We investigate a pool of international chess title holders born between 1901 and 1943. Using Elo ratings we compute for every player his expected score in a game with a randomly selected player from the pool. We use this figure as players merit. We m
easure players fame as the number of Google hits. The correlation between fame and merit is 0.38. At the same time the correlation between the logarithm of fame and merit is 0.61. This suggests that fame grows exponentially with merit.
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 w
ith 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 Landaus ranking.
We analyze access statistics of a hundred and fifty blog entries and news articles, for periods of up to three years. Access rate falls as an inverse power of time passed since publication. The power law holds for periods of up to thousand days. The
exponents are different for different blogs and are distributed between 0.6 and 3.2. We argue that the decay of attention to a web article is caused by the link to it first dropping down the list of links on the websites front page, and then disappearing from the front page and its subsequent movement further into background. The other proposed explanations that use a decaying with time novelty factor, or some intricate theory of human dynamics cannot explain all of the experimental observations.
We present empirical data on misprints in citations to twelve high-profile papers. The great majority of misprints are identical to misprints in articles that earlier cited the same paper. The distribution of the numbers of misprint repetitions follo
ws a power law. We develop a stochastic model of the citation process, which explains these findings and shows that about 70-90% of scientific citations are copied from the lists of references used in other papers. Citation copying can explain not only why some misprints become popular, but also why some papers become highly cited. We show that a model where a scientist picks few random papers, cites them, and copies a fraction of their references accounts quantitatively for empirically observed distribution of citations.
