About Rationally Speaking

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).
So there.


  1. If I am not mistaken, the word "interpretation" was deliberately chosen for the Copenhagen interpretation simply because the Copenhagen interpretation was beyond confirmation.

  2. First, on Many Worlds vs Copenhagen:
    The Many Worlds Interpretation begins with the observation that the microscopic rules of quantum mechanics do in fact translate to classical physics at the macroscopic level. It's a complicated process (called decoherence), but even Copenhagen partisans must accept that it exists. Decoherence makes predictions about where the quantum becomes classical, and these predictions can be tested. The question is really whether it's decoherence all the way down, beyond any possible experiment, or if wavefunctions collapse at some point.

    From this point of view, I think Many Worlds is quite appealing, and many physicists agree with me. However, the Copenhagen Interpretation is infinitely more practical and pedagogically useful, and most physicists never need to worry about it either way. The only situation where it might matter is to a theorist looking to go beyond quantum mechanics. But such a person shouldn't be dismissing possibilities out of hand just because they're aesthetically unpalatable.

    Second, on Bayesian arguments for Many Worlds:
    My guess, without reading Yudkowski, is that he thinks Many Worlds is more likely because the more worlds there are, the more likely life is to arise. I think this reasoning is flawed for complicated reasons. In short, this argument favors Many Worlds by a factor of order N, where N is the number of worlds. However, a solid bayesian argument should try different priors to test robustness. I think it is reasonable to vary our priors up to order N, so the argument isn't robust. Empirical evidence would be much more robust.

  3. Massimo, objecting to a hypothesis on the grounds of simplicity & parsimony is not the *mere* subjective value judgment you seem to think it is. Name any scientific theory and I can invent five empirically indistinguishable alternatives. Yudkowsky's point is that empirically indistinguishable hypotheses are NOT equal in the eyes of probability theory - some have larger Kolmogorov complexity than others. But these considerations are not a part of the traditional view of science.

    I think some of your confusion is Yudkowsky's fault, though. He uses the word "Bayes" as a watchword for his entire view of rationality, so he didn't literally mean "Bayes' theorem conflicts with science."

  4. I do not think that Yudkowsky thinks that the non-empirical path is superior. The problem is that we never have (or can have ?) enough data to unambiguously determine our theories. So, something more than just empirical data has always to be used and here simplicity(/”occam's razor”) is as I understand it the additional criterion that has always been applied in science. Empirical data is the most important but unfortunately never by itself enough.

    What Yudkowsky says (as I understand it) is that in ”ideal science” any proposed new theory has to make at least one new prediction, then a new experiment should be made, and the new theory accepted if and only if the experimental result is as predicted. Then this gives the problem that if there are N theories (N> 1) (in practice N theories, maybe infinite number of theories if we allow them to be infinitely complicated) that correctly predicts all empirical data that there can be, then using ”ideal science” we will not choose the simplest one, but the one that happens to be presented first. And even if it is maybe hard to exactly motivate simplicity as a criterion, the criterion that the theory that happens to be presented first is probably the one closest to the truth would clearly be just crazy.

    But the problems here are 1) is this description of ”ideal science” by Yudkowsky correct? I do not think so. It has always been known that simplicity has to be used as a criterion. The problem is of course that it is both hard to motivate and hard to formalise. But seems unavoidable. Particularly since it is so hard to formalise, it is only natural that there exist some bias in favor of the old theory, but at least for a significantly simpler theory at least after some time, it would be preferred. Is this in line with what philosophes of scince think should be done? I guess so, but you are the one who actually are the philosopher Massimo, not me! 2) What does ”bayesianism” say about this? How does the simplicity criterion enter there? (And for that matter, how does time-order of presentation enter in bayesianism? (If not at all, then why not?))

    As for old and new experiments (or empirical data in general), in principle it should not matter if the data that the theory predicts is old or new (obtained before or after the theory was presented). But for not-completely-rational beings, like humans with a lot of biases, new data is stronger evidence. Because that makes it more difficult to to adjust pet theories ad-hoc to agree with the empirical data. But if no new data can be obtained, then of course we should still try to improve our theories.

  5. Thank you for this very helpful and enlightening post.

    My take (again, coming from a very limited understanding of this specific topic in physics) is that the decision between two empirically undifferentiable interpretations can only be done based on parsimony, unless one prefers to be entirely agnostic as the shut up and calculate school you mention. And the problem is then: is many worlds the simpler one because it has the more elegant math (if that is indeed the case, I would not know) or is Copenhagen the simpler one because, well, it contains only one world?

    My gut feeling says the latter, but then, gut feelings are not really scientific either...

  6. According this page, there is an experiment you can do to tell them apart...

  7. Above I posted a small comment about scientific method in general. Here I try to contribute some specific comment of quantum mechanics. (But see also my comments on the previous Julia's picks post.) ”Many worlds” (”MWI”) quantum mechanics (QM) should be much simpler than ”Copenhagen” QM, if just MWI delivers what its proponents say it delivers. Thus I think that the question of which of ”MWI” or ”Copenhagen” is to prefer is much more a technical scientific debate than a debate over different philosophies of science; if MWI actually delivers what its proponets say, then it is so much simpler than ”Copenhagen” that it would be very difficult not to choose MWI on occam's razor arguments.

    In Copenhagen QM one has two different rules for the time developement of the state of a system; one when one is not making a measurement (”unitary time developement postulate”), and another one when one is making a measurement (”the collapse of the wave-function postulate”). This ”collapse” rule of the time developement is chosen so that directly after the measurement one has a definitive value for the physical observable measured (but not generally for other observables). Which value this is is given by a probabilistic rule called the Born probabilities (so the Born probability rule can be said to be one part of the von Neumann collapse postulate (it was John von Neumann that gave the full mathematical formulation so I prefer actually to say von Neumann collapse (or more formally mathematically: projection) to ”Copenhagen”, at the Copenhagen institute they never agreed exactly on what they meant)). At other times one has generally not well-defined values for physical observables, so this is why the postulate for the measurement process is called the collapse postulate: the state of the system (sometimes called the wave-function) ”collapses” to the state representing the value one obtains in the measurement. (So the wave-function is not a probability distribution, the probability distribution is obtained by applying the von Neumann collapse postulate to the wave function.)

    The Collapse in the Copenhagen QM is problematic in several ways. First, it is not really well defined. We have different rules for the time developement when we measure or not, but when is that? ”Measurement” is only a loose informal concept so the theory is only ambiguously informally defined. Second, in the formulation of the theory there are not included any limits of applicability, i.e. QM is claimed to be generally valid. But then it should be able to describe also measurement instruments (or whatever is used in a measurement), so also measurements should be able to describe by ordinary physics (QM). So if there is nothing extraordinary regarding measurements (measurement instruments are built by ordinary atoms that should behave as orinary atoms also when the measurement intrument is in use) it should be described by the same physics as used for ”non-measurements”, i.e. by the unitary time-developemant rule. (There are even more problems, but this is bad enough and will do for now.)

  8. (2)
    So it would be a big advantage if the von Neumann collapse(/projection) postulate could be replaced by something more clear and simple. One possibility would be to replace the collapse postulate by another postulate that operate all the time, not just during measurements, but still makes for definite measurement outcomes and for their probabilities predicted by the theory. Two different well-known proposals along this line are the Bohm so-called hidden variable theory (”bohmian mechanics”) and the Ghirardi, Rimini, and Weber (”GRW”) so-called spontaneous or dynamic collapse theory (collapse occurs by postulate but not by a separate time-developement rule). By both these two theories the described problems of the collapse postulate dissapear, so provided there are no other new problems with them they should be preferred to ”orthodox” von Neumann QM. (Unfortunately there seem to be other problems.)

    Another possibility would be if the effect of the von Neumann collapse postulate was already in the unitary time-developement. I.e. if it (or more exactly the effect of it at measurements: giving (at least the perception of) definite measurement outcomes and giving the correct rule (Born rule) for calculating the probabilities for the values of the outcomes) could actually be derived from the other postulates of the von Neumann formulation of QM. If so, that would definitely be a much more simple formulation, and should definitly be preferrable to von Neumann QM. We get rid of a redundant postulate. And not just any redundant postulate but as explained above a quite problematic one too. This was what was claimed by Everett for his relative state formulation of QM (later called ”MWI”). But his claims where probably exagarated, because he did not use the decoherence concept, and todays proponents of MWI say that decoherence is an important part of managing to get definite measurement outcomes. It remains for me, however, to see a clear technical mathematical derivation of this, not handwaving. Should anyone know one, please post the reference. For now, however, I remain sceptical that the task done by the collapse postulate in the orthodox formulation is actually alreday in the other postulates of that formulation. And the task has to be done, otherwise we have no agreement between prediction and empirical data. (Here are two different possibilties for failure: the MWI gives predictions that are wrong, the MWI does not give predictions. The latter will happen if no probability rule can be derived from the other postulates, because the Born probabilities are the predictions of QM.)

  9. Alex:
    Strictly, Copenhagen contains NOT one world, but many, *all but one of which instantaneously disappear during measurement.*

  10. ianpollock:

    But these considerations are not a part of the traditional view of science.

    But they certainly are, or: what tonyf said. My point is that it may in practice not always be trivial to say what is the simpler explanation.

    Very often it is, however. You cannot honestly pretend, if somebody comes first and says

    "humans evolved from ape-like ancestors and at a certain point god intervened and bestowed a soul upon them that, unfortunately, cannot be examined empirically"

    and then a few years later somebody comes and says

    "Um, no, it seems much more sensible to assume that they evolved from ape-like ancestors through entirely natural processes",

    that the second cannot possibly be accepted because it is empirically indistinguishable and came later. That is not how science works.

  11. Schrödinger's cat's famous last words: I expect the fact that I am dead to be a matter of opinion.

  12. "(And before you ask, yes, those posts too linked to previous ones, but by then I had had enough.)"

    Uh, Massimo, it's fine that you don't want to read a big fraction of what Yudkowsky has written (he's written a _lot_), but it's not fine to complain that you don't see an argument for why Bayesianism favors MWI. Yudkowsky has written such an argument; it's about 30 posts long, if you include the posts that explain basic quantum mechanics.


    As for the main point of the post you decided to critique, ianpollock has it exactly right.

  13. Massimo, your link on paragraph 8 'Baye's theorem' is a no go.

  14. The section on science here has a nice summary of Yudkowsky's views on the topic.

  15. Harry, the link to Bayes' theorem has been fixed.

  16. ianpollock,

    yes, one can invent an infinite number (not just five) of empirically equivalent theories that fit a given data set. This is a well known problem in philosophy of science, known as the underdetermination of theory by data. So Yudkowsky didn't invent anything there. But Bayes' theorem is about evidence, which in this context is empirical evidence. The fact that a particular theory is simpler than another should not alter the priors in Bayes' equation. More fundamentally, as I pointed out in the post (see link to Smolin's book), the history of science is full of simpler theories that turned out to be wrong, with several instructive examples from 20th century physics.


    Yudkowsky has not established the strong thesis that had the many-worlds theory be presented first it would have been accepted. He just wrote a fictional dialogue about it. Pickering (link in my post), on the other hand did the hard philosophical, historical, and sociological work to validate this sort of scenario. And even in his case the conclusion is hardly firmly established. As for simplicity, aside from my comments above, I think part of the problem is that people mean different things by it. The proper interpretation of Occam's razor is that you don't want to introduce new hypotheticals in your theory unless they are demanded by the empirical data. This by all means does not lead to the simplest hypothesis tout court, because sometimes (often?) the data actually require more complex hypotheses. I will not comment on the second part of your post, because as I said I don't have a bone in the fight about which QM theory is better, I am just arguing that Yudkowsky has a bizarre view of either Bayes or science, or both.


    I leave it to the physicists to figure out if the two theories can be separated empirically. As a matter of precaution, though, I don't trust anything that comes from a web site called "anthropic principle."

  17. "The fact that a particular theory is simpler than another should not alter the priors in Bayes' equation."

    On the contrary. If we can view a complex hypothesis as an ANDing together of simpler hypotheses, the priors definitely change, even if the hypotheses are empirically indistinguishable.

    prior(evolution & insertion of soul into H. sapiens) << prior(evolution)

  18. ian,

    good point, I was talking about the posteriors, which are the quantities that is arrived at when one adds new evidence. If all that Yudkowsky is arguing is that one of the two hypotheses ought to be preferred a priori because it is simpler, than (a) he doesn't need to bring Bayes in, and (b) he has to show that the hypothesis he prefers really is simpler. But he still faces my objections to the effect that the history of physics is littered with beautifully simple hypotheses that turned out to be wrong.

  19. These posts are random samples from long sequences on their respective topics. I don't think you have understood much of what Eliezer was trying to say (and I'm not passing judgement on whether that's your fault or Eliezer's).

    - The copenhagen interpretation does _not_ say that a particle collapses to a specific point when measured. The so-called "collapse postulate" refers to disjoint regions of quantum configuration space disappearing.
    - The wavefunction does _not_ describe anything probabilistic. It says that a particle is "smeared" through space and time, no probabilities about it!
    - The topics of the fictional dialogues are covered formally and directly in other posts.
    - Thesis (b) has been argued in detail, and it's pretty clearly true once you do the analysis.

  20. Alex,

    I can't read everything Yudkowsky, or anybody else, for that matter, writes. I was directed to those posts by one of Julia's picks, so my analysis is limited to those posts.

    I stand by what I wrote about quantum mechanics. I am no expert, but that's what I got from general readings about it.

    Thesis (b) needs to be argued in detail, and at any rate - as I have repeated argued above - simplicity per se is not enough to decide between scientific theories.

  21. Furcas,

    sorry, I aint' gonna read 30 posts by Mr. Yudkowsky. Seems to me that at least the outline of an argument could be made in a single post. At the very least Yudkowsky makes no argument at all in the three posts I have read, even though the title of one of those posts implies that one is about to read an argument.

    And no, I don't think ianpollack has it right, but of course intelligent disagreement is the point of this blog.

  22. I must agree, it's hard to know what to make of Yudkoswky. On the one hand, I've read some of his quantum mechanics stuff, and random smattering of other posts, and a lot of what he says seems well-thought out, and makes sense. But then, at random, he'll say something that reminds me that I'm reading someone who thinks that one of the biggest threats to humanity is, paraphrasing, super-smart, evil, artificial intelligences.


    "My guess, without reading Yudkowski, is that he thinks Many Worlds is more likely because the more worlds there are, the more likely life is to arise. I think this reasoning is flawed for complicated reasons. In short, this argument favors Many Worlds by a factor of order N, where N is the number of worlds."

    Perhaps you should go read him. I've read a fair amount of his stuff about quantum mechanics, and I can't imagine him making that argument. It's not even clear that that argument makes sense given his explanation of many worlds, because it isn't a multiverse theory where there are N worlds, but rather that the apparent collapse of wave functions upon measurement is due to the wave function of a 'world' splitting into multiple, non-interacting parts.

    Rather, I think he argues that the Copenhagen interpretation is essentially many worlds, plus the postulate that when the wave function splits as it does in many worlds, there is a single designated "real" world part of the wave function, and all of the other parts disappear. But, this is an extra, (so far) unobservable assumption on our part, and makes the interpretation less simple.

    Regardless of whether he's right about various aspects of this stuff, I do think there's one useful idea in his series of articles: let's stop telling everyone that quantum mechanics is mysterious and hard to understand right off the bat. Even Massimo immediately quotes Feynman's chestnut about how no one really understands quantum mechanics. But that was decades ago, and QM is no longer as new as it once was. What if the reason it has a reputation for being so weird and difficult to understand is merely because people keep repeating the meme and quoting old authorities?

  23. Dan,

    just to make clear, the bit you quote was not from my article, but from a previous commenter.

    I don't know whether Yudkoswky is right abut the difference between the two theories. Seems to me that if it were that obvious a few smart physicists would have figured it out by now.

    But I have to disagree that Feynman's chestnut somehow doesn't apply. QM is the most complex scientific theory we have, and to really understand it one has to understand the math, which most of us (including me) don't.

    One problem, as I pointed out in my post, is that QM seems to be the only theory for which we need to somehow come up with an interpretation - because what it says is so alien to our everyday experience. And when you interpret you are not doing science anymore, at least not in any straightforwardly empirically testable way.

  24. The many-world interpretation is indeed simplier than any other interpretation : it does not require any collapse.

    But it is also incomplete.

    It's merely a mathematical description of everything that may happen / have happened / will happen, the infinite set of all possibilities.

    If you think of a scientific theory as a predictive tool, that is fine : you don't need a collapse, and MWI is the best heuristic choice. But if you think of a scientific theory is a kind of ontological candidate and begin to claim that all the possibilities described by the evolution of the wave function actually exist, then you step into metaphysics and problems will arise...

    You can claim that other branches of reality exist, although you have no way to perceive them. That's not a problem.
    But you can also claim that your past exist : it is indeed described by the theory as a wave function, just as your present is. You don't perceive your past anymore, but that's not a problem, is it ? What is so special with your present to be more "real" than your past?

    And every possible future exists too. And every alternate futures of all your past instants... Everything exists!

    To this point, one could say: ok, everything exists... But what do we mean exactly by "exists"?

    Quantum physics questions the fundaments of science: epistemology itself. What do we mean by "exist" and how can we know something exist? Is there an objective reality ? What exactly is the scientific model, is it a description of reality like a map is the description of a territory, or is it something else?

    Please tell me if you have an answer...

  25. "just to make clear, the bit you quote was not from my article, but from a previous commenter."

    Yes, I should have made that clearer.

    "But I have to disagree that Feynman's chestnut somehow doesn't apply. QM is the most complex scientific theory we have, and to really understand it one has to understand the math, which most of us (including me) don't."

    Lots of people do understand the math though. Even back when Feynman said that, there were people who were well acquainted with the it. And certainly, we expect physics students to be capable. It's not really even especially difficult math. The majority of engineers in the US probably learned enough to understand quantum mechanics.

    Yet it seems to be standard practice to tell people, "this stuff is weird, and you probably won't understand it, and Feynman said no one does." I don't think that's because of the math, but, as you say, "because what it says is so alien to our everyday experience."

    It is alien. I'm sure Yudkowsky would agree. However, the tack he takes is: quantum mechanics is how the universe actually works. Your everyday experience is what is weird, and wrong (sort of). So when quantum mechanics says something alien, you shouldn't just say, "that's weird, and un-understandable." You should instead try to think of the quantum mechanical happenings as natural, because, well, they are. And perhaps, "I won't understand QM because it's weird and alien," won't become a self-fulfilling prophecy.

    He actually doesn't even get into the details of the math much. You can get into some of the unexpected results without it. Like, shooting single photons through a network of mirrors can lead to unintuitive results, but why what happens happens can be explained with simplified math (i.e. solving differential equations isn't the important part).

    I think he's relatively successful, but I'm not a physicist, so maybe I've been duped.

    I actually have experience with something like this elsewhere. I know a certain programming language (Haskell) where some common techniques are introduced to the language via a mathematical construct (monads). For a long time, when explaining this to new folk, people would preface their explanation by how scary and difficult this all was, and how it was related to abstract mathematics (category theory). But, in reality, it isn't all that difficult to understand what's going on on a practical level, and isn't much more difficult to use than more typical languages. So one wonders how much trouble people have had merely because they've been told they *should* have some; that there *is* something especially difficult here to understand.

    QM probably isn't in exactly the same boat, but prefacing explanations by, "you aren't really expected to understand this, because it's weird, and no one does," probably isn't helpful.

  26. Dan,

    I'm all in favor of more people understanding quantum mechanics. But as you point out, there are two levels of "understanding" here. One is the math. Obviously, many people understand that, though I suspect you overestimate most people's math skills in that respect.

    The second issue is whether we understand the reality behind the metaphors. Take the dual nature of light: when we say that it behaves both like a particle and like a wave, that is a gross analogy, because clearly light isn't either a particle or a wave as commonly understood, but something else that we can approximate using those two metaphors combined (even though they are usually antithetical!).

    As for our friend Yudkowsky, my criticism of his three posts was that they don't make an argument, and that if he thinks Bayesianism is opposed to good scientific practice then he is wrong. None of that has much to do with how many people understand QM.

    Last point: we better not be too confident that QM tells us how the world "really is," because plenty of previous scientific theories have claimed that, and it turns out the world was really different. Indeed, if string theory is correct, then the world isn't quite like what QM tells us it is.

  27. Massimo, I have a somewhat tangential but I think important meta-criticism.

    Quote: "It is no secret that my already normally skeptical baloney detector now jumps to deep orange alert any time I hear the word “singularity.”... My later encounters with that particular group of techno-optimists and futurists have not improved my opinion of the whole shebang a bit."

    We don't always have the time or resources to investigate ideas fully, so heuristics are an extremely useful tool for time-constrained rationality. However, every time we use a heuristic like "judge an idea by the personality & conduct of its proponents," or "judge an idea based on surface analogies to religions & cults" as you've done here & in other posts, we should feel a strong twinge of guilt for having failed to really give the idea a fair shake.

    One of the very few recurring mistakes that I feel you & Michael often make (probably unconsciously), is to look at some behaviour (by conservatives or singularitarians, for example) that you disapprove of, & then tacitly imply that you've made some sort of argument against the idea.

    But alas, one cannot learn about the feasibility of, say, recursively self-improving AI, by observing the psychology of transhumanists. As Yudkowsky loves to say, reversed stupidity is not intelligence.

    Now I am not saying you *explicitly* believe that social judgments are crucial to evaluating ideas. But the problem is, it is an empirical *fact* that humans tend to evaluate ideas based on factors such as whether they would like to affiliate with the proponents.

    This bias comes in addition to a majestic suite of others, none of which are easily overridden by conscious effort. This is why being a rationalist is a lot like being a recovering alcoholic.

    Given these epistemic dangers, even *mentioning* personality in passing, in a discussion we wish to be rational, is like bringing vodka to an AA meeting. Yeah yeah, I know, we're not robots, but it would be nice to particularly avoid such comments when the topic under consideration is still legitimately controversial.

    But maybe I'm too hard-line about biases?

  28. Massimo,

    Thank you for that post. As a quantum physicist, I was quite bothered by Yudkowsky’s post, but we’re untrained in Bayes’ theorem so I had no ground to argue on.

    When it comes to the interpretations themselves, it seems to me that most of us are in the “shut up and calculate” camp (I'm not, but I'm not really in any camp). I don’t think a majority of physicists actively subscribe to many-worlds, but I would actually be curious if there was any sociology of science data on what interpretation physicists most subscribe to. Do you know of any?

    For myself, all interpretations seem lacking to me. I’m unsatisfied with many-worlds and Copenhagen. Most interpretations out there smack of our classical brains trying desperately to understand quantum reality.

    And thanks for your plug about the wave-particle duality being a gross analogy. We only use one mathematical object for light (photons): the quantum field (QED for light). It just so happens that it has properties of both particles and waves.


  29. Justin,

    thanks! Great to hear from a real QM physicist! I don't know of any sociological data along the lines you suggest, but I'd certainly be interested.

    > Most interpretations out there smack of our classical brains trying desperately to understand quantum reality. <


  30. Dan,

    If Yudkowski is not making the argument that I thought he was, then good for him. However, I find it rather difficult to imagine what other Bayesian argument you could possibly make for the Many Worlds Interpretation. A Bayesian argument takes some prior probabilities, and finds posterior probabilities given a collection of evidence.

    What is the collection of evidence here? All I see is arguing about prior probabilities. That's great and all (I'm a MWI partisan myself), but how is that a Bayesian argument?

  31. It seems to me that many people don't understand how observation can collapse the wave function. The fact of the matter is that waves interfere with waves and, thus, we get an interference pattern whenever there is "observation." Wave interference causes the initial wave to break up into a trillion little wavelets, which then interact to form the complex system we describe as a particle. It's all waves -- and communicating waves, which communicate using waves. Thus, it is all information -- defined as "that which is without form, which gives form."

  32. Regarding your remarks, you are correct that Yudkowskyis arguing that "The order in which scientists arrive at their theories matters" but he's also arguing that it shouldn't. Essentially his argument boils down to:

    1) Given two theories, scientists are more likely to accept the one that came first even if all data supports them equally.
    2) (1) is bad from a Bayesian perspective.
    3) His example of this is the interpretation of quantum mechanics where he argues that MWI is essentially simpler than most other interpretations of QM and thus if one is accepting an interpretation, MWI should be the one accepted since it is simpler.

    1 and 2 seem reasonable to me. I don't have the expertise to evaluate 3.

  33. miller,

    Unfortunately, I probably know less about Bayesian probability than I do about quantum mechanics, so I don't think I can answer your questions satisfactorily. Most of what I've read by him was the quantum mechanics stuff, because I'd heard it was a good explanation of the many worlds interpretation.

    I gather that what I mentioned earlier, that Copenhagen is the same as many worlds, except that we make some additional, unsupported assumptions, constitutes arguing about prior probabilities?

    In that case, it may be that Yudkowsky would suggest that there *is no* body of evidence that can distinguish the two interpretations. But, you can argue about the priors, and perhaps he considers doing so to fall within Bayesianism.

    That might explain the content of the article that sparked this discussion, too. That is, if there were actual evidence upon which to base an argument for one interpretation over the other, scientists would use it. But, science (allegedly) doesn't allow arguing about prior probabilities to allow one theory to supplant another when they are otherwise indistinguishable based on evidence (instead, preference is given to the theory that came first). So, even though Bayesian probability may model scientific reasoning, it may be that someone acting as a Bayesian accepts arguments that someone acting as a scientist wouldn't.

    But, this is merely a guess about something well out of my area of expertise, so take it with a grain of salt.

  34. Dan,
    Yeah, it seems like Yudkowski is taking Bayesianism to include arguments about prior probabilities. The thing is, those are the weakest kind of Bayesian arguments. Maybe if MWI were vastly simpler than Copenhagen, I would be convinced. But MWI is only a little bit simpler, so I'm only a little bit convinced.

    In any case, I think science really does consider prior probabilities. Steven Novella once explained this as the difference between science-based medicine and "evidence-based medicine" (a term unfortunately adopted by alternative medicine). The trouble with "evidence-based medicine" is that it levels the playing field for wildly implausible claims such as homeopathy.

  35. In my opinion, the Bayesianism argument should not apply to an interpretation, but only to a theory.

    Quantum physics does not need a collapse to be used for prediction, etc., and that's fine. Bayesianism could apply if ever we had an other concurrent theory, I don't think this is the case.

    The problem of an interpretation is very different. The question is how do we interpret the objects of the theory.
    MWI claims that the wave function is real. Copenhague interpretation claims that it's a catalogue of predictions (and the "collapse" is how we infer predictions from the catalogue).

    I don't think that Bayes is of any help for interpreting the objects of a theory.

    Copenhague interpretation sounds more reasonable to me, although it's not fully satisfying. MWI looks very much like a confusion between the scientific model and reality itself (a recurent problem), without any philosophical hindsight.

  36. Q: "Quantum physics does not need a collapse to be used for prediction, etc., and that's fine."

    Well, it would have been fine if it had been actually the case.

    Q, and many others above, the claim that MWI(="von Neumann QM minus projection postulate") is able to predict observed empirical data is a controversial one. Maybe it is able to do this, maybe not, but I repeat my request towards the end of my post September 23, 2010 8:08 PM. I do not claim to know the most recent literature on this but my impression is that it has not been demonstrated that MWI actually does give the predictions. As to whether MWI actually does that or not I am completely (temporarily) agnostic. But much of the other discussions seem to me a bit premature before that technical question has been resolved.

    As for the hypothetical question if MWI is to be preferred if it was actually delivering what its proponents claim/hope: Yes definitely over "Copenhagen". But here comes another limitation of Yudkowsky's presentation, the false dichotomy "MWI versus Copenhagen". Very satisfactory e.g. would (I think) be a local hidden-variable theory which, maybe, could be constructed by means of (microscopic only) causation both forwards and backwards in time. To my knowledge no one has succeeded actually doing that so far. But so I have not so far seen an actually technically working formulation of MWI. Think whatever you want about this particular proposal, it is just an example of my main point that the QM problem is not a dichotomy.

  37. Q: "In my opinion, the Bayesianism argument should not apply to an interpretation, but only to a theory."

    Maybe true and I would like to hear more coments on this from those who know more bayesianism. But you (and many other here) seems uncritically accept that MWI is just an interpretation, not a theory. I doubt that. The "Copenhagen" has rules how we get definite otcomes of measurements (as well as rule for what the probabilities for different possible outcomes should be). Not clearly enough defined rules and "weird" ones too, but it has them. The MWI is a [theory or interpretation] which is defined by the same postulates, save for that you have eliminated the one(s) (the collapse postulate) that gives you the definite measurement results. But from eperience we know that we at least perceive what "Copenhagen"says -- a dead cat or a live cat, not a linear combination of dead and live cat. So clearly "raw MWI" is falsified by empirical data. If MWI should survive we have to do something more to explain that we perceive measurements outcomes as we do. And nowdays we have at least some reasonable hope of being able to do this by decoherence (some think that is already fully accomplished which I doubt, but that's the subject of my previous comment, here it is sufficient to say that at least we have some hope of being able to accomplish it), the quantum correlations are killed or hidden by interaction by the environment. This works only in a universe with a lot of negentropy. We do live in such a universe since the big bang happened to create (for reasons we at the present state of science can only speculate in why) our universe in a state of low entropy. That, I would say, makes it reasonably to regard MWI as a different theory rather than just a different interpretation of the same theory. In "Copenhagen" measurement outcomes really are determinate (in the sense cat either dead or alive) while in the MWI they only are perceived to be so conditionally on the conditions of the universe.

    Now of course those wanting to call it "only interpretation" could say that both "Copenhagen" and "MWI" always give the same perceived experience, because for a universe to have perceiving beings it has to have negentropy. So in that sense they give always the same empirical predictions and should be called just different nterpretation of the same theory. But that I think is to stretch it too much. It is not just different ontologies put on top of the two different [theories or interpretations], it is two very different mathematical formulations -- not at all equivalent in a technical mathematical sense.

  38. Massimo: "One problem, as I pointed out in my post, is that QM seems to be the only theory for which we need to somehow come up with an interpretation - because what it says is so alien to our everyday experience. And when you interpret you are not doing science anymore, at least not in any straightforwardly empirically testable way."
    Interestingly enough this may actually be more the case for the special theory of relativity than for quantum mechanics. Einstein's theory of special relativity gives the same empirical predictions as Lorentz' "ether" theory. But Einstein's theory was immediately accepted due to it larger simplicity. This is also a counterexample to Yudkowsky's claim that if two theories/interpretations have the same empirical contents science chooses the one presented first, since Lorentz' theory was the first. (OK, maybe Yudkowsky could say that in this case practical science did not live up to "ideal science".) Later of course we got also another reason to prefer special relativity; it generalises quite naturally to general relativity which did new predictions that were confirmed empirically. But special relativity was accepted by most leading physicists already before general relativity.

    "alien to our everyday experience": this should not be a problem as long as an unambiguous mathematical formulation can be done?

    Massimo: "Yudkowsky has not established the strong thesis that had the many-worlds theory be presented first it would have been accepted."
    We agree on this one.

  39. @Tonyf

    "Well, it would have been fine if it had been actually the case."

    I agree with you, in any cases, the collapse remains at least as an heuristic method for infering predictions, and it's not certain we can deduce probabilities of observations from MWI.

    The question is wether we need to assume that the collapse is a physical phenomenon or not. This assumption is not required for the physicist's practice, as a "collapse" cannot be practically observed. It's only a matter of interpretation. That's what I meant in the sentence you've quoted.

    "But you (and many other here) seems uncritically accept that MWI is just an interpretation, not a theory"

    I think it is, because other "worlds" are not observable. Neither is the wave function collapse, that's why its nature needs to be interpreted.

    A theory is only a mathematical model + a set of predictions. MWI does not change anything of the model of quantum physics nor its predictions. The question is why do we get such results and how do we interpret the wave function and the "collapse" ?

    "It is not just different ontologies put on top of the two different [theories or interpretations], it is two very different mathematical formulations"

    The mathematic formulations are the same, i.e. QM formalism. Decoherence has been empirically observed and is a consequence of QM formalism. There is no difference.

    "the false dichotomy "MWI versus Copenhagen"."

    I agree with you. Other interpretations exist (objective collapse, transactional interpretation, ...)

    I suggest everyone have a look at Carlo Rovelli's relational interpretation : http://en.wikipedia.org/wiki/Relational_quantum_mechanics

    I find it very promising. The postulate that an absolute objective reality exists is not required, which I find very interesting (and coherent with special relativity and locality of time).

  40. I'm arriving quite late to the party, however I'd like to contribute my two cents.

    I'm a theoretical high-energy physicist and the subject of the "interpretation" of quantum mechanics has always struck me as a bit of a hodgepodge of bad epistemology.

    Allow me to explain: Yes, as Feynman said, you can't understand quantum mechanics, if by "understand" we mean forming quantum mechanical concepts and interactions from the concepts and connections of our experience. Our brains did not evolve in conditions where our capacity to observe quantum phenomena would give us an advantage, so it is easy to understand our imposibility to grasp quantum mechanics like we can grasp classical mechanics.

    Now, in my eyes the "interpretation problem" seems silly: we physicists tell our students and the public that quantum mechanics is a "more fundamental" theory than classical mechanics, which is to say, it explains a larger set of natural phenomena and it includes classical mechanics as a special case.

    In spite of what I have just said we then go into the trouble of "interpreting" QM, which seems to be little more than trying to explain the behavior of a quantum system in terms of classical concepts that our classical minds can grasp. All this discussion of multiple worlds, pilot waves, wave function collapse and what not are all classical ideas, meaning that they are ideas we have gathered from our day to day classical experience.

    So we seem to want to put the "more fundamental" theory in terms of the "less fundamental" one... to some extent it is like trying to undestand biology in terms of sociology.

  41. Jesus Pineda:
    No, the QM (quantum mechanics) measurement problem is a real problem for all variants of the "Copenhagen interpretation" of QM. Read again the last paragraph of my comment September 23, 2010 8:07 PM! The Copenhagen QM is not even well defined, so even if not for anything else it cannot for this reason be considered an acceptable fundamental theory of physics (and there is also a lot else).

    As a pragmatic approach for practical use of QM it does work of course (we do know practically when we have performed a measurement even if it not formally defined in the theory). So the "shut up and calculate interpretation" is fully acceptable for that purpose (even if it should really be called a pragmatic tactic, not an interpretation). The measurement problem remains an important outstanding problem in physics, but not everyone has to be interested in everything so if you want to leave the fundamental problems of the theory to others that is a perfectly acceptable position. But it does not make the fundamental problem dissapear.

    And, no, the Copenhagen QM is not in a true sense an extension of classical physics. It simply postulates two completely different realms of the world: the quantum realm and the classical realm (and this evem without in the theory giving a definition of where the boarder is, another way of stating why the theory is not even well defined). So it does actually not give classical mechanics as a special case. (To be completely fair, it does give a very small part of classical mechanics as a special case. Ehrenfest's theorem (or its many equvalent formulations) and all that. But this is only a tiny part of our empirically observed classical experience. In particular, the infamous cat is not part of the classical world that Copenhagen QM gives in its very limited classical limit!)

    We do not want to explain the quantum world in classical terms. We want to have a well dedfined (mathematically formulated) theory that is consistent with all our empirical data. Including as a special case all our "classical experiences". And Copenhagen QM simply does not deliver on this. Therfore something has to be done, and my personal judgement is that the reasonable position at the current level of knowledge in science is the "more research is needed interpretation" of QM.

  42. Regarding simplicity, the argument that simpler theories are more probable (a priori) can be put on a firm mathematical footing. The trick is to have the appropriate definition of simplicity. The appropriate notion (first articulated by Ray Solomonoff) is Kolmogorov complexity. Roughly speaking, the Kolmogorov complexity of a theory is the length of the shortest computer program which simulates that theory. The simplicity argument for the many worlds interpretation says that the worlds drop out of the math, and thus a computer program which simulates MWI is shorter than a computer program which has to worry about "collapse".

  43. I realize this post is very late and will probably go unread, but I'd like to make a few points. Massimo, I think your negative critiques of Yudkowsky's posts are simultaneously unfair and understandable. They're unfair because those posts are, essentially, conclusions to a lengthy QM sequence Yudkowsky wrote. Critiquing them alone would be like only critiquing the conclusion of a book. However, I think your critique is understandable in that it's often unclear when you first stumble onto LW posts where a sequence starts!

    I think you're fundamentally wrong on your points addressing B and C (in your original post):

    a) There’s no doubt that MWI is simpler than CI. I don’t think any physicists argue this.

    b) The best arguments are as much AGAINST CI as opposed to FOR MWI. CI flies in the face of macro physics being non-local, non-real, and indeterministic; it flies in the face of history, as it would be the first time a theory contradicted an old theory without falsifying the old theory OR subsuming the old theory into a more complete formulation (ala General Relativity with Newton); Worst of all, it does those things without an empirical or mathematical reason for doing so.

    c) One could argue MWI IS supported on empirical grounds. What we'd expect to see if MWI was true is that everything would be in a state of superposition like a particle. So far, we've managed to place 2424 particles in such a state without finding the "split" predicted by CI. MWI can really only be falsified, by, eg, showing how, at some points, large objects STOP being in superposition. If you want a good, short, simple argument on these points from a physicist, see here: http://www.askamathematician.com/2010/10/q-copenhagen-or-many-worlds/

    d) As for what this has to do with Bayes, it affects both priors and posteriors. It affects priors because MWI is more likely to be true a priori by being simpler. You've mentioned several times in these replies that there were times when simpler theories turned out false, which is no different than saying some smokers live long lives and some non-smokers die of lung cancer. The issue is one of probability, and simpler explanations are, a priori, more LIKELY to be true always. It affects posteriors because, thus far, every empirical test supports it and, to some degree, has made CI less likely. It’s made CI less likely because if CI is true there should be SOME split SOMEWHERE between the two worlds. There should come a point when a group of particles isn’t in superposition.

    So, with all that in mind, I think it's a little clearer why Yudkowsky is advocating Bayes "over" Science. I put "over" in quotes because I think many of the points that Yudkowsky makes are more against scientists than science, saying that they are waiting for that one great "eclipse experiment" that will "prove" one interpretation right and win everyone involved Nobel Prizes. In the absence of that, scientists are being far too flippant about just "going" with CI and not realizing how MWI is supported both a priori and by the empirical data. The reason they do is that they aren't making use of Bayes. Yudkowsky certainly isn't saying that Bayes (and MWI) contradicts the existing science. I think his "Bayes over Science" should really be "Bayes IN science,” and in arguing throughout his QM sequence why MWI is by far the best interpretation he’s showing how wrong even science can go when it doesn’t incorporate Bayes.