific person than one who’s randomly chosen from a large population. In other words, you should view the “hate crime” motive as a mitigating factor, not an aggravating one.

2. To put this another way: When you target a specific victim, you do a lot of damage to one person. When you target a randomly chosen Albanian, you do a small bit of damage to each of many Albanians. It’s not immediately obvious in which case you’ve done more total damage. But all of the micro evidence points to the first case, and almost all existing public policy is formulated as if this micro evidence is definitive.

3. Suppose, however, that you believe for some reason that in this case, those arguments don’t apply. For example, you might believe that hate crimes against Albanians tend to unsettle Albanians at higher levels than are commensurate with the actual risks they face. In that case, you might be able to rescue the conclusion that hate crimes cause more harm than non-hate crimes. But you’ll also almost surely be forced to the conclusion that hate crimes against Chinese are worse than hate crimes against Albanians, simply because there are more Chinese than Albanians, each of them feeling outsized distress when crimes are committed against their group. As another application of the same principle, you’ll be forced to conclude that hate crimes against whites should be treated more severely than hate crimes against blacks.

4. The question on the table is: How does the size of the potential victim pool affect the severity of the crime? To focus attention on this question, we can consider Crime A with a victim pool of one (the guy who cuts you off in traffic), Crime B with a much larger victim pool (a randomly chosen black) and Crime C with an even larger victim pool (a randomly chosen white). (Obviously I’m envisioning a locality where whites outnumber blacks; if you live in a locality where the opposite is true, you can reverse Crimes B and C.) If your argument (like that of the blogger I’m responding to) is that “larger victim pools make things worse”, then you’ve got to conclude that Crime C is the worst. If your argument (like the one I’ve sketched, but not endorsed, in point 1) above) is that “smaller victim pools make things worse”, then you’ve got to conclude that Crime A is the worst. But you’d have to go through a lot of contortions to conclude that Crime B is the worst. I am sure a sufficiently clever debater could manage those contortions, but I’m skeptical that he could manage them in a terribly compelling way.

5. Conclusion: My blogger friend, if his argument is both serious and honest, should endorse the conclusion that hate crimes against whites are worse than hate crimes against blacks. Either that, or he should rethink his argument.

6. We really ought to have formulated this question a lot more carefully in the first place. “Which crime should be treated more severely?” is not a well-defined question. Does it mean, for example “Which crime should be prosecuted most vigorously?”, or “Which crime should be punished most harshly?”. Those are not the same question, and I (like my blogger friend) have been careless about conflating them. But I suspect that no matter how careful we are, it’s going to be very hard to avoid some conclusion along the lines of point 5).

7. (This was in my original draft and somehow got inadvertently cut before I posted; I’m restoring it now): You could also argue that the death of an aggressively bad driver is marginally less tragic than the death of a randomly chosen black. If you expand on this argument in the obvious way, it’s an argument for treating hate crimes more severely, but a slight variant (namely, that individual targeting can also deter desirable behaviors) goes the other way. In any event, I take this to be off topic, since the post I’m responding to is specifically about the size of potential victim pools as an argument for or against hate crime legislation.

Addendum: If I ever kill you in a rage, it’s not going to be for cutting me off in traffic; it’s going to be for ignoring the logical consequences of your own arguments. Just sayin’.

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None of which explains why today, fifteen years after Weil’s death, I received an email from the mathematical publisher Springer-Verlag that reads:

Dear Andre Weil,

We are writing today regarding your book *Basic Number Theory (ISBN: 978-3-662-05980-7), and to let you know about our plans
for an electronic archive, the Springer Book Archives.

…

Your author benefits at a glance:

- Your book will be digitized and become an eBook, published on SpringerLink, our online platform, and for e-reading devices such as the Kindle or iPad.

- Your book can never go ‘out-of-print’ and will be preserved for future generations of scientists.

- You will be provided with free access to the electronic version of your book once it is included in the archive.

- You will receive royalties, or can choose to waive them in support of charitable organizations such as INASP or Research4Life,
that help provide the developing world with access to scientific research.

Please go to the following website and select your preferred royalty option.

[URL deleted]

Yours sincerely,

[Etc.]

This mail was sent to an email address I never use and that, as far as I can tell from Google, appears nowhere on the web, though I have it set up to forward to an address I do read.

How should I respond?

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This month’s issue of Cato Unbound is titled “The Political Economy of Recycling”, with a lead essay by Michael Munger of Duke University expanding on these and related points, with responses by Edward Humes, Melissa Walsh Innes and myself.

Over the course of the next month or so, we’ll be posting responses and re-responses to each others’ essays, as the mood strikes us. The best of your comments here might well find their way into some of my posted responses there.

Below the fold, a brief teaser from my essay:

When you cast policy issues in moral terms, you degrade the character of public discourse. You lead people to see conflicting priorities as an occasion for battle, rather than an occasion for compromise. You send the message that policy is best decided by appeals to one’s inner conscience (or, more likely, to the polemics of demagogues), rather than by appeals to impersonal cost-benefit analysis. And this is a very bad thing. If overusing landfills is a bad habit, then branding everything you don’t like as evil is a far worse one.

If we’re determined to instill blind moral instincts that make people behave better most of the time, I’d like to nominate a blind moral instinct to respect price signals and the individual choices that underlie them—an instinct, for example, to recoil from judging and undercutting other people’s voluntary arrangements. I like it when my neighbors dispose of their beer cans properly. I’d like it even more if they’d stop trying to dictate other people’s wages, working conditions, housing contracts, and drug habits.

By concentrating our moral resources on recycling, we not only crowd out that nobler mission; we actually undercut it, by sending the message that price signals are unreliable. Of course, some price signals are unreliable, but the whole point of the moral suasion agenda is to get things right most of the time, not all of the time. Every time a misguided locavore makes the world a poorer place by choosing expensive local food, it’s because she’s absorbed the false lesson that prices are generally a poor measure of social cost – a lesson first absorbed, I suspect, at the feet of the recycling propagandists she first met in elementary school.

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It turns out that last week’s tag-team smear of a young Heritage Foundation economist, executed by Senator Sheldon Whitehouse of Rhode Island and his lackey Paul Krugman of the New York Times, was even worse than we knew.

As you’ll recall, Salim Furth of the Heritage Foundation testified before the Senate Budget Committee, accurately presenting data on economic policy changes in various countries for the years 2007-2012. Then Senator Whitehouse, cheered on by Paul Krugman, spent eight minutes excoriating Furth for inventing those numbers — the sort of accusation which, if it were taken seriously, would surely destroy Furth’s career. (As well it ought to, if it had contained a grain of truth.)

And what was Senator Whitehouse’s evidence for Furth’s “meretriciousness”, as he put it? Well, it was the fact that Whitehouse had gone to Furth’s source, looked for the numbers, and found them to be entirely different.

What Senator Whitehouse didn’t tell you was that he was “refuting” Furth’s accurate report of the historical record with projected numbers, which is to say pie-in-the-sky promises by politicians about what they’re going to do in the year 2016. It was, as I said last week, as if I’d announced plans to lose 30 pounds and then promptly gained 10. When Furth accurately reports my recent weight gain, Whitehouse calls him a liar because a 10 pound gain is not a 30 pound loss.

Paul Krugman, who must know better, cheered on this mendacity when he wrote:

a Heritage Foundation economist has been accused of presenting false, deliberately misleading data and analysis to the Senate Budget Committee.

What’s so shocking? Not the false, misleading data and analysis — that’s SOP at Heritage. … What’s shocking is that they got called on it, in real time.

Now it turns out that Senator Whitehouse’s numbers were even farther off base. Not only was were the numbers invented to begin with; he took those numbers for various years and added them up, even though they were already cumulative. It’s as if I’d announced plans to lose 30 pounds in 2013 and another 20 in 2014 — a total of 50 over two years. What Senator Whitehouse did was the equivalent of adding the initial 30 to the total of 50, and then announcing that my projected weight loss is 80 pounds. And then calling Furth a 90-pound liar for accurately reporting my 10 pound weight gain.

Now as Furth himself points out, Whitehouse’s travesty of addition might well have been an act of gross incompetence, as opposed to an additional layer of mendacity. But — though Furth is too polite to point this out — Paul Krugman doesn’t have that excuse. If you’ve actually been following this stuff (as I’m sure Paul Krugman has), the numbers were just too implausible.

In other words, there’s no way Paul Krugman actually swallowed Senator Whitehouse’s claim that Ireland has “announced fiscal consolidations” of 95% of GDP. (The correct projected number is 18%.) If he was paying any attention at all, he has to have known these numbers were garbage. Yet he endorsed them.

The only alternative theory is that he endorsed these numbers without paying any attention at all, just because they were integral to a partisan hack’s attempt to destroy the career of a good young scholar, and Krugman just couldn’t wait to check before using his megaphone to magnify the smear.

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Here, you see, is what happened this week: Salim Furth, an economist at the Heritage Foundation (and a graduate of the University of Rochester, where I knew him to be a thoughtful and honest researcher) testified before the Senate budget committee, where he presented data from the Organisation for Economic Cooperation and Development (OECD) showing that most European governments have recently increased their spending. (This isn’t surprising for several reasons, one of which is that governments often spend more in recessionary times.)

Enter Senator Sheldon Whitehouse of Rhode Island, who spent eight excruciating televised minutes lambasting Furth and questioning his honesty, by reading out OECD numbers that differed dramatically from what Furth had reported. Some choice comments:

Dr. Furth, I am very concerned about your testimony….

When I look at the graph, for instance, which you source to the OECD — did you actually look at what the OECD says?….

They’ve actually written what the numbers are. And here’s what the numbers actually are, according to the OECD….

I am concerned that your testimony to this committee has been meretricious…I am contesting whether you have given us fair and accurate information.

And then there’s another eight minutes of reading out numbers that are, Senator Whitehouse keeps reminding us actually from the OECD, as opposed to these other numbers reported by Furth, which Furth claims are from the OECD, but obviously can’t be, because Whitehouse has the actual OECD numbers right here, and look how different they are — all of this interspersed with a barrage of attacks on Furth’s character and integrity. (See the video below, if you have the stomach for it.)

Now here’s the thing: There are a couple of legitimate reasons why Furth’s and Whitehouse’s numbers don’t agree. The first is that they’re for different time periods. Furth’s are for the years 2007-2012, while Senator Whitehouse’s are for the years 2009-2016. That’s right, 2016. Which brings us to the other reason these numbers differ: Furth’s come from the historical record, while Senator Whitehouse’s come from somebody’s ass.

More precisely: The numbers Whitehouse quoted come from an OECD report on what various countries plan to do (or say they plan to do) over the next few years. Because these numbers differ from what these countries have actually done, Whitehouse wants you to believe first that Furth’s accurate account of what’s actually happened is irrelevant, and second that Furth is a liar for reporting the truth.

But surely Whitehouse realizes that he can’t actually get you to believe that, which is, I’d guess, why he didn’t bother to tell you that the numbers he was reading were largely nothing but pie-in-the-sky projections from politicians with extremely poor track records of living up to their promises.

It’s as if I’d announced plans to lose 30 pounds over the next year, and then promptly gained 10 pounds. Furth comes before Congress and says “Landsburg tells me he just gained 10 pounds”. Whitehouse says: “I can’t imagine where you got that number, because I have a number here from Landsburg that refers to a loss of 30 pounds — and that comes directly from Landsburg, who you say is your source. This makes me very concerned about your testimony, very concerned about where you’re getting these numbers…..” followed by eight minutes of innuendo suggesting that only sheer dishonesty can account for a discrepancy like this.

Well, yes, only sheer dishonesty — or perhaps an extraordinary failure of competence — can account for a discrepancy like this. But the dishonesty is not on Furth’s part.

This, then, is where Paul Krugman comes in. You know, the Paul Krugman who’s always complaining about dishonest politicians with no respect for actual data? Here’s what Paul Krugman had to say on the matter:

OK, this is really shocking: a Heritage Foundation economist has been accused of presenting false, deliberately misleading data and analysis to the Senate Budget Committee.

What’s so shocking? Not the false, misleading data and analysis — that’s SOP at Heritage …. What’s shocking is that they got called on it, in real time.

Krugman’s other big schtick lately has been about how one-sided all the dishonesty is nowadays, with 90% of it coming from Repulicans. I guess this is Democrat Krugman’s attempt to restore some balance.

Edited to add: It’s possible, of course, that Krugman simply made a rash mistake and posted before he’d realized what the facts were. That happens to everyone from time to time. But this is the same Paul Krugman who has urged us repeatedly not to give anyone else the benefit of this kind of doubt, so a decent respect for Krugman’s worldview really demands that we dismiss out of hand any temptation to cut him some slack.

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Comments are turned off on this post because I want to keep the discussion all in one place. I’ll soon be back with more content, not all of it boxcar-related.

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I am thankful that I acknowledged in advance (at the bottom of Wednesday’s post) that I’m less sure of this one than I am of many others. I’d cheerfully bet $1000 (subject to agreement on a suitable referee) that I’m right about this relativity puzzle. (My answer is here.) And as far this old chestnut goes, my answer is here and I hereby cheerfully renew my offer to bet up to $15,000 on the outcome of a computer simulation. (Or any other amount, as long as it’s over $1000, to make this worthwhile.) Email me if you’re interested.

(This is on my mind because I’ve just had a very unpleasant encounter with a troll in another venue, who, like other trolls, is happy to bluster but runs away when you offer to put money on the line.)

For the first time ever, I am turning off comments on this post, because I don’t want to dilute yesterday’s interesting discussion by allowing it to take place half over there and half over here. Go there to participate. Many thanks to the commenters who have forced me to think harder about this, and thanks to anyone else who can help resolve the controversy.

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(Spoiler warning!)

Answer: It’s a rocket.

______________

Edited to add: In view of some of the comments below, I’m no longer at all confident of this answer. I’m retaining the rest of the post, including the final paragraph in which I say that I’m pretty sure of this answer, but not as sure as I am of some other things. It looks like my hesitation might have been well justified.

________________

Several people got this right in comments; let me summarize:

Most of the water coming out of the hole has traveled rightward to get there, and hence, barring the application of another force, will continue traveling rightward forever. (Another force, which we can call “hitting the ground”, does in fact intervene, but the boxcar doesn’t know about that, so it’s irrelevant to the problem.) Since the total momentum of the system is zero, and since this momentum must be conserved, and since the water has acquired rightward momentum, the boxcar must acquire leftward momentum to cancel the momentum of the water. Therefore the boxcar travels leftward forever or until, like the water, it encounters some external force to stop it.

I’m nearly sure that’s right, though I’m less sure about this one than I am about this other one, less sure of that as I am of the existence of conscious beings other than myself, and less sure of that than I am about this one here. I’m pretty sure of all of them, though.

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This reminded me of several things, not all of them related to the relentless march of time.

For example, once a very long time ago (though it sure doesn’t seem that way) Tom asked me a simple physics question that troubled me far more than I now think it ought to have:

A boxcar full of water sits on a frictionless train track. A mouse gnaws a hole through the bottom of the boxcar, in the location indicated here:

The water, of course, comes gushing out. What happens to the boxcar?

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One of the oldest problems in number theory is the twin primes problem: Are there or are there not infinitely many ways to write the number 2 as a difference of two primes? You can, for example, write 2 = 5 -3, or 2 = 7 – 5, or 2 = 13 – 11. Does or does not this list go on forever? There are very strong reasons to believe the answer is yes, but many a great mathematician has tried and failed to find a proof.

Here’s a related problem: Are there or are there not infinitely many ways to write the number 4 as a difference of two primes? What about the number 6? Or 8? Or any even number you care to think about? It seems likely that the answer is yes in every case, though no proof is known in any case. But….

Just a few days ago, Professor Yi Tang Zhang at the University of New Hampshire announced a major breakthrough. He can’t prove that the answer to any of these particular questions is yes, but he can prove that the answer to at least one of them is yes. Professor Zhang has proved that there is at least one even number — – in fact, at least one even number less than 70 million — that can be written as a difference of primes in infinitely many ways. There seems to be good reason to hope that a refinement of his methods will allow a substantial reduction in that bound of 70 million. Of course if you could reduce the bound all the way to, say, 3, then you’d have solved the twin primes problem.

I thought about trying to explain a little about Zhang’s methods (or about my limited understanding of them), but I cannot hope to do better than this blog post by Emily Riehl.

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