Abstract
The discovery of new exoplanets makes us wonder where each new exoplanet stands along its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf) in the time. We call b-lognormal a lognormal pdf starting at instant b (birth). Then, the lifetime of any living being becomes a suitable b-lognormal in the time. Next, our “Peak-Locus Theorem” translates cladistics: each species created by evolution is a b-lognormal whose peak lies on the exponentially growing number of living species. This exponential is the mean value of a stochastic process called “Geometric Brownian Motion” (GBM). Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign) of each b-lognormal is the measure of how evolved that species is, and we call it EvoEntropy. The “molecular clock” is re-interpreted as the EvoEntropy straight line in the time whenever the mean value is exactly the GBM exponential. We were also able to extend the Peak-Locus Theorem to any mean value other than the exponential. For example, we derive in this paper for the first time the EvoEntropy corresponding to the Markov-Korotayev (2007) “cubic” evolution: a curve of logarithmic increase.
Highlights
International Academy of Astronautics (IAA) and IAA SETI Permanent Committee; IAA, 6 Rue Galilée, Istituto Nazionale di Astrofisica (INAF), Via Martorelli 43, 10155 Torino (TO), Italy
The main question which this paper focuses on is, whenever a new exoplanet is discovered, what is the evolutionary stage of the exoplanet in relation to the life on it, compared to how it is on Earth today? This is the central question for Evo-SETI
My discovery of the Peak-Locus Theorem, which is valid for any enveloping lognormal probability distributions in time,one starting each different time, called mean value (and not just the exponential (GBM), for at theageneral proof seeinstant
Summary
This paper describes the recent developments in a new statistical theory describing Evolution and SETI by mathematical equations. The starting point on the time axis is ts = 3.5 billion (109 ) years ago, i.e., the accepted time of the origin of life on Earth. If the origin of life started earlier than that, for example 3.8 billion years ago, the following equations would remain the same and their numerical values would only be slightly changed. On the vertical axis is the number t t of species living on Earth at time , denoted L ( t ) and standing for “life at time ”. We do not know this “function of the time” in detail, and so it must be regarded as a random function, or stochastic species living on Earth at time t, denoted L(t) and standing for “life at time t”.
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