Mike Williams <mike@econym.demon.co.uk> wrote in message  

That is a lot of ifs. And even if it were to happen, it would be a lot of
effort. It would almost certainly be easier to compete locally for real
estate.

The problem with exponential population growth is that no finite amount
of real estate will be enough.

The problem with exponential population growth is that without magical
drive technologies, you end up with massive overpopulation and a
society that's way too busy coping with incredible and increasing
citizens to mess around with silliness like interstellar colonization.

After 2000 years there's
over a trillion and the planet is getting a bit crowded, so each planet
builds 10 spaceships and send them off to the next nearest set of
uninhabited planets. 

Why does a trillion people on a crowded planet lead you to conclude
that the planet will build 10 spaceships and send them off? Sending
0.00000000002% of your population away isn't going to help with
crowding problems, so that's not the reason, and a society that's
facing disaster (if 1 trillion is crowded, how are they going to
handle 2 trillion and all of the later doublings that are required for
exponential growth) probably isn't going to be all that interested in
abstractions like interstellar colonization. Your 'so' is not
supported by what you've said so far.
 

So after 2000 years there's 100 new colonies.

Another 2000 years later, these second generation colonies are getting
crowded and they each send of 10 spaceships to the next nearest set of
uninhabited planets.

What does getting crowded have to do with sending off interstellar
spaceships? Unless you're arguing that your aliens say "quick! if we
send off 0.00000000002% of our population, everything will be fine",
you really need some more explanation. Shipping vanishingly tiny
fragments of your population away at great cost isn't a solution to
crowding problems.

After a while this pattern breaks down because there aren't enough
nearby uninhabited planets. Terraforming all the material in each
colonised solar system helps slightly, but doesn't affect the overall
picture. So by about 20000 years the picture you end up with is
something like a sphere of stars where every possible inch of real
estate is occupied, 

Yeah, but what happens when the population doubles, not at the edge
but back on some of that real estate that's surrounded by filled real
eastate? Oopsie, looks like mass die-offs since the real estate will
be over full. Now the outer edge can probably just recolonize the
areas where the earlier settlements went extinct from overcrowding.
Hmm.. or maybe the exponential growth keeps up, and the home system
keeps doubling population until the mass of people pressed into that
area causes it to collapse into a black hole.

that's expanding at close to the maximum speed that
their starships can achieve. 

You haven't explained that part, though - again, sending off
0.00000000002% of the planet's population is not going to make any
difference in crowdedness, so why are they launching all of these
colony missions?

And if you say that they don't neccessarily grow exponentially all the
time, then your whole argument falls apart since you assume that they
do.
--
Kevin Allegood