**From:** Cole Kitchen (*kitchenc@mindspring.com*)

**Date:** Sun Oct 07 2001 - 15:11:35 MDT

**Next message:**Edwin Evans: "The Simulation Risk"**Previous message:**Mitch Howe: "Re: "SIMULATIONS: A Singularitarian Primer""**In reply to:**Eliezer S. Yudkowsky: "Re: "SIMULATIONS: A Singularitarian Primer""**Next in thread:**Mitch Howe: "Sysop and Population (was: "SIMULATIONS...")"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

On 06 Oct 2001 at 19:15:41, Eliezer S. Yudkowsky wrote:

*>However, reproductive rates are likely
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*>to be substantially lower, and MLS sustantially higher, if we have to go
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*>all the way to Alpha Centauri at C to obtain more mass. If resource
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*>acquisition is geometric rather than exponential in the long run, then
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*>reproduction will also become slower as time goes on.
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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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