Monday, December 31, 2012

The Net Value of Video Games

One of the Christmas books I received this year (from my younger son) was John Dies at the End by David Wong, an author whose blog post I recently linked to. I liked it enough to finish it, not enough to want to read the forthcoming sequel. One of the things I didn't like was the degree to which the central characters seemed to be acting irrationally, along with consuming considerable quantities of alcohol and, in one case, drugs. Another was the degree to which the whole picture did not entirely make sense and the feeling that that was not an issue the author cared much about. It occurred to me that perhaps my response was the flip side of the objection some readers make to my fiction, that everyone, and everything that happens, is too rational. Partly, I suppose, that is a disagreement about what people are like, partly about what they should be like, partly about what is interesting or entertaining about other people's behavior.

One of the throwaway lines in the book was the suggestion that violent video games are an alien plot introduced recently to human society by agents from an alternate timeline capable of making the introduction retroactive by changing our memories to fit the new reality. Which started me wondering ...  .

My natural prejudice as an economist is to assume that people act in their own interest, hence that spending time playing video games is a net benefit, at least to those who play them—a prejudice perhaps reinforced by the amount of time I have myself spent playing and enjoying video games (mostly the computer versions). But people are not entirely rational, and the designers of successful computer games, like successful creators of earlier forms of entertainment, are presumably skilled at taking advantage of the irrational elements in their customers' behavior. Which suggests several questions:

1. As compared to earlier forms of mass entertainment—novels, movies, television—are video games better or worse for their consumers? Are you more likely to end up failing out of college, losing your job, breaking up with your girlfriend, through devoting too much of your time to playing video games than from the earlier equivalents? As one very mild piece of evidence, I offer my own observation, long ago, that the way you knew a computer game was really good was that when you took a break to go to the bathroom, it was because you really, really had to go. I have never been much of a viewer of movies or television, but I have read a lot of books and do not remember a comparable effect for them. 

On the other  hand, it's easier to read in the bathroom than to play (most forms of) computer games there. 

2. The same question, with regard to the effect on others. The implication of the line in the novel was that video games were designed to coarsen sensitivities, make us more tolerant of people being killed, dismembered, tortured, generally mistreated. I am not sure that is any more true of them than of comic books and thrillers, but I suppose one could argue that the visual element, and the involvement of the player in the plot, makes a difference. You are not just watching someone else engaged in mass mayhem, you are doing it yourself.

But then, one of the reasons thrillers are thrilling is that the reader is imagining himself as the protagonist.

3. What about positive effects? Novels and films can educate (or miseducate) you about history, geography, human behavior. So can computer games. Quite a large fraction of my son's knowledge of geography and history comes from playing war games; he  taught himself to type at a young age in order to communicate with fellow players online and learned to spell so as not to look stupid while doing so. If anything, the interactive nature of computer games ought to make them more educational than earlier equivalents, since doing things wrong, failing to see the logic of the situation, sometimes results in losing, which is less fun than winning.

All of which leaves out the big question which I have discussed in the past: In what sense is doing things in virtual worlds less valuable than doing them in the real world?

Sunday, December 23, 2012

Christmas Books

First, some biased suggestions for presents:

My and my wife's book on medieval and renaissance cooking—more than three hundred recipes, each with the original and how we do it, plus a variety of related articles. Just the thing for the cook in your life—or the medievalist.

This is the bigger book that the previous one is the cooking section of. Recipes, articles on how to make a pavilion, portable period furniture, a Germanic lyre, lots of other things, along with a good deal of my poetry and essays on historical recreation and related matters. Good if any of your friends are into historical recreation from the Middle Ages and/or Renaissance, especially through the Society for Creative Anachronism, a long term hobby of ours.

My most recent nonfiction book, good for futurologists, science fiction readers, and the proverbial intelligent layman. For whom my 


are also possibilities.

But the one I really want you to read, because I want more comments on it, is my second novel, Salamander. Extra credit for physics and math types if you can figure out what my version of magic is modeled on. 

For my unbiased recommendations, here are some of my past Christmas books—each the book that, for one year's Christmas, went to anybody I couldn't think of anything else for because I thought it was neat.

Talleyrand by Duff Cooper. Mostly for the fascinating subject, but it doesn't hurt that the author was the one member of Neville Chamberlain's cabinet who resigned over Munich.

and the book that just occurred to me for this year's Christmas book, some of our presents being given a few days late ...

And, for a final recommendation, His Majesty's Dragon by Naomi Novik, and sequels—a series I am currently rereading.

Tuesday, December 18, 2012

Harsh Self-Help Advice

I just came across a webbed essay by someone I have never heard of that struck me as both well written and, on the whole, sensible, so thought I would link to it.

Friday, December 14, 2012

Is Heaven Worth the Price?

While picking up a prescription in the local drug store, I noticed a book on a rack of Christian literature entitled "Heaven is real." Which started me thinking ...  . 

One possible explanation of religion is that it is wishful thinking. People do not want to die, so they want to believe in life after death. One problem with that explanation is that several of the most successful religions include both Heaven and Hell. The quiet of the grave does not sound very attractive compared to an eternity of bliss. Compared to an eternity of torture, on the other hand, there may be much to be said for it. So why are people attracted to a system of belief that offers the possibility of the former but also the risk of the latter? How high do the customers have to believe the risk is before they would prefer not to buy? Putting it in the jargon of my field, what are the relative Von Neumann utilities of Heaven and Hell?

Heaven and Hell make much more sense as an incentive system, promised reward and threatened punishment as a way of getting people to follow the dictates of a religion. That is a good reason why some people would want others to believe in them. But it does not explain why people choose to themselves believe in them. Perhaps wishful thinking is not, after all, the right explanation.

For an alternative explanation, see an old post of mine that started with the same puzzle.

Wednesday, December 12, 2012

Why Are Law Schools Expensive

There has been a lot of concern of late in the law school world over falling numbers of applicants, poor employment opportunities for graduates, high debt loads, and associated problems. I recently came across a post on another blog discussing the question, and decided that a post here would be more appropriate than a very long comment there.

From the standpoint of potential law school applicants, there are two problems—a shortage of jobs for lawyers, relative to the number of graduates, and the high cost of law school. The current administration will probably help with the former problem, since an increase in the size and intrusiveness of government is likely to lead to an increased demand for lawyers. The purpose of this post is to discuss the latter.

The fundamental problem, as I see it, is with the incentives facing the schools. Law schools are heavily dependent on their reputation to attract students. The two biggest sources of information available to the students are the American Bar Association, which accredits law schools, and the annual U.S. News and World Report ranking. Both of those are based mainly on measures of inputs, not outputs. Thus, for example, the ABA recommends a student to faculty ratio of no more than twenty and takes a ratio of thirty or more as presumptive evidence that the school does not meet the standards for accreditation. Its rules for calculating the ratio count one adjunct as one fifth of a tenure-track professor and it requires that "substantially all" of the first third of a student's coursework be taught by the full-time faculty. The standards include a lengthy list of what must be in a law school library—almost all of which is material currently available to both faculty and students online.

So a school that chose to spend less on its library, have a higher student to teacher ratio, use more inexpensive adjuncts and fewer tenure-track professors, do a variety of other things to cut costs, would risk losing its accreditation, whether or not it was doing a worse job of teaching its students. A school which provided its education in any form other than the conventional number of hours sitting in a classroom would lose its accreditation, since one of the ABA requirements is that:
 A law school shall require, as a condition for graduation, successful completion of a course of study in residence of not fewer than 58,000 minutes of instruction time, except as otherwise provided. At least 45,000 of these minutes shall be by attendance in regularly scheduled class sessions at the law school.
U.S. News and World Report does not publish the details of its ranking system, but a number of people have reverse engineered it. The four factors that together predict the ranking almost perfectly are peer reputation, fraction of graduates employed nine months after graduation, student-faculty ratio, and undergraduate GPA of the students.

The ABA includes in its requirements a measure of what fraction of students pass the bar. That, the USNWR employment measure, and the peer reputation measure, are output measures. Unfortunately, they are not very informative ones.

Start with peer reputation. A professor at one law school is unlikely to know much about how good a job other law schools do educating their students. What he is much more likely to know, and base his opinion on,  is what prominent scholars in his field are at which school—information almost entirely irrelevant to most students. And this criterion has the unfortunate side effect of giving each school an incentive to barrage faculty at all other schools with glossy pamphlets boasting the activities and accomplishments of their own faculty, an expense that does nothing to improve the education of their students.

Bar passage and (very imperfectly measured) employment rates are more relevant. The problem with both of those is that they depend on two different inputs—quality of instruction and quality of students. Top schools get very high bar passage rates not because they do a particularly good job of teaching the skills relevant to bar passage—most of their students take an additional bar preparation course before taking the exam—but because they admit only smart students.

In an old post, I proposed a simple solution to this problem. Schools should report their bar passage rates as a function of some measure of student quality such as LSAT or undergraduate GPA. That would provide the potential applicant with the information that matters to him—what the chance is that a student of his ability who goes to that school will pass the bar. A similar approach could be used for employment statistics.

There are two possible approaches to reforming legal education to lower its cost. One is to recommend specific changes, such as Judge Posner's old proposal to make the third year of law school optional. The other is to recommend changes in the incentive structure that currently prevents such specific changes from being in the interest of law schools to make. At the level of the individual law school, the first is all that can be done—but, short of crisis, mostly will not be, because it is not in the interest of law schools to do a better job for their students at the cost of risking their ABA accreditation and USNWR ranking. 

At the level of the legal education profession, I think the second approach makes more sense. It too, however, faces incentive problems. One effect of the current ABA standards is to increase law school demand for tenure-track faculty, and tenure track faculty have a substantial influence over those standards.


P.S. The post that inspired this one has a delightful comment by a law school student about to take his last exam, detailing what is really need to teach law. His bare bones law school ("Perhaps you feel that your students cannot survive without a cafe? Build/rent your school next to a Panera") would cost students about $10,000 a year. Combine that with Posner's proposal for a two year degree and you have the cost of legal education down to $20,000.

But I don't think the ABA would accredit it.

Tuesday, December 11, 2012

A Modest Request

I have just spent an hour or so on yard work, my usual form of exercise. Much of it consisted of pulling out self-seeded privet, of which my yard produces an inexhaustible supply. I also got rid of some ivy, ditto. Which suggests ...

If someone who does genetic engineering wants to make himself really useful, he should look into engineering vegetable pests to make them good for something. If only my yard grew a variant of ivy whose leaves made a tasty and nutritious lettuce substitute, I would have a lifetime's supply of salads. I am not sure what can be done with privet, other than letting the trees grow up and turning them into lumber, which would make the yard unavailable for its present function of growing fruit trees. But perhaps someone can think of something.

Unsolicited Ad for Genetic Testing

Some time ago, my elder son persuaded me to pay for genetic testing by 23andMe. They send you a test kit, you provide some saliva, they test it. They then tell you what the genetic information implies about medical problems you are more or less likely than average to have and where your distant ancestors come from, and make it possible, if you wish, to get in touch with putative relatives, people who have also been tested and whose genetic information suggests common ancestry not too far back. 

They also invite you to answer a bunch of questions about yourself designed to generate additional information about what genetic characteristics correlate with what outcomes, information that can then be used to, among other things, better inform their other customers. Thus getting tested not only provides some private benefits, it also increases the existing store of information about the results of different gene variants, which strikes me as a good thing to do.

I have two pieces of evidence that their service is real. The main one is that they correctly identified my son as my son. The minor one is that they told me I had an above average chance of a particular sort of tumor. The information was not useful, however, since it arrived after the tumor had been diagnosed and removed.

I recently got an email from them, announcing a sale—$99 for their services, which I think is what I paid but is less than their standard price. I thought some of my readers might be interested, hence this post.

Saturday, December 08, 2012

Observations of Film Making

Quite a long time ago, a libertarian by the name of J. Neil Schulman wrote a novel, Alongside Night. He is currently in the process of turning it into a movie. He asked me to play a bit role, and I have just returned from doing so.

The invitation did not reflect any misguided belief in my acting ability—the role consisted of playing the King of Sweden for about ten seconds in a simulated Nobel Prize award ceremony. The reason he wanted me, pretty clearly, was that his protagonist is the son of a Nobel Prize winning free market economist. So am I—and I expect Neil believes he can get a little free publicity out of the parallel. He told me, many years ago, that the father's personality is actually based on his father, not on mine, but I do not expect that to be obvious to the random viewer or reviewer.

The main payoff for me was the opportunity to spend a day or so observing the process of movie making and chatting with the people involved. I learned a number of interesting things.

Perhaps the most interesting was from a conversation with the costume person, who was making sure that the very formal outfit he had rented for me would fit. By his account, his job is not simply providing costumes from the right date, nationality, social class and the like.  As a character moves through the plot line, different shades, textures, appearance of clothing reflect changes in his role, mood, personality.What the costumer is doing, as he sees it, is creating a work of art one of whose dimensions is time.

Another feature of the process, one which I had only partly allowed for, is how much of a patchwork it is. There is no attempt to start filming at the beginning and go on to the end;  one of the people I talked with said that the last person who made a film that way was Alfred Hitchcock and that doing so was unconventional even then. The approach instead is to shoot individual scenes, each of them many times over. The order in which they are shot is determined by considerations such as which actors are in them or what set they are being shot on. 

I was told that, for a low budget film like this one, the filming typically takes four weeks or so. Assembling the movie from the output of those weeks takes something more like four months. Most of the assembly requires only two people, while the filming seems to require a total crew of about thirty.  The finished film will be about one percent as long as the time spent filming it—and the ratio of filming time to film time is substantially higher for a higher budget production.

Another point that struck me about the experience was my own reaction to the dialogue. My natural inclination, as an author and public speaker, was to critique it, to notice places where what the character said could have been said better. In some cases I may have been right. But I suspect that in others, my critique was really of neither the scriptwriter nor the actor but of the character. What he said could have been said better—but would not have been by that character in that situation. I was reminded of my own dictum after writing my first novel: No plot survives contact with the character. For the same reasons, the author's words ought to change when put into the character's mouth, because the character is not the author and will not say things in the same way the author would.

Which may be relevant to my own writing. One of my weaknesses is a tendency for my characters to sound too similar; I have not yet got the trick of giving each of them his own distinctive voice. Part of the solution may be to remember that they will not necessarily say everything, state every argument, in the best possible way.

It was an interesting twenty-four hours or so. I look forward to seeing, sometime in the next year, how the movie turned out.

Wednesday, December 05, 2012

Jury Nullification and the Enforcement of the Juror's Oath

In a recent post, I discussed the issue of jury nullification, the question of whether a juror ought to vote for acquittal if he believes that the defendant is guilty, but of something that ought not to be a crime. I mentioned being dismissed from a jury some time back as a result of telling the judge that I might do so.

One commenter suggested that my mistake was not that I was willing to vote for acquittal in such a situation but that I told the judge that I was, that I ought to have said I would follow the judge's instructions and then voted for acquittal if the law that the defendant was accused of violating was one I disapproved of. His point was that if I could, at no great cost to myself, keep someone from being jailed for something he did not deserve jail for, I ought to do so.

Another commenter pointed out that, as a juror, I would be required to swear to follow the judge's instructions with regard to the law. Falsely swearing would be perjury, a criminal offense. Which raises two questions ...

The first is a moral question—ought I to be willing to perjure myself under such circumstances. I think the answer is that I should. I am generally unwilling to lie to people, but this is a special case, analogous to lying to a mugger about what money I have on me. I do not regard government as a source of moral authority, so a government trying to imprison someone for (say) smoking marijuana deserves to be treated like anyone else trying to violate rights. I would be uncomfortable lying to a judge under oath and might do it badly, but I do not think doing so would be wicked.

The second is a practical question—how likely is someone who swears to vote according to the judge's instructions on the law and then deliberately fails to do so to get into legal trouble as a result. My guess is that a juror who limits himself to telling the other jurors that he is not convinced of the defendant's guilt and so unwilling to vote for conviction would be pretty safe—unless he had previously put up a blog post defending jury nullification, or in some other way provided clear evidence of what he was doing. Perhaps even then.

But all one vote for acquittal can do is produce a hung jury; if the prosecution is determined to convict, it can always try the defendant again. A more ambitious project would be to try to persuade the other jurors to vote for acquittal on the grounds that what the defendant had done ought not to be illegal. Doing that would produce evidence that the juror had perjured himself in swearing to follow the judge's instructions on the law.  

I'm curious as to whether, in practice, jurors who do that get prosecuted for it, and if so how often. 

One further point occurs to me. In discussing the risks of jury nullification in my earlier post, I took it for granted that it would be used to prevent the conviction of someone guilty of something the juror thought ought not to be a crime. It could also be used to convict someone who was innocent of the crime he was accused of but belonged to a group that the juror disliked. 

I think that is less of a problem, for two reasons.

To begin with, a single juror can't convict; the most he can do is produce a hung jury. So if only a few jurors share the dislike and the willingness to act on it, the result is not to convict the defendant but only to give the prosecution an opportunity to retry him. That might impose serious costs on the defendant, especially if he cannot offer bail, but less serious than conviction.

What about a situation where almost everyone dislikes the group the defendant is a member of and wants to use the legal system against them? In that case, jury nullification could convict the innocent defendant. But it probably isn't needed, since in that situation the government will almost certainly share the dislike and have other ways of acting on it.

Monday, December 03, 2012

Response to Rothbard

There is a webbed essay by Murray Rothbard that takes me to task for not hating the state. His central point is correct. I do not view the state as a wicked conspiracy by evil men seeking to exploit the rest of us, merely as a mistake, an institution that exists primarily because most people mistakenly believe it is useful and necessary.

I have an old blog post responding to the essay. Looking over the second edition of my first book, it occurred to me that it also contained my response to (among others) Rothbard, and that that should be webbed too—linked to his essay.

Don't write a book; my friends on either hand
Know more than I about my deepest views.
Van den Haag believes it's simply grand
I'm a utilitarian. That's news;
I didn't know I was. Some libertairs
Can spot sheep's clothing at a thousand yards.
I do not use right arguments (read 'theirs')
Nor cheer them loudly as they stack the cards.
Assuming your conclusions is a game
That two can play at. So's a bomb or gun.
Preaching to the converted leads to fame
In narrow circles. I've found better fun
In search of something that might change a mind;
The stake's my own—and yours if so inclined.

(From The Machinery of Freedom, 2nd Edition)

True and Dangerous: Jury Nullification

"Some statements are both true and dangerous. This is one of them."

The quote above is my standard example. The fact that a true statement can be dangerous provides an argument for suppressing freedom of speech. Which is why that true statement is dangerous.

I am currently on call for jury duty, which reminds me of an example of the same principle which both I and my readers are considerably more likely to face as a real moral choice. We rarely have the opportunity to suppress speech or writing, whether or not we approve of such suppression. But I, like those of my readers who also live in countries under the Anglo-American jury system, may well have to decide whether or not someone accused of a crime will go to jail for it.

The last time I was here, a year or two back, I got as far as the point at which the judge questioned prospective jurors. She asked me whether, if I disagreed with the law the defendant was accused of violating, I would still be willing to vote for conviction if I thought he was guilty. I replied that I would not—and was dismissed from the jury. 

In that particular case, it was, for me, a real issue, since the defendant was accused of having carried a concealed handgun. The most visible supporter of laws permitting concealed carry has for many years been John Lott, a friend and ex-student of mine. And, well before he coauthored an empirical piece supporting the claim that concealed carry reduced confrontational crimes, I had sketched the theoretical argument in my Price Theory. If I had remained on the jury and concluded that the defendant was guilty, I would probably have voted for acquittal on the grounds that he did not deserve to be punished for breaking a law that ought not to have existed.

That is an example of jury nullification, the doctrine that jurors should nullify bad laws by voting to acquit those accused of violating them—even if they are guilty. 

It is also an example of the "true and dangerous" problem. I do not believe that right and wrong are made by act of Congress or majority vote. Hence I do not believe that it is just to imprison someone for doing something which he has a moral right to do, even if he does not have  a legal right to do it. I do not believe that it is morally legitimate for me to participate in violating someone's rights, save perhaps in extreme circumstances (for examples, see other things I have written, especially Chapter 41 of The Machinery of Freedom). It follows not only that I may acquit someone guilty of doing something that ought not to be illegal, I am in most circumstances morally required to.

But ...

Suppose everyone accepts the principle. Further suppose that some significant fraction of the population, say 20%, believe that certain people do not have rights, or at least do not have the right to live—gays, blacks, communists, illegal immigrants, whatever. One of them goes around murdering such people. When he is arrested, the odds are high—about .93—that at least one of his fellow believers is on the jury. If the doctrine of juror nullification is widely accepted, that is enough to keep him from being convicted.

Some statements are both true and dangerous. Including this one.

Sunday, December 02, 2012

Thoughts on the Trolley Problem

A familiar philosophical conundrum goes roughly as follows:

You are standing by a trolley track which goes down a hill, next to a fork in the track controlled by a switch. You observe, uphill from you, a trolley that has come loose and is rolling down the track. Currently the switch will send the trolley down the right branch of the fork. Four people are sitting on the right branch, unaware of the approaching trolley, too far for you to get a warning to them. 

One person is sitting on the left branch. Should you pull the switch to divert the trolley to the left branch?

The obvious consequentialist answer is that, assuming you know nothing about the people and value human life, you should, since it means one random person killed instead of four. Yet to many people that seems the wrong answer, possibly because they feel responsible for the result of changing things but not for the result of failing to do so.

In another version of the problem, you are standing on a balcony overlooking the trolley track, which this time has no fork but has four people whom the trolley, if not stopped, will kill. Standing next to you is a very overweight stranger. A quick mental calculation leads you to the conclusion that if you push him off the balcony onto the track below, his mass will be sufficient to stop the trolley. Again you can save four lives at the cost of one. I suspect fewer people would approve of doing so than in the previous case.

One possible explanation of the refusal to take the action that minimizes the number killed starts with the problem of decentralized coordination in a complicated world. No individual can hope to know all of the consequences of every choice he makes. So a reasonable strategy is to separate out some subset of consequences that you do understand and can choose among and base decisions on that. A possible subset is "consequences of my actions." You adopt a policy of rejecting actions that cause bad consequences. You have pushed out of your calculation what will happen if you do not act, since in most cases you don't, perhaps cannot, know it—the trolley problem is in that respect artificial, atypical, and so (arguably) leads your decision mechanism to reach the wrong answer. A different way of putting it is that your decision mechanism, like conventional legal rules, has a drastically simplified concept of causation in which action is responsible as a cause, inaction is not.

I do not know if this answer is in the philosophical literature, but it seems like one natural response from the standpoint of an economist.

Let me now add a third version. This is just like the second, except that you do not think you can stop the trolley by throwing the stranger onto the track—he does not have enough mass. Your calculation implies, however, that the two of you together would be sufficient. You grab him and jump.

The question is now not whether you should do it—most of us are reluctant to claim that we are obliged to sacrifice our lives for strangers. The question is, if you do do it, how will third parties regard your action. I suspect that many more people will approve of it this time than in the previous case, even though you are now sacrificing more, including someone else's life, for the same benefit. If so, why?

I think the answer may be that, when judging other people's actions, we do not entirely trust them. We suspect that, in the previous case, the overweight person next to you may  be someone you dislike or whose existence is inconvenient to you. When you take an act that injures someone for purportedly benevolent motives, we suspect the motives may be self-interested and the claim dishonest. By being willing to sacrifice your own life as well as his, you provide a convincing rebuttal to such suspicions.

All of which in part comes from thinking about my response to the novel, Red Alert, on which the movie Doctor Strangelove was based. In both versions, a high ranking air force officer sets off a nuclear attack on the Soviet Union.  In the movie, he is crazy. In the book, he is a sympathetic character. He has good reason to regard the idea of Soviet conquest with horror, having observed atrocities committed by Soviet troops in Germany at the end of WWII. He has concluded, for all we know correctly, that a unilateral nuclear attack by the U.S. will succeed—will destroy enough of the Soviet military so that the counterattack will not do an enormous amount of damage to the U.S. He has also concluded that the balance of power is changing, that in the near future the U.S. will not be able to succeed in such an attack and that in the further future the USSR will triumph.

Under those circumstances, his choice is not obviously wrong. It can, indeed, be seen as the consequentialist choice in the trolley problem—with the number of lives at stake considerably expanded.

But what makes it sufficiently believable to make him a sympathetic character is that part of his plot requires him to commit suicide in order to make sure he cannot be forced to give up the information that will let his superiors recall the bombers he has sent off. The fact that he is willing to pay with his own life to do something he considers of enough importance to justify killing a large number of people makes his reaching that judgement much more believable than it would otherwise be, and makes us feel as though his act is in consequence more excusable, perhaps even right.

As in my final trolley example.

One further point occurs to me. My guess is that, on average, people who think of themselves as politically left are more likely than others to accept the consequentialist conclusion to the trolley problem—and less likely than others to approve of the decision made by the air force officer in Red Alert. Readers' comments confirming or rejecting that guess are invited.