Space Colonies and Cultural and Biological Diversity

Asimov wrote a scientific publication (as opposedto a SF novel, he wrote
quite a few) where he did some calculations about this, I don't remember the
details exactly but it was something along the lines of, assuming a
continuous esponential growth, human population would have a larger mass
than the entire known universe in a matter of few thousands years...
So far for the "space is big enough" idea...