One of the most beautiful commentaries I have seen on mapping the laws of nature to our mental models is given by the Nobel laureate Richard Feynman in The Pleasure of Finding Things Out. In particular, his analogy of castling and pawn transformation really resonate with new rules of nature we discover as we progress. Here is some of the transcript.
One way that’s kind of a fun analogy to try to get some idea of what we’re doing in trying to understand nature is to imagine that the gods are playing some great game like chess. Let’s say a chess game. And you don’t know the rules of the game, but you’re allowed to look at the board at least from time to time and in a little corner, perhaps. And from these observations, you try to figure out what the rules are of the game, what are the rules of the pieces moving.
You might discover after a bit, for example, that when there’s only one bishop around on the board, that the bishop maintains its color. Later on you might discover the law for the bishop is that it moves on a diagonal, which would explain the law that you understood before, that it maintains its color. And that would be analogous to we discover one law and later find a deeper understanding of it.
Then things can happen–everything’s going good, you’ve got all the laws, it looks very good–and then all of a sudden some strange phenomenon occurs in some corner, so you begin to investigate that, to look for it. It’s castling, something you didn’t expect.
We’re always, by the way, in the fundamental physics, always trying to investigate those things in which we don’t understand the conclusions. We’re not trying to check all the time our conclusions; after we’ve checked them enough, they’re okay. The thing that doesn’t fit is the thing that’s the most interesting, the part that doesn’t go according to what you’d expect. Also, we can have revolutions in physics. After you’ve noticed that the bishops maintain their color and that they go along the diagonals and so on for such a long time, and everybody knows that that’s true, then you suddenly discover one day in some chess game that the bishop doesn’t maintain its color, it changes its color. Only later do you discover a new possibility, that the bishop is captured and that a pawn went all the way down to the queen’s end to produce a new bishop. That could happen, but you didn’t know it.
So it’s very analogous to the way our laws are: they sometimes look positive, they keep on working, and all of a sudden, some little gimmick shows that they’re wrong, and then we have to investigate the conditions under which this bishop changed colour happened and so forth, and gradually learn the new rule that explains it more deeply.
Unlike the chess game, though, In the case of the chess game, the rules become more complicated as you go along, but in the physics, when you discover new things, it looks more simple. It appears on the whole to be more complicated, because we learn about a greater experience, that is, we learn about more particles and new things, and so the laws look complicated again. But if you realize that all the time what’s kind of wonderful is that, as we expand our experience into wilder and wilder regions of experience, every once in a while we have these integrations in which everything is pulled together in a unification, which turns out to be simpler than it looked before.