I made an attempt to model intelligence explosion dynamics in this post, by attempting to make the very oversimplified exponential-returns-to-exponentially-increasing-intelligence model used by Bostrom and Yudkowsky slightly less oversimplified.
This post tries to build on a simplified mathematical model of takeoff which was first put forward by Eliezer Yudkowsky and then refined by Bostrom in Superintelligence, modifying it to account for the different assumptions behind continuous, fast progress as opposed to discontinuous progress. As far as I can tell, few people have touched these sorts of simple models since the early 2010’s, and no-one has tried to formalize how newer notions of continuous takeoff fit into them. I find that it is surprisingly easy to accommodate continuous progress and that the results are intuitive and fit with what has already been said qualitatively about continuous progress.
The page includes python code for the model.
This post doesn’t capture all the views of takeoff—in particular it doesn’t capture the non-hyperbolic faster growth mode scenario, where marginal intelligence improvements are exponentially increasingly difficult and therefore we get a (continuous or discontinuous switch to a) new exponential growth mode rather than runaway hyperbolic growth.
But I think that by modifying the f(I) function that determines how RSI capability varies with intelligence we can incorporate such views.
(In the context of the exponential model given in the post that would correspond to an f(I) function where
f(I)=1I(1+e−d(I(t)−IAGI))
which would result in a continuous (determined by size of d) switch to a single faster exponential growth mode)
But I think the model still roughly captures the intuition behind scenarios that involve either a continuous or a discontinuous step to an intelligence explosion.
I made an attempt to model intelligence explosion dynamics in this post, by attempting to make the very oversimplified exponential-returns-to-exponentially-increasing-intelligence model used by Bostrom and Yudkowsky slightly less oversimplified.
The page includes python code for the model.
This post doesn’t capture all the views of takeoff—in particular it doesn’t capture the non-hyperbolic faster growth mode scenario, where marginal intelligence improvements are exponentially increasingly difficult and therefore we get a (continuous or discontinuous switch to a) new exponential growth mode rather than runaway hyperbolic growth.
But I think that by modifying the f(I) function that determines how RSI capability varies with intelligence we can incorporate such views.
(In the context of the exponential model given in the post that would correspond to an f(I) function where
f(I)=1I(1+e−d(I(t)−IAGI))which would result in a continuous (determined by size of d) switch to a single faster exponential growth mode)
But I think the model still roughly captures the intuition behind scenarios that involve either a continuous or a discontinuous step to an intelligence explosion.