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!

- algorithm Apollonian approximation art bar beauty binary binomial coefficients book cards carnival Carnival of Mathematics chocolate circle complex counting decadic decimal diagrams elements factorization fibonacci formula fractal game games gasket graph groups Haskell hyperbinary idempotent integers interactive irrational Ivan Niven Lagrange lehmer lucas MaBloWriMo making Mersenne moebius mu multiplication nim number numbers objects omega order pi prime primitive programming proof puzzle rectangles review roots sequence square strategy subgroups sum symmetry tessellation test triangular unit units unity video visualization X
### Blogroll

### Fun

### Reference

### Categories

- algebra (43)
- arithmetic (59)
- books (28)
- calculus (6)
- challenges (51)
- combinatorics (10)
- complex numbers (6)
- computation (42)
- convergence (9)
- counting (31)
- famous numbers (48)
- fibonacci (18)
- fractals (13)
- games (24)
- geometry (55)
- golden ratio (8)
- group theory (26)
- humor (6)
- induction (7)
- infinity (17)
- iteration (23)
- links (74)
- logic (6)
- meta (40)
- modular arithmetic (24)
- number theory (67)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (81)
- people (20)
- pictures (59)
- posts without words (15)
- primes (34)
- probability (6)
- programming (17)
- proof (64)
- puzzles (11)
- recursion (12)
- review (19)
- sequences (28)
- solutions (28)
- teaching (13)
- trig (3)
- Uncategorized (6)
- video (19)

### Archives

- December 2016 (2)
- November 2016 (6)
- October 2016 (6)
- September 2016 (2)
- August 2016 (5)
- July 2016 (2)
- June 2016 (4)
- May 2016 (4)
- April 2016 (2)
- March 2016 (3)
- February 2016 (9)
- January 2016 (8)
- December 2015 (5)
- November 2015 (29)
- August 2015 (3)
- June 2015 (2)
- April 2015 (1)
- May 2014 (1)
- December 2013 (1)
- October 2013 (1)
- July 2013 (1)
- June 2013 (1)
- May 2013 (1)
- April 2013 (3)
- March 2013 (3)
- February 2013 (2)
- January 2013 (5)
- December 2012 (3)
- November 2012 (4)
- October 2012 (5)
- September 2012 (1)
- August 2012 (4)
- July 2012 (1)
- June 2012 (6)
- May 2012 (2)
- April 2012 (3)
- March 2012 (1)
- February 2012 (4)
- January 2012 (5)
- December 2011 (1)
- November 2011 (7)
- October 2011 (4)
- September 2011 (6)
- July 2011 (2)
- June 2011 (4)
- May 2011 (5)
- April 2011 (2)
- March 2011 (4)
- February 2011 (1)
- January 2011 (1)
- December 2010 (1)
- November 2010 (4)
- October 2010 (2)
- September 2010 (1)
- August 2010 (1)
- July 2010 (1)
- June 2010 (2)
- May 2010 (3)
- April 2010 (1)
- February 2010 (6)
- January 2010 (3)
- December 2009 (8)
- November 2009 (7)
- October 2009 (3)
- September 2009 (3)
- August 2009 (1)
- June 2009 (4)
- May 2009 (5)
- April 2009 (4)
- March 2009 (2)
- February 2009 (1)
- January 2009 (7)
- December 2008 (1)
- October 2008 (2)
- September 2008 (7)
- August 2008 (1)
- July 2008 (1)
- June 2008 (1)
- April 2008 (5)
- February 2008 (4)
- January 2008 (4)
- December 2007 (3)
- November 2007 (12)
- October 2007 (2)
- September 2007 (4)
- August 2007 (3)
- July 2007 (1)
- June 2007 (3)
- May 2007 (1)
- April 2007 (4)
- March 2007 (3)
- February 2007 (7)
- January 2007 (1)
- December 2006 (2)
- October 2006 (2)
- September 2006 (6)
- July 2006 (4)
- June 2006 (2)
- May 2006 (6)
- April 2006 (3)
- March 2006 (6)

### 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.