A sample is a mathematical value akin to the handle of a Bezier curve, there to facilitate the reconstruction of a different waveform that may have little to do

A sample is a mathematical value akin to the handle of a Bezier curve, there to facilitate the reconstruction of a different waveform that may have little to do with the sample's apparent position at all. :) (granted, this is specifically at high frequencies: at low enough frequencies, the sample might as well be the waveform within whatever contstraints the word length puts on you)