It was a warm, quiet morning and the previous day seemed distant and vaguely unreal. But when I went out to the garden Mrs Eagleton wasn’t there tidying the flowerbeds, and yellow police tape still surrounded the porch. On my way to the Institute I stopped at a newsagent on Woodstock Road to buy a paper and a doughnut. In my office, I switched on the coffee machine and opened out the newspaper on my desk. The news of Mrs Eagleton’s death was the lead story in the local news pages, with a banner headline reading ‘Former War Heroine Found Murdered’. There was a photo of a young, unrecognisable Mrs Eagleton and another of the front of the house with a police barrier and cars outside. The article mentioned that the body had been found by a lodger, an Argentinian mathematics student, and that the last person to see the widow alive was her only granddaughter, Elizabeth.
There was nothing in the piece that I didn’t already know; the post-mortem, late last night, apparently hadn’t shown anything new. There were details of the police investigation in a separate box. It was anonymous but, beneath the seemingly impersonal style, I immediately recognised the insidious tone of the reporter who’d interviewed me. He stated that the police were ruling out an attack by an intruder, even though the front door hadn’t been locked at the time. Nothing in the house had been touched or stolen. They did apparently have one lead, which Inspector Petersen didn’t wish to reveal. The reporter was in a position to suggest that the lead might incriminate ‘close members of Mrs Eagleton’s family’. And he went straight on to say that Beth was the only immediate relative and would inherit ‘a modest fortune’. In any case the article concluded, until there were any new developments, the Oxford Times echoed Inspector Petersen’s advice that householders should forget the good old days and keep their doors locked at all times.
I turned the pages, looking for the obituaries. There was a long list of names after Mrs Eagleton’s obituary, including the British Scrabble Association and the Mathematical Institute, in which Emily Bronson and Seldom were both mentioned. I tore out the page and put it in a desk drawer. I poured another cup of coffee and immersed myself for a couple of hours in my Director of Studies’ papers. At one o’clock I went downstairs to her office and found her eating a sandwich, with a paper napkin laid out over her books. She gave a little cry of delight when I opened the door, as if I had just returned safely from a dangerous expedition. We talked about the murder for a few minutes and I told her what I could, but didn’t say anything about Seldom. She seemed dismayed and genuinely concerned about me. She hoped the police hadn’t bothered me too much. They could be very unpleasant with foreigners, she said. She seemed to be on the verge of apologising for suggesting that I rent a room at Mrs Eagleton’s. We talked for a little longer, while she finished her sandwich. She held it with both hands, pecking at it neatly like a little bird.
“I didn’t realise Arthur Seldom was in Oxford,” I said at one point.
“I don’t think he ever left!” said Emily with a smile. “Like me, Arthur believes that if one waits long enough, all mathematicians end up making a pilgrimage to Oxford. He has a permanent position at Merton. But he doesn’t show his face much. Where did you come across him?”
“I saw his name in the Institute’s death notice,” I said cautiously.
“I could arrange for you to meet him, if you’d like. I think he speaks very good Spanish. His first wife was Argentinian,” she told me. “She worked as a restorer at the Ashmolean, on the great Assyrian frieze.”
She broke off, as if she’d inadvertently been indiscreet.
“Did she…die?” I ventured.
“Yes,” said Emily. “Years ago. She was killed in the same accident as Beth’s parents. They were all four of them in the car. They were such close friends. They were on their way to Clovelly for the weekend. Arthur was the only one who survived.”
She folded the napkin and threw it into the wastepaper basket, taking care not to drop any crumbs. She took a sip from a little bottle of mineral water and adjusted her glasses on the bridge of her nose.
“Well now,” she said, peering at me with eyes that were a faded, almost whitish blue. “Have you had time to read my papers?”
It was two o’clock by the time I left the Institute, carrying my tennis racket. It was the first truly hot day and the streets seemed to be asleep beneath the summer sun. A red double-decker Oxford Tour Guides bus turned the corner in front of me, as slowly and heavily as a slug. It was full of German tourists wearing sun visors and caps and pointing admiringly at the red building of Keble College. In the University Parks students were having picnics on the grass. I was overcome by a strong feeling of disbelief, as if Mrs Eagleton’s death had already vanished. Imperceptible murders, Seldom had said. But really, any murder, any death barely ruffled the waters, quickly becoming imperceptible. Less than twenty-four hours had passed and it was as if nothing had been disturbed. Wasn’t I myself now on my way to play tennis, as I did every Thursday? And yet, as I followed the curving path that led to the tennis club, I noticed an unusual stillness, as if small changes had secretly taken place after all. I could hear only the rhythmic striking of a solitary ball against a wall, with its magnified booming echo.
Neither John’s nor Sammy’s car was in the car park, but Lorna’s red Volvo was parked on the grass beside the wire fence of one of the courts. I circled the changing room building and found her practising her backhand against the wall with intense concentration. Even from a distance I could appreciate the beautiful line of her firm, slim legs beneath the very short tennis skirt, and see her breasts tensing and protruding as she swung the racket for each shot. She stopped when she saw me and smiled, as if to herself.
“I thought you weren’t coming,” she said. She wiped her forehead with the back of her hand and kissed me quickly on the cheek. She looked at me with an intrigued smile, as if she wanted to ask me something, or we were part of a conspiracy in which we were both on the same side but she didn’t know her role.
“What happened to John and Sammy?” I asked.
“I don’t know,” she said, innocently opening wide her big green eyes. “Nobody called me. I was starting to think you’d all decided to abandon me.”
I went to the changing rooms and changed quickly, pleasantly surprised by this unexpected piece of luck. All the courts were empty. Lorna was waiting for me by the gate. I lifted the bolt and she went in ahead. In the short distance to the bench she turned to look at me again, hesitating. At last she said, as if she couldn’t help herself:
“I read about the murder in the paper.” Her eyes shone almost with enthusiasm. “My God, I knew her,” she said, as if she were still surprised, or as if it should have protected poor Mrs Eagleton. “I saw her granddaughter in hospital a couple of times too. Is it true you found the body?”
I nodded as I took the cover off my racket.
“Promise you’ll tell me all about it afterwards,” she said.
“I had to promise I wouldn’t say anything,” I said.
“Really? That makes it even more interesting. I knew there was something else!” she exclaimed. “It wasn’t her-the granddaughter-was it? I’m warning you,” she said, pressing her finger into my chest, “you’re not allowed to keep anything secret from your favourite doubles partner. You’ll have to tell me.”
I laughed, and handed her a ball over the net. In the silent, deserted club we started hitting shots from the back of the court. There’s only one thing better in tennis than a hard-fought point, and that’s the initial knock-up from the baseline where, conversely, you try to keep the ball in play as long as possible. Lorna was wonderfully confident on both forehand and backhand, and she held her own, staying near the lines until she found an opening for a drive, counter-attacking from the corner with an angled shot.
We played aiming the ball just within reach, increasing the pace with every shot. Lorna put up a brave defence, leaving long skid marks as she scrambled from one side of the court to the other, her efforts growing increasingly franti
c. After each point she went back to the middle, breathing hard, flicking her ponyta’il behind her shoulder with a charming movement. She was facing the sun and her long, tanned legs gleamed beneath her skirt. We played in silence, concentrating, as if something more important were being settled on the court. During one of our longer points, she was running back to the centre of the court after hitting a sharply angled shot when she had to turn awkwardly to reach my return with her backhand. As she twisted, one of her legs gave way and she fell heavily sideways. She lay still, on her back, her racket some distance from her.
Worried, I ran to the net, but she wasn’t hurt, just exhausted. She was out of breath, arms outstretched, as if she simply didn’t have the strength to get up. I jumped over the net and crouched down beside her. She looked at me, her green eyes sparkling strangely in the sun, both mocking and expectant. I lifted her head and she raised herself up on one elbow, slipping her other arm around my neck. Her mouth was very close to mine and I felt her warm, still laboured breath. I kissed her and she fell back, taking me with her. We moved apart for a moment and looked at each other with the first deep, happy, slightly surprised look of lovers. I kissed her again and felt her breasts pressing against my chest. I slid my hand under her t-shirt and she let me stroke her nipple for a moment, but then she stopped me, alarmed, when I tried to slip my other hand under her skirt.
“Wait, wait,” she whispered, glancing around. “Do you make love on tennis courts in your country?” She laced her fingers in mine to move my hand away gently and gave me another quick kiss. “Let’s go to my flat.” She stood up, rearranging her clothes and shaking the clay dust from her skirt. “When you get your things, don’t shower,” she whispered. “I’ll wait for you in the car.”
She drove in silence, smiling to herself and turning her head slightly to look at me from time to time. At a set of traffic lights, she stretched out her hand and stroked my face.
“So the matter of John and Sammy…” I said.
“I had nothing to do with it,” she said, laughing, but she sounded less convincing than earlier. “Don’t mathematicians believe in coincidences?”
We parked in a little sidestreet in Summertown and climbed the two floors up to Lorna’s place, which was the attic flat of a large Victorian house. She opened the door and we started kissing again as soon as we were inside.
“I’m going to the bathroom for a minute, OK?” she said and headed along the corridor towards a door with a frosted-glass pane.
I waited in the small sitting room and looked around. It was charmingly untidy, full of a motley assortment of possessions-holiday snaps, soft toys, film posters and a large number of books crammed into a small bookcase. I leaned over to read some of the titles. They were all crime novels. I glanced in at the bedroom. The bed was neatly made, with a floor-length bedspread, and an open book lay face down on the bedside table. I went to take a look. I read the title and name above it, frozen with astonishment: it was Seldom’s book on logical series, full of furious underlining and illegible notes in the margins. I heard the sound of the shower and, a little later, Lorna padding along the corridor in bare feet and her voice calling me. I put the book back as I found it and went to the sitting room.
“So,” she said from the door, showing me that she was already naked, “still got your trousers on?”
Seven
There’s a difference between the truth and the part of the truth that can be proved. In fact this is one of Tarski’s corollaries to Godel’s theorem,” said Seldom. “Of course, judges, pathologists, archaeologists all knew this long before mathematicians. Think of any crime with only two possible suspects. Both of the suspects know the part of the truth that matters, i.e. it was me or it wasn’t me. But the law can’t get to that truth directly; it has to follow a laborious, indirect route to gather evidence: interrogations, alibis, fingerprints and so on. All too often there isn’t enough evidence to prove either one suspect’s guilt or the other suspect’s innocence. Basically, what Godel showed in 1930 with his Incompleteness Theorem is that exactly the same occurs in mathematics. The mechanism for corroborating the truth that goes all the way back to Aristotle and Euclid, the proud machinery that starts from true statements, from irrefutable first principles, and advances in strictly logical steps towards a thesis-what we call the axiomatic method-is sometimes just as inadequate as the unreliable, approximative criteria applied by the law.”
Seldom paused for a moment and leaned over to the neighbouring table for a paper napkin. I thought he was going to write out a formula on it, but he simply wiped his mouth quickly and went on: “Godel showed that even at the most elementary levels of arithmetic there are propositions that can neither be proved nor refuted starting from axioms, that are beyond the reach of these formal mechanisms, and that defy any attempt to prove them; propositions which no judge would be able to declare true or false, guilty or innocent. I first studied the theorem as an undergraduate, with Eagleton as my tutor. What struck me most-once I had managed to understand and above all accept what the theorem was really saying-what I found so strange, was that mathematicians had got by perfectly well, without upsets, for so long, with such a drastically mistaken intuition. Indeed, at first, almost everyone thought that Godel must have made a mistake and that someone would soon show that his proof was flawed. Zermelo abandoned his own work and spent two whole years trying to disprove Godel’s theorem. The first thing I asked myself was, why do mathematicians not encounter, and why over the centuries had they not encountered, any of these indeterminable propositions? Why, even now after Godel, can all the branches of mathematics still calmly follow their course?”
We were the last two people left at the long Fellows table at Merton. Facing us in an illustrious row hung portraits of distinguished former alumni of the college. The only name I recognised on the bronze plaques beneath the portraits was T.S. Eliot. Around us, waiters discreetly cleared away the plates of dons who had already gone back to their lectures. Seldom grabbed his glass of water before it was removed and had a long drink before continuing.
“In those days I was a fervent Communist and was very impressed by a sentence of Marx’s, from The German Ideology, I think, which said that historically humanity has only asked itself the questions it can answer. For a time I thought this might be the kernel of an explanation: that in practice mathematicians might only be asking the questions for which, in some partial way, they had proof. Not, of course, unconsciously to make things easier for themselves but because mathematical intuition-and this was my conjecture-was inextricably linked with the methods of proof, and directed in a Kantian way, shall we say, towards what can either be clearly proved or clearly refuted. That the knight’s moves involved in the mental operations of intuition were not, as was often believed, sudden dramatic illuminations but modest, abbreviated versions of what could always be reached eventually with the slow, tortoise-like steps of a proof.”
“I met Sarah, Beth’s mother, at that time. She had just started studying physics and she was already engaged to Johnny, the Eagletons’ only son. The three of us would go bowling or swimming together. Sarah told me about the uncertainty principle in quantum physics. You know what I’m referring to, of course: that the clear, tidy formulas governing physical phenomena on a large scale, such as the motion of celestial bodies, or the collision of skittles, are no longer valid in the subatomic world of the infinitesimal, where everything is far more complex and where, once again, logical paradoxes even arise. It made me change direction completely. The day she told me about the Heisenberg Principle was strange, in many ways. I think it’s the only day of my life that I can recall hour by hour. As I listened, I had a sudden intuition, the knight’s move, so to speak,” he said, smiling, “that exactly the same kind of phenomenon occurred in mathematics, and that everything was, basically, a question of scale. The indeterminable propositions that Godel had found must correspond to a subatomic world, of infinitesimal magnitudes, invisible to normal mathematics.
The rest consisted in defining the right notion of scale. What I proved, basically, is that if a mathematical question can be formulated within the same ‘scale’ as the axioms, it must belong to mathematicians’ usual world and be possible to prove or refute. But if writing it out requires a different scale, then it risks belonging to the world-submerged, infinitesimal, but latent in everything-of what can neither be proved nor refuted. As you can imagine, the most difficult part of the work, and what has taken up thirty years of my life, has been showing that all the questions and conjectures that mathematicians from Euclid to the present day have formulated can be rewritten at scales of the same order as the systems of axioms being considered. What I proved definitively is that normal mathematics, the maths that our valiant colleagues do every day, belongs to the ‘visible’ order of the macroscopic.”
“But that’s no coincidence, I think,” I interrupted. I was trying to link the results that I had presented at the seminar with what I was now hearing and find where they fitted in the large figure that Seldom was now drawing for me.
“No, of course not. My hypothesis is that it is profoundly linked to the aesthetic that has been promulgated down the ages and has been, essentially, unchanging. There is no Kantian forcing, but an aesthetic of simplicity and elegance which also guides the formulation of conjectures; mathematicians believe that the beauty of a theorem requires certain divine proportions between the simplicity of the axioms at the starting point, and the simplicity of the thesis at the point of arrival. The awkward, tricky part has always been the path between the two-the proof. And as long as that aesthetic is maintained there is no reason for indeterminable propositions to appear ‘naturally’.”
The waiter returned with a pot of coffee and filled our cups. Seldom remained silent for a time, as if he was unsure whether I’d followed what he was saying, or was perhaps a little embarrassed at having talked so much.
The Oxford Murders Page 4
