“The Edge of Chaos” (2017) | Hacker News Reader

“The Edge of Chaos” (2017)

bactra.org

23 pointsmeanie24 comments

Let 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!

No worries my dude. I am really happy to read that my book had such a big impact on you (as well as humbled by your praise). It's the little interactions like this that are the true reward for having written a book like CBofN, so I thank you.

I'm a huge fan of your book. Is there anything you'd add in a revised edition 20 years after publication?

Thanks ... I really appreciate the kind words. MIT Press has repeatedly tried to get me to do a 2nd edition and while it was tempting, I always ultimately decided that it was better to keep doing new things. Although, much to my surprise, a Japanese edition of the book just came out this year so there still seems to be some interest.

But that said, I am working on another book now that is meant to be a more accessible successor to CBofN and something of a computational "theory of everything else". I'm about halfway done, but the it's hard to write with the distraction of living in this bizarre timeline of ours.

Can you believe that’s the most exciting news I’ve heard in the past six months?

Yikes! I guess I better finish it now. Although, you should prepare to be bitterly disappointed because the next book will have something to piss off almost everyone (not by design, it's just that simultaneously seeking breadth, depth, and readability will always fall short on at least on dimension).

Logistical maps of chaos are interesting. You can use it to collapse the zeta function when r approaches the onset of chaos when you plug it into the Young modulus in terms of the elastic constants which yields a zero at x = 4/5. From there, you can model the zeta function as z(x) = sin(10(3x + 1) - 180)^(5s + 4) derived from a ramanujan congruency. All sorts of weird things can be conjectured from there.

>I think the evolutionary argument, as usually stated, rests of a big mistake about what nervous systems, immune systems, genetic regulatory nets, etc., evolve to do. This is not transmit information from one place to another, or be "flexible" in some abstract sense, but cause actions which enhance the fitness of the organism they happen to be in.

Biological systems don't evolve to do anything - they randomly mutate and are selected by a stochastic process that loosely correlates with Darwinian fitness. Chaos is the default state of all matter; most systems operate on the edge of chaos not because there is something desirable about that state, but because any amount of order emerging from chaos is highly improbable.

Whoever 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 new state is reached in which things are stable). Living systems (and a few non-living) systems don't work this way, but use a continual input of energy to drive reactions and maintain a "non-equilibrium" state.

Author is Cosma Shalizi

https://en.m.wikipedia.org/wiki/Cosma_Shalizi

There’s also the whole fringe topic of disequilibrium economics, which eschews most of what all economics assume by fiat (that economies are in equilibrium and get shocked out of it, and then resume some kind of trajectory back to the new equilibrium).

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.

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.

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.

Can you give a pointer to any of this “work” that hasn’t been debunked by physicists or engineers?

From wikipedia:

"Prigogine is best known for his definition of dissipative structures and their role in thermodynamic systems far from equilibrium, a discovery that won him the Nobel Prize in Chemistry in 1977. In summary, Ilya Prigogine discovered that importation and dissipation of energy into chemical systems could result in the emergence of new structures (hence dissipative structures) due to internal self reorganization."

Plenty of links on that page if you want to get into his research.

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

> I think the evolutionary argument, as usually stated, rests of a big mistake about what nervous systems, immune systems, genetic regulatory nets, etc., evolve to do. This is not transmit information from one place to another, or be "flexible" in some abstract sense, but cause actions which enhance the fitness of the organism they happen to be in.

Transmitting information and being flexible enhances the fitness of the organism.

It would be an interesting piece if the author elaborated on their claim, as to refute this obvious counterargument.

There's no focused argument here. Mere polemic.

> the evolutionary argument...rests of [sic] a big mistake about what nervous systems, immune systems, genetic regulatory nets, etc., evolve to do. This is not transmit information from one place to another, or be "flexible" in some abstract sense, but cause actions which enhance the fitness of the organism they happen to be in.

What reasons does the author have for maintaining these ideas? Naturally, none are given.

It's just a bunch of disconnected opinions.

The reason for the first sentence quoted is the second sentence quoted.

I, for one, am happy that my homeostatic regulatory nets have not evolved to "the edge of chaos."

Is there something provocative about his thesis, that would require focused argument?

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