On 06 Mar 2011, at 14:18, Andrew Soltau wrote:
On 07/02/11 15:22, Bruno Marchal wrote:
I have debunked more than once on this list the idea that a movie
can think. (It is an error akin to the confusion between a number
and a gödel number of a number, a confusion between a description
of a computation and a computation, it is a confusion of the type
finger and moon (ultrafrequent in the field).
However, a movie can of course represent / be a train of thought.
A movie (figuring a boolean plane computing device doing a
computation) can *represent* a computation and can, as such,
*represent* a train of thought, but it cannot *be* a train of thought.
There is just no computation in the movie, no more than actual cause
in a movie. I have more elaborated argument for showing that a movie
cannot think, except in the sense that all piece of matter sum up all
computations, due to a non trivial fractal aspect of the universal
dovetailing (cf my post to Brent).
Then all you need is the thinker. I am most intrigued to understand
how your theory gives rise to a thinker.
A tiny arithmetical theory, like Robinson Arithmetic (roughly
equivalent with Peano Arithmetic without the induction axiom) can
already prove the existence of all UD-reachable computational states.
So if your current thought is "I am hungry", there is a relative
computational state corresponding to that thinker's feeling, and
Robinson Arithmetic can prove that such state exists.
To explain the stability of such feeling is far more demanding,
because such a stability will rely not only on *all* proofs of the
existence of such states, but also on never terminating proofs (of
false proposition for example) (re)proving the existence of your
states. Non terminating executions of programs and infinite proofs are
the real (with comp) stabilizer of the relative computational states.
Roughly speaking, the thinkers or the dreamers are the universal
numbers relatively to all other universal numbers.
(A universal number is just the (finite) code of a universal (Turing,
Post, Church, Kleene, ...) digital machine.
Assuming comp, as always.
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