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Path: utzoo!attcan!lsuc!watmath!maytag!aftermath!water!nmouawad
From: nmouawad@water.waterloo.edu (Naji Mouawad)
Newsgroups: comp.edu,uw.general
Subject: Re: Recursion Summary
Message-ID: <1990Oct25.164113.2453@water.waterloo.edu>
Date: 25 Oct 90 16:41:13 GMT
References: <1990Oct23.211651.10227@contact.uucp> <9868@milton.u.washington.edu> <9882@milton.u.washington.edu> <9893@milton.u.washington.edu> <1990Oct25.145621.13691@watdragon.waterloo.edu>
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Organization: University of Waterloo
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In article <1990Oct25.145621.13691@watdragon.waterloo.edu>
ccplumb@spurge.uwaterloo.ca (Colin Plumb) writes:

[Part deleted]

>Turing machines are fully capable of recursion.  Nobody has found a
>buildable machine which is fundamentally more capable that a Turing
>machine, i.e. to the best of my knowledge, my own brain is
                                            ~~~~~~~~~~~~~~~~   
>Turing-equivalent (although it would take a *damn* fast Turing
 ~~~~~~~~~~~~~~~~~
>machine and very clever software!).

[Part deleted]

--Colin

As a side note, the underlined sentence implies that the Cartesian
dualism is true and that the Kantian boundary between physics
and metaphysic can be removed.

That the current perception of the brain can be modeled with Turing
machines is true, but that does not mean that the various boundaries
imposed by the digitalisation of the brain (in order to represent it
as a Turing machine with a countable _not necessarly finite _ number
of states) is 'accurate'. It may be that  the continuous process of the
brain activity can be better represented by some other mechanism than
the Turing machine (undecidable question ?). More importantly, mathematics
taught us that there is just no way to represent all the reals by
rationals. Another way of saying the same thing is that reality (analog
process) cannot be entirely 'grabed' by reason (digital process).

Thus, if the Cartesian dualism is false (meaning that the thinking
process depends intimatly on the supporting hardware _ the brain _)
then Turing machines are a pale comparison (in power and flexibility ;) )
to the brain.

--Naji.

P.S. Could someone come up with a Pumping Lemma for the brain ?

-- 
         ---------------+-------------------------------------------
        | Naji Mouawad  |       nmouawad@water.waterloo.edu         |
        |  University   |-------------------------------------------|
        | Of Waterloo   | "Thanks God, we cannot prove He Exists."  |