Moving picture film appears continuous when running at 24 or 36 frames per second, just like digital audio sounds continuous when sampled at 44 thousand times a second. Yet, slowed down we understand the magic trick.
As long as the choppy images or audio are faster than what we can perceive as changing, we agree to accept them as continuous.
Of course, nothing is really continuous. Take our old friend analog as an example. Many will assume that analog is continuous while digital is chopped up as previously described. What we take for granted as a steady tone—say the continuous press of an organ note—is in actuality a series of on and off modulations occurring too quickly for us to hear as anything but continuous.
Our seemingly unbroken analog world is an illusion.
As long as change occurs quicker than we can perceive it’s all analog.