The Great Filter, Branching Histories and Unlikely Events

The Great Filter refers to a highly speculative theory that implicitly claims one can test, via a probability model, whether known aspects of the history of life on Earth are consistent with the hypothesis that emergence of intelligent life was very unlikely. We describe the theory and some of the many objections to it. We give a mathematical argument to show that one objection, namely that it considers only a single possible linear history rather than multitudinous branching potential pathways to intelligence, has no force. Key words, Great filter, Drake equation, Fermi paradox, order statistics, rare events, conditioning paradox. MSC classifications; 60J85, 92D15