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Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
I thought this was going to be about the popsci book with a similar name: Chaos: Making a New Science https://www.goodreads.com/book/show/64582.Chaos
Ah, I loved that book as a teen. Unfortunately I lent it to an ex whom I broke up with before she had returned it and never spoken with eversince. I fondly remember tinkering with a PHP program (that was the only language I knew at the time ¯\_(ツ)_/¯) to draw the bifurcation diagram of the logistic map which then I used as my desktop background.
Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
Edward Lorenz
Cvitanovic's book, and apparently Cvitanovic himself (I've traded an email or two, but he's friends of friends -and seems to always make a big impression in person) is amazing. It's been around in some form or other since I was wrapping up my ph.d. thesis in a related subject, and I remember being mad as hell it didn't exist when I started as it had the most understandable explanations of the Gutzwiller trace formula…
Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
The ability of an observer to keep track of things is not relevant, and even completely computable things like cellular automata can be chaotic [1]. The common definition of chaotic dynamics [2] requires the system to be sensitive to initial conditions, mix the state space, and have dense periodic orbits. [1] https://en.wikipedia.org/wiki/Rule_30#Chaos . [2] https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics
I found this to be the most intuitive example (for myself to grok):
https://en.wikipedia.org/wiki/Double_pendulum#/media/File:De...
This book looks really useful: a complete introduction with all the prerequisites, in one place. (I apologize that this comment is not funny.)
Earlier quoted context omitted.
The ability of an observer to keep track of things is not relevant, and even completely computable things like cellular automata can be chaotic [1]. The common definition of chaotic dynamics [2] requires the system to be sensitive to initial conditions, mix the state space, and have dense periodic orbits. [1] https://en.wikipedia.org/wiki/Rule_30#Chaos . [2] https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics
Thanks. I found this to be the most intuitive example (for myself to grok): https://en.wikipedia.org/wiki/Double_pendulum#/media/File:De...
