All these combinations of turns can now be written down as a table. These are the lifeblood of Group Theory. Every mystery of this secretive, sly subject is contained in such tables. The one that applies to turns of a square is:
It’s read in the same way as the distance chart at the front of a road atlas. It’s not a calculating device; it’s a secretarial way of keeping track of information. If you’re six years old and want to remind yourself what happens when you turn a square once, then turn it again, i.e.:
take the row corresponding to 1, run your chocolaty finger along until you come to the column corresponding to 1, and there’s the answer—it’s equivalent to two turns:
What’s baffling is that there can be anything complicated enough about this “study” of symmetries to bring it out of the playroom in the first place.
45
The papers that slosh about in the basement are (Simon insists I am to say) “carefully, hnnnh, arranged and, uuuh, being sorted in plastic bags.”
But I’ve put my foot down over this: “That’s a lie, Simon. You’re telling me to make things up.”
“I’ve not noticed your reluctance on that front before.”
Simon was taught mathematics by the number 45.
The first written evidence we have of 45’s significance in his life comes from an Atlantic blue notebook dated January 1956 (a year before Simon started school) and titled
Inside, Simon addresses mathematical problems to this number:
(sums for 45, you 45)
performs amusing numerical games:
and emerges briefly, porpoise-like, from his researches to write letters to her:
before re-submerging in a glug of numbers.
Sometimes, 45 wrote back:
45 was Simon’s number for his mother. She was the one who taught him math, up to quadratic equations. Astounding, for a British housewife in the 1950s—no one in the family can explain it.
Once the first Atlantic blue notebook was finished, Simon and his mother started another, in February 1956, just before his fourth birthday. Her handwriting is on the cover this time, and she calls him a monkey:
I wonder who crossed this fondness out.
Once, during these preschool years, Simon was distracted by a word:
But he soon snapped back to numbers with gusto:
9 eSimon
Simon has five types of grunt:
Ask him about his mother,
his father,
or his parents’ marriage,
and you get a happy grunt for the first, a puzzled one for the second, and an incomprehensible bleat concerning the photo above.
It’s possible to extract more interpretation, if you work at it.
“Simon, what do you mean, ‘Uuugheugh…gghuaha… ehhghH?’”
“Haaaghuggh…oooh…ghughghEH.”
“These are your parents. You grew up with them. Is this photo an accurate reflection of their relationship or not?”
“Aaaghurghh…gghahuugh…eeehghuGH…is that a dog in the middle? Oh, it’s a bag. If it had been a dog these might not have been my parents, just people who looked like my parents, because we didn’t have a dog.”
“Don’t you think there’s something remarkable about this picture? Sitting back-to-back on a pebble beach in Southern England with something that looks like a dead bulldog between you?”
Simon looks trapped and panicky.
“Or is this just a snapshot of what marriage always is, to you?”
The grunt-bleat means bafflement. Why should he find something odd about the photograph? It’s a photograph: one of those things (so rare in life) in which a fact is made immutable. Why muddy it with interpretation? Why, if you do muddy it, pick on that particular interpretation? It could be one of a million others.
Simon is, verbally, one of the most adept and playful people I know—as long as he doesn’t have to speak.
Or use metaphor.
Or comment on photographs.
Simon’s parents’ marriage (according to other members of the family) was not happy or unhappy, just mannered and soulless.
The puzzled father-grunt Simon gives about his father signifies a lack of interest. The happy mother-grunt, “loveliness.” Loveliness is the only adjective Simon associates with Helene Norton. She “embodied” the word, he says. There isn’t need for others—and he doesn’t mean “loveliness” because of her startling beauty, which Simon claims he’d never noticed until I started ogling her, but “loveliness” because of…because of…uuuggghhhAH! Grunt Number Four: Frustrated Grunt.
What’s the point of me demanding new words when he’s already given me the one that works to perfection?
“Loveliness” does not mean uncensoriousness, however. When his mother was alive, Simon used to visit her in London every two or three weeks, but she refused to greet him until he’d had a bath.
Then she would criticize his clothes.
“If it wasn’t one thing, it was another,” remembers Simon forlornly. “I got the feeling I could never satisfy her. Did it count if your clothes were wrong in the period before you’d had a chance to spruce up between the front door and the bath?”
After trying to “spruce up” he’d step out of the bathroom in the fresh clothes that his mother kept in a cupboard, ready for his visits, and expecting now to be allowed to kiss her hello. “But I’d almost certainly forget something, and she’d draw attention to that one thing and home in on it. My shirt was wrong, or my shoelaces were undone. I hadn’t done up my trousers correctly.”
He gives a purgatorial groan.
“It was too much for me.”
Two or three days after his mother’s death (Simon remembers it as “rather too quickly”) he and his two brothers let themselves into her five-bedroom apartment near Baker Street, and began picking over her possessions. From their mother’s cupboards and drawers they extracted everything small and unbreakable and piled it on the floor. Then they shuffled among the piles—in my image of this spectral, sacrificial scene I imagine them as three tall birds, and hear the clicking of their feet on the parquet floors—plucking up anything that took their fancy.
There was only one item Simon wanted: a photograph of his mother in old age.
There were paintings of her, when she was young and glorious. Simon wasn’t interested. He’d had nothing to do with her in those days. He doesn’t like portraits at the best of times, but he prefers at least that they correlate to an image already in his brain.
He held out his arms, eyes closed, to any other things the brothers didn’t take, then brought the fifty- or sixty-item windfall back to the small flat he owns in London. There he laid them out, ten layers deep along one edge of the living room, like drying fish fillets.
Simon tells me he would like to hang the pictures up.
His mother has been dead nine years now, but the haul remains stacked against the wall, curing itself slowly of connotations. “Loveliness” now resides only in the photograph of her old age and his memories.
The leftovers in his mother’s apartment—her letters, wrapped in pink ribbon, from a man who was not Simon’s father; her skirts and chemises, brooches, diamond pins, fur coats, perfumes, old swing-band records—the brothers sold, gave away or threw in the dustbin.
“But you also got all your old school reports and exercise books, and the folder of newspaper clippings about when you won the Maths Olympiads and went to Cambridge, your IQ report?”
“As I say, I didn’t want them.”
“Then why take them?”
“Why not take them?”
Simon is always eager to drop in schoolboyish retorts like this. The trick is to become instantly absurd.
“Would you have taken them had they been roast chickens?”
“Heh, heh, heh, hnnn. I took them because it’s the sort of thing people do take, isn’t it?”
See? Simple, when you know how.
To Simon, correct conduct is like a wood. It has many
trees, which represent how things ought to be done; one tree for each circumstance. It is a large wood, sterile and rather dark. The stormy forest where he goes to hunt for the Monster is infinitely more comforting.
Here’s Simon’s brother!
Hello, Michael!
He doesn’t have much to say.
“Is it surprising?” he protests, leaping up, holding out his hand—a strong shake. “I’m ten years older than Simon is. We were like different families. I studied chemistry at university, not mathematics; that’s a different language. Simon is interested in chemistry also? Really? I never knew. His favorite element is boron? I’m surprised! Would you like some tea? Organic Lapsang or elderflower?”
Michael Norton OBE is the author of Writing Better Fundraising Applications, The Worldwide Fundraiser’s Handbook, The Complete Fundraising Handbook and Getting Started in Fundraising. Money—in particular other people’s money—is a big subject in Michael’s life. He wants it to pay for environmental revolution.
His latest book is 365 Ways to Change the World: How to Make a Difference—One Day at a Time. Each day of the year is allocated a noble deed:
January 5: “Start drinking.” Reduce “beer miles” by giving up sewage brands like Heineken or Budweiser, and brew your own beer using oysters and wild rice.
February 22: “Say no to plastic bags.” There are now 46,000 pieces of plastic waste in every square mile of the world’s oceans. In Australia, eighty million plastic bags are added every year to the mist of garbage that floats across the scrub there. Cows eat them and die; then the sack re-emerges from the rotting flesh, is cleaned off by rain, scooped back up by wind, and bundled along to be eaten by another cow: it is, biologically speaking, a protovirus. Simon is therefore a force for salvation. He keeps these protoviruses out of reach. If it weren’t for him, thousands of extra plastic bags from the Excavation would be tumbling through our fields and woodlands.
May 1: “Join the sex workers’ union.” Fight to give prostitutes access to health care, safe places to work and legal support against rapists and pervy Italian prime ministers. “Membership is free.”
“Michael Norton is a one-man ‘ideas factory,’” bellows the Guardian.
“You know, he knows when he comes to dinner here dressed in a dirty T-shirt that he’s doing wrong,” says Michael, stooping under the lintel of his cottage door (he lives in Hampstead, but the house looks as if it’s been airlifted from beside a village brook in Hampshire) and balancing a tea tray. “But there’s no point telling him. You’d physically have to burn his old clothes before he’d get rid of them.”
He’s brought a photograph album into the garden along with the Victoria sponge cake. The album’s green, with a cushioned cover, from 1954, and it’s all the paperwork Michael has that includes Simon. They are not a sentimental family.
“That’s my hand at the edge there, sorting out his food, even at that age. We’re at our summer bungalow in Ferring. This is David…” David is a friend who later murdered his wife by bludgeoning her to death with a champagne bottle:
“And here’s Simon aged…oh dear, not a pleasant-looking young man”:
“Our mother doted on Simon. She was really proud that he was a genius. I don’t think she ever understood why he didn’t sustain that. I mean, he sustained it in his brain, but why is he not a professor? Why has he not got a proper job?”
“He’s too peculiar,” I suggest.
“He’s not that peculiar,” retorts Michael sharply, catching me out, correctly, in one of the phrases I have lately come to use about Simon without thinking. “There are lots of peculiar people in Cambridge. Half the lecturers that I had as a student there were peculiar. There must be somewhere that would give him a home.”
He taps his china cup of elderflower irritably.
“All I can say is that since our mother died, Simon’s become a different person. I noticed that almost immediately. He’s got more sociable. When he comes to dinner, he’s much more at ease. Instead of sitting in a corner reading a book, as he did when she was alive, he joins in. I’ve bought him three clean shirts which hang in a wardrobe here, for him to pick up whenever he comes to London.
“I think my biggest triumph is persuading him to get rid of his money. Did you know he gives £10,000 a year to campaign against cars?”
Francis Norton, Simon’s middle brother, works here…
…in a jewelry shop.
Francis brings in the family money. The company, founded by Simon’s great-grandfather, is the oldest family-run antique jewelry business in the world, patronized by the Queen, pop stars, fringe aristocracy, footballers (if they know what they’re about) and all London people with 100-acre second homes in Wiltshire.
Ten years before Simon was born, S. J. Phillips established itself as the epitome of Englishness by taking part in a famous wartime deception called Operation Mincemeat, later dramatized in the film The Man Who Never Was.
In April 1943, a Spanish fisherman discovered the decomposing corpse of a man floating off the coast of Andalusia. Documents on the body identified him as Major (Acting) William Martin of the Royal Marines. He was handcuffed to a briefcase, which contained a bunch of keys, an expired military pass, two passionate love letters, a picture of a woman in a swimming costume (“Bill darling, don’t let them send you off into the blue the horrible way they do”), a £53 bill for an engagement ring and a letter from Lord Louis Mountbatten to General Alexander revealing the plans for the Allied invasion of Europe.
Spain, though neutral, supported a very efficient network of German agents. They soon found out about the drowned Marine, got hold of the briefcase and carefully extracted the top-secret letter from its envelope. The British had made the greatest intelligence blunder of the Second World War. With ample time to prepare his defenses, Hitler now knew that the Allies were going to invade Europe through Sardinia and the Peloponnesus: the Germans transferred the 1st Panzer Division to Greece and started laying minefields.
It wasn’t until the British got the corpse of Major (Acting) Martin back, a fortnight later, that they knew the Nazis had definitely fallen for the trick. British Intelligence had folded the fake letter to Mountbatten only once before sliding Martin’s dead body into the sea from a submarine off the coast. When the body and effects were returned, investigators spotted under a microscope that the letter had been carefully refolded, creating a second crease.
* * *
Excerpt from an interview with Francis and his wife, Amanda
Amanda: When I met the Norton family, I thought they were all so bizarre.
Francis (nodding): My mother was very, very old-fashioned. It was, you know, “It’s four o’clock in the afternoon, you can go see your mother.” We absolutely adored her.
Amanda: They were just so Victorian. I’d never met anything like it in my life.
Francis: My father always said his ideal was to have a tail-coated butler behind every chair.
Amanda: I’ve never known parents who were so unphysical. In the morning Helene, their mother, would go off and do her charity work, then come home and have a long cigarette, put on her caftan for the afternoon, and sit there doing the crossword puzzle.
Francis: Terribly unfulfilled.
Amanda: I remember once—this is how old-fashioned they were—I’d just had my son Alexander, he was about nine months old, and Dick [Simon and Francis’s father] was standing there, with the table laid with all the silver, and Domingo the butler hovering around. And Dick looks at me and says, “Amanda, darling, has Alexander started masticating yet?”
* * *
A month later, Britain and America began their assault 300 miles west of the location indicated in the letter, through Sicily.
S. J. Phillips, Simon’s family firm, provided the £53 engagement-ring bill—it was seen as the touch that the Germans would regard as unfakably, quintessentially English.
Francis is Simon’s savior. It’s because Francis keeps the family firm alive and p
rofitable that Simon has never had to have a job or a mortgage and, despite using seventeen different variants of bus, train and visitor-attraction discount cards, doesn’t actually need a single one of them.
A mild, self-effacing, apparently undogmatic man (I’ve met him only twice), Francis lives on the other side of Hampstead from brother Michael, and has the talcum-powder-dusted look of the very rich. He is an accomplished cellist.
Every year Francis or Michael invite Simon to their house for Passover; and every year Simon arrives with his shoelaces flapping, his duffel bulging, his bus timetables and his smells, and eats all the parsley.
Now, back to grunts.
The fifth type of grunt emitted by Simon is metaphorical—it’s not a guttural sound, it’s a full sentence. The mathematician Professor John Conway calls it a “Thank you, Simon,” defined as “a statement that is indubitably true, but the relevance of which is obscure.” For example, in the middle of a discussion with me about whether the Monster might in fact not be a large object at all but something very small and everywhere, like a flea, Simon will burst out:
“Incidentally, I was once going on a train and the conductor pronounced that we were now approaching ‘Manea, the center of the universe.’”
What can you say after he’s said that? What does he mean? That the flea-Monster, which Simon suspects contains the solution to the symmetry of the universe, is living in Manea, a village in the Cambridgeshire Fens? It can’t be that. Simon is not a lunatic. Maybe it’s just the word, “universe.” But he clearly expects some sort of reply. So, after a suitable pause, you murmur, with a slight doff of the head,
Simon Page 4
