20 Nov
2003
20 Nov
'03
5:53 a.m.
On Wed, 2003-11-19 at 21:14, William R. Buckley wrote:
In the case of Turing closure, the notion is much
broader. Turing closure
refers
to the ability of a system to perform any and all computations that can be
expressed. Now, there are problems with this notion, since Godel has shown
that some expressible computations in fact can not be computed. Still, the
general notion is: all that can be computed is computable upon a TM, and a
TM
is capable of computing all computations.
Yes, this is correct, and close to what turing wrote in the '36 paper.
The real key to understanding the theory of
computation is to understand the
works of the mathematician David Hilbert, the logicians Kurt Godel, Alonzo
Church, Stephen Cole Kleene, and Emil Post, the linguist Noam Chomsky,
and the mathematician Alan Mathison Turing.
Eh, it's not that hard. Machine modifies it's own program. What's the
big deal? :-)