We always opened our meals by invoking the memory of Saunt Cartas. The gist of it was that our minds might be nourished by all manner of ideas originating from thinkers dating all the way back to Cnoüs, but for the physical nourishment of our bodies we relied upon one another, joined in the Discipline that we owed to Cartas. Deolaters, on the other hand, all had different pre-meal rituals. Bazian Orthodoxy was a post-agrarian religion in which literal sacrifice had been replaced by symbolic; they opened their meals with a re-enactment in effigy of that, then praised their God for a while, then asked Him for goods and services. The priest who ran the retreat center launched into it out of habit, but got unnerved in the middle when he noticed that none of the avout were bowing their heads, just gazing at him curiously. I didn’t think he was all that troubled by our not believing what he believed—he must have been used to that. He was more embarrassed that he’d committed a faux pas. So, when he was finished, he implored us to say whatever sort of blessing or invocation might be traditional in the math. As mentioned we were strangely lacking in sopranos and altos, but we were able to put together enough tenors, baritones, and basses to sing a very ancient and simple Invocation of Cartas. Fraa Jad handled the drone, and I could swear he made the silverware buzz on the tables.
The four monks seemed to enjoy this very much, and when we’d finished they stood up and did an equally ancient-sounding prayer. It must have dated back to the early centuries of their monastic age, just after the Fall of Baz, because their Old Orth was indistinguishable from ours, and it had obviously been composed in a time before the music of the maths and of the monasteries had diverged. If you didn’t listen too carefully to the words, you could easily mistake this piece for one of ours.
The conversation during the meal had to be superficial compared to the events of the last twenty-four hours, given that we had to talk in Fluccish and couldn’t mention the ship in earshot of our hosts. I became frustrated, then bored, then drowsy, and ate mostly in silence. Cord and Rosk talked to each other. They weren’t religious, and I could tell they felt awkward here. One of the young women on the staff made lavish efforts to make them feel welcome, which mostly backfired. Sammann was absorbed in his jeejah, which he had somehow patched into the retreat center’s communications system. Barb had found a list of the camp rules and was memorizing it. Our three Hundreders sat in a cluster and talked amongst themselves; they could not speak Fluccish and didn’t have the Thousander glamor that had made Fraa Jad the center of attention with the Bazian monks. I noticed ”
Excerpt From: Neal Stephenson. “Anathem.” iBooks. that Arsibalt was deep in conversation with Ferman, and that Cord and Rosk had shifted closer to them, so I wandered over to see what they were talking about. It seemed that Ferman had been thinking about the Sconics, and wanted to know more. Arsibalt, for lack of any other way to pass the time, had launched into a calca called “The Fly, the Bat, and the Worm,” which was a traditional way of explaining the Sconic theory of time and space to fids. “Look at that fly crawling around on the table,” Arsibalt said. “No, don’t shoo it away. Just look at it. The size of its eyes.”
Ferman Beller gave it a quick glance and then returned his eyes to his dinner.
“Yeah, half of its body seems to be eyes.”
“Thousands of separate eyes, actually. It doesn’t seem as though it could possibly work.” Arsibalt reached back behind himself and waved his hand around, nearly hitting me in the face. “Yet if I wave my hand back here, far away, it doesn’t care—knows there is no threat. But if I bring my hand closer…”
Arsibalt brought his hand forward. The fly took off.
“…somehow its microscopic brain takes signals from thousands of separate, primitive eyes and integrates them into a correct picture, not merely of space, but of spacetime. It knows where my hand is. Knows that if my hand keeps moving thus, it’ll soon squash it—so it had better change its position.”
“You think the Cousins have eyes like that?” Beller asked.
Arsibalt dodged sideways: “Maybe they’re like bats instead. A bat would have detected my hand by listening for echoes.”
Beller shrugged. “All right. Maybe the Cousins squeak like bats.”
“On the other hand, when I shift my body to swat the fly, it creates a pattern of vibrations in the table that a creature—even a deaf and blind one, such as a worm—might feel…”
“Where is this going?” Beller asked.
“Let’s do a thought experiment,” Arsibalt said.
“Consider a Protan fly. By that, I mean the pure, ideal form of a fly.”
“All eyes. No other sense organs.”
“All right, I’m considering it,” Beller said, trying to be good-humored.
“Now, a Protan bat.”
“Yes. Now a Protan worm.”
“Meaning all touch?”
“Yes. No eyes, ears, or nose—just skin.”
“Are we going to do all five senses?”
“It would start to become boring, so let’s stop with three,” Arsibalt said. “We place the fly, the bat, and the worm in a room with some object—let’s say a candle. The fly sees its light. The bat squeals at it, and hears its echoes. The worm feels its warmth, and can crawl over it to feel its shape.”
“It sounds like the old parable of the six blind men and the—”
“No!” said Arsibalt. “This is completely different. Almost the opposite. The six blind men all have the same sensory equipment—”
Beller nodded, seeing his mistake. “Yeah, but the fly, the bat, and the worm have different ones.”
“And the six blind men disagree about what it is they are groping—”
“But the fly, the bat, and the worm agree?” Beller asked, raising an eyebrow.
“You sound skeptical. Rightly so. But they are all sensing the same object, are they not?”
“Sure,” Beller said, “but when you say that they agree with each other, I don’t know what that means.”
“It’s a fascinating question, so let’s explore it. Let’s change the rules a little,” said Arsibalt, “just to set the stakes a little higher, and make it so that they have to agree. The thing in the middle of the room isn’t a candle. Now, it’s a trap.”
“A trap!?” Beller laughed.
Arsibalt got a proud look.
“What’s the point of that?” Beller asked.
“Now there’s a threat, you see. They have to figure out what it is or they’ll be caught.”
“Why not a hand coming down to swat them?”
“I thought of that,” Arsibalt admitted, “but we have to make allowances for the poor worm, who senses things very slowly compared to the other two.”
“Well,” Beller said, “I expect they’re all going to be caught in the trap sooner or later.”
“They are very intelligent,” Arsibalt put in.
“All right then, it is a huge cavern swarming with millions of flies, bats, and worms. Thousands of traps are scattered about the place. When a trap catches or kills a victim, the tragedy is witnessed by many others, who learn from it.”
Beller considered it for a while as he served himself some more vegetables. After a while, he said, “Well, I expect that where you’re going with it is that once enough time has gone by, and enough of these critters have been caught, the flies will learn what a trap looks like, the bats what it sounds like, the worms what it feels like.”
“The traps are being planted by exterminators who are intent on killing everything. They keep disguising them, and coming up with new designs.”
“All right,” Beller said, “then the flies, bats, and worms have to get clever enough to detect traps that are disguised.”
“A trap could look like anything,” Arsibalt said, “so they must learn to look at any object in their environment and to puzzle out whether or not it could possibly function as a trap.”
“Now, some of the traps are suspended from strings. The worms can’t reach them or feel their vibrations.”
“Too bad for the worms!” Beller said.
“The flies can’t see anything at night.”
“Some parts of the cavern are so noisy that the bats can’t hear a thing.”
“Well, it sounds as though the flies, the bats, and the worms had better learn to cooperate with one another,” Beller said.
“How?” This was the sound of Arsibalt’s trap closing on his leg.
“Uh, by communicating, I guess.”
“Oh. And what exactly does the worm say to the bat?”
“What does all of this have to do with the Cousins?” Beller asked.
“It has everything to do with them!”
“You think that the Cousins are hybrid fly-bat-worm creatures?”
“No,” Arsibalt said, “I think that we are.”
“AAARGH!” Beller cried, to laughter from everyone.
Arsibalt threw up his hands as if to say how could I make this any clearer?
“Please explain!” Beller said. “I’m not used to this, my brain’s getting tired.”
“No, you explain. What does the worm say to the bat?”
“The worm can’t even talk!”
“This is a side issue. The worms learn over time that they can squirm around into different shapes that the bats and flies can recognize.”
“Fine. And—let me see—the flies could fly down and crawl around on the worms’ backs and give them signals that way. Et cetera. So, I guess that each type of critter could invent signals that the other two could detect: worm-bat, bat-fly, and so on.”
“Agreed. Now. What do they say to each other?”
“Well, hold on now, Arsibalt. You’re skipping over a bunch of stuff! It’s one thing to say a worm can squirm into a shape like C or S that could be recognized by a fly looking down. But that’s an alphabet. Not a language.”
Arsibalt shrugged. “But languages develop over time. Monkeys hooting at each other developed into some primitive speech: ‘there’s a snake under that rock’ and so forth.”
“Well, that’s fine, if snakes and rocks is all you have to talk about.”
“The world in this thought experiment,” Arsibalt said, “is a vast, irregular cavern sprinkled with traps: some freshly laid and still dangerous, others that have already been sprung and may safely be ignored.”
“You went out of your way to say that they were mechanical contraptions. Are you saying they’re predictable?”
“You or I could inspect one and figure out how it worked.”
“Well, in that case it comes down to saying ‘this gear here engages with that
gear, which rotates yonder shaft, which is connected to a spring,’ and so on.”
Arsibalt nodded. “Yes. That’s the sort of thing the flies, bats, and worms would have to communicate to one another, in order to figure out what was a trap and what wasn’t.”
“All right. So, same way that monkeys in trees settled on words for ‘rock’ and ‘snake,’ they’d develop symbols—words—meaning ‘shaft,’ ‘gear,’ and so on.”
“Would that be enough?” Arsibalt asked.
“Not for a complicated piece of clockwork. Let’s see, you could have two gears that were close to each other, but they couldn’t engage each other unless they were close enough for their teeth to mesh.”
“Proximity. Distance. Measurement. How would the worm measure the distance between two shafts?”
“By stretching from one to the other.”
“What if they were too far apart?”
“By crawling from one to the other, and keeping track of the distance it moved.”
“Timing the difference in echoes between the two shafts.”
“For the fly it’s easy: compare the images coming into its eyes.”
“Very well, let’s say that the worm, the bat, and the fly have each observed the distance between the two shafts, just as you said. How do they compare notes?”
“The worm for example would tell what it knew by translating it into the squirming-alphabet you mentioned.”
“And what does a fly say to another fly upon seeing all of this?”
“I don’t know.”
“It says ‘the worm seems to be relating some kind of account of its wormy doings, but since I don’t squirm on the ground and can’t imagine what it would be like to be blind, I haven’t the faintest idea what it’s trying to tell me!’”
“Well, this is just what I was saying earlier,” Beller complained, “they have to have a language—not just an alphabet.”
Arsibalt asked, “What is the only sort of language that could possibly serve?”
Beller thought for a minute.
“What are they trying to convey to each other?” Arsibalt prompted him.
“Three-dimensional geometry,” Beller said. “And, since parts of the clock are moving, you’d also need time.”
“Everything that a worm could possibly say to a fly, or a fly to a bat, or a bat to a worm, would be gibberish,” Arsibalt said, leading Beller forward.”
“Kind of like saying ‘blue’ to a blind man.”
“‘Blue’ to a blind man, except for descriptions of geometry and of time. That is the only language that these creatures could ever possibly share.”
“This makes me think of that geometry proof on the Cousins’ ship,” Beller said. “Are you saying that we are like the worms, and the Cousins are like the bats? That geometry is the only way we can speak to each other?”
“Oh no,” Arsibalt said. “That’s not where I was going at all.”
“Where are you going then?” Beller asked.
“You know how multicellular life evolved?”
“Er, single-celled organisms clumping together for mutual advantage?”
“Yes. And, in some cases, encapsulating one another.”
“I’ve heard of the concept.”
“That is what our brains are.”
“Our brains are flies, bats, and worms that clumped together for mutual advantage. These parts of our brains are talking to each other all the time. Translating what they perceive, moment to moment, into the shared language of geometry. That’s what a brain is. That’s what it is to be conscious.