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>From: callahan@blaze.cs.jhu.edu (Paul Callahan)
Subject: Re: Daniel Dennett
Message-ID: <1991Nov24.001806.19636@blaze.cs.jhu.edu>
Organization: Johns Hopkins Computer Science Department, Baltimore, MD
References: <1991Nov21.005355.5696@husc3.harvard.edu> <centaur.690849720@cc.gatech.edu> <1991Nov23.022628.5799@husc3.harvard.edu> <1991Nov23.214707.1663@cc.gatech.edu>
Date: Sun, 24 Nov 1991 00:18:06 GMT
Lines: 48

centaur@terminus.gatech.edu (Anthony G. Francis) writes:

>The universe is, as far as we can tell, finite, and so ...

By similar reasoning, the interval [0,1] on the real line has finite length, 
and therefore it must contain finitely many points. 

Um, no, I don't think that follows.

Now, for all I know, the universe is finite *and* space is divided into little
discrete cells like a cellular automaton, and time moves in discrete clock ticks.
If these statements were all true, your claims would have some legitimacy.
However, it's not my understanding that current physics supports such a model.
Certainly, some things come in "quantum packets" but it's not as simple as a
collection of cells with transition rules.  In a sense, I would find such a
model of universe appealing, since it would appear to be more tractable.  
However, I doubt very much that the universe really cares whether I 
find it appealing, so this isn't much of an argument.

That being said, even if the universe can compute non-recursive functions, it's
not at all clear that the human brain can.  There is no evidence that neurons
make any special use of effects that cannot be simulated to a sufficiently 
good approximation by Turing machines.  Any non-recursive functions that
are computed by neurons are (in my opinion) likely to show up as noise, and 
will be eliminated by redundancy mechanisms.

To use an analogy, analog audio technology should hypothetically be superior to 
digital, since it places no a priori limit on the accuracy of reproduction. 
Assuming ideal components, the analog reproduction should be perfect, while 
the digital reproduction is guaranteed to be inaccurate even if the components
are ideal.   In practice, however, it is easier to build digital equipment to 
guarantee a certain precision than to produce sufficiently good analog 
recording media.  

A digital tape recording contains magnetized spots intended to store either a 
zero or a one.  Clearly, not all "one" spots are magnetized to precisely the 
same degree, since the medium is imperfect, so they "store" more than just one 
bit of information (for all I know, an infinite amount).  Most of this 
information is, however, discarded by the equipment reading the tape.  As a 
result, we can be fairly certain that we will read a "one" if that was the  
value written.  I would not be surprised if something similar held for neurons.
That is, their actual behavior could be far too complex to simulate by a Turing
machine, but the component of their behavior that is actually used in the 
brain can be simulated readily.

--
Paul Callahan
callahan@cs.jhu.edu


