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  1. floatingbones.myopenid.com says:

    Wonderful video, Kipkay. I’ve also appreciated Bill’s other Make projects: his tensegrity tower construction project from issue 06 of Make Magazine. Your pendulums and Bill’s towers are two fantastic projects to share with youngsters.

    The best paper about chaos theory is “The recently recognized failure of predictability in Newtonian dynamics” by Sir James Lighthill in 1986. Lighthill was sitting the chair at the Royal Society that Sir Isaac held in his day. It’s probably the best science paper I’ve ever read. Unfortunately, you have to go by a university library that has a subscription to the Royal Society’s publications, or fork over $22.50 for a copy of the article (GAK!). Most university libraries are quite generous in providing access to individuals who visit their facilities in person.

    Chaos theory is all about the horizon of predictability for a system. For your double pendulums with sizzling ABEC-7 bearings, that horizon appears to be a few milliseconds. For something like our solar system, the predictability horizon is around 5 million years. The Sussman/Wisdom paper “Numerical Evidence that the Motion of Pluto is Chaotic” is a great (and freely available) read on this topic. IMHO, discovering that solar systems (and galaxies) are chaotic is one of the great under-appreciated pieces of science of the 20th century.

    Our local weather has a predictability horizon somewhere around 10 days. What’s remarkable about chaos theory is that increased accuracy in measuring initial conditions has little impact on extending the horizon. Even if we had precise measurement of conditions on every millimeter on the surface of the earth and every bit of the atmosphere, we would push the event horizon out only a tiny amount.

    I like Steve Strogatz’s “Chaos” course by The Teaching Company. He gives a great history of the field from Sir Isaac to Edward Lorenz. Sir Isaac had strong hints that his “clockwork universe” would never quite work; Sussman put the last nail in the coffin of his ideal universe. Lorenz is responsible for the concept of the butterfly effect and strange attractor models. I highly recommend “Chaos”; used copies of this course are available regularly on EBay.

    One thing that Strogatz demonstrates is releasing a pair of the double pendulums simultaneously and showing how rapidly their paths diverge. You could show a similar thing with your LED pendulum by showing images of how the path diverged over time.

    Chaos theory is cool stuff, because it forces us to think about whole systems. The mathematics can get absolutely atrocious, but most anyone can still understand the principles. More stuff is covered in Steve’s book “Sync” and his TED talk (see links at http://tam.cornell.edu/faculty-bio.cfm?NetID=shs7 ).

    Strogatz has a strange attractor model that his students at MIT made on a 3D printer many years ago. It would be cool if someone would figure out how to make one on a makerbot!

    –phil