
“The Edge of Chaos” (2017) - meanie
http://bactra.org/notebooks/edge-of-chaos.html
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qubex
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.

~~~
gwf
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.

~~~
qubex
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!

~~~
gwf
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.

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poletopole
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.

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jdietrich
_> 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.

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PaulDavisThe1st
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.

~~~
alexpetralia
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.

~~~
ssivark
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.

~~~
simonh
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.

~~~
ssivark
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.

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bionhoward
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

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1penny42cents
> 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.

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JacksonGariety
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.

~~~
082349872349872
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?

