Re: poly: Modeling Economic Singularities

Nick Bostrom asks:
>Robin says that on his model, one of the necessary
>conditions for an economic singularity is that the population growth
>remains less than the discount factor ~3%. But suppose that
>population growth rate were to rise to, say, 5% for the next 50
>years. If in 20 years we develop superintelligence plus full
>Drexlerian nanotechnology, why should it make any difference whether
>the average couple has 2.1 children or 2.4 children? This doesn't
>look like the sort of thing that could stop the singularity from
>happening. What am I missing?

In the model I gave, the supply of capital is a hyperbola, which has
two branches. I focused on one branch, which goes negative when
population grows too fast. But the other branch then goes possible,
so perhaps you can have fast growth with a fast population.
You can also get no solution to the equations, however, and I haven't
examined the stability of this solution. But I should revise my
paper to reflect my uncertainty here.

Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/
RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884
140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614
Received on Tue Apr 14 18:35:42 1998