On Sat, Oct 05, 2013 at 02:15:47AM +1300, LizR wrote:
> I'm still slogging through Scott Aaronson's paper, and have now reached
> page 37. It looks as though there are still lots of interesting matters to
> be discussed, but there is something I already have a problem with that
> seems central to what he is saying, namely what is the significance of
> Knightian uncertainty? He has pointed out that it's a valid objection to
> free will being in any useful sense free that all physical processes are
> either deterministic or random (the usual dilemma), but then goes on to say
> that we can get around this if some processes rely on "Knightian
> uncertainty". These are, if I understand correctly, quantum states that go
> back through a causal chain to an initial condition of the universe. These
> states ("freebits") cannot be determined by any measurement. And that
> therefore it's possible that some physical systems contain a source of
> irreducible uncertainty.
>
> To which I have to say - so what? What is the crucial distinction between a
> source of randomness that happens to go back to the big bang, and one that
> doesn't? How does this in any way get around the argument that free will
> isn't usefully free if it merely relies on determinism and randomness?
>
I think that argument is that Knightian uncertainty is absolutely
unpredictable, even by gods or daemons. Ordinary uncertainty is at
least predictable in some sense: "there is a range of outcomes,
following this distribution of probabilities".
I agree with you that I don't see why this distinction should really
be important. Evolutionary speaking, it only really matters that you
are unpredicatable by your enemies, god and daemons aren't particularly
relevant. So whilst I do think the picture of amplifying quantum
uncertainty via chaotic dynamics is a likely strategy for evolution to
have used, I'm not convinced it would choose between Knightian
uncertainty and ordinary quantum uncertainty, or even pseudo random
uncertainty when that suffices.
> I will read on, but I feel that my hope of learning why this type of
> randomness is better than anyone else's is going to go unsatisfied, because
> I think Scott thinks he's already explained why, and I didn't get it.
>
> By the way, it also occurs to me that as time goes on, there will be less
> and less freebits around, since he says they can get turned into "ordinary
> bits" by various processes. So does that mean that a person born in the
> distant future will have less free will than one born now?
>
Yes - exactly. Scott uses that fact to dismiss the Boltzmann brain
argument.
Personally, I don't think that is necessary, as I think Boltzmann
brains can be banished in the same way as White Rabbits, by the
universal prior measure, which must vanish exponentially as a function
of time (or rather as a function of consumed bits of quantum
uncertainty, which is the same thing).
--
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Visiting Professor of Mathematics [email protected]
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