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In the 1970s (or possibly early 1980s), some relatives had a coffee table book about space science, which (if I recall correctly) ended with an essay by Isaac Asimov which speculated about asteroid space settlements slowly dispersing throughout the solar system and beyond. In particular, he predicted that the societies that developed in these settlements would practice zero-population-growth except for brief periods when a settlement reached a new star's Oort cloud, and underwent rapid population growth (creating new asteroid settlements that would also spread at random). I remember Asimov used the term "sessile" to describe the zero-population-growth phase. If I recall correctly, the book also contained speculation (not by Asimov) about FTL via tachyons (and included the term "tardyon" for normal matter).

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This sounds very much like Asimov's essay There's No Place Like Spome, where "spome" is a portmanteau word between "space and "home".

The essay dealt with how a race can spread through the universe. One aspect Asimov focused on was the importance of asteroids:

If an asteroidal belt were encountered about some star, a landfall might, in a sense, be made. The star ship could take up some appropriate orbit. Other asteroids could then be made into spomes. The colony would divide and new ones would be set up...

In fact, there might almost be an “alternation of generations" over the eons as far as the star ships were concerned. There would be a motile generation in which the star ships moved steadily across the vastness of space but in which population increase would have to be tightly controlled. There would then be a sessile generation after an asteroid belt was encountered, when for a long period of time there would be no motion, but the population would proliferate.

In particular the essay notes how populations would first freeze, and then increase when the expansion reached its "sessile" phase.

The essay was first presented as a paper to the American Chemical Society on September 13, 1965. However, with minor changes it was published as The Universe and the Future in a coffee-table like book entitled Is Anyone There? in 1967.

A complete version of the essay is available from Winchell Chung's excellent site, in the section Spome.

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