Matt Gingell wrote:
> I think the original remark misses the depth of Church-Turing. It's
> not just talking about what you can do with a computer, it's talking
> about what you can do with _any conceivable_ formal system. If you can
> find expressible regularities in the universe which can't be described
> under the lambda calculus then you've disproven the conjecture.
With all due respect, I do *not* "miss the depth" of things like Church-Turing-Tarski. I believe the Church-Turing-Tarski thesis is false and will be disproved. I believe there are expressible regularities in the laws of physics that cannot be described under the lambda calculus, by Turing machines, et cetera. Furthermore, I believe that *any* complete causal explanation of an event, which means the complete chain of causality extending back to the reason why anything exists in the first place, *must* contain noncomputable phenomena. I believe that the noncomputability of objectively real phenomena is a necessity, not a coincidence. And, for the record, I believe that the Church-Turing-Tarski thesis is fundamentally *wrong*, not just limited in the space of phenomena it describes; there is *no such thing* as a simulation; it is not possible to "compute" the complete behavior of a quark without creating an actual quark.
I don't know that a genius-in-a-box that naturally evolved in a Life universe could deduce that it was in a simulation, but I know it could deduce that it wasn't looking at the lowest level of reality.
-- firstname.lastname@example.org Eliezer S. Yudkowsky http://pobox.com/~sentience/tmol-faq/meaningoflife.html Running on BeOS Typing in Dvorak Programming with Patterns Voting for Libertarians Heading for Singularity There Is A Better Way