Today I rediscovered radiolab (from WNYC).  It’s an amazing radio show that has an intense and interesting curiosity about all things in the world, written and hosted by people that are similarly intense and interested.

A recent show told us about a video on… parabolas.  See the video here. Sure some of the shapes featured are not parabolas, but it’s the intro when Steve Strogatz is speaking that’s most important.  Among the quotes from Strogatz that I like best, when describing how a pendulum (like on a grandfather clock) has a relationship between the length and the time of a complete swing: ...this really gave me the creeps.  because it was as if this inanimate thing, this pendulum, knew algebra.  how could this thing swinging back and forth know something about parabolas?  or how could that be built-in?  It was in that moment that I understood that there was a ‘law of nature’.

Why is it that of all the functions we know, the ones we first learn in algebra class are so important that they describe such a diverse range of phenomena?  Isn’t it both creepy and amazing that there is this underlying order to the behavior of objects?  Besides the pendulum, which you will hopefully see later in the semester or a further physics course, we see parabolas in the projectile motion equations.  Why parabolas?  Why not y = t^3 or t^(1/3) like BM said on Thursday in class, or any other functional dependence for that matter?  Why not acceleration in the x direction as well as y?

Images compiled from Will Hoffman’s Parabolas (etc.)