** Next:** More Relations to Previous
** Up:** Discussion
** Previous:** Probabilistic Gödel Machine Hardware

##

Limitations of the Gödel machine

The fundamental limitations are closely related to
those first identified by Gödel [10]:
Any formal system that encompasses arithmetics
is either flawed or allows for unprovable but true statements.
Hence even a Gödel machine with unlimited computational
resources necessarily must ignore those self-improvements
whose effectiveness it cannot prove,
e.g., for lack of sufficiently powerful axioms.
In particular, one can construct examples of environments and
utility functions that make it impossible for the Gödel machine to ever
prove a target theorem.
Compare Blum's speed-up theorem [3,4]
based on certain incomputable predicates.

Similarly, a realistic Gödel machine with limited resources
cannot profit from self-improvements
whose usefulness it cannot prove within
its time and space constraints.

Juergen Schmidhuber
2003-10-28

Back to Goedel Machine Home Page