Charles wrote (sometimes ago):
>On the other hand we may eventually learn all there is to learn. That's
>also possible.
There is no unifying complete theory of just number theory or Arithmetic,
neither computer science.
You can try to solve the riddle in "diagonalisation 1". It is a
shortcut for understanding that Church thesis entails varieties of
incompleteness phenomena.
(
http://www.escribe.com/science/theory/m3079.html)
That will have bearing with David Deutsch Cantgotu environments.
Universal machines (like amoebas, brain, fractran, computer and cosmos
apparently) are just sort of relative self-speeding up anticipation on
possible realities.
Even without comp, the simple arithmetical existence of the universal
turing machine, makes any unifying attempt to describe completely reality
infinite.
Even if we are "more than" a universal computing machine, it is easy
to explain there is a sense in which we are *at least* universal
computing machines (even the kind which can know that(°)), and that is
enough for making the world possibly very complex.
There are tranfinities of surprises there, including uncomputable and
even unnameable one. And there is no universal
rules saying how to manage them. Is that not apparent with just
number theory? In any case this follows from incompleteness.
We can bet on rules which manage partially the things;
Chaitin is right there is pure empirical truth in arithmetic, and
this is necessarily so and part of machine's worlds/psychology.
(°) we can know we are universal machine. But we cannot know we are
consistent universal machine (unless we *are* inconsistent ...).
Bruno
Received on Wed Sep 05 2001 - 08:24:33 PDT