God of the Machine – Page 2 – Culling my readers to a manageable elite since 2002.
Dec 142006

Periodically I shall adjudicate blog disputes. There is no appeal.

First on the docket we have Gawain, of Heaven Tree, vs. Conrad Roth, of Varieties of Unreligious Experience. Gawain, upset with the Uffizi museum for neither allowing photographs nor selling reproductions of its collection, is driven to guerrilla tactics. He photographs, presumably illicitly, a bust of Scipio Africanus, and posts it for the world to see.

Conrad defends the Uffizi policy on the paradoxical grounds that it makes the enjoyment of its treasures all the greater for those who can travel there and look at them in person. For they can also delight in thinking of all the poor slobs who can’t make the trip:

For me, elitism is simply the general notion that things are better when fewer people have them, and that the few (whether groups of one member or 500) should be (and are) hostile — snobbish — to the many. There are, of course, an infinity of fews. Everyone belongs to several. And the pleasure of belonging to a few — especially if that few is just oneself — is derived from the fact that it is not a many. Such a pleasure is concurrent with the pain felt by those outside the few who want in; nevertheless, our pleasure outweighs their pain, and I see no reason to deny ourselves the satisfaction. Everyone benefits in the long view.

Conrad means that the pleasure of being in derives from the imagined pain of those who are out, and no amount of shuck and jive about “concurrent with pain” and “not a many” can disguise the fact. It is not enough, for Conrad, to see the treasures of the Uffizi. Others must be prevented from doing so. Or as Gore Vidal once wrote, “It is not enough to succeed. Others must fail.”

There are indeed an infinity of elites, or at least a great many, but Conrad has multiplied them beyond necessity. There are two elites in his argument where there ought to be only one.

One elite is the people who visit the Uffizi. This elite imposes no duties of connoisseurship or discrimination: only the time, the money, and the inclination to visit are required. What really interests, or ought to interest, Conrad is the other elite, whose members, instead of filing dully past the Scipio bust, look it over carefully and see some of what Gawain sees. One can belong to the first and not the second — and now, thanks to Gawain and despite the Uffizi’s policy, to the second and not to the first. Virtually all of Emily Dickinson’s best poems can be found on the web. Anyone can join who is willing to invest the time and effort to grasp the poems. This elite will be tiny to begin with. Would Conrad propose to narrow it further by requiring anyone who wants to read Dickinson to travel to Amherst to study the original manuscripts?

The court finds for Gawain. He is, however, directed to pay damages to the Uffizi, for infringing its reproduction rights, in the amount of $0.10 for each blogger who links to his article. That’s 20 cents and counting. Conrad is directed to stop whinging that Gawain doesn’t leave enough comments on his blog.

Next up are A.C. Douglas, of Sounds and Fury, and Campbell Vertesi, of, um, Campbell Vertesi’s blog. A.C. issued one of his clarion calls for “hierarchical sobriety,” by which he means that pop culture is pop and high culture is high, and not only shall the twain never meet, they shall not even be profitably compared:

Metaphorically speaking (and once one gets past technical considerations of craft, one can speak of the core matters of aesthetics in no other way), the singular principal hallmark of all artifacts of the realm of high culture is their perceived aspiration to transcendence; transcendence of the quotidian world of experience, of the culture within which they were produced, and even of their very selves as works of art. And that singular hallmark is what’s singularly lacking in all the artifacts of the realm of popular culture, their singular principal hallmark being a perceived aspiration to the widely accessible here-and-now entertaining.

Campbell replies that what we call “pop” and “high” is largely an accident of time and place, and that many “high culture” artifacts were written to entertain, or even, God forbid, to make money. As a musician, he adduces Rossini and Gilbert and Sullivan; as a literatteur, I would add Homer and Shakespeare. Some of today’s “pop” artifacts will surely belong to the high culture of the next century, although it is precipitous to speculate which. Campbell goes on to argue that “if no aesthetic judgements are permitted between the two musical traditions, it follows that any two representatives of the fields take on equal status.”

Here he puts his case badly, as A.C., who is nothing if not tireless, points out in his inevitable reply. The conclusion does not follow; but it need not either. What Campbell should have said is that a purported defender of high culture ought to be prepared with a convincing answer to a high school student who asks why he must study The Scarlet Letter instead of the latest X-Men comic. I would want to be armed with a little more than “perception of aspiration to transcendence” myself.

These converted verbs disavow their subjects. “Perception” occurs, without a perceptor; “aspiration” without an aspirant. Campbell reasonably asks who or what is doing the aspiring; A.C. does not deign to answer. It’s a metaphor, you see, and there the matter ends. The “aspiration” (by the artist? the work?) to “transcendence” (of quotidian experience? of the culture? of itself?) is cloaked in the “perception” (of the audience? of Campbell Vertesi? of A.C. Douglas?) and the whole business is wrapped in a metaphor. This is, as Woody Allen once remarked, a travesty of a mockery of a sham. Nothing is at the center except the usual because I say so.

Accordingly, the court finds for Campbell Vertesi, who is nonetheless directed to learn how to spell “transcendence.” A.C. Douglas, for his part, is enjoined from using the word for a period of six months. He is also enjoined, permanently, from employing “bourgeois” as a term of abuse. (“Bourgeois” does not appear in the current case, but this court is acquainted with his past torts.) Come to think of it, this injunction is general. Dismissed.

Dec 082006

The first piece of advice in Strunk and White’s Elements of Style concerns punctuation — the proper use of the apostrophe. I learn that I must write “Charles’s execution,” but “Jesus’ crucifixion.” Already my prose is improving, though not at the rate I would like.

Items 2 through 8 also concern punctuation. I learn to balance my commas, and to handle colons, semi-colons, and em-dashes with aplomb.

Punctuation is important. Its abuse can be a source of unintentional hilarity. (“I would like to thank my parents, God and Ayn Rand.”) Some would go so far as to regard it as an index to character. On its wings a marginally literate Englishwoman has soared to international celebrity. But The Elements of Style purports to be a guide to writing English. A badly punctuated essay can be corrected in minutes. A badly written essay can probably never be corrected at all.

Strunk and White expand their range in Items 9 and 10, which advise, respectively, that subject and verb agree in number and that pronouns be proper case. This is unexceptionable: as most of these errors derive from being unable to determine the subject or the case, it is also useless. With a final warning against dangling modifiers, buttressed by several amusing, if unlikely, examples (“Wondering irresolutely what to do next, the clock struck twelve.”), Strunk and White conclude their “Rules of Usage” and move on to “Principles of Composition.”

There are eleven of these:

1. Choose a suitable design and hold to it.
2. Make the paragraph the unit of composition.
3. Use the active voice.
4. Put statements in positive form.
5. Use definite, specific, concrete language.
6. Omit needless words.
7. Avoid a succession of loose sentences.
8. Express coordinate ideas in similar form.
9. Keep related words together.
10. In summaries, keep to one tense.
11. Place the emphatic words of a sentence at the end.

A strange mix of the anodyne, the obvious, and the risible. Omitting needless words is a fine idea, certainly better than adding them. (And how much better to choose a suitable design than an unsuitable one!) To judge from White’s introduction, it appears to have been a particular favorite of Strunk’s:

In the days when I was sitting in [Strunk’s] class, he omitted so many needless words, and omitted them so forcibly and with such eagerness and obvious relish, that he often seemed in the position of having shortchanged himself — a man left with nothing more to say and yet with time to fill, a radio prophet who had outdistanced the clock. Will Strunk got out of this predicament by a simple trick: he uttered every sentence three times. When he delivered his oration on brevity to the class, he leaned forward over his desk, grasped his coat lapels in his hands, and, in a husky, conspiratorial voice, said, “Rule Seventeen. Omit needless words! Omit needless words! Omit needless words!”

Willy Three Times, with so many minutes to spare, might have mentioned, in order of increasing importance, omitting needless sentences, omitting needless paragraphs, omitting needless chapters, and omitting needless books of advice. He might have touched on how to judge what is needless, which is where the trouble lies. But this would be difficult to do in “a hortatory essay…. of sixty-three words.”

The cabal of linguistics professors at Language Log likes to laugh at Strunk and White. They go especially hard on using the active voice and omitting needless words. Sometimes they lose their cool. A “vile collation of stupid advice and false claims about grammar”? Stupid and false perhaps, but vile? Professor overboard!

At any rate, the merits of the particular principles are mostly beside the point. The list reminds me of the to-do lists I make periodically, which include items like “learn Spanish” and “blog more often,” and items like “take out the trash” and “pick up the dry cleaning.” I somehow never get around to blogging more often or learning Spanish. The Strunk and White reader will never get around to choosing, and holding to, a suitable design either — not that the book would aid him if he did.

The hyphen, parenthesis, quotation mark, and exclamation point — apparently the red-headed stepchildren of punctuation — are relegated to Section Three, “A Few Matters of Form,” along with a few desultory bits of advice about dates, titles, margins, headings, and syllabification that must have fit nowhere else. The Elements is not, shall we say, rigidly organized. What did I read somewhere about choosing and holding to a suitable design?

Section Four, “Words and Expressions Commonly Misused,” parades the usual suspects alphabetically: aggravate vs. irritate, irregardless, nauseous vs. nauseated, try to vs. try and, and so on. Such lists have historical interest at best. Strunk’s original, which included cranks like studentry for student body and forcible for forceful, might have made mildly diverting reading. But White, and subsequent editors (the franchise has fallen to his stepson and fellow New Yorker icon, Roger Angell), felt obliged to keep things current, so the section now reads like a transcript of Patricia T. O’Connor’s NPR show. Ambrose Bierce’s little book, Write It Right, is the same kind of collection, with two advantages over Strunk and White. Bierce is wittier; and he had only one edition to prepare. It is amusing to read his objections to “conservative estimate,” because “having been found to have several meanings, conservative seems to be thought to mean anything”; or to “United States” as a singular noun, because “grammar has not a speaking acquaintance with politics, and patriotic pride is not schoolmaster to syntax.” It is edifying to learn that sideburns, in 1909, was still considered a vulgarism for burnsides.

Although Bierce’s book and Strunk’s original were almost exactly contemporary, they sometimes differ, and where they do Bierce always wins on points. For Bierce — and for me, and for Webster’s 2ndgratuitous means “without cost,” while for Strunk and White it means “unwarranted.” Strunk and White allow clever, in the sense of good-natured, to apply to horses, though not to people; Bierce says that “in this sense the word was once in general use in the United States, but is now seldom heard and life here is less insupportable.”

With Section Four Strunk’s contribution ends. For the first edition White added Section Five, “An Approach to Style,” in an effort not to shortchange his publisher. He begins by asserting that “style is something of a mystery,” which does not stop him from going on for another twenty pages in an attempt to unravel it. He takes as his text the first sentence of Common Sense: “These are the times that try men’s souls.”

Here we have eight short, easy words, forming a simple declarative sentence. The sentence contains no flashy ingredient such as “Damn the torpedoes!” and the words, as you see, are ordinary. Yet in that arrangement they have shown great durability; the sentence is now almost into its third century. Now compare a few variations:

Times like these try men’s souls.
How trying it is to live in these times!
These are trying times for men’s souls.
Soulwise, these are trying times.

It seems unlikely that Thomas Paine could have made his sentiment stick if he had couched it in any of these forms. But why not? No fault of grammar can be detected in them, and in every case the meaning is clear. Each version is correct, and each, for some reason that we can’t readily put our finger on, is marked for oblivion. We could, of course, talk about “rhythm” and “cadence,” but the talk would be vague and unconvincing.

Is this really so mysterious? A cursory consideration of the alternatives immediately removes the second, which sounds personal and petulant, as if Paine were short next month’s rent; and the fourth, with its grisly “soulwise.” The original is a perfect line of iambic tetrameter, with the first foot inverted — a common pattern in English poetry. None of the alternatives, except the hopeless fourth, scan naturally. Paine manages the buzzing sibilants brilliantly, bookending the first half of the line with “these” and “times” to produce a heavy caesura, and placing “men’s” next to “souls” to lengthen, and thus emphasize, the final foot. Strunk, who wrote a book about English meter, could have explained this easily. Unfortunately when White wrote this passage Strunk had been dead for a decade.

White continues with twenty-one more rules, which would be classed, if the book were properly organized, with Strunk’s Principles of Composition, and suffer from most of the same defects. I, for one, find it especially helpful to be told to be clear, to write naturally, not to overwrite or overstate, and not to explain too much. Before White, I used to try to be obscure, write unnaturally and floridly, exaggerate, and beat every point into the ground. White’s advice to write with nouns and verbs I will leave to Language Log. An admonition, contradicting the spirit of the previous eighty-four pages, that “style takes its final shape more from attitudes of mind than from principles of composition” brings The Elements of Style to a merciful close.

This sorry hash has become a modern American classic, selling more than ten million copies. High schools require it. Parents send their children off to college with a copy packed in the luggage. People who ought to know better continue to recommend it, whether out of ignorance or deference is difficult to say. My mother likes it, and she hates everything but Middlemarch.

The Elements of Style, at its birth, had the field to itself. Today writing guides litter the aisles at Barnes & Noble, largely because of its success; but in 1959, when Macmillan commissioned White to whip it up, there was Fowler, who was scholarly and British, and very little else. White was also famous, which is how Americans prefer their how-to authors. Famous mathematicians write primers on mathematics, and famous physicists write primers on physics, but for some reason primers on writing are traditionally consigned to obscurities. Mark Turner and Francis-Noël Thomas, who wrote Clear and Simple as the Truth, the best style book I know, are distinguished academics, but you’ve never heard of them.

The Elements of Style owes its success, above all, to its cramped and pedantic outlook. Strunk and White treat writing from the point of view of the copy editor, as if there were nothing that a vigorous line edit couldn’t fix. In fact there is very little that a vigorous line edit can fix. It certainly would not fix The Elements of Style.

I know only two infallible rules for writing well. First, read good writing: take it apart to see how it works, where it succeeds and fails, and then imitate it as best you can. Who would produce must first consume. (Faulkner recommends reading bad writing as well, but I have tried reading Faulkner, and it did me no good.) Second, write exactly what you think. Certain authors, like Céline and Henry Miller, have survived despite prose that lacks every virtue but this one. Most of us suppress our best material, in the interest of job security or domestic tranquility or not being forced to flee the country.

These rules, in guidebook form, would not sell ten thousand copies, let alone ten million. They require diligence, persistence, and courage to follow. Don’t bother. Spend your time balancing commas, double-checking apostrophes, eliminating adverbs, rewriting passives, and rearranging conjunctions. You’ll make teacher happy, and you won’t have to go into exile.

Update: Maxine Clarke comments. It is odd that in England, of all places, they seem not to have heard of the Oxford comma, but there it is. Frank Wilson comments. Derek Lowe comments. Battlepanda comments. Thudfactor comments.

Nov 222006

If I could require every American schoolchild of normal intelligence to read one book, it would be George Pólya’s How To Solve It. (Second choice is Henry Hazlitt’s Economics in One Lesson. I keep extra copies of both books on hand to give away as necessary.) Pólya was born in Hungary and taught mathematics at several European universities before ending up at Stanford. Like the authors of all the best pedagogical texts, he was a superb practitioner. Pólya made important original contributions in probability theory, combinatorics, complex analysis, and other fields. He published How To Solve It in 1945; it has since sold more than a million copies. He died in 1985 at an immense age.

How To Solve It, among its other virtues, is a model of English prose style; I will let Pólya himself describe what he’s up to:

The author remembers the time when he was a student himself, a somewhat ambitious student, eager to understand a little mathematics and physics. He listened to lectures, read books, tried to take in the solutions and the facts presented, but there was a question that disturbed him again and again: “Yes, the solution seems to work, it appears to be correct; but how is it possible to invent such a solution? Yes, this experiment seems to work, this appears to be a fact; but how can people discover such facts? And how could I invent or discover such things by myself?” Today the author is teaching mathematics at a university; he thinks or hopes that some of his more eager students ask similar questions and he tries to satisfy their curiosity.

Math students are regularly exhorted to “show your work,” while the great mathematicians hide theirs. Euclid’s proof that the angles of a triangle sum to 180 degrees is a masterpiece of logical thought, but however he arrived at it, it was assuredly not by the route shown in the Elements. The proofs came first, the axioms after. One can admire but not emulate. In short, what math education lacks is heuristic, and this is what Pólya endeavors to supply.

The way to write about Pólya is to solve problems with his techniques. Abbas Raza at 3 Quarks Daily provided an occasion by posting fourteen moderately difficult logic problems, none requiring mathematical background. I’ve rearranged them slightly. Most of the problems are famous; you have probably seen some of them before. You may want to have at the problems first before you read my solutions and commentary on how I used Pólya’s techniques to find them.

1. You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: if you light one end of the rope, it will take exactly one hour to burn all the way to the other end. But it doesn’t have to burn at a uniform rate. In other words, half the rope may burn in the first five minutes, and then the other half would take 55 minutes. The rate at which the two ropes burn is not necessarily the same, so the second rope will also take an hour to burn from one end to the other, but may do it at some varying rate, which is not necessarily the same as the one for the first rope. Now you are asked to measure a period of 45 minutes. How will you do it?

Solution: Light the first rope at both ends, and the second at one end. When the first rope has completely burned, 30 minutes have elasped. Now light the other end of the second rope. When the second rope has completely burned, 45 minutes have elapsed.

Commentary: “If you can’t solve a problem,” Pólya says, “there is an easier problem you can solve: find it.” Measuring 45 minutes may seem impossible at first, but how about 30 minutes? Thinking about 30 minutes instead, you may hit on the bright idea of lighting the rope at both ends. From there you need one more bright idea: that you need not light both ends simultaneously. Most people, including me, arrive at the second idea very quickly after thinking of the first; but I once saw an excellent problem solver find the first idea immediately and take quite a while to find the second.

2. You have 50 quarters on the table in front of you. You are blindfolded and cannot discern whether a coin is heads up or tails up by feeling it. You are told that x coins are heads up, where 0 < = x

Solution: You are given x, the number of heads. Create a subgroup of x coins. Flip them all.

Commentary: Pólya asks: Did you use the whole condition? The condition here is more liberal than it looks. You need not know the number of heads in each pile. Neither must the two piles contain the same number of coins, provided the number of heads in the two piles is the same.

Pólya also asks: Did you use all the data? Here we are given the total number of coins, which is doubtfully relevant, except that it is large enough to make the problem difficult. More important, we are given x, the number of coins heads up. The solution is very likely to involve flipping x coins. In fact it is a simple matter of doing just that.

Pólya finally asks: Can you check the solution? Introducing suitable notation, another Pólya suggestion, yields a satisfying way to do so. x is the number of coins that are heads up; 50 – x, then, is the number of coins tails up. We divide the coins into two groups, of x and 50 – x coins. Let y be the number of heads in the x group. Then the number of heads in the 50 – x group is x – y. Now we flip all the coins in the x group. The number of heads becomes x – y. The two groups contain the same number of heads. This also demonstrates, as we suspected, that 50 is indeed irrelevant; the solution works no matter how many coins you begin with.

3. A farmer is returning from town with a dog, a chicken and some corn. He arrives at a river that he must cross, but all that is available to him is a small raft large enough to hold him and one of his three possessions. He may not leave the dog alone with the chicken, for the dog will eat it. Furthermore, he may not leave the chicken alone with the corn, for the chicken will eat it. How can he bring everything across the river safely?

Solution: Bring the chicken across. Return alone and bring the dog across. Return with the chicken, and bring the corn across. Return alone and bring the chicken across.

Commentary: This is a “hill-climbing” problem; you proceed by steps until you reach the goal. It can be difficult to solve because in hill-climbing it is natural to try to proceed directly, which gets you stuck at a local optimum of two items across the river.

Pólya says, translating the Greek mathematician Pappus of Alexandria (circa 300 AD), “start from what is required and assume what is sought as already found.” Next “inquire from what antecedent the desired result could be derived.” Beginning at the end, we can see that on the farmer’s last raft trip he must bring the chicken across, because only the dog and corn can be left together safely. But for the same reason he must also bring the chicken across on his first trip. Putting this to yourself explicitly, you may eventually realize that the chicken must go back and forth and the solution will immediately present itself.

4. Late one evening, four hikers find themselves at a rope bridge spanning a wide river. The bridge is not very secure and can hold only two people at a time. Since it is quite dark, a flashlight is needed to cross the bridge and only one hiker had brought his. One of the hikers can cross the bridge in one minute, another in two minutes, another in five minutes and the fourth in ten minutes. When two people cross, they can only walk as fast as the slower of the two hikers. How can they all cross the bridge in 17 minutes? No, they cannot throw the flashlight across the river.

Solution: Two and One cross (2 minutes). One returns (3 minutes). Ten and Five cross (13 minutes). Two returns (15 minutes). Two and One cross (17 minutes).

Commentary: Pólya asks: If you had a solution, what would it look like? Certainly we know that Ten and Five cannot cross more than once, or we are immediately at 20 minutes plus. But if Ten and Five cross separately we are still over 17 minutes, since there must be three other trips of at least a minute each. Therefore Ten and Five must cross together. This cannot happen at the beginning — otherwise one would have have to return — or at the end — since someone would have to return with the flashlight and would remain. Therefore they must cross in the middle. The solution appears.

Pólya also asks: Do you know a related problem? This problem bears an interesting reciprocal relationship to Problem 3, of the dog, chicken, and corn. There we infer the procedure from the first and last trips; here we infer it from the trip in the middle.

5. You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a loop with all 12 links. What is the smallest number of cuts you must make to accomplish this task?

Solution: Three cuts. You cut all three links of a single chain and use them to connect the other three together.

Commentary: Cutting one link in each of the four chains will obviously do the job, but that’s not interesting enough to be the right answer. Can we do better?

Pólya suggests enumerating the solution space, when possible; or guessing, to put it bluntly. How many different ways can we cut three links? Well, we can cut one from each of three chains: that won’t work. We can cut two from one chain: that doesn’t help either. Or we can cut all three from a single chain… aha!

6. Before you lie three closed boxes. They are labeled Blue Jellybeans, Red Jellybeans and Blue & Red Jellybeans. In fact, all the boxes are filled with jellybeans. One with just blue, one with just red and one with both blue and red. However, all the boxes are incorrectly labeled. You may reach into one box and pull out only one jellybean. Which box should you select from to correctly label the boxes?

Solution: Choose from the box labeled Blue & Red.

Commentary: Another good guessing problem. The solution is obvious. It is functionally equivalent to choose from the Blue or Red box, and the problem stipulates a single answer, which must be Blue and Red.

All that is left is the reasoning. Suppose you choose a red jellybean. Then you know the Blue & Red box should be labeled Red, and that, since the other two boxes are also mislabeled, that the Red box must be Blue and the Blue box must be Blue and Red.

Guess first, reason later: it works more often than you’d think.

7. Walking down the street one day, I met a woman strolling with her daughter. “What a lovely child,” I remarked. “In fact, I have two children,” she replied. What is the probability that both of her children are girls?

Solution: There are four prior possibilities for the sex distribution of her two children: boy-boy, girl-girl, boy-girl, and girl-boy. We’ve seen a girl, so boy-boy is out. Of the three remaining possibilities, once you’ve revealed a girl, a boy remains in two of them. Therefore the probability that the other child is a girl, P(G) = 1/3.

Commentary: The difficulty here is less in finding the answer than in believing it. As with the Monty Hall Problem, many people deny that the solution is true, and they have distinguished company. (The solution depends subtly on the precise wording with which the problem is given; this comment thread has an extensive discussion, which is beyond the scope of this discussion.)

Pólya asks: Can you draw a diagram? No, but you can model the problem experimentally. Dump a bunch of coins on the table and pair them up randomly. Remove all the tail/tail pairs. Now tabulate the results for the rest of the pairs. They will be tail/head approximately 2/3 of the time.

8. A glass of water with a single ice cube sits on a table. When the ice has completely melted, will the level of the water have increased, decreased or remain unchanged?

Solution: The water level sinks, because ice has lower specific gravity than water.

Commentary: Pólya asks: Have you seen this problem before? You have. It’s the famous problem Archimedes solved in his bath. A king asked Archimedes to determine if a crown he owned was pure gold, without melting it down. Archimedes stepped into his bath, watched the water rise, and ran naked into the street, shouting “Eureka!” Maybe not. At any rate, he realized that his body displaced an equivalent volume of water, and he could measure the volume of any irregular object the same way, by submerging it.

Once Archimedes determined the volume of the crown, he simply weighed it against a lump of gold of identical volume. Gold is denser than silver, so if the crown was lighter, it had been adulterated. Water is denser than ice, so the water level sinks as the ice melts.

Abbas Raza, after setting this problem, got it wrong. The floating cube does not “displace its own weight in water”; it displaces its own volume in water. Had he regarded Pólya’s advice to check the solution, by melting a few ice cubes in a glass of water, he would have spared himself some embarrassment. (See the update for who’s embarrassed now.)

9. You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, can you determine which coin is counterfeit using the scale only twice?

Solution: Weigh three against three. If they are equal then the counterfeit is one of two coins and it’s easy. If not, then the counterfeit is one of three coins. Take two of the three and weigh them against each other. Whichever is heavier is the counterfeit, or, if they’re equal, the third is counterfeit.

Commentary: This problem would be far easier if it were given with nine coins instead of eight. The same solution applies, but since three divides nine evenly, and two does not, you would immediately think to weigh three against three. With eight coins the opposite is true. You think of weighing four against four, and it may be some time before you disentangle yourself.

10. There are two gallon containers. One is filled with water and the other is filled with wine. Three ounces of the wine are poured into the water container. Then, three ounces from the water container are poured into the wine. Now that each container has a gallon of liquid, which is greater: the amount of water in the wine container or the amount of wine in the water container?

Solution: The water in the wine is equal to the wine in the water.

Commentary: This problem, like Problem 2, is overspecified. In fact almost all of the given data — how much liquid is in each container, the mixing sequence — is irrelevant. It matters only that the two containers begin and end with equal amounts of liquid. Pólya asks: Did you use all the data? Here that question gets you into trouble.

But Pólya also says that sometimes the general problem is easier to solve. (In computer science the general problem is always easier to solve.) He has caught grief for this remark, and the example he gives is somewhat artificial, but here it bears out. The specifics make the problem confusing.

Of course if you solve the general problem then you have, by definition, not used all the data. Sometimes one procedure works; sometimes its opposite.

11. Other than the North Pole, where on this planet is it possible to walk one mile due south, one mile due east and one mile due north and end up exactly where you began?

Solution: Pólya gives this exact problem in How To Solve It in its more famous form, in which a bear does the walking and the problem is what color is the bear. I will quote his solution, if only to demonstrate how comprehensive his thinking is next to mine:

You think that the bear was white and the point P is the North Pole? Can you prove that this is correct? As it was more or less understood, we idealize the question. We regard the globe as exactly spherical and the bear as a moving material point. This point, moving due south or due north, describes an arc of a meridian and it describes an arc of a parallel circle (parallel to the equator) when it moves due east. We have to distinguish two cases.

1. If the bear returns to the point P along a meridian different from the one along which he left P, P is necessarily the North Pole. In fact the only other point of the globe in which two meridians meet is the South Pole, but the bear could leave this pole only in moving northward.

2. The bear could return to the point P along the same meridian he left P if, when walking one mile due east, he describes a parallel circle exactly n times, where n may be 1, 2, 3… In this case P is not the North Pole, but a point on a parallel circle very close to the South Pole (the perimeter of which, expressed in miles, is slightly inferior to 2Ï€ + 1/n).

Commentary: Before solving the problem Pólya offers the following hints:

What is the unknown? The color of a bear — but how could we find the color of a bear from mathematical data? What is given? A geometrical situation — but it seems self-contradictory: how could the bear, after walking three miles in the manner described, return to his starting point?

12. I was visiting a friend one evening and remembered that he had three daughters. I asked him how old they were. “The product of their ages is 72,” he answered. I asked, “Is there anything else you can tell me?” “Yes,” he replied, “the sum of their ages is equal to the number of my house.” I stepped outside to see what the house number was. Upon returning inside, I said to my host, “I’m sorry, but I still can’t figure out their ages.” He responded apologetically, “I’m sorry. I forgot to mention that my oldest daughter likes strawberry shortcake.” With this information, I was able to determine all of their ages. How old is each daughter?

Solution: The factors of 72 can be combined into three factors with identical sums only one way: 6, 6, and 2; and 3, 3, and 8, both of which sum to 14. “My oldest daughter likes strawberry shortcake” implies that there is one daughter who is older than the other two. (This isn’t quite sound, since two of the daughters could be, say, 6 and 1 month and 6 and 11 months, and even twins are not precisely the same age; but, as Pólya would put it, we idealize the question, as it is more or less understood.) Therefore 3, 3, and 8 are the ages.

Commentary: Pólya might suggest introducing suitable notation. Let the ages of the three daughters be x, y, z. There must be a uniqely oldest daughter, so x > y >=z. Let S be the sum of their ages.

We have:

x * y * z = 72

x + y + z = S

Now we enumerate x, y, and z, looking for those with non-unique sums. Since the prime factors of 72 are (2^3) * (3^2), the job is pretty simple. The solution suggests itself shortly.

13. The surface of a distant planet is covered with water except for one small island on the planet’s equator. On this island is an airport with a fleet of identical planes. One pilot has a mission to fly around the planet along its equator and return to the island. The problem is that each plane only has enough fuel to fly a plane half way around the planet. Fortunately, each plane can be refueled by any other plane midair. Assuming that refuelings can happen instantaneously and all the planes fly at the same speed, what is the smallest number of planes needed for this mission?

Solution: Three planes. Send out all three, flying clockwise. At 45 degrees each plane has burned a quarter of its fuel. Plane 1 gives a quarter of its remaining fuel each to Plane 2 and Plane 3 and uses its remaining quarter-tank to return to base. Planes 2 and 3, now both full, continue to 90 degrees. Plane 2 gives Plane 3 one-half of its fuel and uses its remaining half-tank to return to base. Plane 3 continues to 270 degrees. When it reaches 180 degrees, Planes 1 and 2, having refueled at base (Plane 2 will have just returned by then), fly out counter-clockwise, using the same procedure.

Commentary: Pólya says, first be sure you understand the problem. Abbas Raza specified, in reply to a reader’s query, that the planes may not fly suicide missions. Oddly, if they were permitted to, the answer would still be three, although two of them would plunge into the drink. But then the problem would not be interesting.

14. You find yourself in a room with three light switches. In a room upstairs stands a single lamp with a single light bulb on a table. One of the switches controls that lamp, whereas the other two switches do nothing at all. It is your task to determine which of the three switches controls the light upstairs. The catch: once you go upstairs to the room with the lamp, you may not return to the room with the switches. There is no way to see if the lamp is lit without entering the room upstairs. How do you do it?

Solution: You turn one on. You turn a second one on, wait a minute, then turn it off. Then you go upstairs and see if the bulb is off, on, or warm.

Commentary: Here the question that is so effective for Problem 12 — could you restate the problem? — can lead you astray. Introducing notation will probably also steer you wrong. The solution depends on the physical characteristics of the problem elements, and different, more abstract language may cause you to miss it. (This is why many mathematicians hate this problem.) But that’s why it’s called heuristic, as Pólya explains:

You should ask no question, make no suggestion, indiscriminately, following some rigid habit. Be prepared for various questions and suggestions and use your judgment. You are doing a hard and exciting problem; the step you are going to try next should be prompted by an attentive and open-minded consideration of the problem before you….

And if you are inclined to be a pedant and must rely on some rule learn this one: Always use your own brains first.

Update: On Problem 8, as Adam points out in the comments, Abbas Raza is right and I am wrong. The best correct explanation is here. Pólya does not say, but should, that if you insist on solving problems in public you do so at your peril. I will leave up my own foolishness as a lesson in hubris.

Oct 242006

Discoveries of unpublished poems by famous poets depress me. We already suffer from an enormous glut of poetry — even, perhaps especially, by famous poets — and of art of all sorts. A law that required artists to burn half of their finished product, the way Gogol burned the second half of Dead Souls, would vastly improve public taste. Poems are generally left unpublished when their author does not think they merit publication. There are exceptions, and accidents. A pretty good Philip Larkin poem escaped publication because of girl trouble. Wallace Stevens omitted one of his best poems, “The Course of a Particular,” from his collected verse, although he fortunately remembered to publish it elsewhere. But nearly always the poem is no good. Sometimes it’s not by the famous poet either.

Reading Robert Frost also depresses me. Frost is a popular poet, the closest thing to a poet laureate America ever had. He read at Kennedy’s inauguration, and he is said to have made a living from poetry. There are several reasons for this. Frost usually, and always at his best, writes short rhymed iambic poems; his readers feel assured that they’re reading honest-to-god poetry and not that sissy modern stuff. His themes are simple, his settings are rural, and his vocabulary is small. Frost looks the part, the very model of the crusty New England sage. His name doesn’t hurt either; it’s as good as Cary Grant’s, and he was born with it. Frost also has considerable talent (his best poems are probably here and here), but this is incidental.

I wrote in my last post about characteristic moments in the work of an artist. There is no need to search in Frost: his chief characteristic is a vacillating, go-with-the-flow pseudo-profundity that plays, and pays, especially well in America, and it is everywhere. One could do worse than be a swinger of birches, perhaps, but one could also do a great deal better. Frost is perfectly satisfied with himself, and resents any attempt at improvement:

Suppose someone comes near me who in rate
Of speech and thinking is so much my better
I am imposed on, silenced and discouraged.
Do I submit to being supplied by him
As the more economical producer,
More wonderful, more beautiful producer?
No. I unostentatiously move off
Far enough for my thought-flow to resume.
(“Build Soil”)

Frost hedges this passage a bit with “rate,” but its import is obvious. He is openly hostile to intellect:

So if you find you must repent
From side to side in argument,
At least don’t use your mind too hard,
But trust my instinct – I’m a bard.
(“To a Thinker”)

No thanks. But it is a very American attitude.

To be fair, “The Road Not Taken”, his most famous poem, is celebrated principally because it is misread. It is usually thought to counsel leaving the beaten path, which is pretty pallid moral advice but is not what Frost has in mind. Its title, often misremembered, significantly, as “The Road Less Traveled,” refers to the path that the narrator doesn’t take, not the one he does. The narrator, confronted with the fork in the road, is “sorry that he could not travel both and be one traveler.” Neither path is much less traveled at all: “Though as for that the passing there / Had worn them really about the same.” The traveler’s difficulty is, having chosen one, he misses his chance to choose the other, because “way leads on to way.” The poem does not advocate the road less traveled; it is about the agony of having to choose at all. Had the traveler chosen the way more traveled by, that, too, would have made all the difference. There is something sneaky about his putting the narrator on the less-traveled road, when either road serves the logic of the poem. I suspect Frost of intentionally inviting the common misreading.

Last month’s discovery of an unpublished Frost poem, therefore, occasioned no joy in the GotM household. The complete poem, “War Thoughts at Home,” is available only to subscribers to the Virginia Quarterly Review, which leaves you and me out. But I can piece it together from scattered quotations; and since I am too puny, I trust, for the VQR to sue for copyright infringement, here it is:

On the backside of the house
Where it wears no paint to the weather
And so shows most its age,
Suddenly blue jays rage
And flash in blue feather.

It is late in an afternoon
More grey with snow to fall
Than white with fallen snow
When it is blue jay and crow
Or no bird at all.

So someone heeds from within
This flurry of bird war,
And rising from her chair
A little bent over with care
Not to scatter on the floor

The sewing in her lap
Comes to the window to see.
At sight of her dim face
The birds all cease for a space
And cling close in a tree.

And one says to the rest,
“We must just watch our chance
And escape one by one
Though the fight is no more done
Than the war is in France.”

Than the war is in France!
She thinks of a winter camp
Where soldiers for France are made.
She draws down the window shade
And it glows with an early lamp.

On that old side of the house
The uneven sheds stretch back
Shed behind shed in train
Like cars that have long lain
Dead on a side track.

Frost has one of the best ears among 20th-century poets, and it shows to advantage especially in the first and last stanzas. In the second stanza the grammar wanders. Frost’s preternaturally articulate animals make an egregious appearance (see “The Oven Bird,” “Stopping by Woods on a Snowy Evening,” and passim). Is it me, or is there something ridiculous about blue jays discussing the First World War? The central comparison, of fighting men with fighting birds, is trite. It is not among Frost’s best hundred poems, and if it had never been found no one would mourn its lack.

Its discoverer, Robert Stilling, a graduate student at the University of Virginia, likes it better than I do:

“War Thoughts at Home” dwells in that moment before darkness, doubting the necessity of the bravery that drives a soldier-poet like Thomas [Edward, a friend of Frost’s who was killed in the war] to enlist. Its doubt stands at odds with the poet’s own stoic convictions about war and violence. And the ending, dead on a side track? This is neither fire nor ice, but this is the closest Frost will come in verse to damning the war that took his friend. These stanzas’ troubling lack of conviction may well have given Frost enough reason to abandon the poem along with its disquieting conclusion.

Stilling is shilling for his discovery, and who can blame him? I made too much fuss about a couple of unpublished poems myself, and I’m not bucking for tenure. But my God, Frost made a career out of a “troubling lack of conviction.” If he had abandoned poems on that account there would be nothing left. What we have, in short, is the spectacle of an ambitious graduate student, who has not read Frost with much attention, making his career on the back of a poem that Frost regarded, correctly, as unworthy of inclusion in his permanent work. Which is most depressing of all.

Oct 062006

A friend offered me two free tickets to U2 at Madison Square Garden. So the girlfriend and I up and went.

Every artist has certain characteristic moments, when the mask slips and you say to yourself, “Ah. So that’s what they’re like.” For Emily Dickinson, it’s the last stanza of “What mystery pervades a well,” where she writes of nature, “To pity those that know her not/ Is helped by the regret/ That those that know her, know her less/ The nearer her they get.” For Woody Allen, the moment comes at the end of Manhattan, when Woody soliloquizes into the tape recorder about “what makes life worth living”: “Groucho Marx. Willie Mays. The second movement of Mozart’s Jupiter symphony. Flaubert’s Sentimental Education. Louis Armstrong’s recording of ‘Potato Head Blues.'” Fortified by his list of approved experiences, he promptly runs across town to rekindle his romance with an adolescent Mariel Hemingway. For Quentin Tarantino, it’s “dead nigger storage,” a line that so pleased him that he assigned it to himself.

My first U2 moment is from the version of “Silver and Gold” off their live album Rattle and Hum, which Bono interrupts, before the bridge, with a monologue beginning, “Yup. Silver and gold.” He follows with an eloquent sigh that speaks louder than a hundred pairs of wrap-around sunglasses. After going on a bit about apartheid and “a man like Bishop Tutu” — this was when the whites, not the blacks, were wrecking South Africa — he winds up with, “Am I booggin’ yuh? [Yes.] Don’t mean to boog yuh. [As Robert Plant once asked: “Where’s that confounded bridge?”] OK Edge, play the blues!” OK Edge. You do that little thing.

The second is from The Unforgettable Fire, song of the same name. Here we have two of the numerous biblical references with which Bono litters his songs: “And if the mountains should crumble or fall into the sea,” and, later on, “in a dry and waterless place.” Compare the originals, King James Version. “Therefore will not we fear, though the earth be removed, and though the mountains be carried into the midst of the sea.” Psalms 46:2. “Who led thee through that great and terrible wilderness, wherein were fiery serpents, and scorpions, and drought, where there was no water; who brought thee forth water out of the rock of flint.” Deuteronomy 8:15. The striking imagery belongs to the Biblical authors; the bardic redundancy, to the modern prophet.

I own eight U2 records, which calls for an explanation.

The band simply cannot sound bad: if you woke them all from a dead sleep, held guns to their heads, and demanded that they immediately cover “Long Tall Sally,” it would probably sound terrific. A fanzine once headlined a U2 article “endless fire magic music,” which still strikes me as an apt description of Edge’s shimmery guitar and Larry Mullen’s imaginative drumming. Bono’s voice is a large reason there is a permanent ban in rock criticism on the word “plangent.” Rock music is populated with lucky men: U2’s bassist, Adam Clayton, who joined up by answering an ad and eventually learned how to play his instrument, is perhaps the luckiest.

They certainly sound great live. More than half the material was from their last two, rather weak records, All That You Can’t Leave Behind and the preposterously-titled How To Dismantle an Atomic Bomb (easy: play the blues). At some concerts this makes the audience restive, as it waits for the hits. Not here; the fans cheered as lustily for contemporary, third-rate material like “Elevation” as they did for classics like “One” or “I Will Follow.” The fact that most of them were fifteen to twenty years younger than I am may have had something to do with this.

Of Africa we heard a great deal, and saw considerably less. Even Rush and Metallica, not your big ethnic acts, draw a few blacks when they play the Garden. For U2 the only brothers in evidence were taking tickets and working concessions. The band, it turns out, is especially popular in Boston, which makes sense if you think about it, which I never had. Halfway through the show the background video began to show a checkerboard of random faces from the audience. Instead of the desired Benetton effect, we were treated to row upon row of shanty Irish. As Bono launched into “Sunday Bloody Sunday,” I whispered to the girlfriend, “Do you suppose they have any idea what this song is about?” and then the alarming thought hit me that they probably did.

Bono is not above tweaking his demographic. He introduced one song with a little story about his father, “a working-class man from Dublin” — he paused for the uproarious applause — “who loved opera” — and he paused again, this time for the puzzled silence. He rendered a line from “One” (“did you come here to play Jesus to the lepers in your head”) as “did you come to here to play Jesus (cuz I did).” A prophet needs a sense of humor.

Eventually, inevitably, prophecy obtains the upper hand. When Bono exhorts the audience to pull out their cellphones and send a message to whycantwealljustgetalong.org, “to show your support,” and everyone promptly does so, and waves his phone about in pride, and thousands of phones dot the darkness like fireflies, I can almost enjoy it, as anthropology. But human eyes should be spared certain sights. A little Vietnamese girl, aflame with napalm, running down a road, shrieking and alone. The Microsoft Windows source code. And Bono, crawling on stage, wearing over his eyes a bandana reading “COEXIST” spelled that irksome way you’ve seen, where the ex is a star of David and the tee is a cross, hands stretched out either in supplication to his audience or to find the mike stand. Behind this the video scrolled the Universal Declaration of Human Rights, Article 5 of which clearly states, “No one shall be subjected to torture or to cruel, inhuman or degrading treatment or punishment.” Too late.

Sep 202006

In a footnote in Martin Amis’s memoir, Experience, he has this to say of the ideal reader:

I am not [Saul Bellow’s] son, of course. What I am is his ideal reader. I am not my father’s ideal reader, however. His ideal reader, funnily enough, is Christopher Hitchens.

There is a theory to infer here, once we discard the prissy Platonism of the word “ideal.” A single ideal reader does not exist any more than a single soulmate. Still, some readers are better than others, and for the best of them the word will serve.

An ideal reader is a kindred spirit, not a doppelgänger. Hitch, the Trotskyite, and Kingsley, the Tory, are savage and bloody-minded in a way that Martin is not. Martin and Saul Bellow, on the other hand, both have a taste for wistful picaresque and a sense that even rotten bastards aren’t rotten all the way through. They treat phonies and frauds sensitively where neither Hitchens nor Kingsley would have the patience. (To see how Kingsley handles such people in his novels, read Hitchens on Mother Teresa or Bill Clinton.) It is no accident that The Adventures of Augie March is Martin’s favorite Bellow novel. Martin’s own best novel, Money, is a sort of picaresque itself: its moneyed yob, John Self, blunders and binges through America.

An ideal reader sometimes vastly surpasses his author — Poe’s ideal reader was Baudelaire. The other way around is impossible; understanding presupposes intelligence.

An ideal reader often writes about his author, but he is too near him, temperamentally, to play the judicious critic. He reads the author as the author would want to be read, not as others would want to read him.

The relationship can be, but is usually not, reciprocal. Edith Wharton’s ideal reader was certainly Henry James, although he had died by the time she wrote her best novel, The Age of Innocence; and Henry James’s ideal reader was very likely Edith Wharton.

Just as an author can have multiple ideal readers, so can a reader be ideal for multiple authors. My girlfriend is Quentin Crisp’s ideal reader; also Doug Kenney’s. You now know her better than her immediate family does.

Who is my ideal reader? I thought of Matt McIntosh, but no: he agrees with me too often, and the literary blather obviously bores him. My ideal reader, in an upset, is Conrad Roth, of the scholarly, whimsical, and criminally underrated Varieties of Unreligious Experience. He is literary but has mathematics as well, sympathetic but critical. (I am too poor a linguist to be Conrad’s ideal reader; he’s on his own.)

Whose ideal reader am I? In the world of actual books, I am of course Yvor Winters’ ideal reader. I have occasionally, unfairly, been regarded as a Winters epigone. (This is a Winters epigone.) Winters was a Thomist and a theist. He made more fuss about ranking poems than I do. His theory of free verse scansion differs entirely from mine. But we are both especially attuned to the conflict of the abstract and the particular, the subject of a large percentage of Winters’ favorite poems and an even larger percentage of his own verse. More to the point, we both regard “poetry-lovers” as the very people from whom poetry urgently needs to be rescued.

In the world of blogs, I am owned by Colby Cosh. This began to dawn on me one day, about the middle of last year, when I was contemplating a post about the great AC/DC — now, as ever, 100% irony-free! — only to discover that Cosh had already written it that morning. Several months later the realization was completed when I found myself linking to a few of his posts about hockey, a game I do not understand. His themes include, but are not limited to, the idiot innumeracy of journalists, bureaucratic idiocy, sportswriting idiocy, and idiocy all around. He is a shrewd literary critic, sometimes at my expense, when he cares to indulge. Our cats also look alike.

Who is your ideal reader? Whose ideal reader are you?

Update: Conrad Roth comments. I couldn’t have been a contender either. Megan McArdle comments. I report with embarrassment that I had to look up L.M. Montgomery.

Sep 042006

No one thinks big thoughts about the morality of the shoe salesman, or the morality of the computer programmer, or the morality of the garbageman. But somehow the morality of the artist, who after all purveys a product, just like so many of the rest of us, becomes a source of endless hand-wringing and agonized speculation. Even the industrialist gets off comparatively lightly. Israel informally bans performances of Wagner because he wrote anti-Semitic tracts. Yet as far as I know you can drive a Ford there without getting funny looks, despite old Henry’s ravings in the Dearborn Independent.

In 1975 a career criminal named Jack Henry Abbott began writing Jerzy Kozinski letters from jail. These revolted Kozinski, so Abbott switched to Norman Mailer, a more promising customer. Mailer proclaimed Abbott a literary genius, a “phenomenon,” arranged for extracts from his letters to be published in The New York Review of Books, prevailed upon Random House to edit them down into a book, In the Belly of the Beast, and successfully lobbied the parole board to have him released from jail. Abbott appeared with Mailer on “Good Morning, America.” Susan Sarandon named her son after him. Six weeks into his release Abbott stabbed a waiter, Richard Adan, to death in an East Village restaurant. Adan was himself a promising writer, an irony lost on Mailer. “Culture is worth a little risk,” he noted at the trial. “Otherwise you have a Fascistic society. I am willing to gamble with certain elements in society to save this man’s talent.”

Twelve of the elements with which Mailer was willing to gamble convicted Abbott of first-degree manslaughter and sent him back to jail, this time for good. In 1987 he published one more book, My Return, demanding an apology from society for his treatment. Society demurred. In 2002 he hanged himself in his cell.

Martin Amis, writing about the case in 1981, says:

The first thing to be said about In the Belly of the Beast is that it isn’t any good. It isn’t any good. It is also the work of a thoroughly, obviously, and understandably psychotic mind: as such, it is a manifesto for recidivism. Its author, plainly, could not hope to abjure violence…. You can hear the paranoia snickering and wincing behind every word.

Amis quotes enough to leave the accuracy of his judgment in no doubt. But his relief is palpable. Suppose the book had been good? How in God’s name would that have justified Mailer or anybody else who wanted to let this maniac out of jail? Amis accuses Mailer of the “wishful misapprehension… that a ‘creative individual’ can’t be evil,” even as he labors under the converse, and equally wishful, misapprehension that an evil individual can’t be creative. The blurb copy for a biography of Richard Strauss inquires breathlessly: “Was Richard Strauss the most incandescent composer of the twentieth century or merely a bourgeoisie [sic] artist and Nazi sympathizer?” — as if these were mutually exclusive. Malcolm Cowley’s astonishing remark that “no complete son-of-a-bitch ever wrote a good sentence” represents the apotheosis of this attitude.

A couple weeks ago Terry Teachout divided artistic peccadillos into two classes: “statement-signing” and “wife-beating.” Neither, apparently, is all that awful, though the beaten wives might disagree. And the categories might be adequate to Mailer himself, if we stretch “wife-beating” to include wife-knifing. But one wonders: to which category does brigandage belong? Or male prostitution? Where do we file William “Tell” Burroughs’ little stunt? A new class for negligent homicide?

Since Terry carefully specifies that his categories apply only to “major,” “truly great” artists, one could object that neither Villon nor Genet nor Burroughs is “major.” This is wrong in the first case, right in the second, arguable in the third, and utterly beside the point. Nothing about their despicable behavior excludes them from making great art, just as it would not exclude them from high competence in some other field. Hitler was a lousy painter, but he need not have been. (To become Hitler he of course had to fail at painting, but that’s a completely different question.)

Terry, to his credit, confronts the extreme case directly:

I wouldn’t have any objection to placing a permanent ban on performances of Tristan und Isolde if it were to be revealed tomorrow morning that Hitler, not Wagner, had composed it. I wouldn’t support such a ban, but I wouldn’t actively oppose it, either, any more than I oppose the informal Israeli ban on public performances of Wagner’s music. (It’s been broken once or twice in the past, but never without an outcry of public disapproval.)

Whoa. A permanent ban — on an opera? What does he propose to do about Mein Kampf? Next to that a Hitler-composed Tristan und Isolde looks pretty tame. I used to run a little sideline in picking on Terry, and I don’t mean to do so here. I cite him to show how this topic can derange ordinarily sensible people.

Consumers of art from moral defectives tend to come in three flavors: Transgressive Hipster, Disgruntled Fanboy, and Dime-Store Psychologist. For Transgressive Hipster vice is extra credit; it adds to the mystique of the artist as existential hero. One can chalk up the glowing reviews of In the Belly of the Beast to Transgressive Hipsterism, and no other theory can account for the popularity of Charles Bukowski, excepting possibly the theory that his books are very short. Transgressive Hipster is doubly unfortunate, having imbibed Mailer’s ideas while lacking his talent.

Disgruntled Fanboy thinks of the artist as his friend, and regards the artist’s bad behavior, or even the artist’s expression of opinions different from his own, as a personal betrayal. Of course his relationship with the artist is entirely imaginary, and it is certain that Fanboy, if he had the good fortune to meet his idol, would bore him to death. Disgruntled Fanboy can be observed, in pure form, in the 2003 boycott of the Dixie Chicks.

Dime-Store Psychologist, a Usenet fixture, holds that the life leaches into the work. He spends a great deal of time combing Wagner’s operas for anti-semitism, Yeats’s poetry for fascism, Woody Allen’s movies for pederasty, and so forth. Quite often he finds it. Many of Woody Allen’s movies are pederastic, and if you can’t abide them on that account, I understand. But that has everything to do with the movies and nothing to do with his diddling his teenaged stepdaughter while married to Mia Farrow. Lolita is more unpleasantly and graphically pederastic than anything Woody Allen ever wrote, despite the fact that Nabokov managed, in life, to keep his pants on.

What none of these types is doing is paying attention to the art; they are paying attention, but to something else. Pay attention to the art.

Read the books, look at the pictures, listen to the music. Then, should it prove necessary, call the cops.

Update: Ilkka Kokkarinen comments. I’d trade the navigation gizmo for a name with five k’s.

Aug 262006

I’m a betting man, and yesterday I was offered a betting proposition. The U.S. Bridge Championships are going on now, and the great Nickell team, which has won the event eight years running, has a bye to the semifinals. My friend Justin Lall, a bridge pro, offered me 6:1 odds on $50 on the field: in other words, he would pay off if any team but Nickell won the event.

Ordinarily I would accept happily. 6:1 is very long odds, and no matter how good Nickell is they still have to win two matches against excellent teams. Except Justin informed me that he was getting 6.5:1 on the same 50 bucks from someone else. So taking the bet gives him a freeroll: plus $25 if Nickell loses, break-even otherwise.

I refused the bet, which, from a strictly economic point of view, is irrational. If I like the odds, then I like them. Why should I care if Justin is using me to hedge his risk?

Anxiety mostly — anxiety, first, about one’s place in the dominance hierarchy. One hates to be a pawn in someone else’s game, Es to his Ich, a means to his end. A moment’s reflection will convince you of the idiocy of this attitude, on which several moral philosophies, like Kant’s and Martin Buber’s, have been erected. Regardless of who initiates the transaction, Justin is just as much a means to my own end — obtaining a bet against Nickell at favorable odds — as I am to his of laying off his risk. Hasn’t he also earned a transaction fee for having done the work of negotiating the bet in the first place and then offering it, at a small profit, to me? I regard the philosophies as foolish and atavistic yet, in this case at least, persist in the attitude. If you want an instance of the dictionary definition of “irrational,” this will serve.

Also involved is a related, slightly different form of anxiety which, for lack of a fancy psychological term, I will call shopping anxiety. Mencken defined Puritanism as the haunting fear that someone, somewhere may be happy: shopping anxiety is the haunting fear that someone, somewhere got a better deal. It is not clear to me why it should detract from someone’s pleasure in his new 56-inch plasma TV to discover that his neighbor bought the same model for $200 less. Neither is it clear why it annoyed me that Justin found a better bet than I had, especially since I hadn’t been out looking. But it did.

Finally there is the fact that Justin is a bridge pro. He knows and has played with members of the Nickell team. He is, in short, far more competent than I to evaluate the odds, and he would rather freeroll than eat the risk. Perhaps the bet isn’t as good as I thought it was. This conceivably sound reason, I am sure, influenced me far less than the stupid ones.

Nickell, as I write, has a huge deficit late in its semifinal match. Who’s sorry now?

Update: Despite a furious comeback, Nickell loses. I’m out 300 bones.

Aug 222006

Possibly the most annoying truth in the world is that good qualities cluster. People who are good at something tend to be good at many things.

The psychometric version of clustering is g, or general intelligence. The existence of g is not seriously disputed in the field, and g-deniers like Howard Gardner, with his theory of “multiple intelligences,” or the late paleontologist-cum-Marxist Stephen Jay Gould, are regarded as cranks or axe-grinders. The Wechsler scale, the most complex (and expensive) of all intelligence tests, measures thirteen apparently widely disparate skills, including vocabulary, picture completion, matrix reasoning, and the ability to repeat back a string of digits. Bad news! Each skill, without exception, correlates positively with all the others. Seventy-eight possible correlations, and every one positive. The correlations range from 0.3 (weakish) to 0.8 (very strong), where 0 indicates no relationship and 1 an exact match. If you suck at math, the parsimonious explanation isn’t that your true talents lie in writing or painting. The parsimonious explanation is that you suck.1

Intelligence isn’t everything, you say. Quite so. Nevertheless intelligence correlates quite highly with other happy outcomes, like money and status (0.5 or so), long, healthy lives, and staying out of jail. Not to mention height. About the only negative quality definitely associated with high IQ is myopia.

The news gets worse, much worse. Smart people tend to be good-looking. Since intelligence also correlates significantly with income and status, this should surprise no one. Rich, high-status men marry better-looking women and sire better-looking offspring. QED. Models aren’t stupid after all.2

Jocks aren’t stupid either. Reaction time, essential in many sports, correlates moderately with IQ. The data is spotty for most sports, but pro football players have a significantly higher average IQ than the population at large.3 Again, no surprise; learning an NFL playbook is probably pretty demanding.

Clustering offends the human sense of fairness. The world is frequently imagined as if God gives out qualities one at a time — brains for you, beauty for her, and for him, let’s see, how about a sense of humor? — seeing to it that things somehow even out in the end. Jocks and models must be dumb; they already expended their early-round draft picks on something else. Geniuses are crazy; it’s their handicap. Ugly girls have nice personalities. And most of all, you can be anything you want to be, in Lake Wobegon, where all the children are above average.

1By “you” I mean an abstract individual, a statistical creation, not you, dear reader. No statistics could possibly apply to you. You are special, and Jesus loves you.

2Again, these remarks should not be construed as a reflection on any particular model, like, say, Claudia Schiffer (Schiffer-Brains, as she is known in the industry).

3Assuming the same racial composition.

Update: Matt McIntosh comments. Elsewhere, I mean. The Mechanical Eye comments. I will reply if I can find the time in my busy schedule of feeding Christians to lions, building palaces, and oppressing the peasantry. Ilkka Kokkarinen comments. Degrees of Freedom comments. Noneuklid comments.