Re:Childhood's End: The digital revolution has turned into s...
by aurelian15 on Saturday January 05, 2019 @12:12AM
(#18830033)
Yes, thank you for the clarification, my statement is ambiguous.
I meant to say that the theory required to describe a computation on a practical analogue computer (that is noisy) is no different than the theory required to describe the same computation on a digital computer, because they essentially are both discrete systems.
However, as you point out (at least as I understand your first paragraph), when we analyse/build systems on an abstract level we assume (often as a simplification) that they are ideal continuous systems.
Although your overall point is correct, I disagree with this statement. It is in fact only theory that distinguishes between continuous systems and very high resolution discrete ones, because the time-evolution of an ideal computer is nowhere differentiable while the time-evolution of a physical system is everywhere differentiable.
Indeed, it is not only "discrete" and "continuous" that are indistinguishable below a certain threshold. For any data, there are an infinite number of continuous theories that are all indistinguishable from each other, and also are indistinguishable from an infinite number of discrete theories, which are yet also indistinguishable from each other - all that it takes for this to happen is for us to agree that the data doesn't specify anything below a certain scale. Then, every theory that agrees on the large scale will match the data, leaving room for anything you can imagine at the bottom. So discrete vs. continuous isn't the core point.