The Oxford Murders Page 5

  “What I was most struck by,” I said, “the results that I presented in Buenos Aires, were in fact the corollaries that you published a little later on philosophical systems.”

  “Actually, that was much easier,” said Seldom. “It’s the more or less obvious extension of Godel’s Incompleteness Theorem: any philosophical system which starts from first principles will necessarily have a limited scope. Believe me, it was much easier piercing through all the philosophical systems than through that single thought matrix to which mathematicians have always clung. Because all philosophical systems are simply too ambitious. Basically, it’s all a question of balance: tell me how much you want to know and I’ll tell you with how much certainty you’ll be able to state it. Butt at the end, when I’d finished and I looked back after thirty years, it seemed that that first idea that Marx’s sentence had suggested to me hadn’t been so misguided after all. It had ended up, as the Germans would say, both eliminated from and included in the theorem. Indeed, a cat doesn’t simply assess a mouse, it assesses it as a prospective meal. But the cat doesn’t assess all animals as prospective meals, only mice. Similarly, historically, mathematical reasoning has been guided by a criterion, but that criterion is, deep down, an aesthetic. I found this to be an interesting and unexpected substitution with regard to necessity and a priori Kantians. A condition that is less rigid and possibly more elusive, but which also-as my theorem had shown-was substantial enough to be able, still, to say something and make waves. As you see,” he said, almost apologetically, “it isn’t easy to be free of such an aesthetic: we mathematicians always like to feel that we’re saying something that is meaningful.

  “However that may be, I have devoted myself ever since to studying what I privately call the aesthetic of reasoning in other spheres. I began, as always, with what seemed like the simplest model, or at least the closest: the logic of criminal investigations. I found the parallels with Godel’s theorem very striking. In every crime there is undoubtedly a notion of truth, a single true explanation among all the possible explanations. On the other hand, there are also material clues, facts that are incontrovertible or at least, as Descartes would say, beyond reasonable doubt: these would be the axioms. But then we’re already in familiar territory. What is a criminal investigation if not our old game of thinking up conjectures, possible explanations that fit the facts, and attempting to prove them correct? I began systematically reading about real-life murders, I went through public prosecutors’ reports for judges, I studied the method of assessing evidence and of structuring a sentence or an acquittal in a court of law. Just as when I was a teenager, I read hundreds and hundreds of crime novels. Gradually I began to find a multitude of interesting little differences, an aesthetic inherent in criminal investigations. And errors, too. I mean theoretical errors in criminology, which were potentially much more interesting.”

  “What kind of errors?”

  “The first, and most obvious, is attaching too much importance to physical evidence. Just think of what’s happening now in this investigation. If you recall, Inspector Petersen sent one of his officers to retrieve the note I received. Here once again the same insurmountable gap opens up, between that which is true and that which is provable. I saw the note, and that’s the part of the truth that the police can’t get to. My statement isn’t much use as far as police procedure goes; it doesn’t carry the same weight as the little piece of paper itself. Now, the officer, Wilkie, completed his task as conscientiously as he could. He questioned Brent and got him to go over what he knew several times. Brent clearly remembered seeing a piece of paper folded in two at the bottom of my wastepaper basket, but it hadn’t occurred to him to read it. Brent remembered too that I’d asked him if there was any way of retrieving the paper, and he told Wilkie what he told me: that he’d tipped the contents of the basket into an almost full refuse bag, which he’d put out soon after. By the time Wilkie arrived at Merton, the refuse lorry had been and gone almost half an hour earlier. When Petersen called me yesterday to ask me to describe the handwriting to their artist, I could tell that he was very disappointed at not finding the note. He’s considered to be the best police inspector we’ve had in years. I’ve had a look at the complete notes to several of his cases. He’s thorough, meticulous, implacable. But he’s still an inspector. I mean, he was trained in accordance with police procedure: you can predict the way his mind is going to work. Unfortunately, people like him follow the principle of Ockham’s Razor: as long as there’s no physical evidence to the contrary they always prefer a simple hypothesis to a more complicated one. That’s the second error. Not just because reality tends to be naturally complicated but mainly because, if the murderer really is intelligent and has prepared the crime carefully, he’ll leave a simple explanation for all to see, a smokescreen, like a conjuror leaving the stage. But in the stingy logic of the economy of hypothesis a different reasoning prevails: why assume something strange and out of the ordinary, such as a murderer with intellectual pretensions, if they have more immediate explanations to hand? I could almost physically feel Petersen step back and re-examine his hypotheses. I think he would have started suspecting me, if he hadn’t already checked that I was teaching between one and three that afternoon. I expect they checked out your statement too.”

  “Yes. I was in the Bodleian Library when it happened. They went to enquire about me there yesterday. Luckily, the librarian remembered me because of my accent.”

  “So you were consulting books at the time of the murder?” Seldom raised his eyebrows sardonically. “For once, knowledge really is freedom.”

  “Do you think Petersen will pounce on Beth now? She was terrified yesterday after they questioned her. She thinks the inspector is after her.”

  Seldom thought for a moment.

  “No, I think Petersen is cleverer than that. But consider the dangers of Ockham’s Razor. Suppose for a moment that the murderer, wherever he is, decides that he doesn’t have a taste for murder after all, or that the business with the blood and the police getting involved have ruined his fun; suppose that, for some reason, he decides to disappear from the scene. I think Petersen would then go after Beth. I know he questioned her again this morning, but this may simply have been a diversionary tactic, or a way of provoking the murderer, acting as if they don’t know about him, as if this were an ordinary case, a murder in the family, as the newspaper suggested.”

  “But you don’t really think the murderer is going to quit the game, do you?” I asked.

  Seldom pondered my question much more seriously than I’d expected.

  “No, I don’t,” he said at last. “I just think he’ll try to be more…imperceptible, as we said before. Are you free at all now?” he asked, glancing at the dining room clock. “Visiting hours at the Radcliffe are about to start, and I’m heading there. If you’d like to come along, there’s someone there I’d like you to meet.”

  Eight

  We went out through the gallery of stone arches at the back of the college. Seldom showed me the sixteenth-century Royal Tennis Court on which Edward VII played, which reminded me of a pelota court. We crossed the road and turned down what looked like a cleft between two buildings, as if a sword had miraculously sliced through the stone from top to bottom with a single long blow.

  “This is a short cut,” said Seldom.

  He walked fast, slightly ahead of me because there wasn’t room for both of us in the passageway. We emerged on to a path along the river.

  “I hope you don’t find hospitals too intimidating,” he said. “The Radcliffe can be a little depressing. The building has seven floors. Perhaps you’ve heard of an Italian writer, Dino Buzzati? He wrote a story called exactly that, ‘Seven Floors’, based on something that happened to him when he was here in Oxford to give a lecture. He describes the experience in one of his travel diaries. It was a very hot day and, as he came out of the lecture hall, he fainted briefly. As a precaution, the organisers insisted he be checked out at the Rad
cliffe. He was taken up to the seventh floor, the floor reserved for minor cases and general check-ups. They examined him and carried out a few tests. They told him everything looked fine but they wanted to do some more specialised tests, just in case. For that, they had to take him down a floor; meanwhile, his hosts could wait for him upstairs. He was taken down in a wheelchair, which he found a little excessive, but he decided to put it down to British zeal. Along the corridors and in the waiting rooms on the sixth floor, he saw people with burnt faces, people wrapped in bandages, lying on trolleys, blind, mutilated. He himself was made to lie on a trolley while he was X-rayed. He was about to sit up when the radiologist said they’d detected a small anomaly-probably nothing serious, but he should remain lying down until they got the results of the other tests. He’d have to be kept under observation for a few more hours, so he’d be taken down to the fifth floor, where he could have a room to himself.

  “On the fifth floor the corridors were empty but a few doors were ajar. Inside one of the rooms he glimpsed people lying in bed, arms connected to drips. He was left alone in a room, on a trolley, growing increasingly alarmed, for several hours. At last, a nurse came in, carrying a little tray containing a pair of scissors. She’d come to cut off some of the hair from the back of his head, on the instructions of a doctor on the fourth floor, Dr X, who would be carrying out the final examination. As his hair fell into the little tray, Buzzati asked if the doctor would be coming up to see him. The nurse smiled, as if only a foreigner could have thought such a thing, and said that the doctors preferred to remain on their own floors. But she would take him downstairs herself and leave him waiting beside a window. The building is U-shaped and, looking down from the window on the fourth floor, Buzzati could see the blinds at the first-floor windows which he describes in his short story. Some of the blinds were up, but most were pulled down. He asked the nurse who was on the first floor and she gave him the reply that he reproduces in the story: only the priest worked down on that floor. Buzzati writes that during the dreadful hour that he spent waiting for the doctor, he became obsessed with a mathematical idea. He realised that the fourth floor was exactly halfway in the countdown from 7 to 1 and, out of superstitious terror, he was convinced that if he went down one more floor, everything would be lost. Intermittently, from the floor below, he could hear what sounded like the desperate cries of someone delirious with pain and grief. It was as if the screams were creeping up the lift shaft. Buzzati decided to resist with all his might if they came up with any excuses for taking him down another floor.

  “The doctor arrived at last. It wasn’t Dr X but Dr Y, the consultant. He could speak a little Italian and he knew Buzzati’s work. He took a quick look at the test results and the X-rays and expressed surprise that his young colleague, Dr X, should have given instructions to cut Buzzati’s hair. Perhaps, said Dr Y, he was considering a preventive puncture. Anyway, it wouldn’t be necessary. Everything was absolutely fine. The doctor apologised and said he hoped that Buzzati hadn’t been too upset by the man screaming on the floor below. He was the only survivor of a car accident. The third floor could be very noisy, the doctor told him, a lot of the nurses down there used earplugs. But they would probably soon be taking the poor man down to the second floor and things would be quiet again.”

  Seldom nodded towards the large, dark brick form that now rose before us. He went on, as if struggling to finish the story in the same calm, measured tone: “The entry in Buzzati’s diary is dated 27 June 1967, two days after the car crash in which I lost my wife, the crash in which John and Sarah died. The man in agony on the third floor was me.”

  Nine

  We mounted the stone steps at the entrance in silence. Inside, we crossed a large hall. Seldom greeted almost all the doctors and nurses we passed in the corridors.

  “I spent almost two years in here,” he said. “And I had to come back every week for a whole year after that. Sometimes I still wake in the middle of the night thinking I’m back in one of the wards.” He indicated a bend in the corridor from which rose the worn steps of a spiral staircase. “We’re going to the second floor,” he said. “It’s quicker this way.”

  On the second floor we walked down a long, bright corridor in which a deep, hushed silence reigned, as in a cathedral, and our steps echoed dismally. The floors looked as if they had just been polished, and shone as if few people ever walked across them.

  “The nurses call this the Fish Tank, or the Vegetarian Section,” said Seldom, pushing open the swing doors to one of the wards.

  There were two rows of beds, with far too little space between them, as in a field hospital. In each bed there was a body of which you could see only the head, connected to an artificial respirator. The combined sound of the respirators was a deep, restful gurgling, which really did make you think of an underwater world. As we walked down the aisle between the rows of beds I noticed that a bag collecting faeces hung from the side of each body. Bodies, I reflected, reduced to nothing more than orifices. Seldom caught my expression.

  “Once, I woke up in the night,” he whispered, “and I heard two nurses, who’d been on duty in this ward, whispering about the ‘dirty ones’ who filled their bags twice a day, so the nurses had the extra job of changing them again in the afternoon. Whatever their state, ‘dirty ones’ don’t last long on the ward. Their condition somehow always deteriorates slightly and they have to be transferred elsewhere. Welcome to the land of Florence Nightingale. The medical staff enjoy almost complete impunity because relatives rarely get this far-they visit once or twice in the beginning, then they disappear. It’s like a warehouse. A lot of these patients have been on respirators for years. I try to get here every afternoon because, unfortunately, Frankie has recently become a ‘dirty one’ and I wouldn’t want anything strange to happen to him.”

  We stopped by one of the beds. The man, or what remained of the man lying there, was a skull with a few grey hairs straggling over the ears and an impressively swollen vein at the temple. The body beneath the sheets had wasted away, making the bed seem far too big, and I suspected he might not have any legs. The thin white sheet hardly moved over his chest and, though the wings of his nose quivered, no breath misted the plastic mask over his face. One arm lay outside the sheet, connected by a copper fastening to what I thought at first must be a machine monitoring his pulse. In fact it was a device which held the arm in place over a notepad. A short pencil was attached rather ingeniously between the thumb and index fingers. But the hand, with very long nails, lay limp and lifeless on the sheet of white paper.

  “Perhaps you’ve heard of him,” said Seldom. “He’s Frank Kalman. He extended Wittgenstein’s work on rule-following and language games.”

  I said politely that the name was familiar, though only very vaguely.

  “Frank wasn’t a professional logician,” said Seldom. “In fact he was never the kind of mathematician who wrote papers or attended conferences. Soon after graduating he took a job in a large employment consultancy. His work involved preparing and assessing tests for applicants to various jobs. He was assigned to the department dealing with symbol manipulation and IQ tests. A few years later he was also appointed to set the first standardised tests in British secondary schools. He spent his whole life preparing logical series, of the most basic kind, like the one I showed you: given three symbols in sequence, please fill in the fourth symbol. Or series of numbers: given the numbers 2,4, 8, please write the next number in the series. Frank was meticulous, obsessive. He used to check the mountains of tests one by one, and he started to notice something very odd. There were, of course, perfect exam scripts, about which you could say, as Frank wrote later with wonderful tact, that the candidate’s answers exactly matched the examiner’s expectations. There were also, and these were in the overwhelming majority, those Frank called the normal bell-curve-exam scripts with a few mistakes that belonged to the category of expected errors.

  “But there was a third group, always the smallest, wh
ich drew Frank’s attention. These were almost perfect exam scripts, in which all but one of the answers were the expected ones. But they differed from the usual cases in that the mistake in that single different answer seemed, at first glance, utterly absurd, a continuation picked almost blindly or at random, truly well outside the spectrum of usual mistakes. Out of curiosity, Frank thought of asking the candidates in that small group to justify their answers, and that was when he got his first surprise. The answers that he had considered incorrect were in fact another possible and perfectly valid way of continuing the series, only with a much more complicated justification. The strange thing is that these candidates hadn’t seen Frank’s elementary solution, and instead had jumped well beyond it, as if on a springboard. The springboard image is Frank’s as well; he thought of the three symbols or numbers written on a paper as the diver’s run along the diving board. Seen like that, the analogy seemed to provide him with an initial explanation: the farthest solution comes more naturally to a mind used to taking big leaps forward than the one that’s right in front of it. But this, of course, challenged, at their very roots, the assumptions on which he’d based his life’s work.

  “Frank was suddenly disconcerted. The solutions to his series weren’t in any way unique. Answers that he had so far considered wrong might be alternative and also, in some way, ‘natural’ solutions. He couldn’t even see a way of distinguishing between what might be a random answer and the continuation of a series which an exceptional, and too athletic, mind might choose. It was at this stage that he came to see me and I had to break the bad news to him.”

  “Wittgenstein’s finite rule paradox,” I said.

  “Exactly. Frank had rediscovered in practice, in a real experiment, what Wittgenstein had already proved theoretically decades earlier: the impossibility of establishing an unambiguous rule. The series 2, 4, 8, can be continued with the number 16, but also with the number 10, or 2007. You can always find a justification, a rule, that lets you use any number as the fourth term in the series. Any number, any continuation. This is something Inspector Petersen wouldn’t be too pleased to hear, and it almost drove Frank mad. He was over sixty by then, but he asked me for the references and he had the courage to enter, as if he were a student again, the abandoned cave that is Wittgenstein’s work. And you know about Wittgenstein’s descent into darkness. At one stage Frank felt as if he were on the edge of an abyss. He realised he couldn’t even trust in the rule of multiplying by two. But he emerged with an idea, rather similar to my own. Frank clung with almost fanatical faith to the remains of the shipwreck: the statistics from his experiments. He believed that Wittgenstein’s results were theoretical, from a Platonic world, but that real people thought in a different way. After all, only a tiny proportion came up with the atypical answers. So he conjectured that, though in principle all answers were equally probable, there might be something engraved on the human psyche, or in the approval-disapproval games during symbol learning, which guided most people to the same place, to the answer that seemed the simplest, clearest or most satisfying. He was definitely thinking, as I was, that some kind of aesthetic principle was operating a priori which only let through a few possible answers for the final choice. So he decided to provide an abstract definition of what he called normal reasoning.