The Fermi paradox focuses on the existence of advanced civilizations elsewhere in the galaxy. If these civilizations are out there–and many analyses suggest the galaxy should be teeming with life–why haven’t we seen evidence of them?

Today Carlos Cotta and Álvaro Morales from the University of Malaga in Spain add another angle to the discussion. One consideration is the speed at which a sufficiently advanced civilization could colonize the galaxy. Various analyses suggest that using spacecraft that travel at a tenth of the speed of light, a colonization wave could take some 50 million years to sweep the galaxy. Others have calculated that it may be closer to 13 billion years, which may explain why we have yet to spot extraterrestrials.

Cotta and Morales take a different tack by studying how automated probes sent ahead of the colonization could explore the galaxy. Obviously, this could advance much faster than the colonization wave front. The scenario involves a civilization sending out eight probes, each equipped with smaller subprobes for studying the regions that the host probe visits.

This is not a new scenario. One previous calculation suggests that in about 300 millions years, those eight probes could explore just 4 percent of the galaxy. The question that Cotta and Morales ask is this: what if several advanced civilizations were exploring the galaxy at the same time? Surely, if enough advanced civilizations were exploring simultaneously, one of their probes would end up visiting the solar system. So that fact we haven’t seen one places a limit on how many civilizations can be out there.

The numbers that Cotta and Morales come up with depend crucially on the life span of the probes doing the exploring (and obviously on the number of probes each civilization sends out). They say that if each probe has a life span of 50 million years, and if evidence of their solar-system visits lasts about a million years, there can be no more than about 1,000 advanced civilizations out there now. If, instead, these probes can leave longer-lasting evidence of a visit–evidence that remains for 100 million years–then there can be no more than about 10 civilizations out there.

Of course, we may not have discovered the evidence yet. But if we finally find a black obelisk on the moon, the paradox will be resolved.

Ref: arxiv.org/abs/0907.0345: A Computational Analysis of Galactic Exploration with Space Probes: Implications for the Fermi Paradox