A mathematical theory of fame

TL;DR

This paper develops a mathematical model linking fame to achievement, demonstrating exponential growth of fame with achievement and applying it to estimate achievements of Nobel laureates, with empirical validation using WWI fighter aces.

Contribution

It introduces a stochastic model explaining the exponential relation between fame and achievement and extends this approach to estimate achievements in various professions.

Findings

Fame grows exponentially with achievement among WWI aces.

The distribution of fame follows a power-law due to achievement distribution.

The model allows estimation of achievement levels for Nobel laureates based on fame.

Abstract

We study empirically how the fame of WWI fighter-pilot aces, measured in numbers of web pages mentioning them, is related to their achievement, measured in numbers of opponent aircraft destroyed. We find that on the average fame grows exponentially with achievement; the correlation coefficient between achievement and the logarithm of fame is 0.72. The number of people with a particular level of achievement decreases exponentially with the level, leading to a power-law distribution of fame. We propose a stochastic model that can explain the exponential growth of fame with achievement. Next, we hypothesize that the same functional relation between achievement and fame that we found for the aces holds for other professions. This allows us to estimate achievement for professions where an unquestionable and universally accepted measure of achievement does not exist. We apply the method to Nobel Prize winners in Physics. For example, we obtain that Paul Dirac, who is a hundred times less famous than Einstein contributed to physics only two times less. We compare our results with Landau's ranking.