From: Mu In Taiwan (mu.in.taiwan@gmail.com)
Date: Tue Oct 13 2009 - 13:31:46 MDT
Hello Randall,
If you assume that 'in general' means "For all X...", why would JC use
phrases such as 'given algorithms' and 'random programs'? These distinct
phrases seem to imply he is referring to predictions about samples, rather
than a universal claim.
Also, 'programs' and 'algorithms' are not semantically equivalent except
under certain definitions; many programs would be described as heuristics
rather than algorithms, for example those that abort using a timer after a
given time, and may not produce a result; those that use randomness (e.g.
monte carlo with physical random seed), etc.
Finally, consistency between JC's posts may not be important anyway, given
that they are simply factually inaccurate: JC claims: "what Turing proved is
that in general the only way to know what a random program will do is to
watch it for eternity and see". This is absolutely not what I see AT
actually claiming in that paper.
Mu
On Tue, Oct 13, 2009 at 3:37 PM, Randall Randall <randall@randallsquared.com
> wrote:
> On Tue, Oct 13, 2009 at 05:47:15AM +0100, Mu In Taiwan wrote:
> >
> > your reply to me: "What Turing proved is that in general there is no way
> to
> > prove that any
> > given algorithm will halt."
> >
> > your immediately subsequent reply to Robin: "what Turing proved is that
> in
> > general the only way to know what a random program will do is to watch it
> > for eternity and see."
> >
> > These claims are inconsistent ("any given" != "random", "prove" !=
> "know,
> > watch for eternity and see").
>
> These claims are inconsistent if you assume John is using the usual
> meaning of "in general" as a substitute for "typically". If you take
> it completely literally, it's not inconsistent.
>
> --
> Randall
>
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