poly: Seeking StarFlight Functional Forms

Carl Feynman responds:
>Beat me to it. Oh well, I'll just have to think of another publishable
idea.
>Serves me right for procrastinating.

If you could find substantial time to work on the paper, I'd be happy to
coauthor. If not, I will give a clear and strong acknowledgement.
  
>R(s) = the resources available after growing at an oasis for time s. ...
>Let me suggest a sigmoid form for this. ... lots of things grow this way.

I thought of this, but it didn't capture the insight that there are different
pools of resources, some of which can grow faster than others. Asteriods
might
be fast to mine, planets slower, stars slower still. I could model a sigmoid
for each pool, but then I'd have to know how many pools and their relative
parameters. I was thinking a slowing of growth rates was sortof an average
over such pools.
 
>How about using Gompertz's law of mortality? The mortality rate as a
>function of age rises exponentially. ... It's a generic feature of
>mortality in most species.

Cool! I didn't know about that. Anyone have suggestions on what the param
values for this should be?

>There may well be economies of scale in the construction and launching
>of probes. Many of the good starflight proposals I have seen involve
>the construction of a reusable launcher.

Good point. Unfortunately that introduces another function.
As in: Total-cost = Fixed-cost(v,h) + Unit-cost(v,h) * N-probes.

>Q(P) = the fraction of probes which land at open oases, given
> a fraction P of them are occupied.
>
>Wouldn't this depend on where the probe was relative to the frontier?

Yeah, but P goes to zero as you approach the frontier.
A more elaborate model would be Q(P,P'), saying the local rate of
colonization influences how coordinated they can be.

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 23:56:12 1998