I learned something curious about Feynman the other day.
So, there are these things called Feynman diagrams, they are graphical representations of particle interactions in field theory. They look kind of haphazard but they are actually mathematically precise tools that take the place of otherwise extremely convoluted integrals. The number of connections at each node is determined by the order of the interaction, the number of end points in the graph by the number of particles involved in the interaction, and each connecting line is a “propagator” that moves the particle forward in time or space. The details are not important, really. The point is that these rules are a mathematical mapping between some kind of arduous advanced functional calculus of local fields and rather elementary combinatorics. Say you have a third order interaction and two particles, the question becomes how many different graphs can you draw with two end points and only intermediate vertices that join three lines? Pretty easy. On the other hand, the formal version of this calculation took us 3 classes to get through.
Anyhow what I learned was that Feynman was doing calculations with these diagrams well before their connection with the field theory formalism of the day was established. It took the work of several /other/ field theorists to actually legitimize what he was doing mathematically. That’s awesome. And Schwinger, a real hard-ass and one of Feynman’s contemporaries (who also shared Feynman’s Nobel for QED), was famously quoted muttering something about Feynman bringing “calculations to the masses”. See, Schwinger didn’t believe that there was value in “simplifying” the concepts in his field. He liked being the only guy in the room that could make any sense of the quantum field theory of his day.
But that’s not exactly it. I had a conversation recently with a lab mate where he said that he despised Feynman. He didn’t like his cocky me-first attitude, and he didn’t really buy all that stuff about “intuiting” mathematics and physics. He thought it was imprecise even though it’s impressive and was lucky enough to be able to produce results. I’m pretty sure this guy has the same personality type as Schwinger.
Intuition itself is a pretty fascinating topic. I’m pretty sure, from my experiences as a physics student, that it doesn’t come out of a vacuum. It’s based on past experience and practice and repetition. Kids often like studying mechanics because they find it very “intuitive”– even the first time they learn it. But kids who grow up in a universe with different laws would certainly not find our mechanics curriculum very intuitive. From that perspective intuition is of limited value compared to mathematical rigor.
But there is a different kind of intuition. An abstract pattern recognition across disciplines that I think is extremely valuable. When the Theory of Everything arrives, it’s unlikely to be in a form that fits neatly into our current mathematical framework. Learning to be flexible with our mental models, learning to separate physical content from the language of their representation, will become more and more important in the near future. And so should start playing a bigger role in the science curriculum.