Barkley_Rosser

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.

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 r... (read more)

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 "... (read more)

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,... (read more)

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 somew... (read more)

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...