Something half-baked that I’ve been thinking about lately: I think physics is addicting. In particular, I think learning physics is addicting in a way that math tends not to be.

When one first learns electricity and magnetism, for example, there are a lot of things one just accepts, and places where one learns what is obviously an incomplete picture. Some – like Coulomb’s law – are reasonable to just accept as axioms, but some – like these \(\mathbf{E}\)s and \(\mathbf{B}\)s floating around and the fact that changes in fields propagate at a speed \(c=\frac1{\sqrt{\mu_0\epsilon_0}}\) which is, notably, a constant – make it clear that there’s more going on. So to fill the gaps, one takes another course in E&M, and another in special relativity, in which maybe one notices that the word ``acceleration’’ is conspicuously absent – thence general relativity. And at some point the can of worms that is quantum mechanics gets opened. First it comes as differential equations, but clearly there’s something more going on, so then it becomes linear algebra. But at this point it’s obvious that to really understand things, one needs to learn quantum field theory. By the end of the first course, there are as many gaps in the theory as gaps it fills, and while the second course will (I hope) fix some of those, it’s still not the end of the road. In fact, it’s not clear that anyone knows where the end of the road even is.

Contrast to math. Calculus, as one learns it in high school or early college, is not the most self-contained, but soon thereafter most parts of math stand on their own. Certainly after taking set theory, topology, and analysis, one can claim that all the things one knows, one fully understands. That doesn’t mean there isn’t more to learn – algebra, for example, but it all in some sense builds up on top of the things already learned. Homotopy groups take algebraic topology to understand, but they are, after all, a part of algebraic topology. Where physics builds downwards, filling in the foundation of each concept with the next one, math builds upwards, one concept upon the next.

I don’t know if this means anything about the fields. Maybe it means mathematicians are better at figuring out how to learn things in a way that doesn’t leave lots of gaps, or maybe they are better at coming up with useful abstractions and suitable sets of axioms, or maybe they have an easier job since we do have a reasonable foundation for math. And I think to some extent parts of physics that I know less of may build up more – statistical mechanics, for one. CS definitely does some of each: from basic programming one can go up, to heavier software engineering, algorithms, or AI, or down, to circuits, CPUs, and compilers. But it does seem like an interesting difference to me.