SETI, Evolution and Human History Merged into a Mathematical Model

International Journal of Astrobiology ◽

10.1017/s1473550413000086 ◽

2013 ◽

Vol 12 (3) ◽

pp. 218-245 ◽

Cited By ~ 17

Author(s):

Claudio Maccone

Keyword(s):

Mathematical Model ◽

Exponential Growth ◽

Numerical Estimate ◽

Mean Value ◽

Darwinian Evolution ◽

Human History ◽

The Galaxy ◽

Positive Time ◽

A Cell ◽

Geometric Locus

AbstractIn 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.

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Evolution and mass extinctions as lognormal stochastic processes

International Journal of Astrobiology ◽

10.1017/s147355041400010x ◽

2014 ◽

Vol 13 (4) ◽

pp. 290-309 ◽

Cited By ~ 13

Author(s):

Claudio Maccone

Keyword(s):

Mathematical Model ◽

Stochastic Process ◽

Molecular Evolution ◽

Stochastic Processes ◽

Neutral Theory ◽

Mean Value ◽

Darwinian Evolution ◽

List Type ◽

Mass Extinctions ◽

Human History

AbstractIn a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely calledEvo-SETI. The relevant mathematical tools are:(1)Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black–Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time.(2)The probability distributions known asb-lognormals, i.e. lognormals starting at a certain positive instantb>0 rather than at the origin. Theseb-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists callCladistics.(3)The (Shannon)entropyof suchb-lognormals is then seen to represent the ‘degree of progress’ reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language ofb-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller ‘chaos’), and have their peaks on the increasing GBM exponential. This exponential is thus the ‘trend of progress’ in human history.(4)All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics).(5)But the most striking new result is that the well-known ‘Molecular Clock of Evolution’, namely the ‘constant rate of Evolution at the molecular level’ as shown by Kimura's Neutral Theory of Molecular Evolution,identifieswith growth rate of the entropy of our Evo-SETI model, because they both grewlinearlyin time since the origin of life.(6)Furthermore, we apply our Evo-SETI model to lognormal stochastic processesother than GBMs.For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on aparabolicmean value capable of covering both the extinction and the subsequent recovery of life forms.(7)Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is acubicfunction of the time.In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based uponb-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are theparticular case of exponential growth.

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Pathogen Infection Recovery Probability (PIRP) Versus Proinflammatory Anti-Pathogen Species (PIAPS) Levels: Modelling and Therapeutic Strategies

International Journal Of Medical Science And Clinical Invention ◽

10.18535/ijmsci/v7i08.06 ◽

2020 ◽

Vol 7 (08) ◽

pp. 4925-4930

Author(s):

Sam-Shajing Sun

Keyword(s):

Mathematical Model ◽

Allergic Reaction ◽

Modern Human ◽

Therapeutic Strategies ◽

Severe Hypoxia ◽

Human History ◽

Pathogen Infection ◽

Pathogen Elimination

CoVID-19 pandemic due to SARS-CoV-2 virus has been spreading rapidly worldwide since late 2019, and it may become one of the largest pandemic events in modern human history if out of control. It appears most of the CoVID-19 infection resulted deaths are mainly due to severe hypoxia from dysfunction of the lung, and that could be attributed to host’s immunodysfunctions particularly hyperinflammatory type disorders or allergic reaction. In this brief review and study, a mathematical model is proposed to correlate the Pathogen Infection Recovery Probability (PIRP) versus Proinflammatory Anti-Pathogen Species (PIAPS) levels, where a maximum PIRP is expected when the PIAPS levels are equal to or around PIAPS equilibrium levels at the pathogen elimination or clearance onset. Based on this model, rational or effective therapeutic strategies at right stages or timing, with right type of agents (immuno-stimulators or immuno-suppressors), and right dosages, could be designed and implemented that are expected to effectively achieve maximum PIRP or reduce the mortality.

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