On Wed, Apr 7, 2010 at 8:31 PM, James Propp <jpropp@cs.uml.edu> wrote:
One comment I've already received can be paraphrased as follows: "You describe these computations with infinite decimals as taking place in ordinary time, so that even though each individual digit eventually stabilizes, you have to wait till time omega to be able to read off the answer. Why not imagine a computer in which each carry in the 10^{-n} position takes 10^{-n} seconds, so that the computation finishes in finite time?"
I was wondering if anyone had seen any proposals for (unrealistic) models of computation along these lines.
Yes; there's a whole literature on "unconventional computation". http://en.wikipedia.org/wiki/Unconventional_computing The kind you describe is often set in terms of an observer falling into a black hole; an infinite computation run by a computer left outside the black hole will "finish" before the observer crosses the Schwarzchild radius. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com