From: Stuart Armstrong (email@example.com)
Date: Mon Feb 16 2009 - 04:35:20 MST
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
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