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.

Aug 142006


Idly browsing in the bookstore one day, I found this, carefully wrapped in onionskin and folded into an old edition of Hardy’s Collected Poems. The road to ignorance may be paved with good editions, as Bernard Shaw remarked, but its byways are littered with interesting ephemera.

Dear Mr. Smyth,

The assignment is all of the “Collected Poems” of Hardy. But I asked the class to give particular attention to those on pp. 7, 15, 58, 83, 99, 112, 124, 152, 161, 194, 222, 234, 248, 255, 269, 271, 288, 297, 325, 328, 369, 387, 390, 391-8, 409, 412, 439, 456, 505, 566, 598, 648, 658, 685, 710, 799.

I hope you recover quickly.


The signature is Mark Van Doren’s. Van Doren taught English at Columbia, including a legendary “Introduction to Poetry” course, for almost forty years. The tone of this note aligns with his reputation for brooking no nonsense, regularly tossing students out of class for failing to read the assignment. In his autobiography Van Doren claims (though I find this hard to credit) that a student once attempted to excuse a late term paper on the grounds of being in love. “Then you don’t love her very much,” Van Doren said. “How can you say that?” asked the student indignantly. “You won’t sacrifice a mark for her.”

He was also an excellent poet and critic, who wrote brief and readable books about Shakespeare, Dryden, and E.A. Robinson, among other subjects. The selections available on the web do not do his poetry justice, but this conveys some of the flavor.

Mark Van Doren is remembered only as the father of game-show cheat Charles Van Doren, and then only because of the hit movie made about the scandal, Quiz Show, in which he is played by Paul Scofield, with twinkly donnishness, as the soul of upright virtue — which, by all accounts, he was.

The hapless Mr. Smyth, it appears, was too ill to attend class and had to receive his assignment in writing. He must have quailed when he read it. All of the collected poems? All of them? They run to 800 pages of small print. I have read Hardy, quite assiduously, for years, and have not got round to nearly all of them. Nor do I expect to.

Unfortunately the poems Van Doren singles out for “particular attention” have more pedagogical than poetic interest. They include the Satires of Circumstance, which date badly; one or two philosophical colloquies that neatly clarify Hardy’s views on God and pessimism; and a few anthology favorites. They exclude all of his best poems.

Still, three generations of students found Van Doren inspiring. Even Smyth, once recovered, seems to have bestirred himself sufficiently to make an abortive start on the assignment. The table of contents shows the first six poems dutifully ticked off, and then nothing. One wonders how many times he was thrown out of class. However many it was, he kept the book, at least for a while, and took some pains to keep the note. Something probably got through.

Aug 122006

The idea that aesthetics has a lot to do with self-similarity occurred to Benoit Mandelbrot thirty or so years before it occured to me, although if you ask Mandelbrot there are vanishingly few ideas that didn’t occur to him first. It’s Newton, Einstein, Archimedes, and Mandelbrot, not necessarily in that order.

So it isn’t original, which doesn’t mean it isn’t true. Mandelbrot’s The Fractal Geometry of Nature is one of the best-selling books on mathematics of all time, mostly because it has a lot of pretty pictures. Fractals are fun to look at. Little copies of the whole structure are buried everywhere within it. Zoom in to 10 angstroms, or out to 10,000 feet: in any part of the picture the same intricate patterns appear.

In self-similarity the part resembles the whole. Symmetry, a different affair, describes a relation between parts. Self-similarity implies some form of symmetry. If A and B are both part of C, and both resemble C, then A will also resemble B, in some sense. But the converse is false. Parts A and B may resemble each other without either resembling the whole, C, in the slightest. One tends to think of self-similarity (and symmetry) as visual, but the principle is structural. The play-within-a-play and the colloquy of the gravediggers in Hamlet are instances of self-similarity. For symmetry, take a lesser play, say Noel Coward’s Nude with Violin, in which a famous modern artist resembling Picasso dies and turns out to have hired a different person to produce the work for each of his “periods.” Each act, in which one of the period painters shows up to claim a share of the estate, resembles the others, but none especially resembles the whole. The play is symmetrical but not self-similar.

Christopher Alexander, in The Nature of Order, gives fifteen principles for “living” architecture, at least six of which can be subsumed under self-similarity. “Local symmetries,” “deep interlock and ambiguity,” “echoes,” “positive space,” “good shape,” and “gradients” are all aspects of what I’m talking about. And a lucky thing too, as one of my principles is that no list of principles should reach double digits.

Alexander also includes “roughness” in his list, which is very much to the point. Fractals fall into two categories: exact and approximate. The first known fractal (arguably), the famous Koch curve, a mathematical monstrosity with unbounded perimeter but finite area, is exact. It is also boring. When you’ve seen one level you’ve seen it all. Everyone likes to look at baby animals. What makes them “cute” is that they are copies of their parents, but inexact ones. They belong to category two.

Self-similarity is a deeply ingrained way for people to see the world. All pre-scientific theories of genesis involve self-similarity. Embryos were first thought to be full-grown animals in miniature, with tiny heads and limbs. It sounds absurd now, but if you knew nothing of cell division and had no microscope handy you might make the same guess. Lamarck precedes Darwin because he assumes that all traits are inherited, that is, that self-similarity applies in full.

If art, as is commonly alleged, speaks to our deepest selves, one would expect it to show self-similarity everywhere, and sure enough it does. Pictures, like Hokusai’s “The Great Wave,” which Mandelbrot reproduces in his book, are the first place to look. Jackson Pollock’s drip paintings are fractal. Music, to my untutored ear, is replete with structures that repeat approximately on different scales, such as leitmotifs taken up first by the winds, then the strings, the brass, and eventually the whole orchestra. I will leave this speculation to those who know, as I do not.

Poetry, however, I do know something about, and perfectly symmetrical verse forms have never gained much traction in English. The sonnet has fourteen lines, and in neither of its standard forms do these lines divide into identical groups. The Petrarchan version has its octet and sextet, and the Elizabethan its three quatrains, along with that last awkward couplet that Shakespeare could never quite figure out what to do with. The villanelle, with its six triplets and 19th line, exhibits the same sort of approximate symmetry. Then there’s the Spenserian stanza, eight lines of pentameter with an alexandrine tacked on to the end. A while back I remarked the stupor produced by extended passages of Pope, in reams of closed, perfectly balanced heroic couplets. Neatness is not all your second-grade teacher cracked it up to be.

Great poems exhibit symmetry and, especially, self-similarity in a high degree, though this may not be obvious to the casual reader. Consider Ben Jonson’s To Heaven:

1 Good and great God, can I not think of Thee,
2 But it must, straight, my melancholy be?
3 Is it interpreted in me disease,
4 That, laden with my sins, I seek for ease?
5 O be Thou witness, that the reins dost know
6 And hearts of all, if I be sad for show;
7 And judge me after: if I dare pretend
8 To aught but grace, or aim at other end.
9 As Thou art all, so be Thou all to me,
10 First, midst, and last, converted One and Three,
11 My faith, my hope, my love; and in this state,
12 My judge, my jury, and my advocate.
13 Where have I been this while exiled from Thee,
14 And whither rapt, now Thou but stoop’st to me?
15 Dwell, dwell here still! O, being everywhere,
16 How can I doubt to find Thee ever here?
17 I know my state, both full of shame and scorn,
18 Conceived in sin, and unto labor born,
19 Standing with fear, and must with horror fall,
20 And destined unto judgment after all.
21 I feel my griefs too, and there scarce is ground
22 Upon my flesh t’inflict another wound.
23 Yet dare I not complain or wish for death,
24 With holy Paul, lest it be thought the breath
25 Of discontent; or that these prayers be
26 For weariness of life, not love of Thee.

Jonson longs for death while rejecting that longing intellectually. To understand this you must enter partly into the Christian experience. If you refuse, then a large portion of great art is partly or wholly closed to you, and the loss is not easily afforded. It may help to remember that you would likely be Christian had you been born in England in the 16th century. Human beings were no different then, you are extremely unlikely to be more intelligent than Ben Jonson was, and the number of atheists in England at the time was an engineering zero.

The poem is a prayer and an apology, and contains, in good fractal style, several prayers and apologies within itself. It is written in heroic couplets, but is 26 lines long, and naturally resists, like most of the classic English verse forms, division into equal parts. There are no enjambments until the very end, in lines 24 and 25. Every full stop ends a line. Yet the movement escapes Pope’s monotony because the argument moves forward and the syntactic unit varies. There are nine sentences (if we count the ejaculation that begins line 15 as part of the question); In line count they run two, two, four, four, two, two, four, two, and four.

The first sixteen lines deal mostly with God, the last ten mostly with man. Both sections are syntactically symmetrical. The first opens with two questions of two lines apiece and closes the same way. The second reverses the procedure, surrounding the short sentence with the two longer ones.

In lines 11 and 12 “faith, hope, and love” are exactly the qualities that a Christian might exhibit toward his “judge, jury, and advocate,” respectively — no other order would do. Jonson’s sleight-of-hand at the end of line 10, where he interposes a reference to the Trinity (“converted One and Three”) to break up his literal trinities, simply beggars praise.

The Elizabethan fondness for wordplay is employed tastefully, for once (cf. “when first your eye I eyed”). “Everywhere” and “ever here,” in lines 15 and 16, are effective; but “disease” and “ease,” in lines 3 and 4, are a masterstroke. “Ease” implies “death,” and sure enough we find “death” at the end of line 23, as distant from the end of the poem as “ease” is from the beginning. “Thee” rhymes with “be” to begin the poem, and “be” with “Thee” to end it. “Me” and “Three” and “Thee” and “me” are rhymed again almost exactly in the middle of the poem, separated by one couplet. “[J]udge me after” in line 7 balances “judgment after all” in line 20. “After all,” a throat-clearing device in most writers, including me, is resurrected here to become living language.

Despite a theme that will not resonate with most modern readers, To Heaven remains one of the most beautiful poems in the language. Can there be any doubt that it is largely the structure — the fractal — that we respond to?

Aug 072006

One problem with blogging is that anyone can read your archives and see what an idiot you were. I will spare you the trouble.

  • I used to be a race skeptic. Eventually a cursory reading of Cavalli-Sforza convinced me how wrong I was. The History and Geography of Human Genes is a careful and scholarly demonstration of what everyone already knows: that humans once wandered the earth in small tribes, that these tribes had distinctive genetic profiles, and that they tended to breed together, increasing their differences from other tribes, which are still plainly visible today. (In a few wealthy places miscegenation has begun to attenuate this process, but Dinesh D’Souza’s wishful thinking notwithstanding, it will not be reversed for a long, long time.) The fact that we cannot say how many races there are does not render the concept invalid; it has fuzzy boundaries, like many concepts. If you need a definition, Steve Sailer’s “an extended family that inbreeds to some extent” covers the territory just fine.

    All of this is doubly embarrassing because I was perfectly willing to treat race as a valid category when it suited my purposes.

  • Deep Throat was “obviously” a composite. Obviously. Good thinking there Cool Breeze.
  • Animal rights. I got in a lather here and here about how moral agency distinguishes humans, who have rights, from animals, who don’t. I must have understood “moral agency” then; I don’t now. Agency and rights, I now believe, are constructs. They come in handy, to be sure. We need good alpha approximations to adjudicate claims that would otherwise be too messy. I still think rights are a fine idea, but I won’t get all ontological about them the way I once did.
  • The war. This is the big one. On the one hand, I write: “Human beings are good at estimating first-order consequences, notoriously poor with second order, and the third order is like the third bottle of wine: all bets are off.” On the other hand, I support a long-term, insanely complicated geopolitical strategy to democratize the Middle East, which entails foreseeing third- and further-order consequences up the wazoo. The U.S. government has not done very well at it. Surprise! But what was I thinking?

    I was thinking, first, that Saddam Hussein was a really bad guy. Knocking over the occasional tinhorn despot, if only to keep the rest of them on their toes, has a superficial appeal. When your target despot rules a slapped-together country encompassing three perpetually warring ethnic groups, any two of which can agree only on the necessity of annihilating the third, then it may not be such a hot idea. Should I have seen what was coming? No. Should I have seen that I could not see? Damn straight.

    There was also a certain haste to blame America in the anti-war arguments that bothered me. I have no desire to discourage self-criticism, least of all in this post. But even Jim Henley, who among the long-time opponents of the war most closely resembles a responsible adult, has not exactly emphasized the horrors of a culture that treats suicide bombers like rock stars and stones homosexuals to death. These very horrors, ironically, undercut the case of the warbloggers, who harp on them. Surely the least likely people to successfully impose your political ideas on are those whose core values are utterly alien to your own. You end up just killing them instead.

    I can also go along only partway with the classically libertarian “health of the state” argument. Yes, “the Pentagon is the Post Office with nuclear weapons.” And yes, war is the health of the state. But the man who said that was a pacifist, and only a pacifist could regard it as dispositive. War in Iraq? Health of the state. World War II? Health of the state — as anyone who has tried to rent an apartment in New York City can tell you. Civil War? Health of the state for sure. Should we not have fought them on that account?

    Of course the current Administration has seen the state flourish. It has attempted to arrogate to itself the power to suspend habeas corpus for U.S. citizens (Padilla) and to deny the presumption of innocence to the accused (Hamdi), with only feeble objections from the judiciary. It has decreed a “War on Terror,” which is in effect a permanent war. Health of the state is one thing, and permanent police-state powers are something else.

    The anti-war people were right, and I was wrong, and I hope my caveats do not sound too churlish.

Update: Will Wilkinson comments.

Aug 022006

This blog used to run on Greymatter, a collection of Perl scripts that its creator stopped supporting about ten minutes after I chose it. Greymatter served me well for years, but modern features that I need, like RSS feeds and comment spam control, are alien to it, and my Perl isn’t good enough to add them. Greymatter also stores posts in flat files, which is OK if you just want to display them, but not so good if you want to search or perform any other batch operations. I program computers by trade and therefore report these matters with some embarrassment.

New software was called for, and a cursory survey of the alternatives led me, on a Wisdom-of-Crowds basis, to WordPress, a collection of PHP scripts. The WordPress slogan is “Code Is Poetry.” I agree; but if code is poetry, WordPress code is doggerel. Here’s a sample from their Greymatter import script:

if ($i<10000000) {
$entryfile .= "0";
if ($i<1000000) {
$entryfile .= "0";
if ($i<100000) {
$entryfile .= "0";
if ($i<10000) {
$entryfile .= "0";
if ($i<1000) {
$entryfile .= "0";
if ($i<100) {
$entryfile .= "0";
if ($i<10) {
$entryfile .= "0";

A non-programmer, being told that Greymatter file names are eight characters long and begin with as many zeros as are required to fill out the number of the blog post (e.g., “00000579.cgi”), can probably figure out what this code snippet does. If you said that it prefixes the appropriate number of zeros to the blog post number, you win. If it occurs to you that there are more concise ways to do this than with seven nested if-statements, you may have a future in the burgeoning software industry.

On the other hand, this code, like WordPress itself, has the great merit of actually working. WordPress has a pretty easy-to-use API as well, so people can, and do, write skins that you can borrow and modify to your taste, and other extensions to its functionality. Its administrative interface is excellent. The documentation is extensive and the forums are helpful. You could do worse.

Several flavors of syndication are now available, at the bottom right. Old posts can be left open for comments thanks to proper spam control. Comments are numbered. Posts are (beginning to be) categorized.

The mini-blog is a transparent effort to raise my marks in Deportment, by allowing me to pretend I’m interested in what the rest of you are writing while I’m off Thinking Big Thoughts. It will also improve my discipline: at one short sentence every other day, I’ll have a finished book after forty years.

A few matters remain. The baseball search engine is busted, thanks to an ill-advised upgrade. A new one will be forthcoming, with better-looking results, more search criteria, and updated statistics. A reorganization of The Gee Chronicles, which can still be found at their old location, in their old format, for the time being. Links to old posts still work, but point to their old versions. URLs will eventually be rewritten to point to the new ones, but the old links will always work because permalinks should be permanent.

The banner and layout are mostly the work of my girlfriend. All complaints should be directed to her.