Re: Penrose (Was: Infinities)

Hal Finney (
Sun, 9 Nov 1997 17:38:15 -0800

Leevi Marttila, <>, writes:
> Hal Finney <> writes:
> > I just skimmed Penrose's book, but my impression is that he claims that
> > mathematicians have an instinctive ability to recognize mathematical
> > truth. Machines, which are deterministic computer programs and therefore
> > can be in principle be described as formal systems, are limited by Godel's
> > theorem and are unable to recognize certain truths. Since people are
> > (according to Penrose) unlimited in their ability to recognize mathematical
> > proof, this would mean that they are not formal systems and therefore no
> > machine can do mathematics in the way a person does. (And hence, among
> > other things, uploading and AI are impossible.)
> Wouldn't adding random input to machine make Penrose's argument about
> Godel's theorem irrelevant?

Maybe so - but it is conceding too much, from the point of view of a
believer in uploading and AI. It should not be necessary to add a true
random number generator to a machine in order to make it capable of
consious thought. To the extent that some randomness is needed, then
an algorithmic pseudo random number generator ought to be good enough.
Believing otherwise is tantamount to believing in Penrose's mysticism
regarding the non-algorithmic capabilities of minds.

There are pseudo random number generators which are believed to be
indistinguishable from true random number generators even with all the
computing power in the entire universe (by some definition). Yet adding
such a PRNG to an AI or upload preserves the fact that it is a formal
system, and is still susceptable to Penrose's Godelian argument. If only
true random number generators can escape Godel and become conscious, then
there must be some way of telling them apart from these simulations, which
would go beyond known algorithmic capabilities. There would have to be
something magical going on.

Penrose's argument is weak enough IMO that it should be fought on its
own grounds. We accept that machines have limitations; the absurdity is
the claim that humans have none. (Keep in mind my repeated disclaimer
not to have a deep understanding of his argument.)