Maccone Claudio
International Academy of Astronautics (IAA) and IAA SETI Permanent Committee; IAA, 6 Rue Galilée, 75016 Paris, France.
Istituto Nazionale di Astrofisica (INAF), Via Martorelli 43, 10155 Torino (TO), Italy.
Life (Basel). 2017 Apr 6;7(2):18. doi: 10.3390/life7020018.
The discovery of new exoplanets makes us wonder each new exoplanet 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) . We call -lognormal a lognormal pdf starting at instant (birth). Then, the lifetime of any living being becomes a suitable -lognormal . Next, our : each species created by evolution is a -lognormal whose peak lies on the number of living species. This exponential is the 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 -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.
新系外行星的发现让我们思考每一颗新系外行星在沿着其发展路径演化出如我们所知的地球上的生命的过程。我们的进化搜寻地外文明理论是一种解决这个问题的数学方法。我们借助基于对数正态概率密度函数（pdf）的一些统计方程来描述分支系统学和进化。我们将起始于某一时刻（诞生）的对数正态概率密度函数称为“负对数正态”。然后，任何生物的寿命都成为一个合适的“负对数正态”。接下来，我们的理论表明：进化所创造的每个物种都是一个“负对数正态”，其峰值位于现存物种数量上。这个指数就是所谓的“几何布朗运动”（GBM）。过去的大规模灭绝都是这种几何布朗运动的低谷。此外，每个“负对数正态”的香农熵（取相反符号）是该物种进化程度的度量，我们称之为进化熵。“分子钟”在均值恰好为几何布朗运动指数的任何时候，都被重新解释为时间上的进化熵直线。我们还能够将峰值轨迹定理扩展到除指数之外的任何均值。例如，在本文中我们首次推导出与马尔可夫 - 科罗泰耶夫（2007）“三次方”进化相对应的进化熵：一条对数增长曲线。
