From: Robin Hanson <hanson@econ.berkeley.edu>

Date: Thu Feb 05 1998 - 11:51:00 PST

Date: Thu Feb 05 1998 - 11:51:00 PST

Hi. I'm working on a paper, tentatively titled "Burning the

Cosmic Commons: Evolutionary Strategies for Interstellar

Colonization," building on Carl's insight that we can derive

colonization behavior from the selection effect of what it

takes to stay on the frontier.

Part of the paper proves some general results independent

of specific functional forms, but I also want to include

computer simulations of specific cases. For such specific

cases I need to pick specific functional forms, which I'd like

your advice on choosing.

The basic functions in the model are these:

R(s) = the resources available after growing at an oasis for

time s. R(0) = 1. R'(s) > 0

1/A(x*b(v,h)) = the fraction of probes that survive traveling

distance x at velocity v, with hardness h. A(0) = 1.

A'(x) > 0.

C(v,h) = the resource cost to make one probe with v,h.

Q(P) = the fraction of probes which land at open oases, given

a fraction P of them are occupied.

I'm considering these choices:

Q(P) = 1 - P.

R(s) = exp(lnR(s)), lnR'(s) = lnR0 - lnRd*s.

A(x) = exp(lnA(x)), lnA'(x) = lnA0 + lnAd*x.

b(v) = sqrt(1-v^2).

C(v) = 1 + k*v/sqrt(1-v^2).

Advice on functional forms, or on parameter values, welcome.

Published acknowledgements gratefully given.

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 Thu Feb 5 19:57:10 1998

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