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?"
"I'm not afraid: I just want to get it over with. But . . . go ahead. Prove whatever you think you have to prove, and then we can move on."
Squeak. "That's the plan. But I think we could both use a break now. I'll enable your communications -- for incoming data only." He turned away, reached off-screen, and hit a few keys on a second terminal.
Then he turned back to the camera, smiling -- and Paul knew exactly what he was
"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?"
"I'm not afraid: I just want to get it over with. But . . . go ahead. Prove whatever you think you have to prove, and then we can move on."
Squeak. "That's the plan. But I think we could both use a break now. I'll enable your communications -- for incoming data only." He turned away, reached off-screen, and hit a few keys on a second terminal.
Then he turned back to the camera, smiling -- and Paul knew exactly what he was
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