Eliezer, as you say, you have written hundreds of blog posts. For each blog post, what is, on average, the chance you are wrong about your basic point? If it is even as much as .5%, then you are probably wrong about your basic point in at least one post.

You are overconfident if you claim an accuracy of greater than 99.5%, and you claim that this estimate is calibrated.

You are also overconfident if you do not claim this accuracy, but also do not allow that you are probably wrong in at least one of your basic points.

People (including me) get the impression that you hold to one or the other of these positions, and that is why it seems that you are overconfident.

Another great post. Eliezer I really don't trust you 100% but I try to read and understand everything you write with great interest. I agree with you in that a lot of the negative commenters here seem to underestimate the mental work you have put into all this.

"The balance of arguments is overwhelmingly tipped; and physicists who deny it, are making specific errors of probability theory (which I have specifically laid out, and shown to you)"

I guess this refers to the error of supposing that Occam's Razor literally means "have as few entities as possible", rather than "have a theory as simple as possible", and opposing Many Worlds for that reason. Which is indeed an error.

But perhaps for the last time, I will try to enumerate those problems with your position that I can remember.

1. There is no relativistic formulation of Many Worlds; you just trust that there is.

2. There is no derivation of the Born probabilities, which contain all the predictive content of quantum mechanics.

3. Robin Hanson has a proposal to derive the probabilities, but for now it rests on making vagueness about the concept of observers and worlds into a virtue.

You've given zero public consideration to other possibilities such as temporally bidirectional causation and nonsubjective collapse theories. You've also ignored Bohmian mechanics, a classically objective theory which does make all the predictions of quantum theory. You also haven't said anything about the one version of Many Worlds which does produce predictions - the version Gell-Mann favors, "consistent histories" - which has a distinctly different flavor to the "waves in configuration space" version.

In view of all that, how can you possibly say that Many Worlds is rationally favored, or that you have made a compelling case for this?

I'll repeat my earlier recommendation:

"What you should say as a neo-rationalist is that ... people should not be content with an incomplete description of the world, and that something like Minimum Description Length should be used to select between possible complete theories when there is nothing better, and you should leave it at that."

I wrote a little essay at Nick Tarleton's forum, here, about these problems. I will at some point link from there to my various comments posted here, so it's all in the one place. And I suppose eventually I'll have to write my own views out at length (not just my anti-MWI views). My main unexpressed view is that string theory is probably the answer, and that attempts to make ontological sense of physics will have to grapple with its details, and so all these other 'interpretations' are merely preliminary ideas that may at best be helpful in the real struggle.

In fact, I feel the need to write a bit more.

This blog is the best on the internet and I have never read the principles of rationality explained so effectively. I have the impression(please correct me if I'm wrong) that some people here are a bit envious of Eliezer. Why? Because he didn't go through traditional academia and nevertheless is doing a great job. I guess that for many who spent(or wasted) years in order to get a traditional academic diploma it must be very annoying to see someone overtake them on an intellectual level without having to jump through all the academia hoops.

Furthermore, I really think Eliezer should get all support he needs because he is doing an important job(maybe the most important of all) in trying to solve the FGAI problem. And I guess that must be a tremendous burden for him, both intellectually and emotionally. I know, there are others working on it who also deserve credit.

When Eliezer makes a mistake, point it out, but try to be polite.

I think that maybe and only maybe, Eliezer could be the man to shape the future of the universe, at least one who will make a SIGNIFICANT contribution. So in writing positive comments I'm trying to be supportive (when I'm better off financially I will also consider donating money). And those trying to bring him down are doing us all a disservice.

I know, I know, this comment of mine is 80% emotional and only 20% rational(oops, bias detected). Corrections and criticisms are welcome!

PS: Eliezer, don't get a big head, ok? ;)

I knew Eliezer wouldn't spend so much effort shifting my priors without a good reason :)

Mitchell Porter: "There is no relativistic formulation of Many Worlds; you just trust that there is...You also haven't said anything about the one version of Many Worlds which does produce predictions - the version Gell-Mann favors, "consistent histories" - which has a distinctly different flavor to the "waves in configuration space" version."

I think you are mistaken. It seems to me that consistent histories is basically just many worlds from a different point of view. Basically, both are standard QM with no collapse. In consistent histories you look at things from the point of view of path integrals instead of a wave equation. These are just two equivalent mathematical formalisms. Path integrals adapt more easily to the relativistic case, but it doesn't seem to me that the interpretational issues are any different. Secondly, I'm not sure what you mean that consistent histories "produces predictions." I'm pretty sure that consistent histories does not make any quantitative prediction that differs from standard quantum mechanics and quantum field theory.

Eli: It seems like it would be much better to use the original name "relative state" rather than "many worlds". The word "many" suggests that they can be counted. However, in standard QM we are usually talking about particles whizzing around in the continuum, which gives us an infinite-dimensional Hilbert space. If we restrict ourselves to Hilbert spaces of finite dimension, for example the states of some spins, then naively counting worlds remains bogus, because the number of "worlds" (i.e. entries of the state vector) with nonzero amplitude depends entirely on choice of basis. I suppose in a finite dimensional Hilbert space we could make a sensible definition of world counting as follows: the answer to how many worlds am I in is the rank of my reduced density matrix. However, this seems far removed from the main point of the "MWI". Furthermore, it appears that the term many worlds does actually lead people astray in practice. In the posts many people keep referring to counting the worlds in which something happens in order to assess probability. This is wrong. The probabilities arise from squaring amplitudes, not from counting. If the probabilities arose from counting then in a finite dimensional Hilbert space, all the probabilities would be rational numbers. Standard QM does not have this property.

Stephen: consistent histories works by having a set of disjoint, coarse-grained histories - "coarse-grained" meaning that they are underspecified by classical standards - which then obtain a-priori probabilities through the use of a "decoherence functional" (which is where stuff like the Hamiltonian, that actually defines the theory, enters). You then get the transition probabilities of ordinary quantum mechanics by conditioning on those global probabilities of whole histories.

Some people have a neo-Copenhagenist attitude towards consistent histories - i.e., it's just a formalism - but if you take it seriously as a depiction of an actually existing ensemble of worlds, it's quite different from the more Parmenidean vision offered here, in which reality is a standing wave in configuration space, and "worlds" (and, therefore, observers) are just fuzzily defined substructures of that standing wave. The worlds in a realist consistent-histories interpretation would be sharply defined and noninteracting.

There is certainly a relation between the two possible versions of Many Worlds, in that you can construct a decoherence functional out of a wavefunction of the universe, and derive the probabilities of the coarse-grained histories from it. In effect, each history correponds to a chunk of configuration space, and the total probability of that history comes from the amplitudes occupying that chunk. (The histories do not need to cover all of configuration space; they only need to be disjoint.) ... I really need some terminology here. I'm going to call one type Parmenidean, and the other type Lewisian, after David Lewis, the philosopher who talked about causally disjoint multiple worlds. So: you can get a Lewisian theory of many worlds from a Parmenidean theory by breaking off chunks of the Parmenidean "block multiverse" and saying that those are the worlds. I can imagine a debate between a Parmenidean and a Lewisian, in which a Parmenidean would claim that their approach is superior because they regard all the possible Lewisian decompositions as equally partially real, whereas the Lewisian might argue that their approach is superior because there's no futzing around about what a "world" is - the worlds are clearly (albeit arbitrarily) defined.

But the really significant thing is that you can get the numerical quantum predictions from the "Lewisian" approach, but you can't get it from the Parmenidean. Robin Hanson's mangled worlds formula gets results by starting down the road towards a Lewisian specification of exactly what the worlds are, but he gets the right count in a certain limit without having to exactly specify when one world becomes two (or many). Anyway, the point is not that consistent histories makes different predictions, but that it makes predictions at all.

Eliezer - a suggestion. I'd really welcome a posting that acts a table of contents to the series: An overview of your argument, laying out the basic narrative with links to each of the posts in the best reading order, somethnig that gives shape to the series.

The great thing about a blog format is the way it develops over time. The bad thing about it is that it's a terrible archive... reverse order, etc etc. I'd like to be able to tell someone 'read Eliezer's series on Quantum Physics... here's a link to the overview page...

What Roland said (soppy third comment).

This blog has changed my thinking more than any book I can remember reading. I can only begin to imagine how frustrating it must be to have to start a series from scratch. But this is now a serious body of work, some excellent foundations. I'm not fond of the air of finality in this post, though. Keep it coming!

Shane, I'm planning to read QED to my firstborn at bedtime, will post some results somewhere.

Botogol - Eliezer seems to be quite busy. Fire up Dreamweaver and get to it! Then link us to it.

I have also found Eliezer's series of posts worthwhile, and would like to thank him for writing them. They have improved my thinking on certain topics. I also do not object to his writing on quantum mechanics. First, I don't believe he has been wrong about any major point, and that fact trumps any considerations of his qualifications. Second, to a large extent his QM posts are about thought processes by which one can reach certain conclusions about quantum mechanics. Such cognitive science stuff is squarely within Eliezer's claimed area of expertise. The conclusions themselves are fairly mainstream. (As far as I can tell, among the physicists who have bothered to think about it, very few these days would claim that measurements are somehow special processes that collapse wavefunctions, in contrast to ordinary processes that do not. Whether they describe their beliefs using the term "many worlds" is another matter.)

I want to second botogol's request for a wrapped up version of the quantum mechanics series. Best of all would be a downloadable PDF.

I read a little of Eliezer's physics posts at the beginning, then realised I wasn't up to it intellectually. However, I'd like to come back and have another go sometime. I certainly think I stand a better chance with Eliezer's introduction than with a standard textbook.

I third botogol's comment. I've tried to direct people to the QM series (as well as other ones, such as the one on words), and it can be difficult. "Here, start at this post, and then use the links at the top to go forward, but you'll have to skip some of them because they're by a different author, so you can recognize them by looking for the "Followup to" or "Previously in Series" links at the top..."

It'd be a lot easier to just give them one link to a table of contents.

You seem to be saying that if we have been persuaded by your arguments to share your opinions on many worlds and on identify, we should take your word for new contrarian claims you make even if you do not present similarly detailed arguments for those claims. But what if we expect adverse selection here? That is, what if we expect you to have taken the most trouble to give explicit arguments for the contrarian claims you hold for which you have the strongest explicit arguments to give?

The contents of these blog posts may never make it into a paper book, but I'd love to someday be able to download a .pdf (or other format file) of them so that I could carry them around on an ebook reader, for when I need to explain to someone something that was explained well here.

Unknown: I think that you are using against Eliezer a basic heuristics and biases fallacy that he used, repeatedly and frustratingly, against me back before he learned, from Robin, that knowing about biases can hurt you as a rationalist http://lesswrong.com/lw/he/knowing_about_biases_can_hurt_people/. Every proposition can be converted into an arbitrarily long conjunction. That fact plus the fact that certain people participating in some psychology experiments failed to meaningfully give certainties much greater than 85% does NOT justify your converting any statement that you disagree with, or by anyone you wish to take status from, into an arbitrarily long conjunction as a valid method of lowering its probability to arbitrarily close to zero. This habit is a form of intellectual suicide that closes you off to conflicting opinions or information.

BTW, In actual fact, people make true mathematical proofs with thousands or tens of thousands of steps. Outside of math, and even in math, it is best to independently ground each conclusion with multiple parallel evidential pathways, but doing so is not strictly necessary if one is sufficiently careful.

Robin: Obviously we should assign him the Bayesian level of trust in the future, taking into account this post and also your point. To me, that seems high enough to assign non-negligible, though still low, probabilities from the get-go to any claims he makes that wouldn't, without his endorsement, seem impossible in the "or the universe is a lie" sense, and even on claims which do so long as this seeming is accompanied by a substantial amount of noticed confusion.

Michael Vassar: I have not converted any particular proposition into an arbitrary conjunction. Eliezer has on this blog made many, many distinct claims, many of them controversial and having little to do with mathematics and other areas where one can reach an extreme degree of certainty. This is a fact about this blog; it is not a question of me converting something into a conjunction.

Additionally, I was not raising an objection (at this time) to any particular statement, whether a conjunction or otherwise. The point was that it is unlikely that Eliezer would be correct in every case, i.e. distinct cases. In fact we have a clear example of this (a substantial error) in the article on evolution's speed limit and complexity bound.

One more point: I've learned a lot from this blog, and Eliezer has even got me to change my mind about some things. So the fact that I won't put infinite confidence in his statements does not mean that I "close myself off" from conflicting information.

Unknown: The relevant propositions are "Many Worlds is correct" and "this would be obvious except for historical contingency and ignorance among scientists of the proper application of probability theory". These propositions are carefully argued for. If you deduct subjective probability for people breaking their propositions down into careful arguments you will get wrong answers more often. Furthermore, Bayesian probability theory doesn't say to do it, just a naive misreading of Heuristics and Biases. I certainly don't expect Eliezer to be right in every case, and have argued against specific claims of his including the one you mention, that of evolution's speed limit. I'm glad you have learned things, I wasn't claiming that you did in fact cut yourself off from all new info, simply that you were currently using rhetorical tools that were sufficient to cut yourself off from any new piece of information you chose to.

Eliezer: I think that Aumann and certain bits of Heuristics and Biases are usually toxic to people. People who get Bayesianism should see Aumann as a trivial single step inference. People who are told it see it as a special surprising fact and mis-apply it, guessing its meaning from the name. Maybe we should talk about the "deliberative uncertainty principle" where you can't simultaneously predict your and his next statement in a conversation with an epistemic peer.

Lots of physicists don't believe in many-worlds because they believe in some other theory or interpretation. Parsimony is often used to dismiss many-worlds; mainly because many-worlds doesn't make any predictions so it's difficult to refute on other grounds. That doesn't make it true of course. If you have reason to believe that some other theory or interpretation is worth pursuing then you probably won't spend much time refuting many-worlds. So parsimony will be the lazy way to dismiss many-worlds but not the reason you hold another view.

The reason most physicists working in the foundations of quantum mechanics don't believe in many-worlds is because they take a different view of one or more of the assumptions you made (locality, hidden variables, the wave-function collapse, etc) and not because they don't understand parsimony. They're also in a far better position to judge those assumptions than you are (even by your own admissions). So even if I had no opinion on the subject I wouldn't accept your argument. Your argument for many-worlds relies on claims of why physicists reject many-worlds that have no supporting evidence.

If I could level a general criticism about your essays it would be this: Your focus on other people's modes of reasoning and biases makes you excessively prone to straw men arguments.

Just to be clear, I had no intention of saying anything about Many Worlds, despite the fact that this was Eliezer's main point in this post. My original comment was more of a follow-up to my comments about overconfidence in the post on the Rhythm of Disagreement, and again, I was not accusing Eliezer of any specific error.

I remember sitting there staring at the "linear operators", trying to figure out what the hell they physically did to the eigenvectors - trying to visualize the actual events that were going on in the physical evolution - before it dawned on me that it was just a math trick to extract the average of the eigenvalues.

If anyone else had written this sentence, I would think to myself "Jeez, this guy doesn't know what he's talking about." Did this whole thing start because you don't understand linear algebra? Linear algebra 1. is an excellent formalism for quantum mechanics and 2. can be taught to high school students, provided they can visualize what matrices do to eigenvectors, i.e. scale them. In any case if you don't know much linear algebra, this anonymous blog commenter recommends it very much. It's really useful in all kinds of situations, even for the day to day.

Uh I guess what I'm trying to say is, what do you mean by that Mr. Yudkowsky?

michael vassar: now that I know to look, evolution's limits are really obvious. A shark is not noticeably less complex than a dog. Evolution has been bumping along a glass ceiling since lancelets evolved into fish. The fact it took so long to get intelligence seems indicative to me that we humans exist by the incredible fluke of finding a kind of mind that could be squeezed under the punishingly low complexity limit. However, above you imply you disagree with Eliezer on this topic. I'm really interested to know why.

As one who understood linear operators (as mathematics) for years without having a clue what they might have to do with atoms and quarks (and never seeing this spelled out in writing anywhere), I can relate to Eliezer's sentiments.

Out of curiosity, Eliezer, what should the calculus textbooks have said?

Why does the area under a curve equal the antiderivative? I've done enough calculus to suspect I somehow know the reason, but I just can't quite pinpoint it.

Why does the area under a curve equal the antiderivative?

The rate of area-accumulation is given by the height of the curve, i.e. the value of the function. You can see this easily with constant functions: a horizontal line 2 units above the horizontal axis accumulates area underneath at a rate of 2 square units per unit of length.

At least that's how I like to think about it.

Julian Morrison: Evolution is slow, and formal upper bounds can be established, but the real formal upper bounds are orders of magnitude above what Eliezer was claiming on Overcoming Bias and had been claiming privately for some time. The discussion on the thread lead to some simulations being run which showed this. Actual typical rates of evolution might be below the claimed upper bound most of the time, but that wasn't what was being claimed. The claimed upper bound does hold for asexual reproduction.

I tend to disagree with the claim that finding intelligence was a fluke. The Cambrian Explosion shows how much can be created by evolution in a relatively short period, and a variety of other species show enough intelligence, sometimes grounded in very different neuroanatomy to, make it seem unlikely not to be fairly low hanging fruit. It's easy to think of many things that evolution could build in enough time but which it didn't build before it built human intelligence. Glass trees based on diatom silicon manipulation, smart bones that turn soft in response to excessive force and biological explosive driven projectiles top my casual list.

michael vassar: imagining a histogram of intelligence in multi-cell animalia by species (ignoring insects), there is a definite peak centered in the mouse-to-horse range, and the drop-off on the high intelligence side is steep and down-curving to vertical. Many top or middle predators are dog-smart. Beyond that, parrots, crows, monkeys, dolphins, octopi... widely scattered in taxa, but rare enough to name. A gap. Higher apes. A gap. Chimps. A big gap. Humans. And nothing.

This may be no more than my bias speaking, because it's not real data. Still, it looks pretty obvious to me that there's some serious difficulty crossing the dog-to-hominid gap. Otherwise, intelligence would be more smoothly spread out.

poke: "The reason most physicists working in the foundations of quantum mechanics don't believe in many-worlds is because they take a different view of one or more of the assumptions you made"

I think the more fundamental reason most physicists working in the foundations of quantum mechanics don't believe in many-worlds is that those who do believe in many worlds consider the foundations problem to be solved, and see no need to work on it anymore.

poke: "The reason most physicists working in the foundations of quantum mechanics don't believe in many-worlds is because they take a different view of one or more of the assumptions you made"

I think the more fundamental reason most physicists working in the foundations of quantum mechanics don't believe in many-worlds is that those who do believe in many worlds consider the foundations problem to be solved, and see no need to work on it anymore.

Julian Morrison, the conclusion I draw from your histogram is that monkey/octopus intelligence is easy to reach from dog, but not useful in most niches. Beyond that, it's hard to reason for anthropic reasons. It could be that there's a bottleneck getting past monkeys, but I'd guess that niches for which post-monkey intelligence is useful are extremely rare, but have increasing returns to intelligence and thus have intelligence take-off.

"Oh, look, Eliezer is overconfident because he believes in many-worlds."

I can agree that this is absolutely nonsensical reasoning. The correct reason to believe Eliezer is overconfident is because he's a human being, and the prior that any given human is overconfident is extremely large.

One might propose heuristics to determine whether person X is more or less overconfident, but "X disagrees strongly with me personally on this controversial issue, therefore he is overconfident" (or stupid or ignorant) is the exact type of flawed reasoning that comes from self-serving biases.

Well, first of all, I would like to say a great thanks to you for those posts. They are very interesting, pleasant to read, they follow a clear and coherent progression.

But I disagree with you in one "tactical" point : arguing Many Worlds for arguing that you don't require the same atoms for personal identity seems like building and then using a liquid-helium refrigerated computer to compute 3+5 = 8. I mean, yes, Many Worlds implies that personal identity is not in individual atoms, but even if Many Worlds were false, even without QM at all but just classical chemistry, biology, neuroscience, understanding of neural networks, ... identity is not in individual atoms.

Even after reading the whole QM sequence and other posts in LW/OB, I'm not yet fully convinced about MWI. I do give it a much higher chance of being "right" than the Copenhaguen interpretation. I'm not too sure about the other interpretations (transactional for example) which I didn't dig in fully enough. But well... we still have holes : no way to derivate the Born rule, no answer to quantum gravity. Those two holes are not specific to MWI - but they are in MWI. The day we'll find a way to fill those two holes, it may require a switch to another view of the reality, one we just can't really think about now, like in the 20s they didn't think of MWI, or like Newton didn't think of curvature of space to explain gravity. It may look like MWI, or it may look quite different from it... so I wouldn't bet on MWI with a probability close to 1. Maybe like to 0.5. Or somewhat less, if I read more about the other interpretations. Even if I admit that the timeless MWI looks very ... awesome.

But even before reading LW/OB, I was already betting with almost 1 probability of me not being made of my atoms, if you scan me, disintegrate me and rebuild on Mars close to thermal nose, yes, it's "me". Maybe I'm not the target for that part of those posts in that case... but still, I don't think that we need to go as far as MWI to justify that identity and consciousness is in the way the neurons are organized/interconnected, and the way the currents flows in them, and not in individual atoms. I guess that comes, at least in huge part, from my experience as a computer scientist... so maybe speaking of computer science/artifical intelligence would help for that point ?