**From:** Stuart Armstrong (*dragondreaming@googlemail.com*)

**Date:** Mon Feb 16 2009 - 04:35:20 MST

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A simpler model, based on a comment on "phase space".

Toy model 1: Lego

If we see intelligence as an optimisation process, then a crude

measure of intelligence would be how small a volume in the space of

possibilities it can steer the future into. Call this volume V(i),

where i is the model of the inlligence.

Then define S(i) as the volume taken up, in the space of possible

intelligent machines, by those intelligences with a smaller V(i) (ie

the space of smarter intelligences).

Then if S(i) > V(i), self improvement is possible - the AI is smart

enough to construct smarter machines than itself. If not, it stays

where it is.

Toy model 2: Mecano

In practice, V(i) is probably going to be very small, if the AI has

enough memory space and can take enough time (the volume will not be

zero, in general, since you still need intelligence to interpret

results, even if you can get them by brute force). The more relevant

information is then T(v,i), the time taken by the machine to home in

on a space of volume v, given that it is of model i.

Then fast self improvement is possible if T(S(i),i) is bounded above -

ie there is a bound on how slow self-improvement can become.

If T(S(i),i) is not bounded above, then depending on its behaviour, we

may either reach diminishing returns, or a strict upper bound on

attainable intelligence.

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