Mathematics and the Universe

[Purple Rabbit]

CoxRox asked me to assess the following quote of John Polkinghorne (christian reverend and former particle physicist):

One of the fascinating things about the physical world is that its fundamental structure seems always to be expressed in beautiful mathematics. To me that suggests that there is a Mind behind the structure of the world, and that our minds are somehow attuned to that Mind.

This indeed touches on a subject that interests and puzzles me. Polkinghorne's fascination is akin to the belief that mathematics is the language of nature. This is a view held over the centuries by many prominent scientists and in it most elementary form it asserts that the language of science must necessarily be mathematical. Some even romantically dream of mathematics as something that exists independently of human beings, something that structures our actual physical universe and any possible universe. It should be pointed out however that mathematics is built on formal definitions and these make use of words and symbols that have meaning only in terms of human experience. To state that mathematics is the language of god is pretending to know the mind of god, a rather bold assertion even from a religious viewpoint. All we can say is that mathematics is a formal language developed and understood by humans.

It may be helpful to compare the religious centered view of Polkinghorne on the matter with the science centered view of Einstein. But first some clarification is needed on the religious views of Einstein to place his views in the right context. A popular quote from Einstein on religion is the following:
"I believe in Spinoza's God who reveals Himself in the orderly harmony of what exists, not in a God who concerns himself with fates and actions of human beings." — Albert Einstein
(New York Times, 25 April 1929, p. 60, col. 4. Ronald W. Clark)

Years later he expanded on this in a letter: "I can understand your aversion to the use of the term 'religion' to describe an emotional and psychological attitude which shows itself most clearly in Spinoza," he wrote. "[But] I have not found a better expression than 'religious' for the trust in the rational nature of reality that is, at least to a certain extent, accessible to human reason." So Einstein by using religious terms expresses his unsubstantiated trust in the rational nature of reality. He had found no rational argument to back up the claim that the universe indeed should have a rational nature and the trust on that rational nature he identifies as in essence a leap of faith. And therefore, he concludes, a religious terminology is suited. Notwithstanding this religious terminology Einstein denies any purpose in nature, refutes the idea of a personal god, life after death, the concept of a soul seperate from the body. With Einstein god is the order and lawfulness of the universe itself. This often confuses people.

For me the key point here is that Einstein is very sparse with attributing any characteristics to his 'god'. All he does is identifying the leap of faith which he as a scientist cannot circumvent, i.e. unreasoned trust in the order, lawfullness and rational nature of the cosmos. He (confusingly for many) labels it as a form of religion for which religious terms can and perhaps must be applied. But he does not make any assertions on top of the one he feels he cannot do without. Also it should be noted that this one leap of faith has brought us very spectacular results indeed, and that in itself to me seems enough justification for it.

I suspect that the answer to the question about the relation between mathematics and the universe (famously by Wigner called the unreasonable effectiveness of mathematics) is to be found in the fact that our minds, as a byproduct of necessary adaptation to a a vast range of dynamic situations , have developed rather good pattern recognition faculties. If these faculties are good enough to understand all of it however remains to be seen.

It seems to me, comparing the stances of Polkinghorne and Einstein, the stance of Einstein is the most parsimonious. Polkinghorne adds on top of awe for the order and lawfullness in nature an unreasoned divine purposefull agency and purposeful design, he claims to know the mind of god. I believe these additions to be no more than unsubstantiated leaps of faith.