SETI as a part of Big History

•Big History examines history scientifically from the Big Bang to the present.•Big History needs one or more terms to be inserted in front of the Drake equation.•Geometric Brownian Motions (GBMs) fulfill the Statistical Big History Equation.•GBMs also account for Darwinian evolution and progress of historic civilizations.•Mass Extinctions are shown to be GBMs in the decreasing number of Living Species.

Big History is an emerging academic discipline which examines history scientifically from the Big Bang to the present. It uses a multidisciplinary approach based on combining numerous disciplines from science and the humanities, and explores human existence in the context of this bigger picture. It is taught at some universities. In a series of recent papers ([11] through [15] and [17] through [18]) and in a book [16], we developed a new mathematical model embracing Darwinian Evolution (RNA to Humans, see, in particular, [17] and Human History (Aztecs to USA, see [16]) and then we extrapolated even that into the future up to ten million years (see 18), the minimum time requested for a civilization to expand to the whole Milky Way (Fermi paradox). In this paper, we further extend that model in the past so as to let it start at the Big Bang (13.8 billion years ago) thus merging Big History, Evolution on Earth and SETI (the modern Search for ExtraTerrestrial Intelligence) into a single body of knowledge of a statistical type. Our idea is that the Geometric Brownian Motion (GBM), so far used as the key stochastic process of financial mathematics (Black-Sholes models and related 1997 Nobel Prize in Economics!) may be successfully applied to the whole of Big History. In particular, in this paper we derive(1)Mathematical formulae showing that the Statistical Drake Equation (namely the statistical extension of the classical Drake Equation typical of SETI) can be regarded as the “frozen in time” part of GBM. This makes SETI a subset of our Big History Theory based on GBMs: just as the GBM is the “movie” unfolding in time, so the Statistical Drake Equation is its “still picture”, static in time, and the GBM is the time-extension of the Drake Equation.(2)Darwinian Evolution on Earth may be easily described as an increasing GBM in the number of living species on Earth over the last 3.5 billion years. The first of them was RNA 3.5 billion years ago, and now 50 million living species or more exist, each evolving in a statistical way like the GBM stochastic process does.(3)Also Human History may be rewritten in terms of GBMs, as this author did in recent papers just published in the International Journal of Astrobiology and Acta Astronautica. But those mathematical results will not be repeated in this paper in order not to make it too long. Possibly a whole new book about GBMs will be written by the author.(4)Mass Extinctions of the geological past also are one more topic that may be cast in the language of a decreasing GBM over a short time lapse, since Mass Extinctions are sudden all-lows in the number of living species. In this paper, we give formulae for the decreasing GBMs of Mass Extinctions, like the K-Pg one of 64 million years ago.(5)Finally, we note that the Big History Equation is just the extension of the Drake Equation to 13.8 billion years of cosmic evolution. So, the relevant GBM starting at the Big Bang epoch (13.8 billion years ago) and growing up to nowadays in a stochastically increasing fashion becomes the GBM of the number of evolving galaxies populating the Universe. Our Big History model based on the GBM mathematics is thus complete.