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." Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=14746