“But we can’t be sure yet,” said Seldom, his objection strictly intellectual. “We can’t make an induction with only two cases.”
“I’d like to hear your view anyway,” said Petersen.
Seldom still seemed unsure.
“In both cases,” he said at last, cautiously, anxious to keep to the facts, “the murders were as slight as possible, if that’s the right word. I don’t think the deaths themselves are what really matters to him. The murders are almost symbolic. I don’t believe that the killer is actually interested in killing, but in signalling something. Something that’s undoubtedly linked with the series of figures he’s drawn on the notes, beginning with a circle and a fish. The murders are simply a way of drawing attention to the series and he’s choosing victims close enough to me so that I’ll get involved. I think in fact that it’s a purely intellectual problem, and that he’ll only stop if we somehow manage to prove to him that we’ve determined the meaning of the series; in other words, that we can predict which symbol, or murder, comes next.”
“I’m going to get a psychological profile drawn up this afternoon, though I don’t think we’ve got much to go on yet. But perhaps you can now answer the question I asked you before: do you think it’s a mathematician?”
“I’m inclined to say no,” answered Seldom slowly. “At least, not a professional mathematician. I think he’s someone who imagines that mathematicians are paragons of intelligence and that’s why he wants to challenge them directly. He’s a sort of intellectual megalomaniac. I don’t think it’s a coincidence that he chose to place his second message on the Institute door. I assume there’s a second hidden message to me in it: if I don’t take up the challenge, another mathematician will. And if we’re making conjectures, I’d say that it’s someone who was once unjustly failed in a maths exam, or who missed an important opportunity in life because of an IQ test of the kind Frank Kalman devised. Someone who was excluded from what he considers the realm of intelligence, someone who both admires and hates mathematicians. Possibly he conceived the series as revenge against his examiners. In a way, he’s the examiner now.”
“Could it be a student whom you failed?” asked Petersen.
Seldom smiled.
“I haven’t failed anyone in a long time,” he said. “I only have graduate students now, and they’re all excellent. I’m inclined to believe that it’s someone who hasn’t studied maths formally but who’s read the chapter on serial murders in my book and, unfortunately, thinks that I’m the person he has to challenge.”
“Right,” said Petersen, “as a first step, I can get a list of all the credit-card purchases of your book at the bookshops in town.”
“I don’t think it’ll be much help,” said Seldom. “When the book first came out, my publishers managed to get the chapter on serial murders published in the Oxford Times. A lot of people thought it was a new kind of crime novel. That’s why the first edition of the book sold out so fast.”
Petersen stood up, looking a little discouraged, and examined the two figures on the blackboard for a moment.
“Can you tell me anything more about this now?”
“The second symbol of a series generally provides a clue as to how the rest of the series should be read: whether as a representation of objects or facts from a possible real world-in other words, as symbols in the most usual sense-or, without any connotation of meaning, on a strictly syntactical level, as geometric figures. The choice of the second figure is, again, very clever because the fish is drawn in such a simplified style that it can be read both ways. The vertical position is interesting. It might be a series of figures symmetrical to the vertical axis. If we really are to interpret it as a fish, there are, of course, many other possibilities.”
“The fish tank,” I said, and Petersen turned to me, a little surprised. Seldom nodded.
“Yes, that’s what I thought at first. That’s what they call the floor Ernest Clarck was on at the Radcliffe,” he said. “But that would point directly to someone inside the hospital, and I don’t think he’d choose a symbol that would incriminate him so obviously. And anyway, if that’s the case, what does the circle have to do with Mrs Eagleton?” Seldom paced up and down for a while, head bowed. “Something else that’s interesting,” he said, “and which is implicit in a way in the notes, is that he assumes that mathematicians will be able to find the solution. In other words, there must be something in the symbols that matches the type of problems, or intuitions, related to a mathematician’s way of thinking.”
“Would you like to venture what the third symbol might be?” asked Petersen.
“I have an initial idea,” said Seldom. “But I can see several other ways the series might continue that are, shall we say, reasonable. That’s why in tests you’re given at least three symbols before you’re asked what the next one is. Two symbols still allow too many ambiguities. I’d like to have more time to think about it. I wouldn’t want to get it wrong. He’s the examiner now and another murder would be his way of giving us another bad mark.”
“Do you really believe he’ll stop if we find the solution?” asked Petersen doubtfully.
But there was no such thing as the solution, I thought. That was the most exasperating thing. I suddenly understood why Seldom had wanted to introduce me to Frank Kalman and the second dimension to the problem that was preoccupying him. I wondered how he’d explain minds that took big leaps, Wittgenstein, rule-following paradoxes and the movements of normal bell-curves to Petersen. But Seldom needed only one sentence:
“He’ll stop,” he said slowly, “if it’s the solution that he has in mind.”
Twelve
Petersen stood up and paced about the room, his hands behind his back. He picked up his jacket-which earlier he’d laid on the edge of the desk-turned for a moment to stare at the blackboard, and wiped off the circle with his hand.
“Remember, as far as possible, we’re going to keep the first symbol to ourselves. I don’t want to tempt a copycat killer. Do you think any of the mathematicians downstairs might be able to guess the next symbol, now that they know the second?”
“No, I don’t think so,” said Seldom. “And I’m not sure they’d be interested enough to try. To a mathematician, the only problem that matters tends to be the one he’s working on at the time. It may take more than a couple of murders to tear them away from what they’re doing.”
“Does the same go for you?” Petersen was now staring hard at Seldom; there was cold reproach in his voice. “To be honest, I’m a little…disappointed,” he said, choosing his words carefully. “I wasn’t expecting you to give me a definitive answer today, of course, but I had hoped for four or five possible alternatives, conjectures that we could work on or eliminate. Isn’t that how mathematicians work? But perhaps a couple of murders don’t interest you enough either.”
“I have an initial idea, as I said,” said Seldom, his small pale eyes meeting the inspector’s. “I promise I’ll give the matter my full attention. I just want to be sure that I’m not mistaken.”
“I wouldn’t want you to wait until the next murder to find out if you were right,” said Petersen. Then, as if reluctantly trying to make up for his earlier sharpness, he went on: “But if you really do want to help, please come to my office tomorrow, after six. We’ll have the psychological profile by then. I’d like you to read it: it may bring someone to mind. You’re welcome to come too,” he said to me, and quickly shook hands with both of us.
After Petersen had left there was a long silence. Seldom went to the window and started rolling a cigarette.
“Can I ask you a question?” I said at last cautiously. I was aware that he might not want to tell me anything either, but I decided it was worth a try. “Your idea, your conjecture, is it about the next symbol, or the next murder?”