Hal Finney wrote:
>The article above leads to http://www.frc.ri.cmu.edu/~hpm/book98/ which
>hold links to commentary relevant to Moravec's Robot book. ...
>There is a link from chapter 1 to a page of mathematics by Moravec
>similar to what I presented recently showing how a true Singularity can
>be predicted to arise mathematically with certain assumptions. ...
>The problem with this line of reasoning is that it is unlikely that the
>rate of growth of knowledge can continue to be proportional to total
>computing power. Diminishing returns will kick in, and further there
>will be "friction" losses and inefficiency in coordinating the increasing
>number of computers (and people) in the world.
The more serious problem with such exercises is that they in effect try to reinvent fifty years of economic research into the nature of economic growth. Sure you can write down lots of equations, some of which have singularities, and some of which don't. But the best clues to which equations model it best are the equations that have worked the best so far in explaining the economic growth we see now, and have seen for thousands of years. They are the equations that you want to play with in thinking about how computers might change things.
Bill Brown writes:
> >... Diminishing returns will kick in,
>
>Not anytime soon. "Make faster computers" is more like "make more efficient
>factories" than "make faster airplanes", in that it allows a great deal of
>latitude in taking different approaches to get around physical constraints.
The usual modeling approach is to assume diminishing returns in each particular factor, but to allow for possibly increasing returns in the net return to increasing all factors at once. For example, consider
dY/dt = Product_i (F_i)^(a_i)
where Y is total output, F_i is the amount of each factor i, and a_i < 1 is the importance of each factor. Holding all F_j besides F_i fixed, there are strongly diminishing returns to increasing that one factor. But if Sum_i a_i > 1, there are increasing returns to increasing all factors together.
So when the economy changes in some fundamental way, and you want to know if this will change it from exponential growth to something faster, a key question (given the above model) is whether the newly changing factor is enough to tip the balance from decreasing to increasing returns overall.
The factors that people have considered include physical capital, technology, population, health/lifespan, human capital, etc. For any one of these we expect diminishing returns. But when we put them all together, it may be a different story.
Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu
Asst. Prof. Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030
703-993-2326 FAX: 703-993-2323