🚀 go-pugleaf

In article <37f794$ipf@portal.gmu.edu> herwin@vanish (Harry Erwin) writes:

>Subject: Turtles All the Way Down
>Date: 11 Oct 1994 23:31:48 GMT

>Here's the reason for the original 'turtles' post. It has
>to do with Searle, Pribram, and Penrose's argument that the brain can
>do computational things that a digital computer can't. If that is the

Interesting. I don't know whether it's clear that the difference 
between computer reasoning and brain reasoning (hardware difference) resides 
in the difference between digital and analog processes.

Has it been settled that Godel's theorem is less valid for analog systems?

I think part of Penrose's argument is that what happens in the brain 
may be a result of quantum processes which do not follow ordinary commonplace 
logic. If this is where the difference is, then one could construct 
intelligent machines by harnessing these quantum effects in any hardware.

(Incidentally, an algorithm for such a quantum machine has recently been shown 
to be able to factorize large numbers which can not be factorized by *any*
traditional computer. Realizing the quantum hardware is a different matter...)

>case, then an AI will have to have 'analog' components similar to those
>in the brain, and the question of what those components are becomes
>interesting. Now, consider what processes could result in this. First,
>if the fourth derivatives of the underlying dynamics are bounded, then
>the system can be digitally simulated (using numerical PDE integration).
>Hence, for the SPP argument to hold, the fourth derivatives must be
>unbounded or undefined. That could be a result of significant structural
>discontinuities or possibly a lack of a smallest scale for significant
>structure ('turtles all the way down'). 

>Note that I'm trying to avoid arguments from chaotic dynamics (weak
>based on the Grebogi and Ott results) and from computability (the brain
>as a Turing machine), since neither show the brain doing anything that a
>computer cannot do.

>--
>Harry Erwin
>Internet: herwin@gmu.edu 
>Just a dumb graduate student working on Katchalsky network models....
>(And if you believe that, I have a ranch in California to sell you.)