# ∫ Things I Saw In Stony Brook: Vanity Plate Edition

October 10, 2010 Leave a comment

First off: Why have I been numbering these things? What a stupid thing to do.

Secondly: Is it obvious by now that how busy I am with school work is inversely proportionate to the percentage of my recent posts which are just pictures?

Yeah, well, at least I’m still posting *something.* I promise, as soon as this lab report is done…

Anyway, lets get right to the picture:

If you’re a mathy, sciency, engineery type (or possibly even a musical type?) then you know what this guys plate is about, and you know he’s a nerd. If you don’t, here’s the (brief) explanation:I

It’s a reference to the mathematician Joseph Fourier, whose concept of Fourier Series (and by extension, Fourier Transformation) form the conerstone of, well, like half of modern physics. That’s not quite true, but it’s certainly one of those things you can’t possibly hope to understand physics without. And it’s got to be one of the most widely-applicable little mathematical tricks ever.

The easiest way to think about is through music. If you know about how instruments, you know that the “note” you hear when a piano plays a middle C is composed mostly of the sound wave that corresponds to the frequency of middle C, but that it also contains some higher frequency components mixed in with it (the “overtones”) which determine how exactly the note sounds, not just its apparent pitch. This is why a piano playing a middle C and a violin playing a middle C do not sound the same even though they are both supposed to represent the same “pitch”– this used to puzzle me endlessly when I was a little kid, by the way.

Anyway, a decomposing the sound wave into its Fourier series means separating out each individual contribution (the original note, plus all of the separate overtones) so that you can see what makes up the total sound bit-by-bit. This on its own probably sounds useful as a way of studying the physics of waves, but when you realize that quantum physics is basically the art of treating everything in the world as if it were actually a wave, then you can see how Fourier might have the kind of far-reaching applicability that I’ve described.

By the way, if you know some high-school calculus, then there’s another nice analogy I can draw for you: remember how you learned that any function anywhere can be written as a Taylor series? Which was to say, you could write it as a combination of polynomials (a mixture of X’s, X^2’s, x^3’s, etc..)Well a Fourier decomposition is the same thing, only instead of writing the function as some combination of polynomials, it’s a mixture of Sines and Cosines. You probably like polynomials more than Sines and Cosines, so you might be wondering why on earth you would ever choose the second option. Well, it would be hard to fully explain the answer to that without getting into a big mess, but suffice it to say that a lot of the physical phenomena in the world (light waves, sound waves, vibrations of atoms and molecules, etc) have a periodic nature, and so do Sines and Cosines, whereas polynomials most certainly do not.