论文标题
SETI，进化和人类历史合并为数学模型
SETI, evolution and human history merged into a mathematical model
论文作者
论文摘要
在本文中，我们提出了一个新的数学模型，能够将达尔文进化，人类历史和SETI合并为单个数学方案：1）在过去的35亿年中，达尔文的进化定义为一种特定的随机过程，称为Qeemetric Brownian Motion（GBM）。该GBM在居住在地球上的物种数量的时间内产生了波动。它的平均值曲线是一种增加的指数曲线，即进化的指数增长。 2）在2008年，这位作者提供了Drake方程的统计概括，从而产生了银河系中通信ET文明的数量。 n显示遵循对数正态概率分布。 3）我们称之为“ b-词法”那些从任何正时B（“出生”）大于零开始的对数正态。然后，指数式生长曲线成为一个参数B-牙科家族的峰的几何基因座：这是我们重新定义cladistics的方式。 4）B-识别也可以被解释为任何生物的寿命（牢房，动物，植物，人类，甚至任何文明的历史寿命）。将这种新的数学设备应用于人类历史，从而发现了古希腊与当前美国之间的指数进步，这是2500年来西方文明的所有B-义态的信封。 5）然后我们调用香农的信息理论。事实证明，B-语言的熵是每个历史文明达到的“发展水平”的指数。因此，我们对任何两个文明之间的熵差进行了数值估计，例如1519年的阿兹台克人 - 西班牙人的差异。6）总而言之，我们得出了一种数学方案，能够估计比人类更先进的人类文明，而异国文明将是何时SETI科学家检测到第一个元素的提示。
In this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme: 1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution. 2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution. 3) We call "b-lognormals" those lognormals starting at any positive time b ("birth") larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics. 4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years. 5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of "development level" reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519. 6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.
