Cryptonomicon

Lawrence climbed down the stairs and got on his bicycle and rode through the Pine Barrens. Before long he came to a road that led in the general direction of the light. Most of the time he could not see anything, not even the road, but after a couple of hours the glow bouncing off the low cloud layer lit up flat stones in the road, and turned the barrens' wandering rivulets into glowing crevices.

The road began to tend in the wrong direction and so Lawrence cut directly into the woods, because he was very close now, and the light in the sky was strong enough that he could see it through the sparse carpet of scrubby pines--black sticks that appeared to have been burned, though they hadn't. The ground had turned into sand, but it was damp and compacted, and his bicycle had fat tires that rode over it well. At one point he had to stop and throw the bike over a barbed-wire fence. Then he broke out of the sticks and onto a perfectly flat expanse of white sand, stitched down with tufts of beach grass, and just then he was dazzled by a low fence of quiet steady flames that ran across a part of the horizon about as wide as the harvest moon when it sinks into the sea. Its brightness made it difficult to see anything else--Lawrence kept riding into little ditches and creeks that meandered across the flats. He learned not to stare directly at the flames. Looking off to the sides was more interesting anywa y: the table-land was marked at wide intervals by the largest buildings he had ever seen, cracker-box structures built by Pharaohs, and in the mile-wide plazas between them, gnomons of triangulated steel were planted in wide stances: the internal skeletons of pyramids. The largest of these pierced the center of a perfectly circular railway line a few hundred feet in diameter: two argent curves scored on the dull ground, interrupted in one place where the tower's shadow, a stopped sundial, told the time. He rode by a building smaller than the others, with oval tanks standing next to it. Steam murmured from valves on the tops of the tanks, but instead of rising into the air it dribbled down the sides and struck the ground and spread out, coating the sea-grass with jackets of silver.

A thousand sailors in white were standing in a ring around the long flame. One of them held up his hand and waved Lawrence down. Lawrence came to a stop next to the sailor and planted one foot on the sand to steady himself. He and the sailor stared at each other for a moment and then Lawrence, who could not think of anything else, said, ``I am in the Navy also.'' Then the sailor seemed to make up his mind about something. He saluted Lawrence through, and pointed him towards a small building off to the side of the fire.

The building looked only like a wall glowing in the firelight, but sometimes a barrage of magnesium blue light made its windowframes jump out of the darkness, a rectangular lightning-bolt that echoed many times across the night. Lawrence started pedaling again and rode past that building: a spiraling flock of alert fedoras, prodding at slim terse notebooks with stately Ticonderogas, crab-walking photogs turning their huge chrome daisies, crisp rows of people sleeping with blankets over their faces, a sweating man with Brilliantined hair chalking umlauted names on a blackboard. Finally coming around this building he smelled hot fuel oil, felt the heat of the flames on his face and saw beach-glass curled toward it and desiccated.

He stared down upon the world's globe, not the globe fleshed with continents and oceans but only its skeleton: a burst of meridians, curving backwards to cage an inner dome of orange flame. Against the light of the burning oil those longitudes were thin and crisp as a draftsman's ink-strokes. But coming closer he saw them resolve into clever works of rings and struts, hollow as a bird's bones. As they spread away from the pole they sooner or later began to wander, or split into bent parts, or just broke off and hung in the fire oscillating like dry stalks. The perfect geometry was also mottled, here and there, by webs of cable and harnesses of electrical wiring. Lawrence almost rode over a broken wine bottle and decided he should now walk, to spare his bicycle's tires, so he laid the bike down, the front wheel covering an aluminum vase that appeared to have been spun on a lathe, with a few charred roses hanging out of it. Some sailors had joined their hands to form a sort of throne, and were bearing al ong a human-shaped piece of charcoal dressed in a coverall of immaculate asbestos. As they walked the toes of their shoes caught in vast, ramified snarls of ropes and piano-wires, cables and wires, creative furtive movements in the grass and the sand dozens of yards every direction. Lawrence began planting his feet very thoughtfully one in front of the other, trying to measure the greatness of what he had come and seen. A rocket-shaped pod stuck askew from the sand, supporting an umbrella of bent-back propellers. The duralumin struts and catwalks rambled on above him for miles. There was a suitcase spilled open, with a pair of women's shoes displayed as if in the window of a downtown store, and a menu that had been charred to an oval glow, and then some tousled wall-slabs, like a whole room that had dropped out of the sky--these were decorated, one with a giant map of the world, great circles arcing away from Berlin to pounce on cities near and far, and another with a photograph of a famous, fat German in a u niform, grinning on a flowered platform, the giant horizon of a new Zeppelin behind him.

After a while he stopped seeing new things. Then he got on his bicycle and rode back through the Pine Barrens. He got lost in the dark and so didn't find his way back to the fire tower until dawn. But he didn't mind being lost because while he rode around in the dark he thought about the Turing machine. Finally he came back to the shore of the pond where they had camped. The dawn-light shining on the saucer of calm reddish water made it look like a pool of blood. Alan Mathison Turing and Rudolf von Hacklheber were lying together like spoons on the shore, still smudged a little bit from their swim yesterday. Lawrence started a little fire and made some tea and they woke up eventually.

``Did you solve the problem?'' Alan asked him.

``Well you can turn that Universal Turing Machine of yours into any machine by changing the presets--''

``Presets?''

``Sorry, Alan, I think of your U.T.M. as being kind of like a pipe organ.''

``Oh.''

``Once you've done that, anyway, you can do any calculation you please, if the tape is long enough. But gosh, Alan, making a tape that's long enough, and that you can write symbols on, and erase them, is going to be sort of tricky--Atanasoff's capacitor drum would only work up to a certain size--you'd have to--''

``This is a digression,'' Alan said gently.

``Yeah, okay, well--if you had a machine like that, then any given preset could be represented by a number--a string of symbols. And the tape that you would feed into it to start the calculation would contain another string of symbols. So it's Go[audel's proof all over again--if any possible combination of machine and data can be represented by a string of numbers, then you can just arrange all of the possible strings of numbers into a big table, and then it turns into a Cantor diagonal type of argument, and the answer is that there must be some numbers that cannot be computed.''

``And ze Entscheidungsproblem?'' Rudy reminded him.

``Proving or disproving a formula--once you've encrypted the formula into numbers, that is--is just a calculation on that number. So it means that the answer to the question is, no! Some formulas cannot be proved or disproved by any mechanical process! So I guess there's some point in being human after all!''

Alan looked pleased until Lawrence said this last thing, and then his face collapsed. ``Now there you go making unwarranted assumptions.''

``Don't listen to him, Lawrence!'' Rudy said. ``He's going to tell you that our brains are Turing machines.''

``Thank you, Rudy,'' Alan said patiently. ``Lawrence, I submit that our brains are Turing machines.''

``But you proved that there's a whole lot of formulas that a Turing machine can't process!''

``And you have proved it too, Lawrence.''

``But don't you think that we can do some things that a Turing machine couldn't?''

``Godel agrees with you, Lawrence,'' Rudy put in, ``and so does Hardy.''

``Give me one example,'' Alan said.

``Of a noncomputable function that a human can do, and a Turing machine can't?''

``Yes. And don't give me any sentimental nonsense about creativity. I believe that a Universal Turing Machine could show behaviors that we would construe as creative.''

``Well, I don't know then... I'll try to keep my eye out for that kind of thing in the future.''

But later, as they were riding back towards Princeton, he said, ``What about dreams?''

``Like those angels in Virginia?''

``I guess so.''

``Just noise in the neurons, Lawrence.''

``Also I dreamed last night that a zeppelin was burning.''

Soon, Alan got his Ph.D. and went back to England. He wrote Lawrence a couple of letters. The last of these stated, simply, that he would not be able to write Lawrence any more letters ``of substance'' and that Lawrence should not take it personally. Lawrence perceived right away that Alan's society had put him to work doing something useful--probably figuring out how to keep it from being eaten alive by certain of its neighbors. Lawrence wondered what use America would find for him.

He went back to Iowa State, considered changing his major to mathematics, but didn't. It was the consensus of all whom he consulted that mathematics, like pipe-organ restoration, was a fine thing, but that one needed some way to put bread on the table. He remained in engineering and did more and more poorly at it until the middle of his senior year, when the university suggested that he enter a useful line of work, such as roofing. He walked straight out of college into the waiting arms of the Navy.

They gave him an intelligence test. The first question on the math part had to do with boats on a river: Port Smith is 100 miles upstream of Port Jones. The river flows at 5 miles per hour. The boat goes through water at 10 miles per hour. How long does it take to go from Port Smith to Port Jones? How long to come back?