by godelski | 2025-07-20 20:38:52+00:00
It's been a decade, so I don't have any of the actual tests anymore. But the class used Marion and Thornton's Classical Mechanics[0] and occasionally pulled from Goldstein's book[1]. It was an undergrad class, so we only pulled from the second in the Classical II class.

For these very tough physics (and math) problems usually the most complex part is just getting started. Sure, there would always be some complex weird calculation that needs to be done, but often by the time you get to there you have a general knowledge of what actually needs to be solved and that gives you a lot of clues. For the classical we were usually concerned with deriving the Hamiltonian of the system[2]. By no means is the computation easy, but I found (and this seemed to be common) that the hardest part was getting everything set up and ensuring you have an accurate description which to derive from. Small differences can be killer and that was often the point. There are a lot of tools that give you a kind of "sniff test" as to if you've accounted for everything or not, but many of these are not available until you've already gotten through a good chunk of computation (or all the way!). Which, tbh, is really the hard part of doing science. It is the attention to detail, the nuances. Which should make sense, as if this didn't matter we'd have solved everything long ago, right?

I mean in the experiment section of my optics class we also were tested on things like just setting up a laser so that it would properly lase. I was one of two people that could reliably do it in my cohort. You had to be very meticulous and constantly thinking about how the one part you're working with is interacting with the system as a whole. Not to mention the poor tolerances of our lab equipment lol.

Really, a lot of it comes down to world modeling. I'm an AI researcher now and I think a lot of people really are oversimplifying what this term actually means. Like many of those physics problems, it looks simple at face value but it isn't until you get into the depth that you see the beauty and complexity of it all.[3]

[0] https://www.amazon.com/Classical-Dynamics-Particles-Systems-...

[1] https://www.amazon.com/Classical-Mechanics-3rd-Herbert-Golds...

[2] Once you're out of basic physics classes you usually don't care about numbers. It is all about symbolic manipulation. The point of physics is to generate causal explanations, ones that are counterfactual. So you are mainly interested in the description of the system because from there you can plug in any numbers you wish. Joke is that you do this then hand it off to the engineer or computer.

[3] A pet peeve of mine is that people will say "I just care that it works." I hate this because it is a shared goal no matter your belief about approach (who doesn't want it to work?! What an absurd dichotomy). The people that think the AI system needs to derive (learn) realistic enough laws of physics are driven because they are explicitly concerned with things working. It's not about "theory" as it is that this is a requirement for having a generalizable solution. They understand how these subtle differences quickly cascade into big differences. I mean your basic calculus level physics is good enough for a spherical chicken in a vacuum but it gets much more complex when you want to operate in the real world. Unfortunately there aren't things that can be determined purely through observation (even in a purely mechanical universe).