Rationally Speaking is a blog maintained by Prof. Massimo Pigliucci, a philosopher at the City University of New York. The blog reflects the Enlightenment figure Marquis de Condorcet's idea of what a public intellectual (yes, we know, that's such a bad word) ought to be: someone who devotes himself to "the tracking down of prejudices in the hiding places where priests, the schools, the government, and all long-established institutions had gathered and protected them." You're welcome. Please notice that the contents of this blog can be reprinted under the standard Creative Commons license.
Friday, September 24, 2010
Eliezer Yudkowsky on Bayes and science: what?
By Massimo Pigliucci
It is no secret that my already normally skeptical baloney detector now jumps to deep orange alert any time I hear the word “singularity.” I was not too impressed with David Chalmers’ lecture about it at the City University of New York Graduate Center, and I debated singularitarian guru Eliezer Yudkowsky on BloggingHeadsTV on the same topic. My later encounters with that particular group of techno-optimists and futurists have not improved my opinion of the whole shebang a bit.
Still, in the spirit of open inquiry and of keeping myself on my own toes, I devoted about an hour to reading three not-so-recent posts by Yudkowsky on the theme of quantum mechanics, science and Bayesianism (the philosophy of science related to Bayesian statistics). It may not have been the most productive hour of my life, but I’d like to share it with you.
I actually intended to read only one of Yudkowsky’s posts, intriguingly entitled “The Dilemma: Science or Bayes?” with its implied promise to provide an (novel? stunning?) argument for why Bayesianism is opposed to scientific practice, instead of being a very successful model of the practice of science, as many philosophers of science think.
But I was disappointed. The rather rambling piece presents no argument at all in favor of a novel thesis to answer the bold question of the title. Instead, Yudkowsky embarks on a passionate defense of the many-worlds interpretation of quantum mechanics and a vilification of the classical Copenhagen interpretation.
Bearing in mind the wise words of Richard Feynman to the effect that if one thinks he understands quantum mechanics (I don’t) one most likely does not understand quantum mechanics, let’s take a quick look at what is to be argued about. Both interpretations attempt to resolve the notorious problem with quantum mechanics that gave headaches to Einstein: the universe seems to follow rules at the microscopic (quantum mechanical) level that do not translate to the macroscopic level. The Copenhagen interpretation has been the standard for many decades, and it apparently still is the majoritarian position among quantum physicists. It essentially says that the wavefunction — the probabilistic distribution that describes the state of a given particle — “collapses” to a definite value any time a measurement is carried out. Which is why macroscopic objects are rather more definite in appearance than a probability function (not so electrons, for instance, until they are measured). The Copenhagen interpretation is due to the foundational work of Niels Bohr and Werner Heisenberg, who were active in the Danish capital in the 1920s (hence the name of the theory).
Even Bohr and Heisenberg were quite a bit disturbed by the implications of the idea of a wavefunction collapse for our understanding of macroscopic reality, particularly its nasty tendency to originate all sorts of paradoxes (like Schrödinger's cat). This eventually led to a different, competing interpretation known as many-worlds, originally formulated by Hugh Everett in 1957 (it is now one of many types of multiverse theories, which is a term interestingly coined by philosopher and psychologist William James). The basic idea is that the collapse of the wavefunction is only apparent, and that what happens “in reality” is that the universe keeps splitting into more and more parallel versions, comprising all the possible variants of every single event — we just happen to observe the particular variant that remains attached to our own universe. (Incidentally, whenever you read about these things, you will hear much talk of “quantum decoherence,” so you may want to read up about it.)
Now, I should hasten to say that I don’t really have a dog in this fight. To me both interpretations seem somewhat unsatisfactory, largely because they are interpretations. Call me old school, but I don’t like it when scientific theories need to be interpreted (it reminds me too much of different “interpretations” of the Bible). I’m not alone in this, as several physicists subscribe to what is informally known as the “shut up and calculate” school of quantum mechanics: the theory works in the sense that it predicts the results of experiments to a high degree of precision, no interpretation required. Nonetheless, I do think that science isn’t just about calculating and predicting, it is about understanding the world as it really is, as much as our limited brains can handle. I just don’t feel any particular allegiance to either many-worlds or Copenhagen, chiefly for the reason that neither of them can be tested empirically (they are both equally compatible with the data, as far as I can tell — or they wouldn’t be interpretations).
Now, what does any of this have to do with Bayesianism and the nature of science? Bayesianism is a type of philosophy of science that maintains that one can use Bayes’ theorem about conditional probabilities as a model for how science itself works. Bayesian statistics has become increasingly popular in a variety of fields, from medical research to decision making theory, from phylogenetic analyses in evolutionary biology to a variety of applications in the social sciences. It is based on a beautifully simple equation that relates two important quantities: so-called priors and posteriors. The priors represent the (subjective or objective, depending on the application) probability of a given hypothesis being correct. The posteriors are an estimate of how much said priors should go up or down when new evidence comes in. In other words, Bayes’ theorem provides a formal way to capture the idea that our belief in one theory or another ought to be proportional to the evidence in favor or against said theory (skeptics of course know this as Hume’s dictum — as in “extraordinary evidence” etc.).
(It is interesting to note that Bayes’ theorem also explains under what circumstances people don’t change their minds, regardless of the evidence: if your priors about a given hypothesis are zero — no belief at all, or one — a hundred percent belief, than the equation shows that no matter what the evidence is, your priors ain’t gonna change. In other words, you entered the realm of faith.)
I am very sympathetic both to Bayesian analysis (I have used it in my own research) and to its implications for philosophy of science (though there are some interesting objections that can be raised to it as a model of science tout court — see for example the chapter in Bayesianism here). Which is why the title of Yudkowsky’s column surprised the hell out of me! Alas, as I said, he provides no argument in that post for his suggestion that Bayesianism favors a many-worlds interpretation of quantum mechanics, or for the further claim that somehow this goes against scientific practice because the currently favored interpretation is the Copenhagen one.
But then I noticed that the post was a follow up to two more, one entitled “If many-worlds had come first,” the other “The failures of Eld science.” Oh crap, now I had to go back and read those before figuring out what Yudkowsky was up to. (And before you ask, yes, those posts too linked to previous ones, but by then I had had enough.)
Except that that didn’t help either. Both posts are rather bizarre, if somewhat amusing, fictional dialogues, one of which doesn’t even mention the word “Bayes” (the other refers to it tangentially a couple of times), and that certainly constitute no sustained argument at all. (Indeed, “The failures of Eld science” sounds a lot like the sort of narrative you find in Atlas Shrugged, and you know that’s not a compliment coming from me.)
Don’t get me wrong, I do get the gist of what Yudkowsky is trying to say, and I sure appreciate the millennia-old practice of writing dialogues to make a philosophical point (think Plato!). But the dispute between many-worlds and Copenhagen can’t be settled (or even advanced) that way, and in fact I suspect can’t be settled at all within a Bayesian framework precisely because the data doesn’t help to move the priors.
I take it that a major point made by Yudkowsky is that the entire course of fundamental physics may have been very different in an alternate universe (ah!) where Everett had published his paper before Bohr and Heisenberg. Perhaps, but that point has been made much more thoroughly and convincingly by Andrew Pickering in his highly thought provoking Constructing Quarks: A Sociological History of Particle Physics. Of course it will take you a bit more than an hour to wade through the 475 pages of that book, but I suspect you’ll get much more out of it than I did while perusing the “lesswrong” blog over at the Singularity Institute for Artificial Intelligence. My opinion, mind you.
So, what was Yudkowsky trying to do, exactly? My most charitable interpretation is that he is arguing for some version of the following:
a) The order in which scientists arrive at their theories, matters.
b) Many-worlds is favored on non-empirical grounds, like simplicity, beauty, etc.
c) Point (b) is in agreement with Bayes’ theorem.
d) (Most) Scientists insist that theory choice has to be settled empirically.
e) Therefore most scientists follow a path opposed by Bayesianism.
f) The non-empirical path is superior, scientific practice needs to be revised.
Of course, I may be wrong about my interpretation of Yudkowsky, largely because his argument is, well, indirect to say the least. However, if the above is a reasonable understanding of what he is saying, then:
1) Thesis (a) is probably true in the short term, but should not matter in the long term (at least if you are a scientific realist).
2) Thesis (b) remains to be argued in detail, and my hunch is that it is going to be very difficult to do so. And even a convincing argument along those lines simply wouldn’t settle the matter.
3) Thesis (c) I think reflects a misunderstanding of Bayesianism, of science, or of both.
4) Thesis (d) is trivially true. Most philosophers of science would agree with said scientists.
5) Thesis (e) is not true because of (3) above.
6) Thesis (f) is fundamentally flawed: if science is anything, both as a historical practice and following our understanding of the philosophy of science, it is a search for empirical confirmation or disconfirmation of theories about the reality of the world. Criteria like simplicity and beauty are sometimes invoked, but they are extra-empirical, cannot be justified easily on philosophical grounds (especially aesthetic appeals), and more importantly have been shown often enough to favor the wrong hypothesis in actual historical cases (for several recent and not-so-recent examples of this in fundamental physics see this).