Re: Death of reductionism and emergence of ... well ... emergent phenomenon

PD wrote:
Like most physicists, I was trained to pursue the holy grail of
reductionism -- the theory of everything, which contains no arbitrary
parameters, and from which all other science can be *in principle*
derived (even if not in practice).

To me reductionism is the weaker position that to understand a system made of smaller parts it is (in principle if not in practice) sufficient to understand the parts. But either way, isn't this the /same/ as the idea of emergent phenomena? Emergent phenomena are by definition consequences of lower-level phenomena. At least in the subject line you seem to be setting up emergence as the opposite of reductionism, which makes no sense to me.

This has been fueled by the last
century's realization that many of the laws of physics are driven by
symmetry, and that unification is usually coupled with the acquisition
of a higher-order symmetry and a corresponding underlying simplicity
(in structure, not calculational ease).

Appeals to symmetry are what have worked over the past century, but dreams of a final theory are surely a lot older than that. If your position is just that perhaps we've reached the end of the era of symmetry and should start looking harder at nonsymmetrical theories, then I have no argument with that.

It's worthwhile pointing out that this strategy of reductionism is not
unique to physics, and that other whole areas of science have been
created on the back of this strategy: artificial intelligence,
psycholinguistics, origin of life, axiomatic mathematics, climatology.

Can you give an example of a scientific strategy that's non-reductionist? Right now I don't understand what you mean at all. Is there a non-reductionist way of doing experiments, or of formulating theories? I don't see how experiments are possible without some reductionist assumptions, and I don't think there's ever been any reductionism or anti-reductionism or rhyme or reason to how theories are formulated. Science proceeds very much like biological evolution, with theorists as the agents of mutation and experimentalists as the agents of natural selection. It doesn't matter whether new theories are discovered by formal deduction or by a vision in a dream.

However, of late, there have been a number of developments in
disparate areas which have suggested that there are incompleteness
"theorems" that more or less *demand* that reductionism is a doomed
venture. Some developments are less "theorems" but more significant
failures which are leading now to investigations of an appropriate
incompleteness theorem.

Surely there can be no disagreement that Godel's and Bell's results are theorems and that the other things you mention are not theorems in any sense of the word. I think you want some other word here than "theorems", with or without the scare quotes.

1. Godel's theorem about the incompleteness of axiomatic mathematics
goes without saying.

Whoa, whoa, whoa! It certainly does not! Sure, everybody mentions "Godel's theorem", just like everybody mentions "the speed of light" and "the uncertainty principle", but the vast majority of them have no idea what they're talking about. Any time you invoke a pop-culture cliche you have a larger obligation than normal to demonstrate that you have a good reason. I'm a bit suspicious, partly for the mere fact that you thought there was nothing more to say, and partly because you referred to Godel's incompleteness theorem, singular. There are two of them; did you mean the first or the second? If you can't immediately answer this question then you definitely don't understand Godel's work well enough to cite it in your defense.

There's a chance that you might convince me that one of Godel's theorems is relevant here, but you're going to have to say what formal system you're talking about, argue that it satisfies the premises of the theorem, and then say how you propose to interpret the conclusion.

2. Bell's theorem and the absence of hidden variables in quantum
mechanics, supporting the inevitability of the complementarity built
into QM.

I don't see how this bears on the existence of a final theory; maybe the final theory is just quantum mechanical and that's that. I can sort of see a bearing on my notion of reductionism, but it's very weak, because entanglement with particles outside the system does not affect the behavior of the system any more than classical correlation does.

I disagree with the claim that complementarity is built into QM. If you'd said "the uncertainty principle" then I'd agree, but complementarity has always been too vaguely specified to be a physical principle. And the (vague) statement that systems never exhibit both particle-like and wave-like properties in the same experiment is just not true.

6. Cosmologically, some measurements about really distant objects that
would provide the only clear answer about some fundamental constants
may be limited by photon statistics, which are in turn constrained by
cosmological redshift. Succinctly, it may be impossible to resolve
objects near the observational horizon because of the uncertainty
principle, thus appearing an inherent incompleteness boundary due to
the development of the universe itself.

I don't see how this in any different from the classical fact that we can't see stuff past the particle horizon. You can always just redefine the observable universe to be a little bit smaller.

7. Brooks' experiments in robotics demonstrated that sophisticated
walking behaviors of insects are best imitated by systems that are as
*stupid* as possible, and that the more sophisticated the behavior,
the more successful the more stupid systems are.

I don't know anything about Brooks' experiments, but again, isn't this actually an argument in favor of reductionism? (And in favor of the importance of emergent phenomena, which would appear to be the same thing.)

The void between the
simple algorithm and the complexity of the emergent behavior was also
noted by Wolfram, who thought enough of it to call it a whole new kind
of science.

Whatever you believe about emergence (and I don't necessarily disagree with any of that), Wolfram's book is just vanity-published crackpottery. The only reason anyone paid any attention to it is that he happens to be a minor celebrity.

8. Basal linguistics, wherein Chomsky's rule-based linguistics has
been found to fail at systematizing any language, because the *users*
of the language inherently break the rules of the language to
accomplish communication, thereby leading to an acknowledged
incompleteness theorem of sorts.

Variations of this argument get used a lot, usually with an explicit mention of "Godel's incompleteness theorem". It's invalid because there's no reason to believe that the rules aren't broken in a rule-based way.

-- Ben
.