The Evo-SETI unit of evolution is EE = Earth Evolution = 25.575 bit

Abstract

The discovery of a larger and larger number of exoplanets raises a question: where does a newly-discovered exoplanet stand in its capability to develop life as we know it on Earth?Our tentative answer to this question is our Evo-SETI Theory, a mathematical model aiming at casting Cladistics and the Evolution of Life on Earth over the last 3.5 billion years in terms of a few simple statistical equations based on lognormal probability distributions in the time, rather than in the amount of something else.The first new notion is that of a b-lognormal, i.e. a lognormal probability density function (pdf) starting at time b > 0 rather than at time zero. The lifetime of any living form may then be expressed as a b-lognormal starting at b, reaching puberty at the ascending inflexion point a (“adolescence (end)”), raising up to the peak time p, then starting to decline at the descending inflexion point s (“senility”) and finally going down along a straight line up to the intercept d with the time axis, that is the “death” of the individual. Based on all this, the author was able to derive several mathematical consequences like the Central Limit Theorem of Statistics re-cast in the language of Evo-SETI theory: from the lifetime of each individual to the lifetime of the “big b-lognormal” of the whole population itself to which the individual belongs (“E-Pluribus-Unum Theorem”).In addition, this author discovered the “Peak-Locus Theorem” translating Cladistics in term of Evo-SETI: each SPECIES created by Evolution over 3.5 billion years is a b-lognormal whose peak lies on the exponential in the number of alive Species. More correctly still, this exponential is not the exact curve telling us exactly how many Species were on Earth at a given time in the past: on the contrary the exponential is the mean value of a stochastic process called “Geometric Brownian Motion” (GBM) in the mathematics of finances, so that also the Mass Extinctions of the past are incorporated in Evo-SETI Theory as all-lows of the GBM.But then: what is the Shannon ENTROPY of each b-lognormal representing a Species? Answer: the Shannon ENTROPY (with a reversed sign) is the MEASURE OF HOW EVOLVED THAT SPECIES WAS, or is now, compared to other Species of the past and of the future. That means MEASURING EVOLUTION, at long last: i.e. just a number in bits, typical of Shannon's Information Theory, rather than a mountain of words!One more key point: what is the equivalent of the MOLECULAR CLOCK in Evo-SETI Theory? Answer: it is the STRAIGHT LINE behavior in time of the Shannon Entropy if the exponential is the Peak-Locus curve of all the b-lognormals representing the various Species (called “Evo-Entropy” in our papers).Concluding top remark: this author was able to GENERALIZE his Peak-Locus Theorem from the simple exponential case to the GENERAL CASE when the mean-value Peak-Locus is not just an exponential, but rather an ARBITRARY CURVE that you may chose at will: for instance it as a polynomial of the third degree in the time in the Markov-Korotayev (2007) model of evolution, leading then to a non-linear EvoEntropy. A neat mathematical tool for future biologists willing to understand Evolution by the statistically simple Evo-SETI Theory !And the Evo-SETI UNIT of evolution is 25.575 bits if life on Earth started 3.5 billion years ago. It should be given a name. We propose EE (Earth Evolution).