I was looking for "nightmare math" in the README and was confused because I didn't find any. I guess that's what a theoretical physics degree does to you: that formula looks very harmless to me.
Looks like a horror show to me. Makes me feel embarrassed at leaving my math bs behind and going into cs. I have an insane retirement idea of retiring to some fun mountain town and going to grad school in physics. Where's the best place to go skiing with a college that takes old washed up programmers as students?
Good suggestion, but maybe shooting too high. Checks off the "in the mountains" part of my fantasy life. But a place that has seminars for grad students and working physicists and has many Nobel laureates who attended as students may be above my intellectual grade.
Also, ask string theorists to show you calculations that they need to find the largest paper to perform. I’ve heard people doing calculations where a single line is the width of an A1 paper.
Surely he could have defined some sensible quantities and notations or exploit some symmetry to make that monstrosity a bit more compact, no? I mean the Einstein field equations in its simplest form is something like G=k*T for suitable definitions of G and T. But if you wrote each component of G in terms of the metric tensor, it would become huge. This is just one component of the Riemann tensor: https://i.stack.imgur.com/xkrq9.png
You are not wrong. Eg the original Maxwell equation is so ugly (I think 20 of them) but the ones that are taught nowadays looks so elegant.
The language is important. The more you “understand” something, the simpler it is (over simplification here.) eg I would not consider the Einstein equation expanded out to be natural after understanding it. (Well Maxwell’s equation can be summarized in 1 single elegant equation as well.)
But the reason I’d consider that optics formula to be monstrous is that no matter how you group it into smaller pieces (ie refactoring it), there’s no way to hide the fact that it is not elegant at all. There’s no “understanding” there, it is just so happen the exact solution looks like that.
To put it that way then, often fundamental “master equation” are simple in some ways, but exact solutions to some particular manifestation of that master equation is often quite ugly and monstrous. In that sense then rather than quoting Einstein equation I’d quote its solution eg one with mass and spin and electric charge.
P.S. the solution of quartic equation is also a good example of this category
I recall dimly a period of months during engineering school when I would have been able to parse those symbols and perhaps make a joke about something in the lunch room. Those days are long behind me.
https://rohankulkarni.me/files/notes/heidelberg_qft/12_2.pdf ("12.2 Diagrammatic expansion of partition function for Yukawa theory")