I just got an email from Jos Leys, one of the creators of the *Dimensions* video series (which I wrote about previously), announcing that they have released another video series, this time about Chaos, at http://www.chaos-math.org/en. I haven’t had a chance to watch yet, but if it’s anything like Dimensions then you’re in for a real treat!

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### Meta

These videos are fantastic. Fun but also very interesting.

Thanks for sharing

Great videos, very good for understanding chaos. Unfortunately Chaos is a bit boiled down to sensitivity against initial conditions, as it is done in other popular pieces about Chaos. James Gleick’s Chaos book as an example. This is an unfortunate approach because there is more to Chaos than sensitivity against initial conditions, it’s a necessary condition, alas not sufficient and most people confuse Chaos with sensitivity against initial conditions. Even the most humble Random Walk is sensitive against initial conditions but there is no Chaos involved.

Topological Mixing is another key feature of Chaos, which should have been mentioned.

On the other hand, the density of periodic Orbits, the third key feature of Chaos is probably hard to visualize.

Dear Mustermann,

Thank you for your message on our videos. I fully agree with you that one should not reduce chaos to sensitivity to initial conditions and that many popular presentations give this wrong impression. But this is not at all what we do ! and I wonder if you looked carefully at our videos ?

Most of our chapter 5 deals with periodic orbits in billiards tables.

In chapter 6, we discuss periodic orbits in Smale horseshoe.

In chapter 8 we explain in detail what you say : that one should not reduce chaos to sensitivity and that one should use ergodic methods (event though we do not use the word) : this is more precise than topological mixing. Indeed we give quite a precise description of Sinal Ruelle Bowen measures and discuss their relevance in the final chapter 9.

All in all, I agree with you on the main characters of chaos, but I disagree when you write that we confuse chaos and sensitivity. On the contrary, this is one of the main points in our videos :-)

Sincerely yours,

Etienne Ghys

Sorry for the very late answer.

‘I wonder if you looked carefully at our videos ?’

As it turned out, I did not. Please accept my apology.

Overall, I enjoyed these videos. The first four talking about history of the study of deterministic systems seem a bit slow. These include necessary background for people needing to brush up on differential equations and high school physics, but personally I found the animations to be drawn out too long. The next two videos about the Duhem’s bull and Smale’s horseshoe contained new information for me, some of the animations here were more enjoyable. Chapters 7-9 are where I thought the series shined. These episodes reminded me of the visual appeal of the Dimensions series. The entire series provides a good historical context for the mathematical study of chaotic systems and several fun animations.