Pinkhas Nisanov

We stand at a pivotal moment in human history, not merely facing another crisis but confronting a fundamental shift in our existence. This is not a passing storm but a transformation that demands our attention and understanding. 2025 In my previous blog post " Globalization "  I delved into the demographic research of Russian professor Sergey Kapitsa, " PARADOXES OF GROWTH: LAWS OF GLOBAL DEVELOPMENT OF HUMANITY ".  Kapitsa identified a mathematical model that accurately represents global human population growth, expressed by the differential equation: \begin{equation} \large{}\color{blue}\frac{d N}{d T} = \frac{N^2}{2*10^{11}} \end{equation}Professor Kapitsa presented human population growth not only in form of differential eqation. He also introduced formal formula for calculating human population over time.\begin{equation} \large{}\color{blue}N = \frac{2*10^{11}}{2025-T} \end{equation}where N is number of people over globe and T is year. In picture you can s...

In my previous post, " Life, Death, and 'The Winner Takes It All' " I discussed a simple differential equation that can be used to calculate population size \begin{equation} \large{}\color{blue}\frac{d x}{d t} = x \end{equation} This equation, known as the exponential function, becomes more complex when it incorporates death rates (the logistic function) and competition (the "struggle of information" model). However, the underlying principle of these models remains the same: the growth rate of a population is proportional to its current size. This principle holds true for most species, but there is one notable exception: humans. Humans are unique in that their population growth does not follow the basic principle outlined above. The study of human population size and growth rates is known as demography. Demographers collect statistics on the number of people in different areas and develop mathematical models to represent these numbers as accura...

I want to talk about how one simple differential equation became very useful mathematical model that reflect how different ecosystems (both in nature and in technology) evolve. "Life" One of most known ecosystems used for mathematical modeling is population of rabbits. We assume that next generation of rabbits will have all already living rabbits plus new born rabbits. Number of new born rabbits is proportional to number of existing rabbits. We'll take simplest case when number of additional rabbits equal to number of existing rabbits (when 2 rabbits bring 2 new rabbits). This means that change of number of rabbits equal to number of rabbits, or as differential equation: \begin{equation} \large{}\color{blue}\frac{d x}{d t} = x \end{equation} General solution for this differential equation is: \begin{equation} \Large{}\color{blue} x = e^t \end{equation}(where X is population number, T is time). This equation is known as " exponential function ". Many times thi...

One of the renowned books in software industry is " The Pragmatic Programmer: From Journeyman to Master ". This book offers acomprehensive set of practical guidelines for creating superior software. As I read each section, I contemplated how to implement the advise and what it would look like in practice.   The section on "The Evils of Duplication" introduced the DRY principle (Don't Repeat Yourself) - the idea of having a "single source of truth" for code functionality. My initial thought was to create functionality only once and reuse it wherever needed. This would obviously simplify maintenance and ensure changes are made in just one place if needed. The following section discussed the concept of "Orthogonality." It explained that unintended side effects can occur when fixing software code. Orthogonality means that changes over some dimension will not lead to changes in other (orthogonal) dimension. In other words we need to try to creat...