Things That Matter: Three Decades of Passions, Pastimes and Politics

by Charles Krauthammer

  During Game 8, I found myself in a room with the U.S. chess champion (Lev Alburt), four grandmasters and one legend, former World Champion Mikhail Tal. It was like watching the World Series with five Hall of Famers parsing every pitch and Cy Young correcting them. On Karpov’s 23rd move the parsing got slightly crazy: If Kasparov does A, then Karpov must do B. If Kasparov then tries C and Karpov answers with D, look out: E, F and G follow. But if Kasparov does Z, then …

  Some of these lines were harmony, variations on the main theme of the game. Some were jazz riffs, freestyle and whimsical. Some were just fanciful trills, exotic and occasionally atonal. They all went up on the board fast and furious, as patzers—plodding amateurs—like me struggled to follow the logic.

  Then Karpov did the unexpected: He advanced a pawn, unbalancing the position and not a few grandmasters. Instantly all the heretofore examined lines, entire symphonies of hypothetical variation, vanished into the ether. “Unheard melodies,” murmured the yellow-tied patzer sitting near me. His tone was wry and regretful.

  The move done, the grandmasters wiped the slate clean and began composing fresh music, speculating on what might follow next. This greatly disturbed the dapper young Yugoslav grandmaster Ljubomir Ljubojevic. Shaking his head in disapproval, Ljubo strode up to the board, took down all the moves now being assayed and brought the position back not to Move 23 but to Move 22. If Karpov had pushed the pawn in Move 22 instead of first delivering that ridiculous check, the now animated Ljubo insisted, it would have been a triumph. He then gave a long demonstration of the truth of his analysis.

  Of course by then it was irrelevant. Karpov had played the check first. Enough of history, said the others, impatient to get on with analyzing the world as it now existed. Ljubo insisted on analyzing the world as it should exist. As the groans grew louder, Ljubo’s retort was indignant: “Let’s find some truth here.”

  The yellow-tied patzer had come for beauty, but Ljubo had come for truth. In chess, that means finding not just a good move or even a harmonious move but the perfect move. God’s move.

  Playing chess with divinity can be dangerous, however. The great Steinitz, who once claimed to have played against God and won (he neglected to leave a record of the game), went quite mad. The last great practitioner of truth, Bobby Fischer, after winning the world championship in 1972, disappeared into some apocalyptic sect in California and had the fillings in his teeth removed to stop the KGB transmissions.

  Melodies you can get in any record store. But truth? Where else can you find truth? The next day I saw Ljubo again. It was 12 hours later and he was still shaking his head.

  Down on the Hudson stage, however, the protagonists were engaged not so much in truth seeking as in attempted murder. Kasparov, who calls Karpov “a creature of darkness,” had declared his intent not just to defeat Karpov but to destroy him. Accordingly, Kasparov played the opening games with the confident, reckless belligerence of a young Ali. Karpov, though, was fully Frazier’s equal. The result was mayhem rarely seen at that level of play. It was like a title fight with 10 knockdowns by Round 3 or, for the more delicate, like a ballet performed not on a stage but on a trampoline.

  Even the exalted were amazed by the innovations, the sacrifices, the speculative attacks, the kind of stuff a patzer like me tries out in Washington’s Lafayette Square, not the kind world champions play with $1.7 million at stake. I asked the great and wizened Tal what he thought of the opening games of the match. “Hitchcock movies,” he replied with a grin.

  Beauty, truth and Hitchcock. Now that’s entertainment.

  Time, November 19, 1990

  FERMAT SOLVED

  Fermat’s Last Theorem is solved, and a generation of tormented German graduate students can now go fishing.

  Imagine you have some interest in biblical archaeology and see advertised a lecture on, say, “Calibrated Radiocarbon Chronology of Royal Judean Storage Jars,” or some such. You go to the lecture at the end of which the speaker says, “And, oh, by the way, on Thursday I found the Holy Grail in the basement of a bed-and-breakfast in downtown Jericho. Here it is.”

  Well, something comparable happened in Cambridge, England, last week. A group of mathematicians attended a conference on—hold on—“P-adic Galois Representations, Iwasawa Theory and the Tamagawa Numbers of Motives.” They went, as audiences do, expecting entertainment and instruction. What they got was astonishment.

  They went to hear Prof. Andrew Wiles deliver three lectures on “Modular Forms, Elliptic Curves and Galois Representations.” At the end of the third lecture, Wiles noted that his presentation had just proved Fermat’s Last Theorem, the most famous and elusive mathematical puzzle of the last 300 years.

  If Wiles’ claim holds up—and its 200 pages of reasoning are so difficult that only a handful of mathematicians are in a position to judge—he will be hailed for his mathematical genius. He should be equally hailed for his modesty. Dropping his bombshell at the end of a lecture, without a hint of the now usual “cold fusion”-type advance publicity, is in itself an achievement in this age of hype.

  In science, modesty and genius do not coexist well together. (In Washington, modesty and cleverness don’t.) Einstein is perhaps the most famous exception to the rule. Yet even Watson and Crick, discoverers of the genetic code and not known for their modesty, proved themselves capable of one admirable, indeed immortal, act of understatement. Toward the end of their epic two-page paper revealing the structure of DNA, they noted drily: “It has not escaped our notice that the specific pairing [i.e., zipper-like structure of DNA] we have postulated immediately suggests a possible copying mechanism for the replication of the genetic material.”

  For hundreds of years humans had known that hereditary traits are transmitted from parent to child. But they hadn’t a clue as to how. Watson and Crick had just provided the clue.

  Wiles, however, is due homage not just for his genius and his modesty, but for his courage. Courage is not a quality one normally associates with mathematicians. Yet it should apply to people who work in their attics in secret for seven years without cease on a problem that has eluded the greatest mathematical minds since first proposed in 1637.

  I once had a friend at Oxford who drifted into the study of Hegel, that famously impenetrable German philosopher, and was never seen again. There are intellectual black holes, vortexes of endless regression, that mortals ought to stay clear of. Many mathematicians have felt that way about Fermat’s Last Theorem.

  Its allure lies not just in its longevity but in its simplicity. It can be written on one line: “Xn + Yn = Zn is impossible when n > 2,” meaning that while a square can broken into two smaller squares—25 (the square of 5) can be broken into 16 (the square of 4) plus 9 (the square of 3)—one cannot divide a cube into two smaller cubes, and for that matter, one cannot divide any higher power into two smaller numbers of the same power.

  It is a proposition so vexing and mathematically profound that the French Academy of Sciences offered a gold medal and 300 francs for its solution. That was in 1815, the year Napoleon was just settling into his new digs on St. Helena.

  It is a proposition so famous that perhaps the one person on Earth most grateful for the Wiles solution, after the professor’s wife and daughters (“Daddy’s back!”), is Dr. Martin Kneser of the Göttingen Academy of Sciences. He administers another Fermat prize, the Wolfskehl prize (first offered in 1908, now 7,500 marks). Which means that poor Dr. Kneser must fight his way through the “three meters of correspondence” from every crank on the planet who is sure he has bested Fermat.

  How does he handle the mountain of mail? “In recent decades,” wrote Kneser’s predecessor, “it was handled in the following way: the Secretary of the Akademie divides the arriving manuscripts into (1) complete nonsense, which is sent back immediately, and into (2) material which looks like mathematics.” The second category is given to young research assistants forced by poverty and induced by payment to search for the inevitable mistakes.


  One would-be Fermat slayer sent half a solution and demanded 1,000 Marks before he would produce the other half. Another also demanded money up front, promising 10% of the radio and TV take that would follow his fame and threatening, if denied, to send his solution to Russia.

  Consider, then, what Wiles has wrought. A generation of tormented German graduate students can now go fishing. Kneser is free at last. Fermat is vindicated. And the rest of us are treated to a rare, irrefutable demonstration that the hairless ape with the opposable thumb is indeed, now and then, capable of something that deserves the name progress.

  The Washington Post, July 2, 1993

  BE AFRAID

  As was to be expected, the end of civilization as we know it was announced on the back pages. On Feb. 10, 1996, in Philadelphia, while America was distracted by the rise of Pat Buchanan, the fall of Phil Gramm and other trifles, something large happened. German philosophers call such large events world-historical. This was larger. It was species-defining. The New York Times carried it on page A32.

  On Feb. 10, Garry Kasparov, the best chess player in the world and quite possibly the best chess player who ever lived, sat down across a chessboard from a machine, an IBM computer called Deep Blue, and lost.

  True, it was only one game. What kind of achievement is that? Well—as Henny Youngman used to say when asked, “How’s your wife?”—compared to what? Compared to human challengers for the world championship? Just five months ago, the same Kasparov played a championship match against the next best player of the human species. The No. 2 human played Kasparov 18 games and won 1. Deep Blue played Kasparov and won its very first game. And it was no fluke. Over the first four games, the machine played Kasparov dead even—one win, one loss, two draws—before the champ rallied and came away with the final two games.

  Kasparov won the match. That was expected. Game 1, however, was not supposed to happen. True, Kasparov had lost to machines in speed games and other lesser tests. And lesser grandmasters have lost regulation games to machines. But never before in a real game played under championship conditions had a machine beaten the best living human.

  Indeed Kasparov, who a few weeks ago single-handedly took on the entire national chess team of Brazil, was so confident of winning that he rejected the offer that the $500,000 purse be split 60–40 between winner and loser. Kasparov insisted on winner-take-all. They settled on 80–20. (What, by the way, does Deep Blue do with its 100-grand purse? New chips?)

  Asked when he thought a computer would beat the best human, Kasparov had said 2010 or maybe never. A mutual friend tells me Garry would have gladly offered 1–10, perhaps even 1–100 odds on himself. That was all before Game 1. After Game 1, Kasparov was not offering any odds at all. “He was devastated,” said his computer coach, Frederick Friedel. “It was a shattering experience. We didn’t know what the game meant. There was the theoretical possibility that the computer would be invincible, and that he would lose all six games.”

  True, we have already created machines that can run faster, lift better, see farther than we can. But cars, cranes and telescopes shame only our limbs and our senses, not our essence. Thinking is our specialty, or so we think. How could a device capable of nothing more than calculation (of the possible moves) and scoring (of the relative strengths of the resulting positions) possibly beat a human with a lifetime of experience, instant pattern recognition, unfathomable intuition and a killer instinct?

  How? With sheer brute force: calculation and evaluation at cosmic speeds. At the height of the game, Deep Blue was seeing about 200 million positions every second. You and I can see one; Kasparov, two. Maybe three. But 200 million? It was style vs. power, and power won. It was like watching Muhammad Ali, floating and stinging, try to box a steamroller in a very small ring. The results aren’t pretty.

  What is Deep Blue’s secret? Grandmaster Yasser Seirawan put it most succinctly: “The machine has no fear.” He did not just mean the obvious, that silicon cannot quake. He meant something deeper: Because of its fantastic capacity to see all possible combinations some distance into the future, the machine, once it determines that its own position is safe, can take the kind of attacking chances no human would. The omniscient have no fear.

  In Game 1, Blue took what grandmaster Robert Byrne called “crazy chances.” On-site expert commentators labeled one move “insane.” It wasn’t. It was exactly right.

  Here’s what happened. Late in the game, Blue’s king was under savage attack by Kasparov. Any human player under such assault by a world champion would be staring at his own king trying to figure out how to get away. Instead, Blue ignored the threat and quite nonchalantly went hunting for lowly pawns at the other end of the board. In fact, at the point of maximum peril, Blue expended two moves—many have died giving Kasparov even one—to snap one pawn. It was as if at Gettysburg, General Meade had sent his soldiers out for a bit of apple picking moments before Pickett’s charge because he had calculated that they could get back to their positions with a half-second to spare.

  In humans, that is called sangfroid. And if you don’t have any sang, you can be very froid. But then again if Meade had known absolutely—by calculating the precise trajectories of all the bullets and all the bayonets and all the cannons in Pickett’s division—the time of arrival of the enemy, he could indeed, without fear, have ordered his men to pick apples.

  Which is exactly what Deep Blue did. It had calculated every possible combination of Kasparov’s available moves and determined with absolute certainty that it could return from its pawn-picking expedition and destroy Kasparov exactly one move before Kasparov could destroy it. Which it did.

  It takes more than nerves of steel to do that. It takes a silicon brain. No human can achieve absolute certainty because no human can be sure to have seen everything. Deep Blue can.

  Now, it cannot see everything forever—just everything within its horizon, which for Deep Blue means everything that can happen within the next 10 or 15 moves or so. The very best human player could still beat it (as Kasparov did subsequently) because he can intuit—God knows how—what the general shape of things will be 20 moves from now.

  But it is only a matter of time before, having acquired yet more sheer computing power, Blue will see farther than Garry can feel. And then it’s curtains. Then he gets shut out, 6–0. Then we don’t even bother to play the brutes again. The world championship will consist of one box playing another. Men stopped foot racing against automobiles long ago.

  Blue’s omniscience will make it omnipotent. It can play—fight—with the abandon of an immortal. Kasparov himself said that with Deep Blue, quantity had become quality. When you can calculate so fast and so far, you rise to another level. At some point that happened in biology. There are neurons firing in lemmings and squid, but put them together in gigantic enough numbers and fantastic enough array, as in humans—and, behold, a thought, popping up like a cartoon bubble from the brain.

  We call that consciousness. Deep Blue is not there yet, though one day we will be tempted to ask him. In the meantime he’s done alchemy, turning quantity into quality. That in itself is scary.

  At least to me. However, my son, age 10, who lives as comfortably with his computer as he does with his dog, was rooting for Deep Blue all along. “What are you worried about, Dad?” he says. “After all, we made the machine, didn’t we? So we’re just beating ourselves.”

  The next generation has gone over to Them. No need to wait for the rematch. It’s over.

  Time, February 26, 1996

  THE BEST SHOW IN TOWN

  In that fleeting interval between natural disaster (earthquake, hurricane) and the president’s 57th (or so) major national address next Thursday, I can finally devote a summer column to the finest efflorescence of that season this city has to offer: the Washington Nationals.

  They are a baseball team. Not yet very good, mind you, but it matters not. When you live in a town with a great team, you go to see them win. When you live in a town
with a team that is passing rapidly through mediocrity on its way to contention—the Nats have an amazing crop of upcoming young players—you go for the moments.

  I go to see Ryan Zimmerman charge a slowly hit grounder down the third-base line. This happens roughly once a game. Zim comes flying in, picks up the ball barehanded and throws it across his body to first base, perpendicular to the direction he’s running.

  Except that this cannot be done. You could never get enough (velocity) on the throw to get the out at first. So Zimmerman dives forward, leaving his feet and hovering there for an instant, his body parallel to the ground in order to get more arm extension and thus more on the throw, which by now is nearly underhanded, his fingers almost scraping the ground. Batter out.

  Try this yourself. Aim for a barn door. You will miss. And also dislocate your shoulder.

  Another attraction is rookie second baseman Danny Espinosa. He has what in baseball parlance is known as range. A hard shot is hit to the hole between first and second, and Espy ranges to his left to snag it. Three weeks ago, one shot was hit so hard and so deep that he had to dive onto the outfield grass to reach it, sliding on his side in the general direction of the right-field foul pole.

  Nice grab, but unless you can get the ball to first, it’s just for show. Espy starts to get up. But there is no time for standing. So, from his knees, while still sliding on the grass out toward the stands, he forces himself into a counterclockwise 180-degree spin to throw back toward first base—except that he actually begins his throw mid-turn, while facing the outfield, thereby gaining velocity from the centrifugal force (and probably the rotation of the Earth, although this remains unverified). It’s like throwing on your knees from a spinning merry-go-round that is itself moving laterally in a landslide. Try that.