The Oxford Murders

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, which 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.

“But he took a rather strange route. He started visiting psychiatric hospitals and trying out his tests on lobot-omised patients. He collected examples of individual words and symbols written by people in their sleep. He took part in hypnosis sessions. But mainly he studied the types of symbols that brain-damaged patients in quasi-vegetative states used in attempts to communicate. Actually, he was trying to do something which by definition is almost impossible: to study what remains of reason when reason is no longer there watching over things. He thought he might be able to detect some kind of residual movement or stirring which corresponded to an organically imprinted track or routine pathway created by the learning process. I suppose he already had a morbid inclination which had something to do with what he was planning. He had just found out that he was suffering from a very aggressive form of cancer which first attacks the legs. All doctors can do is cut off limbs one after the other. I came to see him after the first amputation. He seemed to be in good spirits, considering the circumstances. He showed me a book his doctor had given him, containing photographs of skulls partially destroyed in accidents, suicide attempts, or smashed by bats. There was a comprehensive clinical account of the consequences and interconnections arising from brain injuries. Looking very mysterious, he pointed out a page which showed the left hemisphere of a brain with the parietal lobe partially destroyed by a bullet. He told me to read what it said below the photograph. The man, who had tried to commit suicide, had fallen into an almost complete coma, but for months his right hand had apparently kept drawing all kinds of strange symbols. Frank explained that, during his visits to hospitals, he had found a close connection between the type of symbols he was collecting and the occupation of the coma patient during their lifetime.

“Frankie was extremely shy, and this was the only time he confided anything of a personal nature: he told me he regretted never having married and, with a sad smile, he said he hadn’t done much with his life, but he had drawn and manipulated logical symbols for forty years. He was sure he would never find a better subject than himself for his experiment. He was convinced that it would somehow be possible to read the coded residue or substratum that he’d been looking for in the symbols that he would draw. In any case he didn’t intend to be around when they came for his other leg. But he had one last problem to solve, and that was how to ensure that the bullet didn’t cause too much damage, that metal shards didn’t reach the nerve circuits affecting motor function. I’d become fond of him over the years and I told him that I wasn’t prepared to help him with his plan, so he asked if I’d be there to read the symbols, in the event that he succeeded.”

We both suddenly noticed the hand tense spasmodically, gripping the pencil, as if receiving electric shocks. Fascinated and horrified, I watched the pencil move slowly and clumsily across the page, but Seldom seemed not to pay much attention.

“He starts writing at this time of day,” he said, not bothering to lower his voice, “and he continues almost all night. Anyway, Frankie was highly intelligent, he found the solution. An ordinary gun, even a small-calibre one, would leave too great a margin of error because of possible bullet fragments. He needed something that could penetrate the skull and reach the brain cleanly, like a small harpoon. This wing of the hospital was undergoing building work at the time and it seems he got the idea from a workman with whom he had a conversation about tools. In the end, he used a nail gun.”

I leaned forward to try to make out the confused marks appearing on the paper.

“Until recently his handwriting was perfectly legible, but it’s becoming increasingly hard to read,” said Seldom. “In fact he’s only writing four letters, over and over again. The four letters of a name. All these years Frankie has never drawn a single logical symbol or number. The only thing he writes, endlessly, is a woman’s name.”