Scientific American in May 1963 published theoretical physicist Paul Dirac’s article “The Evolution of the Physicist’s Picture of Nature.” It was my last year as a physics undergraduate and the article described important steps in development of relativity and quantum theory and also suggested future developments.
Dirac emphasized the importance of “beautiful mathematics” in describing the world and said, “One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.”
“God is a mathematician” wasn’t original with Dirac. Plato is reported to have said, “God is always doing geometry.” Heisenberg, another founder of quantum theory, described in his scientific autobiography Physics and Beyond how as a student he was both puzzled and intrigued by Plato’s description of the creation of the world from geometric elements.
I didn’t make mathematics my religion, but took seriously the idea that God had created a world according to mathematical pattern. That fits well with the prologue of John’s gospel which says that “all things came into being” through the divine Logos, the Word or Reason of God. These ideas influenced the direction of my later interests in physics and I gave a faculty lecture titled “God is a Mathematician” at a college where I taught.
Before I encountered Dirac I had read Einstein’s essay “On the Method of Theoretical Physics”. Here he emphasized that science must begin and end with experience of the world but that “the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.”
But what mathematics? When Plato spoke of God doing geometry he meant the system that was eventually canonized as Euclid’s Elements. It was the familiar geometry in which the Pythagorean theorem is true, the angles of a triangle add up to 180 degrees, and so on. How else could the world be? If you were smart enough, “pure thought” could figure out how the world is.
But the discovery of consistent non-Euclidean geometries in the early 19th century showed that Euclid’s geometry isn’t the only possible one. There is more than one mathematical pattern God could use in creating a world. That is why observation of the way the world must be is the final test of any theory.
But here’s another bit of my history. In graduate school there was a weekly physics colloquium at which visiting scientists presented recent work which could be from a wide range of topics, theoretical and experimental. If the announced subject didn’t interest those of us who were focused on our own work, we might skip it. Then our advisor, on his way to the colloquium, might see that my office mate and I weren’t planning to go, and would exhort us not to be “pinheads.”
That was a warning against narrow specialization in physics, but the principle is broader. Interest in all of physics, or even science in general, can be too narrow. It’s appropriate to speak about “beautiful mathematics”, but not to say that only mathematics can be beautiful! In fact, we would be hard pressed to quantify the beauty of different mathematical theorems.
We know types of beauty and rationality that can be expressed in music, poetry, the visual arts, and other endeavors as well as in mathematics. There is more to a symphony than the arithmetic relations involved in harmony. Poetry is more than mathematically correct scansion and a perfect cube isn’t great art.
Mathematicians can be interested in other things than mathematics. They don’t have to be pinheads.
That’s true of humans, and also of God. Israel’s wisdom tradition, found in some books of the Old Testament with echoes in the New, is an important part of scripture but contains virtually nothing about mathematics. This, together with the variety and complexity of the natural world, suggests that God is not a pinhead. We can say that God is “a mathematician of a very high order”, but God does other things too.
If that’s the case, perhaps the laws of nature (the real patterns of the world, not just our approximations to them) can’t be expressed entirely in terms of mathematics. To put it more provocatively, perhaps it isn’t really Physik über alles.
That will be called heresy by many physicists, so in support I call to witness another member of that tribe, John Polkinghorne. He suggests “the possibility of downward emergence, in which the laws of physics are but an asymptotic approximation to a more subtle (and more supple) whole.” 1
Polkinghorne points out, as others have done, that the wetness of water is something that only emerges when many H2O molecules are present because “wet” means nothing in terms of the basic laws describing molecules.
More importantly, while biological systems can be analyzed into molecules and atoms which behave in accord with quantum mechanics, the behaviors of living things as living things can’t be completely explained by the laws of physics. (This may remind some of Bohr’s idea that descriptions of a system as alive and as a machine are complementary.)
Such a suggestion will arouse suspicions of “vitalism”, but I think that misses the point. The example of “wetness” shows that we’re not talking only about living things. There is no special material of life, an idea that was disposed of in the 19th century when it was shown that “organic” chemicals could be synthesized from “inorganic” ones. And there are no forces or energies peculiar to biological systems. The basic interactions of physics suffice. Nevertheless,
the behaviors of living things will not be described adequately by solving (if we could) the Schrödinger equation for an immense number of atoms.
If we take these ideas seriously, they have implications for some significant issues in science-theology dialogue. If the laws of nature cannot be expressed exhaustively in terms of mathematics, then it seems likely that they are not completely deterministic. That would mean that God, without violating those laws, would have some flexibility in directing the course of natural processes, over and beyond whatever freedom of action chaos theory or quantum mechanics might confer. And some light might be shed on one of the major unsolved problems of science today, the origin of life (chemical evolution), and God’s involvement with that.
I’ll dive into that problem in my next article.
George Murphy received his Ph.D. in physics from Johns Hopkins for work on general relativity in 1972. He taught at Westminster College (PA), The University of Western Australia and Luther College and did research for eleven years before entering Wartburg seminary. Ordained in 1983, he has served as a pastor in Lutheran and Episcopal congregations. His first article on theology and science was published in 1977 and he has since published six books and numerous articles and continues to speak and lead workshops in this area. His most recent book, Models of Atonement: Speaking about Salvation in a Scientific World (Lutheran University Press, 2013), discusses ways of understanding the saving work of Christ in an evolving world.