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But I am deeply dishonored, having turned out to be the dead Schrodinger's Cat.
"Yes," if Schrodinger's Cat is found to be dead; "no" if it is found to be alive.
Gotta have that continuous support too, which is the real key to converging on a cycle rather than a point.
In the fuzzier world of not a definite for-real underlying distribution, I note that multiple equilibria or basins in dynamical systems can give the multi-modality that within a herding framework can lead to some sort of cycle in bouncing back and forth between the dominant states.
Diaconis and Freedman.
Cyan,
Why should there be convergence to some such point when there is no underlying "true" distribution, either subjective or objective? Are you counting on herding by people? It is useful to keep in mind the conditions under which even in classical stats, Bayes' Theorem does not hold, for example when the underlying distribution is not continuous or if it is infinite dimensional. In the former case convergence can be to a cycle of bouncing back and forth between the various disconnected portions of the distribution. This can happen, presumably in a looser purely subjective world, with even a multi-modal distribution.
Cyan,
OK, I grant your point. However, assuming that there is some "subjectively real" probability distribution that the Bayes' Theorem process will converge is a mighty strong assumption.
The distinction here may be quite simple: an objective Bayesian accepts Bayes' Theorem, a subjective one does not. After all, Bayes' Theorem posits that repeated adjustments of priors based on new posterioris from the latest observations will asymptotically converge on the "true" probability distribution. That is only meaningful if one believes in an objective, "true" probability distribution (and of course assuming that certain necessary conditions hold regarding the underlying distribution and its dimensionality).
As someone whose parents knew Einstein as well as some other major "geniuses," such as Godel and von Neumann, I have long heard about the personal flaws of these people and their human foibles. Einstein was notoriously wrong about a number of things, most famously, quantum mechanics, although there is still research being done based on questions that he raised about it. It is also a fact that a number of other people had many of the insights into both special and general relativity, with him engaging in a virtual race with Hilbert for general relativity that he barely won. Quite a few had the basic ideas for special relativity, including Poincare, but just never quite put it all together.
What is actually more amazing about Einstein's genuine achievements, is that not only was he a patent clerk in 1905, his "miracle year," when he was unable to get an academic position, but for some period of time before that he could not even get any sort of job at all. Continuing to work creatively and innovatively in such an environment did take a special degree of ingenuity, insight, and sheer self-confidence, not to mention good luck. Of course, it can be argued, as some have, that it was precisely this outsider position that allowed him to make his conceptual breakthroughs, that he was at his best when he was a patent clerk in Berne, and that once he found general relativity and achieved fame and prominent professorships, his productivity and innovativess fell way off, although perhaps it was the overly comfortable existence he was provided with by his second wife, who also was more willing to overlook some of his peccadilloes, such as his constant pursuit of other women, although apparently she could not abide a certain Austrian princess who used to leave her underwear behind on the family boat.
Eliezer,
Absolutely. Check out his ethnic dining guide of Washington (available on his website). His recommendations for Sichuan in Northern Virginia are indeed top notch, although I have heard it from some of his colleagues, who will remain nameless, that some of them are getting tired of getting dragged to some of these joints over and over with guest speakers... :-).
You might find my spoof of his guide amusing: "The Latest Washingtoon Ethnic Dining Guide," up on my website at http://cob.jmu.edu/rosserjb.
Eliezer,
Are you angling to become the new Tyler Cowen?
Benquo,
Thanks for the correction r.e. "inflammable" and "flammable." Of course you are right. Not a contradiction between those two.
Well, the "does a tree make a sound when it falls in the forest with nobody there to hear it?" question is really about a different issue than this matter of what is the truth-value of dictionary definitions of words. When Bishop Berkeley posed that original question and said "no," he was asserting an idealistic philosophical perspective that I doubt few of the readers of this blog are particularly sympathetic with, although a lot of mathematician readers are probably bigger Platonists than they might be willing to admit (Did you "discover" that proof?).
Regarding dictionaries and common usage and Caterpillar assertions of "I can make a word mean whatever I want it to mean," well, certainly dictionaries do ultimately simply report reasonably common usages, with the possibility of these simply expanding for any given word. Most of the time these new usages simply evolve in spontaneous and oddly linked ways through similarities between the newer and the older usages.
Things get a bit odd when we have consciously made changes of meaning a la the Caterpillar. Sometimes these are ironic or hip or whatever, often playing off or against an established meaning ironically. This can lead to confusion if the new meaning gets added on with the older ones, especially if the new meaning is somehow logically or factually at odds with older meanings. This means that users of the word will have to be careful about contexty and audience, if they wish to avoid confusion. Sometimes this is conscious, such as "bad" meaning "really coolly good," although I doubt that usage has made it to the OED, if it ever will. Others with deeper historical roots are mysteries. Thus, why do both "inflammable" and "flammable" mean the same thing? And then we have words that have evolved to mean just the opposite of their original meaning, such as "pretty," whose Old English root, "praetig," apparently meant more like "ugly," although I may be slightly off on that one. But, such cases are definitely out there. Should the original person to use some form of "pretty" to mean what it does today have been punished, and why did his or her listeners go along with such an extreme change of meaning (which probably happened sort of gradually anyway)?
As a sideshow, I would note the death of Rasputin, whom some were not so certain was really a man either, although rather than a demi-god possibly like Socrates, some of those doubters thought that he was more like a demon, and I am also unaware of anybody getting involved in such a debate when he refused to die according to the usual causes.
In any case, he was killed by a group of tsarist nobles who were upset about his apparent control over Tsar Nikolai II and his family. So, they invited him to dinner. He was poisoned, he was shut, he was beaten and knifed. None of this did the trick. It required taking him outside and forcing him into an icy river where he presumably both drowned and froze to finally do him in.
Oh, and regarding infinitesimals again, some have argued that the old medieval dispute about how many angels can dance on the head of a pin was really a debate about the existence or nonexistence of infinitesimals.
Regarding calculus, it is possible to accept infinitesimals and thus view dx/dy as meaningful in an absolute sense, and not just as the outcome of a limit process. This is what is done in nonstandard analysis, in which infinitesimals are the reciprocals of superreal numbers that are infinite (although not equal to or equivalent to the infinite cardinals). This is in fact how both Newton and Leibniz thought of the matter. For Leibniz, a monad was a point surrounded by infinitesimals.
However, while infinitesimals are smaller than any positive real number, they are not equal to zero, strictly speaking. Therefore, they are irrelevant to the discussion of the steps in the Heinlein exercise, which is dealing with the actual zero. Indeed, this exercise is a reminder as to why dividing by zero is ruled out. Allowing it allows absurdities such as this exercise. 0/0 can be anything.
My late father was once asked by a young woman in the audience at one of his public lectures, "Is zero a real number?" He replied, "one of the finests, my dear, one of the finest."
Well, the deeper issue is "Must we rely on the Peano axioms?" I shall not get into all the Godelian issues that can arise, but I will note that by suitable reinterpretations, one can indeed pose real world cases where an "apparent two plus another apparent two" do not equal "apparent four," without being utterly ridiculous. The problem is that such cases are not readily amenable to being easily put together into useful axiomatic systems. There may be something better out there than Peano, but Peano seems to work pretty well an awful lot.
As for "what is really true?" Well... . . . .
Well, the real reason why it is useful in arithmetic to accept that 2+2=4 is that this is part of a deeper relation in the arithmetic field regarding relations between the three basic arithmetic operations: addition, multiplication, and exponentiation. Thus, 2 is the solution to the following question: what is x such that x plus x equals x times x equals x to the x power? And, of course, all of these operations equal 4.
J. Thomas is right. Religion can evolve in primitive man for purely selfish reasons. Group selection may be relevant only for competition between religions. Hence, all the prisoners' dilemma arguments and tit for tat and all that is irrelevant. The vocal heretic is the loner who loses group support and thus has a very difficult time surviving.
So, back in the primitive tribe, surely there were plenty of people who had doubts about their tribes Ugu Bugu god. But as long as one did not wish to get tossed out of the tribe by the chieftain who at least appeared to worship and pray to Ugu Bugu, it paid the individual to go along to get along. All hail Ugu Bugu!
I think James Bach was on the right track here, but did not take this far enough. Eliezer's interlocuter was not able to really articulate his argument. Properly argued, probability is completely irrelevant.
So, let us contemplate the position of a serious, hard science creationist, and I hate to say it, but such people exist. So, this individual can fully agree and admit that how a given body grows and develops depends on its DNA structure, so that indeed it is not surprising that different species that appear morphologically and behaviorally to be somewhat similar, such as various canine species or feline species, or for that matter chimps and humans, even if the older creationists got all in fits about having a monkey for an uncle, and so forth, will have very similar DNA structures.
The issue then is how did this come to be. The evolutionist says that it is due to evolution from common ancestors and so forth. The scientific creationist says, "no," this simply reflects that the intelligent designer set them up this way because DNA controls the growth of individual entities, so similar appearing and behaving species will have more similar DNA, and God (or The Intelligent Designer) made it this way fully consciously in accord with the laws of science, which presumably the same Entity is also fully aware of, whether or not this Entity in fact set up those laws his or herself.
It is well known that capable leaders consciously surround themselves with advisers who hold competing views, with at least some able to tell the leader when things are not going well. We have just been seeing a counterexample of this in an important real world position for the last seven years...
Ah, but A is still A, no matter what any of you may say... :-).
Benquo,
You are right. I misread it. The first case is one of irrationality.
Eliezer is correct that lots of people are very bad at calculating probabilities, and there are all kinds of well known biases in calculating when affect gets involved, especially small sample biases when one is personally aware of an outlier example, especially a bad one.
However, the opening example is perfectly fine. Eliezer even has it: the higher insurance is to cover the real emotional pain of losing the more personally valued grandfather clock. How much we subjectively value something most certainly depends on the circumstances of how we obtained it. There is nothing irrational about this whatsoever. Rationality above all involves following that old advice of Polonius: know thyself.
OTOH, if they are creationists who have been reading too much Stephen Jay Gould, who knows what sorts of trouble they might get into. They might even tragically start selecting partners on multi-levels, while disobeying the correct equations, :-).
Oh, tsk tsk. But women with "creationist" brains just don't have the sort of one night stands implied by your story, at least not as often as the ones with "evolutionary" brains, :-).
Ah, finally got some real action out of you guys. Not bad.
Eliezer,
Pretty decent list. Of course, no way we are going to resolve this, especially if we are going to rule out such "objective" measures as citations, where indeed I suspect p.e. will beat most of those. Also, there is the complication that several of those are really extensions of each other, such as Price's equation providing conditions for multi-level evolution, which is also partly connected to reciprocal altruism, not to mention that the since the gene's-eye view tends to imply gradualism, which is hardly dead, p.e. challenges it.
J Thomas,
I would agree that it is of the greatest importance to palenotologists. One importance of p.e., ironically, is that although creationists sometimes tried to use Gould's arguments against evolution, p.e. provides an answer to the old creationist gibe about "where are all the missing links?" (although somehow those folks conveniently ignore good old Archeopteryx somehow).
J Thomas,
So, we are running in circles. Adaptive radiation is just a special case of the more general phenomenon, although it might not be if the rate of change/speciation continues rapidly without convergence to some equilibrium. Adaptive radiation was described in Darwin, without the term, and in some later editions he did note the variabilty of rates of evolution, although he did not exress the idea that much speciation would occur very rapidly followed by long periods of substantial stasis. This idea is never stated anywhere in Origin of the Species, nor does it appear in any writings prior to Eldredge and Gould.
One could say that what is involved here is the stating of a hypothesis, that is then given a label. It is a much broader idea than just adaptive radiation arising from genetic drift, which is indeed something that had been described earlier, but I repeat is only a special case and does not include the crucial addendum regarding long periods of stasis. Indeed, as I noted earlier, it is this latter point that is really the new part of E and G's idea of p.e. Certainly that speciation might occur rapidly under various circumstances, especially when the general environment is changing rapidly, as for example during a Cuvierian "catastrophe" such as wiped out the dinosaurs, was noted previously. But such catastrophes are also essentially special cases, just as is adaptive radiation. It is the adding of the long periods of stasis that distinguishes the idea/hypothesis, or whatever you want to call it. But let us be clear "adaptive radiatiom" does not equal "punctuated equilibrium."
BTW, you will not find my most extensive discussions of evolutionary theory on my website. The most extended discussion appears in my 1991 book, From Catastrophe to Chaos: A General Theory of Economic Discontinuities, Kluwer, especially in Chap. 12.
Again, probably for the last time, I await from anybody an idea appearing in the last 50 years, besides coevolution, that has been more important, or perhaps more influential, than punctuated equilibrium. Without such an offering, I would say my case rests, and very solidly.
Douglas,
I am perfectly willing to buy that Gould's scientific writings are more defensible than his popular writings.
J Thomas,
In my later comment I did not repeat my earlier comment. There I had specified, "one of the top ten ideas in the last half century," not of all time. So, Weber's Law dates from the 19th century, and those of Gause and Fisher from the 1930s. Not relevant. Still waiting for someone to come up with something other than coevolutions, which, as I have already pointed out, is definitely in Darwin, if not the term, neologized by Ehrlich just as Gould and Eldredge neologized punctuated equilibrium, whereas the latter is only ephemerally in Darwin, at best, and only then in later editions of Origin of the Species.
A definition? That a substantial amount of speciation occurred during (geologically) relatively short periods of time, between which were long periods of relative stasis without actual speciation, although gradual changes were always occurring. Gould himself in TSOET emphasizes that p.e is not in contradiction with the neo-Darwinian synthesis of the 1930s and 40s. And I know from talking to some of the developers of that theory that they do not disagree with that statement of his. Rather the issue is seeing this particular outcome as widespread and important rather than as some weird sideshow not even openly discussed, much less labeled. Sorry, but Gould and Eldredge did in fact make a theoretical breakthrough of great importance. Heck, Einstein himself argued that relativity was already implicit in the work of Galileo.
windy,
You are correct about reciprocal altruism. But that does not undo the more general argument. Apologies for getting sloppy, but indeed plenty of people are taking multi-level evolution seriously. And, more to the point, it remains the case the Eliezer is simply dead wrong about the consensus of evolutionary theorists regarding the status of Gould. Again, one might as well make claims about the historical significance of Milton Friedman based on the opinions of Marxist economists. That is effectively the equivalent of what Eliezer attempted here in this post.
BTW, creationists did use Gould at a certain point based on his rhetoric criticizing "fundamentalist Darwinism" to dump on Darwinism and evolutionary theory in general. This probably did feed into the extreme annoyance by some evolutionary theorists with Gould at one point.
Caledonian,
Your distinction between altruism and the more general "group-friendly" is useful and relevant.
TGGP,
Regarding artificial selection it is worth remembering that this was one of the major examples that Darwin himself emphasized in Origin of the Species, the efficacy and effect of efforts at artificial breeding and selection by humans of both plants and animals.
I suggest reading the special issue of the Journal of Economic Behavior and Organization, January 2004, where the matter of multi-level evolution is dealt with at length, with some of the commentators evolutionary geneticists, mathematical ones at that, and at the highest level. The conditions for higher level selection are laid out there. Wynne-Edwards did not know these and was accurately put down by Williams in 1966. They are the Crow-Hamilton-Price equations. I suggest you read it, Eliezer, and, yes, I am the editor of the journal, the leading one in the world on evolutionary economics.
Eliezer,
Gould makes his own mea culpas near the end of the chapter, so you can focus on that zone. Tooby is not an unreasonable guy, and it may well be that Gould's criticism of him was off-base. I have not read that particular exchange.
Let me put Gould in a slightly different frame. He was not the JK Galbraith of evolutionary theory, as Krugman bought into. He was probably closer to being the Milton Friedman, if on the opposite side of the political fence.
Friedman (like Dawkins also) was a great popularizer and author of best-selling books, like Gould and Galbraith. However, unlike Galbraith, he did win a Nobel Prize in economics, which most accept was deserved, even those who do not like Friedman's politics. He is also in all the intro texts, just like Gould, but unlike Galbraith. Even so, there are some, his worst critics, who have always been extremely critical of him, often in very hyperbolic terms and language. Also, he has been proven wrong about some things which he was closely associated with, notably hard core monetarism (he agreed last summer that central banks should not focus on money supply anymore, an ultimately reasonable guy, like Gould).
Nobels are not given out for evolutionary theory, although geneticists get them sometimes (Crick, Watson). So, Mayr, Simpson, Williams, Maynard Smith (he might have gotten an econ one), and other giants did not get one. If they were given, Gould would have gotten one. It is very simple. Whatever his many faults, and they were many, he came up with what has been the single biggest new idea (yes, one can find hints of it in Darwin and some others) in evolutionary theory of the last half century, punctuated equilibrium, now in all the textbooks, just like the most important ideas of Milton Friedman (and unlike Galbraith's major ideas). There are some who say it is wrong, but most say that it is at least partly right. So, Gould was very big and very important, even if he pissed a lot of people off.
Eliezer,
Well, let me see. Where shall I start?
Tooby is not an evolutionary biologist or population geneticist. He is an evolutionary psychologist. This screed from 1997 is about half a whine about Gould's treatment of some of his work. Perhaps the whine is justified, but it is a whine, and most of the rest of it is off-base. The argument about inverted panadaptationism is simply wrong, as a perusal of Gould's 1400 page plus magnum opus, The Structure of Evolutionary Theory, will tell. BTW, Tooby does not make it into the 43 page bibliography of that book, although Williams is discussed at great length and with great respect in it. I would note also that Williams altered his views somewhat between 1966 and his 1992 book. (Just for the record, I like the main book by Cosmides and Tooby.)
Krugman? Excuse me. He admits himself that he does not know much about evolutionary theory. He spends most of his talk noting the similarities between neoclassical economics and the Dawkins view of evolution, praising it. Except of course at the end he notes that it does not always work, and the messier, non-Dawkins stories are sometimes better. Duh.
Sure, there are some people who really dislike Gould (Dawkins, Dennett, and some others) who will make these statements about Gould not being respected by other evolutionary theorists. But his main idea, punctuated equilibrium, has entered the textbooks and is more studied and discussed than ever. Sorry, this is just whinging by the jealous or those who deeply disagree with him (Dawkins especially).
Oh, and as for me being taken in by bluffs, well, I have written on this stuff and have cited Williams, Hamilton, Maynard Smith, and numerous others, beyond those that Krugman claims are not cited by evolutionary economists, as well as Eldredge and Gould.
Finally, I have actually spoken with some of the most senior and distinguished evolutionary theorists, including some now dead. While Gould is often treated with some bemusement for his celebrity and eccentricities and the peculiar evolution of his views, I have not found these people viewing him as worthless or as having a rep worth mud. This is just silly bilge and drivel.
Finally, I would recommend you read Chapter 9 (I know, it is almost 300 pages long) of Gould's magnum opus. He does an excellent job of covering most of these controversies, with a fair amount of mea culpas for some of his own misstatements over the years. A lot more fair-minded than the junk in your post or in your links, frankly.
Well, this is partly a matter of what discipline one is dealing with. So, sure, for AI or computer science more generally, Kolmogorov or Chaitin or Rissanen measures are more useful and reasonably well defined. For other disciplines, other definitions may be more suitable. Thus for economics, I have (following Richard Day) defined complexity in a dynamic way based on erratic dynamics appearing endogenously out of the system (with "erratic" defined more specifically). I laid this out in a paper in 1999 in the Journal of Economic Perspectives, and have a more recent paper up on my website ("Computational and Dynamic Perspectives on Economic Complexity") comparing the two approaches, at http://cob.jmu.edu/rosserjb.
Hmmm, well there is an endogeneity problem in that the believability of the police commissioner's statement depends on the degree to which it constitutes legal evidence. To the extent it constitutes legal evidence, it may be less believable precisely because this give police commissioners power that they may be exercising in corrupt and power-hungry ways. A statement that cannot be seen to potentially provide some personal gain to the person making it presumably has greater credibility.
Although it is almost always the case, I can imagine legal evidence that is not necessarily scientific. The problem in my mind is precisely this bad memory of witnesses problem. I guess we have to say that an eye witness account, under oath, is "scientific." It certain is legal evidence, although potentially challangeable by countervailing testimony or evidence. However, a scientist might be more willing to be skeptical, e.g. all those alien encounter accounts that are being discussed in other postings.
BTW, in regard to an earlier thread by Eliezer, of course "norm" does have various mathematical meanings, including the length of a vector (or multi-dimensional equivalent of "absolute value"), and there is the process of "renormalization" in algebra, which has some importance in several theories of physics. However, I remain unconvinced that any of these play an important role in establishing the earlier argument.
Eliezer and Peter, I think the problem is statics versus dynamics. Your set of equations are correct only at a specific point in time, which makes them irrelevant to saying anything about what happens later when new information arrives. That would entail subscripting H by time. For any given t, sure. But, that says nothing about what happens when new information arrives. P(H) might change.
The obvious example is indeed the black swan story, which we all know is what is lying behind this discussion. So, at a point in time before black swans are observed, let H be "all swans are white." Perhaps there were a few folks who thought this might not be true, so say P(H) was 95%. Sure, your equations hold at a point in time, but so what? The minute the word comes in about the observation of a black swan (assuming it is accepted), P(H) just went to zero, or not much above zero, perhaps after having gradually drifted over time to 95%. Remember, your story was one about new information coming in and changes over time. But that is not what your equations are about.
This is the fatal flaw in your nice new law, Eliezer.
Eliezer,
Fair enough. You get credit, then, for coining the term. However, the problem remains, why should that equals sign be there? Sure, if you put it there, the logic holds up, my niggles about Bayes' Theorem and time to convergence and all that aside. But, it is not clear at all that the equals sign should be there, or is there in any meaningfully regular way. Your defense has been to cite an essentially empirical argument by Robin. But that empirical argument is much contested in many arenas. Sure, Burton Malkiel posed that financial markets are a random walk, but that argument has undergone a lot of modifications since he first posed it in a best-selling paperback. In that regard, your proof essentially amounts to one of these "proofs" of the existence of God, wherein the proof arises from another assumption that gets snuck in the backdoor that gets one the result, but that is itself as questionable or unprovable, much like the old complaint by Joan Robinson about the magician making a big deal about pulling the rabbit out of the hat after having put it into the hat in full view of the audience.
Eliezer,
I just googled "law of conservation of expected evidence." This blog came up. Nothing else like it. Frankly, I don't think you are selling a law here. You are asserting one that nobody else is aware of.
Stuart,
Argentina recently defaulted and all but got away with it. Yes, there were demonstrations in the streets, but there are also on a regular basis in the US. What is your definition of "civil disorder" then? Elections were held, there was no revolution or coup.
In fact, the Argentine example might yet come to mind in the next decade if not-so friendly foreign creditors start to give the US a hard time. I think it was Keynes who argued that if you owe somebody a million dollars you have a problem, but if you owe him a trillion dollars, he has a problem (have changed the numbers to account for inflation). We could default and view it as "screw them" act.
Stuart Armstrong,
I think you are way overstating things. Did you read earlier comments? Are you aware how close we came to defaulting in the 1990s when Congress and the president gridlocked over a budget? We have a systemic setup in contrast with all those countries with parliamentary systems that could let it happen much more easily with nothing near some kind of horrendous catastrophe. And if we began to experience some kind of serious pressure from a foreign creditor, China anyone? on top of some internal deep conflict and economic problems (and US politics is not all polarized, now is it?), it could happen.
Regarding this business of the foreign creditors, there is an important reason why most Americans simply pay no attention to our mounting foreign indebtedness: up until now the that humongoug foreign net indebtedness has not resulted in a noticeable net deficit on the investment income part of the current account part of the US international balance of payments. However, as that foreign net indebtedness increases, this will inevitably change. When we start to see several hundred billions of dollars flowing on net overseas as interest on that debt, and the accompanying upward pressure on US interest rates start to negatively impact the US economy, there might even be an outright move to do what Argentina did to our bankers, and what New York state did to British bankers back in the nineteenth century regarding the debts for financing the Erie Canal construction: consciously default.
The bottom line on why we even fuss about the "risk-free rate" is that it is a necessary input to the standard formuli for pricing all kinds of options and derivatives via Black=Scholes and its variations. Something has to go in there, even if the wise really do understand that the underlying asset on which that rate is based is not really so risk free after all.
Hopefully Anonymous,
That is according to US based bond raters. A lot of people think there is politics in that. Do you really think the US government is more reliable about paying back its bonds than the Japanese one? Really?
Rather than some blowup like al Qaeda smuggling in nukes, a more likely scenario would be something much more mundane and stupid, e.g. a political gridlock between the President and the Congress, as happened briefly back in the 90s between Clinton and the Newt Gingrich-led House. Various government activities were shut down. It never got far enough to lead to not paying interest on the national debt, but it would not take all that much more of a conflict to do it, especially if we had pressure from abroad, with our humongous foreign debt. It has long been a ridiculous joke that Moody's downgraded the quality of Japanese bonds, when they sit on nearly $1 trillion in forex reserves, while US securities get top rating, while the US owes over $3 trillion abroad, a substantial chunk of that to the Japanese.
Another way of looking at this is to realize that we are all pretty much hard wired to operate in a surface reality that more or less fits a Newtonian-Euclidean model of the world. We now know that this does not hold at high accelerations or at very large or very small scales in a lot of ways. So, these deviations, many of which have been clearly established beyong any doubt, seem weird to most people when they first hear of them, and may even still "feel weird" even after they have long come to intellectually comprehend and accept them.
Heck, even now, after quite a few decades, there is a part of me that finds the simple outcomes implied by special relativity with respect to time dilation still a bit weird at an emotional level, although delightfully and fascinatingly so, even though they are clearly the direct logical implications of the (apparently) "universal" constancy of the speed of light.
Eliezer,
What is ironic about this posting is your indignation. Offhand it sounds like you are as guilty as those you criticize.
There is nothing weird about people finding a theory to be weird that does not correspond with their everyday surface perceptions, even when they are able to comprehend it intellectually. Also, and others have noted this more or less, there are a lot of different interpretations out there of what quantum physics "really means," and some are a lot weirder than others. Is it ontological that Schrodinger's Cat does not either exist or not exist until actually observed being one (or not) being the other?
And again, I remind all that we do not have the definite answer on how to put quantum mechanics and general relativity together, leaving some doubt about some fundamental aspects of both. Some of the proposed resolutions are perceived by many as even weirder than either, e.g. string theory, but given that it has neither been proven nor disproven, should we all get on a big high horse about people who find string theory to be "weird"? There have just been some pretty intelligent books out criticizing it, with some of their arguments in some sense coming down to how weird it is, although that is not the terminology used.
Maybe when we finally figure all this out, if we do, quantum physics might be redone in a way that makes it seem "less weird" than it does now (and again, some of its most extreme apparent "weirdness" comes from some interpretations of it that are not universally accepted).
Eliezer,
I would agree that there are different variations on the multiverse theory, more than the ones you listed, and that they will give different answers. Of course, within our sufficiently narrowly defined "universe" we like to believe that there are universal laws (including even some constants) that apply everywhere, although we do not know that for sure.
Regarding gravity more particularly, yes the examples I gave involved surface applications. I regularly tell students that the fact that a helium balloon floats upward does not prove that the law of gravity is false.
However, there is a higher level problem, that general relativity, and especially its parts dealing with gravity, remain unreconciled clearly with other parts of apparent physical law, notably quantum mechanics, with the clearest surface manifestation of the problem being the continued inability to "unite" gravity with the other three basic forces (which have been pretty much shown to be "unitable" within existing frameworks). Of course this is what string theory, quantum loop theory, and some other candidates have been trying to achieve, but the failure to clearly find such a GUT leaves a certain level of doubt at a very fundamental level regarding the complete universality of the "law of gravity" in its general relativistic conceptualization.
Two very different points. One is the whole "multiverse" theory. In that view, different physical laws could hold in different "universes." To the extent that we might ever be able to travel between them, would this not violate the "(multi)universality" of those laws?
Also, of course, there is the problem that the conditions under which such laws do not always hold, indeed may never hold completely. The law of gravity holds precisely only in a perfect vacuum. But there are no perfect vacuums. Now there are plenty where it holds very closely, but there are also many quite relevant to use where it does not even come close to holding, as when air resistance is sufficient to substantially change the rate at which a body's movement towards the earth accelerates, even possibly changing the sign for a period of time (watch the helium balloon go up into the air, dear).
Eliezer,
So, an "optimal prior" is either a subjectively guessed probability or, more optimally, probability distribution that coincides with an objective probability or probability distribution. That is it would equal the posterior distribution one would arrive at after the asymptotic working out of Bayes' Theorem, assuming the conditions for Bayes' Theorem hold.
But, what if those conditions do not hold? Will the "optimal prior" be equal to the "objective truth" or to the distribution that one arrives at after the infinite working out of the posterior adjustment learning process, even assuming that we do not have the sort of inertial slow learning that seems to exist in much of reality?
To give an example of such a non-convergence, consider the sort of example posed by Diaconis and Freeman, with an infinite dimensional space and a disconnected basis, one can end up in a cycle rather than on the mean.
Well, it is not every day that I can cite something that occurred at a conference that both Robin Hanson and I attended. But, we were at a conference honoring the work of David Grether, a giant of the field of Bayesian decision theory and econometrics, which was held on the George Mason campus on Friday, 4/6.
Anyway, a theme of several papers was that people are slow to update their priors in reality in many situations, although details are important. It is not clear what the source of this "inertia" is.
Douglas Knight,
There is an older literature for sure, but it was largely dismissed during the heyday of the rational expectations revolution in the 1970s and 1980s. The first break was the presidential speech to the American Finance Association in 1985 by Fischer Black, pubbed in 1986 in the Journal of Finance as "Noise," followed by the 1987 stock market crash, and then a pair of rigorous papers in 1990 and 1991 in the QJE and Journal of Business by the formidable quartet of Bradford DeLong, Andrei Shleifer, Lawrence Summers, and Robert Waldmann. They in particular argued that a rational trader must take into account the beliefs and actions of the noise traders, which can then get one into the realm of the old problem, going back to Keynes, of self-fulfilling prophecies. The issue is not false beliefs, it is understanding that the market may be driven by people who are not following long-run fundamentals and taking accurate advantage of their behavior. It is a matter of accurately forecasting a market, in the case of a bubble, accurately forecasting the path of the bubble, and those who do so can and will make more money than the safe, fundamentalist trader who stays away from the bubble.