X-Message-Number: 14746
Date: Fri, 20 Oct 2000 12:02:40 -0700
From: Hugh Hixon <>
Subject: Turing: Beyond Turing (Computers and Brains)

The arguments here are *still* 50 years behind Alan Turing.  You are invited
to read:

Alan Turing's Forgotten Ideas in Computer Science
 B. Jack Copeland and Diane Proudfoot 

      Neural networks and hypercomputation are hot ideas for
      transcending the limits of traditional algorithmic computing. What
      few realize, however, is that both concepts were anticipated in
      detail decades ago by Alan Turing, the British genius better
      remembered for laying the groundwork for artificial intelligence. 

in the April, 1999 *Scientific American*.  After which discussion can continue.

Unless someone can find a *full-text-plus-illustrations*  of the above
article on the net, you'll have to touch paper.

Hugh
----------------------
From the article:

"Outside the confines of mathematical logic, Turing's O-machines have
largely been forgotten, and instead a myth has taken hold.  According to
this apocryphal account, Turing demonstrated in the mid-1930s that
hypermachines are impossible.  He and Alonzo Church, the logician who was
Turing's doctoral adviser at Princeton, are mistakenly credited with having
enunciated a principle to the effect that a universal Turing machine can
exactly simulate the behavior of any other information-processing machine.
This proposition, widely known as the Church-Turing hypothesis, implies that
that no machine can carry out an information-processing task that lies
beyond the scope of a universal Turing machine.  In truth, Church and Turing
claimed only that a universal Turing machine can match the behavior of any
human mathematician working with pencil and paper in accordance with an
algorithmic method -- a considerably weaker claim that certainly does not
rule out the possibility of hypermachines."

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