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Home , Charles Glover Barkla, Gabriel Lippmann, George Paget Thomson, Hendrik Lorentz, Karl Ferdinand Braun, Manne Siegbahn

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 . 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 . 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 . 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 β and C. because we used them for fighter pilots aces in curate historical data exists for the number of The fact that β 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 β and are parameters determined by C 7 –4 10 regression. C turns out to be about 5.3, and β 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 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 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 Karl Ernst Ludwig Planck 10,600,000 7.77 0.911 6,300,000 7.25 0.850 1,890,000 6.04 0.709 1,730,000 5.95 0.698 1,110,000 5.51 0.646 987,000 5.39 0.632 Erwin Schrödinger Erwin Schroedinger 375,000 4.43 0.519 330,000 4.30 0.504 Wilhelm Röntgen Wilhelm Conrad Röntgen 272,000 4.10 0.481 Wilhelm Conrad Roentgen Wilhelm Roentgen Paul Adrien Maurice Dirac 255,000 4.04 0.474 Paul A.M. Dirac Louis-Victor de Broglie 201,000 3.80 0.446 Lord Rayleigh Lord John William Strutt Rayleigh 167,000 3.62 0.424 142,000 3.45 0.405 Hendrik Antoon Lorentz 119,000 3.28 0.384 Robert Millikan 112,000 3.22 0.377 109,000 3.19 0.374 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 74,500 2.81 0.329 Joseph John Thomson 73,700 2.80 0.328 Antoine Becquerel Antoine 70,300 2.75 0.323 Arthur Holly Compton 66,800 2.70 0.317 52,600 2.46 0.289 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 46,800 2.34 0.275 45,900 2.32 0.273 Karl Manne Georg Siegbahn 45,000 2.30 0.270 Philipp Eduard Anton Lenard 40,000 2.19 0.256 Carl Ferdinand Braun 40,000 2.19 0.256 Gustav Hertz 37,800 2.13 0.250 35,100 2.06 0.241 Sir George Thomson 29,900 1.90 0.222 Clinton Joseph Davisson 29,100 1.87 0.219 28,600 1.85 0.217 26,400 1.77 0.208 Owen Richardson Willans Richardson 24,900 1.71 0.201 Charles 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. Most of the some physicists achieved additional fame for to get a measure of the lifetime achievement of things invented by other people from our list reasons other than their scientific achieve- a physicist we would like to find a value forC . have no practical applications, and those which ment – for example, for their role in public life. The most famous physicist in Table 1 is do have applications tend to be very dangerous. However, we should emphasise that similar . His was, most probably, also Thermo-nuclear devices, for example, should things happened to the fighter pilot aces we the greatest achievement. Therefore, we will use always be handled with care. So we shall not studied earlier. For example, Hermann Göring him as a unit of achievement, which we denote sneer at Dalén’s modest contribution to the got additional web hits for his political activity. as AE, and measure the achievements of others happiness of mankind; nevertheless, we will He is the second most famous German First in einsteins (or perhaps, for non-Nobel physi- side with the contestants and assign Dalén World War ace, though with 22 victories he is cists, millieinsteins) – their achievements as a the achievement of 0. Then we can substitute only about 60th in terms of acing achievement. fraction of his. From equation (2) we then get: Dalén’s fame, FD , for C: (Manfred von Richthofen, the so-called “Red Baron” and ace of aces, was officially credited ln / A ()FC A ln()FF/ D with 80 victories.) The data shown in the fig- = (3) ≈ (4) A ln FC/ ures include all such cases. EE() AE ln()FFED/ Another objection that we encountered where A/AE is our scientist’s achievement in This gives the achievement, in einsteins, of a is that Max Planck achieved a great deal of einsteins and F is his fame. Theβ , as you can see, physicist whose Google-fame is F. fame due to a singular : in 1948 the has disappeared, but we still need to findC. It is an estimate, rather than an actual Kaiser Wilhelm Society, Germany’s foremost While exact determination of C is impos- achievement, and it is the lower bound of esti- scientific association, was renamed the Max sible, we can find an upper bound for it. It is the mates. We have used the highest possible value Planck Society. All the institutes under the fame of the least famous person in the list: C for C to obtain it; lower values of C will give auspices of the society became Max Planck cannot be more than that because in that case higher estimates of achievement – for everyone institutes. Every scientific paper published by the achievement of the least famous person but Einstein, at least. the members of Max Planck institutes auto- will become negative. The least famous person The estimates of achievement computed matically mentions Max Planck in its address on our list is Nils Dalén. His Nobel Prize from equation (4) are given in the last column line. Similarly, when a news article or a blog (awarded in 1912) is also the most contested: of Table 1. We should note that the data entry discusses a discovery by a member of many believe his achievement is not worthy of presented in the table are very noisy since one of the institutes, it mentions the scientist’s it. Dalén received the Nobel for his invention of the automatic sun valve, which regulates a gaslight source by the action of sunlight, turn- ing 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, 1895. Digital image by Lidingö. Source: AGA AB, An AGA cooker. Dalén invented it after being blinded by a factory explosion. At home he wondered why his wife Lidingö, history archive. was so busy, and concluded that she needed an easier-to-use stove. Photo: Rbirkby.

march2011 25 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, , 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 esti- mate, 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 Einstein in 1921. Photo: Ferdinand Schmutzer to our estimate than to a naïve estimate equat- ing fame and achievement. The agreement becomes worse in the cases of Heisenberg and winning physicists is similarly based on statisti- 4. Garfield, E. (1979)Citation Indexing. New Bohr where we estimate that they achieved 0.6 cal analysis of numbers of web pages mentioning York: Wiley. and 0.7 einsteins correspondingly. However, them. The fact that our results agree fairly well 5. Simkin, M. V. and Roychowdhury, V. earlier in his life, during the 1930s, Landau with Landau’s expert opinion may be another P. (2005) Stochastic modeling of citation slips. used another classification7. According to it demonstration of the wisdom of crowds. Scientometrics, 62, 367–384. Lorentz, Planck, Einstein, Bohr, Heisenberg, 6. Simkin, M. V. and Roychowdhury, V. P. (2007) A mathematical theory of citing. Journal Schrödinger and Dirac all belonged to the References of the American Society for Information Science and first class. Our results are compatible with this , 58(11), 1661–1673. 1. Simkin, M. V. and Roychowdhury, V. P. Technology earlier classification by Landau. 7. Livanova, A. (1993) Landau. Moscow: A lot of recent attention has been given (2006) Theory of aces: Fame by chance or merit? Znanie (in Russian). http://sgtnd.narod. to studies8 where statistical analysis of very Journal of Mathematical Sociology, 30, 33–42. 2. Bagrow, J. P., Rozenfeld, H. D., Bollt, E. ru/wts/rus/Landau.htm many non-expert opinions leads to estimates 8. Surowiecki, J. (2004) M. and ben-Avraham, D. (2004) How famous The Wisdom of . New York: Doubleday. that agree with reality as well as or better is a scientist? – Famous to those who know us. Crowds than expert opinions. Every webpage about a Europhysics Letters, 67, 511–516. particular person expresses its creator’s opinion 3. Baez, J. (2010) The Bogdanoff affair. Mikhail Simkin and Vwani Roychowdhury are at the of the worthiness of the person in question. http://math.ucr.edu/home/baez/ Department of , University of Our estimate of achievements of Nobel Prize bogdanoff/ California, Los Angeles.

26 march2011