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the pilot when to fly right or left—or sometimes, more urgently, when to increase altitude—fast.

      GCA was welcomed enthusiastically by the RAF Bomber Command, which every day was losing more aircraft over Europe through bad weather than through enemy action. In 1943 the Mark 1 and its crew were stationed at an airfield in St. Eval, Cornwall. An RAF crew headed by Flight Lieutenant Lavington was dispatched to join them. Lavington was assisted by the newly commissioned Pilot Officer Arthur C. Clarke.

      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 might 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. And just to make it a little tougher on me, I will do it even if you cover up as many coins in the row as you like, from either end, so that I won’t be able to tell how many there are in the row.

      Impossible, right? Care to try to figure it out? I’ll come back to you on this, but not right away.

      The second thing that I think might be relevant happened some twenty years later, when I found myself for the first time in my life spending a few weeks in the island empire of Japan. I was there as a guest of Japanese science-fiction fandom, and so was Brian Aldiss, representing Britain, Yuli Kagarlitski, representing what then was still the Union of Soviet Socialist Republics, Judith Merril, representing Canada, and Arthur C. Clarke, representing Sri Lanka and most of the rest of the inhabited parts of the earth. Along with a contingent of Japanese writers and editors, the bunch of us had been touring Japanese cities, lecturing, being interviewed, and, on request, showing our silly sides. (Arthur did a sort of Sri Lankan version of a Hawaiian hula. Brian got involved in trying to pronounce a long list of Japanese words, most of which—for our hosts loved a good prank—turned out to be violently obscene. I won’t tell you what I did.) For a reward we were all treated to a decompressing weekend on Lake Biwa, where we lounged about in our kimonos and depleted the hotel’s bar.

      We spent most of the time catching one another up on what we’d been doing since the last time we had been together. I thought Judy Merril had the most interesting story to tell. She had come early to Japan, and had sneaked a couple of days in Hiroshima before the rest of us had arrived. She was good at describing things, too, and she kept us interested while she told us what she had seen. Well, everyone knows about the twisted ironwork the Japanese preserved as a memorial when every other part of that building had been blown away by that first-ever-deployed-in-anger nuclear bomb, and about the melted-down face on the stone Buddha. And everyone knows about—the one that nobody can forget once that picture enters their minds—the shadow of a man that had been permanently etched, onto the stone stairs where he had been sitting, by the intolerably brilliant nuclear blast from the overhead sky.

      “That must have been bright,” someone said—I think Brian.

      Arthur said, “Bright enough that it could have been seen by a dozen nearby stars by now.”

      “If anyone lives there to be looking,” someone else said—I think it was me.

      And, we agreed, maybe someone might indeed be looking… or at least it was pretty to think so.

      As to those mathematical parlor tricks:

      I don’t think I should explain them to you just yet, but I promise that before this book is ended, someone will.

      That someone will probably be a bright young man named Ranjit Subramanian, whom you are bound to meet in just a few pages.

      After all, this book is basically Ranjit’s story.

       THE THIRD PREAMBLE

      Atmospheric Testing

      In the spring of the year 1946, in a (previously) unspoiled South Pacific atoll named Bikini, the American navy put together a fleet of ninety-odd vessels. They were battleships, cruisers, destroyers, submarines, and assorted support craft, and they came from many sources. Some were captured German or Japanese ships, the spoils of battle from the recently ended World War II; most were war-weary or technologically outmoded American vessels.

      This fleet was not meant to sail off into a giant naval battle against anyone, or indeed to go anywhere at all. Bikini Atoll was the vessels’ last stop. The reason the fleet had been assembled was simply so