It had been many years since I last read any books by or about Feynman. Unfortunately, I never had the chance to hear him speak in person. I also had never read the book version of “The character of physical law” before so there were several things that struck me after watching some of the lectures. The first was that Feynman was extremely philosophical and cultured. This was somewhat surprising because the mythology surrounding Feynman, promoted by his own autobiographies, is that he was the no-nonsense street-smart kid from Brooklyn who used common sense and cunning to outsmart the so-called intellectuals with highfalutin ideas. I never fully bought into that myth but now after watching three of the lectures I feel as if they can be completely dispelled. Feynman was extremely intellectual and very interested in the humanities. He just disagreed with how they were being carried out and done at that time.
In the second lecture, Feynman talks about the relationship between mathematics and physics. He says that mathematics is the language of physics but not the same as physics. He uses the metaphor of “Greek” and “Babylonian” mathematical traditions. In this metaphor, the Greek approach was axiomatic. Math is reduced to exploring the logical outcomes of a fixed set of rules or axioms. Everything connects to everything else within that system. The Babylonian method is to learn mathematics through examples and heuristics. The connection between these individual results may or may not be known. To Feynman, physics uses the Babylonian approach and it is only by doing it that way can new discoveries be made since theorems can pop out where they shouldn’t. He uses the example of the conservation of angular momentum, which was noticed by Kepler in his law that planets sweep out equal areas in equal times and shown to be true by Newton from his laws of motion and gravitation. However, it was a leap of faith that the same conservation law was applicable to a figure skater who uses muscle power to spin and even more to subatomic particles. Feynman argues that one must use the Babylonian method to make these leaps since they could not be deduced axiomatically. As long as we don’t have a complete theory of physics, the axiomatic approach will not be useful.
Another example Feynman brings up in this context is that there are equivalent formulations of physical laws that cannot be distinguished experimentally but can lead to different insights so it is important to be aware of all of them and not be biased against any of them. Classical mechanics can be described by Newton’s laws, (which requires action at a distance), in terms of a field like the gravitational potential (which can be obtained from purely local information), or through a minimization of the difference between kinetic and potential energy (least action principle). He then says that when you now include more information like there cannot be action at a distance then Newton’s laws fail miserably but the field and least action formalisms can be modified to account for the new information. Hence, since you’ll never know when modifications will be needed a physicist must be a Babylonian and keep all points of view. The axiomatic approach of mathematics is not efficient in this regard.
In the final minutes of his lecture, Feynman becomes almost whistful and somewhat agitated. He says that the laws of nature are described by mathematics and there is no simplification. You can use all sorts of analogies but the only way to really understand and appreciate nature is to learn her language, which is mathematics. Just as it is really impossible to truly describe what music is like to a deaf person, you really are missing out on something very beautiful if you don’t learn mathematics so you can understand physical theories. It is as if he has found something beautiful that he wants to share but not only will no one listen but there are people that are actively thwarting him. He ends his lecture rather abruptly with a shot at those people in “the other culture” that C.P. Snow wrote about who believe that nature can be understood qualitatively with the line “It is perhaps that their horizons are [so] limited, which permit such people to imagine that the center of the universe of interest is man”.