Permutation City

of it meant.

And yet no Copy buried in the data itself -- ignorant of the details or not -- could have the slightest trouble making sense of it all in an instant.

Squeak. 'Trial number three. Time resolution twenty milliseconds.'

'One. Two. Three.'

For time to pass for a Copy, the numbers which defined it had to change from moment to moment. Recomputed over and over again, a Copy was a sequence of snapshots, frames of a movie -- or frames of computer animation.

But . . . when, exactly, did these snapshots give rise to conscious thought? While they were being computed? Or in the brief interludes when they sat in the computer's memory, unchanging, doing nothing but representing one static instant of the Copy's life? When both stages were taking place a thousand times per subjective second, it hardly seemed to matter, but very soon --

Squeak. 'Trial number four. Time resolution fifty milliseconds.'

What am I? The data? The process that generates it? The relationships between the numbers?

All of the above?

'One hundred milliseconds.'

'One. Two. Three.'

Paul listened to his voice as he counted -- as if half expecting to begin to notice the encroachment of silence, to start perceiving the gaps in himself.

'Two hundred milliseconds.'

A fifth of a second. 'One. Two.' Was he strobing in and out of existence now, at five subjective hertz? The crudest of celluloid movies had never flickered at this rate. 'Three. Four.' He waved his hand in front of his face; the motion looked perfectly smooth, perfectly normal. And of course it did; he wasn't watching from the outside. 'Five. Six. Seven.' A sudden, intense wave of nausea passed through him but he fought it down, and continued. 'Eight. Nine. Ten.'

The djinn reappeared and emitted a brief, solicitous squeak. 'What's wrong? Do you want to stop for a while?'

'No, I'm fine.' Paul glanced around the innocent, sun-dappled room, and laughed. How would Durham handle it if the control and the subject had just given two different replies? He tried to recall his plans for such a contingency, but couldn't remember them -- and didn't much care. It wasn't his problem any more.

Squeak. 'Trial number seven. Time resolution five hundred milliseconds.'

Paul counted -- and the truth was, he felt no different. A little uneasy, yes -- but factoring out any squeamishness, everything about his experience seemed to remain the same. And that made sense, at least in the long run -- because nothing was being omitted, in the long run. His model-of-a-brain was only being fully described at half-second (model time) intervals -- but each description still included the results of everything that 'would have happened' in between. Every half-second, his brain was ending up in exactly the state it would have been in if nothing had been left out.

'One thousand milliseconds.'

But . . . what was going on, in between? The equations controlling the model were far too complex to solve in a single step. In the process of calculating the solutions, vast arrays of partial results were being generated and discarded along the way. In a sense, these partial results implied -- even if they didn't directly represent -- events taking place within the gaps between successive complete descriptions. And when the whole model was arbitrary, who was to say that these implied events, buried a little more deeply in the torrent of data, were any 'less real' than those which were directly described?

'Two thousand milliseconds.'

'One. Two. Three. Four.'

If he seemed to speak (and hear himself speak) every number, it was because the effects of having said 'three' (and having heard himself say it) were implicit in the details of calculating how his brain evolved from the time when he'd just said 'two' to the time when he'd just said 'four.'

'Five thousand milliseconds.'

'One. Two. Three. Four. Five.'

Besides, hearing words that he'd never 'really' spoken wasn't much stranger than a Copy hearing anything at all. Even the standard millisecond clock rate of this world was far too coarse to resolve the full range of audible tones. Sound wasn't represented in the model by fluctuations in air pressure values -- which couldn't change fast enough -- but in terms of audio power spectra: profiles of intensity versus frequency. Twenty kilohertz was just a number here, a label; nothing could actually oscillate at that rate. Real ears analyzed pressure waves into components of various pitch; Paul knew that his brain was being fed the preexisting power spectrum values directly, plucked out of the nonexistent air by a crude patch in the model.

'Ten thousand milliseconds.'

'One. Two. Three.'

Ten seconds free-falling from frame to frame.

Fighting down vertigo, still counting steadily, Paul prodded the shallow cut he'd made in his forearm with the kitchen knife. It stung, convincingly. So where was this experience coming from? Once the ten seconds were up, his fully described brain would remember all of this . . . but that didn't account for what was happening now. Pain was more than the memory of pain. He struggled to imagine the tangle of billions of intermediate calculations, somehow 'making sense' of themselves, bridging the gap.

And he wondered: What would happen if someone shut down the computer, just pulled the plug -- right now?

He didn't know what that meant, though. In any terms but his own, he didn't know when 'right now' was.

'Eight. Nine. Ten.'

Squeak. 'Paul -- I'm seeing a slight blood pressure drop. Are you okay? How are you feeling?'

Giddy -- but he said, 'The same as always.' And if that wasn't quite true, no doubt the control had told the same lie. Assuming . . .

'Tell me -- which was I? Control, or subject?'

Squeak. Durham replied, 'I can't answer that -- I'm still speaking to both of you. I'll tell you one thing, though: the two of you are still identical. There were some very small, transitory discrepancies, but they've died away completely now -- and whenever the two of you were in comparable representations, all firing patterns of more than a couple of neurons were the same.'

Paul grunted dismissively; he had no intention of letting Durham know how unsettling the experiment had been. 'What did you expect? Solve the same set of equations two different ways, and of course you get the same results -- give or take some minor differences in round-off errors along the way. You must. It's a mathematical certainty.'

Squeak. 'Oh, I agree.' The djinn wrote with one finger on the screen:

(1 + 2) + 3 = 1 + (2 + 3)

Paul said, 'So why bother with this stage at all? I know -- I wanted to be rigorous, I wanted to establish solid foundations. But the truth is, it's a waste of our resources. Why not skip the bleeding obvious, and get on with the kind of experiment where the answer isn't a foregone conclusion?'

Squeak. Durham frowned reprovingly. 'I didn't realize you'd grown so cynical so quickly. AI isn't a branch of pure mathematics; it's an empirical science. Assumptions have to be tested. Confirming the so-called 'obvious' isn't such a dishonourable thing, is it? And if it's all so straightforward, why should you be afraid?'