First things first:
Now… for the actual physical explanation, you can read it here. And for the historical precedent, you can read about it here. (via Kottke)
UPDATE: An applet here.
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Continuous Everywhere but Differentiable Nowhere 
I remember doing a project on coupled mechanical systems in 8th grade. It just involved two pendulums swinging from the same cord, and the phases were opposite rather than coincident, but the general concept was the same.
It’s amazing what will stick with you from that age – I’ll have to try to be more diligent about inspiring my students.
Wow! I never learned about that in junior high. The first time I learned about coupling pendulums was in college. I doubt we ever really *really* learned about it.
You’re totally right about how random things just *stick* with you. I don’t know why that is, and I don’t know if you can engineer those moments, really. But if you teach with enough of those sorts of “wow!” moments, I guess one is bound to stick.
But I don’t know what I’m talking about.
I started reading the paper about why this works, but I got tired. I think I’m going to try to make a post explaining it, if I figure it out myself. It might have to be a series of posts (one on a single pendulum, one on a coupled pendulum fixed to a table, one on a coupled pendulum on a moving board).
never learned about that in junior high
We probably wouldn’t have, either. It happened during one of those science fair type project things, where students have to come up with their own science projects. Even though it was a fairly middle of the road (now bottom of the barrel) junior high, it happened that a couple of us in that class had Caltech professors as parents, and for some reason those couple all ended up doing related but not identical experiments on coupled pendulums.