Cryptonomicon

Al delicately asked him, one day, if Lawrence would terribly mind calling him by his full and proper name, which was Alan and not Al. Lawrence apologized and said he would try very hard to keep it in mind.

One day a couple of weeks later, as the two of them sat by a running stream in the woods above the Delaware Water Gap, Alan made some kind of an outlandish proposal to Lawrence involving penises. It required a great deal of methodical explanation, which Alan delivered with lots of blushing and stuttering. He was ever so polite, and several times emphasized that he was acutely aware that not everyone in the world was interested in this sort of thing.

Lawrence decided that he was probably one of those people.

Alan seemed vastly impressed that Lawrence had paused to think about it at all and apologized for putting him out. They went directly back to a discussion of computing machines, and their friendship continued unchanged. But on their next bicycle ride-an overnight camping trip to the Pine Barrens-they were joined by a new fellow, a German named Rudy von something-or-other.

Alan and Rudy's relationship seemed closer, or at least more multilayered, than Alan and Lawrence's. Lawrence concluded that Alan's penis scheme must have finally found a taker.

It got Lawrence to thinking. From an evolution standpoint, what was the point of having people around who were not inclined to have offspring? There must be some good, and fairly subtle, reason for it.

The only thing he could work out was that it was groups of people-societies-rather than individual creatures, who were now trying to out-reproduce and/or kill each other, and that, in a society, there was plenty of room for someone who didn't have kids as long as he was up to something useful.

Alan and Rudy and Lawrence rode south, anyway, looking for the Pine Barrens. After a while the towns became very far apart, and the horse farms gave way to a low stubble of feeble, spiny trees that appeared to extend all the way to Florida-blocking their view, but not the head wind. 'Where are the Pine Barrens I wonder?' Lawrence asked a couple of times. He even stopped at a gas station to ask someone that question. His companions began to make fun of him.

'Vere are ze Pine Barrens?' Rudy inquired, looking about quizzically.

'I should look for something rather barren-looking, with numerous pine trees,' Alan mused.

There was no other traffic and so they had spread out across the road to pedal three abreast, with Alan in the middle.

'A forest, as Kafka would imagine it,' Rudy muttered.

By this point Lawrence had figured out that they were, in fact, in the Pine Barrens. But he didn't know who Kafka was. 'A mathematician?' he guessed.

'Zatis a scary sing to sink of,' Rudy said.

'He is a writer,' Alan said. 'Lawrence, please don't be offended that I ask you this, but: do you recognize any other people's namesat all? Other than family and close friends, I mean.'

Lawrence must have looked baffled. 'I'm trying to figure out whether it all comes from in here,' Alan said, reaching out to rap his knuckles on the side of Lawrence's head, 'or do you sometimes take in new ideas from other human beings?'

'When I was a little boy, I saw angels in a church in Virginia,' Lawrence said, 'but I think that they came from inside my head.'

'Very well,' Alan said.

But later Alan had another go at it. They had reached the fire lookout tower and it had been a thunderous disappointment: just an alienated staircase leading nowhere, and a small cleared area below that was glittery with shards of liquor bottles. They pitched their tent by the side of a pond that turned out to be full of rust-colored algae that stuck to the hairs on their bodies. Then there was nothing left to do but drink schnapps and talk about math.

Alan said, 'Look, it's like this: Bertrand Russell and another chap named Whitehead wrote Principia Mathematica.

'Now I know you're pulling my leg,' Waterhouse said. 'Even I know that Sir Isaac Newton wrote that.'

'Newton wrote a differentbook, alsocalled Principia Mathematica, which isn't reallyabout mathematics at all; it's about what we would todaycall physics.'

'Then why did he call it Principia Mathematica?'

'Because the distinction between mathematics and physics wasn't especially clear in Newton's day-'

'Or maybe even in zis day,' Rudy said.

'-which is directly relevant to what I'm talking about,' Alan continued. 'I am talking about Russell's P.M., in which he and Whitehead started absolutely from scratch, I mean from nothing, and built it all up-all mathematics- from a small number of first principles. And why I am telling you this, Lawrence, is that-Lawrence! Pay attention!'

'Hmmm?'

'Rudy-take this stick, here-that's right-and keep a close eye on Lawrence, and when he gets that foggy look on his face, poke him with it!'

'Zis is not an English school, you can't do zese kind of sing.'

'I'm listening,' Lawrence said.

'What came out of P.M., which was terrifically radical, was the ability to say that all of math, really, can be expressed as a certain ordering of symbols.'

'Leibniz said it a long time before zen!' protested Rudy.

'Er, Leibniz invented the notation we use for calculus, but-'

'I'm not talking about zat!'

'And he invented matrices, but-'

'I'm not talking about zat eezer!'

'And he did some work with binary arithmetic, but-'

'Zat is completely different!'

'Well, what the hell are you talking about, then, Rudy?'

'Leibniz invented ze basic alphabet-wrote down a set of symbols, for expressing statements about logic.'

'Well, I wasn't aware that Herr Leibniz counted formal logic among his interests, but-'

'Of course! He wanted to do what Russell and Whitehead did, except not just with mathematics, but with everything in ze whole world!'

'Well, from the fact that you are the only man on the planet, Rudy, who seems to know about this undertaking of Leibniz's, can we assume that he failed?'

'Youcan assumeanything that pleases your fancy,Alan,' Rudy responded, 'but Iam a mathematician and I do not assume anything.'

Alan sighed woundedly, and gave Rudy a Significant Look which Waterhouse assumed meant that there would be trouble later. 'If I may just make some headway, here,' he said, 'all I'm really trying to get you to agree on, is that mathematics can be expressed as a series of symbols,' (he snatched the Lawrence-poking stick and began drawing things like + = 3) [square root of -1][pi] in the dirt) 'and frankly I could not care less whether they happen to be Leibniz's symbols, or Russell's, or the hexagrams of the I Ching....'

'Leibniz was fascinated by the I Ching!' Rudy began.

'Shut up about Leibniz for a moment, Rudy, because look here: You-Rudy-and I are on a train, as it were, sitting in the dining car, having a nice conversation, and that train is being pulled along at a terrific clip by certain locomotives named The Bertrand Russell and Riemann and Euler and others. And our friend Lawrence is running alongside the train, trying to keep up with us-it's not that we're smarter than he is, necessarily, but that he's a farmer who didn't get a ticket. And I, Rudy, am simply reaching out through the open window here, trying to pull him onto the fucking train with us so that the three of us can have a nice little chat about mathematics without having to listen to him panting and gasping for breath the whole way.'