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> "the halting probability Ω, which is irreducibly complex (algorithmically random), maximally unknowable, and dramatically illustrates the limits of reason" I
by chairmanwow 10y ago
> "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.
- nemo1618 10y agoI think you would also enjoy some of the statements here: http://www.mathrix.org/liquid/archives/the-history-of-the-chaitin-leibniz-medallion 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."
- prmph 10y agoMy philosophical take: the halting problem illustratres how free will can exist in a deterministic universe
- datadata 10y agoThis 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?
- Retra 10y agoFree 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.
- prmph 10y agoHow do you model true non-determinism in a deterministic system? And if that can indeed be done, would that not support my original point?