Chapter Five Number Theory
Five
Number Theory
Lyra found Ionides on a bench near the fountain, reading a newspaper in the full sun.
It was just past midday, and men in shirtsleeves and women with parasols were strolling comfortably through the square, tempted this way or that by the smell of grilling meat or spices or baking bread, or sitting on the low wall around the fountain to enjoy the coolness of the drifting spray.
Lyra sat down beside Ionides and took off her royal ribbon.
“You not a queen now?” he said.
“No. I’m traveling incognito.”
“And me no more sorcier?”
“No. You’re in disguise as a poet.”
His gecko daemon laughed, a little silvery sound. He folded his newspaper. “Not the first time,” he said cheerfully.
“Come and walk with me. I want to find somewhere quieter under the shade of some trees, a garden of some kind or a park. I’m sure you could find somewhere like that.”
“This way,” he said. “The Ambassador of Brazil was a generous man. He give his embassy and garden to the people of Aleppo in memory of his wife. Is very romantic. Lot of trees.”
“What did the Brazilian government have to say about that?”
“He not tell them yet. Too late now.”
The sidewalks were too crowded to let them talk easily, so Lyra said nothing as Ionides led the way.
No doubt the people now coming out of their workplaces for lunch would take a siesta afterwards, unless the desire to make more money was stronger than the desire to lie down in a cool place.
Again Lyra was struck by the charm of the city, the pleasure in the faces and voices around her, the straightforward sensuous joy in the fact of having a body in a world that suited it so well.
She hadn’t felt anything like that since Pan left—in fact, since before that: the last time she’d felt so uncomplicated was on one of those long summer evenings with Dick Orchard by the river, his hands on her body and hers on his, kissing and being kissed while Pan and Dick’s pretty vixen daemon played nearby.
As she and Ionides entered the embassy garden, she felt a pang so sharp that she couldn’t help a soft murmur of pain and loss.
Ionides stepped a little closer, as if to catch her if she stumbled, but he said nothing. They walked along a graveled path to a bench under a wide-spreading cedar tree.
She sat, and then he joined her.
“Now, Mr. Ionides,” she said, “I want you to tell me about the good numbers and the spaces between them.”
“Good numbers? Forty is a good number for dollars,” he said. “And the space between me and forty dollars is very wide.”
“Well, all right, that was a good answer. Let’s get that over with first.” She counted out thirty dollars. “That is what I owe you, and this”—an extra ten—“is what I’ll add to it if you agree to go with me to Karamakan.”
“Same rate as to Aleppo?”
“Certainly, provided we can agree on the distance and the time.”
“All right, Miss Silver, I trust you. We shall count as we go.”
They shook hands. His grip was firm and dry and cool. He folded the money away.
“Now,” she said, “again. I want to know about the good numbers. Don’t try to fool me.”
“How you know if I fool you or not?”
“When you’re not telling the truth, your left eyelid flickers. I’ve noticed it before. Now come on, I want to know.”
“Where you hear about good numbers?”
“In the dead city. In Madinat al-Qamar. There were voices speaking to me, and they said they came from the gulfs between the good numbers. They wouldn’t tell me any more than that.”
“You mind if I smoke?”
“Can you smoke and talk at the same time?”
“Yes. Easy.”
“Then I don’t mind. What do you know about good numbers?”
He fished a cigarette from a battered packet and struck a match. He blew a thin stream of smoke, watching her with eyes whose lids didn’t flicker at all.
“There is so many kind of numbers,” he said. “There is numbers on the number line, like one and two and minus forty-six and eleven point five. Then there is numbers that go on forever, like pi. Then there is prime numbers. You know prime numbers?”
“Yes.”
“Then there is infinity.”
“Is that a number?”
“No. But this is where we think about it. Then there is imaginary numbers, like square root of minus one.”
Lyra remembered: that laboratory on the very edge of the world, the endless Arctic night, her father explaining something…She nodded. “I know about them,” she said. “Go on.”
“Question for you, Miss Silver. Square root of minus one. Did it exist before someone think about it?”
“It must have done…I think. It was hidden, but it was there.”
“And you think that is the only kind of number that is there but we can’t see?”
“No,” she said slowly. “Probably. There might be others we haven’t thought about. Actually there must be.”
“Like maybe good numbers.”
“Ah.”
“Maybe.”
He blew a smoke ring that floated away and wavered and frayed and broke up. It wasn’t difficult, Lyra decided, to imagine him in the academic dress of a scholar, giving a lecture on mathematics to a room full of students.
“Is that all?” Lyra said.
“There might be moving numbers,” he said. “Or Viennese numbers. Or dark numbers, or heavy numbers. Or bad numbers.”
“Those words could mean anything.”
“They could be names for kinds of numbers we haven’t discovered yet.”
Something from a physics class stirred in her memory. She tried to see it clearly, but it shimmered for a moment, like a goldfish, and then retreated into the depths.
“You know about fields?” she said. “I mean, fields like the gravitational field or the electromagnetic field. Spaces where some kind of influence works.”
“I know what field means. What is it you mean?”
“I wondered if the good numbers could describe points in a particular field.”
He didn’t say anything for over a minute.
His expressions changed rapidly: abstract, troubled, calculating, speculative, amused, mischievous, melancholy.
He might have been acting: perhaps none of them meant any more than that he knew she was watching him.
Or they might have been true pictures of his thought.
His left eyelid didn’t flicker, but she’d made that up anyway.
“Well?” she went on. “Suppose, like numbers we can’t see yet and we can’t see them because we haven’t imagined how they could exist…If we didn’t know about that particular field, we wouldn’t have thought it needed particular numbers to describe it. What then?”
“How would we know?” he said.
“We’d have to…I suppose we’d need an instrument that didn’t exist yet. Or a process.”
“Or just look in different way.”
“What sort of way? What would your friend the Indian holy man say?”
“He would say you are very curious, Miss Silver. Never in all his life he meet someone so curious. He also say we have answer to many things before we know what question is. We just have to find the best way to see it.”
“That makes it sound very easy.”
“No, is not easy, but you can do it. You ask me once about something you call the secret commonwealth. You remember?”
“Yes, I do. You said you’d never heard of it.”
“Yes. Then you explain, and I recognize it.”
“You didn’t say so.”
“No, I understand. I know the thing you talk about. What you say just now, about fields—suppose it is a field, your secret commonwealth. Like gravitational field, which is everywhere, and no one knew about it till Mr. Lord Newton see an apple fall and wonder why it go down and not up.”
“Wait a minute. The secret commonwealth is a field…”
“Yes.”
“And that’s your different way of looking at it?”
“Yes. It’s good, no?”
She laughed. So did he.
“But…” she said.
“Another example for you. Like calculating pi. You could go on forever. A hundred digits, a thousand, a million billion, you never come to the end, never exactly right, always an approximation. People take a lifetime and go mad doing it. But like this…”
He bent forward and traced a circle in the gravel with his finger, and then drew a line across the middle.
“How long that take? Two seconds? And there it is, perfect picture of pi. Of the idea of pi. The ratio between this line and that line. You see it, you understand. Not approximate. Exact.”
“Hmm,” she said. “Yes. All right.”
“Same thing, different way of seeing it.”
“So if I saw the secret commonwealth as a field instead of…however I used to see it…”
“Might be clearer.” He looked at her watching him, and yet another expression came into his eyes, as if he were assessing her in some way.
“Nothing is empty,” he said more slowly.
“You can’t see nothing in this cup or that box or that room with nothing in it, but they are all full of fields.
Of every kind. Some we know about, some we don’t, and some we don’t even think are fields at all. Consciousness…”
But he stopped, as if he’d said too much.
“Consciousness is a field? Is it?” she said.
“Yes.” He looked uneasy.
“The Rusakov field? D’you mean that?”
He found a scrap of smokeweed on his tongue, and worked it to his lips, and spat it out. “Maybe,” he said. “It’s possible.”
“I’ll think about that. It’s interesting.”
He pinched out the burning end of his cigarette with finger and thumb. Lyra flinched, but Ionides didn’t seem to feel anything.
He said, “Now another question, Miss Silver. This time something I want to know.”
“What?”
“Where we go. You say Karamakan. Well, by God, that is a damn big place. Full of sand. Where exactly you want to go?”
“A place called Tashbulak, near the edge of a lake called Lop Nor. There was a botanical research station there. Within a few days’ journey of that there is a red building in the desert, and that’s where I want to go.”
“Why? They don’t let you in. They don’t let nobody in.”
“How do you know that?”
“Abdel Ionides, he know everything.”