X-Message-Number: 8648
Date: Tue, 30 Sep 1997 22:29:41 -0700
From: Hara Ra <>
Subject: Real Number Turing Machines

Message #8633
From: Thomas Donaldson <>:

>The reference is by HT Siegelmann, ED Sontag, SCIENCE (268(1995) 545-548).
>In the particular article given, they discussed neural nets and how their
>results with such real-number computers led to conclusions about neural
>nets also (their article naturally refers to previous work on such 
>computers). It turns out that a neural net with real-number weights on 
>each connection cannot be imitated by a Turing machine. FULL STOP. This,
>in a way, is a version of an analog Turing machine, but we have to be
>careful what we mean by "analog". Their general results apply not just to
>Turing machines but to other computing devices also. The two authors have
>basically shown that computing with real numbers can do MORE than a Turing
>machine can do. In each case the infinite real number isn't used directly;
>instead, as part of the computation it is calculated out to the required
>number of decimal places for the computation the machine is performing.

Biological neurons have a limitation which makes the computational
abilities of using real numbers in Turing Machines moot. This is noise.
Some estimates suggest that the resolution of biological neurons may be
as low as 4 bits. I don't think it is quite that bad, but will go along
with a 32 bit resolution limit for neurons.

This of course leads to the notion that any neural network can be
simulated with a Turing Machine, and therefore a mind may be uploaded
and all of that, using a suitable digital technology. Neural networks
and digital computers are not different in terms of computability.
Obviously practical problems abound and I don't expect to see any
workable solutions before I enter the dewar.
 
O----------------------------------O
|  Hara Ra <>  |
|  Box 8334  Santa Cruz, CA 95061  |
O----------------------------------O

Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=8648