This is the data we looked at here at UT when deciding whether to ask for the Physics subject GRE or not. Unlike UGrad GPA, the physics GRE was a good predictor on whether a sudent would complete their PhD or not. We ended up abandoning it anyway.

Steve Ballmer reveals the interview test Microsoft used to separate problem-solvers from gamblers: "I'm thinking of a number between 1 and 100. First guess, I give you $5. Then $4, $3, $2, $1. After that, you pay me." "There are far more numbers on which you lose than win."

Ok so I did the experiment as described here, trying to wrap my mind around the Yang-Mills theory. The idea is to see if Wittgenstein was right about the expressibility of even deep ideas: if I can glean the intuition of this thing without immersing myself in 2 years of theoretical-physics material, perhaps he was. Some “experimental setup”: In total I spent about 2 hours talking to Claude, most of which were spent on reading its initial message to my prompt, although subsequent clarifications were essential. It really helped that this was such an fascinating theory, I might have given up this thankless task otherwise. My initial prompt was, “Explain the Yang-Mills theory to me. I don't have background in it (only computer-science math, not a theoretician), so please try to abstract away the details and notations to the extent possible, and focus on the ideas, significance, positioning, motivation, etc.” My actual background: aced special relativity and kinetics in undergrad, almost failed second-semseter electro-Maxwell shit; this was years and years ago, though. From popular science I know, and it turned out to be useful, that the 2 important models of physics are the Standard Model, understood to govern “anything really small” (like electrons and other particles), and General Relativity, understood to govern “anything not super small”, like planets and black holes and biological cells and people. (Not even sure where molecules fall.) Interestingly, the SM models 3 forces (electromagnetism and 2 others — none of which are gravity) whereas GR models gravity alone. What I learned here: the Yang-Mills theory allowed physicists to cast the behaviors of all 3 forces in the Standard Model(*) under one general framework where, for each force: (1) Every point in spacetime is associated with a mathematical entity that I’ll call “potential” (concretely a vector/tensor or some such). (2) The differential of potential across any given path in spacetime, i.e., to how potential changes across spacetime, isn’t path-invariant. Two paths from A to B accrue different changes in potential. A specific measurement of this path-insensitivity (roughly, measuring change in a small-loop path (?)) corresponds to the “field”, i.e., the physical reality that’s operating on particles in that point in spacetime. (3) Here’s where it gets interesting: the potential has degrees of freedom, you can transform the potential _at any point in spacetime separately_ and it will imply the same field. This is called local symmetry. And, the field’s behavior is the ~unique solution to the requirement that there should be local symmetry under a specific type of transformation. IIUC this was all known about EM force before Yang-Mills. What Yang-Mills showed was that, if you consider a “more elaborate” transformation (somewhat like matrix multiplication is “more elaborate” than scalar multiplication) than what had been considered until then, you can get different unique solutions. With time (decades later!), it turned out that two such unique solutions (corresponding to different "elaborate" transformation types) behave *exactly* like the weak and strong nuclear forces, the two other forces in the Standard Model. Which is like super cool. That’s it — there goes the least authoritative scientific post you’ll ever see from me. Hopefully not completely embarrassing, and ideally vindicating Wittgenstein, whose work I’ve never actually read (too dense, keep it simple man). (*) I actually want to say it also expresses the way gravity behaves, but there is some sort of nuance whereby the SM forces are just forces and gravity bends spacetime itself (?) maybe I’ll dig in another time…