X-Message-Number: 15376 Date: Wed, 17 Jan 2001 23:43:55 -0500 From: Thomas Donaldson <> Subject: more re computers and brains Hi everyone! I guess I must repeat. The fact that the connections of some given individual will never become exponential is irrelevant to the arguments I have made. At any given time the POSSIBLE connections are factorial. It is this possibility that makes the use of Turing machines difficult (as I said before, even if we forget the importance of TIME in studying just how we work and whether or not Turing machines are important). The same issue that Mike Perry raises (that the number of connections will go up polynomially) shows up in ordinary computers. No one would assess the ability of a computer by looking at its lifespan from its original owner to its disposal as junk by simply adding up the calculations and programs which it ran during that period. Certainly that figure will be way below the POSSIBLE programs it might have run, but it also says nothing at all about applicability of Turing's ideas to computers of that kind. You want to get a bound on what ANY computer of that design might achieve; the way to do so is to work out the limits of their possible computations, not those of any particular instance. And it is in looking at those limits that we can reasonably think about Turing machines at all. (Yes, I would agree that Turing's computer serves as a model for a single sequential computer, if we also limit the memory available to it, but I am not discussing single sequential computers!). I hope that my point is clearer now. Best wishes and long long life for all, Thomas Donaldson Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=15376