Von Richthofen, Einstein and the AGA Estimating achievement from fame

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1 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. We can estimate fame from Google; can this tell us about actual achievement? It was a famous victory. We instinctively rank the achievements of great men and women by how famous they are. But is instinct enough? And how exactly does a great man s fame relate to the greatness of his achievement? 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 compared 1 the fame of First World War fighter pilot aces (measured in Google hits) with their achievement (measured in victories); and we found that fame grows exponentially with achievement. Is the same true in other areas of excellence? Bagrow et al. have studied the relationship between achievement and fame for physicists 2. The relationship they found was linear. The measure of achievement used in that study was the number of papers the physicists had published. However, in popular French TV presenters Igor and Grichka Bogdanoff published Manfred von Richthofen (in cockpit) with members of his socalled flying circus, Source: Deutsches Bundesarchiv (German Federal Archive) The Royal Statistical Society

2 five papers in a number of respectable journals including Classical and Quantum Gravity 3 and Annals of Physics. The problem was that their papers consisted of incoherent streams of buzzwords from modern physics. Their affair casts doubt on using the number of published papers to measure scientific achievement. How, then, can we measure it? Some have used the number of citations of the scientist s papers as a true measure of achievement 4. But in another study 5, 6 we have shown that this measure is also questionable, since citations multiply by mere copying. There is a cascade effect. If scientist A is cited in paper B, then a third author citing B may include in it a citation of A as well; and if our third author gets cited in turn, D may cite not only C but anything that C cites, including B and A even if he has not actually read A s paper at all. While the number of citations may be increasing with the size of scientific contribution made in the paper, the exact relation between these variables is not obvious. So again, finding a measure of achievements of physicists is a problem. Here, we made the hypothesis that the exponential relationship between fame and achievement that we found for fighter pilots holds also for people of other professions, such as scientists. We can then use the scientists fame (measured in Google hits) to infer their achievement. Let us emphasise that we do not insist that web hit counts are preferable to citation counts. These two measures of fame are strongly correlated. We used web hits because we used them for fighter pilots aces in our earlier study. The point of this article is not that one should use web hits, but that to make an estimate of achievement one should take a logarithm of fame. In our study of fighter pilots 1 we found that fame, F, depends on achievement, A, according to the following equation: Fame = C exp(b Achievement) (1) Here β and C are parameters determined by regression. C turns out to be about 5.3, and β is about To be precise, the real data of fame as a function of achievement present not a smooth curve, but a scatter plot (see Figure 1) and equation (1) gives the curve that is the best fit to it. It is not a perfect fit; nonetheless, given the value of achievement, we can use the equation to greatly reduce the uncertainty in the value of fame. Similarly, given the value of Fame (number of Google hits) Achievement (number of victories) Figure 1. A scatter plot of fame versus achievement for 392 German First World War aces. The correlation coefficient of 0.72 suggests that % of the variation in fame is explained by the variation in achievement. The straight line is the fit using Eq.1 with C 5.3 and b There are many aces with identical values of both achievement and fame. Therefore, for display purposes random numbers between 0 and 1 were added to every value of achievement and fame. This way the scatter plot represents the true density of the data points fame, we can try to estimate achievement, by simply inverting equation (1): Achievement = ln(fame/c)/b (2) We will first see how accurately it works using the aces data, where we do know both fame and achievement. We looked at 392 German First World War fighter pilots 1. Their achievements were easy to quantify, since accurate historical data exists for the number of Probability density Fame (Google hits) enemy aircraft each pilot shot down. For our fighter aces, therefore, we can measure both fame (in Google hits) and real achievement directly. We can also estimate each ace s achievement from his fame, using equation (2). For every ace we computed this estimate of achievement. We then compared it to his real achievement. Our estimates did not turn out to be very accurate. With 50% probability our estimated achievement was between 0.7 and 1.44 of real achievement. And with 85% probability the real achievement was between 0.5 and 2 times the estimate. Even these crude estimates, however, can provide some insight in the fields where we have no clue of how to measure achievement such as in physics. What is achievement in physics? So let us now try to estimate the achievement of different physicists based on their fame. Table 1 shows the names of 45 Nobel Laureates in Physics before the Second World War, ranked according to their fame. (The only winner excluded is Charles Wilson, whose Nobel Prize was awarded in 1927; he has so many namesakes that Googling his name reflects the fame of too many other people as well.) Figure 2 shows the probability density of their fame distribution, and how it is very similar to the fame distribution of aces. We hypothesize that the relation between achievement and fame for physicists is, as with aces, given by equation (2). A big difference from the case of aces is that we do not know the values of β and C. The fact that β is unknown is irrelevant, as it Fame (Google hits) 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 Probability density 23

3 Table 1. Winners of the Nobel Prize for Physics before the Second World War, ranked by fame Physicist Alternative names used in Google search, all joined using OR June 2008 Google hits Log over Dalén Lower bound on the most likely achievement in einsteins Albert Einstein 22,700, Max Planck Max Karl Ernst Ludwig Planck 10,600, Marie Curie 6,300, Niels Bohr 1,890, Enrico Fermi 1,730, Guglielmo Marconi 1,110, Werner Heisenberg 987, Erwin Schrödinger Erwin Schroedinger 375, Pierre Curie 330, Wilhelm Röntgen Wilhelm Conrad Röntgen 272, Wilhelm Conrad Roentgen Wilhelm Roentgen Paul Dirac Paul Adrien Maurice Dirac 255, Paul A.M. Dirac Louis de Broglie Louis-Victor de Broglie 201, Lord Rayleigh Lord John William Strutt Rayleigh 167, Max von Laue 142, Hendrik Lorentz Hendrik Antoon Lorentz 119, Robert Millikan Robert Andrews Millikan 112, James Franck 109, James Chadwick 99, Charles Guillaume Charles Edouard Guillaume 89, Ernest Orlando Lawrence 89, Albert Michelson Albert Abraham Michelson 76, William Lawrence Bragg 74, Joseph John Thomson 73, Antoine Becquerel Antoine Henri Becquerel 70, Arthur Compton Arthur Holly Compton 66, Wilhelm Wien 52, Gabriel Lippmann 49, Johannes van der Waals Johannes Diderik van der Waals 48, Pieter Zeeman 47, William Henry Bragg 46, Johannes Stark 45, Manne Siegbahn Karl Manne Georg Siegbahn 45, Philipp Lenard Philipp Eduard Anton Lenard 40, Carl Ferdinand Braun Karl Ferdinand Braun 40, Gustav Hertz 37, Heike Kamerlingh Onnes 35, Sir George Thomson George Paget Thomson 29, Clinton Davisson Clinton Joseph Davisson 29, Jean Baptiste Perrin 28, Carl David Anderson 26, Owen Richardson Willans Richardson 24, Charles Barkla Charles Glover Barkla 24, Chandrasekhara Raman Chandrasekhara Venkata Raman 22, Victor Franz Hess 17, Nils Dalén Nils Gustaf Dalén Nils Gustaf Dalen 4,

4 cancels out from the ratio of achievements, but to get a measure of the lifetime achievement of a physicist we would like to find a value for C. The most famous physicist in Table 1 is Albert Einstein. His was, most probably, also the greatest achievement. Therefore, we will use him as a unit of achievement, which we denote as AE, and measure the achievements of others in einsteins (or perhaps, for non-nobel physicists, millieinsteins) their achievements as a fraction of his. From equation (2) we then get: rural kitchen, the AGA stove. Most of the things invented by other people from our list have no practical applications, and those which do have applications tend to be very dangerous. Thermo-nuclear devices, for example, should always be handled with care. So we shall not sneer at Dalén s modest contribution to the happiness of mankind; nevertheless, we will side with the contestants and assign Dalén the achievement of 0. Then we can substitute Dalén s fame, FD, for C: ln ( F / C ) A = AE ln ( FE / C ) ln ( F / FD ) A AE ln ( FE / FD ) (3) where A/AE is our scientist s achievement in einsteins and F is his fame. The β, as you can see, has disappeared, but we still need to find C. While exact determination of C is impossible, we can find an upper bound for it. It is the fame of the least famous person in the list: C cannot be more than that because in that case the achievement of the least famous person will become negative. The least famous person on our list is Nils Dalén. His Nobel Prize (awarded in 1912) is also the most contested: many believe his achievement is not worthy of it. Dalén received the Nobel for his invention of the automatic sun valve, which regulates a gaslight source by the action of sunlight, turning it off at dawn and on at dusk. It was used for very many years in Swedish lighthouses. Many will also thank him for inventing that most comforting icon of every northern European Nils Gustaf Dalén and his bicycle in the photo studio, Digital image by Lidingö. Source: AGA AB, Lidingö, history archive. (4) This gives the achievement, in einsteins, of a physicist whose Google-fame is F. It is an estimate, rather than an actual achievement, and it is the lower bound of estimates. We have used the highest possible value for C to obtain it; lower values of C will give higher estimates of achievement for everyone but Einstein, at least. The estimates of achievement computed from equation (4) are given in the last column of Table 1. We should note that the data presented in the table are very noisy since some physicists achieved additional fame for reasons other than their scientific achievement for example, for their role in public life. However, we should emphasise that similar things happened to the fighter pilot aces we studied earlier. For example, Hermann Göring got additional web hits for his political activity. He is the second most famous German First World War ace, though with 22 victories he is only about 60th in terms of acing achievement. (Manfred von Richthofen, the so-called Red Baron and ace of aces, was officially credited with 80 victories.) The data shown in the figures include all such cases. Another objection that we encountered is that Max Planck achieved a great deal of fame due to a singular event: in 1948 the Kaiser Wilhelm Society, Germany s foremost scientific association, was renamed the Max Planck Society. All the institutes under the auspices of the society became Max Planck institutes. Every scientific paper published by the members of Max Planck institutes automatically mentions Max Planck in its address line. Similarly, when a news article or a blog entry discusses a discovery by a member of one of the institutes, it mentions the scientist s An AGA cooker. Dalén invented it after being blinded by a factory explosion. At home he wondered why his wife was so busy, and concluded that she needed an easier-to-use stove. Photo: Rbirkby. 25

5 affiliation and therefore Max Planck. Together they contribute a large share of web hits. A Google search for Max Planck Institute or Max Planck Institut produces 6.5 million hits. If we subtract this number from the total number of his hits, we are left with 4.1 million. This shifts Max Planck from second place to third, below Marie Curie. The estimate of his achievement in einsteins falls by 12% from 0.91 to 0.8. The effect is thus not very large. The estimate of achievement of every physicist listed in Table 1 (with the exception only of Dalén) is at least 15% of Einstein s achievement. For example, Dirac and Schrödinger, who are 90 and 60 times less famous than Einstein, appear to achieve only two times less. This may seem shocking to some people. Are these results meaningful? Half a century ago a Nobel Prize winning physicist, Lev Landau, classified theoretical physicists according to their achievement using a logarithmic scale7. According to his ranking system, a member of a lower class achieved ten times less than a member of the next class above. He placed Einstein in a class by himself, labelled half. In the first class he placed Bohr, Schrödinger, Heisenberg, Dirac, and Fermi. Thus, he thought that Einstein contributed to physics 10 3 times more than Dirac or Schrödinger. This is close enough to our estimate, according to which Einstein achieved 2 times more than Dirac or Schrödinger. (Landau placed himself in class 2.5, but later changed his mind and made himself a 2.) Taking into account our error bands of two times more or two times less, this agreement is perfect. Note that Landau s ranking is incomparably closer to our estimate than to a naïve estimate equating fame and achievement. The agreement becomes worse in the cases of Heisenberg and Bohr where we estimate that they achieved 0.6 and 0.7 einsteins correspondingly. However, earlier in his life, during the 1930s, Landau used another classification7. According to it Lorentz, Planck, Einstein, Bohr, Heisenberg, Schrödinger and Dirac all belonged to the first class. Our results are compatible with this earlier classification by Landau. A lot of recent attention has been given to studies8 where statistical analysis of very many non-expert opinions leads to estimates that agree with reality as well as or better than expert opinions. Every webpage about a particular person expresses its creator s opinion of the worthiness of the person in question. Our estimate of achievements of Nobel Prize 26 Einstein in Photo: Ferdinand Schmutzer winning physicists is similarly based on statistical analysis of numbers of web pages mentioning them. The fact that our results agree fairly well with Landau s expert opinion may be another demonstration of the wisdom of crowds. References 1. Simkin, M. V. and Roychowdhury, V. P. (2006) Theory of aces: Fame by chance or merit? Journal of Mathematical Sociology, 30, Bagrow, J. P., Rozenfeld, H. D., Bollt, E. M. and ben-avraham, D. (2004) How famous is a scientist? Famous to those who know us. Europhysics Letters, 67, Baez, J. (2010) The Bogdanoff affair. bogdanoff/ 4. Garfield, E. (1979) Citation Indexing. New York: Wiley. 5. Simkin, M. V. and Roychowdhury, V. P. (2005) Stochastic modeling of citation slips. Scientometrics, 62, Simkin, M. V. and Roychowdhury, V. P. (2007) A mathematical theory of citing. Journal of the American Society for Information Science and Technology, 58(11), Livanova, A. (1993) Landau. Moscow: Znanie (in Russian). ru/wts/rus/landau.htm 8. Surowiecki, J. (2004) The Wisdom of Crowds. New York: Doubleday. Mikhail Simkin and Vwani Roychowdhury are at the Department of Electrical Engineering, University of California, Los Angeles.