Adroit gaucherie

A left-handed backhand tribute

David Berlinski has brilliantly resolved the sovereign conundrum of his existence: How can he remain modest while being the smartest member of an anti-intellectual cult? His elegant solution is to not even try. Another effortless triumph!

He again puts his sumptuous vocabulary and self-conscious prose on display as he preeningly pretends to celebrate the life of the late Christopher Hitchens. While Hitchens was a master of the finely honed, sharp-edged phrase, Berlinski prefers to poke about with a dull-tipped poniard. The jewels on his stiletto's hilt are of more interest to him than the blunt tip's inability to make a point. Watch as he uses his supposed tribute to Hitchens as a vehicle for self-aggrandizement, attempting to clamber up to Hitchens' level and stand by his side as a co-equal polemicist. It is an intriguing spectacle. Some excerpts:

Christopher Hitchens's reputation rests on his literary works, his panache as a public speaker, and on his defiant atheism. He wrote on a very wide range of subjects, and his book reviews were often very fine. He liked to praise the writers and poets he loved: Oscar Wilde, Vladimir Nabokov, Evelyn Waugh, W.H. Auden, Wilfred Owen, James Fenton, many others. He read closely and he read well. As an essayist, Christopher Hitchens is often compared to George Orwell. The comparison is careless, and it is one that in his final interview with Richard Dawkins, he rejected. Hitchens wrote fluently, Orwell, unforgettably. The difference is very considerable, but it is not to Hitchens's discredit. No man is obliged to be what he might have been.

Poor Hitch. He was no more than he was, but that's not his fault. Berlinski understands, and sympathizes. (As well he should.)

Hitchens was an engaging public speaker, and he had the gift of gracefully holding an audience. His intimate interviews were often wonderful because invariably, he was more elegant and far more articulate than his interlocutors. When faced with a rhetorical bruiser like George Galloway, his natural register failed him, and he did not have the dexterity to secure by means of an ironical divagation what he was otherwise unable to secure by matching bruise to bruise.

Poor Hitch. He was better at fencing than at crotch-kicking. (Really? Perhaps Berlinski overlooked Hitchens' well-known stone-crushing skills. Or maybe David wisely kept his knees clasped tightly together during his debate with Christopher.)

With the publication of God Is Not Great, Christopher Hitchens reached a mass audience. He became celebrated. When he discovered how well he had been received by the public, he tended to regard his own religious beliefs with the indulgence of a man who on discovering that he has been lucky in attracting admirers very naturally concludes that he has been justified in attracting them.

Poor Hitch. He mistakenly thought he deserved the attention he got. Berlinski desperately wants to know how he got that attention and would sell his soul to achieve the same level of recognition. (Perhaps he already has. The house intellectual of the Discovery Institute has a lot to answer for.)

His atheism nonetheless had a kind of shambling boisterousness that made Christopher Hitchens seem a Mirabeau to Richard Dawkins's Saint Just [sic] or Sam Harris's Robespierre.

Poor Hitch. Did he never suspect that he was playing a part in a zany recapitulation of the French Revolution? (By the way, David, the name of Louis Antoine de Saint-Just is usually rendered with a hyphen. Not, of course, that this significantly detracts from your light-shedding simile. Pas du tout!)

Hitchens was uninterested in subtle analysis. On the masthead of the Daily Hitchens, there is the legend: What can be asserted without proof can be dismissed without proof. The difficulty with this assertion is straightforward. If it has been asserted without proof, why should it be believed, and if not, where is the proof?

I asked Hitchens about this during a break in our debate. We had retreated to a forlorn hotel loading ramp in order to have a cigarette. “Well, yes,” he said, “it's just a sentence.”

Oh, that Hitchens! Such a sly boots, and yet hoist by his own petard when caught making a statement without proof about statements without proof. Sneaky, clever Berlinski, to catch him out like that! It was also wise of Berlinski, who routinely plays the part of a math expert, to refrain from making the obvious point that every theoretical discussion must begin with unproven axioms at its foundation. Ceding this point to Hitchens would have deflated Berlinski's elegant gotcha. How unfortunate that Hitchens neglected to cringe in humiliation at Berlinski's sly riposte.

Christopher Hitchens found objectionable the very idea of a source of authority, and so of power, greater than his own. This has seemed to some of his readers all of the time, and all of his readers some of the time, both defiant and uplifting. The very same idea is at work in the terrible crimes of the twentieth century. It is inseparable from them.

I hasten to point out that Berlinski is not running afoul of Godwin's law here. Our elegant elegist deftly ducked this faux pas by not elucidating the nature of the twentieth century's terrible crimes. Hitler is only implied. We all understand perfectly well that Hitchens would never have supported Hitler—that is, of course, if he had only possessed the wit to realize that “the very same idea” of disdaining an ultimate authority is “inseparable” from campaigns of mass murder.

At least, that's one way to read Berlinski's prolix paragraph. Antecedents are difficult to pin down. (Does “the very same idea” refer to “the very idea of a source of authority” or the notion that this source itself was “objectionable”?) One of the glories of his prose is that the author will be on a firm footing if he objects to this characterization on the grounds that the sentences are ambiguous and subject to many (and divergent) interpretations.

Christopher Hitchens chose to greet death publicly. Had he thought of it, he might well have invited an orchestra. We signed books together after our appearance in Birmingham, and to admirers on his very long line inquiring after his health, Hitchens replied that he was dying. It was a response that inevitably took his interlocutor aback, the more so since it was true. I followed his interviews and read his essays about cancer and death. I found them moving. But they do not evoke the man.

And neither does Berlinski's supposed encomium.

Contrapositing Berlinski

Derbyshire gets it right

The columnists who hang out at National Review Online are a peculiar assemblage of right-wing flacks who can be relied upon to distinguish themselves from the reality-based community. John Derbyshire, however, occasionally breaks ranks. In addition to being a conservative columnist, The Derb is also a mathematician. I have read and enjoyed Prime Obsession, a history of the Riemann hypothesis, and Unknown Quantity, a history of algebra and the iconic “x the unknown.” Mathematicians tend to respect the formal aspects of argument and proof. This may be why Derbyshire recoiled in horror from Expelled: No Intelligence Allowed.

He must pay for this apostasy.

And today here comes David Berlinski to take Derbyshire to the woodshed. While Berlinski is also a popularizer of mathematics (of the snob-appealing obscurantist school of overwriting), he has also aligned himself with the Discovery Institute and serves as one of Ben Stein's shills in Expelled. What better nemesis could intelligent design creationists hope to sic on Derbyshire than Berlinski? It is a grudge match made in heaven (although both combatants decline to affirm belief in heaven's existence).

Topping off the bile reservoir on his word processor, Berlinski gets right to work in his rebuke of Derbyshire:

John Derbyshire has declared that the documentary Expelled contains a blood libel against Western Civilization. His is an exercise of striking vulgarity, the more so since, as he insouciantly admits, he has not “seen the dang thing.” A blood libel, one might recall, refers to the charge that the Jewish people are irredeemably stained by their occasional, if modest, need for Christian blood. Some terms have acquired through their historical associations a degree of repugnance that persuades sensitive men and women not to use them. If Derbyshire has been repelled by the smell of blood, it is a revulsion that he has successfully overcome.

---

For the uninitiated, permit me to point out that Berlinski has unleashed here the powerful reflexive-rebuttal rhetorical device, also known in less sophisticated circles as the “I know you are, but what am I?” argument.

Expelled's audience has been less than its producers might have hoped for, box office receipts indicating an outside chance of earning back the costs of production and promotion. Nevertheless, no interested party can be unaware of the specific points being made by Ben Stein's propaganda piece. In a nutshell, Expelled asserts that (a) intelligent design is a worthwhile scientific hypothesis that the research establishment is successfully suppressing, (b) evolutionists are epitomized by atheism and hostility to religion, and (c) evolutionary thinking set the stage for the Nazi atrocities of the 20th century. The movie trailers, reviews, and interviews with Expelled's principals make all of that clear, whether or not one has endured the entire movie itself.

Berlinski does not accept this, and mocks Derbyshire for not going to see Expelled:

Having not seen the documentary that he proposes to criticize, Derbyshire is nonetheless quite certain that he knows what it conveys. “It is pretty plain,” he asserts, “that it is a piece of creationist porn.” Perhaps I will be forgiven for suggesting that John Derbyshire’s late-night scrutiny of the Internet may have corrupted his habitual search for le mot juste. Expelled has nothing to do with creationism, and if it is pornographic, the details have not become widely known.

---

See how Berlinski pokes gentle fun at Derbyshire for the latter's choice of words and amusingly implies that The Derb has looked at too many naughty pictures on the Internet? Naughty, naughty Derb! Funny, funny Berlinski!

Expelled makes a point far plainer than pornography and points to a phenomenon just as widespread.

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Hey! Wait a minute! How does Berlinski know so much about the pervasiveness of porn? By his own reasoning in twitting Derbyshire, Berlinski is admitting to a certain expertise, n'est-ce pas? Let's be charitable and put that down to an inadvertent slip.

After first considering the possibility that Ben Stein was financed by secret Saudi funds—Je m’imagine cela—Derbyshire at once reprises two errors. The first is that the animations in Expelled were copied.

They were not.

And the second is that the brief segment of a John Lennon song used in the film required Yoko Ono’s permission before it could be aired.

It did not.

The facts are easily available from the Expelled website.

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It's good of Berlinski to cite such an unimpeachable source as documentation for his statements. It's a good choice, too, because Berlinski would not have found support for his categorical statements had he gone elsewhere. For example, David Bolinsky is the medical illustrator who led the team that created The Inner Life of the Cell for Harvard University and he argues strongly that Expelled's version of his team's original creation is a point-by-point rip-off. (Perhaps, unlike Berlinski, Derbyshire did not limit his reading to the special pleadings on the Expelled website.) And, of course, the United States has a draconian copyright law that severely inhibits “fair-use” claims, so it's not at all clear that Yoko Ono's lawsuit is an inherently frivolous nuisance action.

Derbyshire’s generous conviction that Expelled is an exercise in dishonesty owes much to the charge that those participating in the film were duped. It is an accusation made by both P. Z. Myers and Richard Dawkins. I appear in the film, and I read and signed the same release that Myers and Dawkins did. I knew precisely what the film proposed to do. So did they.

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In reality, in case Berlinski still cares about such things, neither Myers nor Dawkins knew the intent of the proposed documentary. Both Myers and Dawkins have provided accounts of the dishonest way they were approached.

Myers and Dawkins now regret their appearance. This is because they seriously overestimated their own ability to think nimbly before a camera. They are as result appalled either by how they look or by what they said. A veritable Internet scourge, Myers sits before the camera in solemn stupefaction. He has nothing to say and says nothing. Dawkins goes much further. Without ever once realizing that he is about to topple into the badlands of absurdity, he allows Ben Stein to force him into the acknowledgment that life as it appears on earth may well have been designed by space aliens.

---

Being mild-mannered is the same as “solemn stupefaction” to Berlinski. (Perhaps P.Z. disappointed by breathing no fire.) I wonder how Berlinski would characterize his own appearance in Expelled, sitting on the back of his neck with his knees up in the air, nonchalantly declaring that Darwin was a necessary (though not sufficient) condition for the rise of the Nazis and the implementation of their program of mass-murder. Not stupefaction, surely, but stupefying, certainly.

Berlinski also mischaracterizes the response of Dawkins to Stein's badgering him over how intelligent design could be true. Despite having his remarks edited to his maximum disadvantage, Dawkins still manifests his underlying exasperation in conceding to Stein that it is, of course, conceivable that a highly advanced alien race could foster life on a barren planet. (Nothing Dawkins says justifies Berlinski's phrasing: “life as it appears on earth may well have been designed by space aliens.” He spun that version out of whole cloth.) For some unaccountable reason, the editors of Expelled let stand Dawkins's statement that such a science-fiction scenario was scarcely a triumph for ID. It would merely push off the question of origins to a different world—the world where the aliens evolved by natural means. Since there is ample fossil evidence to document humanity's development on this planet, the scenario prompted by Stein is not even a live proposition. Like intelligent design itself, it's a crank hypothesis without substance. Dawkins looked embarrassed while he outlined it in response to Stein's insistence.

Berlinski cranks up the engines of his rhetoric for the home stretch of his essay, confident that he will leave Derbyshire in shreds:

Having found in Expelled an occasion to exercise his organs of indignation, Derbyshire proceeds in his essay to squeeze them until they squeal. The Discovery Institute is a special target. He regards its very existence as an affliction. His indignation has prompted him to impertinence. Knowing nothing of my life, he has nonetheless concluded that I am one of a number of “eccentric non-Christian cranks keen for a well-funded vehicle to help them push their own flat-earth theories.”

Non-Christian? There is no need for euphemism. I am a secular Jew, reason enough apparently for Derbyshire carelessly to suggest that I am in it for the money.

Ah, that old familiar smell—blood, I mean.

---

Observe Berlinski in full martyr mode. It is a deeply affecting spectacle.

As for my eagerness to affirm that the world is flat, I believe it round, and have said so many times.

---

Berlinski seems to believe that Derbyshire was being literal in his criticisms, or—could it be?—he is cleverly pretending to take them literally.

Berlinski moves deftly from his pose of martyrdom to his pose of agnosticism on the question of ID itself:

Beyond this settled conviction, I have no theories to offer—not even theories of intelligent design, which I have rejected in the pages of Commentary.

---

Berlinski, you see, is the bad boy of intelligent design creationism. He merely—almost reluctantly—points out over and over again that “Darwinism” is fatally flawed and doomed to reside on the ash-heap of history. What will replace it? Oh, dear, he really couldn't say. And then the Discovery Institute, having discovered an opportunity to demonstrate its own universal tolerance of divergent points of view, snatches Berlinski up and makes him a Senior Fellow (as in “he's a jolly good”).

All this would be trivial, if tawdry, were it not for the single serious charge that Derbyshire makes: That Intelligent Design is a disguised form of creationism.

In the United States, at least, creationism is a doctrine of Biblical inerrancy. Intelligent Design is otherwise. It is the thesis that living creatures appear designed because they are designed. It is said to be Darwin’s great merit that he successfully dissolved the appearance of design in life. Those who believe that the design of living systems is real believe correspondingly that Darwin’s theory is false, or, at best, incomplete.

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Here Berlinski conveniently forgets that Expelled vigorously seeks to link evolution with atheism. That's exactly why the producers insisted on nonbelieving scientists to represent the scientific side of the evolution mini-controversy. While many ID exponents are careful to declare with some frequency that the identity of the intelligent designer is not addressed in ID, others (like Dembski) are quick to acknowledge it's the G-o-d of Genesis. That's creationism, folks, and it pervades the ID movement.

Like so many men who have reached late middle age, John Derbyshire suffers the impression that the “the barbarians are at the gate.” Women no longer topple blood-ripe into his lap. A “gaggle of fools and fraudsters” is everywhere disturbing his tranquility. Things that he treasures are under ceaseless attack.

---

Berlinski unkindly forgets to mention he is three years older than Derbyshire.

And where awe is merited, none is forthcoming. “And now here is Ben Stein,” Derbyshire objects, “sneering and scoffing at Darwin.”

Stein is, in fact, doing no such thing, and I have seen the documentary in which he appears. He is asking that certain possibilities in thought not be struck from the table prematurely. In so doing, he is offering Darwin the homage that a serious thinker deserves. It is the only homage to which he is entitled.

As for the rest of John Derbyshire’s agitated geschrei, what can one say? A talented writer is entitled to make a fool of himself at least once.

Why not Derbyshire?

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And that is why you have to love David Berlinski! Who else could so casually write that a “talented writer is entitled to make a fool of himself at least once”? I suspect he thinks this does not apply to him. Could it be because of the adjective in front of “writer”?

Expulsion revulsion

Ben Stein ist nicht Einstein

Oy veh. I have been to see Expelled. Verily, I say unto you: intelligence was not allowed. This movie may be effective with certain audiences, but it relies heavily on the ignorance of its viewers. As the Expelled Exposed website amply documents, the movie's cavalcade of martyrs is actually a parade of pretenders. As a work of cinematic art, Expelled is a pretense impasto.

The movie gets off to a quick start in its framing of the alleged controversy, showing black-and-white clips of the erection of the Berlin Wall. This is Expelled's particular leitmotif, the intercutting of portentous commentary by Ben Stein with historical clips of communists, Nazis, and (of all things!) school training videos (“Now, children, do we know when to be quiet?”). The much-sinned-against martyrs tell their poignant tales of woe and repression, Ben Stein exudes astonishment and empathy, and then Joe Stalin, Nikita Khruschev, or Adolf Hitler take their little turn on the catwalk. It happens over and over again.

But let's be fair. If it wasn't mind-numbingly repetitive, how would we know it's a propaganda video?

Almost the first words out of Ben Stein's mouth are a falsehood. His opening scene occurs in a lecture hall at Pepperdine University. He greets his attentive audience, calling them “students.” As Michael Shermer informs us, hardly any of them are. They're extras, hired by the production company to fill the hall and react appropriately on cue. The script must have said that Stein's address was brilliantly successful, because the “students” applaud like loons at its conclusion.

Each supposed martyr at the hands of Darwin's Gestapo is introduced with a document flashed on the screen. Certain words are highlighted in yellow as they occur in Stein's voice-over, while others are selectively blacked out. What are these documents and why are they censored? In keeping with the general tenor of the movie, I suspect they are just props, cooked up by Expelled's producers to make it appear that they are exposing the secretive machinations of the Darwinian elite. It's just cardboard stage scenery. Actually, less than cardboard.

You have to listen attentively to catch some of the more interesting details in the testimony of those who claim to have been victimized by the Darwinian establishment. One peculiar inadvertent admission came from Robert Marks, a Baylor University professor whose ID-friendly website was suspended from the school's servers. The university was concerned that hosting the site would imply to others that the views expressed by Professor Marks were endorsed by the institution. Marks called his site the “Evolutionary Informatics Laboratory,” although there was actually no lab and no publishable work was produced. In talking with Stein about his ordeal, Marks said that it was important to promote oneself in the quest to obtain research grants, which was one of the reasons he did things like “put up labs.” I'm not a research scientist, but I'm fairly certain that putting up a website with a laboratory title is not the same thing as doing any actual science. If it is, then this is a remarkably efficient way of creating labs ex nihilo.

The voices in favor of evolution are carefully selected by the producers of Expelled. When Eugenie Scott of the National Center for Science Education is permitted to point out that most Catholics and mainstream Protestants have no problem accepting evolution, we quickly discover it's only so that Stein can curl his lip and intone, “Oh, really?” He then trots out a string of nonbelievers like Richard Dawkins, Daniel Dennett, and P.Z. Myers to imply that evolution is really just another word for atheism. Declining to be as deferential toward religion as Eugenie Scott, Dawkins explains that learning science was his route to freedom from superstition. Stein is horrified, of course, that Dawkins dismisses religion so callously. (Time for more atheistic monsters of history to be paraded across the screen in black and white.)

From the celebratory comments on blogs and other sites friendly to intelligent design creationism, one might think that Stein baits Dawkins into self-revelatory comments that leave him looking a fool. To the contrary, Dawkins acquits himself rather well. He tends to speak in complete, well-modulated sentences that are difficult to edit into sound-bites more appropriate for a baby-munching antichrist. Stein tries to recoil in consternation at frank admissions of nonbelief, but Stein is not a very persuasive actor. (He runs the gamut, as Dorothy Parker once said of Hepburn, from A to B.) Dawkins seems quite bemused when Stein insists on quizzing him concerning his disbelief in the gods of other religions (not just the God of the Bible), as if a declaration of atheism requires an individual abjuration of each and every deity. (Let us give thanks that Stein did not know the nine billion names of god.)

Stein finds a boon companion in David Berlinski, whom he tracks down in Paris. Berlinski lounges languidly in a low-slung chair in his apartment while Stein bandies words with him. From most camera angles we see Berlinski peering over one of his knees as he pontificates. He's too cool to sit up straight. Sometimes you can glimpse what is probably his Princeton diploma (Ph.D. in philosophy) hanging on the wall over his head. Berlinski explains to Stein that Dawkins is philosophically incompetent, lacking the basic knowledge necessary to address even the most elementary of the questions he raises in The God Delusion. (Contrariwise, it's all right for philosopher Berlinski to offer sententious pronouncements on biology.) When Stein damns Dawkins with faint praise by saying that Berlinski has to admit Dawkins is quite smart, Berlinski grudgingly agrees: “Oh, yes. But he is a bit of a reptile.”

Coming from Berlinski, this charge struck me as particularly amusing. If the lounging lizard had deigned to dart his tongue from between his lips a few times, the image would have been complete.

With suitable hand-wringing, Berlinski notes that it's difficult to connect Darwin with Hitler because of the decades separating them (and, he admits, in a chuckle-inducing comment, “one was English and the other was German”). Nevertheless, he'll give it a try. He opines that Darwinism was not a sufficient condition to give rise to the Nazis; it was, however, a necessary condition. No Darwin, no Hitler. If you read Mein Kampf, claims Berlinski—especially, he adds superciliously, if you can read it in the original German—you'll discover that it's pure Darwinism. More black-and-white video. Then, in case he hasn't rubbed our noses in it enough, Stein tours a site of Nazi atrocities and bemoans man's inhumanity to man. I don't doubt Stein's visceral horror at the treatment of his people, but I have great contempt for his manipulative exploitation of it.

A lot of screen time was also given to William Dembski, who waxed indignant at the blindness of those who would deny a fair hearing to intelligent design. For some reason, however, he failed to seize the opportunity to describe his body of work in establishing the theoretical underpinnings of ID. Perhaps it was modesty. Perhaps he did describe his role as “the Isaac Newton of information theory,” but the producers wisely left it on the cutting-room floor during editing. I suspect it's more likely that Dembski has learned to shy away from opening himself to further questions on when he would finally deliver the long-promised rigorous formalization of his explanatory filter for the detection of design. Since the book he published last year failed to do it, this particular task remains to be accomplished.

Any day now.

Near the end of the movie, Stein tells his Pepperdine audience that “There are people out there who want to keep science in a little box, where it can't possibly touch a higher power, cannot possibly touch God.” Perhaps Stein has it backward. It is God that is in a little box, and the box gets smaller all the time. His god-of-the-gaps used to be required to push the planets about in their orbits, to make the rain fall, and the sun shine, but that was all once upon a time. Science has deprived this god of most of his once-vital functions. Science cannot possibly touch God? Sorry, Ben. There's been a lot of touching going on. God has the bruises and the gap-toothed smile to show for it, too.

I attended an afternoon showing of Expelled at a local multiplex. At first I was the only person in the theater, but people trickled in and there were eventually two or three dozen of us in the house. If the producers of Expelled were hoping for a boffo opening day box office, we certainly did not do our part. Besides, the ticket stub in my pocket was for Kevin Spacey's 21, the movie that was playing in the adjacent theater.

Ma vie en prose

Many, and over-ripe!

If this young man expresses himself
in terms too deep for me,
Why, what a very singularly deep young man
this deep young man must be!

Life has been kind to faux mathematician David Berlinski. Reviewers praised the turgid but high-flown prose of A Tour of the Calculus to the skies, fooled by the author's ruffles and flourishes into thinking they were learning something about mathematics. I'm jealous, of course. Perhaps I should learn a lesson from him and tart up my writing.

But no. I have too much self-respect.

On the other hand, no one else seems to have as much respect for David Berlinski as David Berlinski himself. I inadvertently discovered more evidence of this while innocently browsing the offerings of a local bookstore. There on the table was a paperback edition of Infinite Ascent, Berlinski's venture into the world of math history. Struggling through Tour was all the exposure I felt I needed to his ham-handed treatment of mathematical topics, but I didn't resist the impulse to pick up the book and page through it. On page 106, I encountered a gemlike example of Berlinski's lapidary skill (note particularly the sentence which I render in bold):

Like a Parisian jeweler setting out the rarest of stones, he published only those of his papers that he believed had reached a state of formal perfection and lucidity.

It is a policy that I myself follow.

Berlinski is talking about Gauss (and himself!) here. Carl Friedrich Gauss is a towering figure in mathematics—the Prince of Mathematicians—who took seriously his motto of “Few, but ripe” in his approach to publishing his discoveries.

Berlinski fancies himself cut from the same cloth. He hasn't even the mild grace to say “It is a policy that I myself strive to follow.” Oh, no! Gauss's policy is his own. (Please to overlook the fact that he precedes this claim with a sentence that eloquently testifies to the contrary.)

I laughed aloud in the midst of the bookstore, fished a scrap of paper out of my pocket, and jotted down Berlinski's deadly example of deathless prose for the uncharitable purpose of making fun of it. And now I have done so.

But let us not stop there. Perhaps the passage in Infinite Descent is a fluke, an exception to the author's Gaussian standard. Let's peek into A Tour of the Calculus, shall we?

My copy has 314 pages. The random number generator on my HP calculator suggests I look at page 280. Can I find a silly sentence on this randomly selected page? How about this one?

This simple and dramatic appeal to the area underneath a curve succeeds not only in creating a new function—that was guaranteed by the very definition of the indefinite integral—but in creating a new function with precisely the properties required by the natural logarithm, so that the appeal to the function 1/t and the indefinite integral suggests more than anything else an actor slapping on grease paint in what seems a slap-dash way only to emerge moments later as precisely the character in a Shakespearean play whose vivid features figure in the program notes.

Bravo! Author! Author! Gauss has met his match! [Snicker]

I swear I am not cherry-picking. I really let my calculator select that page. Once more unto the breach, dear friends. My calculator chooses page 227. What ripeness do we find thereon? This ripeness:

“Antidifferentiation is an operation that involves a reversal of form,” I say, “and if a pictorial image is wanted it should be drawn from the world of fencing, as when the fencing master thrusts—differentiation—and with an enigmatic smile playing on his features after his opponent murmurs touché, backs up and retracts his elegant foil—antidifferentiation.”

That's quite a heaping helping of pellucid prose, ain't it? This is what prompted the San Francisco Chronicle to claim that Berlinski's “writing is so clean and powerful.” Touché! (Perhaps in la tête.)

Words fail me, although not in quite the way that they fail Berlinski. People fall all over themselves to declare him an expository genius. We can expect similar paroxysms of delight over his latest book, an attack on nonbelievers: The Devil's Delusion: Atheism and its Scientific Pretensions. I do not have this new volume (which carries the delightful publication date of April Fool's Day), but it's further evidence of Berlinski's utter inability to catch himself at self-parody. He has been most notable in recent years for his scientific pretensions as a senior fellow of the Discovery Institute's Center for Science and Culture. Despite being a self-professed agnostic, Berlinski specializes in giving aid and comfort to the Discovery Institute's theistic creationists, lending his supposed scientific credentials (degrees in math and philosophy) to their cause. Hence the new book. No doubt The Devil's Delusion is one of his greatest works.

And I mean that entirely sincerely.

So much smarter than you

Ogawd, not more Berlinski!

Just this once more, okay? Then I promise to stop. I'm sure I can. It's just that—well, how should I say it?—this is so damned weird! I'm scratching my head and need to get this off my chest. (Nice mixed metaphor there, if you'll excuse my patting myself on my own back. Ow!) I promise you will find this amazing.

Let's begin with a little math lesson. That's always a good way to gather a crowd. Come a little closer, kids, and Dr. Z will astonish you with his great wisdom! I take for my text a reading from the book of Tom the Apostol, Chapter 3, Section 2:

The equation lim_x→p f(x) = A is read: “The limit of f(x) as x approaches p is equal to A,” or “f(x) approaches A as x approaches p.” It is also written without the limit symbol, as follows:

f(x) → A as x → p.

This symbolism is intended to convey the idea that we can make f(x) as close to A as we please, provided we choose x sufficiently close to p.

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That was a perfectly straightforward description of the notion of a mathematical limit. Here's a concrete example to show you that you understand the basic idea:

Let f(x) = x², which is often called the squaring function (the reason for this is left as an exercise for the student). Evaluating function notation is no big deal in a simple case like this. If you're told that x = 3, you just plug in 3 wherever you see x (the number you plug in is called the argument of the function), like so:

f(3) = 3² = 9.

Okay? If we revisit the limit idea with the squaring function in mind, replacing p with 3 and A with 9, we find ourselves looking at the statement that

x² → 9 as x → 3.

Does that seem reasonable? As x gets closer and closer to 3, x² gets closer and closer to 9. If you look at the accompanying graph of y = x², you may be able to persuade yourself that this is true. You would be correct to think there are subtleties which we have avoided here, but feel free nevertheless to congratulate yourself on having grasped a key fact about the squaring function: when two numbers are close together, their squares are also close together. The closer the numbers, the closer their squares. It's not exactly rocket science at this point.

Once upon a time in Prague

I finally got around this year to reading David Berlinski's A Tour of the Calculus, the 1995 book that tried to popularize calculus and helped him make his mark as an author. Since I usually assign some outside reading to my calculus students in order to keep them from thinking that everything is in the pages of their textbook, I welcomed the appearance of the Berlinski book and its nontechnical approach. Before I found the time to read it on my own, however, some of my colleagues shared their disdain of Berlinski's prolix prose and metaphor mania. My ardor cooled and the book got shoved to the back of my stack of reading material, where it's languished the past decade.

In the intervening years, Berlinski has been busily pimping for the Discovery Institute, where he is a senior fellow with DI's Center for Science and Culture. Despite his yeoman service on behalf of the exponents of intelligent design, Berlinski claims a general agnosticism about the topic and does not profess to be a creationist. He prefers merely to lob his mathematically laden bombs at the theory of evolution. Such nonsense made me even less inclined to dig out his book on calculus, because he struck me more and more as a player of perverse intellectual games, pretending a kind of neutrality while focusing all of his attacks on the scientific side of the evolution/creation argument.

Berlinski has not escaped unscathed. I wrote about his wrongheadedness myself in David Berlinski vs. Goliath, but for a real nuts-and-bolts evisceration of his arguments, see what Mark Chu-Carroll has to say about Berlinski's Bad Math at Good Math, Bad Math:

In my never-ending quest for bad math to mock, I was taking a look at the Discovery Institute's website, where I found an essay, On the Origin of Life, by David Berlinksi. Bad math? Oh, yeah. Bad, sloppy, crappy math.

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This surfeit of criticisms of Berlinski, although I fully agreed with them, finally tweaked my conscience and reminded me of the unread calculus book. Perhaps Berlinski's seduction by the dark side of creationism had drawn him away from more constructive efforts. I had read enough of his prose and seen him on enough video to remain wary of his tendency to talk down to people, but A Tour of the Calculus was supposed to be an attempt to speak to the general public. I needed to read it to see for myself.

It didn't take too many pages for me to see that all of Berlinski's pomposity is at full play in A Tour of the Calculus. He lards the text with digressions and obscure allusions (perhaps I am not educated enough to appreciate him). The mathematical concepts are recast in odd ways that confuse rather than shed light. The writing is self-indulgent. These are disappointments rather than surprises. Nevertheless, I promised you a surprise, and it's time for me to deliver. I began with a short math lesson on the squaring function because it is at the center of a bizarre tale recounted by Berlinski in Chapter 15, A Prague Interlude.

Berlinski goes to Prague University to lecture on Tychnoff's theorem, a sophisticated result from topology. One of his hosts is Professor Swoboda, a mathematician. “Swoboda is extraordinarily intelligent,” Berlinski tells us. Please remember these things. Berlinski is giving a math talk attended by an extraordinarily intelligent mathematician. Here is an extended quote from the middle of his narration:

I am supposed to talk about Tychonoff's theorem, but to my surprise I find myself explaining the elementary calculus to a roomful of mathematicians, re-creating in my own mind the steps that Bolzano took in order to define continuity. For some reason I feel it absolutely crucial to explain how the concept of a limit is applied to functions. No one seems to mind or even notice.

“A function indicates a relationship in progress, arguments going to values. Given any real number, the function f(x) = x² returns its square, tak? ... In go arguments 1, 2, 3, out come the values, 1, 4, 9.... As the arguments of f get larger and larger, its values get larger and larger in turn.* ... Now imagine,” I say, “arguments coming closer and closer to the number 3, tak?”

I walk back to the blackboard and show the men in my audience what I mean, writing, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, ..., before the function.

“What then happens to the function? How does it behave?” I ask, realizing with a sense of wonder somewhat at odds with the hard-boiled pose I usually affect, that a function is among the things in this world that behaves—it has a life of its own and so in its own way participates in the drama of things that are animate.

“I mean,” I say, “what happens to the values of f as its arguments approach 3?”

I look out toward my audience. Swoboda and Schweik are looking at me intently, their faces serene, without irony. It is plain to me that they do not know the answer yet.

“They approach, those values, the number 9, so that the function is now seen as running up against a limit, a boundary beyond which it does not go.”

Swoboda leans back and sighs audibly, as if for the first time he had grasped a difficult principle. The room, with its wooden pews and narrow blackboard, is getting close.

I say, “The concept of a limit, as it is applied to functions, is forged in the fire of these remarks.”

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There's more. Much more. But enough. Can you explain this passage to me? Berlinski begins by admitting he is talking about elementary calculus, but then has his roomful of mathematicians rapt in awe as he reveals that values of the squaring function approach 9 as its arguments approach 3. College students would not be surprised by this result, let along a roomful of mathematicians.

I presume Berlinski intends this as an extended metaphor, because otherwise he is cruelly mocking his Hungarian Czech colleagues. The point of the metaphor, however, is completely and entirely lost on me. His absurdist account continues with yet another elementary limit. A moderately competent Calculus I student would dispatch it promptly and math teachers could do it in their heads, but Berlinski presents it to his audience with drama and mystery. The mathematicians leave the seminar at its conclusion and trudge down the street, exhausted. “Their tread is heavy and tired.”

I know how they feel.

Update: David Berlinski has complained of his rough treatment at the hands of the proprietor of Good Math, Bad Math. While trying to defend his mathematical arguments against Mark Chu-Carroll's criticisms, Berlinski mentions my comment about his visit to Prague University and objects:

If you check the index to my A TOUR OF THE CALCULUS under 'limits' you will find page references to a complete and precise definition. The section in Prague was, of course, intended to be dream-like. It is not the mathematicians who are diminishing in sophistication, but the narrator.

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Was that supposed to clear things up? If you have the stomach for more, Berlinski has returned to Good Math, Bad Math for Round 2. If, like me, you're ready for a rest cure, here's an opportunity to avert your gaze. (But don't forget to bookmark Good Math, Bad Math for future reference. Good stuff is added every week.)

*Berlinski is assuming that the x values are positive. If negative values are permitted, then larger x values do not always result in larger squares. For example, −1 is greater than −2, but (−1)² is smaller than (−2)².

David Berlinski vs. Goliath

This time Goliath wins

Intellectuals don't win too many popularity contests. The “smart kid” in class is often the target of bullies. Speaking as a former smart kid, I find it perplexing that we sometimes become bullies ourselves. We should know better, although it may be that some of us cannot resist taking a turn when circumstances change. Perhaps this is what happened to David Berlinski, a peculiar icon of the anti-evolution movement.

Berlinski is an intellectual bully, a trained mathematician who enjoys using his special status to confuse and abuse others. His biographical sketch on the website of the Discovery Institute notes that Berlinski earned a Ph.D. in mathematics philosophy from Princeton, no shabby accomplishment. His book A Tour of the Calculus was a very successful semi-popular account of the work of Newton and Leibniz and its consequences. The hardcover edition's book jacket includes a paragraph about the author on its back flap; it contains this sentence: “Having a tendency to lose academic positions with what he himself describes as an embarrassing urgency, Berlinski now devotes himself entirely to writing.” As is usually the case with someone who has failed to find himself an academic niche, Berlinski's fame rests on matters other than his research papers. These days he is more recognized as an anti-Darwin skeptic than as a mathematician.

Nevertheless, it is as a mathematician that Berlinski rides into combat against his evolutionary targets. What could be more natural for him than to hurl numbers at his opponents?

Could I ask you to give us your best estimate of the number of changes required to take a dog-like mammal to a sea-going whale?

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The quote is from William F. Buckley's Firing Line on PBS. The installment on December 4, 1997, was devoted to a debate on the proposition, “Resolved: The evolutionists should acknowledge creation.” Berlinski's position among the creationists was ambiguous, since he purports to have no opinion on creation itself; he is simply making common cause with those who attack Darwin and evolution. His question on the evolution of the whale was aimed at Eugenie Scott of the National Center for Science Education, an organization dedicated to promoting sound science education and opposing creationism.

It was a theme to which Berlinski returned several times in his exchanges with the evolutionists on the Firing Line panel. He variously denounced natural selection as “Que sera, sera” and archly demanded to know whether Darwinism comprised any actual theory “that would be recognizable by any physicist or a mathematician.” Berlinski is particularly enamored of physics, which is highly mathematized and fraught with numbers. To the degree that evolution is not numerical, Berlinski appears to argue, it is not really a science. For him, science seems to be an absurdly all-or-nothing proposition. Witness this exchange between Berlinski and Barry Lynn of Americans United for Separation of Church and State. (I have abridged the discussion to remove some of the repetitions and digressions. The full text is available here.)

DB: I do have a scientific question to ask you. Every significant paleontologist says that there are gaps in the fossil record. Do you have a particular reason for demurring?

BL: Of course it has gaps.

DB: Okay, so to that extent the evidence does not support Darwin's theory of evolution.

BL: No, that is absolutely wrong.

DB: It follows as the night the day.

BL: Of course not. How could you have a cell, for example, hundreds of millions of years old, that would leave a fossil record? It would disintegrate. It would quite literally not be able to be found in the fossil record.

DB: I never suggested that there may not be explanations of the gaps. But the fact [is] that the fossil record does not on its face support Darwin's theory of evolution.

BL: No, it does. And once again I say, how many times do we have to find those intermediate fossils?

DB: All I'm asking for is enlightenment on a significant point. Darwin's theory requires a multitude of continuous forms. We do not see that in the fossil record. In fact, major transitions are utterly incomplete. Would you accept that as an empirical fact?

BL: No, you sound like a guy who is writing a story about baseball, comes in in the fourth inning, and says, “Well, you know, I'm going to write about the fourth inning on; the first three innings didn't happen because I wasn't there to see them.”

DB: We can't find any of the major transitions between the fish and the amphibian.

BL: Of course we find them. It's just that when we find them, doctor, you say it's still not enough.

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The method to Berlinski's madness is easily characterized: Darwin's theory requires continuity in transitional forms. No continuity, no evolution. Simple as that. Q.E.D. While no serious scientist would argue that the absence of mathematical continuity in a fragmentary fossil record would imply there was no continuity in the first place, Berlinski's non-serious approach is perfectly compatible with such an absurd conclusion. It might be helpful at this point to remind everyone that a single gap in a mathematical proof is enough to invalidate it. While this standard is a natural and necessary part of mathematics, where a partial proof is no proof at all, it is completely out of place in the observational sciences. Berlinski either does not know this, or pretends not to.

I watched the Firing Line debate when it was originally broadcast in 1997. Somewhere around here I have a videotape of the whole two hours. Reading the on-line transcript reminded me how much is lost in the translation from video to text. The page does not fully convey Berlinski's supercilious manner as he combines spurious arguments with intellectual disdain. He was going to browbeat his opponents into submission with the immensity of his mathematical knowledge and he oozed contempt for their counter-arguments.

I learned a valuable and frightening lesson watching Berlinski in action. Please never let me lapse into behavior like his! And the bullies who beat the snot out of him in school have a lot to answer for.