27 March 2005

The role of the anthropic question in theoretical physics

Scientific inquiry generally asks questions that fall into two broad categories: (i) Describe the world we live in, and (ii) List all possible worlds. These questions can, of course, inform each other --- an answer to (i) better be on the list in (ii), and if (ii) only ends up finding one possible world, then that better be the answer to (i) --- and different disciplines specialize in one or the other of the two questions. Psychology and botany, for instance, seem basically interested in question (i), whereas "pure" math and literature seem mostly interested in (ii). To a physicist, the chemist who figures out all possible ways for carbons to fit together into cholesterol-like chemicals is certainly answering question (i), whereas to a pharmacist that same chemist is investigating question (ii). (I'd be interested to know the chemist's take.) Both questions should be guided by empirical as well as theoretical arguments; traditionally intelligent people tried to answer both questions without recourse to empirical data, and many still try to answer question (ii) that way. Paying attention to the empirical world is important both to guide our questioning --- a poorly-stated version of question (ii) might lead to the answer "anything" --- and to remind us of when we're inappropriately generalizing from what we're used to (as when, for example, a mathematician assumes that induction works without nuance for infinite entities).

Modern physics, it seems, sometimes confuses these two questions. Or, perhaps, it fails to keep these questions in mind, and that's why physicists occasionally ask poorly-formed questions that do not fall into either class. Most notably in this regard is what I'll call the "anthropic question", which loosely asks why it is that our universe would happen to support life.

There are a number of assumptions wrapped into this anthropic question that I'd like to elucidate. We have first a very important (and clearly true) answer to question (i) above: our universe supports (intelligent) life. This may or may not be remarkable; there is quite a lot of debate on whether it is, and my position is not as simple as one might like. The anthropic question, however, assumes that it is remarkable that there is life here. It bases this opinion (can a question actively hold an opinion?) on an observation from the modern answer to question (ii): within a general modern-physics framework there seem to be around twenty different parameters, all of which must be finely tuned to support our kind of life. Thus one can construct a not-entirely-cogent argument for why the existence of life is remarkable: for each parameter there is a fairly low probability that a random in universe it would have the right value, so the chance that a random universe supports life is exceedingly low.

There are a number of fallacies with the anthropic question and its proposed answers (which come in two main and not-necessarily-contradictory flavors: "design" and "multiverse"). One of these is a lack of imagination: certainly it's the case that carbon-based, terran-style life is exceedingly unlikely, but SF writers like Greg Egan have proved quite adept at constructing extremely alien intelligent life, so it's not unreasonable to think that radically different universes could also support intelligent life --- in fact, I am a firm believer that there is a suitably broad definition of intelligent life such that there is non-Terran intelligent life in this universe, but that it is so alien, possibly with different understandings of space and time from ours, that we won't recognize it as life for at least quite a while.

This objection is not deep, however. It's remarkable enough that our universe supports carbon chemistry; most universes don't. In fact, current models hold that supporting any kind of chemistry is remarkable: most universes don't last long enough to support anything at all, or expand so fast that all there is is a thin gas of hydrogen. So let's rephrase that anthropic question: how is it that this universe happens to support carbon chemistry? Such a universe is so unlikely that perhaps its existence should lead us to various metaphysical conclusions.

In fact, no such conclusions are possible, as has been argued strongly by scholars like Stephen Jay Gould. Because we are only asking the question because _we_ are living in this universe. Those trying to argue from the improbability of a given universe supporting carbon-chemistry life try to rigidly define this universe: "Rigidly label this universe A. A priori it's very unlikely that a specific universe would support carbon-chemistry life. Thus, the existence of a carbon-chemistry-supporting universe is much higher given a metaphysics that includes an intelligent designer or a multiverse, as opposed to a singular-universe metaphysics. Arguing from Bayesians, then, the existence of a universe that supports carbon chemistry greatly increases our credence in a multiverse or an intelligent designer. And here's a universe A which does support carbon chemistry."

As tight as this argument seems, it fails, in large part because we cannot rigidly label our universe. Even our language shows this fallacy: one always remarks on the unlikelyhood that "our universe" contains life. Of course our universe would contain our style of life; if not, we wouldn't notice it. If someone notices some other universe that contains some other kind of life, that's cause for surprise, rejoicing, and more studies, but not because it influences much our metaphysical credences (it would, of course, lend more weight to some sort of multiverse hypothesis, if only because then there would be at least two universes, and infinitely many universes seems much more likely than two).

In fact, I argue that a priori there is nothing remarkable about our universe containing our style of life. To make this position clearer, I'd like to argue by analogy with, say, planets.

There are trillions of celestial bodies in the galaxy, and at least a million planets, most of which, current data suggests, do not support Terran-style life. In fact, it would be remarkable if many planets (like in Star Trek) did support Terran life, given that modern astrobiology and ecology studies show that there are many parameters on which planets vary, and they must be "fine-tuned" for life to be particularly favorable. For a random planet to independently evolve Terran-style life, as I assume it did here on Terra, is even more unlikely, so unlikely in fact that if we find carbon-chemistry life on other planets I will assume that either it is genetically related to Earth life (for example, Earth and Mars trade rocks all the time, so it's not unreasonable for us to find carbon-based microbes on Mars that share a common ancestor with those on Earth), or that this universe is endowed with an extremely uncreative God. That's right: the existence of Earth-style extraterrestrial life would increase my belief in the existence of a Creator, and decrease my respect for It.

Yes, it would be remarkable if a random planet evolved Terran-style life. But Terra is not a random planet --- far from it: Terra is exactly the planet on which life evolved. What would be truly remarkable is if non-Earth-style life evolved on Earth. Imagine finding a species that has evolved on a planet it is exactly not suited for. Now _that_ would be surprising. (Similarly remarkable would be if we lived in a universe that didn't support life. If, for example, the physicists answer question (i) by showing conclusively that the universe collapsed a few seconds after the Big Bang, then we would have some explaining to do.)

No one seriously wonders why they happened to be born in the country in which they were born, as opposed to some other country, and the answer to why my hair happens to be brown is not that there are lots of people, and so the chances of fine-tuned hair are high. The people who study hair color are interested in other kinds of mechanisms, like the chemistry of hair dies and the biology of genetics, and maybe the social pressures that select for certain colors. There are interesting historical reasons that lead to certain people being in and having kids in certain countries, but to ask a question about why one person in particular was born in a certain place, does that increase the chances that there are other planets or countries or gods?, presupposes too much metaphysics. (Why God chose to create this universe may be an interesting question if you already assume that there's a God, but otherwise it doesn't make much sense.)

There's a problem, however, with this version of the anthropic principle, the version that argues that the anthropic question is uninteresting, because we will always live in a universe that can support our kind of life, and that is that it's not conventionally falsifiable. No physics experiment can disprove an assertion that something isn't interesting, just like no physics experiment can disprove the existence of God. As little predictive power as has the anthropic question, my position that it is uninteresting has even less predictive power. It is just as useless as a standard ethical relativist position denying the worth of the ethical project.

In fact, the observation that there is life in this universe should inform our answer to question (i). It leads to a series of interesting questions not unrelated to the anthropic question that specifically look for mechanisms that would bring about a universe with life. Some of these mechanisms have been established: biologists have a pretty good understanding of much of Darwinian evolution, and can predict the rates and details that determine how different kinds of selection work, and organic chemists have proposed cogent models of how protocells might have formed from inorganic materials. Astronomers have various theories for the proximate causes that led to an Earth with the right materials and location to support Earth-style life. It would be interesting to know the proximate cosmological mechanisms that led to a life-friendly universe: cosmologists should track the events that gave us a universe of this size and density, and should keep in mind that a (big bang, say, or string) theory that predicts a lifeless universe is probably wrong, or rather not the correct model. One proposal by Lee Smolin, a loop quantum geometer and author of, among other things, Three Roads to Quantum Gravity (a very good and deeply philosophical popular physics account of quantum gravity), I find fairly attractive. Smolin observes that Earth-style life and black-hole formation both seem to require similar carbon chemistry, so proposes that universes propagate and evolve analogously to organisms. To wit, Smolin suggests that perhaps black holes spawn universes with similar, but not exactly the same, properties and fundamental constants as have their parents. Thus physics that supports long-living universes with high rates of black-hole formation will be evolutionarily favorable and selected for, and proposes that perhaps complex carbon chemistry is one such trait. This is an eventually testable theory: a deeper understanding of black hole creation will make clearer the role of carbon chemistry (it plays a role in the formation of supermassive stars, from which most black holes come), and a more fundamental understanding of cosmology will determine whether or not universes spawn in black holes, and whether those universes have the same, similar, or radically different physicses. The observation that our universe has this carbon chemistry does not make Smolin's proposal any more likely, but it does play an important role: it inspires Smolin's proposal in the first place.

That's the appropriate role for the anthropic question. Given physical possibilites, one cannot conclude from the existence of life anything about the existence of a multiverse or a creator; existence of life is not evidence for any of these standard metaphysical theories, and we should not increase our credence in them just because we happen to exist. But there is a value to this kind of naive theorizing: consciously thinking about the remarkableness of our own existence can inspire real ideas, like Wheeler's multiverse.

I am, in fact, a fairly firm believer in something like Wheeler's multiverse, but not particularly because of the existence of life. I take it as axiomatic that there exists a Universe (which may contain a Wheeler-like multiverse), that I and everyone else interact with the Universe, and are part of it, and that the Universe has fundamental laws that can be described via aesthetic mathematical formulae, presumably understood as something like a Hamiltonian by the physicists, but which can also be understood in many other mathematical paradigms. The Universe will be in some "mix state", involving lots of different "universes" like ours, in such a way that the expected values of all simple, canonical "observables" (in the quantum sense) will be aesthetic numbers like 0, 1, and e. Given that the expected values of many of the seemingly canonical observables in this universe (the strength of the electric charge, for instance, or the total mass, or the ratio of the amounts of electrically charged and magnetically charged material) are inaesthetic, I would rather believe that we are in an aesthetic multiverse. But that's an aesthetic judgment, heavily biased by an immersion in modern theoretical physics, and not based on any deductive arguments from empirical evidence. Rather, I generalize from a variably aesthetic universe to an axiom that there is an appropriate universal aesthetic on which to judge physics proposals, and that the Universe is fundamentally aesthetic. Without these axioms, the project of theoretical physics seems lost, in the same way that, in order to work on the project of ethics, one must hold as an axiom that there is a real world with other people and that there are real ethical principles to follow.

I am perfectly willing to admit the aesthetics of a universe in which the fundamental laws, or, indeed, mathematics, are inconsistent. It's even possible that such laws don't exist, and that other models and levels of analysis are the only viable ones --- a unified theory won't replace psychology or sociology, which are at least as important descriptions of the universe, but it might complement them. Ultimately, however, the goal of science (as opposed to mathematics and art) should be to answer question (i) with a description of the Universe (at all levels of analysis, with all mechanisms that lead to it, and an appropriate understanding that different descriptions can equally describe the same phenomena on different levels). Question (ii) is important to inform question (i), and is an interesting question on its own right, but just like epistemology is not the ultimate goal of ethical philosophy, a list of possible universes is not the same as a description of the Universe. The chemist who lists all possible hydrocarbons is answering (ii) according to the pharmacist, and (i) according to the physicist, and similarly a string theorist who thinks she is working on (ii) might actually, in a Wheeler multiverse model, be answering (i). The most important value of considering issues like the anthropic questions is the possibility of inspiring new ways to turn answers to question (ii) into an answer to question (i). By itself, however, it cannot select any given answer.

(For a more detailed discussions of anthropic principles, multiverses, observational effects, and philosphy of probability, check out www.anthropic-principle.com. In particular, Nick Bostrom, the site administrator, as published online the first five chapters of his book Anthropic Bias: Observation Selection Effects in Science and Philosophy, available as a pdf. I know have to go to the library to read the other six chapters.)


Kenny said...

Some of the things you're saying remind me a lot of things I've talked about with Darren Bradley - see his papers on the Doomsday argument, but I think he also gave a talk once that I saw about the anthropic principle and what he called the "inverse gambler's fallacy" (actually, I think he was responding to Bostrom in that talk). The gambler's fallacy says that if you roll the dice a lot and never get a 12, then you're more likely to get a 12. The inverse gambler's fallacy says that if you see a particular die roll and see that it's a 12, then this roll must be part of some long sequence of rolls. And it's just what you're talking about here. Except I think you got it backwards - it's because we can only rigidly designate our own universe that we don't get any Bayesian effect from learning that it contains life (just as seeing a roll of the dice that comes up 12 doesn't increase your probability that the gamblers were playing for a while, although hearing that there was a roll that came up 12 does increase your probability that they played for a while).

When you talk about the fundamental constants of the universe being "aesthetic" you forget that there are units on these things. I think most physicists use the value 1 for as many of them as possible. (I don't know what they do for things like fine structure constants that don't have units.)

Now, there's a lot of equivocation between questions (i) and (ii). In fact, I was just e-mailing Darren about that this evening with regards to whether a multiverse theory is talking about one world or many. I think it's talking about just the one, because it seems reasonable to say "there are in fact many universes in the multiverse, but there could have been only one". (ii) in general seems to be a fairly vague question, depending on what sort of modality it is you're talking about.

Theo said...

It's exactly the unitless constants that are inaesthetic. The problem is that there are more constants in the universe than units, so there will be ways to combine them that give unitless values. When physicists talk about "mysteries" of cosmology, they usually mean trying to explain why something is inaesthetic. The fine structure constant (which exactly measures the charge of an electron), for instance, is one such seemingly inaesthetic constant. The cosmological constant is another. More generally are questions about why, for instance, the plank mass is so much more than the mass of a proton. Even if not fine-tuned, these do seem fairly random, and that is one of the reasons I support a Wheeler-type multiverse. The point is that my support is explicitly based on a principle that the Universe should be aesthetic.

I might be misusing the term "rigidly define". My point is that there is no way to define the universe without referencing ourselves. And then the probability that a universe exists that supports life conditioned on the fact that we exist is one. But any of our credences are conditioned on our existence, no? So conditioning on whether a life-supporting universe exists doesn't have any effect.

I'll think more about reverse gambler's fallacy. The site I linked to provides some discussion of it, but I haven't read all of it. I think the analogy is false, but I also think I need to better understand what the gambler's credences should actually be in any particular case. (One thing I will observe right now is that a straight-forward calculation shows that before the game, the expected number of roles that it will take for the gambler to be called in is, in this case, exactly 36.)