Exactly at the level chosen, is a bit fuzzy because it switches from one state to another, but the change is quite small. It was essentially an even worse case of the situation described in the previous paragraph. With regard to the early history of computing, yes, much of the early programming was mathematical, but not all. The famous Turing test had nothing to do with mathematical calculations, but communication with a human in such a way that the human could not detect the computer. I've often thought that the metaphor of numbers in the computer was misleading.
Time is analog as is sound.
Thus a digital representation of time is breaking the continuum up into tiny chunks. At the pool recently I wore an old watch with small marks at the quarter hour points and found it difficult to tell time with. I decided some time ago that at this time of my life, I don't need to know the time more precisely than what I can see by the position of the hands. Phonograph records and needles must be of very high quality to produce excellent sound, and they are subject to damage. Cassette tapes get crinkled and stretched.