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> I think that's partly because the simple experiments, like cellular automata, he used to come up with this principle actually explore the 'space of simple rul
by kouru225 2y ago
> I think that's partly because the simple experiments, like cellular automata, he used to come up with this principle actually explore the 'space of simple rules', not the 'space of ordered sets of states of systems'.
I think it’s the opposite actually. He chose to study these recursive systems because they seem to describe reality, and then when he found more evidence that they do a good job describing reality, he kept studying… so on and so forth. Basically a sort of hermeneutic circle type deal.
You do a much more thorough job of describing it. I should’ve mentioned the recursive part earlier. I just kinda assume we all already know we’re talking about recursion and time steps and that’s not a useful assumption
- kridsdale3 2y agoIt's pretty dang hard to give the output to Fibonacci(x) for any x up to infinity without having done the work up to that point.
- Xcelerate 2y agoActually there’s an explicit formula for Finonacci(x) that involves phi. I think you can use generating functions to derive it. (But your overall point still stands.)
- kouru225 2y agoGood point. We’re still not describing it perfectly. Admittedly I’m doing it by my memory of the last time I read Wolframs ideas. I think we unfortunately have to describe it using Kolmogorov complexity: what is the length of the shortest computer program that produces the object as an output? What Wolfram means by computational irreducibility is that he asserts that reality itself is the shortest length computer program that can produce its own output, and it can’t be shortened (reduced) any further without losing information. Edit: sorry I think I still haven’t fully described it. Will have to come back to it tomorrow when I’ve had some sleep