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>closed-form minimum-fuel solutions My dad used something called variational calculus to solve physics problems. It's beyond my understanding, but I gather it

>closed-form minimum-fuel solutions My dad used something called variational calculus to solve physics problems. It's beyond my understanding, but I gather it was more useful in the slide rule days. A former co-worker of his commented that once you could just throw computing power at a problem, being able to construct the elegant solutions was basically obsolete.

monocasa 5y ago
Yeah, there was a similar comment from one of my greybeard coworkers. That one of the biggest changes he had to get over as engineering moved on over the years was the gradual shift from very symbolic, human friendly (one might say 'elegant') mathematics into more brute force, pure crunching techniques.
- ur-whale 5y ago
  > was the gradual shift from very symbolic, human friendly (one might say 'elegant') mathematics into more brute force, pure crunching techniques. Conversely, in these days when anyone can go buy themselves a couple of teraflops at the shop round the corner, when you look at the way they solved problems back in day it feels very strange. But then, they didn't have a choice of course. However, when you look at modern physics courses (worst offender IMO is standard quantum mechanics courses), where huge swaths of times are expanded trying to find closed form solutions to Schrödinger's equation, it feels very bizarre (and a giant waste of time).
  - selimthegrim 5y ago
    Just the other day I used variational techniques to show the bound on a Mott transition in terms of electron density to an undergrad who had been complaining to me that they "hadn't learned any of this stuff in class just Dirac notation"
bodhiandphysics 5y ago
Trust me, calculus of variations is still used! It’s even more important now that we have lots of computing power. Actually, the major way we solve differential equations, the finite element method, is a variational technique!
- ur-whale 5y ago
  > the finite element method, is a variational technique! Many calculus of variation (searching for extrema in function space) can be converted to a differential equation via Euler-Lagrange.
  - bodhiandphysics 5y ago
    And cleverly vice versa. Many differential equations can be covered to problems in viv. Computers are great at optimization!
DarmokJalad1701 5y ago
> but I gather it was more useful in the slide rule days It is definitely useful today as well. There is some modern work done on using variational calculus for solving real-world optimization problem. See this book if you want: https://www.springer.com/gp/book/9781461489443 https://www.springer.com/gp/book/9781461489443
admissionsguy 5y ago
> My dad used something called variational calculus to solve physics problems. It's beyond my understanding, but I gather it was more useful in the slide rule days In (theoretical) physics, variational calculus is such a basic tool, it is no more obsolete than trigonometry! It's also quite mind-blowing and beautiful, how a single quantity (the Lagrangian) contains all information needed to derive complete equations of motion for a system, or the correspondence between symmetries and conserved quantities via Noether's theorem.
- immmmmm 5y ago
  as a former physicist i couldn't agree more. in fact you can construct a lagrangian almost uniquely from the underlying symmetries of the system. it's literally the most used tool in theoretical physics, and it's so powerful and elegant that actually convinced myself to do physics in the first place.
- wyager 5y ago
  I would argue that it seems quite likely that Lagrangian mechanics is more fundamental, in some sense, than any other classical formulation. The path integral formulation gives you a mathematical trick for understanding how the lagrangian “generates” other physical models (like Newtonian physics) via its effect on action/phase.

monocasa 5y ago

Yeah, there was a similar comment from one of my greybeard coworkers. That one of the biggest changes he had to get over as engineering moved on over the years was the gradual shift from very symbolic, human friendly (one might say 'elegant') mathematics into more brute force, pure crunching techniques.

ur-whale 5y ago
> was the gradual shift from very symbolic, human friendly (one might say 'elegant') mathematics into more brute force, pure crunching techniques. Conversely, in these days when anyone can go buy themselves a couple of teraflops at the shop round the corner, when you look at the way they solved problems back in day it feels very strange. But then, they didn't have a choice of course. However, when you look at modern physics courses (worst offender IMO is standard quantum mechanics courses), where huge swaths of times are expanded trying to find closed form solutions to Schrödinger's equation, it feels very bizarre (and a giant waste of time).
- selimthegrim 5y ago
  Just the other day I used variational techniques to show the bound on a Mott transition in terms of electron density to an undergrad who had been complaining to me that they "hadn't learned any of this stuff in class just Dirac notation"

bodhiandphysics 5y ago

Trust me, calculus of variations is still used! It’s even more important now that we have lots of computing power. Actually, the major way we solve differential equations, the finite element method, is a variational technique!

ur-whale 5y ago
> the finite element method, is a variational technique! Many calculus of variation (searching for extrema in function space) can be converted to a differential equation via Euler-Lagrange.
- bodhiandphysics 5y ago
  And cleverly vice versa. Many differential equations can be covered to problems in viv. Computers are great at optimization!

DarmokJalad1701 5y ago

> but I gather it was more useful in the slide rule days It is definitely useful today as well. There is some modern work done on using variational calculus for solving real-world optimization problem. See this book if you want: https://www.springer.com/gp/book/9781461489443 https://www.springer.com/gp/book/9781461489443

admissionsguy 5y ago

> My dad used something called variational calculus to solve physics problems. It's beyond my understanding, but I gather it was more useful in the slide rule days In (theoretical) physics, variational calculus is such a basic tool, it is no more obsolete than trigonometry! It's also quite mind-blowing and beautiful, how a single quantity (the Lagrangian) contains all information needed to derive complete equations of motion for a system, or the correspondence between symmetries and conserved quantities via Noether's theorem.

immmmmm 5y ago
as a former physicist i couldn't agree more. in fact you can construct a lagrangian almost uniquely from the underlying symmetries of the system. it's literally the most used tool in theoretical physics, and it's so powerful and elegant that actually convinced myself to do physics in the first place.
wyager 5y ago
I would argue that it seems quite likely that Lagrangian mechanics is more fundamental, in some sense, than any other classical formulation. The path integral formulation gives you a mathematical trick for understanding how the lagrangian “generates” other physical models (like Newtonian physics) via its effect on action/phase.