Simon is in the process of transferring the shading from one Philip’s atlas to a new one. It isn’t easy to discover why this record of the-tarmac-I-have-known he’s covered matters so much to him.
“Is it a sort of stamp album? Are you hoping to collect all the roads of Britain in it?”
“No.”
“A record of every bus journey you’ve ever made?”
“No.”
“Would you like it to be like that? Would that be the ultimate? Is it your memory? Are you being peculiar and trying to write out a sentence in bus journeys across the surface of the country?”
“No!”
One of the things I enjoy about Simon is his revulsion at my attempts to make him novelistically tidy.
Some of the pencil lines in his road atlas shoot into the sea. An amphibious bus service, was it? An inch or two free of land they start to arc, as though compensating for the curvature of the earth, and become obvious boat trips, ending up at the Isle of Man, Skye, Eigg, Wight.
Within these islands, none of the roads are shaded.
Why else would Simon have gone to those isolated spots, except to cover all roads?
“Have these islands got a mental tick beside them?”
“No.”
The sticker on the cover of the atlas said £6.99. “Actually, it was £1.99 in Budgens,” he confessed, folding the book shut, delighted at the low cost of pricelessness. Then he picked up his map again, darted glances through the windows on either side of the rail car to remember his point of departure from three dimensions, and slid back into silence.
Fretful with impatience, Simon bustled down Woking platform as fast as his duffel and gout would permit, noted with satisfaction that the local bus service was three minutes late and, worried that those minutes might suddenly pick on us instead and delay all his plans, made quickly for the center of town with me trotting behind.
The Martian is at the end of a dreary pedestrian walkway, its legs buckled with despair at finding that it’s traveled sixty million miles, the last hope of a dying civilization, and ended up in Woking. In Woking, being (as the photo shows) punched by a lamppost and chased by fake Victorian bollards.
Standing on a colored microbe, Simon admired the sculpture, consulted a street map and ate a pack of Bombay mix he’d found wandering about his bag.
“Do you like this Martian?” I asked.
“It’s all right,” he said.
“Do you like Woking?”
“H . It’s all right. When I got older, I used my grandmother as my springboard. I used her to bounce all over the Southwest.”
We walked up the hill, and through a brick gateway into a private compound of 1930s houses, set, as in the American Midwest, among redwoods. The private roads rested on grass, between daffodils; the buildings, three times the size of city houses, were stockaded by laurel hedgerows and topiary yews.
“H (with contentment) this is it, my grandmother’s house,” announced Simon.
But the moment we stepped in to look around, Simon got frightened that we were trespassing, and ran away.
*13
Saucy Miss Triangle!
* * *
The Outrage so far: An equal-sided triangle is symmetrical. It looks unchanged when you manhandle it through a third of a turn, two-thirds of a turn, or turn it all the way round.
Similar base operations can be performed on a square:
* * *
* * *
If you have the energy to perform two or more of these misdeeds at once, you can keep track of the overall effect with the help of a grid that looks like a sudoku table:
* * *
There’s another symmetry operation—nothing to do with rotations—that allows us to have our way with Triangle, and still leave it to all appearances untouched. We can flip it back to front:
Inwardly, Triangle may adjust its spectacles and primly pat its skirt, but outwardly it looks unperturbed. We record the act in our diaries by a new symbol:
Remember: this is not the triangle itself. This is what we have done to it:
The embloomered shape represents the act of turning an equal-sided triangle over:
Irregular triangles, naturally, are not so circumspect. Flip one of these misshapes over and it shows very definite signs of adjustment. Anyone watching immediately spots what you’re up to. There’s none of Triangle’s finishing-school ability to keep the secret under wraps:
If we add all the ways we can flip an equal-sided triangle—
—to the three ways we can rotate the triangle, and construct a Group Table to keep track of how all these symmetry operations interact, we get the following lumbering object:
Next, a page for ladies:
We can do a similar flipping operation with Square:
Turn off the light, flip Square over, turn the light on again, and Square looks delightfully unchanged.
Now we’re almost there. The critical, central idea—Subgroups—discovered by a French schoolboy in the nineteenth century. From this child’s revolutionary insight spring most of the complexities of Group Theory and a first glimpse of the Monster.
14
I don’t like your books, Alex. I don’t like your mother’s books either.
Simon, to the author
Humming odiously, Simon expressed satisfaction.
Hnnnnneeeuuucch, hmmm, tllahdlllah, hnnnnn.
Outside Woking, on the way back to Cambridge, we’d stopped off at a National Trust country house to listen to a concert of Beethoven sonatas. A Japanese pianist—scraped-back hair, keyboard ribs showing through the V of her dress—stepped up to the piano, bowed, sat down, stood up, smiled at the audience, smiled at the parquet floor, smiled at the portraits on the walls, sat down a third time…
The piece was the Kurfürsten Sonata in E flat major, WoO 47.
—ambled her hands into mid-air—
“The first of his posthumous sonatas,” said Simon in an attempt at a whisper.
…and hit the keys in a sprightly fashion. As you might expect from the first attempt by a corpse, the Kurfürsten is a simple piece (written, in fact, when Beethoven was thirteen, but added to the catalogue of his works only after his death). It sounds like a mouse let loose in a toy room.
Fidget maestro at other times, Simon was clamped in obedient stillness. Until cramped. Then he twisted and arched through the final bars, his eyes fixed, colorless, dead to the world, looking—hnnn!—inside himself—uuhhgh!—at his ache.
Simon has an upright piano in the back room of the Excavation, keyboard lid open and Beethoven’s Moonlight Sonata on the stand. The last time those keys made a noise of any kind was eight years ago, when Simon accidentally knocked the chessboard off the top of the piano and the avalanche of pieces cudgeled a few notes on the way down.
Beethoven is Simon’s favorite composer. He enjoys the “unexpected modulation” and the fact that “as with impressionism, the melody does not include every note.” His cassette tapes, stained heavily with brown splotches, are arranged in two rows, neatly: Beethoven Sonatas Nos. 14, 22 and 29, played by Sviatoslav Richter; Beethoven Klaviersonaten, Nos. 11, 21, 27 (Buchbinder); Beethoven Sonatas, Nos. 28 and 29 (Maria Yudina); Beethoven, Violin Concerto in D (Milstein); Beethoven, Symphony No. 3 in E flat; Beethoven, Piano Sonatas Ops. 2, 49, 81a (Alfred Brendel); Beethoven, Symphonies 1 and 6 (Norrington); Beethoven, Piano Sonatas, Moonlight, Appassionata, Pathétique. Eight Gilbert and Sullivans; two Flanders and Swanns; and one (which I still haven’t got round to investigating) called “Mud in Your Eye”!
(“I didn’t know I had that,” says Simon. “It’s about canals.”)
Simon doesn’t listen to music at home. He doesn’t listen to the radio at home. Home is for silence.
During the interval, Simon fell into conversation with a retired piano teacher. Bad pianists play “along a line,” she said. They don’t stray out into nuance, interpretation and expression. They get trapped, like tired artists and tired biographers and
tired mathematicians, in a rut. It seemed to her that one of the three pieces this afternoon had been played a little “along a line.” Doesn’t Simon agree?
But Simon never likes to be rude about anyone. Or to make requested aesthetic judgments. So he hurriedly descended into squirms. He had heard the Kurfürsten, he confessed, “played faster,” then he edged toward the refreshment table.
“When I was at a conference in Santa Cruz,” he popped back a minute later, “I asked a German there if Beethoven’s ‘Moonlight Sonata’ could equally well be translated as the ‘Moonshine Sonata,’ and he said that it could.”
“My girlfriend,” I observed, “saw an art installation in Chichester, at which they beamed a recording of the Moonlight Sonata at the moon, let it bounce off the surface, then replayed the noise that was reflected back to earth after it had been picked up by a satellite dish. They said it was the Moonlight Sonata, as performed by the moon. She said it sounded jolly peculiar. All the bumps and lumps of the moon had distorted it. I don’t think, Simon, you’re meant to take five chocolate biscuits.”
Just because Simon compares his favorite composer to impressionism, it doesn’t follow that he likes impressionism. He doesn’t. He doesn’t like any art, with the exception of “some modern stuff,” which turns out (predictably, for a mathematician) to mean M. C. Escher. On his jaunts he occasionally inserts himself into a gallery and scurries around the walls, nodding off whatever paintings he passes, “Because one ought to,” but “I don’t enjoy it.” In particular, he doesn’t like portraits or cartoons.
His own early artworks, produced when he was ten years old, are startling: exuberant, abstract, artistically poised, made from lurid combinations of tissue paper. I discovered them in the Excavation squeezed between the groyne corner cupboard and the chest of drawers with the returnable Tango bottles. What makes them especially interesting is that the shapes he uses for these compositions are the shapes we’ve been looking at in the mathematical sections of this book: the founding forms of Group Theory.
Untitled #1, Yellow, red and brown squares. Mount: evening-blue sugar paper.
Untitled #2, Multicolored squares and circles and sticky shapes. Mount: shocking-orange sugar paper.
The emphases on the clam-like, suggestive hiddenness of patterns (Untitled #1); interdependence (Untitled #2); and balance, not simple regularity (Untitled #3, below), capture the essence of Simon’s eerie mathematical insights fifteen years later.
Untitled #3, Yellow (circle), pea green (square), on rectangular field of blue shades. Mount: shocking-orange sugar paper.
After the Beethoven concert ended, the retired piano teacher drove us to a village train station. Kind gestures such as this are always falling in Simon’s way, but he never knows what to do at the end of them.
“U ,” he grunted when we got out of the woman’s car.
“A .” His eyes tightened, his shoulders stiff with impending duty.
“H .” He backed up—tried to remember what the duty was.
“Thank you,” he recollected at last, but only because I’d said it a second before. “Goodbye,” he added, overhearing me again. “As I say…A …can we go now?”
He bolted off to the platform.
“There! That’s where I first picked up…”
I glanced up from my seat in the train and caught the last glimpse of a platform with a picket fence and hanging baskets rattling past in the evening light.
“…the magazine Thirdrail. Published by British Rail Southern Region, to encourage rail travel.” It was a tough objective. The issue Simon discovered in the ticket hall as a little boy was Number 6, the last produced. After that, the editors gave up the battle against the rise of car travel: the magazine folded.
“Here!”
A second small station: two guards were watering a splosh of tree in a cask. “Merry Makers Mystery Tours!” shouted Simon, as the train went in a tunnel and the batter of rails was replaced by an oceanic rush of annoyed air. “My first leaflet about them: that’s where I picked it up. Kept me occupied during the 1970s.”
For twenty miles around his grandmother’s house in Woking the countryside is marked for Simon by autobiographical signposts: asexual, calm and related to paper.
“Incidentally, if you do have to use the derogatory word ‘excavation’ to describe my basement, you could emphasize the sense in which it is very apt, namely, that you have excavated a lot of information about me there. Then you could feed in something about my interest in archaeology, and maybe you could mention Woking Palace, in view of the importance of Woking in my life—saying that, during all the decades during which I visited Woking, I never heard of it!”
At Kingston upon Thames, he fell asleep.
Power cables, veering and swooping. Over the points they hit jumbles, great knottings, new cables crashing in from all sides, frenzied dogfights—and out flashed two or three solitary lines—free! unencumbered!—and against the sunset the joyous lunges alongside our train car began again.
I felt a biographer’s contentment. What had we achieved today? Seen a statue; listened to sonatas; run away from a house. Not much. But something in these small events seemed to characterize Simon and his by-and-large unremarkable, happy life. I didn’t want to think closely about what this something was. Expression might have done it harm.
I took out a book I’d been reading: Havelock Ellis’s A Study of British Genius. Havelock Ellis formed his conclusions about the origins of genius by selecting 1,030 “eminent men” from The Dictionary of National Biography and subjecting their entries to a vigorous attack of statistical analysis, investigating the intellectual influence of parentage, upbringing, schooling, place of birth, number of siblings and place in sequence, illness early in life. With one exception, none of his conclusions applies usefully to Simon. He believed men of genius were often unhappy or ill as children (Simon was not); were averse to ordinary work (which Simon certainly is, but so are burglars and politicians); had one brilliant parent or at least one who was dead (Simon had neither, although his mother was clearly much brighter than his father); and noted Aristotle’s insistence that all men of ability are melancholy (Simon is not) and have a mixture of insanity in them (Simon does not).
The genius-insanity cliché is so absurd it’s worth quoting Havelock Ellis’s dismissal:
“Among poets and men of letters, of an order below the highest, insanity has been somewhat apt to occur,” he agreed, but not among the truly great, or mathematicians. Antiquarians, he added, possess “marked eccentricity almost amounting to insanity,” but these people turn out to be otherwise so low on brainpower “that the question of their inclusion in my list has been a frequent source of embarrassment.”
Havelock Ellis’s mentor, the brilliant sociologist Cesare Lombroso, thought prodigies like Simon were related to murderers and bank robbers, a morally degenerate form of mankind.
Simon’s only mental pathology is an excessive desire to obey local housing law.
If Simon were in charge of anything, it would grind to a halt under his honesty.
Simon says he’s a fluke of genetics. Every birth is a gamble by Nature, a throwing in the air of infinite possibilities. The good freaks that result are as random as the bad. In Simon’s case, “the molecules settled in my favor. Neither of my brothers is particularly intelligent.”
(One of these brothers once tried to convince me he’d scored 120 percent in a school exam.
“But you can’t score 120 percent,” I’d complained.
“They had to hush it up.”)
In “Why productivity fades with age: The crime-genius connection” (2002), Satoshi Kanazawa applied Havelock Ellis’s technique to The Biographical Dictionary of Scientists—but this article is such garbage! Kanazawa makes a couple of guesses about the high point of each scientist’s genius, shows that the ages over which these pinnacles of brilliance occur follow a similar pattern to the ages at which criminals perform their worst deeds, and then—his b
izarre conclusion?
That geniuses and gangsters have the same underlying motivation: the urge to seduce women.
Simon is not interested in women.
After 300 pages, covering the fourth to the nineteenth centuries and including the additional reading of 300 further biographies, the only common characteristic of genius that Havelock Ellis could find that is relevant to Simon is that these brainy men all have gout.
Moreover, the eminence of these gouty subjects is as notable as their number. They include Milton, Harvey, Sydenham, Newton, Gibbon, Fielding, Hunter, Johnson, Congreve, the Pitts, J. Wesley, Landor, W. R. Hamilton and C. Darwin, while the Bacons were a gouty family. It would probably be impossible to match the group of gouty men of genius, for varied and pre-eminent intellectual ability, by any combination of non-gouty individuals on our list. It may be added that these gouty men of genius have frequently been eccentric, often very irascible…
15
When Noël was still two the doctor pronounced that his brain was much in advance of his body and advised that he should be left very quiet, that all his curls should be cut off and that he was to go to no parties.
Cole Lesley, The Life of Noël Coward (1976)
“Two, two, two…”
Simon, have you had a stroke?
Simon Page 7
