This post is part of the Quantum Physics Sequence.
Followup toQuantum Explanations

"Why are you doing these posts on quantum physics?" the one asked me.

"Quite a number of reasons," I said.

"For one thing," I said, "the many-worlds issue is just about the only case I know of where you can bring the principles of Science and Bayesianism into direct conflict."  It's important to have different mental buckets for "science" and "rationality", as they are different concepts.  Bringing the two principles into direct conflict is helpful for illustrating what science is and is not, and what rationality is and is not.  Otherwise you end up trusting in what you call "science", which won't be strict enough.

"For another thing," I continued, "part of what goes into becoming a rationalist, is learning to live into a counterintuitive world—learning to find things underneath the surface that are unlike the world of surface forms."  Quantum mechanics makes a good introduction to that, when done correctly without the horrible confusion and despair.  It breaks you of your belief in an intuitive universe, counters naive realism, destroys your trust in the way that your cognitive algorithms look from inside—and then you're ready to start seeing your mind as a mind, not as a window onto reality.

"But you're writing about physics, without being a physicist," the one said, "isn't that... a little..."

"Yes," I said, "it is, and I felt guilty about it.  But there were physicists talking complete nonsense about Occam's Razor without knowing the probability theory of it, so my hand was forced.  Also the situation in teaching quantum mechanics is really awful—I saw the introductions to Bayesianism and they seemed unnecessarily difficult, but the situation in quantum mechanics is so much worse."  It really is.  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. Okay, but... can't you just tell me that up front?  Write it down somewhere?  Oh, I forgot, the math doesn't mean anything, it just works.

"Furthermore," I added, "knowing about many worlds, helps you visualize probabilities as frequencies, which is helpful to many points I want to make."

"And furthermore," I said, "reducing time to non-time is a powerful example of the principle, in reductionism, that you should reduce something to something other than itself."

"And even furthermore," I said, "I had to break my readers of trust in Science, even trust in physicists, because it doesn't seem possible to think and trust at the same time."

"Many-worlds is really a very clear and simple problem," I said, "by comparison with the challenges you encounter in AI, which are around a hundred times less clear-cut.  And many scientists can't even get many-worlds, in the absence of authority."  So you are left with no choice but to aspire to do better than the average scientist; a hell of a lot better, in fact.  This notion is one that you cannot just blurt out to people without showing them why it is necessary.

Another helpful advantage—I often do things with quite a few different purposes in mind, as you may have realized by this point—was that you can see various commenters who still haven't gotten it, who are still saying, "Oh, look, Eliezer is overconfident because he believes in many-worlds."

Well, if you can viscerally see the arguments I have laid forth, then you can see that I am not being careless in having an opinion about physics.  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) that they might not be expected to know about.  It is not just a matter of my forming strong opinions at random.

But would you believe that I had such strong support, if I had not shown it to you in full detail?  Ponder this well.  For I may have other strong opinions.  And it may seem to you that you don't see any good reason to form such strong beliefs.  Except this is not what you will see; you will see simply that there is no good reason for strong belief, that there is no strong support one way or the other.  For our first-order beliefs are how the world seems to be.  And you may think, "Oh, Eliezer is just opinionated—forming strong beliefs in the absence of lopsided support."  And I will not have the time to do another couple of months worth of blog posts.

I am very far from infallible, but I do not hold strong opinions at random.

"And yet still furthermore," I said, "transhumanist mailing lists have been arguing about issues of personal identity for years, and a tremendous amount of time has been wasted on it."  Probably most who argue, will not bother to read what I have set forth; but if it stops any intelligent folk from wasting further time, that too is a benefit.

I am sometimes accused of being overconfident and opinionated, for telling people that being composed of "the same atoms" has nothing to do with their personal continuity.  Or for saying that an uploading scan performed to the same resolution as thermal noise, actually has less effect on your identity than a sneeze (because your eyes squeeze shut when you sneeze, and that actually alters the computational state of billions of neurons in your visual cortex).  Yet if you can see your nows braided into causality of the river that never flows; and the synaptic connections computing your internal narrative, that remain the same from one time to another, though not a drop of water is shared; then you can see that I have reasons for this strong belief as well.

Perhaps the one says to me that the exact duplicate constructed on Mars, is just a copy.  And I post a short comment saying, "Wrong.  There is no copy, there are two originals.  This is knowable and I know it."  Would you have thought that I might have very strong support, that you might not be seeing?

I won't always have the time to write a month of blog posts. While I am enough of a Traditional Rationalist that I dislike trust, and will not lightly ask it, I may ask it of you if your life is at stake.

Another one once asked me:  "What does quantum physics have to do with overcoming bias?"

Robin Hanson chose the name "Overcoming Bias"; but names are not steel chains.  If I'd started my own personal blog for the material I'm now posting, I would have called it "Reinventing Rationality" or something along those lines—and even that wouldn't have been the real purpose, which would have been harder to explain.

What are these series of posts, really?  Raw material for a popular book on rationality—but maybe a tenth of this material, or less, will make it into the book.  One of the reasons I write long posts, is so that I can shorten them later with a good conscience, knowing that I did lay out the full argument somewhere.  But the whole quantum physics sequence is probably not going to make it into the popular book at all—and neither will many other posts.  So what's the rest of it for?

Sometimes I think wistfully of how much more I could have accomplished in my teenage years, if I had known a fraction of what I know now at age 15.  (This is the age at which I was a Traditional Rationalist, and dedicated and bright as such ones go, but knew not the Way of Bayes.)  You can think of these blog posts, perhaps, as a series of letters to my past self.  Only not exactly, because some of what I now write, I did already know then.

It seems to me, looking back, that the road which took me to this Way, had a great deal of luck in it.  I would like to eliminate that element of luck for those who come after.  So some of what I post, is more formal explanations of matters which Eliezer-15 knew in his bones.  And the rest, I only wish I had known.

Perhaps if you prime someone with enough material as a starting point, they can figure out the other 95% on their own, if they go on to study the relevant sciences at a higher technical level.  That's what I hope.

Eliezer-15 was led far astray by the seeming mysteriousness of quantum mechanics.  An antiproject in which he was aided and abetted by certain popular physicists—notably Sir Roger Penrose; but also all those physicists who told him that quantum physics was "mysterious" and that it was okay not to understand it.

This is something I wish I had known, so I explained it to me.

Why not just tell me to ignore quantum physics?  Because I am not going to "just ignore" a question that large.  It is not how we work.

If you are confronting real scientific chaos—not just some light matter of an experimental anomaly or the search for a better theory, but genuine fear and despair, as now exists in Artificial Intelligence—then it is necessary to be a polymath.  Healthy fields have healthy ways of thinking; you cannot trust the traditions of the confused field you must reform, though you must learn them.  You never know which way you'll need to draw upon, on venturing out into the unknown.  You learn new sciences for the same reasons that programmers learn new programming languages: to change the way you think.  If you want to never learn anything without knowing in advance how it will apply, you had best stay away from chaos.

If you want to tackle challenges on the order of AI, you can't just learn a bunch of AI stuff.

And finally...


There finally comes a point where you get tired of trying to communicate across vast inferential distances.  There comes a point where you get tired of not being able to say things to people without a month of preliminary explanation.  There comes a point where you want to say something about branching Earths or identical particles or braids in the river that never flows, and you can't.

It is such a tremendous relief, to finally be able to say all these things.  And all the other things, that I have said here; that people have asked me about for so long, and all I could do was wave my hands.  I didn't have to explain the concept of "inferential distance" from scratch, I could just link to it.  It is such a relief.

I have written hundreds of blog posts here.  Think about what it would be like, to carry all that around inside your head.

If I can do all the long sequences on Overcoming Bias, then maybe after that, it will be possible to say most things that I want to say, in just one piece.


Part of The Quantum Physics Sequence

(end of sequence)

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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.

@Unknown: You're assuming Eliezer's failure probabilities are independent. That seems wrong, because Eliezer doesn't think randomly.

He's using some collection of heuristics to generate the thoughts we see in the posts. If his heuristics were broken, we'd see a lot more than one mistaken post.

So a .5% error probability per post does not necessarily imply a high probability that he made at least one serious mistake.

Now before anyone accuses me of believing otherwise, let me say that Eliezer is not infallible. Heck, I caught him making a mistake two days ago.

So, I don't think Eliezer has gotten it all right. I do think that he's probably gotten the main ideas right. But there's a difference between saying that every supporting detail of an argument is correct and saying that the main ideas are correct. Eliezer is much more cautious with the main lines of his arguments than with the illustrative examples (and there are entire posts which are illustrative examples or are mostly so.)

Also, Eliezer often gives arguments in parallel rather than in series (ie. making several arguments in favor of the same claim) and in these cases, the failure probability should go down, not up.


Most of the entire quantum sequence has been wrong, as has been pointed out in the comments. I think the error rate is much, much higher than you are estimating when he is talking out of his depth...

As far as I can tell, this is wrong. Over the years many people with a graduate background in quantum physics have fact-checked the sequence, and as far as I can tell there are no significant factual errors in it. Of course there are philosophical disagreements about how to evaluate the evidence about things like MWI, but in terms of basic facts that can meaningfully be checked, the sequence seems to hold up quite well, and I would take a bet that you can’t find a simple error in it that hasn’t been addressed.


It appears we didn't read the same comments? I've just gone through the whole quantum sequence, chronologically, and read the comments too. Every single post where Eliezer says something not in line with current physics thought (or takes cheap shots at academia), there's someone in the comments with a graduate degree in physics telling him it's nonsense. Like for example, which presents Barbour's pseudoscience as fact despite multiple comments pointing out that his theory is nonsense, not worked out in detail, cannot be worked out in detail because it ignores asymmetrical relationships between space and time in the underlying physical equations, and is soundly rejected by peer review. Yet this forms the basis of his entire philosophy of physics and reality, his whole reason for writing the sequence in the first place!

There is a reason that scientific articles are not written in the strong first-person persuasive style that Eliezer prefers. It engages the wrong parts of our social-status and political brains making us ignore the content and evaluate arguments based on rhetorical competence, which rationalists shouldn't do. Strip the quantum sequence of this persuasive style and the naked content is left wanting. It's basically a reasonable explanation of standard quantum mechanics (which is fine), followed by baseless rants against a caricature of the academic world of physics and graduate studies (which only demonstrate he has no academic experience), then promotion of pseudo-science as if it were fact, and drawing even more tenuous philosophical conclusions from that pseudoscience. Eliezer is clearly talking outside of his depth, yet he does so with confidence like he is certain of the truth of what he is saying, and attacking the intelligence of naysayers. Not his best moment by a long shot.

I have an undergraduate degree and some graduate coursework in physics. My adviser's specialty was quantum computation, a field which I've kept tabs on since it intersects with my own work on cryptography. His understanding of physics is amateurish, and his attacks on the academic environment of physics research falls way off the mark.

Eliezer wonders why the academic world doesn't take his theories (e.g. timeless/functional decision theory) seriously. It's because he comes off like a crank. And perhaps it is because in this sequence, he reveals himself to *be* a crank.

I came back to read these early sequences again because I recently found a good use case for functional decision theory and I thought I'd see if there's any other good insights to draw from Eliezer's writings. However I'm coming away from this thinking he was more of a one-trick pony than a possessor of rationalist superpowers.

Wait, the comments there are mostly pointing out that the parts of Barbour that Eliezer is referring to are obvious and nothing novel. Not that what he is saying is wrong!

His first idea, that time is simply another coordinate parameterizing a mathematical object (like a manifold in GR) and that it's specialness is an illusion, is ancient. His second idea, that any theory more fundamental than QM or GR will necessarily feature time only in a relational sense (in contrast to the commonly accepted, and beautiful, gauge freedom of all time and space coordinates) is interesting and possibly true, but it is most likely not profound. I can't read all of his papers, so perhaps he has some worthwhile work.

As far as I can tell, Eliezer is referring to the much more "trivial" aspects of Barbour's work as described here. 

To be clear, I am not a huge fan of the post in question here, but it is important to separate saying wrong things from saying confusing things. 

I also want to separate making wrong claims from attacking academic institutions. I think it's fine to say whatever you want about Eliezer's tone, but your original comment said: 

Most of the entire quantum sequence has been wrong

Which is primarily a claim about factual correctness, which I think is quite misplaced. Though I am not super confident, so if you do have a comment that points out a concrete error in one of his posts, then that would definitely convince me (though still leave me skeptical about the claim of "most", since a lot of the sequence is just really introductory quantum mechanics that I myself can easily verify as correct).


The wave function evolves differently through time than space. This is expressed in the equation itself which has a first derivative for one and a second derivative in the other. This prevents Barbour from actually achieving his unification and is what makes work quackery. The first post which introduces Barbour’s timeless formulation has a comment response from a physicist pointing this out. Just like the first post introducing the Born probabilities has a comment pointing out that the probabilities fall out of the Taylor expansion on state evolution and are not in fact mysterious at all. (Alternatively you can show this from the decision theory formulation.)

I stand by my statement that aside from a few introductory posts, the quantum physics sequence is factually wrong.

I'm not happy with the Barbour post either, but the rest of the sequence seems better. There was a post on this topic.

Just like the first post introducing the Born probabilities has a comment pointing out that the probabilities fall out of the Taylor expansion on state evolution and are not in fact mysterious at all. (Alternatively you can show this from the decision theory formulation.)

Can you link to this please? And explain the decision theory thing if that's not part of the comment you're referring to?


Apparently LessWrong comments are not indexed by google, so I don't have a non-time-intensive way of tracking down that comment. I remember reading it in one of the earlier posts in the quantum sequence.

Here's a paper by David Wallace on Deutsch's decision theory formulation of the Born probabilities:

Apparently LessWrong comments are not indexed by google, so I don’t have a non-time-intensive way of tracking down that comment.

Comments should be indexed by Google (I've seen comments show up in my search results before), but maybe not completely? Can you send a note to the LW team (telling them why you think comments are not being indexed) to see if there's anything they can do about this? In the meantime, have you tried LW's own search feature (the magnifying glass icon at the top)?

Here’s a paper by David Wallace on Deutsch’s decision theory formulation of the Born probabilities

I actually wrote a comment about that back in 2009 but haven't revisited it since. Have you read the response/counterargument I linked to, and still find Wallace's paper compelling?

Comments should be indexed by Google. I just went to 5 very old posts with hundreds of comments and randomly searched text-strings from them on Google, and all of them returned a result: 

If anyone can find any comments that are not indexed, please let me know, and I will try to fix it, but it seems (to me) that all comments are indexed for now. 

I've read through the whole Quantum Physics Sequence once or twice, and whenever Eliezer talks about actual science, it is popularized, but not wrong. Some parts are explained really nicely, too. Unfortunately, those are the parts that are also irrelevant to learning rationality, the whole impetus for Eliezer writing the sequence. And the moment he goes into MWI apologia, for lack of a better word, it all goes off the rails, there is no more science, just persuasion. To be fair, he is not alone in that. Sean Carroll, an excellent physicist from whose lecture notes I had learned General Relativity, has published a whole book pushing the MWI onto the unsuspecting public.

One area where the Quantum Physics sequence is useful for rationality is exposing how weird and counter-intuitive the world is, and feeling humbled about one's own stated and unstated wrong assumptions and conclusions, something we humans are really bad at. Points like "All electrons are the same. This one here and that one there" "Actually, there are no electrons, just fields that sometimes look like electrons".

Where the sequence fails utterly in my view is the pseudo-scientific discussions about "world thickness" and the fictional narratives about it.

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...

If somebody wrote a good children's book that explained the essence of timeless MWI physics... I wonder if they would intuitively wrap their head around the idea more easily than us adults who have spent decades thinking about the world in a totally different way?

I very much doubt they would. We really are born with powerful (and wrong) intuitions about physics; see the Naïve physics Wikipedia article for some details.

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 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.

Yes, I know and knew perfectly well that a linear operator separates out the eigenvectors, multiplies each one by a scalar eigenvalue, and puts them back together again. But I thought that was supposed to be physically happening to the wavefunction. Not that it was a math trick developed for extracting the average of the eigenvalues when you took the operated-on wavefunction's dot-product with the pre-operated-on wavefunction.

The quantum physics textbooks I read were happy to define linear operator-ness in great gory detail, but they never actually came out and said, "This is not something physically happening to the wavefunction. We are just using this math trick to extract an average value."

Why would they say it? After all, quantum physics is meaningless. The wavefunction doesn't really exist. All you can do is memorize certain math tricks that make predictions. All the math tricks are on an equal footing; it's not that some are physical and some aren't.

So I would stare at the operators and their definitions, trying to figure out what was physically happening, until finally - I think while looking at the "position operator" - I realized it was a math trick, not an event description.

I haven't felt so indignant since I realized why the area under the curve was the antiderivative, and realized that at least two different calculus textbooks neglected to mention this in favor of elaborate formal definitions.

The quantum physics textbooks I read were happy to define linear operator-ness in great gory detail, but they never actually came out and said, "This is not something physically happening to the wavefunction. We are just using this math trick to extract an average value."

I think is is a common problem for many mathematical conventions in physics.

The same thing happened be me in high school physics. I was confused by the torque vector, and I spent an entire year thinking that somehow rotation causes a force perpendicular to the plane of motion. I just could not visualize what the heck was going on.

Finally I realized the direction of the torque vector is an arbitrary convenience. My teacher and textbook both neglected to explain why it works like that.

The "why's" are important!

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.

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.

Bravo. This potential for systematic bias on certain questions can be generalized and ought to have a name. It suggests that we should reduce the weight that we place on expert opinion on certain questions in any field, to the extent that the choice to work in the field will depend on how a person answers those questions.

So when we decide whether to rely on expert opinion, we ought to keep in mind that certain biases will tend to afflict precisely the experts, making non-experts in some cases more reliable guides.

But there is a foundational problem left, namely the Born statistics!

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 ?