Cryptonomicon

'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 Godel'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 tiding 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?

Lawrence immediately saw that it was a trick question. You would have to be some kind of idiot to make the facile assumption that the current would add or subtract 5 miles per hour to or from the speed of the boat. Clearly, 5 miles per hour was nothing more than the averagespeed. The current would be faster in the middle of the river and slower at the banks. More complicated variations could be expected at bends in the river. Basically it was a question of hydrodynamics, which could be tackled using certain well-known systems of differential equations. Lawrence dove into the problem, rapidly (or so he thought) covering both sides of ten sheets of paper with calculations. Along the way, he realized that one of his assumptions, in combination with the simplified Navier Stokes equations, had led him into an exploration of a particularly interesting family of partial differential equations. Before he knew it, he had proved a new theorem. If that didn't prove his intelligence, what would?

Then the time bell rang and the papers were collected. Lawrence managed to hang onto his scratch paper. He took it back to his dorm, typed it up, and mailed it to one of the more approachable math professors at Princeton, who promptly arranged for it to be published in a Parisian mathematics journal.

Lawrence received two free, freshly printed copies of the journal a few months later, in San Diego, California, during mail call on board a large ship called the U.S.S. Nevada.The ship had a band, and the Navy had given Lawrence the job of playing the glockenspiel in it, because their testing procedures had proven that he was not intelligent enough to do anything else.

The sack of mail carrying Lawrence's contribution to the mathematical literature arrived just in the nick of time. Lawrence's ship, and quite a few of her sisters, had until then been based in California. But at just this moment, all of them were transferred to some place called Pearl Harbor, Hawaii, in order to show the Nips who was boss.

Lawrence had never really known what he wanted to do with his life, but he quickly decided that being glockenspiel player on a battleship in Hawaii during peacetime was a long way from the worst life you could possibly have. The harshest part of the job was sometimes having to sit or march in very warm conditions, and enduring occasional fluffed notes by other band members. He had abundant free time, which he spent working on a series of new theorems in the field of information theory. The field had been invented and pretty much encompassed by his friend Alan, but there was much detail work to be done. He and Alan and Rudy had sketched out a general plan of what needed to be proved or disproved. Lawrence tore through the list. He wondered what Alan and Rudy were up to in Britain and Germany, but he couldn't write to them and find out, so he kept his work to himself. When he wasn't playing the glockenspiel or working out theorems, there were bars and dances to go to. Waterhouse did some penis work of his own, got the clap, had it cured[1], bought condoms. All of the sailors did this. They were like three-year olds who shove pencils in their ears, discover that it hurts, and stop doing it. Lawrence's first year went by almost instantly. Time just blazed by. Nowhere could be sunnier, more relaxing, than Hawaii.

Chapter 2 NOVUS ORDO SECLORUM

'Filipinos are a warm, gentle, caring, giving people,' Avi says, 'which is a good thing since so many of them carry concealed weapons.'

Randy is in Tokyo's airport, ambling down a concourse with a slowness that is infuriating to his fellow travelers. They have all spent the last half-day strapped into bad chairs, stuffed into an aluminum tube aslosh with jet fuel. Over the safety-engineered nubs molded into the jetway floor, their rolling suitcases drone like fighter planes. They graze the backs of his knees as they bank around his husky columnar body. Randy is holding his new GSM phone to the side of his head. Supposedly it works anywhere in the world, except for the United States. This is his first chance to try it out.

'You sound clear as a bell,' Avi says. 'How was the flight over?'

'All right,' Randy says. 'They had one of those animated maps up on the video screen.'

Avi sighs. 'All the airlines have those now,' he announces monotonically.

'The only feature between San Francisco and Tokyo was Midway Island.'

'So?'

'It kind of hung there for hours. MIDWAY. Mute embarrassment all around.'

Randy reaches the departure gate for Manila, and pauses to admire a five-foot-wide high-definition TV set