poly: ESS for HPLD

I'm just tickled pink that the creators of this list saw fit to do it, and
that I get to be on it.

And, just to get things off on the right foot, here's some thoughts I've
been having about the intersection between evolution and astrophysics.

First, an unpacking of the abberivations in the subject line:

ESS = evolutionarily stable strategy. This is a strategy that will persist
indefinitely in a population of contending replicators using a variety of
strategies.

HPLD = highest possible level of development. This is a concept (and
abbreviation) from a Stanslaw Lem story. The idea is that there is an
end-state of technological evolution, when it is possible to carry out
everything consistent with physical law, and that this end-state is
essentially unique. Because of the uniqueness of this state, it is
possible to theorize usefully about it, while the paths between here and
there are shrouded by mind-boggling complexity (AKA the Singularity).

So what can we say about the HPLD? Well, if it expands toward occupying
the available space (i.e. the entire universe), it will eventually fragment
into separately replicating units, since communication over sufficiently
large distances at the speed of light will be too slow to permit central
control. And if it is fragmented into separately replicating units, it
will eventually expand toward occupying the available space, since
replicators near the edge that choose to copy themselves will obtain an
evolutionary advantage. In other words, colonization of unoccupied matter
is an ESS. So there are two consistent states: a static, unified one, and
an expanding, fractious one.

In this message, I'll consider the expanding case. We can model this as
follows: on the frontier is a set of replicators, each competing to
organize the matter on the other side of the frontier. I will assume the
matter comes in clumps called oases (plural of oasis), which may be
interstellar dust grains, comet nuclei, planets, stellar systems, or
galaxies. The definition of an oasis is that resources are relatively
abundant within an oasis and scarce between oases, and that given HPLD
technology, it is usual that each oasis is occupied by a single
replicator, but that is is not uncommon that nearby oases are controlled by
different replicators. The size of oases is set by the relative economies
of scale of attack and defense.

Why am I assuming that attack and defense are reasonable things to think
about at the HPLD? Surely, you may say, highly advanced entities would be
able to settle things by negotiation? Well, to the extent that sets of
entities are bound together peaceably, they can be considered parts of the
same replicator, like cells in a body or workers in a company. So if all
you see is harmonious relations, you're looking too close. Try zooming out
by a few orders of magnitude until you see evolution, red in tooth and
claw. Note that I am not saying that conflict needs to actually occur;
just that credible threats of attack and defense need to be taken into
account by the replicators when they choose strategies.

The cycle of growth looks like this: an inter-oasis seedship arrives at a
previously uncolonized oasis, and frantically begins to constuct an
industrial base, using self-reproducing technology. Once enough of the
oasis is under control, it begins to construct more inter-oasis seedships
to colonize the next set of oases beyond the frontier. It may at the same
time need to defend its oasis against other late-arriving seedships from
other replicators. Similar things are happening all across the surface of
the frontier. Each replicator will aim its seedships perpedicular to the
frontier, since it has a competitive advantage at getting to that volume
first. This will cause the frontier as a whole to approximate a sphere,
or, when viewed locally, a plane (I think this is true whether or not the
oases are uniformly distributed, but I haven't proven it yet).

If the rate of growth within an oasis is fast compared to the scatter in
travel time between oases, whoever gets to an oasis first will have a
massive competitive advantage. For example, if oases are stellar systems,
and it is possible to double one's industrial base in a week, even if
seedships move at 90% of lightspeed, the second arrival in a system will be
at a crushing disadvantage, arriving months or years after the first
seedship.

What is the optimal strategy for choosing the next oasis to jump to? We
know that the seedships should be sent out roughly perpendicular to the
frontier, but how far out should they be sent? This depends on the
distance-versus-time behavior of the colonizing process. Consider the
curve whose horizontal axis is the expected time between the arrival of a
seedship in an oasis, and the arrival of its first descendant in another
oasis. The vertical axis is the distance between the two oases. The
optimal distance to send to is the point on this graph with the highest
distance-to-time ratio. The overall rate of expansion of the frontier is
the distance divided by the time at this point.

What does a typical curve look like? Let's consider the case where oases
are stellar systems, and seedships travel at 0.9c, with all of their
acceleration and deceleration occuring at the ends of the journey. When a
seedship arrives in a new system, it takes a year to build a new seedship,
and builds one seedship a year for the next three years before giving up
(kind of a stupid strategy, I know, but it's easy to model). Seedships
have a 10% chance of running into a dust grain and being destroyed for
every year of flight time. In this case, the curve starts at 0, and
remains flat for the first year. It then begins to go up at 0.9c,
initially in a straight line, but eventually begins to droop as the
probability of the first ship getting through drops. I append a GIF file
containing the graph, with axes being years and light-years. In this case,
the optimal distance is 6.0 light years, and the speed is 0.77c.

This is, as I said, a stupid strategy. A better strategy would be to grow
the industrial base exponentially, and send out an exponentially increasing
wave of seedships, to multiple destinations. But I haven't done the ESS
analysis for this case yet. It seems to devolve into a twisty maze of
strategies and counter-strategies.

In the long run, a replicator that has a larger average speed will
outcompete others, since its region of the frontier will begin to bulge
outward, and increase in area at the expense of its neighbors. This process
will end when all the repicators are running at the (same) maximum speed.
It is interesting to consider what effect this has on the universe. The
HPLD entities would agree with the Italian race-car driver who threw away
his rear-view mirror: "What is behind me no longer matters!" Any effort,
up to and including the total destruction of the oasis, would be justified
if it slightly increased the average speed. The HPLD would propagate
across the universe as an unstoppable wildfire, moving close to the speed
of light, transforming everything in its path into cinders and derelict
machinery.

--CarlF