```X-Message-Number: 587
Date: 22 Dec 91 05:22:07 EST
From: "Steven B. Harris" < var s1 = "71450.1773"; var s2 = "CompuServe.COM"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
Subject: Limits to Growth

Kevin Brown writes: >>David, if you look REALLY long-term,
population control still appears necessary, even if we scatter
throughout space in all directions at almost the speed of light.
This is because, unless we change our habits, population will
grow exponentially with time (R^T for some R > 1) whereas the
space available for that population can grow only polynomially
with time ((cT)^3).  Eventually, the exponential function will
overwhelm the polynomial function (although I am not sure that
that will happen within the lifetime of this universe).<<

Comment:  Well within the life of the universe!  It's a
straightforward problem best worked just as you present it: If
doubling time of 40 years (about our present rate), and you give
each immortalist a jail cell sized living volume allotment of
(say) 15 cubic meters, then you find that we absolutely run out
of any more room in our light cone to put new people, between 163
and 164 doublings.  In other words, in a bit less than 6500
years.

Of course, if you look at the number of people implied in this
calculation (6.5e58 or so), it's at least tens of millions of
times more mass than the *universe* is thought to contain, so
obviously the limit to exponential reproduction is availability
of MATTER before volume.  (The basic reason for this, if you want
to look at it that way, is that matter in our universe is
distributed a lot more thinly than the density of people in
apartment complexes, and a good thing too or it would all have
collapsed long ago).   Actually, I suspect the real limit to
exponential growth is likely to be the availability of free
energy.*

Just for the fun of it, how much are we limited by avail-
ability of mass alone, exclusive of free energy?  I estimate that
if we had unlimited ergs we can turn the solar system entirely
into people, at our present growth rate, in only 2500 years (yum-
- soylent chips, anyone?).  Of course, by that time the advancing
front of humanity will have enveloped and eaten another billion
stars, but all that matter will keep us going only another 1200
years, and not too far and not long after that we'll have more
appetite for stars than we can get to at speed ~c.  If we
eliminate Death and Electric Bills, then, my math implies that by
4,000 years from now, even Roman Catholics will have to accept
condoms.