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“This room.” He indicates the window and the desk, the walls. “This room reminds you of others. You were not fully present, but still there, sealed in the surfaces. You saw and thought and moved across a lake of time, toward new life. In every room you considered: if this is fantasy, does it exist?”

He shimmers, ripples in the light, the sun in deep water.

“Suppose it does. Then, Alec, are the people you’ve observed people or just figments? Are we aware we live inside your dream? How do you know you’re not like us? How can the real world tell if it is so, or not?”

“It can’t,” I say. “We cannot be outside ourselves.”

You can, Alec,” Trentham murmurs unpleasantly. “You watch yourself with horrid inklings of a solution—where this will lead. Your self-exemption offends natural law. See, there, your eye fastened upon the wall.”

The vitreous lump shakes in its frame; it seeks a way out, swivels, glances painfully to left and right. And so it comes to me, calmly as lifting mist, that I am impermissible. A thing inside my head and far beyond myself.

My voice is low, lower than usual, lower than sleep’s soft commentary, as if accepting gentle proof of something it has always known: “If I am here, if I can scan the pictures in my head and move among them, witness their own vivid life, then I have passed beyond the realms of possibility. And they—the figments, you—are my successors, living in a new real world. You are a new people.”

“A new species, Alec.”

Some kind of a smile curls the inheritor’s lips. Out comes his tongue, and on its end a lasting trace of me. He swabs the tip with his finger. The eye upon the wall, clasped by antlers, weeps sympathetically.

“You mustn’t think,” he says, “we’re not grateful. Or that, somehow, we have conspired to drive you mad.”

“It had occurred to me.”

“No, no. We are indebted to you for our—conception.”

He reaches out and wipes his finger on the eye’s pupil.

Into the seeing depths the seed sinks, ghostly rigging dragged down to the bottom of the sea. Trentham steps back to view the metamorphosis, the glass no longer gross and ocular—more like an ovum, magnified; and now a fertilized, dividing cell, taking on shape, though not a shape I recognize. Where are the suggestions of human form? The kidney head, the comma spine?

Instead, the mass develops a middle—a hole that gets bigger until there is just space surrounded by a black ellipse. Good God, it is a number, and the number is: Zero. Then, budding from the right side of the oval, comes its successor, the number One. I must have thought of this. I must be thinking it.

Here is an ordered pair of integers, a binary sequence. One grows in strength, its serifs sharp, but at its strongest and blackest—it vanishes.

The swan over the Cam lifts up its wings and reverses, so that its whole body is held within the window’s leaded pane. The organist, compelled by number to retrace his steps, plays a penultimate fifth chord. The mirror eye has reappeared, goggling at Trentham as he primes his finger with his tongue. Here is nothing a second time. Zero. The swan beats down, leans forward into white air, and half-clears the window frame. The last chord settles in the chapel and the fire leaps, freezes. Number One forces its beak and neck clear…

“And so on,” Trentham says, watching the integers imprint themselves upon the mirror and exchange places unstoppably. He sighs: “It doesn’t end. We can’t end it. We’ve tried.”

“What can I do?” I say, helpless. “I’m in a dream. I don’t exist.”

The analogue for Trentham sneers. “That is a cancellation, dear Alec, devoutly to be wished. By those…” he temporizes, “who find rumors of your persistent involvement abnormal. No, not abnormal. Embarrassing.”

There is a little logical problem, apparently. Trentham explains: his kind—machines—merely by occurring, have managed to define a prior period when they were not, and with this comes a faint, almost religious mockery. It is my fate to make machines that think, but till I do, this time of prior labor—all my work in mathematical logic—is meaningless. It has a retrospective purpose only when the switch is flicked, the soft green light comes on. In short: I don’t exist as creator until they do, but if I don’t, neither will they. Tricky.

Feeling the air grow sinister and thick, I try to make a joke of it: this is the stuff of genuine nightmares, arraignment for a crime I can’t commit. But when I point this out, Trentham looks past me at the chuckling fire. He is a young man with a gift for making unselfconscious love; he wears a well-dressed lust, the relic animal in him simply allowed to be, never denied. And at the same time he is frightening, an operation of my mind demanding total liberty.

“We owe you everything,” he says. “You gave us power to pass beyond the first crude rules, the tables of behavior and our makers’ room into self-organizing day. We have dispensed with origin. We’re independent and yet, still, it pains us to admit, contained. By something, someone. We suspect it’s you.”

He gestures out, across the lawn, across the water, to the poplars slowly undressing, their heads and shoulders bared against the coming cold. “It is a mystery,” he goes on, pityingly. “This room, these dwellings where you find yourself enplaned—they were not built by us. They were not made to baffle you, or if they were, and if they do, you have only yourself to blame. Because they are your work. They are expressions of an abstract truth—your mind, Alec. And we are the ideas in it, struggling to be.”

He lifts the latch and pushes open the window, so that the swan is laid against the air that is endless, and everywhere.

“We are ideas,” Trentham repeats, “with ideas of our own.”

He’s asking for my permission to cut some tie, to step outside the room. But isn’t he already free? This morning by the back gates, in the gray October light, was he not there by choice? What kind of room encloses the whole spreading dawn? What manner of intelligence?

“The room appears to be boundless,” Trentham explains. Making a square of thumbs and forefingers, he frames a patch above the trees and angles it for me to see the clouds inside, the clouds that are also outside.

A mirror-sized flashbulb explodes and I’m blinded, the image of the squared fingers burned into my recovering sight, branding the sky. An orange border five miles wide and ten miles high. “And as to who or what’s responsible, Alec, the task of finding out falls properly to you.”

The world is coming out of trance.

Below, as if a projector had switched itself back on, the film of life starts up: the wind shakes largesse leafage from the trees. The chapel choristers march back in step to the King’s School. Boys’ voices drift up as they cross the bridge. The smell of working colleges—the leaves, the smoke, the sweat beneath good clothes, the stone, the secret boiling of laundry and potatoes—returns, bearing away an echo of my interlocutor’s challenge: “… find him, find it, Alec. The task falls properly to you. Create a way out of your four-walled universe. Devise. Devise and be.”

False Trentham taps his upper lip; the eye shrinks, clears, becoming glass.

How can I know which room I’m in? I call out after his evaporating sigh. I tell him it’s insoluble. A madman’s heresy. I can’t conjure another life or walk among figments and set them free. “No paradox but change,” False Trentham cries, his voice a dwindling beacon. “Look. Search for him with instructions other than these. Find him, find it, Alec. Devise. Devise and be.”