Re: poly: Re: Why interest rates may stay low

 hanson@econ.berkeley.edu (Robin Hanson) writes:
>> I expect that in the not-too-distant future, there will be at least
>>one investment opportunity will test this upper limit of investment
>>supply. I'm thinking primarily of the opportunity to launch self-reproducing
>>probes at near lightspeed to colonize large parts of the galaxy, although
>>it's also conceivable that a race to produce a molecular assembler or
>>the first AI could do similar things.
>
>It is possible that one might make a case that one of these techs is a big
>exception to our historical experience, but I think a careful analysis would
>be needed to make such a case persuasive. You have to persuade us that tech X
>would create so many attractive investments that even when well over half
>of world income is devoted to (prematurely) investing in tech X, the worst
>investments would still be expected to have a persistently large real ROI
>(say over 20%/yr continuing over a decade). This must be true even when one
>considers the rise in price of any bottleneck property rights, such as
>patents, LEO slots, or a limited number of relevantly skilled professionals.

 Ok, I'll start with a very simplified version of the colonizing probes.
I assume that at time T a group of people figure out the design of a probe
capable of reaching 0.99999c and establishing possesion of at least one
solar system. I assume the total mass needed to launch each probe is Mprobe
grams, and that up to 10^10 solar systems massing an average of 10^33 grams
each at an average distance of 50000 light years can be acquired by such
probes. I assume that by the time the first probe has been launched, most
value consists of ownership of mass/energy.
 In the reference frame of the probes, the average time to the destination
is a little over 200 years. I assume that makes the average time to destination
from today about 300 years. My calculations show the following rate of return
to acquiring mass as a function of Mprobe:

 Mprobe || Annualized % return
==================================
  10^25 || 6
  10^20 || 10.5
  10^15 || 15
  10^10 || 19
  10^5 || 23

 I expect that the ability to throw a few orders of magnitude more reaction
mass into a launch than a mass-efficient design requires will allow less
efficient designs to reach the target speed earlier, producing some of the
interest rate reducing effects you mentioned. But I expect that once the
mass used per probe gets up around 10^20 grams, the advantages of using
more mass will be out be outweighed by factors such as the delays associated
with constructing a large enough system to use all the mass, or the value
of using some of that mass to launch probes at other targets.

 I can't see any other effect which would bring the annualized return below
about 10%, although I have doubts about whether it is meaningfull to compare
value across this kind of singularity.

-- 
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Peter McCluskey  |  pcm@rahul.net  | Has anyone used http://crit.org
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