> "the halting probability Ω, which is irreducibly complex (algorithmically random), maximally unknowable, and dramatically illustrates the limits of reason"
"God has chosen that which is the most simple in hypotheses and the most rich in phenomena. But when a rule is extremely complex, that which conforms to it passes for random."
"Everything can be summarized in one thing, but the thing itself cannot be reached."
"Mathematical facts are true by chance."
"To make all things from nothing, unity suffices."
This is a really interesting comment, could you elaborate on it a bit more? Which part of a deterministic universe would the halting problem serve to enable free will? -The universe as a whole? -Any agent claiming to have free will? -Some physical process that couldn't be simulated faster by something else in the universe?
Free will is just what it feels like to have a mind that can construct models of realities that are not fact. And you can model nondeterminism in a deterministic system just fine.
So I would argue that it illustrates nothing of significance under either of those issues.
http://www.mathrix.org/liquid/archives/the-history-of-the-ch...
"God has chosen that which is the most simple in hypotheses and the most rich in phenomena. But when a rule is extremely complex, that which conforms to it passes for random."
"Everything can be summarized in one thing, but the thing itself cannot be reached."
"Mathematical facts are true by chance."
"To make all things from nothing, unity suffices."