From: Nick Hay (nickjhay@gmail.com)
Date: Mon Oct 15 2007 - 20:48:05 MDT
On 10/15/07, Matt Mahoney <matmahoney@yahoo.com> wrote:
> A singularity is necessarily a recursive self improvement process because once
> we achieve superhuman intelligence, those intelligences will be able to make
> further improvements faster than we can. Legg proved [1] that an intelligence
> (using the universal definition [2]) cannot completely predict the behavior of
> a greater intelligence.
This is not true. Shane proved, roughly, there is a c such that any
intelligence of complexity x bits cannot correctly predict ALL systems
of complexity x+c bits. The all is crucially important: one can
construction predictors that succeed on arbitrarily complex systems of
a specified form, and one can successfully build arbitrarily complex
bridges.
The proof is that for any system of complexity x bits you can
construct a devil system of complexity x+c bits which models what you
do and deliberately does the opposite. This is interesting, but
certainly doesn't exclude predicting all complex systems.
-- Nick
>
> References
>
> 1. Legg, Shane, (2006), Is There an Elegant Universal Theory of Prediction?,
> Technical Report IDSIA-12-06, IDSIA / USI-SUPSI, Dalle Molle Institute for
> Artificial Intelligence, Galleria 2, 6928 Manno, Switzerland.
> http://www.vetta.org/documents/IDSIA-12-06-1.pdf
>
> 2. Legg, Shane, and Marcus Hutter (2006), A Formal Measure of Machine
> Intelligence, Proc. Annual machine learning conference of Belgium and The
> Netherlands (Benelearn-2006). Ghent, 2006.
> http://www.vetta.org/documents/ui_benelearn.pdf
>
>
>
>
>
> -- Matt Mahoney, matmahoney@yahoo.com
>
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