Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!psuvax1!rutgers!njin!princeton!phoenix!kpfleger
From: kpfleger@phoenix.Princeton.EDU (Karl Robert Pfleger)
Newsgroups: comp.ai
Subject: Re: Algorithms, Turing, Semantics
Message-ID: <12945@phoenix.Princeton.EDU>
Date: 15 Jan 90 17:18:34 GMT
References: <12883@phoenix.Princeton.EDU> <91Eq02wy7eX=01@amdahl.uts.amdahl.com>
Reply-To: kpfleger@phoenix.Princeton.EDU (Karl Robert Pfleger)
Organization: Princeton University, NJ
Lines: 33

In article <91Eq02wy7eX=01@amdahl.uts.amdahl.com> kp@amdahl.uts.amdahl.com (Ken Presting) writes:
>In article <12883@phoenix.Princeton.EDU> kadickey@phoenix.Princeton.EDU (Kent Andrew Dickey) writes:
>>
>>1) Could someone name one process which cannot be broken down into an
>>algorithm?  That is, many people have said the mind may not be simulated
>>through an algorith, but personally, no other examples of
>>non-alogorithmical processes occur to me.  Please, someone, tell me what
>>obvious example I'm missing.
>
>There has been a discussion here lately as to whether all processes are
>algorithmic, and some controversy perhaps remains.  Algorithms are finite
>sets of rules determining transitions among a finite set of states.
>Physical systems usually have an infinite number of states, so any
>algorithm can at best approximate the behavior of a physical system. In
>a physical system with unstable components (where a small perturbation
>can produce large changes) the approximation may never be good enough.

First of all, algorithms can determine transitions among an infinite
amount of states. There is no reason why an algorithm can't operate on
analog quantities. For instance, I consider Gaussian reduction to be an
algorithm for solving systems of equations.

Second, I see no reason why a variable can't be part of a rule with the
stipulation that the rule is usable for an infinite number of possible
values of the variable. This can be considered an infinite number of set
rules. (minor point)

Lastly, there is no proof that physical systems have an infinite number
of states. Space could be discrete. Time could be discrete. Either could
be finite.

-Karl		kpfleger@phoenix.princeton.edu
		kpfleger@pucc (bitnet)