Two Matters

1. Evolution in the Political Context Again: A Reference

In the January 11 edition of Inside Higher Ed’s “Views,” one Jason R. Wiles has written a nice piece, “The Huckster’s Artful Dodging on Evolution,” reviews Mike Huckabee’s “record on the teaching of evolution in the public schools — an issue that is not specific to higher education, but that ultimately can have a major impact on science education policy and the nature of intellectual debate in the United States.”

Neatly correlative to that summary of the history of Huckabee on evolution is an equally helpful comment by one R.W. Hoyer, “Why Mike Huckabee Should Not Be President,” presenting us with some pause-provoking data on the views of the American public on the topic. To give you a sense of the latter, Royer tells us that “according to a 1987 Newsweek survey just 700 of 480,000 life and earth scientists (0.14%) assign any credence at all to so-called creation-science, yet 87 million adult Americans (47%) support that perspective.”

I have already, in previous postings, devoted more of my very finite intellectual energy to Huckabee’s views than they deserve, at least on their own intrinsic merits. So I’ll content myself here with just giving you the URL that should take you to the article and comment: http://insidehighered.com/views/2008/01/11/wiles.

2. More on Theology and Mathematics: an Epi-Digression

With the matter of the relationship between mathematics and religion or theology on my mind, itself a digression from the matter of the relationship between science and religion or theology that I have been focusing on, I found myself reading a relevant review in the January 13, 2008, The New York Times: Jim Holt’s “Proof,” a review of John Allen Paulos, Irreligion: A Mathematician Explains Why the Arguments for God Just Don’t Add Up (Hill & Wang).

The review’s opening paragraph immediately caught my eye.

A physicist, a biologist and a mathematician walk into a bar. Bartender says, “Any of you believe in God?” Which of the three is most likely to say yes? Answer: the mathematician. Mathematicians believe in God at a rate two and a half times that of biologists, a survey of members of the National Academy of Sciences a decade ago revealed. Admittedly, this rate is not very high in absolute terms. Only 14.6 percent of the mathematicians embraced the God hypothesis (versus 5.5 percent of the biologists).

In my January 2, 2008, posting, “Religious Experience and Mathematical Experience I,” I quoted a statement from the The Mathematical Experience of Philip J. Davis and Reuben Hersh (p. 111-112) that sees the theologian’s belief in a nonmaterial reality as making it easier for a mathematician to believe in “mathematical objects which are simply one particular kind of nonmaterial object.”

Belief in a nonmaterial reality removes the paradox from the problem of mathematical existence, whether in the mind of God or in some more abstract and less personalized mode. If there is a realm of nonmaterial reality, then there is no difficulty in accepting the reality of mathematical objects which are simply one particular kind of nonmaterial object.

The results of the National Academy of Sciences survey suggest that the reverse may alos be the case: the mathematician’s belief in a nonmaterial reality may make it easier for a theologian to believe in a divine reality which is simply one particular kind of nonmaterial object.

I found Holt’s second paragraph equally arresting, for it bears on the Platonism of many mathematicians, including Davis and Hersh, that I noted in the January 6, 2008, posting, “Mathematical and Theological Realities: Responses to Two Comments.”

But here is something you probably didn’t know. Most mathematicians believe in heaven. Not a heaven with angels, but one populated by the abstract objects they devote themselves to studying: perfect spheres, infinite numbers, the square root of minus one and the like. Moreover, they believe they commune with this realm of timeless entities through a sort of extrasensory perception. Mathematicians who buy into this fantasy are called “Platonists,” since their mathematical heaven resembles the realm of the Good and the True described in Plato’s “Republic.” Some years ago, while giving a lecture to an international audience of elite mathematicians in Berkeley, I asked how many of them were Platonists. About three-quarters raised their hands. So you might say that mathematicians are no strangers to belief in the unseen. (Of course, mathematicians don’t drag their beliefs into the public square, let alone fly planes into buildings.)

Noting, parenthetically, that (Paulos, of course, is a mathematician who does drag his beliefs into the public square), let me go on to use Paulos’s own exposition (on pp. 46-47) to illustrate just how Platonist mathematicians can be.

Another example of creating something, the positive whole numbers, literally out of nothing is the mathematician John von Neuman’s recursive definition of them. Two preliminary notions are needed: The first, the union of two sets A and B, is the set of elements in one or the other or both of the two sets. It is symbolized as A È B. The second, the empty set, is the set with no elements. It is sometimes symbolized by a pair of empty braces: {}. The number 0 von Neuman simply defines to be the empty set. Then he takes the number 1 to be the union of 0 and the set containing 0. The number 2 he takes to be the union of 1 and the set containing 1, and the number 3 he takes to be the union of 2 and the set containing 2, and so on. Each number is thus the union of all its predecessors and derives ultimately from the empty set.

And so on infinitely.

Let me close this post by (1) asking why, if a mathematician can thus define numbers into existence, a theologian cannot similarly define God into existence and (2) stating that I can’t believe that the act of definition is up to the task in either case.

Addendum: The Wikipedia article (http://en.wikipedia.org/wiki/John_von_Neumann) on von Neumann begins:

John von Neumann (Hungarian Margittai Neumann János Lajos) (December 28, 1903 – February 8, 1957) was a mathematician who made major contributions to a vast range of fields including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics and game theory, computer science, numerical analysis, hydrodynamics (of explosions), and statistics, as well as many other mathematical fields. He is generally regarded as one of the foremost mathematicians of the 20th century.

Also, for what it is worth, the article points out that:

Along with Edward Teller and Stanislaw Ulam, von Neumann worked out key steps in the nuclear physics involved in thermonuclear reactions and the hydrogen bomb.

Postscript: I promise to do my best, in the next posting, to get back to the point I was trying to make with Davis and Hersh and the notion of mathematical experience and then, in the next or nearly next one, to return to my discussion of Polkinghorne’approach to science and theology. But I’ve been having so much fun.