From: Cole Kitchen (kitchenc@mindspring.com)
Date: Sun Oct 07 2001 - 15:11:35 MDT
On 06 Oct 2001 at 19:15:41, Eliezer S. Yudkowsky wrote:
>However, reproductive rates are likely
>to be substantially lower, and MLS sustantially higher, if we have to go
>all the way to Alpha Centauri at C to obtain more mass. If resource
>acquisition is geometric rather than exponential in the long run, then
>reproduction will also become slower as time goes on.
Actually, a geometric progression (that is, a sequence of numbers whose nth
term is of the form {a X r^[n - 1]}, e.g., {1,2,4,8,16,...}) *is* an
exponential function of n.
What you would get if limited to scrounging for (uniformly distributed} new
resources via near-light-speed starships is a resource total that is a
*polynomial* (not geometric) function of time. The amount of resources at
time t would be proportional to the volume of a sphere with radius c't
(where c' is some value slightly less than the speed of light C), which is
in turn proportional to t^3.
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