So if our universe is essentially computational, what are the implications of Godel's incompleteness theorem? Doesn't this mean there must be an infinite number of axioms our universe is generated from?
If Wolfram is right, our universe would be a mathematical "function" not a mathematical "system". Godel showed that every system of sufficient complexity has facts about it that can't be proven. There is no reason to think though that every function within a complex goes back on itself. x = y, for example, doesn't loop around no matter how far out you go.
For my part however I don't believe it's possible for the universe to be "pure math" (that is, its reality comes from an equation and nothing else besides it) in the sense that we understand "math". Nevertheless, it might be that there is an equation that can predict everything we experience. We may as well search for it.
Wolfram's a lot smarter than I am, but I believe he also believes the function is discrete and not continuous. In fact, he makes the point in NKS that we may have went off the rails with Newton and the calculus. It may turn out that the universe is discrete and that our understanding of it as continuous is just an artifact of not having the computational power to see how discrete functions can effectively look continuous at a much larger scale (sort of a reverse proof of the integral)
It blows my mind. But if you're a genius, might as well have a hobby, right? I'm just glad he took this up instead of bowling.
Just thought I would add that clarification in there, because I know the word "function" has a lot of meanings to people.
The problem I see is 'truth' that is not generated by the system the universe is a function within. To then maintain truth is that which corresponds to reality gets hard. Kinda trippy.
