Transcript:

So, a couple of days ago, I posted a video on how Fourier transforms are at the heart of how an eye can see. But the way I explain Fourier transforms, it fails the Feynman test. What Feynman says is that if you can't explain something without using jargon, you've not understood a damn thing.

So here's another attempt to explain Fourier transforms. So, let's say the problem is this. You are given a sum of three digits. From that sum, you have to determine exactly which three digits went into the sum, and you can decide how to do the summation.

So, let's say the number is six. And if I don't give you any rules, six does not allow me to resolve it. It could be one plus one plus four, or it could be one plus five plus zero; it could be any number of things.

But let's say I set the rules like this. Take the first digit, multiply it by 100. Take the second digit, multiply it by 10. And then add these two to the third digit and tell me the answer.

Now I know exactly what's going on. If the answer is 627, I know it is six plus two plus seven. If the answer is 721, I know it is seven plus two plus one. Very simple.

So that's the basic idea of Fourier transforms, except Fourier generalized this to an arbitrary continuous function. That's the brilliance of Fourier.