X-Message-Number: 9255 From: eli+@gs160.sp.cs.cmu.edu Subject: "non-Turing" Date: Sun, 8 Mar 98 22:27:12 EST Thomas Donaldson wrote: >The first thing I thought when I read about the nonTuring neural net was >that it was a counterexample to the notion that not all machines must be >Turing machines. It is that, if you mean "not all abstract machines", but this notion is flimsy to begin with. Deliberately constructing counterexamples is easy: pick a problem that's not Turing-computable, and define an abstract machine that's a TM augmented with an `oracle' for the problem. This neural net model is simply another example of an abstract machine that's too powerful to be physically reasonable. (If you weren't happy with the argument I posted the last time this came up, specify your disagreement and I will undertake to dig up my xerox of that paper.) >The particular features of the counterexample aren't so >important: what it tells us, more than anything else, is that we cannot make >the ASSUMPTION that Turing machines can emulate everything we find in the >world. Agreed, that's a bad assumption. The Church-Turing thesis is (in some interpretations) a statement about the world, and could be empirically falsified. http://plato.stanford.edu/entries/church-turing/ may be of interest. (though I don't think the distinction between "computable by a machine" in Copeland's "Thesis M" and "`rule of thumb' or `purely mechanical'" in Turing's thesis will bear nearly as much weight as Copeland wants it to.) -- Eli Brandt | eli+@cs.cmu.edu | http://www.cs.cmu.edu/~eli/ Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=9255