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Comment by a_olt | Hacker News Reader

No. 16, 'Chaos Theory' is actually called the 'Logistic Equation' and it is used in biology to model populations. It does exhibit transition to a chaotic regime for certain values of k, but it's improper to refer to it as 'Chaos Theory equation'.

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Yep, if anything the Restricted 3-Body Problem (R3BP) should be considered the "chaos theory equation", since it was Poincaré study of chaotic solutions in the R3BP that led to the discovery of sensitivity to initial conditions. Smale's horseshoe map would be another apt equation, since it succinctly describes the dynamics of chaotic systems, through the twisting and warping of the map. The Lorenz attractor is another important example that highlights the concept of deterministic chaos.

I don't quite get how chaos theory changed the world. All of the other equations I get (although whether Shannon's equation changed the world or merely described the change is probably arguable.)

How did chaos theory change the world?

Understanding deterministic chaos has been the cornerstone of a wide range of fields, including physics, medicine, economics, and business. There are a wealth of everyday applications. Control systems in the real world have to deal with the underlying structure of the dynamics that govern how such systems naturally behave in the feedback loop.

There are a few different resources you can find that list practical applications of chaos theory. Here are a few that I found that I think you will find interesting:

* http://www.slideshare.net/anthaceorote/chaos-theory-an-intro...

* https://www.csuohio.edu/sciences/dept/physics/physicsweb/kau...

* [PDF] http://math.arizona.edu/~shankar/efa/efa4.pdf

And there's plenty more!

It has very important epistemological implications: it means a phenomenon may follow a deterministic law which, due to its mathematical properties, would nevertheless make long-term predictions impossible. So even though you would have a mathematical model for the phenomenon, you wouldn't be able to make real-world long-term predictions. The problem lies in the sensitive dependence on initial conditions.

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