Mathematics

Pi in the Sky

By Mark Vernon
Big Questions Online, November 30, 2010

Edited by Andy Ross

George V. Coyne and Michael Heller
A Comprehensible Universe: The Interplay of Science and Theology
Springer, 2008

Mathematics seems to be a universal language. The natural world is a complex place, packed with variations and permutations, random events and patterns so complex they are far from obvious to the eye. And yet, mathematics can capture much of that intricacy.

Mathematics seems to be discovered, not created. Discoveries about the physical world often start as discoveries in mathematics. Physics is about discovering the laws of nature, and those laws appear to be written in the language of mathematics. Mathematical predictions must be verified by observation, but that they are verified at all is the issue. Mathematics looks miraculous.

Michael Heller, winner of the 2008 Templeton Prize, said in his book:

In the human brain, the world's structure has reached its focal point: the structure of the world has acquired the ability to reflect upon itself ... In this conceptual setting, science appears as a collective effort of the Human Mind to reach the Mind of God ... The Mind of Man and the Mind of God are strangely interwoven.

But there is a gap between the kind of deity implied by mathematics and the deity worshiped by Christians, Jews and Muslims.

Roger Penrose holds a Platonic view. First, there is the physical world, the natural world that surrounds us. But there’s also the Platonic world of mathematics. The Platonic world maps onto the natural world in some way, perhaps via the imaginative power of human mental activity. We need not assume that the Platonic and natural world are wrapped up in some kind of divine embrace.

At the level of quantum physics, mathematics is not continuous but discrete, not smooth but lumpy. This suggests that mathematics is just one more messy part of the fabric of the universe. If that turns out to be right, the miracle looks less impressive. Maybe pi is not in the sky after all.
 

AR  I read Heller's book when it came out (thanks to my Springer connections) and now I feel the urge to say a lot about this issue. But I shall need to write a book to do so.