The Relationship of Physics to Math (Feynman 2)

Yesterday morning I read the first chapter of Richard Feynman's The Character of Physical Law, a series of lectures he gave at Cornell in 1965, fifty years ago. This morning I read the second chapter, "The Relation of Mathematics to Physics." In this chapter you really catch a glimpse of this man's genius, as well as his uncanny ability to explain things.

This chapter is full of insights that, interestingly enough, I have caught these last twenty years or so at IWU, especially being friends with the likes of Keith Drury and Russ Gunsalus. These are insights that were part of the founding of Wesley Seminary, insights that are hard to catch, hard to communicate, hard to convince. When they train you to be a scholar, they do not teach you to think like Feynman, a physicist. They teach you to think like a mathematician.

1. Feynman of course is not disparaging of mathematicians in the least. Indeed, he ends the chapter by apologizing to the layman for the difficulty of mathematics. "If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in" (58), by which he means math. In the chapter, he references people like me, who read book after book, hoping that the next person will finally be able to explain to me what is going on with quantum physics.

But in the end it is just tough. Either you can hack the stuff or you can't. In the words of Euclid to a king, wanting an easier explanation, "There is no royal road to geometry" (58). In the words of the nineteenth century physicist Jeans, "The Great Architect seems to be a mathematician."

This is a powerful statement: "To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature... [there are] people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once."

2. Still, Feynman spends most of the chapter indicating that physics is quite distinct from math. He wonders if the mathematicians will prove to be right in the end, that all of nature can be boiled down to certain axioms, certain "building blocks" of knowledge, as it were. He calls this the Greek approach to math, to start with foundational claims and build all other claims from there.

But we are not there yet at all, he indicates. Even in math, he suggests, you can start at different places and get to the same destination. But in physics, things are much more like the Babylonian way of doing math. By his description, the Babylonian way of doing math is that you know a collection of things that are true.

You do not break them down into truth atoms. You see some connections between these various mathematical truths and you intuit when to use one tool and when to use another. There are many analogies in physics, he says, where there are no clear connections between differing rules at all, but they have an uncanny similarity to each other.

3. This is the state of physics right now. It is impossible in physics right now to know what the first principles are--or whether there even are first principles. When Newton was asked what his theory of universal gravitation meant, he indicated that it didn't mean anything. It simply describes how things move.

I have said this many times here and it is in my philosophy book. Science is a collection of very precise myths that express the mystery of the world's operations.

Feynman gave as an illustration three completely independent and apparently unrelated ways to express the phenomenon of movement. The first was Newton's "action at a distance model," where a force is acting on an object at a distance. But there is a second model that looks only on the mass and potential of the object itself. And there is a third model, Euler's principle of least action. This last one was the inspiration for Feynman's claim to fame in quantum physics. Somehow, particles know to take the path of least action.

These three expressions (myths, if you would) are completely unrelated, apparently, but they all explain the motion of a body from one point to another correctly, at least on a macro-scale. "The correct laws of physics seem to be expressible in such a tremendous variety of ways" (55).

4. Practical theology is much more like physics than it is mathematics, in that regard. There are these macro-truths. It isn't always helpful to try to break them down into fundamental truth atoms. As a Biblehead, the game we often play of trying to break down life into Bible atoms (i.e., proof texts) is really embarrassing. It's really just a silly game.

But I digress. There are times when the "physics" of life and morality isn't working right and you need to bring in the "mathematicians." And sometimes the "mathematicians," while exploring the beauty of thought for its own sake, will generate useful tools for life without thinking of its relevance.

Feynman would say that the physicists need the mathematicians at key points, although most of what physicists do, in his own words, is fly by the seat of their pants, to see if something works in the real world. And, of course, Feynman was also very good at math.