Tuesday, June 22, 2004

Inspirational Reading

I suppose it was highly presumptuous of me to provide a 4 paragraph summary of Clinton's memoirs that precludes the need for you to read 900 pages of his lip-biting blather, without leaving you with other reading alternatives to carry with you to the beach. Let me now ammend that discourtesy.

For those of you looking for a good read this summer, I highly recommend The Perfect Mile, the story of Roger Bannister's pursuit of the sub-4 minute mile fifty years ago. Bannister was in a virtual race with an Aussie, John Landy, and an American, Wes Santee; I say virtual because Santee never faced either Landy or Bannister head to head, and Bannister and Landy, aside from racing against each other in the Helsinki Olympics of 1952 when Landy was a nobody, didn't race each other until shortly after each had broken the 4 minute mile. Landy did it six weeks after Bannister ran 3:59.6, eclipsing Bannister's world mark by 1.6 seconds. Landy came to Finland that summer to escape the Australian winter because he knew he wouldn't be able to wait out another season without either Bannister or Santee going sub-4.

Bannister trained with two Brits who rabbited him through the first 3.5 laps, at which point he brought it home himself. Santee, in contrast, was told by the AAU, the governing body of amateur athletics at the time in the US, that if there was any hint that someone was rabbitting him, they would not recognize any American record. Landy, like Santee, never ran with a rabbit, and ran about 6 sub 4:02 miles, leading each from start to finish, prior to Bannister reaching the coveted milestone. When Landy finally did break the record, it was when Bannister's primary rabbit, Chris Chadaway, traveled to Finland to race Landy; though Landy led from the first lap on, Chadaway stayed on his heels for 3+ laps, which was enough to push Landy. Santee never broke 4 minutes in the mile, as his running career was cut very short when he entered the Marines shortly after college. He had a devastating kick, and many believed at the time that he would have won any head to head race with his 2 international rivals.

The singular pursuit of the distinction of running the first sub-4 minute mile made for a riveting story. Another book (far less light), that deals with similarly amazing human efforts is entitled the Riemann Hypothesis, subtitled the Greatest Unsolved Problem in Mathematics. In A Beautiful Mind, the movie about John Nash, there is a scene where he incoherently lectures to a hall filled with mathematicians, after having claimed that he would prove the Riemann Hypothesis. He was institutionalized shortly after that lecture, and some speculate that he was driven mad by the effort to prove Riemann.

The author also tells the recent story of the 1996 solving of what was considered the second greatest unsolved problem in mathematics, called Fermat's last theorem. The mathematician who solved it is Andrew Wiles, of Princeton University. He toiled away on the problem for years, making progress, but never discussing his efforts, or even that he was making efforts, to prove a theory that eluded the best efforts of mathematicians for over a century. When he was convinced he had finally proved it, and came out with his proof, many mathematicians who had been toling on the proof for years resented his isolated efforts. They knew that progress he had made six years ago was ahead of where they stood even in 1996, and resented the fact that they spent so much time on dead-ends they could had avoided had they known of his progress.

There is a similarity to the stories - Bannister and Wiles had the faith in themselves that allowed them to attempt to overcome challenges that had eluded the best efforts of many fine men who came before them, and in the face of many who no doubt said such feats were impossible. But there is also an interesting difference - Landy could still try to eclipse Bannister's world record, even if he couldn't be the first to run sub-4. In contrast, there is no satisfaction in being a mathematician who fails to prove the Reimann Hypothesis, but sees it done by another. Unlike Landy, proving the same hypothesis a month later in a slightly more elegant manner brings no accolades. That makes for interesting competition - it is the intellectual equivalent of the primitive form of basketball played by the Aztecs, where the loser, rather than being able to go back and sharpen his game in preparation for the next, got his head chopped off.

The name Bannister is well known among most sports fans, and perhaps always will be. Wiles, as a mathemetician, enjoys less general fame, but believe it or not, his efforts led to an off-Broadway musical entitled Fermat's Last Tango, wherein the following immortal lines are spoken:

"In order to transform your elliptic curves into Galois representations so they could be counted against the set of modular forms, you assumed they met the requirements of an Euler system, when in fact they do not!"

Not exactly Shakespeare, but of course Fermat's Last Theorem (let alone its proof) doesn't pre-date Shakespeare, so who knows - maybe with different timing? The good news for you is that you don't have to read the book - just go see the musical. And the same goes the Perfect Mile, which reportedly is being made into a movie by the makers of Seabiscuit.


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