Eliezer S. Yudkowsky writes:
>But if you mean "Why is a sharp jump upwards plausible at any given point?",
>my answer is that, for any reasonable function f() of optimization and
>intelligence, solving the differential equation y' = f(y) yields a curve which
>is either flat or sharp. Either the increases in I and O are self-sustaining,
>yielding further increments, or they peter out.
>
>In technology progress with constant intelligence, you have t' = t, which
>gives us the exponential growth we all know and love. If intelligence were a
>function of technology (i = t), and given that intelligence sets the rate of
>exponential technological growth, I think a more realistic model is t' = e^t,
>which yields -log(-t), which goes to infinity.
"I think a more realistic model is" is not a sufficiently detailed argument.
for t' = a*e^(b*(t+c)). And even accepting this form, substantial growth
could still take centuries, depending on the values of a,b,c.
Your argument here seems awfully close to the claim that "the doubling time
of computer hardware efficiency is proportional to the computer operations
per second devoted to R&D in computer hardware, or within all of computer-aided
`humanity.'" If you recall, this was my summary of the assumption behind an
analysis from a web page of yours, and I gave specific empirical criticisms
of it. You have not yet responded to them.
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