From: Robert J. Bradbury (bradbury@ilr.genebee.msu.su)
Date: Wed Nov 17 1999 - 08:38:00 MST
I'm returning to this discussion since if I don't I'm sure Robin will
never let me forget about it. :-?
On 17 Sep 1999, Robin wrote:
> Consider the function P(m) which describes the most P(ower) you can extract
> from a star given a certain amount of available M(etal). Since you can
> choose not to use metal, P must be an increasing function.
> If you have two stars, and are trying to extract the most power from them,
> and you have a certain amount M of metal available, your problem is
max P(m1) + P(m2) such that m1 + m2 = M
m1,m2 and m1 >=0, m2 >=0
> You are suggesting that an optimum is m1 = 0 and m2 = M, putting all the
> metal at one star so as to get every last photon and reradiate at near 3K,
> while completely leaving the other star alone. This requires that
> P''(m) > 0 on average, with *increasing*, not diminishing, returns.
The metal may have 2 uses: computation, which presumably requires
energy, or memory, which requires very little energy (occasional
rewriting to offset cosmic ray damage in excess of ECC limits
seems unavoidable).
The computational throughput of a parallel processing "computer" system
will be highest value when the material resources are utilized in such
a fashion that you get the greatest amount of computation done with the
minimal amount of interprocessor communication delays and energy costs.
So the best situation to setup is m1 at the thermodyanmic limits
and m2 with the leftovers. For example, this could be m1 = 0.999(m1+m2)
and m2 = 0.001(m1+m2). You can't use any more metal at m1 because
you are using all the power of your star *and* are radiating at
the lowest background temperature possible. You may develop
m2 but it is hardly worth the trouble, since the cost of shipping
information to m2 (in terms of energy and months to years of transit
time) makes it hardly worth the effort of any additional computation
you got back (after more months to years).
> Instead I expect any plausible model of metal-limited Dyson sphere to show
> decreasing returns: The first few tons gives lots of power while the last
> few tons gives a lot lot less. This implies that to get the most power one
> should spread the metal evenly across the two stars:
> m1 = m2 = M/2 .
I agree that metal-limited Dyson spheres *do* show decreasing returns.
The further out from the star you go, the cooler the layers get and the
less energy you have to do useful work. If you want a "global" maxima,
your conclusion is correct. But *unless* the AS-SI has agreed to work
for me full time for the next 10 billion years (for free of course),
it makes little sense to split m1 & m2 evenly. It makes much more sense
to make the RB-SI a Matrioshka Brain (hiding the star, operating at the
thermodynamic limits) and make the AS-SI a Jupiter Brain (harvesting a
small fraction of the stellar output, waiting for more metal to be produced).
In a subsequent message, I wrote
>
>> No. I'm suggesting that there are always decreasing *local* optima.
>> If there were *no* costs to transfering material (or information) from
>> 1 to 2, then doing that would make sense. But if the costs of the
>> material/information transfer *exceed* the cost of local manufacture
>> then it makes sense to reject remote information/material (if you
>> have to pay for it).
To which Robin replied:
> But mass transport costs make the puzzle worse! Let n1 and n2 be
> the initial metal amounts at the two stars. The problem then is: max
> P(m1) + P(m2) such that m1 + m2 = n1 + n2
> m1,m2 - T*abs(m1-n1) and m1 >=0, m2 >=0
>
> (Note that abs(m1-n1) = abs(m2-n2).) Assume without loss of generality
> that n1 > n2. If P(m) has diminishing returns (P''(m) < 0), then when
> transport costs are very high, m1 = n1 and m2 = n2, so nothing moves.
I agree, if transport costs are high, you don't go harvest metals
and ship them home. You either breed them locally or make do with
what is available.
> And when transport costs are zero, m1 = m2 = (n1 + n2)/2. And for
> intermediate transport costs n2 is in the range [n2,(n1+n2)/2].
In the long run, you will orbit to places where transport costs
are lower (in theory, if you can predict the motions of all of the
stars in the Galaxy, you can apply small delta-V's that over long
time scales (millions of years) bring you in very close proximity
to locations (stars or gas clouds) where quantities of metals are
available and transport costs are very low.
> So we should see at least P(n2) power intercepted from star 2.
Only if it is of some benefit! We always come back to this
point. Say m2 is enough for an AS-SI-JBrain. Is there any
point to the construction of this if over the last billion+
years, billions of JBrains have been constructed and they have
"thought" everything that JBrains are capable of thinking?
Do cockroaches question whether to reproduce? No. They do
it because they are programmed for it. Do humans question
whether to reproduce? Yes. Because they consciously question
whether the benefits exceed the costs. If we assume the
evolution of intelligence goes hand-in-hand with the evolution
of rational-thought, then you have to answer the question of
what justifies the production of something that is only capable
of thinking things that you thought ages and ages ago?
The point of reproduction (IMO), is to hopefully get something new
and better. If you are up against thermodynamic limits, that
probably becomes increasingly difficult as the universe ages.
If you believe sacrificing your potential for that of another entity
then equi-division of metals might make sense. Once you have decided
to harvest everything that provides benefit in excess of the
investment, then the question is whether there is any benefit to
leaving behind "handicapped" JBrains. That sounds like a pretty
sadistic thing to do. As a JBrain it is going to be pretty clear
that you got somebody's leftovers.
>
> So in this model the only way to explain all those stars we see is
> to say they all have very little metal near them, so little that even
> when it is all used to intercept starlight, less than 1% of the light
> is intercepted. This isn't true of our system, and I doubt it is true
> of a great many.
>
It takes a small fraction of the metal in a system like ours to harvest
all of the sunlight (and hide the star in the visible region). It
[probably] takes more metal than we have available even after
dismantling all of the planets to *optimally* use the energy the
sun is producing. So we can rapidly evolve to the low-SI level with
a hidden star but may take eons to evolve to high-SI levels.
Sure, a few of the textropians can go off and colonize nearby
stars, but they are going to be *years* behind us on the SI
evolutionary curve. You could set your sights on a bigger
star (more energy), but that has a shorter lifetime and
suffers from larger inter-SI node propagation delays (bigger
stars with more energy means the radii of the "hottest"
computronium layer must be larger to prevent melting). You
could shoot for a metal rich star that would have a resource
base for faster post-SI evolution, but as soon as you got
a few million moon-sized telescopes up and running you might
discover the sky filled with individuals who have been
pursuing your strategy for much, much longer.
I certainly agree that the math outlined above makes sense.
If we were striving for some "global galactic optima" your
argument might sense. But in striving for any galactic optima,
you have to solve a planning problem that involves information
this is ~100,000 years out of date (the light-speed distance
across the galaxy). On SI timescales a *lot* can happen in
that length of time.
If we could assume that drives & justifications for colonization
in humans would apply in SIs, then staking out metal claims might
make sense as well. But if *you* are going to claim them, the
claiming entity must be an "owned", non-self modifying subsidiary.
Questions:
- If Columbus had known the Americas were populated with cultures
far older, wiser and more powerful than his, would he have set sail?
- Is there a galactic market for metals claimed given the high costs
of transporation?
I'm optimistic that *if* SIs exist already, we will see them before
we have the ability for interstellar colonization. So framing
the exploration/colonization question within that framework is useful.
If SIs do not exist, then survival scenarios (enclaves, escaping
bio-nano-goo, etc.), interstellar colonization and galactic optimization
discussions are useful. If this is the case, then we also have another
interesting problem to discuss -- why is the development or survival of
intelligent life so darn difficult?
Also, some of my claims regarding communications costs have raised
some eyebrows. A very brief & rough summary of my thoughts in
this area, and the references (what people really want) is now up at:
http://www.aeiveos.com/~bradbury/MatrioshkaBrains/LogP.html
I'll do my best to answer questions but it may take another 2 months.
Robert
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