A Whistling Woman

by A. S. Byatt

  When it came to Lucy’s turn, everyone was very gentle. She spoke from the dock and a social worker sat near her. I sat across the courtroom with Ramsden. She looked steadily at him, all the time she was talking. Her voice was small and husky, as though she didn’t know for certain it would be there.

  She said Gunner had attacked her with the rake. She said he often attacked her, especially when he had been drinking. No, he had not been drinking on that occasion. Yes, she had followed him to the hen-house and stabbed him with the trowel. She had done that in the middle of a further violent argument, yes, to defend herself. He had been going to hit her with something heavy. Possibly a spanner, yes. She hadn’t been seeing straight. She was crying. Yes, she was afraid. Yes, she was afraid for her life.

  Why had she left the children? She looked at Ramsden for help with this question. She said, she didn’t know, she remembered nothing clearly.

  Who had hurt the children? She looked at Ramsden again, and answered, Gunner had hurt them. She added “He hurts people easily without thinking.”

  She had not hurt the children herself?

  No, she said.

  Had she ever hurt them?

  She began to shake her head from side to side. “Why do you ask that? Why? I wouldn’t. I don’t. They are my children.”

  “They are Gunner’s children.”

  “He doesn’t think, when he’s in that mood.”

  So why had she followed Gunner to the hen-house and left the children, who were in need of help?

  She stared quite desperately at Ramsden.

  “I don’t know why. It was all over, I knew it was all over. People don’t always do the best thing, the sensible thing.”

  “What do you mean, it was all over?”

  “Well, it was. It was all finished. Everything was.”

  Her little round face was a mask of misery. Pity rose in everyone, including me. She was convicted of actual bodily harm, and placed under a probation order, on condition she attend a psychiatric hospital. You can see that the police, and the Social Services, and the court, had a presumption in favour of Lucy. The police, too, have had several run-ins with Gunner, pub-fights, dangerous motor-biking. Gunner said he was shaking the soil of the place from off his feet and stomped away. The house and land were Lucy’s not his, and it was always assumed he married her for them. Now it turns out they were not in fact married because he had a wife in Iceland all the time. He was a seaman, not a farmer, before they “married.”

  All the same, Elvet, for the first time I wondered. Who hurt the children? What exactly happened? We ask our careful, neutral, probing questions and come up with muddle and mystery. I don’t know if anybody any more knows what happened, that day, or will, now.

  But I need most urgently to see you yourself, to talk to you. For Lucy proposes to give Dun Vale Hall to the Spirit’s Tigers, to found a religious (therapeutic) community. That is, really, she proposes to give it to Joshua Ramsden. And whilst, on balance, if the good Quakers come, I think this will do good, not harm—it could indeed do much good to many people—the potential for harm is also there, and not inconsiderable. I need to see you, to discuss Ramsden’s state of mind—“state of health” seems presumptuous—to discuss Lucy—to discuss the legalities of letting them both go, and the definition of the new group.

  Ramsden is walking tall. He says “This is our chance to make a good thing in this world.” We do have to take risks, sometimes. Don’t we?

  Chapter 14

  At the end of the autumn term, the Non-Maths Group was reduced to a rump, which met in the Argus Eye, in Blesford, and consisted essentially of four people, Vincent Hodgkiss, Luk Lysgaard-Peacock, Marcus Potter and John Ottokar. Marcus had been made convenor by Professor Calder-Fluss, and John Ottokar represented the university’s computer.

  The Vice-Chancellor was absent, Hodgkiss explained, because of administrative problems. The Anti-University grew, he said, like the Hosts of Midian. Plastic tents sprouted like mushrooms. Caravans and camping-cars came and went. The students of the UNY streamed steadily into the Anti-University’s courses. Jonty Surtees’s semisituationists now had regular meetings with Nick Tewfell, the Students’ Union president. There were now formal protests against the unique four-year course, with its required maths and languages. “They want ‘theory and praxis of living situations,’ ” said Hodgkiss in his high-pitched Oxford-drawl, leaning back in the wooden settle.

  Luk asked what was taught at the Anti-University. Hodgkiss said there had been a 13-hour-long discussion, led by, that was, initiated by, Avram Snitkin, on whether anything at all should, or could, be discussed in artificially constructed forums of the kind they might at that moment find themselves in. There had also been an enthusiastically attended teach-in against exams, and a course on “de-sanctification of oppressive structures.” And a 36-hour-long television-watching orgy, “against passive consumerism” at the end of which the television had been hammered to bits and burned to ashes.

  There were also Lady Wijnnobel’s courses, which drew crowds, from inside and outside UNY. She gave lectures—orations—on Mystic Identity, Visionary Astrology, the Secret Wisdom of the Ancient World. She also gave “interactive sessions” on things like chiromancy, oneiromancy, geomancy, and horoscope-casting.

  Luk said Gerard Wijnnobel was either a fool or a saint.

  Hodgkiss said he was certainly not a fool. It was possible that he was a saint. He was a born liberal who took the line that self-expression was a right, and that in the end the students would be amenable to a judicious mixture of eloquence and reason.

  “Reason is oppression,” said Marcus. “I quote a sticker on the wall of the Maths Tower.”

  Hodgkiss said that, as Dean of Students, he was himself, so to speak, the secular arm, and should perhaps do something. Something authoritarian, or something machiavellian. “Both not in my nature. I prefer to sit here reading Wittgenstein and drinking beer. I do not think scholars are good at authority. As for Wijnnobel’s wife, she is not his chattel. She has signed no vow of silence.”

  Luk said he thought the Vice-Chancellor carried altruism to absurd lengths. Hodgkiss murmured that the iron seemed to have entered Luk’s soul, to which Luk did not respond. No one had remarked on Jacqueline’s absence. John Ottokar was still struggling with the complicated programmes needed to analyse her action potential spikes, but he said nothing to or about her as far as the Non-Maths Group went. He was also helping Luk with the equally difficult maths of his paper about sex and altruism. Luk had been very interested in John Maynard Smith’s searching questions about the greater cost for a species (in energy used up) by sexual reproduction than by parthenogenesis. Why do creatures not simply bud, or clone. He had established that the northern black slug, Arion alter, was self-fertilising, and its populations were a dispersed clone. The southern slug, Arion rufus the red slug, was, in the usual hermaphrodite way, a sexual being, aggressively manoeuvring for sexual advantage, and, moreover, cannibalistic. If you carried home a bucketful of the gentle clones, they would huddle together companionably. Whereas a bucketful of rufus would tear each other into a soup, with one or two self-selected, fit survivors. If you put them in huts in hot dry conditions, the black slugs would lovingly offer each other a shared damp slime, whereas the red ones would swelter and shrivel in justified mistrust.

  Hodgkiss remarked that biologists did something disconcerting to the word “altruism.” Which was used to describe human social care for others, even love. A man giving his life for his friend. The exquisite courtesy of Gerard Wijnnobel (if that was what it was). Not simply the preservation of the germ-line.

  “We all grew up,” said John Ottokar the Quaker, “with the image of the mother-skylark, pretending to drag a wounded wing to draw away the hunter. We were told, this showed that love, and altruism, were part of the natural world—”

  “According to the maths of all this,” said Luk, “which you understand better than I do—this is simply a case of the odds on
protecting more of her genes by self-sacrifice. According to this statistical view of love, of course, perfect love wouldn’t be mother-love. It would be—it could only be—monozygotic twins. Clones, like my black slugs.”

  “A monozygote,” said John Ottokar slowly, “is its twin’s mother and sibling. Parthenogenesis after sexual propagation.”

  Luk was about to embark on a complicated exegesis of kin-theory when he realised that for John, the problem of monozygotes was personal. He said

  “Bill Hamilton has been working on the mathematics of spite. Looking for examples in the non-human world of successful malice, or malevolence. Spite as opposed to selfishness. Ethics sit uneasily with biology. I don’t think the red slugs are spiteful. I think it’s like overcrowded hens in batteries tearing each other’s flesh. They pick on the weakest.”

  “Scapegoats,” said Hodgkiss.

  “That’s a religious idea,” said Luk. “Religion is a construction to explain things. Not an examination of cause and effect.”

  “Humans are spiteful,” said John Ottokar. “Humans enjoy executions. Humans get together in gangs and torment the odd and the weak. They pull wings off flies and burn cats.”

  “Humans invented self-sacrifice and simple kindness,” said Hodgkiss. “Respect for other selves. The unit of ethics is the biped in its skin. Not the molecule in the helix.”

  “They have always needed religion to keep them to that,” said John.

  “No one can defend truth with lies,” said Luk. Hodgkiss’s slightly prissy mouth pursed with a mixture of glee and pugnacity over this wild statement. How the discussion would have gone on was never known, for it was interrupted.

  A woman and a child appeared in the door of the bar, hand in hand, with flaming hair. It was Frederica and Leo, up North for the Christmas holidays, come to look for Marcus, at Winifred’s request. She strode towards the maths table, pleased to see them. They were not pleased to see her. She broke the circle.

  Leo said enthusiastically, “John O—John O—” and, since John looked somehow dangerous and frowning, said more doubtfully—“it is John? It isn’t—Paul, is it? I know it’s John, it is, isn’t it?”

  “Does it matter?” said John, heavily.

  “Mummy wondered—” said Frederica to Marcus. She looked round. “How nice you’re all here. Where’s Jacqueline? I suppose the snails are in hibernation. It’s very cold. I wanted to talk to you, Luk, I wanted to ask you, whether you’d be interested in being on an odd television programme ...”

  Luk stood up.

  “No,” he said. “I wouldn’t. I’ve got to go.”

  “Perhaps I could come and talk to you ...”

  “I shouldn’t bother. I see no point in trying to say complex things in simple phrases in very short sentences with joky distractions. No point. I’ve got to go.”

  He went. Frederica stared after him. The barman came over and pointed out that Leo was a little boy, and was not allowed to be in there. John Ottokar said “Come on, Leo, I’ll take you out.”

  Frederica, crestfallen, gave her mother’s message to Marcus. Vincent Hodgkiss, leaning back in his settle, looked at brother and sister and thought to himself that the theory of kin selection broke down a little, here. The woman resembled the angry biologist—also red-headed, also bristling with energy—more than the delicate, reticent mathematician, owl-eyes downcast. He did not know—then—that Marcus was also thinking how little tie there was between him and Frederica. When Stephanie had been alive, Marcus thought, they had all three been connected. He then remembered her death, as he tried not to do. He had not been required to sacrifice himself. Only to show enough presence of mind to throw an electric switch. Which he had failed to do. He stared gloomily at the beer-rings, and said he was coming soon, he’d call his mother, he had things ...

  “We’re having dinner,” said Hodgkiss. “We have things to discuss.”

  Marcus looked up, and then down. Hodgkiss thought, he’s not interested in people, and it’s never occurred to him—until this moment—that I’m interested in him.

  Frederica stood, having destroyed a harmonious group completely involuntarily. Then she turned, and went out to her son, and her lover, about whom she had no idea what to do.

  Blesford’s only restaurant was a cramped pseudo-Trattoria. Hodgkiss drove Marcus out into the moor, to a hotel, the Rose of York. The dining-room was formal with a large wood fire. There were three other hushed couples in the carpeted quiet. There were candles in silver candlesticks on white damask tablecloths, and a very bright central chandelier. Hodgkiss asked if this could be dimmed. There were green curtains with a design of white roses and briars. Hodgkiss ordered a bottle of white burgundy, a bowl of spinach soup, and a grilled sole. Marcus ordered the same.

  “Don’t look troubled. This is coerced altruism. I need your help with a problem. And you looked hungry.”

  “Did I?”

  “You did.”

  Marcus stirred his soup. Hodgkiss thought, he never looks at people. He’s a monad. Shall I tell him so? Better not. He watched Marcus stir his soup the other way, take a cautious sip, wipe his mouth. I shall never tempt him with the delights of the flesh, thought Hodgkiss, offering a bread roll. He said

  “I thought you might be able to make me understand Cantor’s mathematics of infinite sets.”

  Marcus put down his spoon and took a mouthful of wine.

  “Wittgenstein gave a course of lectures in 1939 on the Foundations of Mathematics. He attacked Cantor’s Diagonal Proof. With extraordinary vehemence.”

  Marcus looked up.

  “Why?”

  “Can you describe it to me, so that I can understand it? So that I can have enough of an idea to think about it?”

  “Oh yes,” said Marcus. He smiled. His smile was gentle and tentative and opened his mild face.

  He explained. The Diagonal Proof is a way—which can be visualised as geometry—of relating finite sets to infinite sets. Two infinite sets are equal if they can be put into a one-to-one correspondence with each other. They are said to have the same “cardinality.” Like, for instance, the set of all even numbers, or the set of all “natural” numbers. 1, 2, 3, 4 and so on. They can be represented with a set of branching diagonals. He fumbled in his jacket pocket, found an envelope, and drew a rough, forking grid. Hodgkiss produced a leather-bound notebook. They bent over it, heads together. Marcus’s hair smelled young, and his skin smelled faintly of witch-hazel in baby-soap. His fine fingers multiplied lines, through the soup and the sole, moving surely across the paper. When his pencil broke, Hodgkiss gave him his own pen, and watched him adjust his grip, test the slant of the nib and the flow of the ink. It was a stubby, mottled pen, black and midnight-blue. It produced, in Marcus’s grip, a string of spider-webs, of ghosts of branches, of shapes like the graduated spines on the fish skeletons.

  “And then you can arrange all the rational fractions systematically and beautifully—like this ...”

  Hodgkiss watched the confident fingers weaving and felt—quite agreeably—like a heavy schoolboy watching a light agile boy swinging and dancing, far above his head in the gymnasium, on ropes he couldn’t even begin to mount.

  “I see. I almost see. I see while you’re talking. Does this relate to Godel’s ideas about incompleteness?”

  “Oh yes.”

  Marcus drew more lines, and drank two glasses of wine. He explained the Continuum Hypothesis, and said that Cantor had gone mad, and it was believed to be the Hypothesis which had caused him to do so. A shadow came over his face. He put down Hodgkiss’s pen.

  “I can understand that,” he said.

  “Going mad with maths?” Hodgkiss asked lightly. Marcus looked up from the bony remnants, boiled white eye and gaping flatfishmouth on his plate, and met Hodgkiss’s eye.

  “Why did Wittgenstein hate the Diagonal Proof?”

  “Here you come up against my incapacity to understand what it is—which means I don’t understand his objections to it. H
e treated it almost as though it was demonic. He spoke of it as a kind of glamour, like witchcraft, cast over mathematicians, who were led to believe that because it was mathematically and logically coherent it was somehow true and incontrovertible. Hilbert the mathematician said “No one is going to turn us out of the paradise which Cantor has created.” Wittgenstein used to tell his classes he wouldn’t dream of trying to drive them out of this paradise. He would simply demonstrate that it was no paradise. It was a swamp, a quagmire full of philosophical will-of-the-wisps and mess—and delusional metaphysics. When they saw it clearly, he said, they would leave of their own accord. Wittgenstein said they would leave. I take it you would prefer to stay?”

  “It is very beautiful,” Marcus said slowly.

  “And real?”

  “To me, yes. I, I feel it is infinitely more real than the everyday world.” He looked around. “More real than this soup, the candle, the spoon, the flame. Though number is in all those.”

  He glimpsed the dissolution of the liquids and solids and gases, the shining silver, the vegetable fibre, into spinning forms of molecules, made of movements of particles. He looked up, and met Hodgkiss’s enquiring eyes.

  “As I understand it,” said the philosopher, “there are mathematicians who believe that finite numbers are real things you can discover—intuit—in the real world. But they don’t all believe that completed infinite sets are real in the same way. Mental phantoms, perhaps. Fictions? You tell me.”