Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
Chaos, and what to do about it (2018)
11–20 of 27 posts
Re: Chaos, and what to do about it (2018)
#12Cvitanovic'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. The late Dieter Wintgen's papers were also good, but not as didactic, and without so many examples.
I should work out all the problem sets in J and publish the results. Seems like a properly impish trolling.
Re: Chaos, and what to do about it (2018)
#13Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
Chaos is what happens when the torus in your dynamical phase space breaks up. Or, thought of another way; it's a deterministic process that generates random bit strings (because, no torus/periodic orbits).
Re: Chaos, and what to do about it (2018)
#14Is "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
Re: Chaos, and what to do about it (2018)
#15Is "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
That's a perfect answer.
Re: Chaos, and what to do about it (2018)
#16I 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.
Re: Chaos, and what to do about it (2018)
#17Earlier quoted context omitted.
I was hoping for the Warhammer 40k type of chaos. Oh well, one can dream ...
I was hoping to read what's it about here in the comments, without opening the website, but ... For people like me: It's a book about theory of chaos. To quote: > By now, there are also many physics textbooks on "chaos". Most lack depth, and many of them are plain bad, emphasizing pictorial and computer-graphics aspects of dynamics and short changing the student on the theory. That's a pity, as the subject in its bea…
I was hoping to find a comment like this.
Re: Chaos, and what to do about it (2018)
#18Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
While there is a mathematical definition, there are uses of the term exactly described by you. For example, the Edge of Chaos (https://en.wikipedia.org/wiki/Edge_of_chaos) has a mathematical definition, but has been used in many additional areas because it so clearly seems to describe what happens as systems become so complex that they become effectively chaotic to a human's ability to order them. This edge can shift as tools improve and push back this edge.
Re: Chaos, and what to do about it (2018)
#19Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
While there is a mathematical definition, there are uses of the term exactly described by you. For example, the Edge of Chaos ( https://en.wikipedia.org/wiki/Edge_of_chaos ) has a mathematical definition, but has been used in many additional areas because it so clearly seems to describe what happens as systems become so complex that they become effectively chaotic to a human's ability to order them. This edge can shi…
[deleted]
Re: Chaos, and what to do about it (2018)
#20Cvitanovic'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…
I've never had a strong incentive to read it, so I have only looked through it, but I love it. I fantasize about writing a book just like it on a subject that I know well.