“What table, sir?”
Uproar in the class. I was put at a separate desk to learn my tables. The numbers crowded before my eyes. I looked at the nine-times table. I saw at once, with the clarity of instinct, that the integers in the answer to each calculation themselves added up to 9: 9 × 2 = 18, 1 + 8 = 9, 9 × 3 = 27, 2 + 7 = 9. And so on up to 10. I drew my teacher’s attention to this and received my first words of praise.
What made me notice this? What made me see the pattern? And what kind of conjuring trick in that most abstract of worlds is being played here? I am not saying that I felt in some way blessed, but I do consider that some sort of inkling was being offered to me here. Since that first day at school and since that discovery the realm of mathematics was, for me, teeming with promise. What other secrets would I find? What other insights?
It is said that there are two types of mathematicians. Ninety percent see in figures. Ten percent see in pictures. The most brilliant, the most profound, come from that 10 percent. In my own case I think that for a few early years I saw the world of numbers in pictures, that I had the gift up to the age of ten and then, for some reason, it faded into mere proficient numeracy. But the great mathematicians never lose that facility. Perhaps that is why infant prodigies occur only in the worlds of maths, music and chess. These regions can be surveyed pictorially; patterns and shapes can be perceived there. Order can be discerned among randomness, sense separated from contingency. Or at least that is what I used to think. I have abandoned explanations now. Mathematics and physics have led me to greater, more disturbing truths than these, as I shall reveal to you. Sense, order, pattern, meaning … they are all illusions.
Hamish Malahide, of course, was one of those 10 percent. I like to think we all are at birth, but the tabula rasa is quickly scored with confusing hieroglyphics that we never manage to erase again. I was lucky. I had that guileless vision for a few extra years. Hamish never lost it. He was extraordinary. Mathematicians, like artists, tend to have their peak periods. Hamish did also, and as a young man produced the celebrated Malahide Paradoxes I and II. There was a brief refulgence in the 1940s with the discovery of the Malahide Number, but after his twenties the creative power waned, almost like a form of aging. But his perception remained ever vigorous and acute, right to the end of his desperately unhappy life.
At Minto Academy it took me some time to realize his qualities. At school he was a reviled and unpopular figure because of his appalling acne. Even Mrs. Leadbetter, the matron, gave up any pretense of medical impassivity in her vain attempts to keep it under control. She wore cotton gloves when she dabbed the goo and patent lotions on his face, her nostrils tight with disgust. Some of the school wits called him Job and the name stuck. In summer we often went to the Tweed to bathe and Hamish had to swim downstream from the rest of us. Even I, his only friend, had to admit that unclothed he did look repulsive. Consequently I often found myself divided in that role. There were things about him that I found potently intriguing, but if I looked too closely at those vivid encrusted spots my scalp literally began to crawl and my eyes water. But Hamish, with his typical sensitivity, sensed my dilemma. One day he showed me a small pot of ointment.
“What’s that?”
“My mother sent it to me: ‘Dr. Keith Harvey’s Emulsion. Cures Warts, Acne, Lupus, Locomotor—Ataxy and St. Vitus’s Dance.’ She sends me these things once a month.” He smiled. “For my rotten plooks.”
“Oh yes,” I said, as if I had just noticed them. “It must be a …” I could not think of a word—“nuisance” seemed such a grotesque understatement.
“A curse,” he said. “I’ve been cursed, I know.”
The candor was sufficient to remove the awkwardness between us. After that we often spoke about his spots. I even read the Book of Job in the Bible.
“They’ll go,” I said. “My brother had spots—they all went.”
“But what’ll I look like underneath?” he asked with a weird grin. “I can’t imagine what my face’ll be like, clean.”
“Normal … won’t it?”
“I’m not so sure.”
My friendship with Hamish grew as that first term passed. Although we were both maths specialists, he was so far advanced he might have been doing another subject altogether. To take an architectural analogy: while the rest of us were designing cab shelters and public lavatories, Hamish was building Gothic cathedrals. From time to time he spoke about mathematics and I began to gain some insight into the strange and beautiful workings of his mind.
In our class Minto had set us a project to discover all the prime numbers up to 1,000,000. (A prime number, for those of you who do not know, is a number that is not divisible by any other counting number—apart from itself and 1. Eleven is a prime number, so is 19, so is 37.) The project was a long-term one and had been going on for years. Successive generations of schoolboys had been like Minto’s researchers, scrabbling away among the numbers from 1 to 1,000,000, and coming up, like gold prospectors, with the occasional nugget—a prime. As we discovered them we wrote them on a vast wall chart. We were systematically organized by Minto, each one having a few thousand numbers to sift. The project was completed shortly after I arrived. We counted up and had a total of 41,539 primes. Then Minto, with the air of a conjurer producing a rabbit from a hat, showed us a calculation for estimating how many primes lay between any two given numbers. But, interestingly, the figure the calculation produced was sixty-seven numbers out. Checks established that the calculation, while close, was never exactly right.
“Why is it only approximate, sir?” Hamish asked. “Why can’t we get it right?”
“Because we can’t.” Minto seemed irritated. “That’s the nature of primes.”
On his own Hamish tried to improve the accuracy of the calculation, but with no success.
“I can’t get any more accurate. Just can’t,” he said to me one day as we watched a rugby match.
“Never mind.”
“It bothers me.… There must be something significant about primes—the way they exist in the way they do. It must be telling us something.”
“Do you think so?”
“Numbers are infinite, so there must be an infinite number of primes.”
I had no idea what he was talking about.
“But there’s no pattern. They don’t crop up in any order. That calculation we did—it’s never exact. Why? Why can’t we pin them down? What are they trying to tell us?”
“Are you feeling all right?”
“Why is there no pattern? There should be.”
“Did prime numbers exist before we thought about them?” I was surprised at my own question, unsure of its implications. But Hamish seemed to know.
“Exactly, Todd, exactly. Think of the first man who started counting, started adding up.… Look where it’s got to now.”
It made no sense to me. Now I understand more of what Hamish saw as a fourteen-year-old. For him the world of abstract mathematical explanation was like an entrancing, enchanted forest to an avid explorer. He was already far down a jungle path, beckoning me to follow.
I soon settled into the routine at Minto Academy, but because of my friendship with Hamish it was a little difficult to establish any closer aquaintance with the other boys. It did not perturb me. There was little bullying. The dormitories were segregated by age, with one senior boy appointed dormitory leader and responsible for discipline. These were, in fact, the only ranks in the school, off the sports field. There were eighteen in our dormitory. We slept on iron beds separated by thin wooden wardrobes. Hamish’s bed was four away from mine (yes, I had eaten his wax bogey). Apart from vigorous masturbation there was little vice. A few boys chose to creep into each other’s beds, but no one objected or thought it unduly strange. Food was plentiful but unimaginative. Porridge, milk and bread in the morning. A joint of meat—mutton, nine times out of ten—at lunch, and the same joint cold in the evening with vegetables, and cocoa to drink.
At we
ekends, the Saturday was spent watching the rugby team win at home or away. And on Sunday the entire school was taken on an immensely long walk by a drab Mr. Fry or a sad Mr. Handasyde. Time passed, and not so slowly. I found that my homesickness had left me after a week. My only regret was that I received few letters. Oonagh could not write, my father was too busy and Thompson could not be bothered. I thought about taking up my aunt Faye’s offer but could not summon up the courage. I received the occasional postcard from my father. I still possess one. I reproduce it in full.
3 Kelpie’s Court
Edinburgh
October 21, 1913
Dear John James,
Thank you for your letter. Yes, your friend Malahide may consult me if you wish, but it sounds as if a dermatologist might be more efficacious. I regret to say that the rice diet had no significant effect on my patients. Thank you for asking.
Thompson is well; Oonagh sends her cordial greetings.
Your affect, father
I. M. Todd
I wrote once to Donald Verulam, on the pretext of some photographic business, and he replied promptly and fully asking me to write again. I meant to, but never got round to it. The school was not what I had feared; and in it, to my vague surprise, I felt I had discovered a kind of freedom. As my friendship with Hamish cemented I found I had all the companionship and stimulation I required. I was not a gregarious child and tolerance by my fellows was all that I asked.
At the end of my first term something peculiar occurred. One night, long after lights-out, Hamish woke me. Everyone was asleep, the house absolutely still.
“Come with me,” he whispered.
I got out of bed and followed him out of the dormitory.
“What is it?”
“Ssh.”
He led me down the corridor to the locker room. I went through the door after him. Suddenly he turned and clamped a damp rag over my mouth. My head filled with a rank chemical smell. Before I blacked out the room went bright yellow, then scarlet, then purple. I thought I saw my father’s face.
I came round, so Hamish told me later, after half an hour. I opened my eyes. I was nauseous and cold. He was squatting beside me. My head boomed with a headache. Feebly, I punched him in the ribs.
“Steady!” he said.
“Shagging Job!” It was the first time I had used his nickname. “Shagging maniac!” I sat on the floor, head hanging. My brain seemed to steep in some alchemical brew. I suddenly felt uneasy.
“What did you do to me?”
“Chloroform. I chloroformed you.”
“Great. You didn’t do anything while—”
“No, no. I just watched. Checked your pulse from time to time.”
“For heaven’s sake, Malahide, you can’t just chloroform someone when you feel like it!”
“I had to test it. I knew you’d never volunteer. It has to be a secret.”
“Test it? What for?”
“Something we’re going to do next year. I’ll tell you after the holidays.”
There was a science lab at the school where elementary chemistry and physics were taught. Hamish had lately been spending a lot of time there. He told me he had made up the chloroform himself. An unsuspecting Minto had ordered the chemicals himself. The ambush of me was to test the strength of the potion.
I sulked for a couple of days, but Hamish’s insouciance confirmed that my role as guinea pig had been solely in the interests of science. Besides, I was by now intensely curious to know what plan he had in mind. But he would not tell me, said merely that all would be revealed next term.
We had a quiet Christmas that year. Thompson was away, for some reason, and my father seemed even more preoccupied with his patients. I went with Oonagh to a tedious pantomime at the King’s Theatre and, with more enthusiasm, to a noisy variety show at the Pavilion in Leith. The dark winter nights and the low gray days seemed to hold Edinburgh in a hunched frozen posture, as though pinioned by the cloud blanket. A scowthering east wind lashed the streets at all hours of the day and night, numbing your face in seconds. Now that I had been away from it for a few months I discovered a strange affection for my home and was content to stay indoors. Oonagh disguised her pleasure at seeing me again and said she was sure I had grown. My Christmas present (was my father guilty?) was developing equipment and an enlarger and I converted one of the spare bedrooms into a temporary darkroom. From time to time I ventured out in search of pictures.
Hamish wrote to me from Perth, where his family lived. We had made plans about a visit, but in the end nothing materialized.
The New Year—1913—arrived and our first visitor was Donald Verulam. We had quite a jolly party that night when various of my father’s colleagues and their wives appeared. My father drank more than I had ever seen him do before. At the bells he sought me out. I was the only member of his family present (Thompson was still away—in Birmingham, I think—on church business).
“Happy New Year, Father.”
He shook my hand and would not let it go. I remember vividly the texture of his grasp: his palm cool, dry, oddly farinaceous. He looked at me, his eyes a little glazed, maudlin. Did he see his wife in my face?
“How are you, boy?”
“Fine.”
“How’s school? It’s not so bad, is it?”
“It’s fine.”
“That’s the spirit. My son the mathematician, eh?”
Then he did something I can only describe as an attempt at an embrace, though from my point of view it resembled more a cross between a cuff and a shoulder charge. In the event he managed to brush roughly against portions of my body with certain portions of his. It was odd—I remember thinking even at the time—for we never touched each other, except to shake hands. He moved off, and I was taken up by the wife of one of his colleagues and made a fuss of. People allowed themselves to feel sorry for me at occasions like these—I became a legitimate catalyst for selfless fellow feeling. I was kissed, had my hair ruffled, was praised and flattered. I wondered if, had I looked like Hamish, I would have received the same treatment. I felt a sudden intense liking for my curious friend and for an instant experienced vicariously what his life must be like. At this very hour people would be avoiding him as industriously as they sought me out. I could not imagine any professor’s wife pressing her lips to his livid cheeks.
After a while I went through to the kitchen. Oonagh sat on one chair, her legs stretched out upon another. She was drinking whiskey from a sherry glass and munching on a square of shortbread.
“C’mere, darlin,’ ” she said. “Happy New Year, Johnny.”
Without getting up she pulled me to her. I smelled her whiskey-sweet breath, felt her strong grip around me, heard the starch crackle on her pinny. She kissed me again and again on my left temple, muttering Gaelic endearments. I hugged her in return, my forearm innocently squashing her breasts. My face was crushed against her cheek. I pouted my lips. My first kiss freely given. That gentle pressure made her turn her head and as she did I kissed her again, quickly, full on the mouth.
“Happy New Year, Oonagh,” I said. “Let’s hope it’s better than the last one.”
There was the briefest knowing pause before she spoke.
“Aye,” she said. “Let’s.”
If anything, Hamish’s spots looked worse in cold weather: something to do with the skin tightening, making the knobbled quality of the pustules more evident. In the oblique washed-out afternoon light, his skin looked more like bark or a section of wall from a pebble-dashed villa.
It was four in the afternoon, night coming on fast. We were crouched behind some bushes, shivering slightly as we waited for the light in the art rooms to go out. The art rooms were in a small cottage some distance beyond the stable block. Hamish held some rag wadding in one hand and a small bottle of his homemade chloroform in the other. We were waiting for the object of his revenge.
This was a boy named Radipole. He was one of the black buns, possessing both a talent for drawing and
the ability to run very fast. He was a tall, fit youth with reddish hair and curious slanted eyes—almost Eastern in configuration. He was known, imaginatively, as Chink. Apparently he had been the chief instigator of the urine soaking Hamish had received the previous term. It was he who had encouraged the mob to bundle Hamish over the railings and he had been the first to lift up his kilt and let fly. Hamish had never forgotten, never forgiven. But his mind worked with its own cool logic. Hamish decided to postpone his getting even for many months. So he presented to Radipole a face of resigned amusement, a grudging acceptance of the rag—sure, it had not been very pleasant, but still, no point in making a fuss over a bit of good-natured horseplay. Radipole duly forgot all about it. He and Hamish were not friends but there was no animosity between them. The whole point of this, Hamish reasoned, was that when he did eventually strike he would be one of the last people Radipole would suspect. No one could recall a four-month-old slight, and Radipole, being a boisterous unfeeling lout, had made many enemies since.
“He’s coming,” Hamish said. A light had gone out in the art room. “Remember,” he said to me, “count to three after he goes past.” Hamish crept off.
By now the light was almost gone. The evening meal and evening roll call were an hour away. The gloomy pines and ash trees that lined the path to the schoolhouse made it even darker here. I saw Radipole coming down the path. He was whistling through his teeth, kicking at fir cones as he went. I crouched behind a tree. He passed by. One, two, three.
“Hey, you!” I called in a deep voice.
Radipole stopped and turned, looking back curiously. Hamish stepped up behind him and clamped the rag over his mouth and nose. Radipole gave a shudder, an arm flailed and he went down. We dragged him off the path and further into the small grove of trees. We heaved him upright against a trunk and, with Hamish holding him fast, I ran a length of washing line several times around him and the bole of the tree and tied it secure. We stepped back and looked at him. He was semi-upright, his head lolling, making small snoring sounds. He had all the inert limpness of someone shot by a firing squad. A long string of drool hung from his bottom lip.