This is my third post about Feynman mythology, and I think what I really want to say is this
- Observation: Feynman gives these great intuitive pictures, and once you understand them, you can figure a lot of stuff out about the system without math
- Incorrect conclusion: Feynman did not have to use math, he could just use intuitive pictures
The incorrect conclusion doesn’t follow because Feynman couldn’t just read a Feynman lecture. He didn’t get to skip the math the way you do. He had to come up with the picture.
That’s why I think teh conclusion is invalid, but I also think it’s really incorrect. Here’s some quotes related to how Feynman worked.
David L. Goodstein & Gerry Neugebauer - Special Preface to the Feynman Lectures on Physics:
Why did Feynman devote more than two years to revolutionize the way beginning physics was taught? One can only speculate, but there were probably three basic reasons. One is that he loved to have an audience, and this gave him a bigger theater than he usually had in graduate courses. The second was that he genuinely cared about smdents, and he simply thought that teaching freshmen was an important thing to do. The third and perhaps most important reason was the sheer challenge of reformulating physics, as he understood it, so that it could be presented to young students. This was his specialty, and was the standard by which he measured whether something was really understood. Feynman was once asked by a Caltech faculty member to explain why spin ½ particles obey Fermi-Dirac statistics. He gauged his audience perfectly and said, “I’ll prepare a freshman lecture on it.” But a few days later he returned and said, “You know, I couldn’t do it. I couldn’t reduce it to the freshman level. That means we really don’t understand it.”
I always found it incredible. He would start with some problem, and fill up pages with calculations. And at the end of it, he would actually get the right answer! But he usually wasn’t satisfied with that. Once he’d gotten the answer, he’d go back and try to figure out why it was obvious. And often he’d come up with one of those classic Feynman straightforward-sounding explanations.
So if you’re not Feynman, you get the straightforward-sounding explanation, but if you are Feynman, you need to work with something that hasn’t already been made simple, and I think that involves a lot of math.
Which I think says something about what math is for in science… ok, so here’s my correct conclusion, what I think is the correct conclusion:
- Part of what Feynman did at work was come up with simple intuitive pictures, using his previously constructed intuitive pictures, as well as lots of math
So that’s part of what you can do with math, is construct simple intuitive pictures, and make sure they’re actually giving the right answers. Which is outside the dichotomy “crunch numbers or symbols and get an answer without a picture” vs “just ponder the physical situation and use your intuition”. Building your intuition and getting an understanding of the physical situation are part of what you use the math for.
I remember my grandpa telling me he thought his math classes had run out of useful things to tell him when they started teaching him about inequalities, since math is supposed to be exact. He didn’t get why so much of advanced math is actually qualitative
