I chose the name The Chaostician for this blog. To live up to this name, this blog should be about chaos, in particular, what a physicist means when referring to ‘chaos theory’.
This seven eight part series is my explanation of chaos theory to a popular audience. Chaos is a mechanism that allows deterministic objects to behave unpredictably. I will explain why this happens and what kinds of predictions we can make when something is chaotic.
Those of you who are already experts in nonlinear dynamics know that there are many ways to approach chaos. In this series, I will focus on behavior on strange attractors in dissipative chaos. In particular, the goal is to explain the ideas underlying periodic orbit theory and the trace formulas you can use to calculate expectation values. Other posts and series will address other approaches to chaos.
Part I: Introduction.
Part II: The Simplest Chaotic System.
Part III: Lyapunov Exponents.
Part IV: Strange Attractors.
Part V: Continuous Time.
Part VI: Stretch and Fold.
Part VII: Partitions and Symbols.
Part VIII: Periodic Orbit Theory.
Prerequisites: High school level math. There will be no calculus or anything harder. If you don’t understand anything, please ask – in the comments or by emailing thechaostician@gmail.com.
Originally Written: December 2016.
Confidence Level: Established science since the mid twentieth century. Occasional philosophy mixed in.
Colloquially, the word ‘chaos’ is used as the antonym of order. I dislike this definition because this usage leads people into thought patterns that thwart an understanding of chaotic systems.
Objects in the real world know how they are going to behave. Regardless of how difficult it may be to predict, or even just describe, the evolution of the shapes of clouds, the clouds themselves exactly realize this process.[1]I am not saying that clouds are conscious – just that they behave exactly the way clouds are supposed to behave. An ordered system is something for which it is easy for us humans to recognize the structure of reality. A disordered system is something for which the structure of reality is less transparent.
The antonym of order is confusion.
So what is chaos, if not the opposite of order? Chaos is a mechanism by which complexity arises. Complexity can arise completely by chance, but randomness is not the mechanism that we are interested in. Chaos is the study of how complicated (perhaps even random-looking) motion, structure, or behavior arises even in completely deterministic systems. We are interested in understanding as much of the structure of these chaotic systems as possible.
References
| ↑1 | I am not saying that clouds are conscious – just that they behave exactly the way clouds are supposed to behave. |
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