Sure but the hard part to understand and accept is that ANY squiggle can be represented by a weighted sum of sinusoids...I mean, that's really an amazing insigh

Sure but the hard part to understand and accept is that ANY squiggle can be represented by a weighted sum of sinusoids...I mean, that's really an amazing insight, and I don't think it's obvious even after-the-fact. Forget about the details of computing coefficients - just the fact that it works at all remains counter-intuitive to me. (A neat visualization would ask the user to wiggle their mouse, producing a sparkline of some finite length, and then, in real-time, update a frequency domain representation of the motion, perhaps represented as a bunch of connected circles that rotate steadily but at different rates to produce an equivalent graph)