As nightmarishly lethal, memetically programmed death-machines went, these were the nicest you could ever hope to meet. In the tradition of his namesake (the Puritan writer John Bunyan, who spent much of his life in jail, or trying to avoid it) the Rev. Waterhouse did not preach in any one place for long. The church moved him from one small town in the Dakotas to another every year or two. It is possible that Godfrey found the lifestyle more than a little alienating, for, sometime during the course of his studies at Fargo Congregational College, he bolted from the fold and, to the enduring agony of his parents, fell into worldly pursuits, and ended up, somehow, getting a Ph.D. in Classics from a small private university in Ohio. Academics being no less nomadic than Congregational preachers, he took work where he could find it. He became a Professor of Greek and Latin at Bolger Christian College (enrollment 322) in West Point, Virginia, where the Mattaponi and Pamunkey Rivers came together to form the estuarial James, and the loathsome fumes of the big paper mill permeated every drawer, every closet, even the interior pages of books. Godfrey’s young bride, nee Alice Pritchard, who had grown up following her itinerant-preacher father across the vastnesses of eastern Montana—where air smelt of snow and sage—threw up for three months. Six months later she gave birth to Lawrence Pritchard Waterhouse.
The boy had a peculiar relationship with sound. When a fire engine passed, he was not troubled by the siren’s howl or the bell’s clang. But when a hornet got into the house and swung across the ceiling in a broad Lissajous, droning almost inaudibly, he cried in pain at the noise. And if he saw or smelled something that scared him, he would clap his hands over his ears.
One noise that troubled him not at all was the pipe organ in the chapel at Bolger Christian College. The chapel itself was nothing worth mentioning, but the organ had been endowed by the paper mill family and would have sufficed for a church four times the size. It nicely complemented the organist, a retired high school math teacher who felt that certain attributes of the Lord (violence and capriciousness in the Old Testament, majesty and triumph in the New) could be directly conveyed into the souls of the enpewed sinners through a kind of frontal sonic impregnation. That he ran the risk of blowing out the stained-glass windows was of no consequence since no one liked them anyway, and the paper mill fumes were gnawing at the interstitial lead. But after one little old lady too many staggered down the aisle after a service, reeling from tinnitus, and made a barbed comment to the minister about the exceedingly dramatic music, the organist was replaced.
Nevertheless, he continued to give lessons on the instrument. Students were not allowed to touch the organ until they were proficient at the piano, and when this was explained to Lawrence Pritchard Waterhouse, he taught himself, in three weeks, how to play a Bach fugue, and signed up for organ lessons. Since he was only five years old at the time, he was unable to reach both the manuals and the pedals, and had to play standing—or rather strolling, from pedal to pedal.
When Lawrence was twelve, the organ broke down. That paper mill family had not left any endowment for maintenance, so the math teacher decided to have a crack at it. He was in poor health and required a nimble assistant: Lawrence, who helped him open up the hood of the thing. For the first time in all those years, the boy saw what had been happening when he had been pressing those keys.
For each stop—each timbre, or type of sound, that the organ could make (viz. blockflöte, trumpet, piccolo)—there was a separate row of pipes, arranged in a line from long to short. Long pipes made low notes, short high. The tops of the pipes defined a graph: not a straight line but an upward-tending curve. The organist/math teacher sat down with a few loose pipes, a pencil, and paper, and helped Lawrence figure out why. When Lawrence understood, it was as if the math teacher had suddenly played the good part of Bach’s Fantasia and Fugue in G Minor on a pipe organ the size of the Spiral Nebula in Andromeda—the part where Uncle Johann dissects the architecture of the Universe in one merciless descending ever-mutating chord, as if his foot is thrusting through skidding layers of garbage until it finally strikes bedrock. In particular, the final steps of the organist’s explanation were like a falcon’s dive through layer after layer of pretense and illusion, thrilling or sickening or confusing depending on what you were. The heavens were riven open. Lawrence glimpsed choirs of angels ranking off into geometrical infinity.
The pipes sprouted in parallel ranks from a broad flat box of compressed air. All of the pipes for a given note—but belonging to different stops—lined up with each other along one axis. All of the pipes for a given stop—but tuned at different pitches—lined up with each other along the other, perpendicular axis. Down there in the flat box of air, then, was a mechanism that got air to the right pipes at the right times. When a key or pedal was depressed, all of the pipes capable of sounding the corresponding note would speak, as long as their stops were pulled out.
Mechanically, all of this was handled in a fashion that was perfectly clear, simple, and logical. Lawrence had supposed that the machine must be at least as complicated as the most intricate fugue that could be played on it. Now he had learned that a machine, simple in its design, could produce results of infinite complexity.
Stops were rarely used alone. They tended to be piled on top of each other in combinations that were designed to take advantage of the available harmonics (more tasty mathematics here!). Certain combinations in particular were used over and over again. Lots of blockflötes, in varying lengths, for the quiet Offertory, for example. The organ included an ingenious mechanism called the preset, which enabled the organist to select a particular combination of stops—stops he himself had chosen—instantly. He would punch a button and several stops would bolt out from the console, driven by pneumatic pressure, and in that instant the organ would become a different instrument with entirely new timbres.
The next summer both Lawrence and Alice, his mother, were colonized by a distant cousin—a stupendous badass of a virus. Lawrence escaped from it with an almost imperceptible tendency to drag one of his feet. Alice wound up in an iron lung. Later, unable to cough effectively, she got pneumonia and died.
Lawrence’s father, Godfrey, freely confessed that he was not equal to the burdens now laid on his shoulders. He resigned from his position at the small college in Virginia and moved, with his son, to a small house in Moorhead, Minnesota, next door to where Bunyan and Blanche had settled. Later he got a job teaching at a nearby normal school.
At this point, all of the responsible adults in Lawrence’s life seemed to arrive at a tacit agreement that the best way to raise him—certainly the easiest—was to leave him alone. On the rare occasions when Lawrence requested adult intervention in his life, he was usually asking questions that no one could answer. At the age of sixteen, having found nothing in the local school system to challenge him, Lawrence Pritchard Waterhouse went off to college. He matriculated at Iowa State College, which among other things was the site of a Naval ROTC installation in which he was forcibly enrolled.
The Iowa State Naval ROTC had a band, and was delighted to hear that Lawrence had an interest in music. Since it was hard to drill on the deck of a dreadnought while playing a pipe organ, they issued him a glockenspiel and a couple of little dingers.
When not marching back and forth on the flood plain of the Skunk River making loud dinging noises, Lawrence was majoring in mechanical engineering. He ended up doing poorly in this area because he had fallen in with a Bulgarian professor named John Vincent Atanasoff and his graduate student, Clifford Berry, who were building a machine that was intended to automate the solution of some especially tedious differential equations.
The basic problem for Lawrence was that he was lazy. He had figured out that everything was much simpler if, like Superman with his X-ray vision, you just stared through the cosmetic distractions and saw the underlying mathematical skeleton. Once you found the math in a thing, you knew everything about it, and you could manipulate it to your heart’s content with nothing more than a
pencil and a napkin. He saw it in the curve of the silver bars on his glockenspiel, saw it in the catenary arch of a bridge and in the capacitor-studded drum of Atanasoff and Berry’s computing machine. Actually pounding on the glockenspiel, riveting the bridge together, or trying to figure out why the computing machine wasn’t working were not as interesting to him.
Consequently he got poor grades. From time to time, though, he would perform some stunt on the blackboard that would leave his professor weak in the knees and the other students baffled and hostile. Word got around.
At the same time, his grandmother Blanche was invoking her extensive Congregational connections, working the angles on Lawrence’s behalf, totally unbeknownst to him. Her efforts culminated in triumph when Lawrence was awarded an obscure scholarship, endowed by a St. Paul oat-processing heir, whose purpose was to send Midwestern Congregationalists to the Ivy League for one year, which (evidently) was deemed a long enough period of time to raise their IQs by a few crucial points but not long enough to debauch them. So Lawrence got to be a sophomore in Princeton.
Now Princeton was an august school and going there was a great honor, but no one got around to mentioning either of these facts to Lawrence, who had no way of knowing. This had bad and good consequences. He accepted the scholarship with a faintness of gratitude that infuriated the oat lord. On the other hand, he adjusted to Princeton easily because it was just another place. It reminded him of the nicer bits of Virginia, and there were some nice pipe organs in town, though he was not all that happy with his engineering homework of bridge-designing and sprocket-cutting problems. As always, these eventually came down to math, most of which he could handle easily. From time to time he would get stuck, though, which led him to the Fine Hall: the headquarters of the Math Department.
There was a motley assortment of fellows wandering around in Fine Hall, many sporting British or European accents. Administratively speaking, many of these fellows were not members of the Math Department at all, but a separate thing called IAS, which stood for Institute for Advanced something-or-other. But they were all in the same building and they all knew a thing or two about math, so the distinction didn’t exist for Lawrence.
Quite a few of these men would pretend shyness when Lawrence sought their advice, but others were at least willing to hear him out. For example: he had come up with a way to solve a difficult sprocket tooth shape problem that, as normally solved by engineers, would require any number of perfectly reasonable but aesthetically displeasing approximations. Lawrence’s solution would provide exact results. The only drawback was that it would require a quintillion slide-rule operators a quintillion years to solve. Lawrence was working on a radically different approach that, if it worked, would bring those figures down to a trillion and a trillion respectively. Unfortunately, Lawrence was unable to interest anyone at Fine Hall in anything as prosaic as gears, until all of a sudden he made friends with an energetic British fellow, whose name he promptly forgot, but who had been doing a lot of literal sprocket-making himself lately. This fellow was trying to build, of all things, a mechanical calculating machine—specifically a machine to calculate certain values of the Riemann Zeta Function
where s is a complex number.
Lawrence found this zeta function to be no more and no less interesting than any other math problem until his new friend assured him that it was frightfully important, and that some of the best mathematicians in the world had been gnawing on it for decades. The two of them ended up staying awake until three in the morning working out the solution to Lawrence’s sprocket problem. Lawrence presented the results proudly to his engineering professor, who snidely rejected it, on grounds of practicality, and gave him a poor grade for his troubles.
Lawrence finally remembered, after several more contacts, that the name of the friendly Brit was Al something-or-other. Because Al was a passionate cyclist, he and Al went on quite a few bicycle rides through the countryside of the Garden State. As they rode around New Jersey, they talked about math, and particularly about machines for taking the dull part of math off their hands.
But Al had been thinking about this subject for longer than Lawrence, and had figured out that computing machines were much more than just labor-saving devices. He’d been working on a radically different sort of computing mechanism that would work out any arithmetic problem whatsoever, as long as you knew how to write the problem down. From a pure logic standpoint, he had already figured out everything there was to know about this (as yet hypothetical) machine, though he had yet to build one. Lawrence gathered that actually building machinery was looked on as undignified at Cambridge (England, that is, where this Al character was based) or for that matter at Fine Hall. Al was thrilled to have found, in Lawrence, someone who did not share this view.
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 headwind. “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.
“Zat is 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 names at 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 ch
urch 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 different book, also called Principia Mathematica, which isn’t really about mathematics at all; it’s about what we would today call 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!”