Re: The Meaning That Immortality Gives to Life

From: Nick Hay (
Date: Mon Oct 15 2007 - 20:48:05 MDT

On 10/15/07, Matt Mahoney <> 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

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.
> 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.
> -- Matt Mahoney,

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