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pdf23ds,
Yes, there is even a stronger motive for computer programmers than for just plain old mathematicians. Real money is involved in shortening those programs.
Regarding Taoism and economics, there has long been a dialectic in Chinese culture and philosophy between Taoism and Confucianism. The former is "the scholar out of power," opposing state power over the economy and society, practiciy we wei and so on; while the latter is "the scholar in power," supporting hierarchy and imperial state power over the economy and society in a supposedly harmonius balance.
Raymond Smullyan used to pull dimes out of my ears when I was a kid, no kidding.
My old man, a friend of Smullyan's (hence his access to my youthful ears), used to argue that a major motivation for mathematicians was "laziness," a desire to figure out ways to solve problems with less effort.
David Kelley,
Maybe you were the first to use the terms "open and closed systems" within Objectivist discourse and publications, but to claim that you "coined" them is utter nonsense. They have been in widespread usage within systems theory and related fields for well over a half century in works by such people as von Bertalanffy and Vernadsky, some of this actually going back as far as the 1920s, if not earlier. Please...
J Thomas,
I have already given a definition, which is close to what you will find in Wikipedia, if you go look there. Of course one can argue endlessly (and many do) about whether or not particular cases fit the definition or not.
Adaptive radiation can be viewed as a special case of punctuated equilibrium, although it is one that involves genetic drift, first identified by Sewall Wright in the 1930s, with Mayr emphasizing geographic separation arising from genetic drift as a key form of this. Adaptive radiation in particular refers to a case where a population wanders into an isolated and underpopulated area, where it can "radiate" quickly into a bunch of different niches. The classic case goes all the way back to Darwin, his finches on the Galapagos islands, although the term was cooked up much more recently. But, this is only one way one can get such rapid evolution in a short time.
The crucial figure on genetic drift was Sewall Wright, one of the "trinity" of the 1930s neo-Darwinians, along with Fisher, whom you praised, and Haldane. Wright's position with them is very controversial. He lived to 1988, and I actually knew him and talked with him on several occasions. Gould's account of his interactions with Wright in TSOET is fascinating, a very complicated relationship. I also note that Wright's statistical work had importance for econometrics, with a paper by him and his father being the first to identify the identification problem.
Anyway, J Thomas, I think you are the one who needs to show that you know what the hell you are talking about. No, you do not control when this scrolls off so that "we are waiting." We are waiting, or at least I am, for you or anybody else here to come up with an idea, any idea, that you can claim on any grounds, you describe them, please, more important in evolutionary theory in the last half century. Neither you nor anybody else has done so yet, despite my repeated challenges.
BTW, I have a website, easily found as the second entry by googling my last name. You can go read my own publications on these matters. Have you ever published anything on evolutionary theory? Has Eliezer besides on blogs?
J Thomas,
Well, this is about to scroll off, but I would ask: 1) Did anybody prior to Eldredge and Gould point out this argument? (Answer: NO) 2) Is it important? (Answer: YES, at least it is in all the textbooks and is widely studied and discussed) 3) Do you or anybody else have a more important new idea in evolutionary theory that has appeared in the last half century??? I asked this some time ago. Nobody has stepped forward, other than myself with coevolution. Are you going to? Are able to? I doubt it.
You are just making yourself look as foolish and off the wall on this matter as Eliezer.
Eliezer,
So, who is your McCabe?
Wiseman,
Wise crack.
I'm back.
Eliezer,
I agree that ultimately the empirical issue will be more important than this model versus that model. I am not going to get into the debate about the specific math of your model as others have already done so. If you really think you have a strong and new result, submit it to my journal. The referees will be some of the top mathematical population geneticists in the world.
McCabe was the third coauthor on the piece with Smith and Houser of GMU in the Jan. 2004 JEBO special issue that took the hardest pro-Dawkins line. So, when he says "never never never..." this factoid should be kept in mind.
Also, if you do submit the paper, change the title. Indeed, while "Tragedyy of Group Selection" may get the adrenaline flowing for some readers, it is pretty absurd. Tragedy? Who died or was killed or even just had their marriage break up? (maybe a couple arguing about group selection?). Hitler's racist eugenics was tied to millions being killed in the Holocaust. That was tragedy. Stalin's support of the goofy Lamarkism of Lysenko was tied with millions dying in Soviet famines and many better scientists being thrown in jail for disputing Lysenko. This was a tragedy. Get real, please.
Oh yes. While you suggest that the hypercycle is a "whole 'nother story," I would say not really. There are links, even if the precise equations are somewhat different.
TGGP,
Congrats on the reasonably informative links.
Caledonian,
Once you are dealing with hominids, which may be the most important example, indeed "enforcement" may well be important. There is a growing lit on how reciprocal altruism ultimately depends on punishment of free riders, that is, enforcement.
Ian Nowland,
I do not know where Gould fitted on that scale. I suspect he was in different places at different times.
OTOH, offhand I am not sure what is so "immoral" about #4, per se. Don't lots of people going into the hard sciences want to improve society, such as medical researchers? Certainly it is not surprising that people will think that what improves society is what agrees with their own ideology, even if perhaps you disapprove of their ideology. I think the potential problem here is the main topic of this blog: when people lie about or distort actual scientific findings or research in order to fit in with some ideological agenda. Certainly people have charged Gould with being motivated for parts of his research by his ideology. However, I am not aware of anybody successfully claiming that he actually distorted or lied about findings in the process of doing so. If not, then the charge of "immorality" is way overblown, just like most of Eliezer's charges against him, drawn from sources who were his worst enemies and strongest opponents.
Douglas Knight,
Not sure without further discussion what my "non sequitors" were, but your statement about Gould as a (non) theorist is amazingly empty. How is that you say hs is not an important theorist? While some have labeled it as "just relabeling," or something like that, I have yet to see anybody here offer up even one, much less ten, new ideas in evolutionary theory more important than Gould's of punctuated equilibrium.
I will offer one: coevolution, due to Paul Ehrlich. However, even more than punctuated equilibrium, this is one that one can find strong precursors of in Darwin, big time.
Eliezer,
Maybe I will get back to you on that point, and maybe I will not. I am about to leave town, and I spend 30 hours a week editing a journal, along with being a full professor of economics. This is why I turned down Robin's invitation to become a co-blogger here. Too damned busy. This is not meant to be a copout or an escape. I already spent a couple of hours I did not have last night digging through Gould again on your other posting.
I will note that the special issue I edited includes a wide variety of views and that there remain sharply contrasting opinions regarding the bottom line. Interestingly, the hardest line defenders of the Dawkins position (he was invited to participate, as were Tooby and Maynard Smith, although they declined), was a paper by GMU's Vernon Smith and Dan Houser, two economists. The political scientist, Axelrod, was also defending that view. The mathematical population geneticists were defending multi-level evolution, at least in principle under the right conditions.
For the record, I think you are a smart guy. If I have the time, I shall get into responding to your specific question. But I gotta go now.
michael vassar,
Yes, but that "common sense" was widely ignored by most evolutionary theorists before Gould pointed it out. His approach is now in all the textbooks. He has also emphasized against some of his less fair critics that his original papers on this were specifically addressed to the paleontologists.
Another part of it, not so obvious and definitely not part of the general lexicon, is the idea of long periods of stasis. This was a point not at all emphasized by anybody prior to Eldredge and Gould, and was the real core of the original aspect of it.
So, what are the top ten ideas of the last half century ahead of it and where are they in the textbooks?
Regarding Darwin, the picture is muddled in that his remarks that look open to p.e. appear in later edtions of Origin of the Species, but not in the first one, where a more hardline gradualist scenario is presented.
Eliezer,
Well, the statement from Tooby that you quote says exactly nothing precise. He refers to a "tangle," but nothing specific. Then he gives his shopping list of evolutionary biologists whom he considers more important/worthy than Gould. Fine, some of those certainly are and some others may be. This is hardly some slam dunk comment, but reeks all too much of the jealousy of the less popular for the more popular. I might as well get all bent out because Tyler Cowen and Bryan Caplan have written bigger selling books than I have.
Regarding Williams' argument, the issue is indeed the locus of evolution. Saying that it is the gene that gets passed on does not cut it. The question is the locus of activity that determines which genes get passed on. In the case of Dawkins and Williams this locus was generally (pretty much always in the case of Dawkins) the individual. Williams actually allowed for higher level selection as an occasional possibility. However, he ruled it out in general, and did so on essentially prisoner's dilemma, game theoretic grounds, the basis of Maynard Smith's position as well, the developer of the concept of the evolutionarily stable strategy. Maynard Smith was also very impressed with how easy it is for individuals to undermine cooperative strategies.
So, now we know better. Groups that cooperate can outcompete and replace groups that degenerate into internal back-stabbing and cheating. The evolution of such cooperation remains one of the really big questions out there. It turns out that the Crow-Hamilton-Price equations in fact give conditions for when such higher level evolutionary processes can become the dominating factor in determining which genes get passed on.
Regarding Gould, again, I am not going to defend him against all criticisms. I am not surprised that he has not always properly cited others. Certainly he had a large ego and did a lot of self-advertising. And I am perfectly willing to accept that he may have engaged in some oversimplifications or even obfuscations and confusions regarding evolution in terms of public knowledge. This is unfortunate to the extent it is true. But his debates with Dawkins and Williams and Maynard Smith were serious debates, regarding which on at least some issues the consensus is moving more in his direction now.
As for people dumping on his politicis, fine. But please do not pretend that you are making scientific arguments. These are essentially ad hominem arguments of the worst sort.
Eliezer,
You are in way over your head on this one. It is clear that you are behind on current literature. The "selfish gene" is old hat and out of date. Multi-level evolution is increasingly widely accepted by many geneticists, with such mechanisms as reciprocal altruism being keys. The equations for when the Williams argument on this matter breaks down have been around since James F. Crow first put them out back in 1953, although they were re-codfied and more widely distributed in the 1970s as the Hamilton-Price equations.
I am in my office where I do not have copies of the relevant books, and I never read the one by Gould that has you most worked up. It may well be that Gould claims excessive credit for ideas that were due to Williams in it. I do not know. I do know that while they disagreed on various things, Gould certainly does cite Williams in other places and writings and clearly recognized his role in various matters, at least in other places, if not in this particular book. There is little doubt that you are wildly exaggerating his sins in this particular matter.
Also, while one can find the idea of a variable rate of evolution in Darwin, there is no doubt that he saw evolution as fundamentally continuous and extremely gradual. "Nature non facit saltum" is the frontispiece for all editions of his Origin of Species, which comes ultimately from Leibniz. The guy you linked to dismisses Gould's (and Eldredge's) idea of "punctuated equilibrium" as already known to Darwin and thus derivative. Excuse me, but this is horse manure. Gould and Eldredge may have overstated the case, but they completely altered the discourse, and the awareness of the possibility of much more rapid evolution is now much more widely accepted.
Indeed, these ideas are linked, as I suspect you know. The possibility of more rapid evolution is indeed tied up with the idea of multi-level evolution, if only partially. It is indeed a "hardline, fundamentalist Darwinian" position that denies this, as it has been by Dawkins (and Williams earlier).
Not sure if this is cranky or not, but when I was youthful I noticed that the Lorentz transformation of space-time due relativistic effects, square root of one minuc v squared over c squared, implies an imaginary solution for an v greater than c, that is for traveling faster than the speed of light. Now, most sci fi stories suggest that one would go backwards in time if one exceeded the speed of light, but I deduced that one would go into a second time dimension.
Of course the problem is that as long as Einstein is right, it is simply impossible to exceed the speed of light, thereby making the entire speculation irrelevant.
Eliezer,
This is about to scroll off, but, frankly, I do not know what you mean by "normative" in this context. The usual usage of this term implies statements about values or norms. I do not see that anything about this has anything to do with values or norms. Perhaps I do not understand the "wholel point of Bayes' Theorem." Then again, I do not see anything in your reply that actually counters the argument I made.
Bottom line: I think your "law" is only true by assumption.
Eliezer,
I do not necessarily believe that likelihood ratios are fixed for all time. The part of me that is Bayesian tends to the radically subjective form a la Keynes.
Also, I am a fan of nonstandard analysis. So, I have no problem with infinities that are not mere limits.
Furthermore, I remind one and all that Bayes' Theorem is asymptotic. Even if the conditions hold, the "true" probability is approached only in the infinite time horizon. This could occur so slowly that it might stay on the "wrong" side of 50% well past the time that any finite viewer might hang around to watch.
There is also the black swan problem. It could move in the wrong direction until the black swan datum finally shows up pushing it in the other direction, which, again, may not occur during the time period someone is observing. This black swan question is exactly the frame of discussion here, as it is Taleb who has gone on and on about this business about evidence and absence thereof.
Tom,
Bayes' Theorem has its limits. The support must be continuous, the dimensionality must be finite. Some of the discussion here has raised issues here that could be relevant to these kinds of conditiosn, such as fuzziness about the truth or falsity of H. This is not as straightforward as you claim it is.
I would agree that the lack of sabotage cannot be argued as support for accepting an increase in the probability of the existence of a fifth column. But it may not be sufficient to lower the probability that there is a fifth column, and certainly may not be sufficient to lower a prior of greater than 50% to below 50%, even assuming that one is a Bayesian.
Eliezer,
Of course you are assuming a strong form of Bayesianism here. Why do we have to accept that strong form?
More precisely, I see no reason why there need be no change in the confidence level. As long as the probability is greater than 50% in one direction or the other, I have an expectation of a certain outcome. So, if some evidence slightly moves the expectation in a particular direction, but does not push it across the 50% line from wherever it started, what is the big whoop?
This is one of those rare moments where the usually horribly heterodox economist, me, defends orthodox economic theory. So, looked at very closely, orthodox microeconomic says nothing at all about peoples' preferences themselves, which presumably involve their emotional reactions to various things. What is assumed is certain things about these preferences, that people know what they are, that they exhibit continuity, that they have a degree of internal consistency in the sense of exhibiting transitivity, and it also makes people behave more "rationall" and exhibit continuous demand functions if their utility functions exhibit convexity. So, rationality is not about what your preferences are or the degree to which they are based on one's emotions. They are that one know what they are, that they have a degree of internal coherence or consistency, and the, the biggie, that people actually act on the basis of their real preferences.
A lot of the problems regarding "irrationality" involve people behaving in internally consistent manners, especially over time. Behavioral economists are now arguing it out whether one should deal with this via multiple personality (or preference systems) models or approaches that stress focusing on "rationality" and keeping mind one's "real" preferences. Thus, hyperbolic discounting involves "time inconsistency." I want things now that I shall regret having wanted so much later. I eat the candy bar now and wake up fat later, etc. etc. Is this a combat of two preference systems or just "irrationality," People like Matthew Rabin who tend to use the latter approch, in fact say that the goal is to have people be "rational," to know their own real preferences and to act on them. If they really do not mind being fat, then go ahead and eat the candy bar. But in any case, it is perfectly OK either way to have the caring about being fat or not caring about being fat to be based on one's emotional reactions. One should undertand one's own emotional reactions. That is rationality.
Hal,
You are being a bad boy. In his earlier discussion Eliezer made it clear that he did not approve of this terminology of "updating priors." One has posterior probability distributions. The prior is what one starts with. However, Eliezer has also been a bit confusing with his occasional use of such language as a "prior learning." I repeat, agents learn, not priors, although in his view of the post-human computerized future, maybe it will be computerized priors that do the learning.
The only way one is going to get "wrong learning" at least somewhat asymptotically is if the dimensionality is high and the support is disconnected. Eliezer is right that if one starts off with a prior that is far enough off, one might well have "wrong learning," at least for awhile. But, unless the conditions I just listed hold, eventually the learning will move in the right direction and head towards the correct answer, or probability distribution, at least that is what Bayes' Theorem asserts.
OTOH, the reference to "deep Bayesianism" raises another issue, that of fundamental subjectivism. There is this deep divide among Bayesians between the ones that are ultimately classical frequentists but who argue that Bayesian methods are a superior way of getting to the true objective distribution, and the deep subjectivist Bayesians. For the latter, there are no ultimately "true" probability distributions. We are always estimating something derived out of our subjective priors as updated by more recent information, wherever those priors came from.
Also, saying a prior should the known probability distribution, say of cancer victims, assumes that this probability is somehow known. The prior is always subject to how much information the assumer of a prior has when they being their process of estimation.
Eliezer,
Ah, so you are a constructivist, perhaps even an intuitionist? Even so, the point of such theorems is that they can happen in a long transient within finite constraints, with the biggie here being the non-connectedness of the support. One can get stuck in a cycle going nowhere for a long time, just as in such phenomena as transient chaos. With a suitably large, but finite, dimensionality and a disconnected support, one can wander in a wilderness with not much serious convergence for a very long time.
I find the idea of a "prior learning" to be a bit weird. It is an agent who learns, although the prior the agent walks in with will certainly play a role in the ability of the agent to learn. But the problem of inertia that I raised has more to do with the nature of agents than with their priors.
Getting to the raison d'etre of this blog, the question here is does bias arise from the nature of the prior an agent brings to a decision or analytical process, or is it something about the open-mindedness or willing to adjust posteriors in the face of evidence that is more important? Presumably both are playing at least some role.
Eliezer,
Yes, thank you for correcting my sloppy wording.
So, it is the marginal posterior probabilities that exhibit inertia, or slow updating through learning, not the eternally unvarying "priors."
knackeredhack,
Forecasting markets in general is a mug's game, only made worse when bubbles go on. Go read all the debates about the (maybe) housing bubble going on over at Econbrowser. There is a deep argument, which Jim Hamilton has long been one of the main promulgators of, that one can never identify for certain econometrically if one is in a bubble or not, although one may be able to do so pretty much for certain sometimes with closed-end funds, where there is a well-defined fundamental in the net asset value of the fund.
Regarding Sornette, his model is one of a rational stochastically crashing bubble, which requires a sharp upward acceleration to provide risk premia for the rising probability of the inevitable crash. These tend to go to infinity at a certain point, which is the basis for forecasting the crash that Sornette uses. Of course there is plenty of reason to believe that people in bubbles are not fully rational, and therefore it is not surprising that Sornette has had a rather mixed record in his forecasting.
I think the English measurement story is simply one of path dependence. It is entrenched, lots of people know it, and it would cost a lot in infrastructure and learning to switch, just like the QWERTY keyboard. OTOH, the English language has considerable nuance, given the many languages that go into it.
The Pareto distribution argument is in the right direction. Think of a skewed distribution versus a normal one. So, the mean of the normal one might be higher than that of the skewed one. On average it does better, and hence may be more popular. But the skewed one has this tail that does much better than the normal one a non-trivial amount of the time, so that risk lovers are attracted to it. This is not all that different from the argument about how noise traders survive in financial markets. Most go bankrupt, but those who actually did buy low and sell high do better than anybody else in the market and definitely survive.
OTOH, there was this accumulation of Talmud, with later commentaries continuing to be added, Mishnah, and on and on. So, one can argue that there was this degradation function as one moves further away from the original source, but this is presumably at least partly offset by the accumulation of the commentaries themselves. Do they accumulate more rapidly than the degradation occurs?
BTW, there is something similar in the debates over the various Islamic law codes, the various Shari'as. An issue is which of the reputed sayings of the Prophet Muhammed, collectively known as the Hadith, are to be accepted as genuine and therefore to serve as part of the foundation of a proper Shari's (along with the Qur'an and some other things). The validity of a given saying was based on a chain of witnesses: Abdul heard it from Abdullah who heard it from Abu-Bakr who heard the Prophet, and so forth. Part of the argument is that the longer this chain of reputed witnesses is, the less reliably a part of the Hadith the supposed saying is, and indeed, some sayings are accepted in some Shari'as, while the stricter ones rule them out for having overly long chains of witnesses. The strictest of the Sunni Shari'as is the one accepted in Saudi Arabia, the Hanbali, which accepts only the Qur'an and a very small Hadith as bases for the law.