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No. Yes to the overhype, no to the "not really". I don't see how better understanding non-linear systems and global dynamics can be not be considered useful. F

by chermi 1y ago

No. Yes to the overhype, no to the "not really". I don't see how better understanding non-linear systems and global dynamics can be not be considered useful. For starters, better control of nonlinear systems/keeping them from turning them chaotic is incredibly useful. So many hard problems can be approximately reduced to "keep this non-linear system stable." Staying in the "edge of chaos" regime has proven to be an optimal choice for a plethora of problems.

MountDoom 1y ago
I think that's a bit of a scope creep. The study of dynamical systems is obviously important and is sometimes rolled into chaos theory, but it predates it - and tellingly, it almost never concerns itself with chaotic behavior, because you can't do a whole lot with that. So it's sort of like saying that the physics of black holes are very useful to us day-to-day because we want to make sure we don't fall into any black holes. I'm not saying that chaos theory isn't interesting. It's just that it's pretty hard to find any concrete application of it, beyond hand-wavy stuff like "oh, it somehow helped us understand weather".
- jbay808 1y ago
  You can do a lot with chaos. One of the things it lets you do is find an unforced trajectory from the vicinity of any state to the vicinity of any other (accessible) state. Sensitivity to initial conditions means sensitivity to perturbations, which also means sensitivity to small control inputs, and this can be leveraged to your advantage. Multibody orbits are one such chaotic system, which means you can take advantage of that chaos to redirect your space probe from one orbit to another using virtually zero fuel, as NASA did with its ISEE-3 spacecraft.
- chermi 1y ago
  Fair enough. I basically had to make the not-very-compelling case that controlling non-linear systems to avoid chaos is... and application of chaos? Lol, you got me.

by chermi 1y ago

MountDoom 1y ago

I think that's a bit of a scope creep. The study of dynamical systems is obviously important and is sometimes rolled into chaos theory, but it predates it - and tellingly, it almost never concerns itself with chaotic behavior, because you can't do a whole lot with that. So it's sort of like saying that the physics of black holes are very useful to us day-to-day because we want to make sure we don't fall into any black holes. I'm not saying that chaos theory isn't interesting. It's just that it's pretty hard to find any concrete application of it, beyond hand-wavy stuff like "oh, it somehow helped us understand weather".

jbay808 1y ago
You can do a lot with chaos. One of the things it lets you do is find an unforced trajectory from the vicinity of any state to the vicinity of any other (accessible) state. Sensitivity to initial conditions means sensitivity to perturbations, which also means sensitivity to small control inputs, and this can be leveraged to your advantage. Multibody orbits are one such chaotic system, which means you can take advantage of that chaos to redirect your space probe from one orbit to another using virtually zero fuel, as NASA did with its ISEE-3 spacecraft.
chermi 1y ago
Fair enough. I basically had to make the not-very-compelling case that controlling non-linear systems to avoid chaos is... and application of chaos? Lol, you got me.