9 ms·

Well now you have to show us something you would consider nightmare math

mr_mitm 3y ago
I'm pretty sure I used to get nightmares from Christoffel symbols and Riemannian geometry: https://i.stack.imgur.com/Njf17.png https://i.stack.imgur.com/Njf17.png
KolenCh 3y ago
https://petapixel.com/2019/07/05/goodbye-aberration-physicist-solves-2000-year-old-optical-problem/ https://petapixel.com/2019/07/05/goodbye-aberration-physicis... Another example is standard model of particle physics. There’s a way to write down the Lagrangian of the standard model very compactly: https://visit.cern/content/standard_model_formula_t_shirt https://visit.cern/content/standard_model_formula_t_shirt But if you expanded all the implied sums and terms, it probably would be monstrous. After all it is supposed to contain all the terms that this figure contains for example: https://commons.wikimedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg https://commons.wikimedia.org/wiki/File:Standard_Model_of_El... 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.
- mr_mitm 3y ago
  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 https://i.stack.imgur.com/xkrq9.png
  - kelipso 3y ago
    There is a ton of repetition, so you could probably replace it with like five relatively small equations. Still...glad I didn't get into optics lol.
  - KolenCh 3y ago
    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'm pretty sure I used to get nightmares from Christoffel symbols and Riemannian geometry: https://i.stack.imgur.com/Njf17.png https://i.stack.imgur.com/Njf17.png

KolenCh 3y ago

https://petapixel.com/2019/07/05/goodbye-aberration-physicist-solves-2000-year-old-optical-problem/ https://petapixel.com/2019/07/05/goodbye-aberration-physicis... Another example is standard model of particle physics. There’s a way to write down the Lagrangian of the standard model very compactly: https://visit.cern/content/standard_model_formula_t_shirt https://visit.cern/content/standard_model_formula_t_shirt But if you expanded all the implied sums and terms, it probably would be monstrous. After all it is supposed to contain all the terms that this figure contains for example: https://commons.wikimedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg https://commons.wikimedia.org/wiki/File:Standard_Model_of_El... 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.

mr_mitm 3y ago
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 https://i.stack.imgur.com/xkrq9.png
- kelipso 3y ago
  There is a ton of repetition, so you could probably replace it with like five relatively small equations. Still...glad I didn't get into optics lol.
- KolenCh 3y ago
  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