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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.
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
2003-09-29

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