The Dilemma: Science or Bayes?

Followup toIf Many-Worlds Had Come First, The Failures of Eld Science

"Eli: You are writing a lot about physics recently.  Why?"
        —Shane Legg (and several other people)

"In light of your QM explanation, which to me sounds perfectly logical, it seems obvious and normal that many worlds is overwhelmingly likely. It just seems almost too good to be true that I now get what plenty of genius quantum physicists still can't. [...] Sure I can explain all that away, and I still think you're right, I'm just suspicious of myself for believing the first believable explanation I met."
        —Recovering irrationalist

RI, you've got no idea how glad I was to see you post that comment.

Of course I had more than just one reason for spending all that time posting about quantum physics.  I like having lots of hidden motives, it's the closest I can ethically get to being a supervillain.

But to give an example of a purpose I could only accomplish by discussing quantum physics...

In physics, you can get absolutely clear-cut issues.  Not in the sense that the issues are trivial to explain.  But if you try to apply Bayes to healthcare, or economics, you may not be able to formally lay out what is the simplest hypothesis, or what the evidence supports.  But when I say "macroscopic decoherence is simpler than collapse" it is actually strict simplicity; you could write the two hypotheses out as computer programs and count the lines of code. Nor is the evidence itself in dispute.

I wanted a very clear example—Bayes says "zig", this is a zag—when it came time to break your allegiance to Science.

"Oh, sure," you say, "the physicists messed up the many-worlds thing, but give them a break, Eliezer!  No one ever claimed that the social process of science was perfect.  People are human; they make mistakes."

But the physicists who refuse to adopt many-worlds aren't disobeying the rules of Science.  They're obeying the rules of Science.

The tradition handed down through the generations says that a new physics theory comes up with new experimental predictions that distinguish it from the old theory.  You perform the test, and the new theory is confirmed or falsified.  If it's confirmed, you hold a huge celebration, call the newspapers, and hand out Nobel Prizes for everyone; any doddering old emeritus professors who refuse to convert are quietly humored.  If the theory is disconfirmed, the lead proponent publicly recants, and gains a reputation for honesty.

This is not how things do work in science; rather it is how things are supposed to work in Science.  It's the ideal to which all good scientists aspire.

Now many-worlds comes along, and it doesn't seem to make any new predictions relative to the old theory.  That's suspicious.  And there's all these other worlds, but you can't see them.  That's really suspicious.  It just doesn't seem scientific.

If you got as far as RI—so that many-worlds now seems perfectly logical, obvious and normal—and you also started out as a Traditional Rationalist, then you should be able to switch back and forth between the Scientific view and the Bayesian view, like a Necker Cube.

So now put on your Science Goggles—you've still got them around somewhere, right?  Forget everything you know about Kolmogorov complexity, Solomonoff induction or Minimum Message Lengths.  That's not part of the traditional training.  You just eyeball something to see how "simple" it looks.  The word "testable" doesn't conjure up a mental image of Bayes's Theorem governing probability flows; it conjures up a mental image of being in a lab, performing an experiment, and having the celebration (or public recantation) afterward.

Science-Goggles on:  The current quantum theory has passed all experimental tests so far.  Many-Worlds doesn't make any new testable predictions—the amazing new phenomena it predicts are all hidden away where we can't see them.  You can get along fine without supposing the other worlds, and that's just what you should do.  The whole thing smacks of science fiction.  But it must be admitted that quantum physics is a very deep and very confusing issue, and who knows what discoveries might be in store?  Call me when Many-Worlds makes a testable prediction.

Science-Goggles off, Bayes-Goggles back on:

Bayes-Goggles on:  The simplest quantum equations that cover all known evidence don't have a special exception for human-sized masses.  There isn't even any reason to ask that particular question.  Next!

Okay, so is this a problem we can fix in five minutes with some duct tape and superglue?

No.

Huh?  Why not just teach new graduating classes of scientists about Solomonoff induction and Bayes's Rule?

Centuries ago, there was a widespread idea that the Wise could unravel the secrets of the universe just by thinking about them, while to go out and look at things was lesser, inferior, naive, and would just delude you in the end.  You couldn't trust the way things looked—only thought could be your guide.

Science began as a rebellion against this Deep Wisdom.  At the core is the pragmatic belief that human beings, sitting around in their armchairs trying to be Deeply Wise, just drift off into never-never land.  You couldn't trust your thoughts.  You had to make advance experimental predictions—predictions that no one else had made before—run the test, and confirm the result.  That was evidence.  Sitting in your armchair, thinking about what seemed reasonable... would not be taken to prejudice your theory, because Science wasn't an idealistic belief about pragmatism, or getting your hands dirty.  It was, rather, the dictum that experiment alone would decide.  Only experiments could judge your theory—not your nationality, or your religious professions, or the fact that you'd invented the theory in your armchair.  Only experiments!  If you sat in your armchair and came up with a theory that made a novel prediction, and experiment confirmed the prediction, then we would care about the result of the experiment, not where your hypothesis came from.

That's Science.  And if you say that Many-Worlds should replace the immensely successful Copenhagen Interpretation, adding on all these twin Earths that can't be observed, just because it sounds more reasonable and elegant—not because it crushed the old theory with a superior experimental prediction—then you're undoing the core scientific rule that prevents people from running out and putting angels into all the theories, because angels are more reasonable and elegant.

You think teaching a few people about Solomonoff induction is going to solve that problem?  Nobel laureate Robert Aumann—who first proved that Bayesian agents with similar priors cannot agree to disagree—is a believing Orthodox Jew.  Aumann helped a project to test the Torah for "Bible codes", hidden prophecies from God—and concluded that the project had failed to confirm the codes' existence.  Do you want Aumann thinking that once you've got Solomonoff induction, you can forget about the experimental method?  Do you think that's going to help him?  And most scientists out there will not rise to the level of Robert Aumann.

Okay, Bayes-Goggles back on.  Are you really going to believe that large parts of the wavefunction disappear when you can no longer see them?  As a result of the only non-linear non-unitary non-differentiable non-CPT-symmetric acausal faster-than-light informally-specified phenomenon in all of physics?  Just because, by sheer historical contingency, the stupid version of the theory was proposed first?

Are you going to make a major modification to a scientific model, and believe in zillions of other worlds you can't see, without a defining moment of experimental triumph over the old model?

Or are you going to reject probability theory?

Will you give your allegiance to Science, or to Bayes?

Michael Vassar once observed (tongue-in-cheek) that it was a good thing that a majority of the human species believed in God, because otherwise, he would have a very hard time rejecting majoritarianism. But since the majority opinion that God exists is simply unbelievable, we have no choice but to reject the extremely strong philosophical arguments for majoritarianism.

You can see (one of the reasons) why I went to such lengths to explain quantum theory.  Those who are good at math should now be able to visualize both macroscopic decoherence, and the probability theory of simplicity and testability—get the insanity of a global single world on a gut level.

I wanted to present you with a nice, sharp dilemma between rejecting the scientific method, or embracing insanity.

Why?  I'll give you a hint:  It's not just because I'm evil.  If you would guess my motives here, think beyond the first obvious answer.

PS:  If you try to come up with clever ways to wriggle out of the dilemma, you're just going to get shot down in future posts.  You have been warned.

 

Part of The Quantum Physics Sequence

Next post: "Science Doesn't Trust Your Rationality"

Previous post: "The Failures of Eld Science"

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Eliezer,

I think you are too harsh with the Science-goggles.

I was taught that, when first proposed, the Copernican theory did not explain the then available data any better than the Ptolemaic system.

It's main attraction (to Science-goggles-wearing types, though not to Bible-goggles-wearing ones) was simplicity: it just had to be true!

I don't know if Copernicus ever invoked Ockham's name in defense of its theory, but the latter triumphed much before Rev. Bayes's (or Solomonoff's) birth.

So maybe "simplicity" - like many other concepts - has always been one element of the Science-goggles, even before a formal mathematical definition of it was available.

According to:

http://www.hedweb.com/everett/everett.htm#believes

...most "leading cosmologists and other quantum field theorists" thought that the "Many-Worlds Interpretation was correct 10 years ago.

Supporters tend to cite not Solomonoff induction, but simply Occam's razor.

Solomonoff induction is simply an attempt to formalise Occam's razor around an impractical theoretical model of serial computation.

Eli: Nice post. I think your dichotomy between "rejecting scientific method" or "embracing insanity" is a bit excessive. I can see how some people feel that having all these multiple worlds around doesn't seem like the "simplest" explanation. They accept Bayesian reasoning and Occam's razor, but the notion of simplicity that they use is intuitive. Thus, I would view the essence of this post to be: if one views complexity in terms of minimum effective description length then WMI is a better explanation than Copenhagen.

I would also note that asking physicists to be strict Solomonoff/Bayesian/Occamists is asking for rather a lot considering that something like half the statisticians in the world are not Bayesian, and of those who are relatively few know of Solomonoff induction.

Finally, while this went part of the way to answering my question, the connection to AGI safety isn't yet obvious to me.

Tim: "impractical theoretical model of serial computation". Just because a theory isn't practical doesn't make it wrong. For example, should we define randomness in a way that is easy to test for? No, if we did it would break the very concept of what randomness means. Also, what does "serial" have to do with it? There is no concept of time in Kolmogorov complexity and a serial machine can emulate a parallel one, thus this distinction isn't relevant.

Something wrong with this post, which I didn't appreciate back in 2008, when it was made, is that it misunderstands how quantum mechanics is interpreted by most practicing physicists.

According to the post, physicists believe in wavefunction collapse, and in doing so they follow the rules of Science, but if they followed the rules of Bayes, they would believe that the wavefunction does not collapse, and thus in many worlds.

Now quite apart from the problems of many worlds, which I have pointed out here and at other posts, it is not even true that physicists, as a rule, believe in wavefunction collapse in the way it is represented here, i.e. as an actually occurring physical process.

The cognitive facts about what all the world's physicists individually believe regarding quantum mechanics would be rather complicated - there is a diversity of opinion among physicists, and an internal inconsistency of opinion within many individual physicists - but the standard view is not wavefunction realism. The wavefunction (or quantum state vector) is like a probability function; it is a mathematical entity from which probabilities of outcomes can be calculated. There is no wavefunction in space, which evolves smoothly when not observed and which jumps discontinuously when it is observed. What's actually there are particles (fields, strings, whatever), with quantitative properties ("observables") which take values with probabilities derived according to the projection postulate (or according to some mathematically equivalent rule).

Theoretical physics lacks an agreed-upon picture which specifies which observables take what values and when, at all times. Quantum mechanics only says "if you care, this is what it might be doing right now"; it offers a dynamics for the wavefunction, i.e. for the probabilities, but it doesn't offer an underlying objective dynamical framework from which wavefunction dynamics can be derived. There are various proposals (e.g. Bohmian mechanics), but they all have problems, and there are well-known difficulties (e.g. Kochen-Specker theorem, Hardy's theorem) facing the construction of a fully objective theory which reproduces quantum mechanics.

The prevailing attitudes in physics towards quantum foundations may be confused or even deplorable, but nonetheless, my point is that the argument of this article is wrong. In fact it's wrong twice over. First of all, most physicists do not believe in wavefunction collapse as a physical process - this is what I have just been saying - and so the starting point of the argument only describes the views of a minority. Second, the assertion that many worlds provides a quantitatively simpler theory than objective wavefunction collapse is a highly dubious one, because there is no good derivation within many worlds of the probabilities which contain all of the actual predictive content of quantum mechanics. It's as if I were to say, "My theory of physics is blah blah blah, and though I can't explain why in terms of blahs, my theory happens to give exactly the same predictions as orthodox quantum mechanics. Therefore, it is at least as good as orthodox quantum mechanics." Which is the criticism I was making back in 2008.

My problem with the collapse version of QM - and this may stem from the fact that Eliezer's explanation is the only one I've read that I've actually had a decent understanding of it (such that I am relatively confident I could pass along the basic concepts to someone else without becoming "Goofus" in some of EY's earlier examples) - is that there is no apparent reason for the collapse.

Take a coin toss. We say the probability of a heads or tails on a fair coin is .5 for each outcome. When heads eventually happens, the truth of the matter is that if we had information like the state of the coin pre-flip, the position of the hand flipping the coin, the force of the arm as it moves up and the exact position and force of the thumb on the coin itself, we could raise our estimation of the probability for that flip to be heads up to probably .9+. Given more precise information, we could conceivably get the probability up to .99. Excluding quantum effects, the actual probability that the coin would come up heads in that particular instance was essentially 1.

This does not seem to be the case with quantum mechanics. There does not seem to be any new information that could give any insight as to why the electron went through the first slit instead of the second, or vice versa. It's not just that the information is hidden, it doesn't seem to exist at all. Instead, the probability itself appears to be "baked into" reality, with no reason to prefer one outcome over the other. The CI response seems to be "It just does, Born probabilities blah blah blah accept it" without even attempting to explain what seems to me to be a major problem with the way reality works under this interpretation. CI doesn't actually explain the Born probabilities any better than MWI, as far as I've read, they just seem to have "claimed" them. For this reason, I don't think CI satisfies your criteria of having a "derivation... of the probabilities which contain all of the actual predictive content of quantum mechanics" criteria either. At least not any better than MWI.

If the wave functions aren't a real property of the universe, then why the hell does reality seem to follow them? And if they are real, why did A happen when there is no reason B didn't happen? This seems to imply that luck is a fundamental property of the universe!

It's these two basic questions that I haven't seen answered satisfactorily from the CI or more general collapse perspective (if such a thing exists separate from mainstream CI). The fact that most physicists believe some variation MWI bolsters my confidence, even though the idea that decoherance effectively produces zillions of universes continuously simply blows my mind.

Eliezer,

Manon de Gaillande: I don't believe most scientists would make such huge mistakes.

This is the main doubt I was expressing in my comment you quoted. I withdraw it.

Physicists are susceptable to irrational thinking too, but I went and stuck a "High Arcane Knowledge" label on QM. So while I didn't mind understanding things many doctors don't about mammographies, or things many biologists don't about evolution, thinking I knew anything fundamental about QM many physicists hadn't figured out set off a big "Who do you think you are?" alarm.

I hereby acknowledge quantum physicists as human beings with part-lizard-inherited, spaghetti-coded-hacky brains just like me, and will try to be more rational about my sources of doubt in future.

Hi Eliezer,

Have you ever read about the so-called Bayesian approach to quantum mechanics promoted by Caves, Fuchs, and Schack? These three are the most radical Bayesians I know, and they all reject many worlds. If you really care about overcoming bias, you should seek out their papers and give them a read.

Have you ever read about the so-called Bayesian approach to quantum mechanics promoted by Caves, Fuchs, and Schack?

"Comparisons have also been made between QBism and the relational quantum mechanics espoused by Carlo Rovelli and others" (WP)

;-)

I'd like to know what you're implying with this post, but I'm unable to make a confident guess. Are you claiming that this WP quotation has something to do with many worlds?

They only depend to within a constant factor. That's not the problem; the REAL problem is that K-complexity is uncomputable, meaning that you cannot in any way prove that the program you're proposing is, or is NOT, the shortest possible program to express the law.
I disagree; I think the underspecification is a more serious issue than the uncomputability. There are constant factors that outweigh, by a massive margin, all evidence ever collected by our species. Unless there's a way for us to get our hands on an infinite amount of cputime, there are constant factors that outweigh, by a massive margin, all evidence we will ever have a chance to collect. For any two strings, you can assign a lower complexity to either one by choosing the description language appropriately. Some way to make a good enough (not necessarily optimal) judgement on the language to use is needed for the complexity metric to make any sense.

The uncomputability is unfortunate, but hardly fatal. You can just spend some finite effort trying to find the shortest program that produces the each string, using the best heuristics available for this job, and use that as an approximation and upper bound. If you wanted to turn this into a social process, you could reward people for discovering shorter programs than the shortest-currently-known for existing theories (proving that they were simpler than known up to that point), as well as for collecting new evidence to discriminate between them.

I don't believe you.

I don't believe most scientists would make such huge mistakes. I don't believe you have shown all the evidence. This is the only explaination of QM I've been able to understand - I would have a hard time checking. Either you are lying for some higher purpose or you're honestly mistaken, since you're not a physicist.

Now, if you have really presented all the relevant evidence, and you have not explained QM in a way which makes some interpretation sound more reasonable than it is (what is an amplitude exactly?), then the idea of a single world is preposterous, and I really need to work out the implications.

Surely "science" as a method is indifferent to interpretations with no observable differences.

Your point seems to be that "science" as a social phenomenon resists new untestable interpretations. Scientists will wander all over the place in unmappable territory (despite your assertion that "science" rejects MWI, it doesn't look like that to me).

If Bayesianism trumps science only in circumstances where there are no possible testable consequences, that's a pretty weak reason to care, and a very long tortured argument to achieve so little.

If there is a "very convincing philosophical argument" that we should go with the majority, and yet we see the majority holding countless silly beliefs that even a little bit of primary evidence and some cursory examination show as being invalid, what does that tell us?

It tells us that the very convincing argument has at least one fatal error. It tells us that our ability to be convinced is falliable. And it tells us that our argumental-validity-checking has some bugs.

This may be nitpicking and I agree with your overarching point, but I think you're drawing a false dichotomy between Science and Bayes. Science is the process of constructing theories to explain data. The theory must optimize a tradeoff between two terms:

1) ability to explain data 2) compactness of the theory

If one is willing to ignore or gloss over the second requirement, the process becomes nonsense. One can easily construct a theory of astrology which explains the motion of the planets, the weather, the fates of lovers, and violence in the Middle East. It just won't be a compact theory. So Science and Bayes are one and the same.

Eli - As you said in an earlier post, it is not the testability part of MWI that poses a problem for most people with a scientific viewpoint, it is the fact that MWI came after Collapse. So the core part of the scientific method - testability/falsifiability - gives no more weight to Collapse than to MWI.

As to the "Bayesian vs. Science" question (which is really a "Metaphysics vs. Science" question), I'll go with Science every time. The scientific method has trounced logical argument time and time again.

Even if there turns out to be cases where the "logical" answer to a problem is correct, who cares if it does not make any predictions? If it is not testable, than it also follows you can't do anything useful with it, like cure cancer, or make better heroin.

Eliezer, I guess the answer you want is that "science" as we know it has at least one bias: a bias to cling to pragmatic pre-existing explanations, even when they embody confused thinking and unnecessary complications. This bias appears to produce major inefficiencies in the process.

Viewing science as a search algorithm, it follows multiple alternate paths but it only prunes branches when the sheer bulk of experimental evidence clearly favours another branch, not when an alternate path provides a lower cost explanation for the same evidence. For efficiency, science should instead prune (or at least allocate resources) based on a fair comparison of current competing explanations.

Science has a nostalgic bias.

The science world, as much as the rest of the "worlds" comprised by people who share something which everybody cherishes, has to have the status quo bias. (the enigmatic add-on: One cannot escape the feeling that there is such thing as time)

Whichever helps me win in the situation I am currently in. Since I don't currently need to create more advanced physics formulas, and they have the same dollar value otherwise it doesn't make much difference.

If I believe in collapse rather than decoherence is Inspector Darwin going to come and declare me bankrupt?

In fact worrying about the difference is a negative point for me anyway, I should be doing other things and devoting time, memory and processing power to this, reduces the amount I have to apply to my problems.

Collapse theories can do something many worlds can't do: they can make the predictions! As can Bohmian theories.

Many worlds, like at least one other prominent interpretation (temporal zigzag), is all promise and no performance. Maybe Robin Hanson's idea will make it work? Well, maybe Mark Hadley's idea will make the zigzag work. Hadley's picture is relativistic, too.

Many worlds deserves its place in the gallery of possible explanations of quantum theory, but that is all.

People who want to get fundamental physics out of cellular automata could be a lot more imaginative than they are. What about small-world networks? Maybe you could get quantum nonlocality. What about networks which are only statistically regular? Maybe you could get rotational symmetry in the continuum limit. And how about trying to do without a universal time coordinate? What about creation and destruction of cells, not just alteration of cell states? Euclidean, gridlike CAs like Fredkin's should only be a training ground for the intuition, not the template for modeling the real world.

With respect to the topic of this article, though I've flamed many-worlds for not really delivering on its promises, cellular-automata physics is not remotely comparable. Even billiard-ball physics is better empirically - at least it can reproduce Newtonian gravity! CAs haven't even done that. You can't say "Occam's razor favors X" if you haven't actually got X to work yet.

Ah, but Mitchell, the collapse interpretation doesn't explain why the Born probabilities are what they are.

So the version of many-worlds that I believe in, as a predictive theory, is:

(1) The wavefunction is real and evolves unitarily.
+
(2) For some unknown reason, experimental statistics match the Born probabilities.

In combination, these statements constitute a predictive theory.

As for the objection that (2) hasn't been explained, collapse "explains" it by tacking on, "And the reason for (2) is that parts of the wavefunction spontaneously vanish faster than light for some unknown reason, leaving only one survivor because we like it that way, and in the lone survivor, for some unknown reason, experimental statistics match the Born probabilities." If you look closely, this explains (2) by strictly containing it.

Tom, Nick, MWI does not make predictions! Well, there is a version of MWI that does, but it is not the one being advocated here.

What makes predictions is a calculational procedure, like sum-over-histories. That procedure has an interpretation in a collapse theory: the theory explains why the procedure works. The version of MWI that Eliezer has expounded cannot do that. He has said so himself, repeatedly - that the recuperation of the Born probabilities is a hope, not an existing achievement.

Is that clear? I feel like I had better say it again. The bare minimum that all quantum physicists share is an algorithm for making predictions. An objective collapse theory offers an explanation as to why that algorithm works. It is a theory about what is actually there, and how it actually behaves, from which that algorithm can be derived.

Many worlds is also a theory (or a class of theories) about what is actually there. But when you count the worlds, the numbers come out wrong, badly wrong. So something has to change. Robin Hanson has suggested a different approach to the problem; but as I have objected, it remains vague on the crucial detail of exactly when the transition between one world and many worlds takes place. In any case, this brand of many worlds simply cannot yet offer an exact justification of the predictive algorithm in the way that a collapse theory can. It's not true that MWI and collapse make the same predictions; rather, the hope is that MWI will predict what collapse already predicts, once we understand it properly.

Among all these comments, I see no appreciation of the fact that the version of many worlds we have just been given CANNOT MAKE PREDICTIONS, whereas "collapse theories" DO.

Yes, Schrödinger evolution plus collapse is more complicated than just Schrödinger evolution. But the former makes the predictions, and the latter does not. We have been given the optimistic assertion that maybe the predictions are already somewhere inside the theory without collapse, but this remains to be shown. That's what the meaning of this whole "quest for the Born probabilities" is about! It is, precisely, the quest to restore the predictive capacity of quantum mechanics after you've taken collapse away. And the fact that it's a quest tells you that this is a research program whose goal is not accomplished.

"Of course I had more than just one reason for spending all that time posting about quantum physics. I like having lots of hidden motives, it's the closest I can ethically get to being a supervillain."

Your work on FAI is still pretty supervillain-esque to most SL0 and SL1 people. You are, essentially, talking about a human-engineered end to all of civilization.

"I wanted to present you with a nice, sharp dilemma between rejecting the scientific method, or embracing insanity. Why? I'll give you a hint: It's not just because I'm evil. If you would guess my motives here, think beyond the first obvious answer."

The obvious answer is that the scientific method is simply an imperfect approximation of ideal rationality, and it was developed before Bayes' Theorem was even proposed, so we should expect it to have some errors. So far as I know, it was never even defined mathematically. I haven't thought of any non-obvious answers yet.

"I don't believe you. I don't believe most scientists would make such huge mistakes."

It took thirty years between the original publication of Maxwell's laws (1865) and Einstein's discovery of their inconsistency with classical mechanics (~1895). It took another ten years before he published (1905). In the meantime, so far as I know, nobody else realized the fundamental incompatibility of the two main theories of classical physics.

Well, the ideal simplicity prior you should use for Solomonoff computation, is the simplicity prior our own universe was drawn from.

Since we have no idea, at this present time, why the universe is simple to begin with, we have no idea what Solomonoff prior we should be using. We are left with reflective renormalization - learning about things like, "The human prior says that mental properties seem as simply as physical ones, and that math is complicated; but actually it seems better to use a prior that's simpler than the human-brain-as-interpreter, so that Maxwell's Equations come out simpler than Thor." We look for simple explanations of what kinds of "simplicity" our universe prefers; that's renormalization.

Does the underspecification of the Solomonoff prior bother me? Yes, but it simply manifests the problem of induction in another form - there is no evasion of this issue, anyone who thinks they're avoiding induction is simply hiding it somewhere else. And the good answer probably depends on answering the wrong question, "Why does anything exist in the first place?" or "Why is our universe simple rather than complicated?" Until then, as said, we're left with renormalization.

Silas, in this post I'm contrasting ideal but traditional Science - the idealized version of what Max Planck might have believed in, long before Solomonoff induction - with Bayes. (Also, I've never communicated with Dawkins.)

RI, be suspicious if you think you understand something most evolutionary biologists don't know about evolution. (I don't know about biologists who just sit around looking at cells all day.)

I'm not a physicist, I'm a programmer. If I tried to simulate the Many-Worlds Interpretation on a computer, I would rapidly run out of memory keeping track of all of the different possible worlds. How does the universe (or universe of universes) keep track of all of the many worlds without violating a law of conservation of some sort?

This comment is old, but I think it indicates a misunderstanding about quantum theory and the MWI so I deemed it worth replying to. I believe the confusion lies in what "World" means, and to whom. In my opinion Everrett's original "Relative-State Formalism" is a much better descriptor of the interpretation, but no matter.

The distinct worlds which are present after a quantum-conditional operation are only distinct worlds according to the perspective of an observer who has engaged in the superposition. To an external observer, the system is still in a single state, albeit a state which is a superposition of "classical" states. For example, consider Schrodinger's cat. What MWI suggests is that quantum superposition extends even to the macroscopic level of an entire cat. However, the evil scientist standing outside the box considers the cat to be in state (Dead + Alive) / sqrt(2), which is a single pure state of the Cat System. Now consider the wavefunction of the universe, which I suppose must exist if we take MWI to its logical end. The universe has many subsystems, each of which may be in superpositions of states according to external observers. But no matter how subsystems might divide into superpositions of states, the overall state of the universe is a single pure state.

In sum: for the universe to "keep track of worlds" requires no more work than for there to exist a wavefunction which describes to state of the universe.

And you can simulate the single worlds interpretation on a computer without running out of resources?

Infinity squared=Infinity, and if the universe is continuous, it can be said (in a mathematical sense), that it takes no more processing power to do one universe than multiples. Besides for the fact that you have to calculate all of the worlds anyway just to get a single world.

Tim Tyler: According to Hedweb, most "leading cosmologists and other quantum field theorists" thought that the "Many-Worlds Interpretation was correct 10 years ago.

Ah, but did they have to depart from the scientific method in order to believe it? The question isn't what scientists believe; scientists don't always follow the scientific method. The physicists who embrace MWI are acting rationally; the physicists who reject it are acting scientifically - that's the theme of this post.

Manon: I don't believe you.

Then you certainly understood me. This is another comment that makes me want to cheer, because it means you really got it.

This is the only explaination of QM I've been able to understand - I would have a hard time checking.

Go back and look at other explanations of QM and see if they make sense now. Check a textbook. Alternatively, check Feynman's QED. Find a physicist you trust, ask them if I got it wrong, if I did post a comment. Bear in mind that a lot of physicists do believe MWI.

I myself am mostly relying on the fact that neither Scott Aaronson nor Robin Hanson nor any of several thousand readers have said anything like "Wrong physics" or "Well, that's sort of right, but wrong in the details..."

(what is an amplitude exactly?)

It's always treated as a complex number with a real and imaginary part, though I prefer Feynman's calling it a "little arrow", since that makes it clear there's no preferred direction of the little arrows.

then the idea of a single world is preposterous, and I really need to work out the implications.

The most important implication is that the scientific method can break down. There are some minor ethical implications of many-worlds itself (e.g., average utilitarianism suddenly becomes a lot more appealing) but mostly, it all adds up to normality.

Maybe it's because I was hung-over during most of my undergrad math lectures, but one of the things I"m having trouble coming to terms with is the fact that imaginary (rather, complex)numbers turn out to be so real. I can deal with the idea of amplitude have two dimensions and rotating through them, and with amplitudes canceling each other out because of this, but it's not clear to me, if there is "no preferred direction" for amplitudes, why the square root of minus one is involved.

Are there other mathematical formulations possible? Or a good source for this that could re-align my intuitions with reality?

I can deal with the idea of amplitude have two dimensions and rotating through them, and with amplitudes canceling each other out because of this, but it's not clear to me, if there is "no preferred direction" for amplitudes, why the square root of minus one is involved. Are there other mathematical formulations possible?

Matrices of the form ((a, -b), (b, a))---that is, compositions of a scaling and a rotation in the plane---are isomorphic to complex numbers, which makes sense because when we multiply complex numbers in polar form, we multiply their magnitudes and add their arguments.

I also think you are taking the MWI vs. Copenhagen too literally. The reason why they are called interpretations is that they don't literally say anything about the actual underlying wave function. Perhaps, as Goofus in your earlier posts, some physicists have gotten confused and started to think of the interpretations as reality. But the idea that the wave function "collapses" only makes sense as a metaphor to help us understand its behavior. That is all that a theory that makes no predictions can be -- a metaphor.

MWI and Copenhagen are different perspectives on the same process. Copenhagen looks at the past behavior of the wave function from the present, and in such cases the wave function behaves AS IF it had previously collapsed. MWI looks at the future behavior of the wave function, where it behaves AS IF it is going to branch. If you look at it that way, the simplest explanation depends on what you are describing: if you are trying to talk about YOUR past history in the wave function, you have no choice but to add in information about each individual branch that was taken from t_0 to t, but if you are talking about the future in general, it is simplest to just include ALL the possible branches.

Eliezer_Yudkowsky: You discuss whether training in the art of Bayes would produce scientists who don't make these errors. What do you make of (as per Robin_Hanson's account) how in the movie Expelled, Richard_Dawkins places a >1% probability on earth life having been designed? Is this an instance of a major not "getting" Bayesian inference, since he doesn't also advocate diverting research funds to that idea?

(Incidentally, when I corrected, here, Richard_Dawkins's definition of a "good theory" on edge.org, his entry there was shortly thereafter changed. If you passed on my correction to him, I would be interested in knowing why you didn't tell him it was me.)

chuckles... I wrote a whole bunch about string theory, but I've decided to simply mention it. I have a TON of mathematical notation to learn before I can subject that glittery...whatever...to analysis.

As for many worlds... I like the way many of the ""paradoxes" of quantum mechanics don't even LOOK like paradoxes in many worlds. starting with-you don't need to specify a special exemption to the no-ftl rule. "information" for "collapse" happens because the little pieces of the waves almost-touch and slip past each other when you perform the comparison operation...at least, that's how I visualize it.

This post is beating a strawman. Beating a strawman is bad.

"The latter, since there are no Garden of Eden patterns in physics."

Thank you for your excellent job of communicating (and the GoE link decreased possible ambiguities, too).

How do we know that there are no Garden of Eden patterns? That is a very interesting claim. In attempting to reverse-engineer it, I remembered that according to quantum theory, each wavefunction is nowhere zero. Thus, any collection of particles could tunnel into place over any distance in any organization you could possibly specify. Is that the key to the proof?

At any rate, I'm "sticking to my guns" about many-worlds not affecting the desirability of average utilitarianism. The sum over all direct results of my actions over all worlds is still overwhelmingly determined by already determined macroscopic causes not known to me, NOT by as-yet undetermined quantum decoherences splitting worlds; my probability computations are dominated by unknowns, not by unknowables.

I'm not arguing that average utilitarianism is wrong; I'm just saying that MW doesn't seem to appreciably affect its desirability.

Let me pull the money quote from the article:

"The tradition handed down through the generations says that a new physics theory comes up with new experimental predictions that distinguish it from the old theory."

This is superficially correct, but I think it's irrelevant. Quantum theory is already a theory with well-established laws. None of the contending interpretations of those laws -- many-worlds, collapse, hidden-variables, and so on -- are theories, and none of them propose new laws (suggesting that there might be a law we don't know doesn't count). They're all attempts at models, and they all suck. Models should have explanatory power; none of these add any explanatory power.

The real reason some people don't care about Many Worlds isn't that they're irrationally wedded to Copenhagen (although some people are). It's that both Copenhagen and MW suck so badly that the only way to stick to one is to be irrationally wedded to it. Back when all we had was Lorentz' equations there were tons of possible ways to explain them; as soon as Einstein proposed a fruitful model all of the other explanations vanished (well, as soon as the fruitfulness became obvious).

I feel that I'm equivocating, though. I used the term 'fruitful', which hides the meaning "producing experimental results". I suppose that makes me a devotee of Scientism as opposed to Bayesianism. I have much reading to do on this site, and I'm thrilled to have the opportunity. Thanks for interacting with us.

I am interested in the answer to John Maxwell's question as well.

In that vein, let me re-ask a question I had in a previous post but was not answered:

How does MWI not violate no-faster-than-light-travel itself?

That is, if a decoherence happens with a particle/amplitude, requiring at that point a split universe in order to process everything so both possibilities actually happen, how do all particles across the entire universe know that at that point they must duplicate/superposition/whatever, in order to maintain the entegrity of two worlds where both posibilities happen?

This dilemma feels forced. I see where you're coming from, and I do feel that a waveform disappearing spontaneously is a massive, unwarranted detail, but I don't see how this sets up a contradiction.

The further a scientific prediction feels from our intuitive human experience, the harder it is to internalise. Physicists wanted an explanation for why we only see one world. They postulated that the waveform collapses into the world we see. And fair enough, it's not difficult, on the face of it, to feel that that must be true, even if it isn't. But how is that any different from saying the Sun goes round the Earth, because that's what we 'see'? The former is no more 'science' than the latter - it's just wearing a flashier lab coat. Learnt that reading this blog.

Eliezer, you've spent so much time showing us that only experiment is admissible in science. Well then collapse is not science as you would define the term, right? Sure, you can demonstrate that our single world is there. But if our (consistently verified) theory predicts extra worlds as well, saying 'they must disappear, since we only see one' is adding a Cosmological Constant (Quantum Constant?). Collapse now sets the 'Anthropocentrism, Not Science!' warning light off in my head, for this reason. Hence I don't feel your dilemma.

Am I getting this wrong somewhere?

P.S. Dave - dangerous attitude. It's impossible to know whether or not your theory will or won't make a prediction at some point. Better to work out what's correct and bear it in mind as you go than consign it to the dustbin of irrelevance if it doesnt prove itself right away.

Um... there really aren't any extremely strong arguments for majoritarianism. That position confuses conclusions with evidence.

Just as there really aren't any good reasons to abandon the scientific methodology just because you've declared 'Bayesianism' to diverge from it. Given that the scientific methodology has been extremely successful and is extraordinarily widely adopted among people who count, if we accept your contention that Bayesian thinking diverges from its requirements, shouldn't that cause us to be suspicious of Bayesianism?

But when I say "macroscopic decoherence is simpler than collapse" it is actually strict simplicity; you could write the two hypotheses out as computer programs and count the lines of code.
Computer programs in which language? The kolmogorov complexity of a given string depends on the choice of description language (or programming language, or UTM) used. I'm not familiar with MML, but considering that it's apparently strongly related to kolmogorov complexity, I'd expect its simplicity ratings to be similarly dependent on parameters for which there is no obvious optimal choice.

If one uses these metrics to judge the simplicity of hypotheses, any probability judgements based on them will ultimately depend strongly on this parameter choice. Given that, what's the best way to choose these parameters? The only two obvious ways I see are to either 1) Make an intuitive judgement, which means the resulting complexity ratings might not turn out any more reliable than if you intuitively judged the simplicity of each individual hypothesis, or 2) Figure out which of the resulting choices can be implemented cheaper in this universe; i.e. try to build the smallest/least-energy-using computer for each reasonably-seeming language, and see which one turns out cheapest. Since resource use at runtime doesn't matter for kolmogorov complexity, it would probably be appropriate to consider how well the designs would work if scaled up to include immense amounts of working memory, even if they're never actually built at that scale.

Neither of those is particularly elegant. I think 2) might work out, but unfortunately is quite sensitive to parameter choice, itself.

It isn't really that hard to wriggle this question. Why do I have to choose Science or Bayes, can't I just choose not to have an opinion until I am more capable of making a decision? It would seem suicidal from the perspective of bias to choose a side, especially when the stakes are currently so low. Question wriggled. I don't have to choose between Science and Bayes, I can use them both when they are useful, and simply not hold an opinion in the area where they are in some form of conflict.

IMHO, Fredkin picked cellular automata for good reason. Regularity helps explain how light travels in straight lines across long distances. There /are/ asynchronous CAs, but asynchrony is mostly an unneeded complication in this context - synchronous CAs are hard enough to work with, thank you. CAs can be universal, so they can do anything any other discrete model can. CAs are low-level modelling tools, that are not easy to build things with - but it seems extremely likely that low-level modelling tools will ultimately be needed to explain physics.

Something just clicked for me. I mean, regarding the subject of the original post. There is a true dilemma, and in that dilemma, the choices of a pure Bayesian will look crazy to a Scientist, and vice versa.

The hard difference between Science and Bayes is that Bayes does not require a model; Science does. Bayes simply predicts probabilities; Science attempts to establish a model that explains the probabilities.

Thus, a Bayesian won't care about the quality of the model he's given, EXCEPT that it must not be complex (a nonexistent model will work just fine).

MW (like all the others I've seen) is a lousy model, so science is not satisfied with it; but to a Bayesian, the quality of the model is irrelevant, so a Bayesian can accept the model or ignore it and not even ask for something better.

I'm definitely sounding like I disapprove of this pure Bayesian thinking. I'm starting to see that science plus bayes is more complex than bayes alone (which is a win for pure Bayesian thought), but I'm still not sure that not being able to make models is a good tradeoff for pure simplicity.

This is a stupid analogy, but:

Suppose we have a software package, UnitaryQM, of predefined functions. There is a competition, the Kolmogorov Challenge, in which you have to implement a new function, Born(). There are two development teams, Collapse and MWI. Collapse does the job by handcoding a new primitive function, collapse(), and adding it to the library. The MWI team really wants to use just the existing functions, but MWI 1.0 actally gives the wrong answers. The current hope for MWI 2.0 is a function called mangle(), but mangle only exists as pseudocode. The MWI team know how they want it to behave in certain limits, but to completely specify it requires an arbitrary parameter, objectiveDecoherenceThreshold.

Now interestingly, there have been two generations of Collapse as well. In Collapse 1.0, collapse has to be called directly by the user, from a command line. In Collapse 2.0, collapse can be called from within another function; but of course, now you can't rely on the user to determine when it happens. So instead there is an adjustable parameter, objectiveCollapseFrequency.

The Collapse 2.0 team are at peace with the fact that their implementation of Born requires a free parameter, and they have consequently submitted some actual code to the Kolmogorov Challenge. The MWI 2.0 team are not. As a result, they haven't submitted any code, just pseudocode. Obviously Collapse 2.0 wins by default.

That's a rather good explanation of the issue at hand.

Give me a single example of a successful use of Bayesianism that is not predicated on its being an explanation of the success of the scientific method and maybe then I'll consider choosing Bayes over science.

Various people:

The reference machine is chosen to be simple, usually by limiting its state x symbol complexity. That's not perfect and various people have tried to come up with something better but as yet none of these efforts have succeeded. In terms of prediction it's not a problem as Solomonoff's predictor converges so amazingly fast - faster than 1/n where n is the number of bits of input data (this isn't quite true and Li and Vitanyi don't quite get it right either, see Hutter: On universal prediction and Bayesian confirmation. Theoretical Computer Science, 384, 33-48, 2007 for the gory details). Anyway, the convergence is so fast that the compiler constant for a simple UTM (and we know they can be just a few hundred bits) quickly becomes irrelevant.

In terms of determining the generating semi-measure ("true hypothesis") things are a bit more difficult. If two hypotheses assign the same probability to the observed data (same likelihood value) then the data will not cause the relative probability of these in the posterior to change, they will simply be scaled by the evidence factor. Of course this is no problem for prediction as they agree, but it does mean that Solomonoff induction is somewhat crude in deciding between different "interpretations". In other words, if the data can't help you decide then all you have left is the prior. The best we can do is to tie down the reference machine complexity.

In any case I think these things are a bit of a side issue. In my view, for anybody who doesn't have a "we humans are special" bias, MWI is simpler in terms of description complexity because we don't need to add a bunch of special cases and exceptions. Common sense be damned!

Specifying a language with all the data already specified as one of the symbols doesn't help, because with the MML standard, you'd have to include that, AND the data you're explaining, which makes it longer than any theory that can find regularity.

But you still need to pick a language to express (language+data) in. Infinite regress.

"If the exact physical state is underdetermined by the problem description, then there will be separate branches of the wavefunction for each possible state, although they might have diverged arbitrarily long ago. So, yes."

Are you seriously proposing that my use of ambiguous language splits the universe? This is unbelievable. I understand how incoherency would split the universe, but how can ambiguous language do that? How about false information -- if my bank tells me that my paycheck came in, is there an alternate world where my paycheck in fact DIDN'T come in?

I just don't buy this. I think I get the quantum MW model; it makes a certain kind of sense. What I don't get is how it enables you to claim that there are any number of worlds that you want! I think you can only claim a quantum split where there is actually decoherence, and that the splits will contain only events which had a nonzero "quantum probability" in that decoherence.

There may be a world in which my paycheck didn't actually come in to my bank -- but the explanation for that lack is NOT "because I just imagined it", or "because it's the negation of something that did happen"; rather, it's because of some specific quantum decoherence which could eventually result EITHER in my paycheck arriving or NOT arriving.

What am I missing?

Sebastian_Hagen: Specifying a language with all the data already specified as one of the symbols doesn't help, because with the MML standard, you'd have to include that, AND the data you're explaining, which makes it longer than any theory that can find regularity.

William_Tanksley: The fact that K-complexity isn't computable doesn't matter for determining which scientific theory is superior; you only need to know the maximum K-complexity across all known algorithms. Then, if our theories are equally good at predicting, but your max. K-complexity is longer, we don't throw up our arms and say, "hey, I guess I can't prove mine is better"; rather, we see that with the current state of knowledge mine is best. If at a later point you discover an algorithm that can generate your data and theory with less code, THEN yours becomes better -- but to do that, you had to find a regularity we didn't see before! which itself advances our knowledge!

"That's Occam's razor, not Science. The scientific method >is taken to suggest< that an untestable theory is of no use."

Watch that passive voice -- unless you're going to actually claim that the scientific method suggests that, I don't care what someone somewhere took it to suggest.

The scientific method doesn't suggest anything. It's a method, not a philosophy. As a method, it gives you steps to follow. A hypothesis is untestable; a theory's been tested. A model integrates theories. MW is a model.

"What's more, Occam's razor isn't some unmutable natural law: it's just a probability - the simplest explanation is >usually< the right one, and so why not start there and move up the ladder of complexity as required: that way, you can cover the most likely (all other aspects being equal) explanations with the minimum amount of work."

Occam's razor is part of science, not to be distinguished from the rest. Without it, there's absolutely no way to distinguish experimental results from lab noise -- without it the "best explanation" for an unexpected but reproduced experimental result might be "sorry, I must have messed something up, and the guy attempting to reproduce my results must have messed the same thing up in the same way to get the same result."

You're right that it has to be applied as a rule of thumb, but it's also fundamental to science as a reductionist pursuit.

Re: "a serial machine can emulate a parallel one, thus this distinction isn't relevant."

Kolmogorov complexity/Solomonoff induction are language-specific. Not all languages are equivalent, and descriptions in different languages may be totally different lengths. It is true that any universal machine can simulate any other - but it takes a description of that simulator to do so, and that takes up space, which is a big deal, if the simulation is not tiny.

Re: They only depend to within a constant factor. That's not the problem [...]

That /is/ a problem, when the "constant factor" is of the same order of magnitude as the things you are measuring. How complex it PI? "Print PI;" is not very complex, but its complexity grows if you have to implement a whole interpreter first.

The issue of what language to use /is/ a real issue. IMO, the case for using Turing machines is poor, because they are crappy one-dimensional serial computers, which were never intended for actual use.

My position is that we ought to use real small machines to measure complexity if we are doing practical things, such as judging scientific laws. But this is a moving target - and it means that we don't know how to measure complexity properly yet, because we cannot yet construct molecular computers.

...but even in our current state of ignorance, we can do better than use a Turing machine. Almost anything is better than using a Turing machine.

Re: "I don't believe most scientists would make such huge mistakes" - the CI really is pretty stupid, retrospectively, IMHO.

William_Tanksley et al: Correct me if I'm wrong, but I had immediately assumed that the framing "science or Bayes" means "the scientific world as it exists today, or Bayes", not "ideal scientific research vs. Bayes". Eliezer_Yudkowsky presumably equates ideal scientific research with following Bayes.

"I disagree; I think the underspecification is a more serious issue than the uncomputability. There are constant factors that outweigh, by a massive margin, all evidence ever collected by our species."

Agreed. The constant factors really are a problem. If one has taken a few information theory courses, it's easy to disregard it as one usually uses Kolmogorov on e.g. symbol sequences in the infinite limit. When comparing two theories though, they have finite size and thus constants does matter. It is probably possible to find two Turing machines such that two competing models have equal length on their respective best machines even if they differ greatly when tested on one of them.

It may be possible to construct an argument that favors an interpreter over all others, Sebastian Hagen gave a few ideas above, but it is highly non-trivial.

"The most important implication is that the scientific method can break down."

I don't understand how this is a consequence of MW. We've always known that the scientific community can and does break down. The scientific method breaks down even theoretically (if you use K-complexity to assess it). And I'm not even sure that the MWI situation is a breakdown... It seems there are more than two interpretations (it's not just collapse versus many-worlds).

"There are some minor ethical implications of many-worlds itself (e.g., average utilitarianism suddenly becomes a lot more appealing) but mostly, it all adds up to normality."

Question: Does every event with two possible/plausible outcomes result in two distinct worlds? I don't think that's the case -- it seems that multiple plausible outcomes also result from an ambiguous problem description (even if the situation is actually completely deterministic). It seems that the primary source of multiple outcomes in ethics is not the same as the source of multiple worlds in quantum theory -- therefore you can't sum across the multiple worlds of quantum theory to get an ethical probability of 1.

-Wm

"Um... there really aren't any extremely strong arguments for majoritarianism. That position confuses conclusions with evidence."

What's more, it implies that human beliefs are normally distributed. I posit they are not, with extra weight being given to concepts that are exciting/emotional or arousing. We have a built in bias in the direction of things that are evolutionarily important (ie - babies, scarey stuff).


"I'm trying to comprehend how this is a dilemma... Science supposedly teaches that for any two theories that explain the same data, the simplest one is correct. Bayes can't talk about explaining data without invoking the science that collected the data... Can he?"

That's Occam's razor, not Science. The scientific method >is taken to suggest< that an untestable theory is of no use. This isn't the case, since every theory starts out untestable, until someone devises a test for it. What's more, Occam's razor isn't some unmutable natural law: it's just a probability - the simplest explanation is >usually< the right one, and so why not start there and move up the ladder of complexity as required: that way, you can cover the most likely (all other aspects being equal) explanations with the minimum amount of work.

I call false dichotomy on this Bayes vs Science lark. It's perfectly reasonable to work with untestable theories, even ones that remain implicitly untestable, and even ones that go against observed phenomenon, as long as one recognizes that, somewhere, there is hole in the grand equation. "Spooky action at a distance", anyone?

Re: "Tim, I thought there was only one "shut up and calculate" interpretation, and that's the one where you shut up and calculate - rather than talking about many worlds. Perhaps you mean it's a "talk rather than calculate" interpretation?".

No, I mean those interpretations are functionally equivalent - in that they make the same predictions. That is not true of CI, or other collapse theories - e.g. see: http://www.hedweb.com/everett/everett.htm#detect

"Computer programs in which language? The kolmogorov complexity of a given string depends on the choice of description language (or programming language, or UTM) used."

They only depend to within a constant factor. That's not the problem; the REAL problem is that K-complexity is uncomputable, meaning that you cannot in any way prove that the program you're proposing is, or is NOT, the shortest possible program to express the law.

Well you can obviously prove that it isn't the shortest program by stating a another, shorter program, but I suppose you mean that there is no shortcut to this shorter one.

I'm trying to comprehend how this is a dilemma... Science supposedly teaches that for any two theories that explain the same data, the simplest one is correct. Bayes can't talk about explaining data without invoking the science that collected the data... Can he?

It would seem that the theory of science includes Bayesian theory.

On the other hand, the practice of science requires either exhibiting evidence for theories or testing falsifiable theories. Many Worlds can trivially be falsified by actually finding a collapse, while its main distinguishing feature cannot be directly demonstrated. Thus, science focuses on searching for a collapse.

So... I still don't see the contradiction.

I also have to speak up in favor of metaphysics -- one poster claimed he'd take Science over Metaphysics anytime. Does he realize that that statement is itself metaphysical? Science cannot determine whether Science has priority over other things, and metaphysics by definition has priority over physics.

I wanted to present you with a nice, sharp dilemma between rejecting the scientific method, or embracing insanity. Why?

Rational agents should WIN. Not lose scientifically, or socially acceptably, WIN. :-)

I hope you talk about normative implications eventually, address bambi's point, so we know just why this mistake matters. (Well, actually, implications of multiverse theories generally, so MWI doesn't practically matter if we live in a multiverse for some other reason.)

The scientific method has trounced logical argument time and time again.

Humans need empiricism as a check because we're, in absolute terms, pretty bad reasoners. Eliezer's "Science" (which is a bit of a strawman, but excusable) goes too far in the right direction from overconfident pure rationalism. (I believe this is the point of the Aumann example, maybe even of the whole post.) This should diminish confidence in pure logical argument, even where experiment is silent, but the case for MWI still looks strong to this non-physicist.

Computer programs in which language? The kolmogorov complexity of a given string depends on the choice of description language (or programming language, or UTM) used.

This confuses me as well.

Re: "Collapse theories can do something many worlds can't do: they can make the predictions".

Uh, the MWI is a "shut-up-and-calculate" interpretation. It mostly makes the same predictions as the other QP interpretations - except when it comes to interference patterns involving interfering observers and the like.

This is an old article, and it's possible that this question has already been asked, but I've been looking through the comments and I can't find it anywhere. So, here it is:

Why does it matter? If many-worlds is indistinguishable from the Copenhagen Interpretation by any experiment we can think of to do, how does it matter which model we use? If we ever find ourselves in a scenario where it actually does matter which one we use -- one where using the wrong model will result in us making some kind of mistake -- then we now have an experiment we can do to determine which model is correct. If we never find ourselves in such a position, it doesn't matter which model we decided on.

When phrased this way, Science doesn't seem to have such a serious problem. Saying "Traditional Science can lead to incorrect conclusions, but only about things that have no actual effect on the world" doesn't sound like such a searing criticism.

Why does it matter?

Good question -- it does not matter. Opinions on untestable questions are about taste, and arguing about taste is a waste of everyone's time. The "LW consensus" is just wrong to insist on Everett (and about lots of other things, so it should not be too surprising -- for example they insist on Bayes, and like EDT).

like EDT

I know there are lots of people here who argue for EDT or various augmentations of EDT, but I hope that doesn't count as a LW consensus.

Obviously LW opinion isn't monolithic, I merely meant that UDT et al seems to be based on EDT, and lots of folks around here are poking around with UDT. I gave a talk recently at Oxford about why I think basing things on EDT is a bad idea.

I want to watch your talk but videos are slow and the sound quality didn't seem very good. So I'll just point out that the point of UDT is to improve upon both EDT and CDT, and it's wildly mischaracterising LW consensus to say that the interest in UDT suggests that people think EDT is good. They don't even have much in common, technically. (Besides, even I don't think EDT is good, and as far as I know I'm the only person who's really bothered arguing for it.)

No, there are other folks who argue for EDT (I think Paul did). To be fair, I have a standing invitation for any proponent of EDT to sit me down and explain a steelman of EDT to me. This is not meant to trap people but to make progress, and maybe teach me something. The worry is that EDT fans actually haven't quite realized just how tricky a problem confounding is (and this is a fairly "basic" problem that occurs long before we have to worry about Omega and his kin -- gotta walk before you fly).

I would be willing to try to explain such to you, but as you know, I was unsuccessful last time :)

I think you have some un-useful preconception about the capabilities of EDT based on the fact that it doesn't have "causal" in the name, or causal analysis anywhere directly in the math. Are you familiar with the artificial intelligence model AIXI?

AIXI is capable of causal analysis in much the same way that EDT is. Because although neither of them explicitly include the math of causal analysis, since such math is computable, there are some programs in AIXI's hypothesis space that do causal analysis. Given some certain amount of data we can expect AIXI to start zooming in on those models and use them for prediction, effectively "learning about causality".

If we wrote a hypothetical artificially intelligent EDT agent, it could certainly take a similar approach, given a large enough prior space—including, perhaps, all programs, some of which do causal analysis. Of course, in practice we don't have an infinite amount of time to wait for our math to evaluate every possible program.

It's slightly more practical to simply furnish your EDT calculation (when trying to calculate such things as your HAART example by hand) with a prior that contains all the standard "causal-ish" conclusions, such as "if there is a data set showing an intervention of type X against subject of type Y results in effect Z, a similar intervention against a similar object probably results in a similar effect". But even that is extremely impractical, since we are forced to work at the meta-level, with hypothesis spaces including all possible data sets, (current) interventions, subjects and effects.

In real life we don't really do the above things, we do something much more reasonable, but I hope the above breaks your preconception.