“Let’s say that the Geometer you’re talking to has been inculcated in his civilization’s equivalent of the Sconics. He’ll say, ‘Wait a minute, you can’t really know, you’re not allowed to make statements about, things in themselves—only about your perceptions.’”

“True.”

“So you need to rephrase your statement in terms of the givens that are actually available to you.”

“All right,” I said, “instead of saying, ‘Orolo is wrapped in bolt-stuff,’ I’ll say, ‘When I gaze at Orolo from where I’m standing, I see mostly bolt, with bits of Orolo—his head and his hands—peeking out.’ But I don’t see why it matters.”

“It matters because the Geometer can’t stand where you are standing. It has to stand somewhere else, and see me from a different angle.”

“Yes, but the bolt wraps all the way around your body!”

“How do you know I’m not naked in back?”

“Because I’ve seen a lot of bolts and I know how they work.”

“But if you were a Geometer, seeing one for the first time—”

“I’d still be able to surmise that you were not naked in back, because if you were, the bolt would hang differently.”

“What if I got rid of the bolt and stood here naked?”

“What if you did?”

“How would you describe me to the Geometer, then? What would meet your eye, and the Geometer’s?”

“I would say to the Geometer ‘From where I stand, all I see is Orolo-skin. From where you stand, O Geometer, the same is likely true.’”

“And why is it likely?”

“Because without skin your blood and guts would fall out. Since I can’t see a puddle of blood and guts behind you, I can infer that your skin must be in place.”

“Just as you infer that my bolt must continue all the way round me in back, from the way in which its visible part hangs.”

“Yes, I guess it’s the same general principle.”

“Well, it seems that this process you call consciousness is somewhat more complex than you perhaps gave it credit for at first,” Orolo said. “One must be able to take in givens from sparse dustings of probability waves in a vacuum—”

“I.e., see stuff.”

“Yes, and perform the trick of integrating those givens into seemingly persistent objects that can be held in consciousness. But that’s not all. You perceive only one side of me, but you are all the time drawing inferences about my other side—that my bolt continues round in back, that I have skin—inferences that reflect an innate understanding of theorical laws. You can’t seem to make these inferences without performing little thought experiments in your head: ‘if the bolt didn’t continue round in back it would hang differently,’ ‘if Orolo had no skin his guts would fall out.’ In each of those cases you are using your understanding of the laws of dynamics to explore a little counterfactual universe inside of your head, a universe where the bolt or the skin isn’t there, and you are then running that universe in fast-forward, like a speely, to see what would happen.

“And that is not the only such activity that is going on in your mind when you describe me to the Geometers,” Orolo went on, after a pause to swallow some water, “because you are forever making allowances for the fact that you and the Geometer are in different places, seeing me from different points of view, taking in different givens. From where you’re standing you might be able to see the freckle on the left side of my nose, but you have the wit to understand that the Geometer can’t see that freckle because of where it is standing. This is another way in which your consciousness is forever building counterfactual universes: ‘if I were standing where the Geometer is, my view of the freckle would be blocked.’ Your ability to have empathy with the Geometer—to imagine what it would be like to be someone else—isn’t a mere courtesy. It is an innate process of consciousness.”

“Wait a second,” I said, “you’re saying I can’t predict the Geometers’ inability to see the freckle without erecting a replica of the whole universe in my imagination?”

“Not exactly a replica,” Orolo said. “Almost a replica, in which everything is the same, except for where you are standing.”

“It seems to me that there are much simpler ways of getting that result. Perhaps I have a memory of what you look like when viewed from that side. I call up that image in my memory and say to myself, ‘Hmm, no freckle.’”

“It is a perfectly reasonable thought,” Orolo said, “but I must warn you that it does not really buy you much, if what you seek is a simple and easy-to-understand model of how the mind works.”

“Why not? I’m only talking about memory.”

Orolo chortled, then composed himself, and made an effort to be tactful. “Thus far we have spoken only of the present. We’ve talked only of space—not of time. Now you would like to bring memories into the discussion. You are proposing to pull up memories of how you perceived Orolo’s nose from a different angle at a different time: ‘I sat on his right last night at supper and couldn’t see the freckle.’”

“It seems simple enough,” I said.

“You might ask yourself what in your brain enables you to do such things.”

“What things?”

“Take in some givens one evening at supper. Take in another set of givens now—or one second ago—two seconds ago—but always now! And say that all of them were—are—the same chap, Orolo.”

“I don’t see what the big deal is,” I said. “It’s just pattern recognition. Syntactic devices can do it.”

“Can they? Give me an example.”

“Well…I guess a simple example would be…” I looked around, and happened to notice the contrail of an aerocraft high overhead. “Radar tracking aerocraft in a crowded sky.”

“Tell me how it works.”

“The antenna spins around. It sends out pulses. Echoes come back to it. From the time lag of the echo, it can calculate the bogey’s distance. And it knows in what direction the bogey lies—that’s dead easy, it’s just the same direction as the antenna is pointing when the echo hits it.”

“It can only look in one direction at a time,” Orolo said.

“Yeah, it’s got extreme tunnel vision, and compensates for that by spinning around.”

“A little bit like us,” Orolo said.

We had begun descending the mountain, and were walking side by side. Orolo went on, “I can’t see in all directions at once, but I glance to the side every so often to make sure you’re still there.”

“Yeah, I guess so,” I said. “You have in your head a model of your surroundings that includes me off to your right side. You can maintain it for a while by holding down the fast-forward button. But every so often you have to update it with new givens, or it’ll get out of whack with what is really going on.”

“How does the radar system manage it?”

“Well, the antenna rotates once and takes in echoes from everything that’s in the sky. It plots their positions. Then it rotates again and collects a new set of echoes. The new set is similar to the first one. But all of the bogeys are now in slightly different positions, because all of the aerocraft are moving, each at its own speed, each in its own direction.”

“And I can see how a human observer, watching the bogeys plotted on a screen, would be able to assemble a mental model of where the aerocraft were and how they were moving,” Orolo said, “in the same way as we stitch together frames of a speely to form a continuous story in our minds. But how does the syntactic device inside the radar system do it? It has nothing more than a list of numbers, updated from time to time.”

“If there were only one bogey, it would be easy,” I said.

“Agreed.”

“Or just a few, widely separated, moving slowly, so that their paths didn’t cross.”

“Also agreed. But what of the hard case of many fast bogeys, close together, paths crossing?”

“A human observer could manage it easily—just like watching a speely,” I said. “A syndev would have to do some of what a human brain does.”