## The bullet-swallowers

Question for the day: what do libertarianism and the Many-Worlds Interpretation of quantum mechanics have in common? Interest in the two worldviews seems to be positively correlated: think of quantum computing pioneer David Deutsch, or several prominent posters over at Overcoming Bias, or … oh, alright, my sample size is admittedly pretty small.

Some connections are obvious: libertarianism and MWI are both grand philosophical theories that start from premises that almost all educated people accept (quantum mechanics in the one case, Econ 101 in the other), and claim to reach conclusions that most educated people reject, or are at least puzzled by (the existence of parallel universes / the desirability of eliminating fire departments). Both theories seem to have a strong following with nerds who read science fiction and post to Internet discussion groups, but a relatively poorer following with both John Q. Public and Alistair K. Intellectual. (Needless to say, these stereotypes tell us almost nothing about the theories’ validity.)

My own hypothesis has to do with bullet-dodgers versus bullet-swallowers. A bullet-dodger is a person who says things like:

Sure, obviously if you pursued that particular line of reasoning to an extreme, then you’d get such-and-such an absurd-seeming conclusion. But that very fact suggests that other forces might come into play that we don’t understand yet or haven’t accounted for. So let’s just make a mental note of it and move on.

Faced with exactly the same situation, a bullet-swallower will exclaim:

The entire world should follow the line of reasoning to precisely this extreme, and this is the conclusion, and if a ‘consensus of educated opinion’ finds it disagreeable or absurd, then so much the worse for educated opinion! Those who accept this are intellectual heroes; those who don’t are cowards.

In a lifetime of websurfing, I don’t think I’ve ever read an argument by a libertarian or a Many-Worlds proponent that didn’t sound like the latter.

We know plenty of historical examples where the bullet-swallowers were gloriously right: Moore’s Law, Darwinism, the abolition of slavery, women’s rights. On the other hand, at various points within the last 150 years, extremely smart people also reasoned themselves to the inescapable conclusions that aether had to exist for light to be a wave in, that capitalism was reaching its final crisis, that only a world government could prevent imminent nuclear war, and that space colonies would surely exist by 2000. In those cases, even if you couldn’t spot any flaws in the arguments, you still would’ve been wise to doubt their conclusions. (Or are you sure you would have spotted the flaws where Maxwell and Kelvin, Russell and Einstein did not?)

Here’s a favorite analogy. The world is a real-valued function that’s almost completely unknown to us, and that we only observe in the vicinity of a single point x0. To our surprise, we find that, within that tiny vicinity, we can approximate the function extremely well by a Taylor series.

“Aha!” exclaim the bullet-swallowers. “So then the function must be the infinite series, neither more nor less.”

“Not so fast,” reply the bullet-dodgers. “All we know is that we can approximate the function in a small open interval around x0. Who knows what unsuspected phenomena might be lurking beyond it?”

“Intellectual cowardice!” the first group snorts. “You’re just like the Jesuit schoolmen, who dismissed the Copernican system as a mere calculational device! Why can’t you accept what our best theory is clearly telling us?”

So who’s right: the bullet-swallowing libertarian Many-Worlders, or the bullet-dodging intellectual kibitzers? Well, that depends on whether the function is sin(x) or log(x).

### 111 Responses to “The bullet-swallowers”

1. MattF Says:

Not to mention that if the infinite series has arbitrarily large gaps, the function has a natural boundary and can’t be analytically continued beyond some finite limit.

2. Pedro Pinheiro Says:

You can always be in between the two positions, and be an agnostic. Be prepared to accept the universe can be anything at all, but decide with what you know. Being proven wrong in the future is not such a big deal. Except if you’re talking about dodging/swallowing real bullets, of course.

3. MarkyMark Says:

Really? I just don’t get it. I have no experience with “many worlds people” and have never noticed a correlation with libertarianism. It is true, that there are some wacko libertarians. But I do not see them reflected in this image. My pseudo embrace of libertarianism is actually the opposite of the standard argument. Libertarians generally think the individual knows best and thus the power of the state should be limited. I, on the other hand, think people are generally so stupid that the optimal solution is to limit the government those stupid people will elect.

4. Scarybug Says:

Wow, excellent essay.

My issue with Libertarianism is the same as my issue with Marxism, it’s a utopian system that only works if everyone agrees to do it right and fair.

Many-worlds, on the other had, is something I’d really like to be true, though I’m completely agnostic about it.

5. John Armstrong Says:

MarkyMark: I think agnosticism is the point of the first position. It says, “other forces might come into play”, which leaves wide open the possibility that the suggested extreme actually happens.

6. Scott Says:

MarkyMark: I was thinking of the sort of libertarian who says things like, “there can be no such thing as a market failure: if it ‘fails,’ then ipso facto it isn’t a market.” (For example, Walter Block and others of the Austrian School, and of course Ayn Rand.) To them, that government has no defensible role except preventing the initiation of force (and maybe printing money and enforcing contracts), follows so transparently from a priori reasoning that anyone who doesn’t accept this must be corrupt or an idiot.

Your reason for being a libertarian is indeed different. You might enjoy Bryan Caplan’s book The Myth of the Rational Voter, which argues that more power ought to be given to professional economists, since ordinary voters (favoring passion over reason) can’t understand why layoffs, deregulation, shipping jobs overseas, etc. are all for their own good. (Incidentally, I’m eagerly awaiting the sequels: “The Myth of the Healthy Big Mac,” “The Myth of the Harmless Shark”… )

7. MarkyMark Says:

John: I am not agnostic about the stupidity of the populace.

8. roland Says:

Given two different branches in the many worlds tree. Is it possible to decide that they won’t interfere any more?

9. ScentOfViolets Says:

Scott, in my experience, the two are correlated as well. But – again in my experience – the causal factor is reading science fiction. I’ve also observed that libertarians are far more likely than most to believe that it is possible to physically travel faster than light, or at the least, that superluminal transmission of information is possible. Somehow, I don’t think that follows from fearlessly pursuing the consequences of a supposition to the very end. At least, none that I’m aware of.

10. Niel Says:

Ugh, Scott. What’s with the hatin’?

Sure, there isn’t compelling evidence for MWI — just as there isn’t compelling evidence for Bohmian Mechanics, or any other “merely statistical” theory, or for spontaneous collapse theories. (The latter has the advantage of being testable in principle, which makes it more interesting, but it still has the same empirical status of the intepretations of quantum mechanics). But each side has its own partisans who argue for it strongly, and sometimes belligerently, making them resemble some sort of political extremist or idealist.

People object to MWI because it seems fantastic and abundant, in opposition to the maxim of Occam’s Razor. But it basically posits the the simplest “mechanics”, at least on the level of events. Other interpretations have to posit extremely complicated motions of hypothetical particles, or some other cludge, to explain what we see: and while they avoid producing fantastic conclusions, that’s because they’ve used more complex premises to achieve that effect. I make no claim that the MWI is necessarily correct, but can it honestly be said that any other interpretation is clearly “simpler”?

The minimalist description of how MWI works (as opposed to the seemingly abundant conclusion it reaches) is also compatible with gravity-driven collapse theories (i.e. due to widely-distributed superpositions of massive bodies), and quantum logic (which is more of a highly refined refusal to interpret than an interpretation). — None of this makes the MWI true, it just makes it appealing. It could perhaps be said that such broad compatibility is a sign that it actually provides no information: and that would be a fair critique to make — of all of the interpretations of QM. (All such arguments must be forbidden in any debate about enumerating angels on pinpoints.)

I posit that perhaps the problem is not with MWI advocates, but rather with the most vocal ones; and more generally anyone who feels that it is very important which interpretation people believe in.

Meanwhile, let’s hope that an interesting collapse theory turns out to be true, in order to give us something new to talk about.

11. Scott Says:

ScentOfViolets: I hadn’t thought about the FTL connection! Yes, sci-fi (and personal identification with one of its favorite images, the lone hero/inventor defying the scientific establishment) might indeed explain a lot of the correlation. It would be interesting to disentangle all these factors.

12. Scott Says:

Niel: What hatin’?

13. Scott Says:

Roland: The only way for two branches of the MWI tree to interfere is if they later become equal in all respects. This is usually compared to an egg unscrambling itself (indeed in the modern understanding, the decoherence of MWI branches is just another manifestation of the Second Law).

14. Robin Hanson Says:

A great observation Scott! I see it as biting the bullet of what you see as a very solid theory. In your examples of aether for light, a capitalist crisis, world gov to stop nuke war, and space colonies soon, only aether seems a strong example of biting a solid theory bullet.

15. Scott Says:

Thanks, Robin! At risk of being tautological, communism (at least) seemed like an extremely solid theory to those who believed it. I admit I’m not sure of the theory that would justify space colonies soon: “time-bounded technological determinism”?

16. Silas Says:

I don’t know which blog I should post this on, but I thought I’d bring up Schmidhuber’s speed prior.

Relevance: in determining which theory is “simpler”, Eliezer_Yudkowsky invoked the MML/Solomonoff induction metric. This does not assign any penalty to “RAM” use, i.e. the actual amount of data storage you need *as* you unfold the prediction. His explanation why not to penalize RAM when applying Occam’s Razor was very brief: “Because, historically speaking, that heuristic doesn’t work.”

However, the justification of the speed prior is very convincing, and it would weigh heavily against the existence of many worlds. Is there some more rigorous reason not to use the metrics that penalize resource-intensive theories?

17. Sean Carroll Says:

Definitely an interesting observation. The final question, “Who’s right?”, by construction has no a priori correct answer — we’ll have to wait and see! Empirically, sometimes it will be the bullet-dodgers (“no, energy is still conserved, there must be a new particle emitted in beta decay”) and sometimes it will be the bullet-swallowers (“no, there is no way to make quantum mechanics deterministic and still agree with the data”).

That’s why you should be a good meta-capitalist and encourage a diversified portfolio of approaches to doing science.

18. Naw Says:

I am reminded of the joke about mathematicians and cows. When I googled it, a comment on this blog was the first hit.

This is apparently the wording from The Curious Incident of the Dog in the Night-Time, but it might be more appropriate with computer scientists, physicists, and mathematicians.

“There are three men on a train. One of them is an economist and one of them is a logician and one of them is a mathematician. And they have just crossed the border into Scotland (I don’t know why they are going to Scotland) and they see a brown cow standing in a field from the window of the train (and the cow is standing parallel to the train). And the economist says, ‘Look, the cows in Scotland are brown.’ And the logician says, ‘No. There are cows in Scotland of which at least one is brown.’ And the mathematician says, ‘No. There is at least one cow in Scotland, of which one side appears to be brown.’ And this is funny because economists are not real scientists and because logicians think more clearly, but mathematicians are best.”

19. IceBogan Says:

Interesting comparison. But you can be Libertarian “in the neighborhood of x_0” without accepting all the reductio ad absurdum arguments — you can vote for a little less government, a little lower taxes, a little more personal responsibility. You can’t be a little bit Many Worlds.

20. Scott Says:

Silas: Yeah, I was struck too by Eliezer’s discussion of whether the universal prior should assign greater weight to programs that use fewer resources, as opposed to just shorter programs. My two immediate reactions:

(1) That it’s a beautiful way of thinking about lots of debates that I’m interested in, not just the MWI one. (For example, whether quantum computers can be built, and whether Nature can solve NP-complete problems in polynomial time.)

(2) That unlike Eliezer, I’m not at all convinced that assigning lower prior probability to programs that use more time and memory is always a bad idea. Sure, we’ve seen over the past few centuries that Nature often “wastes” astronomical amounts of computational effort (indeed, one could almost define the word ‘astronomical’ as ‘so quantitatively great as to defy humanly-imaginable purposes’). But by computer science standards, these amounts still aren’t nearly as astronomical as they could be!

For example, we’ve never seen a physical device that solves the halting problem, or that solves NP-complete problems in polynomial time. Should we weight against such devices in our prior? I.e. if two explanations seem equally simple and consistent with evidence, should we prefer the explanation that doesn’t require Nature to be solving an NP-complete problem? It’s not obvious to me that we shouldn’t. Call it Occam’s Complexity-Theoretic Aftershave.

21. Michael Bacon Says:

Admittedly, I’m a partisan of the MWI, but of not much of libertarianism — although I’m not adverse to attempting market-based solutions to problems. And, while I pretty much agree with Niel (except of course for the “hatin’” part :)), I think Sean is right when he advocates a diversified portfolio of approaches. I’d be curious what brought on this particularly entry Scott? Sounds like you just came off a philosophical night at the pub.

22. Max Says:

The funny thing is that your “bullet-dodgers” almost always prefer the exactly opposite dimension of libertarianism and do the same on their playground of political believe. The difference is that libertarianism leaves an open door to other ideas to thrive within it, as long as there is a market, a need for it and as long as there is tolerance for different opinions.

Of course, it often takes it to the extreme, but that is only because we are sitting at point x0 and x_extreme is far off from our current point on the curve and we cannot fathom how we could ever be there. But then, could the romans on point x0_t_old fathom the world of today?

So, yes, you are right, they often try to go to logic extremes, but they also leave open spaces for bullet-dodgers and are often bullet-dodgers themselves. The only difference is that x0 to x_bullet-dodgers in modern societies is almost infinitisimal and x0 to x1 is growing larger rapidly…

But does this make them narrow-minded?

23. Scott Says:

I’d be curious what brought on this particularly entry Scott?

Michael: I actually noticed this connection years ago, but the proximate trigger was reading Rebbe Yudkowsky’s fiery MWI sermons and Bryan Caplan’s The Myth of the Rational Voter in the same week.

24. jb Says:

I am the libertarian many-worlds believer you stereotype here

FWIW, I disagree with the strawman claim that libertarianism requires everyone to be good and fair. The entire point of the concept is that people will do what they want, for selfish reasons, and the government is there to constrain the ones who violate crimes against property or person. There are plenty of logical flaws in the libertarian philosophy, for instance around issues of light and noise pollution, ocean and river rights and so forth. However, those are policy details, not a fatal blow to the general concept of limited government and social and economic liberty.

The Many Worlds hypothesis attracts me because it is a logical and reasonable abstraction from the current data. I don’t *know* that it’s true – there are many things out there that we don’t know that could cause it not to be true.

But libertarianism is, in general, the belief that people should be free to act in their own self-interests, and evidence shows that in such an environment, ideas, innovation and trade will thrive and complex systems will emerge spontaneously A simple concept that fits what we know about evolution and trade, that doesn’t require a lot of exceptions, addendums and white-paper clarifications.

Many Worlds is generally the same – it is simple, follows from the basic premise, and fits the data that we currently have. I think that’s why it’s attractive – free market economics are so manifestly proven optimal by such a broad consensus of scientists, that I feel reasonably confident that the same extrapolation of facts is reasonable as a starting point.

BUT, I will be the first to admit that there is simply not enough data to make any claims of certainty about MW.

Frankly, based on what I know of physics and software, it seems as likely, if not more likely, that we are all just constructs living in a simulated universe inside some unfathomably large computer (which, ironically, could be just a toy on the arm of some meta-child)

It has all the simple logical elegance of MW, with some additional facts – in a universe that’s 15 billion years old, how is it possible that no other species evolved spaceflight and colonized the universe before us? How is it possible that we were so lucky as to be the first – if we had developed just a million years earlier, we would already have colonized much of the Milky Way, if not several additional galaxies beyond!

To argue against the simulation theory, we must assume that there is an unfathomably small chance of intelligent life developing, or that every intelligent civilization self-destructs, or that every intelligent civilization is not expansionist, or that computers can’t get much more complex than they are now.

None of those are particularly logically sound. None. It is *possible* that we are the first, or within a few thousand years of being the first civilized species, but how incredibly unlikely. It is possible that *every* intelligent civilization self-destructs, but again, how incredibly unlikely. Based on genetic self-interest, the idea that no other intelligent civilization is expansionist seems ludicrous. Which leads us to the last possibility – computers can’t get much more complex than they are now. Of all of those, this is the most ridiculous.

Ironically, if we accept the possibility that we are living in a simulation, there’s no need or justification for a Many Worlds physics – the meta-computer chooses a path and runs with it. There’s also no justification for a belief in “strongly defined” free will (i.e. free will that operates outside the constraints of the physical world) [as opposed to the weak free will which we all experience]

Note that while I find the Simulated Universe theory compelling, it is also one of the hardest for free-will libertarian types to accept.

Discuss!

25. Eliezer Yudkowsky Says:

Scott, you spend way more time than the average physicist arguing with people who think they can solve crazy expensive problems using exotic physics. This may give you an exaggerated idea of the Speed Prior’s heuristic usefulness, compared to what you would have if you’d also lived through the discovery of atoms and galaxies. Being unable to solve NP-hard problems may be a deep physical principle, but computing physics itself cheaply is not.

Right now, to the best of our knowledge, quantum physics is not computable in polynomial time (otherwise we’d have a polynomial algorithm for factoring composites, right?) and the Speed Prior assigns cumulative prior probability at most 1/N to all explanations with running time >N. Not 1/log(N), 1/N.

This means that if you’d performed one experiment per second over your entire life, you couldn’t possibly have accumulated enough evidence to believe that a 50-micron object could go into a state of coherent superposition – tests of which are apparently currently underway.

From Schmidhuber’s Speed Prior paper:

Now we are ready for an extreme application. Assuming that the entire history of our universe is sampled from $S$ or a less dominant prior reflecting suboptimal computation of the history, we can immediately predict:

1. Our universe will not get many times older than it is now [22] — the probability that its history will extend beyond the one computable in the current phase of FAST (that is, it will be prolongated into the next phase) is at most 50 %; infinite futures have measure zero.

2. Any apparent randomness in any physical observation must be due to some yet unknown but fast pseudo-random generator PRG [22] which we should try to discover.

2a. A re-examination of beta decay patterns may reveal that a very simple, fast, but maybe not quite trivial PRG is responsible for the apparently random decays of neutrons into protons, electrons and antineutrinos.

2b. Whenever there are several possible continuations of our universe corresponding to different Schrödinger wave function collapses — compare Everett’s widely accepted many worlds hypothesis [5] — we should be more likely to end up in one computable by a short and fast algorithm. A re-examination of split experiment data involving entangled states such as the observations of spins of initially close but soon distant particles with correlated spins might reveil unexpected, nonobvious, nonlocal algorithmic regularity due to a fast PRG.

3. Large scale quantum computation [1] will not work well, essentially because it would require too many exponentially growing computational resources in interfering “parallel universes” [5].

So the secondary reason for rejecting the RAM/time bounds is that it doesn’t follow the conjunction-rule logic of the rest of Occam’s Razor. The primary reason is that it gives stupid predictions on physical problems.

26. AwesomeRobot Says:

I think evidence shows that Libertarianism turns the global economy into a giant pyramid scheme.

27. Ari Says:

“Aha!” exclaim the bullet-swallowers. “So then the function must be the infinite series, neither more nor less.”

“Not so fast,” reply the bullet-dodgers. “All we know is that we can approximate the function in a small open interval around x0. Who knows what unsuspected phenomena might be lurking beyond it?”

Crazy analytic philosophers …

28. steven Says:

Everett himself was apparently a libertarian: http://space.mit.edu/home/tegmark/everett/everett23_lynch.html

29. Nick Tarleton Says:

An obvious difference here is that physics carries a stronger expectation of simplicity, and possibly a weaker expectation of the validity of our intuitions, than politics.

30. randomwalker Says:

I came across this paper a while ago: http://arxiv.org/abs/0709.4024 , the so-called “null interpretation” of quantum mechanics. It took me a while to figure out what the hell the author was talking about, but once I did it blew my mind. I don’t know nearly enough quantum mechanics to prefer one interpretation or the other, but I’m wondering if you could share your opinions about this?

Oh, and I’m a libertarian. I disagree with your characterization (but not in the way you think We don’t start from assumptions that most people accept. With regard to the fire department, for instance, I believe that those who don’t have the foresight to pay for fire insurance deserve to get screwed. An assumption most people I talk to vehemently disagree with.

31. Scott Says:

Right now, to the best of our knowledge, quantum physics is not computable in polynomial time (otherwise we’d have a polynomial algorithm for factoring composites, right?) and the Speed Prior assigns cumulative prior probability at most 1/N to all explanations with running time >N. Not 1/log(N), 1/N.

Well, it does if you define it that way!

I’ve spent a fair amount of time arguing with computer scientists like Leonid Levin and Oded Goldreich, who essentially do assign an exponentially small prior probability to explanations with exponential running time, and for that reason (combined with Shor’s factoring algorithm), reject quantum mechanics! Of course I don’t agree with them, but what I like about this Speed Prior perspective is that it gives one way of pinpointing what our difference is.

Personally, if it makes any sense at all to talk about my prior over computable theories of physics (and I’m not convinced that it does), the prior would have to be a complicated one, not describable by some simple weighted combination of program length and (classical) running time. For example, programs with huge classical running times could still get decent prior probabilities, so long as they had efficient quantum implementations. On the other hand, programs that solved NP-complete problems “free of cost” would be penalized heavily.

If this all sounds a bit contrived and post hoc to you — well, that’s why I’m not a Bayesian in the first place! Rather, I’m only a Bayesian in Taylor series expansion about small regions of configuration space — namely, those regions where I’m convinced there’s some prior that reasonably corresponds to how I think.

32. Scott Says:

randomwalker: If you’re publishing papers advocating the Shut-Up-And-Calculate Interpretation, then clearly you’re not really on board with it! Maybe it’s time for SUAC to be retired, and replaced by the even more radical Interpretation About Which Nothing Can Or Should Be Said After Stating Its Name.

33. harrison Says:

I’m not an MWI believer (I guess I’m more-or-less agnostic — all of the potential interpretations of QM weird me out), but I think I’m a fairly hard-core libertarian. (Who sometimes espouses neoconservative ideas just to annoy the hell out of the liberal staff of his school newspaper…but whatever).

As such, I’m gonna go ahead and mount a defense of the bullet-swallowing approach, which goes as follows: If the bullet-swallowers are wrong (especially in scientific disciplines), the worst that can happen is they’ll be embarrassed and progress will start anew. If the bullet-swallowers are right, on the other hand (and they are a positive proportion of the time), they have a head start in getting research done and extrapolating from what everyone eventually agrees is the new starting point. Which is I think unambiguously a Good Thing.

The more cautious group, on the other hand, isn’t really doing that much. The most that can be said for them (again, in a scientific setting; obviously questions of politics can sometimes be measured in lives) is that they tend to dampen undeserved hype (cf. D-Wave, cold fusion). When they’re right, this is again a Good Thing, although much less so than before; when they’re wrong, it actually ends up contributing to the scientific illiteracy of our populace. And when bullet-dodging is taking to an extreme, you get the Flat Earthers and the moon landing people.

I don’t disagree with the general point that libertarians (and MWIers, and some string theory types, and Harry/Hermione shippers, and…) tend to be more dogmatic, even extremist, in their defense of their positions. But if I may quote Barry Goldwater, “Extremism in the defense of liberty is no vice…and moderation in the pursuit of justice is no virtue.”

Anyway, that’s my two cents.

34. harrison Says:

If this all sounds a bit contrived and post hoc to you — well, that’s why I’m not a Bayesian in the first place!

Incidentally, I wonder if there’s a correlation between Bayesianism and libertarianism? They seem to overlap in most of the science-y libertarians or libertarian-y scientists I know…

As a libertarian I see it more as debugging the legal code by turning off functions with side effects.

Federal Resevrve -> distortion of currency value making the market inefficient
Death Penalty -> removes defendant’s right to appeal
IRS -> just overhead unless you have an asset backed currency or have to divert GDP to a major war
War on Weed -> stoners cost a lot less to maintain on their couch

There is also the aspect of fault tolerance i.e. separation of powers between the executive, judical, and legislative.

Also, as the US legal system has classes that must be inherited to the lower levels, additional rules specified by a parent can be devastating to the computational power of classes lower on the hierarchy.

36. onymous Says:

Scott, what do you mean by “Many Worlds”? I don’t care too much for interpretations, so maybe I’m misunderstanding, but I thought it was just an overly-evocative name for the idea that there is no non-unitary collapse. Am I wrong? Because I thought that was the obviously correct interpretation of quantum mechanics, i.e. that decoherence is the real culprit for “collapse” and for the probability interpretation. And I think libertarians are evil.

37. Scott Says:

Harrison: As a factual matter, I’m not convinced that MWIers are “getting more done” than anyone else. Certainly Deutsch was inspired by MWI to think about quantum computing; to me, that’s one of the strongest arguments in MWI’s favor. But many other seminal contributions I know about were made by people who were agnostic or even hostile to MWI. John Bell’s favorite interpretation was Bohmian mechanics (though I’m not sure if he actually “believed” it); Bells attacks MWI in his book “Speakable and Unspeakable.” Umesh Vazirani is, in my experience, skeptical of all interpretations. Peter Shor has written on this blog that

if the many-worlds interpretation makes it easier to think about the research you’re doing in April, and the Copenhagen interpretation makes it easier to think about the research you’re doing in June, the Copenhagen interpretation is not going to smite you for praying to the many-worlds interpretation. At least I hope it won’t, because otherwise I’m in big trouble.
38. Scott Says:

I wonder if there’s a correlation between Bayesianism and libertarianism?

The theory I advanced in this post would very strongly predict one.

39. Scott Says:

onymous: Yeah, I think of Many-Worlds as basically the conjunction of three beliefs.

(1) The entire universe, including human observers, is governed by the Schrödinger equation.

(2) All the decoherent branches implied by (1) are “equally real,” with the anthropic probability of finding yourself in a given branch weighted by |ψ|2.

(3) Statement (2) is actually meaningful.

40. Anatoly Says:

In a different gratuitous analogy from analysis, perhaps we’re trying to learn the universe function sitting at x_0 = 0, but we can’t really see its values, we can only learn the terms of its Taylor series (=set up experiments and see the results). And the n-th term of the series turns out to be 0, again and again, no matter how high an n we manage to estimate.

The bullet-dodgers will say – the fact that it’s been 0 for some n doesn’t mean that it’ll remain 0 all the way, that’s just absurd. The bullet-swallowers will say – you’re just afraid to face the data: in fact the Taylor series is identically 0, and the universe is trivial. And in reality, maybe, just maybe, the universe function turns out to be something like e^(-1/x^2).

41. Eliezer Yudkowsky Says:

Scott, I accept (1) and (2) but deny (3).

42. Robin Hanson Says:

I think Nick has a good point – the stronger the theory and the less we trust our intuitions, the more it makes sense to bite whatever bullets the theory gives us. And what theory has stronger support than quantum mechanics, and where else do we expect our intuitions to be worse?

43. milkshake Says:

Communism looked solid and inescapable to its followers not because of its radical, far-reaching logic – but because of the complete lack of it. It was a mix of sham, fervent wishes, raw ambition and group-think, much like the teachings of the Church of Scientology. By applying the ideologic labels, it provided ready-made answers to its converts while being sufficiently turgid to be “studied seriously” and flexible to allow declaring a class enemy arbitrarily – you became “objectively fascist”, or “lackey” or “serving the interests of reactionary forces” the moment you deviated from the party line.

44. steven Says:

Another correlation I find very striking is the one between MWI and “transhumanism” or whatever you want to call an unusual interest in things like life extension, artificial general intelligence, etc. Some examples: David Deutsch, Max Tegmark, Mike Price of the Everett FAQ, and of course both Eliezer and Robin.

45. Scott Says:

It was a mix of sham, fervent wishes, raw ambition and group-think, much like the teachings of the Church of Scientology.

Speak for yourself. Personally, I find the Church of Scientology to be a highly rational and self-critical organization, whose members patrolling the blogosphere would NOT want to sue me, break into my apartment, and call everyone who knows me looking for dirt…

46. steven Says:

Oh, and I forgot Frank Tipler, heh.

47. Utilitarian Says:

If Scott’s theory is correct then utilitarians/consequentialists should also be more likely to endorse MWI. This group overlaps significantly with some identified as libertarians (Robin and Eliezer’s systematic ethical commitments would seem to be much better described as consequentialist than libertarian), but is distinct.

On the distinction between nerd and academic endorsement of weird results, part of that may reflect the vulnerability of each to attack: nerds working in the technology industry or with many weird beliefs face few additional social penalties for endorsing MWI.

48. ScentOfViolets Says:

Steven, per your #44: again, the likely culprit is science fiction. Can you think of any sf tropes that you cannot correlate with libertarianism? The High Frontier – libertarianism. Uploaded minds or Minds – libertarianism. Robots (the sf sort) – libertarianism. Nanotech – libertarianism.

Hmmm . . . I’m sitting here avoiding grading a final in ‘business calc’ . . . the only readily identifiable trope in sf I can’t readily associate with libertarianism after five minutes of thought is time travel. Possibly. I think. I’m not a strong believer in any of the above, btw, and I read cheesy sf, cheesy detective stories, cheesy fantasy, cheesy regency romance . . . and YA novels, some of them quite good.

49. John Sidles Says:

ScentOfViolets says: “Can you think of any sf tropes that you cannot correlate with libertarianism?”

The short answer is “yes.” Norman Spinrad’s outrageously transgressive SF novel The Iron Dream portrays the classic SF tropes as amounting to … well … Nazism … by asking “What if Adolf Hitler had failed as a painter, but succeeded as a SF writer?”

Rudy Rucker’s excellent Master of Space and Time explores many of the same themes, but Rucker emphasizes comedy rather than satire.

Other SF novels whose comedic exterior cloaks darker themes are Herbert Schenck’s ur-steampunk classic The Steam Bird and Harry Harrison’s Bill, the Galactic Hero.

50. ScentOfViolets Says:

But those aren’t tropes like rockets & rayguns.

51. Ian Durham Says:

I must take issue with one thing. I’m a libertarian (though a pragmatic one, and perhaps that’s the difference), and I don’t buy MWI. As to why, it has to do with permutation invariance, but I won’t bore you. If you’re dying of curiosity, see here.

52. onymous Says:

All the decoherent branches implied by (1) are “equally real,”

I have no idea what “real” means, so probably by this definition I’m not a Many Worlder. Thanks! (I was afraid if you were lumping me in a barrel with some libertarians, one of them might get hungry and eat me.)

53. Drew Arrowood Says:

At one time, it was generally accepted that the way in which scientific theories changed was an “old guard” died off, and the “young turks” took over.

Of course, Kuhn showed in the case of the quantum theory that this simply wasn’t true, marching his way through the data point by point.

This opposition of the bullet-swallowers and the bullet-dodgers i(who is right more often) is subject to just such a test — by looking at the historical record. It would be evidence, I think of the pragmatic value of one or another outlook based upon the historical record of “contests won”.

54. Joseph Hertzlinger Says:

Libertarians currently make up a disproportionate fraction of SF fans, but it’s not the first choice of SF political philosophy. The ideal State would be liberal fascist — a benevolent planned society under the benign guidance of SF fandom. (This explains the popularity of stories featuring the Second Foundation, Lensmen, or the Psychology Sevice.) A few decades ago, many of us came to our senses and realized the likelihood of such a society is of the same order of magnitude as the Statue of Liberty turning cartwheels. We then decided to settle for the next best thing, which is to ensure the mundanes have as little power as possible.

55. ScentOfViolets Says:

There is also the issue of classifying what sorts of hypotheses go into the ‘dodging the bullet’ column and what goes into the ‘swallowing the bullet column’ before the fact, as opposed to after. Take the example given above of the prediction of the neutrino. iirc from Gamow’s “Thirty Years That Shook Physics”, it was not at all obvious which was the more fantastic hypothesis at the time, positing a particle like the neutrino, or the violation of the conservation of energy. To here Gamow tell it, Pauli would have assumed that a new particle would be dodging the bullet, while others like (iirc) Bohr would have said it was a clear case of swallowing it. So there needs to be some selection criteria before Scott’s question can be analyzed.

56. cody Says:

just want to say, i really think your numerical approximation analogy is excellent, i find it reminiscent of Wheeler’s suggestion:
“We live on an island surrounded by a sea of ignorance. As our island of knowledge grows, so does the shore of our ignorance.”
(though i have no source, ive seen it attributed to him.)

i wish i had more (enough) time to follow this discussion more closely.

57. Alex Says:

Sorry to deviate from the subject, but why does everybody dismiss Marx’s prediction that capitalism will soon end in a crisis? While he might have been wrong on some other questions, his arguments for why capitalism was soon to collapse seem pretty convincing to me. Maybe his prediction isn’t totally wrong, he was just wrong about how soon. He just didn’t take into account certain (unforeseeable at the time) factors like outsourcing and immigration, which provided alternative sources of cheap labor, and hence delayed, not prevented the crisis.

58. Scott Says:

Alex: For me the key points are that

(1) contrary to Marx’s prediction, conditions in capitalist countries got better, not worse, as they co-opted a few aspects of communism while rejecting most of it, and

(2) the fact that “full-scale communism” immediately devolved into a horrific farce everywhere on earth it was tried, casts doubt on the idea that the admittedly-severe crises of capitalist countries are because of their capitalism.

Incidentally, funny story. Some friends and I went to an anti-Bush rally in New York in 2004, partly out of curiosity. A large group of Republicans “infiltrated” the rally, holding up signs like “COMMUNISM ONLY KILLED 100 MILLION PEOPLE: IT’S TIME TO GIVE IT ANOTHER CHANCE” and “YASSER ARAFAT: TERRORIST OF THE YEAR.” After a few minutes of screaming back and forth, physical fights actually broke out between some of the “true” protesters and some of the “infiltrators,” which had to be broken up by police, and the Republicans left. Had I been able to talk to them under sane conditions, I would’ve told them I completely agreed with them about the sufficient falsification of communism and many other questions — yet found that perfectly consistent with despising Bush!

59. Alex Says:

Here’s a tentative argument in defense of Marx:
Capitalism’s success and the total disaster that communism turned into are stated as the reasons for why Marx was wrong:
1- There are three major places where capitalism was a success. The U.S: Managed to offset the crisis by continuously importing laborers who accepted to work under horrendous conditions. Japan: Managed to offset crisis by implementing communism in disguise by relegating the role of the state to large corporate groups (lifetime employment, housing provided by the company you work for, etc…). Western Europe: Managed to offset the crisis by doing a little of both (socialist welfare and labor laws, and immigration).

I am probably wrong, but I seems totally possible to me that when the 3rd world catches up economically and industrially with The U.S, Japan and W.E, then Marx;s predicted crisis might happen.

Also that communism failed doesn’t mean that there isn’t any problem with capitalism. It just means that communism isn’t the solution.

60. harrison Says:

Joseph: Of course, see that old Tears for Fears song…

61. Robin Hanson Says:

Utilitarian is right, preference utilitarian consequentialism is a better analogy than libertarians, as it has longer chains of reasoning from the theory to the counterintuitive conclusions.

62. Cliff Says:

I know nothing about MWI but would consider myself a libertarian. I disagree with your lumping libertarianism in with anti-capitalist beliefs and space colonies. It is no coincidence that many expert economists are libertarians/libertarian-leaning.

To me, the distinction is a deep abiding belief in common sense and intuition. Libertarians don’t have it. The average person, when presented with a conclusion that intuitively seems wrong, simply dismisses it without considering how it was arrived at, because it does not mesh with accepted wisdom.

Libertarians (to over-generalize) believe that intuition is frequently wrong and that we have to use the best tools at our disposal and trust in their results even when they seem counter-intuitive. Many such results are testable at least in a limited way and all available evidence supports the general superiority of expert analytical tools wielded by experts over common sense.

63. docmerlin Says:

I am a physics graduate student, NOT a many worlder and am a Libertarian. I am a libertarian, mostly because I don’t believe that people are good enough or perfect enough to have a working, fair functioning government past a certain size.

64. Jesse Walker Says:

It’s obvious, isn’t it? Libertarians like the idea of parallel universes because they would allow us to establish Nozickian utopias on a cosmic scale.

65. Jesse Walker Says:

(That was a joke.)

66. Mario Says:

There is a nice article over at that holdout of the “Austrian” school that might be interesting in this context. It is rather lengthy, but I think it is fair to say that it advocates ignoring evidence in favor of purely rational argument, on the basis that there exists “self evident truths” with which you can start. If evidence appears that seems to refute a logical consequence of such a self-evident truth, then, obviously, the evidence is wrong for some reason. The piece is this one:

http://mises.org/story/1999

67. Scott Says:

I think it is fair to say that it advocates ignoring evidence in favor of purely rational argument

Which is what we tried to do for a couple thousand years. Alas, outside of pure math, we’re not nearly as good at it as we think.

68. Niel Says:

Scott: I was referring to the the sort of “hatin'” that, for instance, wouldn’t allow you to see that I was playing along with you when I said that you were “hatin'”. Also, the sort of “hatin'” that leads you to posit an isomorphism between MWI with a naive political ideology, and describing its followers as dangerously foolish in the first place, even if in jest.

I find the idea that there are Many Worlds as far-fetched as the fact that -1 has a square root, and basically feel that these two ideas have the same ontological status. (I should probably remark here that I am a formalist.) I just find it strange that so many people who readily accept the latter complain so energetically about the former.

I consider the analogy with sqrt(-1) almost exact — if there the MWI correlates with some sort of naivete, it is not that of the political ideologue, but rather of the mathematical platonist. But even then, platonism isn’t necessary to find the MWI very appealing, any more than it is necessary to find Argand diagrams appealing.

69. ScentOfViolets Says:

Are there any examples of bullet dodging or bullet swallowing in pure mathematics? I can think of a number of surprise results, but maybe by definition such categories are disallowed. Does this mean that the proportion of libertarians to non-libertarians is about what you’d expect it to be ?

70. wolfgang Says:

Scott,

there are of course various sub-categories of every philosophy.
In the case of the MWI one could distinguish between those willing to play Russian Roulette and other less extreme proponents.
Only those in the first sub-category are true bullet – swallowers in my opinion.

71. Ian Durham Says:

It’s obvious, isn’t it? Libertarians like the idea of parallel universes because they would allow us to establish Nozickian utopias on a cosmic scale.

Or, perhaps, Paulian utopias…

72. Scott Says:

Also, the sort of “hatin’” that leads you to posit an isomorphism between MWI with a naive political ideology

I love it: some criticize my hypothesis because they think it tarnishes libertarianism, others because it tarnishes MWI…

73. Scott Says:

Are there any examples of bullet dodging or bullet swallowing in pure mathematics?

It’s funny you ask: I was going to use Gödel’s Theorem as an example where the bullet-dodgers turned out to be right. That is, in the 75 years since the theorem was proved, we arguably haven’t seen a single example of a “normal” problem — not essentially dealing with Gödel sentences or transfinite set theory — proven independent of ZFC. So someone who “bit the bullet” in the 30’s and decreed the end of mathematical certainty would arguably have been wrong. However, this example raised too many side issues: for instance, did any serious mathematicians bite the bullet that way? If they did, wouldn’t it have been just a guess rather than an extrapolation from a theory? Could P vs. NP and lots of other “normal” problems be independent of ZFC but we just don’t know it?

74. John Says:

I don’t think that Libertarianism is necessarily a ‘bullet swallowing’ theory. Libertarianism can work – but so what? That’s not earth shattering nor would the existence of a working Libertarian society give us any insight into the underlying behavior of the universe – something I would deem far more significant – like the existence of MWI would.

I believe ‘working’ social behaviors are a function of the behavior of those who make up the society. The interest in Libertarianism merely stems from the fact that Libertarianism emerges as a good ‘working’ social behavior for the general behavior of those that would likely be interested in something like MWI – a relatively esoteric subject. Therefore those that would typically be interested in MWI would also typically be interested in Libertarianism.

It proves nothing about the validity of Libertarianism.

75. g Says:

From “Shut up and calculate”: “So here’s a testable prediction of the mathematical universe hypothesis: if we exist in many parallel universes, then we should expect to ﬁnd ourselves in a typical one… If we ﬁnd that this distribution makes the value measured in our own universe highly atypical, it would rule out the multiverse, and hence the mathematical universe hypothesis.”

Would it? A particular distribution is only “atypical” with respect to some mathematical formulation. The measurement is not falsification that the mathematical universe hypothesis is wrong, but rather that your particular formula of everything – wherein the measurement is atypical – is incomplete.

To argue against the mathematical universe hypothesis itself, you’d need to demonstrate that the measurement is atypical for the entire set of otherwise-consistent formulas of everything (or perhaps just “most” of them). Without that, the measurement simply indicates that your formula is wrong – which is exactly how we handle measurements that are atypical with respect to our current and historical formulas.

76. Silas Says:

we arguably haven’t seen a single example of a “normal” problem — not essentially dealing with Gödel sentences or transfinite set theory — proven independent of ZFC

Scott_Aaronson: My math terminology knowledge is lacking, but IIRC:

“X is independent of ZFC” = ZFC axioms do not suffice to prove or disprove X

“‘normal’ problem” = problem that the average person would interpret as meaningful to real-world scenarios; “This statement is false” does not count.

So, you’re saying that since the time of the proof of Goedel’s theorems, the only examples of statements mathematicians can find, that are true but unproveable, are “meaningless” statements like “This statement cannot be proven”?

Because I thought this common response was at some time refuted?

(Sorry if I don’t meet the prerequisites for posting here.)

77. Scott Says:

It proves nothing about the validity of Libertarianism.

Let me be clear: I wasn’t claiming any such thing. (I do have disagreements with libertarianism — particularly in its strong “Austrian” version — but that’s for another post.)

78. Michael Bacon Says:

“I love it: some criticize my hypothesis because they think it tarnishes libertarianism, others because it tarnishes MWI.”

False dichotomy: it can in fact tarnish both

79. Michael Bacon Says:

Or neither . . . .

80. Scott Says:

Silas: There are no prerequisites for posting here.

The experts should correct me if I’m wrong, but AKAIK all statements that have been proved independent of ZFC fall into two categories:

(1) Metamathematical statements like “This statement cannot be proved”, together with their encodings into Diophantine equations and other mathematical structures. (These encodings are often highly nontrivial, but still don’t yield specific Diophantine equations, etc. that mathematicians would care about for non-logical reasons.)

(2) Statements about transfinite set theory — like the Continuum Hypothesis, that there are no sets smaller than the reals and larger than the integers. (These statements have the property that they can’t be phrased using first-order quantification over integers, i.e., in terms of Turing machines and whether they halt. To me, that’s close to a definition of “irrelevant to the real world” in this context.)

We do know some reasonable statements about integers that are provably independent of PA, like the famous Goodstein’s Theorem. But those statements are provable in ZFC.

81. Luca Aceto Says:

Caveat: I am not an expert on these matters. However, an example that does not seem to me to fall into either group is the Whitehead problem in algebra, which has been shown to be independent of ZFC by Shelah. He also showed that the Whitehead problem remains undecidable even if one assumes the Continuum hypothesis.

82. Paranoid Android Says:

It sounds like a normal statement about group theorie but it has been proven undecideble in ZFC.

83. Scott Says:

Luca and Paranoid: I hadn’t heard of the Whitehead problem; thanks! Reading about it, it seems pretty clearly to fall into category (2). That is, it asks about abelian groups of uncountable orders, which of course aren’t finitely generated. (Note that the problem for countable abelian groups does have a definite answer.) And a priori, there’s no reason to expect questions about uncountable groups to be first-order over the integers (i.e., expressible in terms of Turing machines and whether they halt), which is my key criterion. Since Gödel and Cohen, one’s already reconciled oneself to natural questions about uncountable sets being potentially undecidable.

I certainly don’t mean to denigrate independence results — they were one of the highlights of 20th-century mathematics! But while it didn’t have to turn out this way, natural problems that are expressible in terms of Turing machines seem to have mostly escaped the Gödelian scythe.

84. Jack in Danville Says:

Scott,

I may have misunderstood:

“..the Continuum Hypothesis…close to a definition of ‘irrelevant to the real world’…”

Intuitively I’ve thought the Continuum Hypothesis describes an aspect of the real world.

Good essay! I think the failure of libertarianism is a crisis for western culture and civilization in general. I’ve lately thought about starting a blog dedicated to the subject, but between work and home improvement projects I don’t feel I have the time to give it the serious attention it deserves. In other words I’m chickening-out and “tending my garden”, as Voltaire advised (but didn’t necessarily practice).

85. John Sidles Says:

This is a fun topic!

To make progress on these difficult quantum questions, perhaps we need something stronger than a mere metaphor … perhaps we need the power of an allegory?

Let us choose as an allegorical text Goldilocks and the Three Bears., viewing the bowls of porridge as allegories for quantum state-spaces.

The mama bear’s bowl is stated to be “just right” — neither too large or too small. This can only be a reference to the linear Hilbert space of orthodox quantum theory, which is neither too large (so as to solve NP-complete problems in polynomial time) nor too small (so as to be simulated with classical resources). On these spaces model order reduction is accomplished by the elegant techniques of group theory.

The baby bear’s bowl is stated to be “too small”. This likely refers to the reduced-order polynomial state-spaces of quantum chemistry, matrix product states, etc. … algebraic varieties whose Kahler potentials are multilinear. On these spaces model order reduction is accomplished by (essentially) the Dirac-Frenkel variational calculus, which amounts to geometric projection of linear quantum theory onto curved manifolds.

The papa bear’s bowl is stated to be “too big”. Gosh … a quantum state-space bigger than Hilbert space!? What mathematical object could this be?

For readers conversant with compressive sampling (CS) theory, one possible candidate is an (overcomplete) dictionary of states. We imagine a matrix whose columns are normalized Hilbert space vectors. If we require that each column be exactly orthonormal to all the others, than (obviously) the number of columns in this matrix cannot exceed the number of rows.

But recently it has been shown (by Candace and Tao, and many others) that if require only that the columns be approximately orthonormal—technically the columns must satisfy a restricted isometry principle (RIP)—then there can be exponentially more columns than rows … even if the number of rows is the dimensionality of the Hilbert space.

These column states can be regarded as “words” in a dictionary … a dictionary with exponentially more words than Hilbert space has basis vectors. This immediately calls to mind Borges’ Infinite Library. From a more concrete point of view, it raises the mathematical question of how to construct such an RIP dictionary … which in turn allows all the mathematical techniques of coding theory to be brought to bear.

What has been gained? Well, suppose we focus on states that can be written as sums of a small number of (not necessarily orthonormal) columns. In CS theory such states (whether classical or quantum) are called compressible objects. It turns out that calculations involving compressible objects can made be very efficient (even when the number of columns is super-exponential) via the techniques of convex optimization—potentially even more efficient than calculations based on mama bear and baby bear state-spaces.

All of these ideas are very well known to the (rapidly growing) compressive sampling community, but they are only beginning to be applied to practical quantum calculations.

Yeah, but what fundamental insights are gained by dining from the quantum papa bear bowl? One possible answer is provided by John Wheeler’s famous quest to derive “it from bit.” Namely, CS theory provides a concrete mathematical starting point for undertaking Wheeler’s quest: maximize the informatic quantity/quality of it computed from a minimal quantity/quality of bit.

The CS version of “it from bit” can be as mundane as computing the clearest possible picture from the smallest quantity of camera data, or as abstruse as estimating a quantum state from the smallest number of measurements — both problems are in “the papa bear bowl” … in the sense that the same CS algorithms solve both problems with equal facility.

The resulting mathematics is very beautiful (as readers of Terence Tao’s blog know). And history indicates that beautiful quantum physics and beautiful quantum mathematics are always found near to one another.

My own opinion is that it’s pretty the same porridge in all three bowls—in the sense that Kahlerian algebraic varieties, Hilbert spaces, and CS dictionaries all basically describe the same fundamental mathematical object … even if we at present only dimly perceive what that fundamental object might be, and how best to make practical use of it.

Did anything good come of this allegorical investigation? Well, it suggested some fun mathematical problems … like the problem of reconstructing quantum states from sparse random projections. Which in turn inspired our group to create a QSE/QIT slide with a picture of “The Three Bears” on it!

But more usefully, the “Three Bears” allegory provides a concrete alternative to the dichotomy of “dodging the bullet” versus “swallowing the bullet”.

86. Douglas Knight Says:

Harvey Friedman is trying to produce natural combinatorial statements that are independent of ZFC (and, in fact, equivalent to higher cardinal axioms). My understanding is that he hasn’t produce examples that are natural enough, but I think he has produced examples that pass SA’s test.

87. Scott Says:

Douglas: I’ve seen Harvey Friedman’s examples, and they don’t pass the “natural” test. But I wish more people were pushing in the same direction that he is.

88. Mario Says:

I think it is fair to say that it advocates ignoring evidence in favor of purely rational argument

Which is what we tried to do for a couple thousand years. Alas, outside of pure math, we’re not nearly as good at it as we think.

Now now. Yours is an “evidence suggests” kind of argument – and that won’t work! (FTR: I too find this “austrian” school bizarre, not least because of such articles as the one I linked to).

89. Cliff Says:

John, It’s not the Mama bear’s bowl that was just right, it was the baby bear’s! Don’t worry, you’re not the only one that gets this wrong… I won a bet about it.

90. John Sidles Says:

Cliff — until recently, our QSE Group has dined mainly from the baby bear’s bowl … but as this picture of the Three Quantum Bears shows, we are seriously contemplating dining from the papa bear’s bowl too!

I’m curious … what was the bet, and how did you win it?

91. JOE Says:

It seems to me this guy is smart but has not studied psychology. His bullet epitaphs seem sophomoric. He could just say indecisive and decisive. I’m all for dividing people into two kinds of people. I even have a list on a word file in my documents for just that purpose. I would not add this to my list. The decision to be decisive or indecisive is not situational.

92. John Sidles Says:

With regard to Cliff’s bet … in the words of Mark Twain … “the fact that he had been played upon with a joke had managed to bore itself, like another Hoosac Tunnel, through the solid adamant of his understanding.”

… Cliff, you were talking about the literal Goldilocks story, not the quantum allegory. Doh!

And your bet was absolutely winning … contrary to all laws of thermodynamics, the Goldilocks story claims that the mama bear’s medium-sized porridge bowl cooled fastest.

Even as a small child, I remember thinking that was odd.

93. Walt Says:

I live to pose as an expert, Scott. Your two points are basically true. You can quibble over the first point in that the reality of it can be hidden to a great extent. (So for example there is an initial configuration for the Game of Life so that it is undecidable in ZFC whether it has a final configuration. This is not a natural configuration in that you would never come up with it if you weren’t looking for it, but this is still a pretty concrete example.)

Also, there are lots of examples of natural but undecidable second-order statements (the Continuum hypothesis is third-order), which means that real analysis is plagued by incompleteness.

94. Scott Says:

the Continuum hypothesis is third-order

Interesting! If we can’t explicitly construct a set of size Aleph1 (say because we don’t have AC), then does CH become fourth-order? (“For all subsets of reals, either there exists a bijection with the reals (a pairing such that for every element there exists a unique partner), or else there exists a bijection with the integers.”)

If so, it reminds me of Andy Drucker’s observation, that we seem to need the existence of complete problems to reduce P=NP from a third-order to a second-order sentence. And thus, for example, it’s not clear how to express P=BPP with only two quantifiers.

95. Bob Hearn Says:

Both theories seem to have a strong following with nerds who read science fiction and post to Internet discussion groups, but a relatively poorer following with both John Q. Public and Alistair K. Intellectual.

I’m late to this party, but my impression is that MWI or MWI-like interpretations are perhaps the predominant current views of most cosmologists, as well as most string theorists.

(For the record, I’d describe myself as an MWI-er, perhaps in a generalized sense, but not a libertarian.)

96. Jens Hartree Says:

@John Sidles:

These column states can be regarded as “words” in a dictionary … a dictionary with exponentially more words than Hilbert space has basis vectors.

I know the post was jestful, but I’m confused whether it’s meant to be true or crackpot-ish? Assuming it’s meant in earnest:

1) Then the states cannot be linearly independent: Any vector space, Hilbert or other, has dimension equal to the cardinality of a linearly independent spanning subset. Any linearly independent set that spans the space is called a basis, and any such set will have the same cardinality.

2) The space needed to describe any physical system I could even imagine would be infinitely dimensional. I have never, ever seen a quantum problem that can be described exactly with finite dimension: most observables are not even discrete, but have spectra containing both a discreet and a continuous part! What is the meaning of “exponentially more” than infinitely many?

contrary to all laws of thermodynamics, the Goldilocks story claims that the mama bear’s medium-sized porridge bowl cooled fastest.

Even as a small child, I remember thinking that was odd.

I’ll be a party pooper and note that mama bear’s porridge was not too cold, but rather too salty, obeying all laws of thermo dynamics.

97. John Sides Says:

Hi Jens! I cheerfully stipulate to having borrowed those (seemingly paradoxical) ideas on over-complete sets of states from Emmanuel Candes and Terence Tao!

Rather than write a long account of how these ideas work, I refer you to two fine blogs (here and here) that Tao has written on this subject (these two blogs are highly recommended to anyone who with an interest in quantum mechanics and/or information theory)

Translating Candes and Tao’s ideas to the quantum domain is easy. We begin with the statement: “Visual fields are compressible objects, in the sense that we naturally record them as (large) TIFF files, and we naturally store them as (compressed) JPEG files.”

Then we map quantum statesvisual fields, Hilbert vectorsTIFF files and matrix product statesJPEG files.

And we’re done!

Namely, we find that all of the remarkable mathematics of Candes and Tao works just fine in the quantum domain … including seemingly wild mathematics like algorithms for high-fidelity reconstruction of quantum states from sparse random projections … and the construction of sets of basis vectors that are nearly orthonormal, and yet have a dimension that is exponentially larger than Hilbert space!

There is of course a deeply mysterious aspect to the undoubted practical utility of this mathematics. Namely, why is it that classical state vectors are ubiquitously compressible? I leave this question to the readers of this blog to answer!

As for why quantum state vectors are ubiquitously compressible, that’s not nearly as big a mystery: pretty much any quantum state that has been in contact with a measurement-and-control apparatus … or a thermal reservoir … is a compressible object in the sense of Candes and Tao.

98. Walt Says:

Scott:

In the sense I’m thinking of, your formulation is still third-order (About a single real = second order, about sets of reals = third order).

Though otherwise what you say is true. Most of real analysis seems to be about third order concepts (it’s full of talk about “the set of all open sets of a topological space”), but can for all practical purposes can be reduced to second order by use of complete problems.

99. Eric H Says:

Seems to me this can be taken in many directions. For example, the people who have found they can use second best theory to justify any state intervention — aren’t they also bullet swallowers? They seem to believe that their anti-libertarianism can also be derived from basic principles. Some of them claim an empirical route (frequently deriving ought from is), but I think this is usually an effort to demonstrate their ideology-freeness.

Also, MWI seems both plausible and irrelevant to me so long as there is no interaction between this and the other worlds. I guess I’m in the “mental note” category. I’d say I was a libertarian, but not of any form that I think can be derived as you describe it. David Friedman’s Machinery of Freedom makes a case why it cannot be, and my passing acquaintance with Gödel hammered that home.

Well, libertarianism can be seen as a conglomerate of ideas started in different domains with somewhat similar political consequences. There are moral logicians, then there are empiricists, utilitarians and a lot of other non-ideological groups. Libertarianism per se is not a political theory, rather an umbrella group with a broad purpose, but no leadership, nor a coherent platform.

MWI differs fundamentally from libertarianism in that it has no stake in morality, politics, or life in general. Whereas, many people have a stake and a moral/emotional investment in government.

All prejudice about MWI will be eliminated with the first conclusive experiment and their proponents, if they call themselves scientists, will have to accept these consequences. But it’s unlikely those heavily invested will abandon their ideas so readily.

As for my personal touch. Libertarianism may not be correct because it is economically efficient, but that it extends some common sense ideas of morality: don’t steal, don’t defraud, don’t harm without provocation. Because, after all, which criteria do we use? Economics only gives us a set of tools, the actual choice is made by people, hence moral.

Regards.

101. Raoul Ohio Says:

JB’s remark,

After reading JB’s remark, I suspect those who think galactic colonization is possible are likely to be Libertarians and believe in MWI. Does anyone want to to guess a probability that that a human will ***ever*** go to Mars and return alive? I will put my guess out first: P(H2M2EA) = 0.01.

102. John Sidles Says:

For those who are interested in reading further on the topic of larger-than-Hilbert dictionaries of states, two key search term is restricted isometry property (RIP) and uniform uncertainty principle (UUP).

As yet, there is no standard reference on the subject … in part because the subject is new, and in part because RIP-related research touches very many other areas of mathematics, quantum physics, and information theory.

Three recent arxiv preprints (there are dozens more) that are RIP-related are 0804.4666 for classical information theory, 0805.1190 for quantum chemists, and our own QSE Group’s 0805.1844 on practical recipes for simulating large-scale quantum spin systems.

None of these preprints reference one another … in fact you have to read pretty closely to realize that the quantum chemists are talking about RIP-related mathematics.

Only slowly is the realization dawning that we are all working on pretty much the same set of fundamental problems … using pretty much the same set of conceptual tools … and reaching pretty much the same (enjoyable) mathematical conclusions … about the surprising virtues of state-spaces that have many more dimensions than usual … even more dimensions than Hilbert space.

My own opinion is that once the practical implications of RIP geometry is better understood, the resulting algebraic/ geometric/ informatic mathematical arena will be cheerfully explored by the fundamental quantum theorists and philosophers … it’s happened before!

103. John Sidles Says:

As a follow-up to the above reference to arxiv:0804.4666, Combining geometry and combinatorics: a unified approach to sparse signal recovery, today’s Nuit Blange has a link to Anna Gilbert’s talk on this work, along with links to several other talks from the just-concluded workshop Nonlinear approximation techniques using L1.

AFAICT, there were *zero* talks on quantum information theory at this L1 workshop … but there *should* have been … because the mathematical themes of QIT mesh almost perfectly with the themes of L1 informatics that are developed in Anna’s talk.

One wonders, for example, how the surprising capabilities of L1 reconstruction relate to Scott’s equally surprising theorems on the learnability of quantum states?

Equally interesting (IMHO) was the talk by Dobrev, Guermond, and Popov titled Approximating PDE’s in L1. Those of you who have been tracking Terence Tao’s lectures on the Poincare Conjecture will recognize the overlap in subject matter … it would be interesting indeed (IMHO) if Perelman’s proof could be simplified via these emerging L1/PDE techniques.

The point being, that even though this thread began as a meditation on highly abstract questions of fundamental physics and information theory, some of the most interesting and powerful new mathematical tools for answering these high-level questions are emerging from a classical nuts-and-bolts context.

104. Gasarch Says:

A simple question/speculation:

Libertarians (and others with extreme views) DO serve
a purpose— they force us to re-examine our own point of view.
This is healthy and good. And, on some issue, they
may be correct OR at least lead us to modify our views.

QUESTION: Do many-worlders serve the same purpose?

105. John Sidles Says:

I recall reading somewhere that many cosmologists regard the visible universe as being uncomfortably small … because if the visible universe were the size of a large domed stadium, galaxies would be the size of dimes. Cosmologists regard the visible universe as being kinda skimpy!

I often have the same feeling with regard to Hilbert space … it is a very awkward size … the universe would be better-designed IMHO if its quantum state-space dimensionality were either much smaller (as Ashetkar and Schilling would have it) or much bigger (as Candes and Tao would have it).

Unfortunately (or fortunately) it seems that any one of these three eventualities is amazingly good at emulating the other two … of all the mysteries of quantum mechanics, its dimensional quasi-invariance is for me the most central.

For further meditation … with tongue-in-cheek … I comment this video meditation on how much bigger the world is, than we might at first imagine it to be … voiceover by Stephen Hawking, music by the Dixie Hummingbirds, and concept-bending “footage” by the never-imitated Rodney Mullen.

106. Scott Says:

Libertarians (and others with extreme views) DO serve
a purpose— they force us to re-examine our own point of view.
This is healthy and good. And, on some issue, they
may be correct OR at least lead us to modify our views.

QUESTION: Do many-worlders serve the same purpose?

Bill, that’s actually a really perceptive point. In my experience, yes, many-worlders can serve a similar purpose — as can Bohmians and other people with strong views about quantum mechanics.

107. Ian Durham Says:

I must take issue with another point. While “mainstream” Libertarianism (if there is such a thing) may be viewed as extreme, there are an awful lot of people like myself who call themselves Libertarian but who really see themselves as moderate and see many Libertarian ideals as being just that – a balance between right and left (and up and down – the usual dichotomy is really not terribly accurate and the Libertarian party actually has a little graphic about this on their website). So, for instance, we could still support many excellent causes while cutting the federal budget if we spent our money more wisely (the old ’80’s joke about the Pentagon spending \$500 on a toilet seat still holds true today). Though perhaps the entire concept of government (not to mention economics) ought to be fundamentally rethought from the ground up (not that anything will ever really change, of course).

108. Raoul Ohio Says:

Ian, I would like to point out that governments (not to mention economics) are complex entities that have evolved from competing forces of all sorts. Nobody can even understand how they work, let alone rethink how to build a better one from scratch.

Nevertheless, many think they have the perfect government figured out. Sometimes they get in power. When their dingbat ideas are confronted by reality, they often resort to killing people to prove they are right. An exceptional example is Pol Pot, who is often credited with hitting the 0.25 mark before retirement.

Those proclaiming simple fixes for intractable problems (government, the environment, aging, …), might notice they get humored a lot.

109. Chris Drost Says:

I was mostly a libertarian until I read Mike Huben’s Non-Libertarian FAQ and realized that something about libertarianism just smelled funny to me. (I had also flirted with Ayn Rand and importanceofphilosophy.com, but I quickly realized that their worldview was too simplistic and dogmatic.)

I paid lip-service to the many-worlds interpretation until I came up against refutations of Cartesian dualism. At around that point, I reflected on how obvious it seemed that we are a part of the world and that we shouldn’t deny that of ourselves. The most straightforward many-worlds theory I knew was something I called the buckyball-manyworlds theory, which holds that dualism is true, there is a multiverse consisting of all possible material states and configurations, like a graph, and our conscious experience more or less “walks” from node-to-node, sometimes consciously (e.g. decisions), and sometimes unconsciously (e.g. the passage of time). The name came from the complicated graph-like pictures of buckyball molecules that you saw in the news in the early 2000s, before Jan Hendrik Schön was revealed to be a fraud.

But then I got access to a wonderful set of The Teaching Company lectures on Philosophy of Mind, by John Searle. His criticism of dualism and emphasis on the obvious picture — that brains somehow cause minds, and minds somehow cause things like body-movements et cetera — really struck a chord with me. Also, I took Cornell’s applied-physics course on QM and listened to the Feynman lectures on QM; I read QED. The whole process was really fast-paced, but it gave me a better appreciation of the field.

I don’t know what can be learned from my experience. Maybe libertarianism and the many-worlds interpretations are both simply unable to handle the complexity of the real world. In that case, the libertarian and the many-worlds proponent both correlate strongly with the set of people who can’t see the large-scale complex consequences of their small-scale simple philosophies; and perhaps they then correlate with each other indirectly via that set.

110. fishfry Says:

Scott, I really like your blog. This is the first time I’ve had occasion to think you’re losing it.

Libertarians don’t want there to be fire departments? Nonsense. Perhaps some libertarians want fire departments privatized, but that’s not the same as not wanting to put out fires. After all, the doctor who removes someone’s tumor doesn’t work for the government, and that’s certainly a life-saving function.

Secondly, you referred to your “lifetime of web surfing.” That would make you about 12 years old, at best.

111. Scott Says:

This is the first time I’ve had occasion to think you’re losing it.

Really? Then you must not have been reading much…

Perhaps some libertarians want fire departments privatized, but that’s not the same as not wanting to put out fires.

Sorry; I assumed readers would understand I was talking about the former.

Secondly, you referred to your “lifetime of web surfing.” That would make you about 12 years old, at best.

I was born in 1981, and started using the web in 1993. Even if it had been invented by 1981, I couldn’t have used it for much before about 1988. So “lifetime” seemed pretty accurate.