How Rare Are Extraterrestrial Civilizations, and When Did They Emerge?

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Abstract
It is shown that, contrary to an existing claim, the near-equality between the lifetime of the Sun and the timescale of biological evolution on Earth does not necessarily imply that extraterrestrial civilizations are exceedingly rare. Furthermore, on the basis of simple assumptions it is demonstrated that a near-equality between these two timescales may be the most probable relation. A calculation of the cosmic history of carbon production that is based on the recently determined history of the star formation rate suggests that the most likely time for intelligent civilizations to emerge in the universe was when the universe was already older than about 10 Gyr (for an assumed current age of about 13 Gyr).
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