Wednesday, October 7, 2020

 

Back to the S curve: while we have great math machinery to discuss the form and functional properties of the logistic equation, despite my research, there’s no phenomenological explanation of why the shape of the curve is as it is! The applied math literature discusses the application of the equation to various cases and even literature review like the paper by the late Dutch statistician, JS Cramer (2002), does not reveal the inner working of the equation. If the equation applies to a wide array of population phenomena, it’s puzzling to explain why we have three distinct phases of the growth phenomena: the slow start, fast ramp, and the slow demise or end. To attribute the three aspects to the form of the equation does not explain how come this behavior? I have been working on a conceptual explanation of this behavior where the background to this growth curve needs to be considered. In this sense, it is indeed the interaction with the background to the foreground growth that modulates the overall form. Ali

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