Thursday, February 26, 2009

Mathematical Monks and the Multiverse

I recently read a truly excellent SF novel by Neal Stephenson entitled Anathem. It's about an alternate universe that has monks whose interests are more on mathematics rather than theology; and they have an alternate philosophical history that parallels the real one. I highly recommend it to pretty much everyone (especially Elliot at CotC if he hasn't already read it).

Part of my motivation for bringing it up is that at one point the monks discuss the Anthropic Principle, and give an excellent account of it:

Paphlagon said, "The cosmogonic processes that lead to the creation of the stuff we are made of -- the creation of protons and other matter, their clumping together to make stars, and the resulting nucleosynthesis -- all seem to depend on the values of certain physical constants. The most familiar example is the speed of light, but there are several others -- about twenty in all. Theors used to spend a lot of time measuring their precise values, back when we were allowed to have the necessary equipment. If these numbers had different values, the cosmos as we know it would not have come into being; it would just be an infinite cloud of cold dark gas or one big black hole or something else quite simple and dull. If you think of these constants of nature as knobs on the control panel of a machine, well, the knobs all have to be set in just the right positions or --"

Again Paphlagon looked to Moyra, who seemed ready: "Suur Demula likened it to a safe with a combination lock, the combination being about twenty numbers long."

"That is right. If you dial twenty numbers at random you never get the safe open; it is nothing more to you than an inert cube of iron. Even if you dial nineteen numbers correctly and get the other one wrong -- nothing. You must get all of them correct. Then the door opens and out spills all of the complexity and beauty of the cosmos."

"Another analogy," Moyra continued, after a sip of water, "was developed by Saunt Conderline, who likened all of the sets of values of those twenty constants that don't produce complexity to an ocean a thousand miles wide and deep. The sets that do, are like an oil sheen, no wider than a leaf, floating on the top of that ocean: an exquisitely thin layer of possibilities that yield solid, stable matter suitable for making universes with living things in them."

However, to get around the theistic repercussions, Anathem appeals to the multiverse hypothesis. Stephenson does this very cleverly: any view that argues that the physical universe isn't all that exists is a sort of multiverse hypothesis. So the Platonic world of forms is positing a multiverse, in which one is a universe of pure forms (in the Anathem alt-history Plato = Protas and Platonist = Protist). Similarly, any theistic explanation of the Anthropic Principle is a multiverse hypothesis, since it holds that there is another world that has some effect in this one. Stephenson's monks conclude from this that, if we have to posit another world in order to account for this one, there can be no reason for limiting the number of other worlds to one.

"It is a legitimate move in metatheorics. You have to be continually asking yourself, 'why are things thus, and not some other way?' And if you apply that test to this diagram, you immediately run into a problem: there are exactly two worlds. Not one, not many, but two. One might draw such a diagram having only one world -- the Arbran Causal Domain -- and zero arrows. That would draw very few objections from metatheoricians (at least, those who are not Protists). One might, on the other hand, assert 'there are lots of worlds' and then set out to make a case for why that is plausible. But to say 'there are two worlds -- and only two!' seems no more supportable than to say 'there are exactly 173 worlds, and all those people who claim that there are only 172 of them are lunatics.'"

Of course, in this post I pointed out that there is a reason for limiting the number of worlds to two: Occam's Razor. The more entities you have to posit, the less likely your theory is correct. The Anthropic Principle shows that we have to posit a world in addition to this one in order to account for the fact that this world has the very specific properties necessary for the existence of life. But unless we have a reason to posit a third or fourth or 173rd world, then to do so simply violates Occam's Razor.

Ironically, part of Anathem's alternate history includes a parallel to Occam's Razor, which is frequently referenced by the characters:

Gardan's Steelyard: A rule of thumb attributed to Fraa Gardan (-1110 to -1063), stating that, when one is comparing two hypotheses, they should be placed on the arms of a metaphorical steelyard (a kind of primitive scale, consisting of an arm free to pivot around a central fulcrum) and preference given to the one that "rises higher," presumably because it weighs less; the upshot being that simpler, more "lightweight" hypotheses are preferable to those that are "heavier," i.e., more complex. Also referred to as Saunt Gardan's Steelyard or simply the Steelyard.

So, basically, the multiverse hypothesis violates the Steelyard: the anthropic coincidences make it absurdly implausible that this world is the only one that exists; but unless it is absurdly implausible that only two worlds exist, it is invalid to think there are more than two. Anathem contains the refutation of one of its premises without realizing it.

However, I'm willing to give Stephenson some grace here, since such an acknowledgment would essentially destroy the premise of the entire book. Now go read it.

(cross-posted at Agent Intellect)

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