December 20, 2005

Landis: An Approach to the Fermi Paradox Based on Percolation Theory

The Fermi Paradox: An Approach Based on Percolation Theory
Geoffrey A. Landis
Ohio Aerospace Institute
NASA Lewis Research Center, 302-1
Cleveland, OH 44135 U.S.A.
Published in Journal of the British Interplanetary Society, London, Volume 51, page 163-166 (1998). Originally presented at the NASA Symposium "Vision-21: Interdisciplinary Science and Engineering in the Era of Cyberspace" (NASA CP-10129), Mar. 30-31, 1993, Westlake, OH U.S.A.

If even a very small fraction of the hundred billion stars in the galaxy are home to technological civilizations which colonize over interstellar distances, the entire galaxy could be completely colonized in a few million years. The absence of such extraterrestrial civilizations visiting Earth is the Fermi paradox.

A model for interstellar colonization is proposed using the assumption that there is a maximum distance over which direct interstellar colonization is feasable. Due to the time lag involved in interstellar communications, it is assumed that an interstellar colony will rapidly develop a culture independent of the civilization that originally settled it.

Any given colony will have a probability P of developing a colonizing civilization, and a probability (1-P) that it will develop a non-colonizing civilization. These assumptions lead to the colonization of the galaxy occuring as a percolation problem. In a percolation problem, there will be a critical value of the percolation probability, Pc. For PPc, small uncolonized voids will exist, bounded by non-colonizing civilizations. When P is on the order of Pc, arbitrarily large filled regions exist, and also arbitrarily large empty regions.
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