yOn Wed, 22 Jul 1998, Robin Hanson wrote:
> Eugene asks Damien:
> > > magical SI through AI seems a bit incoherent; you exploit the
> > > Church-Turing thesis, then assume the result does something beyond
> > > Turing-completeness...
> >
> >I can't follow your reasoning here. Would you care to explain?
>
> Damien has an essay on the topic at:
> http://www.ugcs.caltech.edu/~phoenix/vinge/antising.html
Damien's essay makes much of the fact that all universal Turing machines are equivalent, in the sense of the class of functions they may be used to compute.
A simple objection to this argument is that different types of computer may require very different physical resources to compute some class of functions.
For example, a plausible though not watertight argument can be made that quantum computers will be capable of solving problems involving quantum simulation of a few humdred qubits that would require physical resources exceeding those available in the observed Universe, if those resources were exploited in a classical fashion. (Similar comments about factoring and certain search problems can also be made).
For such classes of problems, I think it is fair to say that classical computational devices, such as the brain, may be qualitatively weaker than is allowed by physical Laws.
Damien concludes with:
"My very vague thesis: All undamaged human beings, and other sentiences, share the same area of comprehensibility."
Michael Nielsen
http://wwwcas.phys.unm.edu/~mnielsen/index.html