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Showing posts from July, 2023

Innovation vs. Creativity (or Tactics vs. Strategy)

Nokia Nokia. My first cellular phone was Nokia. Those days Nokia created best cellular phones. Nokia, once a dominant force in the mobile phone industry, has experienced a dramatic decline. From a market capitalization of $550 billion in 2000, it plummeted to just $18 billion. This decline prompts a critical question: Why did Nokia fail while companies like Apple soared to unprecedented heights ? While Nokia excelled at producing high-quality cellular phones, it missed the boat on the smartphone revolution. Smart phones slowly gain more and more customers, and, of course, who bought smart phone did not buy cellular phone. Nokia did not lost it's domain of cellular phones. Nokia just missed this moment when new market of smartphones was created. Those two markets could not coexist. Such situation defined by " Struggle of Informations " model as "antagonistic informations" where only one information will survive and other will totally disappear. The critical ques
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"Life", "Death" and "The Winner Takes It All"

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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
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