A Mathematical Model for Evolution and SETI
A Mathematical Model for Evolution and SETI
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进化和 SETI 的数学模型
DOI：
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发表时间：
2011
影响因子：
2
通讯作者：
C. Maccone
中科院分区：
文献类型：
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作者：
C. Maccone
达尔文进化论可以被认为是SETI理论的一部分，因为德雷克方程中的因子f1代表了适合生命的行星中真正出现生命的行星的比例。本文首先给出了Drake方程的一个统计推广，其中因子f1服从对数正态概率分布。这种对数正态分布是统计的中心极限定理(CLT)的结果，该定理指出，当因素数增加到无穷大时，一些概率密度未知且相互独立的独立随机变量的乘积接近对数正态分布。此外，我们还证明了达尔文进化中典型物种数量的指数增长可以看作是时间轴和指数增长曲线之间的单参数对数正态分布族(b-对数正态分布)峰值的几何轨迹。最后，由于该家族中的每个b-对数正态分布又可以被视为大量(实际上是“无穷大”)独立对数正态概率分布的乘积，因此为进一步将达尔文进化论转化为数学理论铺平了道路，这与其典型的生命物种数量指数增长和统计德雷克方程是一致的。
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually “an infinity”) of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.