Von Richthofen, Einstein and the AGA Estimating achievement from fame Every schoolboy has heard of Einstein; fewer have heard of Antoine Becquerel; almost nobody has heard of Nils Dalén. Yet they all won Nobel Prizes for Physics. Can we gauge a scientist’s achievements by his or her fame? If so, how? And how do fighter pilots help? Mikhail Simkin and Vwani Roychowdhury look for the linkages. “It was a famous victory.” We instinctively rank the had published. However, in 2001–2002 popular French achievements of great men and women by how famous TV presenters Igor and Grichka Bogdanoff published they are. But is instinct enough? And how exactly does a great man’s fame relate to the greatness of his achieve- ment? Some achievements are easy to quantify. Such is the case with fighter pilots of the First World War. Their achievements can be easily measured and ranked, in terms of their victories – the number of enemy planes they shot down. These aces achieved varying degrees of fame, which have lasted down to the internet age. A few years ago we compared1 the fame of First World War fighter pilot aces (measured in Google hits) with their achievement (measured in victories); and we found that We can estimate fame grows exponentially with achievement. fame from Google; Is the same true in other areas of excellence? Bagrow et al. have studied the relationship between can this tell us 2 achievement and fame for physicists . The relationship Manfred von Richthofen (in cockpit) with members of his so- about actual they found was linear. The measure of achievement used called “flying circus”, 1917. Source: Deutsches Bundesarchiv achievement? in that study was the number of papers the physicists (German Federal Archive) 22 march2011 © 2011 The Royal Statistical Society five papers in a number of respectable journals 10000 enemy aircraft each pilot shot down. For our including Classical and Quantum Gravity3 fighter aces, therefore, we can measure both and Annals of Physics. The problem was that fame (in Google hits) and real achievement di- their papers consisted of incoherent streams of 1000 rectly. We can also estimate each ace’s achieve- buzzwords from modern physics. Their affair ment from his fame, using equation (2). casts doubt on using the number of published For every ace we computed this estimate papers to measure scientific achievement. How, of achievement. We then compared it to his 100 then, can we measure it? real achievement. Our estimates did not turn Some have used the number of citations out to be very accurate. With 50% probability of the scientist’s papers as a true measure of our estimated achievement was between 0.7 4 5, 6 10 achievement . But in another study we have Googlehits) of (number ame and 1.44 of real achievement. And with 85% shown that this measure is also question- F probability the real achievement was between able, since citations multiply by mere copying. 0.5 and 2 times the estimate. Even these crude There is a cascade effect. If scientist A is cited 1 estimates, however, can provide some insight in paper B, then a third author citing B may 5 25 45 65 85 in the fields where we have no clue of how to Achievement (number of victories) include in it a citation of A as well; and if our measure achievement – such as in physics. third author gets cited in turn, D may cite not Figure 1. A scatter plot of fame versus achievement for 392 German First World War aces. The correlation only C but anything that C cites, including B 2 coefficient of 0.72 suggests that 0.72 ≈ 52% of the What is achievement in physics? and A – even if he has not actually read A’s variation in fame is explained by the variation in paper at all. While the number of citations achievement. The straight line is the fit using Eq.1 with So let us now try to estimate the achievement may be increasing with the size of scientific C ≈ 5.3 and b ≈ 0.72. There are many aces with identical of different physicists based on their fame. contribution made in the paper, the exact rela- values of both achievement and fame. Therefore, for Table 1 shows the names of 45 Nobel Laure- display purposes random numbers between 0 and 1 tion between these variables is not obvious. So were added to every value of achievement and fame. ates in Physics before the Second World War, again, finding a measure of achievements of This way the scatter plot represents the true density ranked according to their fame. (The only win- physicists is a problem. of the data points ner excluded is Charles Wilson, whose Nobel Here, we made the hypothesis that the Prize was awarded in 1927; he has so many exponential relationship between fame and fame, we can try to estimate achievement, by namesakes that Googling his name reflects the achievement that we found for fighter pilots simply inverting equation (1): fame of too many other people as well.) Figure holds also for people of other professions, such 2 shows the probability density of their fame Achievement = ln(Fame/C)/b (2) as scientists. We can then use the scientists’ distribution, and how it is very similar to the fame (measured in Google hits) to infer their We will first see how accurately it works fame distribution of aces. We hypothesize that achievement. Let us emphasise that we do not using the aces data, where we do know both the relation between achievement and fame for insist that web hit counts are preferable to fame and achievement. We looked at 392 physicists is, as with aces, given by equation citation counts. These two measures of fame German First World War fighter pilots1. Their (2). A big difference from the case of aces is are strongly correlated. We used web hits achievements were easy to quantify, since ac- that we do not know the values of b and C. because we used them for fighter pilots aces in curate historical data exists for the number of The fact that b is unknown is irrelevant, as it our earlier study. The point of this article is not that one should use web hits, but that to make Fame (Google hits) Fame (Google hits) 4 5 6 7 8 an estimate of achievement one should take a 1 10 100 1000 10000 10 10 10 10 10 –1 5 logarithm of fame. 10 10 In our study of fighter pilots1 we found –2 that fame, F, depends on achievement, A, ac- 10 6 cording to the following equation: 10 –3 Fame = C × exp(b × Achievement) (1) 10 Here b and are parameters determined by C 7 –4 10 regression. C turns out to be about 5.3, and b 10 is about 0.72. To be precise, the real data of fame as a function of achievement present not –5 10 Probability density Probability density 8 a smooth curve, but a scatter plot (see Figure 10 1) and equation (1) gives the curve that is the –6 best fit to it. It is not a perfect fit; nonetheless, 10 given the value of achievement, we can use the 9 10 –7 equation to greatly reduce the uncertainty in 10 the value of fame. Similarly, given the value of Figure 2. Distribution of fame of First World War aces (left) and Nobel Prize winning physicists (right). Solid lines are power-law fits with exponent 1.9 and 1.5, respectively march2011 23 Table 1. Winners of the Nobel Prize for Physics before the Second World War, ranked by fame Physicist Alternative names used in Google June 2008 Log over Lower bound on the most search, all joined using OR Google hits Dalén likely achievement in einsteins Albert Einstein 22,700,000 8.53 1 Max Planck Max Karl Ernst Ludwig Planck 10,600,000 7.77 0.911 Marie Curie 6,300,000 7.25 0.850 Niels Bohr 1,890,000 6.04 0.709 Enrico Fermi 1,730,000 5.95 0.698 Guglielmo Marconi 1,110,000 5.51 0.646 Werner Heisenberg 987,000 5.39 0.632 Erwin Schrödinger Erwin Schroedinger 375,000 4.43 0.519 Pierre Curie 330,000 4.30 0.504 Wilhelm Röntgen Wilhelm Conrad Röntgen 272,000 4.10 0.481 Wilhelm Conrad Roentgen Wilhelm Roentgen Paul Dirac Paul Adrien Maurice Dirac 255,000 4.04 0.474 Paul A.M. Dirac Louis de Broglie Louis-Victor de Broglie 201,000 3.80 0.446 Lord Rayleigh Lord John William Strutt Rayleigh 167,000 3.62 0.424 Max von Laue 142,000 3.45 0.405 Hendrik Lorentz Hendrik Antoon Lorentz 119,000 3.28 0.384 Robert Millikan Robert Andrews Millikan 112,000 3.22 0.377 James Franck 109,000 3.19 0.374 James Chadwick 99,100 3.09 0.363 Charles Guillaume Charles Edouard Guillaume 89,900 3.00 0.351 Ernest Orlando Lawrence 89,500 2.99 0.351 Albert Michelson Albert Abraham Michelson 76,600 2.84 0.333 William Lawrence Bragg 74,500 2.81 0.329 Joseph John Thomson 73,700 2.80 0.328 Antoine Becquerel Antoine Henri Becquerel 70,300 2.75 0.323 Arthur Compton Arthur Holly Compton 66,800 2.70 0.317 Wilhelm Wien 52,600 2.46 0.289 Gabriel Lippmann 49,300 2.40 0.281 Johannes van der Waals Johannes Diderik van der Waals 48,800 2.39 0.280 Pieter Zeeman 47,200 2.35 0.276 William Henry Bragg 46,800 2.34 0.275 Johannes Stark 45,900 2.32 0.273 Manne Siegbahn Karl Manne Georg Siegbahn 45,000 2.30 0.270 Philipp Lenard Philipp Eduard Anton Lenard 40,000 2.19 0.256 Carl Ferdinand Braun Karl Ferdinand Braun 40,000 2.19 0.256 Gustav Hertz 37,800 2.13 0.250 Heike Kamerlingh Onnes 35,100 2.06 0.241 Sir George Thomson George Paget Thomson 29,900 1.90 0.222 Clinton Davisson Clinton Joseph Davisson 29,100 1.87 0.219 Jean Baptiste Perrin 28,600 1.85 0.217 Carl David Anderson 26,400 1.77 0.208 Owen Richardson Willans Richardson 24,900 1.71 0.201 Charles Barkla Charles Glover Barkla 24,500 1.70 0.199 Chandrasekhara Raman Chandrasekhara Venkata Raman 22,100 1.59 0.187 Victor Franz Hess 17,200 1.34 0.157 Nils Dalén Nils Gustaf Dalén 4,490 0.00 0 Nils Gustaf Dalen 24 march2011 cancels out from the ratio of achievements, but rural kitchen, the AGA stove.