Fuzzy Techniques, Laplace Indeterminacy Principle, and Maximum Entropy Approach Explain Lindy Effect and Help Avoid Meaningless Infinities in Physics

Authors

Julio C. Urenda, The University of Texas at El PasoFollow
Sean R. Aguilar, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

5-1-2021

Comments

Technical Report: UTEP-CS-21-34a

Abstract

In many real-life situations, the only information that we have about some quantity S is a lower bound T ≤ S. In such a situation, what is a reasonable estimate for S? For example, we know that a company has survived for T years, and based on this information, we want to predict for how long it will continue surviving. At first glance, this is a type of a problem to which we can apply the usual fuzzy methodology -- but unfortunately, a straightforward use of this methodology leads to a counter-intuitive infinite estimate for S. There is an empirical formula for such estimation -- known as Lindy Effect and first proposed by Benoit Mandelbrot -- according to which the appropriate estimate for S is proportional to T: S=c*T, where, with some confidence, the constant c is equal to 1. In this paper, we show that a deeper analysis of the situation enables fuzzy methodology to lead to a finite estimate for S, moreover, to an estimate which is in perfect accordance with the empirical Lindy Effect. Interestingly, a similar idea can help in physics, where also, in some problems, straightforward computations lead to physically meaningless infinite values.