Monstrous Moonshine: a biography of Simon Philips Norton

Monstrous Moonshine: a biography of Simon Philips Norton

Beneath my study stomps one of the great prodigies of mathematics today: Simon Philips Norton. His basement living quarters extend from the front bay window, blocked off with blinds, into a long school-science-block-type extension that ends with its French windows nuzzled against a wall of brambles. The roof of the extension used to be my patio, where I drank coffee in the morning sun. It is hard to know what to call such a dank living place. ‘Flat’ is technically wrong, ‘rooms’ is too polite. Simon has lived in this excavation since 1981.

In his teens and early twenties Simon was considered, potentially, the greatest British mathematician since Newton. Now his hair is bedlam, his trousers torn; his blue T-shirt is sprinkled with blobs from the Chinese takeaway. He has no ambition whatsoever to wear smart clothes, or any clothes, and thinks it would be better to be a nudist. He wonders if he’d prefer life as a woman. But there is no sexual overtone to these comments: they are just part of the grammar of his thoughts. Wherever he goes, he hoicks about a holdall (currently black) with its handles clenched in the crook of one arm and his body straining against the weight to stop himself tipping over.
I want to write a book about Simon. What is it like to grow up a genius? How do you spend your days when the brilliance fades? At primary school he passed his time reading undergraduate textbooks on imaginary numbers. Aged 15, he represented Britain at the International Mathematical Olympiad and won gold. The next year, gold again, and a score of 100 per cent. I have seen his answer papers from this competition, which he was allowed to keep as a memento of his triumph: they are stacked, among the stalagmites of maps and bus timetables, beneath where I used to water my tomatoes.
The Mathematical Olympiads are designed to test innate ability. They use only terms and Methods that A-level students know. What makes Simon’s solutions beautiful to read is not their complexity, but their simplicity. Without drafts or false starts, he laid down his pellucid solutions, to questions involving complex geometry and infinity and the distribution of primes, with the grace of a ballerina unfolding her hands.
As a professional mathematician, Simon made his name in a subject known as group theory, or the study of symmetries. Groups are mathematical objects that can look very similar to Sudoku tables, and are constructed according to four basic rules that even someone who has failed every level of school mathematics can understand. In the 19th century someone noticed a little oddity about these numerical arrangements – the rules allowed for a sort of pattern within a pattern, a sub-Sudoku table within the original Sudoku table. Investigation of this peculiarity led to the outing of others, and within 50 years the subject was considered one of the most complex areas of all mathematics. Quantum Theory, Relativity Theory, predictions about the number and types of sub-atomic particles, the codes used to scramble military and financial information – all of it is now fundamentally reliant on the study of groups. They have even been used (very successfully, as it happens, by Claude Lévi-Strauss in The Elementary Structures of Kinship) to investigate incest among Namibian tribes.
Simon studies one of the most complicated groups of all: the Monster. He is, still, the world expert on it. A Sudoku grid has nine rows and nine columns, making 81 numbers in all. Monster has 808017424794512875886459904961710757005754368000000000.
Last July Simon and I took a boat trip together, up the coast of Norway, past the Arctic Circle and over Lapland; then back by train through St Petersburg, the forests of western Russia and Belarus.
Sitting on his cabin bed, eating mackerel fillets with Bombay mix squashed on top, Simon tells me he has a quasi-religious faith in Monster. One day, he says, stirring up the blend with a plastic fork, Monster will expose the structure of the universe.
The difficulty with this book is that, although Simon says he is keen for me to write a book about him and his work on Monster and his obsession with buses, he doesn’t like talking, has no sense of anecdotes or extended conversation, and can’t remember (or never paid any attention to) 90 per cent of the things I want him to tell me about in his past. It is not modesty. Simon is not modest or immodest: he just has no self-curiosity. To Simon, Simon is a collection of disparate facts and no interpretative glue. He is a man without adjectives. His speech is made up almost entirely of short bursts of grunts and nouns.
This is the main reason why we spent three weeks together, in a heat wave, and him with only three pairs of socks for the whole journey: I needed to find a way to make him prattle.
We met in Scrabster. The northernmost port in mainland Britain, Scrabster is exactly as it sounds. A few houses and a muggy bar quickly peter out into slabs of parking concrete, groups of cyclists with windcheaters and maps in plastic sponge bags, who have arrived six hours too early, and a long concrete buttress against the savagery of the North Sea. Seals bob about in the dock, nagging the fishing boats whenever they putter back home with the day’s catch.
Simon arrived on the back of a bus, teeth bared in excitement as he snapped glances out of the windows, then eyes back again to check the precision of his finger on the map. He had travelled all the way up Britain like this, checking off each unfamiliar stop and landmark against the lines on his Ordnance Survey map. Across the bay is Thurso: burnt-out payphones, half-scoffed takeaways and mothers younger than the babies they’re pushing in prams.
There is one thing only to do in Scrabster: leave.

We were in Bergen next afternoon.
The journey up the shattered, mountainous coast of Norway into 24-hour daylight takes six days. It is managed by the 13 liveried ships of the Hurtigruten line, which are in constant rotation, bringing supplies and vast parcels on pallets to the coastal villages and greeting each other daily among the islands and towering fjords with a clangour of fog horns. Our ship was the 11,000-ton Richard With, named after the man who began the coastal express service in 1893. As a contender for the ‘journey of a lifetime’ this ranks high on the list. As a literary exercise, it was a disaster.
Aside from a recent mugging on Jesus Green, in Cambridge, when three men forced him on to his knees and made him beg for mercy because they said he looked like a homeless person, Simon’s life is untroubled by excitement. It doesn’t move from incident to incident like it does for most of the rest of us; it dwells either in satisfaction, or out of it. You can bob alongside Simon for hours without saying a word or feeling that a single thought has passed through his head. Here, on board ship, among the vertiginous cliffs and billow of mountains, and the langoustine, crevettes and caviar that Hurtigruten lays out on platters like pearled swatches every lunchtime, his sole phrase is ‘it’s all right’.
My elation, after the success of my last book [Stuart: a Life Backwards], about Stuart Shorter, who had spent many years living on the streets in Cambridge, is beginning to fade. Stuart talked passionately and incessantly. Every day in his life was a hum of casual outrages. You could never be certain that, though happy and full of plans on Monday, he wouldn’t be in prison or hospital by Friday. ‘Homelessness – it’s not about not having a home. It’s about something being seriously f***ing wrong.’ ‘Stop asking why! I don’t know why! I was so off-key, half the time me mind had a head of its own.’ ‘Down where I been clichés don’t work any more.’ ‘Alexander, sort it out – you’re the writer. I just done the living.’
From 6am until midnight, meals and excursions aside, Simon spent his time on deck, in a state of trance. There is just one subject that animates Simon out of his equanimity: cars.
‘What was that ditty you invented to remember the names of the lanthanide chemical elements in the periodic table?’
‘Loathsome Cars Produce Noxious Polluting Smelly Exhaust Gases: They Destroy Human Environments, Take Young Lives.’
‘And the actinides?’
‘Avoid These Perils. Use No Private Automobiles. Cars Bring Complete Enslavement For Mankind, Not Liberation!’
He picks up his map again, darts glances to either side to re-establish his position, and slides back into silence. Occasionally, in the evenings, if there was a brief period when we were not in among the islands but out to sea, I could push aside the socks starched with sweat and try to conduct an interview, but it was hard to fix his attention. Simon’s nose was always furtively rising, drawing his head and body up after it – as if he really thought I might not notice – so that he could get his eyes over the cabin window ledge and see out.
Or he was afflicted by hunger, and had to lunge around in his holdall looking for Bombay mix, then would re-emerge, sucking grease and beige bits off his fingers, with in the other hand yet another map: more than 10 minutes away from a map and he starts to feel he has lost his connection with the world. As I set up the tape recorder and clipped the microphone to his T-shirt, he was constantly fidgeting and bouncing. He’d dive in his bag again and come up for air a minute later with the Thomas Cook European railway timetable. He needed to know: had the boat not been running, how long would it have taken to travel this stretch of Norway had we gone by train? What are the bus helpline numbers in Tromsø? Where is Chernobyl? Is there a train going there, too – one that stops to pick up radioactive passengers? Are there restaurant cars in… ‘Simon,
please! Concentrate.’
‘Sorry.’
I clicked the record button. ‘When did you first discover you were a genius?’
‘Five. Can we stop now? I think I’d like a banana.’
As you go further north, the houses become increasingly blockish and made with more corrugated iron. The needs of survival are more evident: oil storage tanks, fish processing plants, mobile-phone masts, ship yards – instead of being set aside from the town, these sorts of municipal objects start to gather round the high street with all the houses, as if cringing against the cold. By the time we reach the North Cape the battle to jolly things up is lost.
On Meagre Island, 75 miles above the geographical tree line, the wind blasts away any vegetation above toe-height.
‘They have here two supermarkets and, ja, a retirement home, thank you!’ announced the tour guide with a proud puff.
There is more life in the air, and much more under water, than on the land of Meagre Island. In winter even the reindeer vamoose. The 7,000-strong herd that grazes here, gnawing the specks of lichen from the rocks, belong to six Sami families. Every spring they ship the reindeer over on military landing vessels and, at the end of every summer, before the weather turns imbecilic with nastiness, they herd the animals up again, goad them to the edge of the water, and make them swim across the strait to the mainland. After that, it is a three-week trek through Norway, over Sweden, back to the Finnish-Russian border where the Sami have their farms. On the few days of the year when the water reaches above 10C the locals nip out to a dire 50ft stretch of grey sand to have a swim. They call it Copacabana
Puffin Island is a motorway diner for birds. The sea serves up huge fish suppers all summer long to 35 different types of winged thing that react by screaming and fighting and killing each other as they jostle for table space and turn the rocks white with excrement. The puffins are so tubby that they land on water by bumping into little waves, bouncing their plump breasts from crest to crest until they stop, and sink.
On the way back from Puffin Island, an awful, high-pitched noise came from behind my left ear. I turned to see Simon, bleating foully – ‘humming,’ he pronounced it.
‘Beethoven’s Sonata. Number 19. A prime number!’ he declared joyously.
The ecstasy of the birds had driven him to music.
‘What is your first mathematical memory?’
‘Calculating two to the power of 30.’
That’s two multiplied by itself 30 times over.
‘The answer is 1,073,741,824. I liked the patterns the numbers made.’
‘What do you mean, “patterns”?’
‘The arrangement of the digits. Two to the power of 23 was my favourite.’
‘Why?’
‘It spells “scissors”.’
Night above the Arctic Circle is not like ordinary daylight. It is autumnal light, a bit egg-yolk coloured, but also grey. Warm, cushioned, soft, it makes you feel slightly sick. Each night I tried to stay up to make sure the sun truly didn’t ever pop off for a snooze, but I fell asleep before the miracle happened: somehow between 4am and 6am, the day is replenished with freshness. Strawberries and cherries grow readily in north Norway, force-fed by 24 hours of sun, dense with the sort of sweetness you normally only read about in children’s books. In winter, said a banker from Tromsø, the day isn’t really quite black either, but blue, he said, ‘as if just drowned.’
What Simon means by 223 spelling ‘scissors’ is that the answer, 8,388,608, has its digits set out, like a game in a holiday puzzle book, in the same arrangement as the letters in the word. But the next day I put my finger on the flaw in Simon’s arithmetic. 8,388,608 has seven digits and ‘scissors’ has eight letters, so therefore it can’t spell ‘scissors’.
‘But it does,’ retorted Simon with excitement, ‘if you thought it was spelt the way I did when I did the calculation: ‘S-I-S-S-O-R-S.’
‘How old were you?’
‘Five.’
I asked him about primes. These are numbers not divisible by any other number except one and themselves, and as miraculous as black magic. 2, 3, 5, 7, 11, 13… are all primes. 4, 6, 8, 9, 10, 12… are not, because each is divisible by other numbers (eg, 12 can be divided by 2, 3, 4 and 6). Primes are the building blocks of numbers. Every number in the universe can be reached by multiplying primes together, and there are an infinite number
of them…
‘Not necessarily,’ interrupted Simon, not looking up from his map. ‘Only a finite number in a pring.’
‘What’s a pring?’
‘A ring. I invented prings.’
‘A pring is a ring?’
Simon nodded. ‘With power.’
‘So, what’s a ring?’
‘Uuugh, let’s see, if you have a system in which you can add, subtract and…’ he began, released at last from muteness and with the same bright-eyed optimism that he starts all his attempts at mathematical explanation with me, then stopped. ‘Uugh… are you allowed to eat tinned corn uncooked?’ He had found a tin in the holdall and put it on the table. Simon has been eating sweetcorn for 20 years, but since it doesn’t say on the label that you don’t have to heat the stuff, he’s doesn’t want to risk it. ‘I like to find a formula that works and stick to it.’
Salads, he says, are ‘awkward things’. Except when in Montreal, he boils his kippers in the tin. Kippers come in a different-sized tin in Canada and ‘I don’t want to take the chance of doing something wrong.’ In Montreal he eats fresh fish – not because he prefers it, but because the packet tells him what to do, which is comforting, although he never grills, ‘because you can’t see what’s going on’.
‘Yes, I am a worrier. My mother was a worrier.’
By the time we reached our final port, Kirkenes, and set off in a minibus across the Russian border towards the disgusting city of Nikel, I had not got much further in understanding Simon, or the state of his genius, or what Monster is up to these days. At Cambridge Simon worked (with a team) on a book that became one of the most important mathematical publications of the 20th century; then, somehow, he began to slip from view. There was rumour of a spectacular collapse of talent (he denies it). He appeared less often in the mathematics faculty; more often under bus shelters. He lost his paid position in the department, although he continues to publish in respectable journals and give lectures (usually in Canada) that are loudly applauded – but the mania for mathematics has gone, like an illness.
What he brings back now to his excavation, for his late-night study, are plastic bags squashed full of British and European public transport timetables, and leaflets about day trips in the Midlands.
As we made our last tour of the empty deck while the gangplank lowered on to the dock, I took a photo.
‘Smile!’
And, since Simon smiles more readily than any other person I know, he smiled merrily. At that point one useful thing did occur: I thought of a possible subtitle to the book: ‘Simon Philips Norton: the biography of a happy man’.