(The latter are, of course, also physical, but see many previous posts for details on significant differences. Essentially, the latter involve largely arbitrary maps between real world magnitude values and internal numeric representations of those values.)
I’ve focused on the nature of causality in those two kinds of systems, but part of the program is about clearly distinguishing the two in response to views that conflate them.
While stocking up on groceries for the coming storm (I haven’t seen the grocery store that crowded in a while), I was thinking about indeterminate systems.
There is an old mechanistic view of reality that it works like a kind of clockwork, each action following precisely from a previous one.
So, reality is fuzzy, and there is an element of randomness to it.
So even math and computing are fuzzy.
And note that the limits are fundamental. They are not due to our lacking technology or skill or knowledge.
Reality really is fuzzy at the edges, math really can’t prove all true statements, and there are no computational oracles.
The point, my brain bubble, is simply this:
Heisenberg’s Principle applies to physical systems, not information systems. (It applies to their physical instances, of course, but algorithms and mathematics are not themselves subject to Heisenberg Uncertainty.)
Gödel’s Incompleteness and Turing’s Halting apply to information systems, not physical systems. (Some do try to apply Gödel to real life, but it’s just a metaphor. His Theorems apply strictly to mathematics.)
So here again is an example of the stark and (I would think) undeniable difference between physical systems and numeric systems.
The former submit to Heisenberg; the latter submit to Cantor, Gödel, and Turing. Two rather different worlds!
Stay out of da Nile, my friends!