Fourier Series in Everyday Life.

I'm going to talk about math, and then I'm going to get philosophical, so stick with me.

There is this thing called a Fourier Series.  The Fourier Series is the subject of my favorite joke of all time, and no one ever gets it and that is one of life's cruelties. 

Basically, let's say you have a weird function and you want to find the equation for it. 

Like this step function I made in MS Paint.

Sometimes, it's just too hard to get the exact equation because the function you want was drawn in a default image editor, so you decide to get as close as you can and just use that. 

Oh yeah!  Looking good!

So I draw a sine wave (the blue line), which gets the up and down part but leaves something to be desired.  This first guess is called the first order term, or the first thing you do.  But we can do more.  We can take another sine wave, add it to this one, and together they add and subtract from each other to bring us closer to what we want.

A graph I didn't draw in MS Paint

So here, the black shows the first order term.  The blue shows the first order term added to another sine wave, and the red shows an even higher order term to get pretty close to that blocky function we wanted.  Ta dah!  Close enough!

Yesterday, I realized that I approach projects as if they were Fourier Series.  The first draft or the first try is like the first order term.  It's general and not even really close to what you want, but it's a start.  Then you go over it and make it a touch better, then a touch better than that.  The corners of your blocky function stat to come in.  You iron out individual pieces.  Only later can you start working out details until you get close enough to what you want.