Jun 30, 2010 14:40
". . . a logical machine following definite rules may never come to a conclusion. It may go on grinding through different stages without ever coming to a stop, either by describing a pattern of activity of continually increasing complexity, or by going into a repetitive process like the end of a chess game in which there is a continuing cycle of perpetual check. This occurs in the case of some of the paradoxes of Cantor and Russell. Let us consider the class of all classes which are not members of themselves. Is this class a member of itself? If it is, it is certainly not a member of itself; and if it is not, it is equally certainly a member of itself. A machine to answer this question would give the successive temporary answers: 'yes,' 'no,' 'yes,' 'no,' and so on, and would never come to equilibrium."
-- Norbert Weiner, Cybernetics (p. 126)
knots,
mathematics,
logic,
machines