From: tomh.bbs@cybernet.cse.fau.edu
Newsgroups: comp.ai.philosophy
Subject: Re: Robert Rosen & Physical form of Church's Thesis
Date: 10 Apr 92 22:27:47 GMT
Organization: Florida Atlantic University, Boca Raton

In article <1992Apr10.142424.29056@mp.cs.niu.edu> rickert@mp.cs.niu.edu 
(Neil Ri
ckert) writes:

>In article <TogZiB1w164w@cybernet.cse.fau.edu> 
tomh.bbs@cybernet.cse.fau.edu wr
ites:

>>Rosen claims that the physical form of Church's Thesis is false.
>>This means there are physically realizable processes that are
>>not effectively calculable.  He also claims that life and probably
>>'intelligence' are such processes.
>
>  Has anybody claimed that life is effectively computable?

See my response to Harry Erwin - Wolfram (and many others, I suspect)
hold that all of physics is computable (including life).  The case of
interacting quantum fields is still undecided, though - Feynman
commented that one of the marvelous things about the universe was how
quantum processes could do an infinite amount of computation in finite
time.  I don't know about such things, but I know I used to agree with
Wolfram, and now I'm not so sure.

>>One candidate is a turbulent flow, which (mathematically) is
>>aperiodic.  Clearly, any simulation on a digital computer is
>>going to be periodic, by the finiteness of the number of states
>>of the computer.  Therefore a digital computer cannot simulate an
>>aperiodic process perfectly.
>
>  It would not surprise me if turbulent flow were shown to be not 
effectively
>computable.  But the argument based on periodicity is quite 
unconvincing.
>Even a very small computer has enough states that it can change state 
every
>nanosecond and not repeat itself for a time much longer than the 
expected
>life time of the galaxy containing the turbulent flow.

Yea, I agree.  But I have had programming experiences where using
floats produced periodic behavior after only a few hundred iterations,
and using doubles pushed it back to where I couldn't tell anymore.
Sometimes the effective number of states isn't so large.

>>Issues this raises are:
>>1) Is a physical turbulent flow really aperiodic?  If not then brains
>>   are computers and we can all go home.
>
>  It is not apparent how you reach this conclusion about brains.

If physical processes like turbulence (a kind of 'worst case') are
periodic, then they can be simulated by sufficiently large computers.
If in fact, there are NO aperiodic phenomena, then everything is
simulable.  The brain, being physical, would then be simulable.

This is really asking if the universe is discrete (simulable) or not.

>>3) What happens if we use an analog computer instead of a digital one?
>
>  Unless you hypothesize an analog computer of infinite precision, I 
don't
>see what the analog computer would provide.  You can simulate an analog
>computer on a digital computer.

That's true.

>>Another way to say this is that two simulations of a brain (with even 
the
>>tiniest difference in input) will diverge from each other, as well as
>
>  This sounds like a way of saying that even two identical twins will 
not
>always behave identically.  I don't see it as causing any problems as 
far
>as AI is concerned.

I probably should have compared real brains and simulations, rather
than two simulations.  So:

The point is that what brains do may not be simulable (or
computable).  So if you tried to simulate a brain, your simulation
would fail somewhere to do the "right" thing.  The question is really
whether this difference would be significant to the simulation.  If
the simulation "stayed on the attractor" despite the failure, even
though the exact trajectory was different, then everything, I
suspect, would be fine.  If the simulation froze up, or went into an
infinite loop, that would be bad.

>  Neil W. Rickert, Computer Science               <rickert@cs.niu.edu>
>  Northern Illinois Univ.
>  DeKalb, IL 60115                                   +1-815-753-6940

Tom Holroyd
Center for Complex Systems and Brain Sciences
Florida Atlantic University, Boca Raton, FL 33431 USA
tomh@bambi.ccs.fau.edu