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.

Bruno


http://iridia.ulb.ac.be/~marchal/



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