The Last Theorem - Arthur Charles Clarke [1]
Actually, Clarke should not have been in the Royal Air Force at all. As a civilian he had been a civil servant in H.M. Exchequer and Audit Department and hence had been in a reserved occupation. However, he had rightly suspected that he would soon be unreserved, so one day he sneaked away from the office and volunteered at the nearest RAF recruiting station. He was just in time. A few weeks later the army started looking for him—as an army deserter who was wanted by the medical corps! As he was unable to bear the sight of blood, particularly his own, he obviously had a very narrow escape.
By that time Arthur Clarke was already a keen space-cadet, having joined the British Interplanetary Society soon after it was formed in 1933. Now, realizing that he had at his command the world’s most powerful radar, producing beams only a fraction of a degree wide, one night he aimed it at the rising moon and counted for three seconds to see if there would be a returning echo.
Sadly, there wasn’t. It was years later before anyone did actually receive radar echoes from the moon.
However, although no one could have known it at the time, something else may have happened.
THE SECOND PREAMBLE
Frederik Pohl says:
There are two things in my life that I think have a bearing on the subject matter of this book, so perhaps this would be a good time to set them down.
The first: By the time I was in my early thirties, I had been exposed to a fair amount of mathematics—algebra, geometry, trigonometry, a little elementary calculus—either at Brooklyn Tech, where for a brief period in my youth I had the mistaken notion that I might become a chemical engineer, or, during World War II, in the U.S. Air Force Weather School at Chanute Field in Illinois, where the instructors tried to teach me something about the mathematical bases of meteorology.
None of those kinds of math made a great impression on me. What changed that, radically and permanently, was an article in Scientific American in the early 1950s that spoke of a sort of mathematics I had never before heard of. It was called “number theory.” It had to do with describing and cataloging the properties of that basic unit of all mathematics, the number, and it tickled my imagination.
I sent my secretary out to the nearest bookstore to buy me copies of all the books cited in the article, and I read them, and I was addicted. Over the next year and more I spent all the time I could squeeze out of a busy life in scribbling interminable calculations on ream upon ream of paper. (We’re talking about the 1950s, remember. No computers. Not even a pocket calculator. If I wanted to try factoring a number that I thought might be prime, I did it the way Fermat or Kepler or, for that matter, probably old Aristarchus himself had done it, which is to say, by means of interminably repetitious and laborious handwritten arithmetic.)
I never did find Fermat’s lost proof, or solve any other of the great mathematical puzzles. I didn’t even get very far with the one endeavor that, I thought for a time, I might actually make some headway with, namely, finding a formula for generating prime numbers. What I did accomplish—and little enough it is, for all that work—was to invent a couple of what you might call mathematical parlor tricks. One was a technique for counting on your fingers. (Hey, anybody can count on his fingers, you say. Well, sure, but up to 1,023?) The other was accomplishing an apparently impossible task.
I’ll give you the patter that goes with that trick:
If you draw a row of coins, it doesn’t matter how long a row, I will in ten seconds or less write down the exact number of permutations (heads-tails-heads, heads-tails-tails, etc.) that number of coins produces when flipped.