This area definitely needs deeper investigation. It is compelling from an intuitive sense and we see tons of practical evidence of chaos being handy in the real world. I’ve been using EoC initialization for Transformer networks in RL recently and look forward to try it in the helmholtz machine adaptation of the same. One thing I see (anecdotally) is it can easily break, but if it doesn’t, it works better (in terms of performance), so these approaches are probably a lot more useful in systems which do have some homeostasis, such that they can robustly pull themselves back from the abyss
“The Edge of Chaos” (2017)
11–20 of 25 posts
Re: “The Edge of Chaos” (2017)
#12Whoever wrote this doesn't seem to make the connection with Prigogine's work on non-equilibrium thermodynamics, which seem to me to have as much to do with the "edge of chaos" idea(s) as anything from the cellular automata world. The overly quick summary: most convention thermodynamics/chemistry concerns itself with systems that reach equilibrium (various reactions take place, energy is consumed or produced, and a ne…
Maybe this is a dumb question, but if you are able to maintain a certain state by maintaining a certain energy input, how is this not an equilibrium state over time? It feels like the distinction between non-equilibrium and equilibrium is semantic.
Re: “The Edge of Chaos” (2017)
#13Whoever wrote this doesn't seem to make the connection with Prigogine's work on non-equilibrium thermodynamics, which seem to me to have as much to do with the "edge of chaos" idea(s) as anything from the cellular automata world. The overly quick summary: most convention thermodynamics/chemistry concerns itself with systems that reach equilibrium (various reactions take place, energy is consumed or produced, and a ne…
Maybe this is a dumb question, but if you are able to maintain a certain state by maintaining a certain energy input, how is this not an equilibrium state over time? It feels like the distinction between non-equilibrium and equilibrium is semantic.
The energy has to “flow” throughout the system, from the input, and then eventually “dissipate”. That sets up a pattern of behavior/dynamics very different from equilibrium systems, where there are no such “coherent” flows.
As an example of the practical consequences of non-equilibrium, look up a recent HN discussions (couple of days ago) on how hot water could freeze faster than cold water.
Re: “The Edge of Chaos” (2017)
#14Whoever wrote this doesn't seem to make the connection with Prigogine's work on non-equilibrium thermodynamics, which seem to me to have as much to do with the "edge of chaos" idea(s) as anything from the cellular automata world. The overly quick summary: most convention thermodynamics/chemistry concerns itself with systems that reach equilibrium (various reactions take place, energy is consumed or produced, and a ne…
What you state is not "edge of chaos", it's simply the non-equilibrium steady state. There's no connection really. Non-equilibrium states can be chaotic, non-chaotic, or at the edge of chaos etc.
Re: “The Edge of Chaos” (2017)
#15Whoever wrote this doesn't seem to make the connection with Prigogine's work on non-equilibrium thermodynamics, which seem to me to have as much to do with the "edge of chaos" idea(s) as anything from the cellular automata world. The overly quick summary: most convention thermodynamics/chemistry concerns itself with systems that reach equilibrium (various reactions take place, energy is consumed or produced, and a ne…
Can you give a pointer to any of this “work” that hasn’t been debunked by physicists or engineers?
Re: “The Edge of Chaos” (2017)
#16Let me drop in a plug for my favourite book, William Gary Flake’s The Computational Beauty of Nature (1997), by far the best exploration of these kinds of concepts I have ever encountered. It’s rich in discussion, beautiful diagrams, formulae & equations, and even compilable code—kind of like Stephen Wolfram’s A New Kind of Science (2003) but without the bombast and done right.
As the author of CBofN, I thank you for the plug. But just one little correction: Gary is my first name and William is my middle.
Re: “The Edge of Chaos” (2017)
#17Earlier quoted context omitted.
Maybe this is a dumb question, but if you are able to maintain a certain state by maintaining a certain energy input, how is this not an equilibrium state over time? It feels like the distinction between non-equilibrium and equilibrium is semantic.
The energy has to “flow” throughout the system, from the input, and then eventually “dissipate”. That sets up a pattern of behavior/dynamics very different from equilibrium systems, where there are no such “coherent” flows. As an example of the practical consequences of non-equilibrium, look up a recent HN discussions (couple of days ago) on how hot water could freeze faster than cold water.
That’s just homeostasis, which is an equilibrium state, sometimes described as dynamic equilibrium. Encyclopaedia Britannica, Oxford and Merriam Webster describe it as a form of Equilibrium. Wikipedia links to Homeostasis from the master page on Equilibrium and references it in its description. I don’t see how this is in contention.
Re: “The Edge of Chaos” (2017)
#18Earlier quoted context omitted.
The energy has to “flow” throughout the system, from the input, and then eventually “dissipate”. That sets up a pattern of behavior/dynamics very different from equilibrium systems, where there are no such “coherent” flows. As an example of the practical consequences of non-equilibrium, look up a recent HN discussions (couple of days ago) on how hot water could freeze faster than cold water.
That’s just homeostasis, which is an equilibrium state, sometimes described as dynamic equilibrium. Encyclopaedia Britannica, Oxford and Merriam Webster describe it as a form of Equilibrium. Wikipedia links to Homeostasis from the master page on Equilibrium and references it in its description. I don’t see how this is in contention.
Uh, not quite. Dynamic equilibrium (Eg: during chemical reactions) means something very specific & constrained, and doesn’t include any steady influx/outflux of energy, material, etc. On top of that, one can have not just flows, but also active regulation mechanisms which maintain homeostasis, possibly with periodic temporal behavior (which can never happen in “equilibrium”). So even though “equilibrium” and “dynamic” as English words might seem somewhat descriptive of homeostasis, I think the physics concept of “dynamic equilibrium” is distinct enough to be worth not conflating. Eg: entropy can be constant in a system in dynamical equilibrium, but (to our best understanding) homeostasis always generates entropy.
Re: “The Edge of Chaos” (2017)
#19Let me drop in a plug for my favourite book, William Gary Flake’s The Computational Beauty of Nature (1997), by far the best exploration of these kinds of concepts I have ever encountered. It’s rich in discussion, beautiful diagrams, formulae & equations, and even compilable code—kind of like Stephen Wolfram’s A New Kind of Science (2003) but without the bombast and done right.
As the author of CBofN, I thank you for the plug. But just one little correction: Gary is my first name and William is my middle.
I'm a huge fan of your book. Is there anything you'd add in a revised edition 20 years after publication?
Re: “The Edge of Chaos” (2017)
#20Let me drop in a plug for my favourite book, William Gary Flake’s The Computational Beauty of Nature (1997), by far the best exploration of these kinds of concepts I have ever encountered. It’s rich in discussion, beautiful diagrams, formulae & equations, and even compilable code—kind of like Stephen Wolfram’s A New Kind of Science (2003) but without the bombast and done right.
As the author of CBofN, I thank you for the plug. But just one little correction: Gary is my first name and William is my middle.
Oh God, I can’t believe I made that mistake... and Oh God, you’re my bloody idol.
You’re the reason I chose to study mathematics. You’re the reason I chose to delve into the rather esoteric field of symbolic computation. You’re the reason I delved into the fringe universe of disequilibrium economics!