These quotations are the main places that characters explain the polycosmic interpretation of quantum events and parallel universes. They are certainly "spoilers" if you have not read the book.
Most anyone familiar with comic books and science fiction stories has read some flavors of "alternate futures". The idea is that each time an event could resolve in multiple ways the world branches to follow each possibility. For example, each time Superman fights Lex Luthor there are futures in which Superman wins or Luther wins, and we perceive the former as "real" simply because that's the brach in which we also live.
In Anathem this idea is extended. Because of quantum mechanics, everything is branching continually. The result is not shaped like a tree, but an infinite-dimensional configuration space.
"Yes," Orolo said, "and can you guess which model, which terminology, I am partial to?"
"The more polycosmic the better, I assume."
"Of course! So, whenever I hear you talking of quantum phenomena using the old terminology--"
"The fid version?"
"Yes, I must mentally translate what you're saying into polycosmic terms. For example, the simple case of a particle that is either spin up or spin down--"
"You would say that, at the moment, when the spin is observed--the moment when its spin has an effect on the rest of the cosmos--the cosmos bifurcates into to complete, separate, causually independent cosmi that then go their separate ways."
"You've almost got it. But it's better to say that those two cosmi exist before the measurement is made, and that they interfere with each other--there is a little bit of crosstalk between them--until the observation is made. And then they go their separate ways."
"And here," I aid, "we could talk about how crazy this sounds to many people--"
Orolo shrugged. "Yet it is a model that a great many theors come to believe in sooner or later, because the alternatives turn out to be even crazier in the end."
"All right. So, I think I know what comes next. You want me to restate your theory of what the brain does in terms of the polycosmic interpretation of quantum theorics."
"If you would so indulge me," Orolo said, with a suggestion of a bow.
"Okay. Here goes," I said. "The premise, here, is that the brain is loaded up with a pretty accurate model of the cosmos that it lives in."
"At least, the local part of it," Orolo said. "It needn't have a good model of other galaxies, for example."
"Right. And to state it in the terminology of the old interpretation that fids are taught, the state of that model is a superposition of many possible present and future states of the cosmos--or at least of the model."
He held up a finger. "Not of the cosmost, but--?"
"But of a hypothetical alternate cosmi differing slightly from the cosmos."
"Very good. Now, this generalized cosmos-model that each person carries around in his or her brain--do you have any ida how it would work? What it would look like?"
"Not in the slightest!" I said. "I don't know the first thing about the nerve cells and so on. How they could be rigged together to create such a model. How the model could be reconfigured, from moment to moment, to represent hypothetical scenarios."
"Fair enough," Orolo said, holding up his hands to placate me. "Let's leave nerve cells out of the discussion, then. The important thing about the model, though, is what?"
"That it can exist in many states at once, and that its wavefunction collapses from time to time to give a useful result."
"Yes. Now, in the polycosmic intepretation of how quantum theorics works, what does all of this look like."
"There is no longer superposition. No wavefunction collapse. Just a lot of different copies of me--of my brain--each really existing in a different parallel cosmos. The cosmos model residing in each of those parallel brains is really, definitely in one state or another. And they interfere with one another."
He let me stew on that for a few moments. And then it came to me. Just like those ideas we had spoken of earlier--suddenly there in my head. "You don't even need the model any more, do you?"
Orolo just nodded, smiled, egged me on with little beckoning gestures."
I went on--seing it as I was saying it. "It is so much simpler this way! My brain doesn't have to support this hugely detailed, accurate, configurable, quantum-superposition-supporting model of the cosmos any more! All it needs to do is to perceive--to reflect--the cosmos that it's really in, as it really is."
"The variations--the myriad possible alternative scenarios--have been moved out of your brain," Orolo said, rapping on his skull with his knuckles, "and out int the polycosm, which is where they all exist anyway!" He opened up his hand and extended it to the sky, as if releasing a bird. "All you have to do is perceive them."
"But each variant of me doesn't exist in perfect isolation from the others," I said, "or else it wouldn't work."
Orolo nodded. "Quantum interference--the crosstalk among similar quantum states--knits the different versions of your brain together."
"You're saying that my consciousness extends across multiple cosmi," I said. "That's a pretty wild statement."
"I'm saying that all things do," Orolo said. "That comes with the polycosmic interpretation. The only thing exceptional about the brain is that it has found a way to use this."
(Pages 546-548)
And that was how I came to spend the entire main course recounting my two Ecba dialogs with Orolo: the first about how, according to him, consciousness was all about hte rapid and fluent creation of counterfactual worlds inside the brain, and the second in which he argued that this was not merely possible, not merely plausible, but in fact easy, if one thought of consciousness as spanning an ensemble of slightly different versions of the brain, each keeping track of a slightly different cosmos. Paphlagon ended up saying it better: "If Hemn space is the landscape, and one cosmos is a single geometric point in it, then a given consciousness is a spot of light moving, like a searchlight beam, over that landscape--brightly illuminaiting a set of points--of cosmi--that are close together, with a penumbra that rapidly feathers away to darkness at the edges. In the bright center of the beam, crosstalk occurs among many variants of the brain. Fewer contributions come in from the half-lit periphery, and none from the shadows beyond."
(Page 695)
Fraa Jad threw his napkin on the table and said: "Consciousness amplifies the weak signals that, like cobwebs spun between trees, web Narratives together. Moreover, it amplifies them selectively and in that way creates feedback loops that steer the Narratives."
(Page 701)
"So the feedback pulls worldtracks close to one another as time goes on?" Ignetha Foral asked. "Is this the explanation we've been looking for of why the Geometers look like us?"
"Not only that," put in Suur Asquin, "but of cnoöns and the HTW and all the rest, if I'm not mistaken."
...
"So if is true that the PAQD share the Adrakhonic Theorem and other such theorical concepts with us," said Fraa Lodoghir, "those might be nothing more than attractors in the feedback system we have been describing."
"Or nothing less," said Fraa Jad.
We all let that one resonate for a minute. Lodoghir and Jad were staring at each other across the table; we all thought something was about to happen.
A Procian and a Halikaarnian were about to agree with each other.
(Pages 704-705)
UPDATE: Here is a related article, about how our brains really do blend past memories and present input.
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