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A stochastic process approach of the drake equation parameters

Published online by Cambridge University Press:  09 January 2012

Nicolas Glade
Affiliation:
Joseph Fourier University, AGeing, Imagery and Modeling (AGIM) Laboratory, CNRS FRE3405, Faculty of Medicine of Grenoble, 38700 La Tronche, France
Pascal Ballet
Affiliation:
European University of Brittany (UEB) – University of Brest, Complex Systems and Computer Science Laboratory (LISyC) – EA3883, 20 Avenue LeGorgeu, 29238 Brest Cedex, France
Olivier Bastien*
Affiliation:
Laboratoire de Physiologie Cellulaire Végétale. UMR 5168 CNRS-CEA-INRA-Université Joseph Fourier, CEA Grenoble, 17 rue des Martyrs, 38054, Grenoble Cedex 09, France

Abstract

The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually calculated by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the Search for ExtraTerrestrial Intelligence (SETI) field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression. An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation does not provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process that will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2012

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References

Annis, J. (1999). An astrophysical explanation for the great silence. J. Br. Interplanet. Soc. 52, 1922.Google Scholar
Bastien, O. (2008). A simple derivation of the distribution of pairwise local protein sequence alignment scores. Evol. Bioinf. 4, 4145.Google Scholar
Bromm, V. & Loeb, A. (2002). The expected redshift distribution of gamma-ray bursts. Astrophys. J. 575, 111.Google Scholar
Burchell, M.J. (2006). W(h)ither the drake equation? Int. J. Astrobiol. 5(3), 243250.Google Scholar
Capiński, M. & Kopp, E. (2002). Measure, Integral and Probability. Springer-Verlag, Berlin.Google Scholar
Cirkovic, M.M. (2004a). Earths: rare in time, not space? J. Br. Interplanet. Soc. 57, 53.Google Scholar
Cirkovic, M.M. (2004b). The temporal aspect of the drake equation and SETI. Astrobiology 4(2), 225231.CrossRefGoogle ScholarPubMed
Cirkovic, M.M. & Bradbury, R.J. (2006). Galactic gradients, postbiological evolution and the apparent failure of SETI. New Astron. 11, 628639.Google Scholar
Dick, S.J. (2003). Cultural evolution, the postbiological universe and SETI. Int. J. Astrobiol. 2, 6574.Google Scholar
Diehl, R., Halloin, H., Kretschmer, K., Lichti, G.G., Schönfelder, V., Strong, A.W., von Kienlin, A., Wang, W., Jean, P., Knödlseder, J. et al. (2006). Radioactive 26Al from massive stars in the Galaxy. Nature 439, 4547.Google Scholar
Drake, F. (1965). The radio search for intelligent extraterrestrial life. In Current Aspects of Exobiology, ed. Mamikunian, G. & Briggs, M.H., pp. 323345. Pergamon, New York.Google Scholar
Drake, F. & Sobel, D. (1991). Is anyone out there? Simon and Schuster, London.Google Scholar
Foata, D. & Fuchs, A. (2002). Processus Stochastiques. Processus de Poisson, chaînes de Markov et martingales. Dunod, Paris.Google Scholar
Forgan, D.H. (2009). A numerical testbed for hypotheses of extraterrestrial life and intelligence. Int. J. Astrobiol. 8(2), 121131.Google Scholar
Forgan, D.H. (2011). Spatio-temporal constraints on the zoo hypothesis, and the breakdown of total hegemony. Int. J. Astrobiol. 10, 341347.CrossRefGoogle Scholar
Glade, N., Ben Amor, H.M. & Bastien, O. (2009). Trail systems as fault tolerant wires and their use in bio-processors. In Modeling Complex Biological Systems in the Context of Genomics, Proceedings of the Spring School, Nice 2009, ed. Amar, P. et al. , pp. 85119.Google Scholar
Gonzalez, G., Brownlee, D. & Ward, P. (2001). The galactic habitable zone: galactic chemical evolution. Icarus 152(1), 185200.Google Scholar
Gowanlock, M.G., Patton, D.R. & McConnell, S.M. (2011). A model of habitability within the milky way galaxy. Astrobiology 11(9), 855873.CrossRefGoogle Scholar
Hair, T.W. (2011). Temporal dispersion of the emergence of intelligence: an inter-arrival time analysis. Int. J. Astrobiol. 10, 131135.Google Scholar
Heavens, A., Panter, B., Jimenez, R. & Dunlop, J. (2004). The star-formation history of the Universe from the stellar populations of nearby galaxies. Nature 428, 625627.Google Scholar
Itô, K. (2004). Stochastic Processes. Springer-Verlag, Berlin.Google Scholar
Juneau, S., Glazebrook, K., Crampton, D., McCarthy, P.J., Savaglio, S., Abraham, R., Carlberg, R.G., Chen, H.W., Borgne, D.L., Marzke, R.O et al. (2005). Cosmic star formation history and its dependence on galaxy stellar mass. Astrophys. J. Lett. 619(2), L135.Google Scholar
Koroliouk, V. (1978). Aide-Mémoire de théorie des probabilités et de statistique mathématique. Edition de Moscou, Moscou. pp. 51.Google Scholar
Lineweaver, C.H., Fenner, Y. & Gibson, B.K. (2004). The galactic habitable zone and the age distribution of complex life in the Milky way. Science 303(5654), 59.Google Scholar
Maccone, C. (2010). The statistical drake equation. Acta Astronaut. 67(11–12), 13661383.Google Scholar
Ortet, P. & Bastien, O. (2010). Where does the alignment score distribution shape come from? Evol. Bioinf. 6, 159187.Google Scholar
Prantzos, N. (2008). On the “galactic habitable zone”. Space Sci. Rev. 135, 313322.Google Scholar
Reber, G. & Conklin, E.H. (1938). UHF receivers. Radio 225, 112.Google Scholar
Shermer, M. (2002). Why ET Hasn't Called. Scientific American 8, 21.Google Scholar
Shklovsky, I.S. & Sagan, C. (1966). Intelligent Life in the Universe. Holden-Day, San Francisco.Google Scholar
Skorokhod, A.V. & Prokhorov, I.U.V. (2004). Basic Principles and Applications of Probability Theory. Springer-Verlag, Berlin.Google Scholar
Vukotic, B. & Cirkovic, M.M. (2007). On the timescale forcing in astrobiology. Serb. Astron. J. 175, 4550.Google Scholar
Vukotic, B. & Cirkovic, M.M. (2008). Neocatastrophism and the Milky way astrobiological landscape. Serb. Astron. J. 176, 7179.Google Scholar
Walters, C., Hoover, R.A. & Kotra, R.K. (1980). Inter- stellar colonization: A new parameter for the Drake. Equation? Icarus 41, 193197.Google Scholar
Wilson, T.L. (1984). Bayes’ theorem and the real SETI equation. Q. J. R. Astron. Soc. 25, 435448.Google Scholar