Its a small world – Erdös, Bacon and other numbers

Paul Erdos (1913-1996)

Paul Erdos (1913-1996)

Just for fun, mathematicians like to quote their degrees of published separation from Paul Erdös, one of the most prolific modern writers of mathematical papers ( So one day when I needed a break from work, I thought I would find out if I had a finite Erdös number. I found one set of paths through Gary King and another set through Robert May (Baron May of Oxford to you peasants): both giving me an Erdös number of 6.

An Erdös Path for Colin Mathers

  1. Persi Diaconis and Paul Erdös, On the distribution of the greatest common divisor. A festschrift for Herman Rubin, 56–61, IMS Lecture Notes Monogr. Ser., 45, Inst. Math. Statist., Beachwood, OH, 2004.
  2. Persi Diaconis, Susan Holmes, Radford M. Neal, Analysis of a nonreversible Markov chain sampler. Ann. Appl. Probab. (2000), 10(3): 726–752.
  3. Robert E. Kass, Bradley P. Carlin, Andrew Gelman, and Radford M. Neal, Markov chain Monte Carlo in practice: a roundtable discussion. American Statistician (1998)   52: 93-100.
  4. Andrew Gelman, Gary King, and Chuanhai Liu. Not asked and not answered: multiple imputation for multiple surveys. Journal of the American Statistical Association (1998) 93: 846-874
  5. Gary King, Christopher J.L. Murray, Joshua A. Salomon and Ajay Tandon. Enhancing the Validity and Cross-Cultural Comparability of Measurement in Survey Research. American Political Science Review (2003), 97: 567-583.
  6. Lopez AD, Mathers CD, Ezzati M, Jamison DT, Murray CJL. Global and regional burden of disease and risk factors, 2001: systematic analysis of population health data. The Lancet (2006) 367(9524):1747-57.

Another Erdös Path for Colin Mathers

  1. P. Erdös, and J. Galambos, Asymptotic distribution of normalized arithmetical functions, Proceedings of the American Mathematical Society 46 (1974), 1-8.
  2. J. Galambos, E. Seneta, Regularly varying sequences. Proceedings of the American Mathematical Society 41 (1): 110–116
  3. Cohen JE, Iwasa Y, Rautu Gh, Ruskai MB, Seneta E, Zbaganu Gh. Relative entropy under mappings by stochastic matrices, Linear Algebra and its Applications, 179 (1993), 211–235.
  4. Franziska Michor, Steven A. Frank, ,Robert M. May Yoh Iwasa and Martin A. Nowak, Somatic selection for and against cancer. Journal of Theoretical Biology (2003) 225(3):377-382
  5. Neil F. Cramer and Robert M. May, Energy loss of fast test ions in a plasma in a weak magnetic field, Physics Letters A (1969) 30(1): 10-11.
  6. Colin D. Mathers and Neil F. Cramer, The Effect of Ionization and Recombination on the Resistivity of a Partially Ionized Plasma in a Magnetic Field.  Australian Journal of Physics 31: 171-9 (1978).

From my brief career as a physicist, I also have an Einstein number of 7 via Baron May of Oxford. Unlike Erdös, Einstein published very few papers with collaborators, and also most of his publications were around 70-100 years ago, so I think an Einstein number of 7 is quite respectable for someone who was only briefly a physicist.

  1. Albert Einstein and Wolfgang Pauli, Non-existence of regular stationary solutions of relativistic field equations, Annals of Mathematics, ser. 2, 44 (1943) 131-137.
  2. Wolfgang Pauli, L Rosenfeld and Victor F. Weisskopff . Niels Bohr and the development of physics. New York: Pergamon Press (1955) – 195 pp.
  3. John M Blatt, Victor F Weisskopf. . Theoretical nuclear physics. New York: Chapman and Hall (1952) – 896pp.
  4. JM Blatt, Stuart T Butler. Superfluidity of an ideal Bose-Einstein gas. Physics Review (1955) 100: 476-480.
  5. Stuart T Butler, Robert M May. Production of Highly Excited Neutral Atoms for Injection into Plasma Devices. Physics Review (1965) 137: A10–A16
  6. Robert M May, Neil F Cramer. Energy loss of fast test ions in a plasma in a weak magnetic field. Pgysics Letters A (1969), 30: 10-11.
  7. Colin D Mathers, Neil F Cramer.  The Effect of Ionization and Recombination on the Resistivity of a Partially Ionized Plasma in a Magnetic Field.  Australian Journal of Physics  (1978) 31: 171-9.

And one I won’t be adding to my CV: I have 2 degrees of (handshake) separation from Adolf Hitler. Back in 2003, I shook hands with a woman who had shaken hands with Hitler.

Kevin Bacon

Kevin Bacon

But I pine for a finite Erdös-Bacon number (= Erdös number + (Kevin) Bacon number). That means I have to get a part in any film with a real actor in it who has a finite Bacon number.  My friend James has a Bacon number of 3, and he just needs to offer me a part in his next film!

Incidentally, four of the lead actors in the film James was in have Bacon numbers of 2, and the other 3. Apparently, among professional actors the mean Bacon number is 2.871 with standard deviation 0.66 and it is essentially impossible to find an actor with a Bacon number of more than 4. In contrast, among mathematicians, the median Erdos number is 5 and the mean is 4.65.

Most scientists don’t have a Bacon number, though many will have an Erdos number. Several scientists have the lowest known Erdos-Bacon number of 3, as does a baseball player, Hank Aaron, if you count autographing the same baseball as Erdos as giving him an Erdos number of 1. Natalie Portman has an Erdos-Bacon number of 6, second-lowest among professional actors.

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1 Response to Its a small world – Erdös, Bacon and other numbers

  1. Pingback: The world is getting smaller – my Erdös and Einstein numbers drop | Colin Mathers

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