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

Date: Fri Dec 05 1997 - 09:36:32 PST

Date: Fri Dec 05 1997 - 09:36:32 PST

Carl F. considers technological statis among competing entities expanding

out to colonize the universe, jumping from oasis (e.g. star sys) to oasis.

Carl F. assumes an evolutionary pressure for maximum speed (which Carl A.

questions) and shows a example calculation of optimal jumping distance.

I didn't follow his analysis - I think he needs to give more explicit math.

But I found the question interesting enough to do my own analysis.

Assume (with Carl F.) that spores traveling between oases at a constant

speed V have a 1/A chance of being destroyed per unit distance. Thus given

N1 initial spores the number of spores surviving after distance X is

N1*exp(X/A).

Assume that spores deliver unit wealth to an oasis, and at an oasis wealth W

grows a fractional rate of 1/G per unit time, up to a maximum Wmax. At any

point growth can be stopped and N2 = W/C spores can be sent out, where C is

the cost per spore. Thus after time T, N2 = exp(T/G)/C spores can be sent.

Finally, assume a delay D for spores to accelerate, decelerate, and set up

shop.

And assume only a fraction S of oases are discovered on arrival to be

suitable.

The maximum possible speed is where on average only one spore survives to

grow in a new oasis per each previous colonized oasis. So assume N1 = N2.

A little algebra shows X = A*ln(WS/C) and T = D + g*ln(W) + X/V .

So now we just vary things like W,A,V,D to minimize T/X, being sure to

consider their effects on cost C.

Varying W we find that we want W=Wmax, regardless of the other parameters.

So you always stay at an oasis until you completely exhaust it, then move on

all at once.

Varying A we find we want to maximize A*ln(N), so engineers should be willing

to spend huge sums to improve this parameter. Doubling A is just as good as

squaring the number of probes send out.

I haven't put in plausible functional forms for C(V,D) and D(V) to learn more

about optimal V. Anyone want to try this? Also, anyone want to flesh out

this model with plausible values for parameters?

I've been working out a differential equation to address the question of

whether

max speed is really the best idea, but that will have to wait for another

post.

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 Fri Dec 5 09:37:34 1997

*
This archive was generated by hypermail 2.1.8
: Tue Mar 07 2006 - 14:45:29 PST
*