poly: ESS for HPLD

At 09:36 AM 12/5/97 -0800, Robin Hanson wrote:
>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.

I agree my model wasn't very good-- I was making it up as I composed the
message. I'll try to come up with a better model. At least your response
is clear enough to criticize (:-).

You make an assumption:
>
>At any
>point growth can be stopped and ... spores can be sent out

after some analysis the conclusion is:

>So you always stay at an oasis until you completely exhaust it, then move on
>all at once.

but wasn't this implicit in the assumption? It seems to me the optimal
strategy is to devote some fraction of your resources to reinvestment, and
some fraction to sending out spores. Immediately after arrival in an
oasis, reinvestment is important. But as time passes, spore production
becomes relatively more important. Once all the accessible resources in an
oasis have been converted into wealth, reinvestment is pointless and pure
production is the thing to do. If you wait too long before producing
spores, your neighbors will beat you to the next oasis. But if you don't
grow exponentially, you won't be able to shoot for distant oases where your
spores are likely to be destroyed on the way. It's a variational game
theory problem, yuck.

>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.

And, just to confuse matters further, A depends on V, since collisions with
dust grains are more severe at higher speeds.

--CarlF
Received on Fri Dec 5 11:50:27 1997