Re: Penrose vs the Robot


Stephen Harris wrote:

>
> Here is David Chalmers musing on the possibilities (1989) and
> doesn't seem to be conclusive.
>
> "Basic question: is the universe an infinite-state-machine or a
> finite-state-machine?

I have difficulties accepting that this is an exhaustive choice, in the
sense in which Chalmers probably means "machine" - as some kind of
serial, deterministic thing.

> **If the second, then it is WEAKER than a Turing
> machine, so these analog solutions are essentially weak theoretically. If
> the first, then is it true that it is STRONGER than a Turing machine? At the
> very least, it seems that it has different theorems of computational
> complexity.
> The only way a Turing machine can accomodate 'parallelism' is through its
> states.

Well ok, but two Turing machines in parallel (which can communicate)
are not equivalent to a (deterministic) Turing machine. Its behaviour
can be (take your pick based on your preference) non-computable or
non-deterministic, because what gets communicated depends on the timing
behaviour of the two machines.

(As some point Marvin Minsky will arrive and say, that's not true! and
anyway we thought of that back in the 1950s!)

<snip, some of which I didn't understand>

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