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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?
by Razengan 7y ago
Is "chaos" simply the point where humans lose the ability to keep track of things, or is there a more ..universal definition?
- scottlocklin 7y agoChaos 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).
- chr1 7y agoThe 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 https://en.wikipedia.org/wiki/Rule_30#Chaos. [2] https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics
- hankstenberg 7y agoThat's a perfect answer.
- Razengan 7y agoThanks. I found this to be the most intuitive example (for myself to grok): https://en.wikipedia.org/wiki/Double_pendulum#/media/File:Demonstrating_Chaos_with_a_Double_Pendulum.gif https://en.wikipedia.org/wiki/Double_pendulum#/media/File:De...
- nexus2045 7y agoMade me think of: https://en.wikipedia.org/wiki/Three-body_problem https://en.wikipedia.org/wiki/Three-body_problem
- cwingrav 7y agoWhile 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 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.
- deleted 7y ago[deleted]
- novaRom 7y agoNo universally accepted mathematical definition of chaos exists. My guess we only at the beginning of understanding it and more theories will emerge.
- hprotagonist 7y ago[deterministic] Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Edward Lorenz