Saturday, March 31, 2007

Living In An Ocean Of Uncertainty

Like we’ve got a choice.
Posted by olvlzl.
My thanks to ProfWombat, a distinguished habituee of Eschaton, for steering me to this wonderful paper, The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner, in response to some questions about the eight-dimensional object defined by David Vogan* .

The questions were about the number of possible dimensions, the limits to the possible calculation of them, the limits of calculation itself, and the presence of these dimensions in the physical universe. Do these dimensions impinge on our lives? What are the limits of our knowledge of the possible impact could be?

The article, published in 1960, is about the surprising relevance of math in the physical sciences. It surprised me by containing several passages relevant to recent postings here. Here are just three:

"How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?" It has to be admitted that we have no definite evidence that there is no such theory.

The complex numbers provide a particularly striking example for the foregoing. Certainly, nothing in our experience suggests the introduction of these quantities. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.

A much more difficult and confusing situation would arise if we could, some day, establish a theory of the phenomena of consciousness, or of biology, which would be as coherent and convincing as our present theories of the inanimate world. Mendel's laws of inheritance and the subsequent work on genes may well form the beginning of such a theory as far as biology is concerned. Furthermore,, it is quite possible that an abstract argument can be found which shows that there is a conflict between such a theory and the accepted principles of physics. The argument could be of such abstract nature that it might not be possible to resolve the conflict, in favor of one or of the other theory, by an experiment. Such a situation would put a heavy strain on our faith in our theories and on our belief in the reality of the concepts which we form. It would give us a deep sense of frustration in our search for what I called "the ultimate truth." The reason that such a situation is conceivable is that, fundamentally, we do not know why our theories work so well. Hence, their accuracy may not prove their truth and consistency. Indeed, it is this writer's belief that something rather akin to the situation which was described above exists if the present laws of heredity and of physics are confronted.

I don’t know if forty-seven years later we have any more reason to be optimistic about the possibility of a coherent theory of consciousness. There doesn’t seem to be much more progress of even defining what consciousness might be or, when it suits the purpose of the pseudo-skeptics, if it exists. I doubt it’s possible.

Also this week, the statement repeated by Richard Dawkins on Terry Gross’ program that he can prove that the probability of there being an intelligent god is virtually nil has got to count as one of the most astoundingly absurd and arrogant things that a scientist of his standing has said in at least as long. As I recall Dawkins heaped quite a bit of mockery on some deluded Bayesians for attempting to prove the existence of God through their version of probability. But what other standards of probability he could hope to use in his debunking effort?

Two things jump out. First is the impossibility of even figuring out the possible outcomes to the question.** Without those, how could probability be estimated. Second, and most clear, is that there isn’t any way to know if any form of probability would apply to anything that is supernatural. Probability, like all math, is derived from the experience of the physical universe and human imagination. The belief in its applicability to any proposed supernatural entity is a leap of faith larger than that required to believe in any unique, supernaturally instigated miracle. I don’t happen to believe in miracles of that kind, though I’d point out that they would be, by definition, outside of the usual experience of the universe. As in that little piece about “prayer studies”, being unique and outside of nature you couldn’t do honest science about them.

If I was one of Dawkins professional rivals or enemies I’d go back and check his math, especially anything approaching the application of probability.

And that was just one of the absurd things Dawkins is still pushing on the subject. But I don’t really care about that. Reading Creation "Science" Is the Christian Right's Trojan Horse Against Reason by Chris Hedges scared me. We don’t have time to follow Dawkins, Harris and Dennet down the cul-de-sac from which there isn’t any emerging. This is an emergency. For the left, we’ve got real problems with fundamentalists, here and now. We don’t have political capital to spend on getting involved with this nonsense. We have to defeat the religio-fascists politically and that will require everyone, progressive believers and non-believers alike. Getting involved in unsolvable arguments is worse than a waste of time, it will end up with us divided and so the success of the fundamentalists.

* Vogan’s M.I.T. website is pretty delightful in itself. Those with an eye for that kind of thing should look at the flat representation of his eight-dimensional object. Considering his acknowledgment that his project left a trail of super-computers crashed, this notice thrilled me.

I have followed the department's instructions for creating a home page, and copied the home page of Richard Melrose. I regret the inevitable errors that this process must have introduced.

** Karen Armstrong’s classic book “A History of God” goes into some discussion of how a number of religious mystics have held that “God doesn’t exist”. That isn’t to say that they didn’t believe that there was a God but that to talk as if God was an object that could exist was meaningless. How would Dawkins figure that into his probabilistic calculations?