The basis for the mathematical roots of non-linear editing begins with its roots in film.
At the end of day of shooting, rolls of film for images, and reels of magnetic tape for sound, were gathered for developing and processing. Once the film was developed, the audio was registered with the image frames, by transfer to a so called “mag track”. If the source film was 35mm, with four perforations per frame, the audio was transferred to a a 35mm mag track, recorded at the appropriate speed such that each four perforations on the mag track corresponded to 1/24 of a second of sound.
A clapper was recorded for each take recorded to film and tape; and a frame was manually marked on the film where the boards of the clapper first visually meet. The audio was then matched to the film so that the peak in the audio recording of the clapper matches the frame where the clapper's “sticks” met. The perforations in the film and the audio track provide the increments forward and back that the mag-track can be synchronized