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Is anyone doing anything besides visualizations with this chaos stuff? I liked the article linked below depicting the state space of artificial neurons: https:/

by esafak 1y ago

Is anyone doing anything besides visualizations with this chaos stuff? I liked the article linked below depicting the state space of artificial neurons: https://towardsdatascience.com/attractors-in-neural-network-circuits-beauty-and-chaos/ https://towardsdatascience.com/attractors-in-neural-network-...

MountDoom 1y ago
Not really. Fractals and chaos theory were a bit like blockchain in that it was a "new kind of science" and it was supposed to explain everything, and you could buy pop-science books talking about the implications. And then it sort of fizzled out, because while it's interesting and gives us a bit of additional philosophical insights into certain problems, it doesn't do anything especially useful. You can use it to draw cool space-filling shapes.
- sxzygz 1y ago
  I don’t think you’re remotely correct, but I also don’t know how to dispute your ignorance in any useful way. To @esafak I suggest following @westurner’s post. I like the concept of Stable Manifolds. Classifying types of them is interesting. Group symmetries on the phase space are interesting. Explaining this and more is not work I’m prepared to do here. Use Wikipedia, ask ChatGPT, enrol in a course on Chaos and Fractal Dynamics, etc.
  - MountDoom 1y ago
    I am quite familiar with this space and I will reassert that its by far most significant application is making pretty pictures. The Wikipedia list you're indirectly referencing is basically a fantasy wishlist of the areas where we expected the chaos theory to revolutionize things, with little to show for it. "Chaos theory cryptography", come on.
- 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.
westurner 1y ago
Chaos theory > Applications: https://en.wikipedia.org/wiki/Chaos_theory#Applications https://en.wikipedia.org/wiki/Chaos_theory#Applications People use chaos theory to make predictions about attractor systems that have lower error than other models.
cs702 1y ago
Well, engineers building physical systems like airplanes and rockets use Lyapunov exponents to avoid chaotic behavior. No one sane wants airplanes or rockets that exhibit chaotic aerodynamics! Has progress stalled in this area? I don't know, but surely there are people working on it. In fact I recently saw an interesting post on HN about a new technique that among other things enables faster estimation of Lyapunov exponents: https://news.ycombinator.com/item?id=45374706 https://news.ycombinator.com/item?id=45374706 (search for "Lyapunov" on the github page). Just because we haven't seen much progress, doesn't mean we won't see more. Progress never happens on a predictable schedule.
- deleted 1y ago
  [deleted]
- DavidSJ 1y ago
  To add to this, a moderate amount of turbulence (a type of chaotic fluid flow) in engines and wing surfaces is sometimes deliberately engineered to improve combustion efficiency and lift, and also chaotic flow can induce better mixing in heat exchangers and microfluidics systems.
poslathian 1y ago
Absolutely! These techniques are the key unlocks to robustifying AI and creating certifiable trust in their behavior. Starting with pre-deep neural network era stuff like LQR-RRT trees, to the hot topic today of contraction theory, and control barrier certificates in autonomous vehicles
throwaway173738 1y ago
Chaos is an important part of Control Systems theory from what I understand.
fraserphysics 1y ago
Please take a look at the most recent draft of my book "Hidden Markov Models and Dynamical Systems" https://www.fraserphysics.com/book.pdf https://www.fraserphysics.com/book.pdf In the first chapter I talk about a chaotic model for laser dynamics, and in the last chapter I use the same ideas to analyze ECGs. The code and text are at https://gitlab.com/fraserphysics/hmmds https://gitlab.com/fraserphysics/hmmds. From a Nix command line, "make book" builds the book in about 10 hours. I'd be grateful for any feedback on the book or the software.

by esafak 1y ago

MountDoom 1y ago

Not really. Fractals and chaos theory were a bit like blockchain in that it was a "new kind of science" and it was supposed to explain everything, and you could buy pop-science books talking about the implications. And then it sort of fizzled out, because while it's interesting and gives us a bit of additional philosophical insights into certain problems, it doesn't do anything especially useful. You can use it to draw cool space-filling shapes.

sxzygz 1y ago
I don’t think you’re remotely correct, but I also don’t know how to dispute your ignorance in any useful way. To @esafak I suggest following @westurner’s post. I like the concept of Stable Manifolds. Classifying types of them is interesting. Group symmetries on the phase space are interesting. Explaining this and more is not work I’m prepared to do here. Use Wikipedia, ask ChatGPT, enrol in a course on Chaos and Fractal Dynamics, etc.
- MountDoom 1y ago
  I am quite familiar with this space and I will reassert that its by far most significant application is making pretty pictures. The Wikipedia list you're indirectly referencing is basically a fantasy wishlist of the areas where we expected the chaos theory to revolutionize things, with little to show for it. "Chaos theory cryptography", come on.
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.

westurner 1y ago

Chaos theory > Applications: https://en.wikipedia.org/wiki/Chaos_theory#Applications https://en.wikipedia.org/wiki/Chaos_theory#Applications People use chaos theory to make predictions about attractor systems that have lower error than other models.

cs702 1y ago

Well, engineers building physical systems like airplanes and rockets use Lyapunov exponents to avoid chaotic behavior. No one sane wants airplanes or rockets that exhibit chaotic aerodynamics! Has progress stalled in this area? I don't know, but surely there are people working on it. In fact I recently saw an interesting post on HN about a new technique that among other things enables faster estimation of Lyapunov exponents: https://news.ycombinator.com/item?id=45374706 https://news.ycombinator.com/item?id=45374706 (search for "Lyapunov" on the github page). Just because we haven't seen much progress, doesn't mean we won't see more. Progress never happens on a predictable schedule.

deleted 1y ago
[deleted]
DavidSJ 1y ago
To add to this, a moderate amount of turbulence (a type of chaotic fluid flow) in engines and wing surfaces is sometimes deliberately engineered to improve combustion efficiency and lift, and also chaotic flow can induce better mixing in heat exchangers and microfluidics systems.

poslathian 1y ago

Absolutely! These techniques are the key unlocks to robustifying AI and creating certifiable trust in their behavior. Starting with pre-deep neural network era stuff like LQR-RRT trees, to the hot topic today of contraction theory, and control barrier certificates in autonomous vehicles

throwaway173738 1y ago

Chaos is an important part of Control Systems theory from what I understand.

fraserphysics 1y ago

Please take a look at the most recent draft of my book "Hidden Markov Models and Dynamical Systems" https://www.fraserphysics.com/book.pdf https://www.fraserphysics.com/book.pdf In the first chapter I talk about a chaotic model for laser dynamics, and in the last chapter I use the same ideas to analyze ECGs. The code and text are at https://gitlab.com/fraserphysics/hmmds https://gitlab.com/fraserphysics/hmmds. From a Nix command line, "make book" builds the book in about 10 hours. I'd be grateful for any feedback on the book or the software.