What if Gödel was wrong? That is the question asked in this well
written but very confused short story. The characters in this story
decide to test Gödel's theorem by running a computer
program to check logical completeness and consistency. When they find
that he was wrong, the universe changes accordingly.
Just as
Heisenberg's Uncertainty principle is misused and mythologized by
people who think it means something more than it does, Gödel's
incompeteness theorem is often misused in popular writing. The
author of this story clearly suffers a great many of these confusions
all at once! To set the record straight, let me state that -
The theorem does not say that there would only be a finite
number of true statements in a complete system. It merely defines a
complete logical system as one in which every statement can either be
proved to be true or false. Obviously, in any non-trivial system
there would be infinitely many of these statements whether it is
complete or not!
- Gödel's theorem does not address the question of whether the
universe is deterministic. The question is whether something can be proved in a finite number of steps in a symbolic logic, not how the universe decides what will happen next!
- The theorem also has nothing to say about the existence of "free
will". This story repeats a mistake I have heard many times before --
that of confusing questions of determinism with those of "free will".
The mistake works like this: First suppose the universe was
deterministic and then prove that this contradicts some definition of
"free will". Then act as if this somehow shows that in a
non-deterministic universe there is free will. (In fact, the
arguments against free will in a deterministic universe always seem to
apply in a non-deterministic universe as well. The truth is that free
will is a very slippery term, but that this has nothing to do with
determinism.)
I also really object to the characters claim that pure
mathematical research has never had any consequences in the real
world. (They state explicitly that this experiment they are doing
might be the first time.) I think that mathematics does not get much
credit because it is rarely the last step in the process.
However, we ought to recognize that steps earlier in the process of
invention/discovery are also necessary, and without pure mathematical
research I do not think we would have airplanes, televisions,
computers, reliable cryptography, JPEG standard, global positioning
satellites, etc.
First published in Popular Computing (1985) and reprinted in Mathenauts. |
