> "the halting probability Ω, which is irreducibly complex (algorithmically random), maximally unknowable, and dramatically illustrates the limits of reason"
I really enjoyed the beauty of this statement.
I really enjoyed the beauty of this statement.
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."
So I would argue that it illustrates nothing of significance under either of those issues.