Thursday, June 9, 2011

My Erdös Number

Many people have heard of the "6 Degrees of Kevin Bacon" game, introduced in 1994, where you try to connect a famous person to the actor Kevin Bacon within 6 connections, e.g. X acted in a movie with Y who acted in a move with Kevin Bacon gives a Bacon Number of 2 for actor X and 1 for actor Y.  The idea of six degrees of separation originated in the early 20th century (of course, not with Kevin Bacon) when Frigyes Karinthy conjectured that any 2 people could be connected through at most 5 people.  This was the basis of the Small World Experiment in 1967 by social psychologist Stanley Milgram.

Long before the Bacon Number in the entertainment industry was the Erdös Number (you can also view the Erdös Number Project page) in mathematics.  Paul Erdös was a prolific mathematician authoring the most academic papers in history, many of those in collaboration with others (at least 1,525).  It became a anecdotal measure of prominence in the field to have a low Erdös Number.  So much so, that the American Mathematical Society has a tool to calculate your Erdös Number based on their database of mathematical papers (click here to go to the tool and select the "Use Erdös" button, try "Einstein, A" and you should see his Erdös Number is 2).  Studies seem to show that, if a person has a finite Erdös Number (meaning, have you published a paper with another author that you can use to start your connection), that number is at most 15 with a median number of 5.  It turns out that my number is 5:

1: Paul Erdős & Mark Kac
    Erdös, P.; Kac, M. "The Gaussian law of errors in the theory of additive number theoretic functions",  Amer. J. Math.  62,  (1940). 738–742.
2: Mark Kac & Subrahmanyan Chandrasekhar
    Chandrasekhar, S., Kac, M., Smoluchowski, R., "Marian Smoluchowski: his life and scientific work. Chronological table and bibliography compiled by Alojzy Burnicki. Edited and with a preface by Roman Stanisław Ingarden", PWN---Polish Scientific Publishers, Warsaw, 2000. 141 pp. ISBN: 83-01-00671-4.
3: Subrahmanyan Chandrasekhar & James B. Hartle
    Chandrasekhar, S., Hartle, J. B., "On crossing the Cauchy horizon of a Reissner-Nordström black-hole",  Proc. Roy. Soc. London Ser. A  384  (1982), no. 1787, 301–315.
4: James B. Hartle & Kip S. Thorne
    Thorne, Kip S., Hartle, James B., "Laws of motion and precession for black holes and other bodies",  Phys. Rev. D (3) 31 (1985), no. 8, 1815–1837.
5: Kip S. Thorne & Amber L. Stuver
    B. Abbott, et al., "Detector description and performance for the first coincidence observations between LIGO and GEO," Nucl. Instrum. Methods A 517 (2004), 154 – 179. 

Special thanks to Nathan Urban for finding this low Erdös Number for me (using the tool listed above) - the best I was able to come up with was 8 with a manual search.

NOTE:  I have a revised Erdös Number of 4 - see my next blog post.

Do you have an Erdös Number?  Post it and your connections as a comment below!

Random picture for today's blog: an honest to goodness black widow spider I found dead behind the LIGO Science Education Center today (in Louisiana):


  1. I'm going to call partial shenanigans on this one. Your first link in the chain is a paper with a bazillion coauthors. In fact, I can use the same path to arrive at a Erdos number of 6 for me. I'll have to add the paper

    Rubbo, Holley-Bockelmann, & Finn, Astrophysical Journal Letters 649, L25-L28 (2006)

    with Finn also being an author on the Abbott et al paper.

    All kidding aside, this is cool post. I didn't know the history behind the Erdos number. Thanks.

  2. I wonder if the Chandrasekhar biography should count? It's not a peer reviewed paper.

    For myself, the lowest I've found is 5:

    1. Paul Erdös and Daniel Grieser
    Aigner, M., Erdös, P., and Grieser, D., "On the representing number of intersecting families", Arch. Math. (Basel) 49, 114 (1987)

    2. Daniel Grieser and Eugénie Hunsicker
    Grieser, D. and Hunsicker, E., "Pseudodifferential operator calculus for generalized Q-rank 1 locally symmetric spaces. I.", J. Funct. Anal. 257, 3748 (2009)

    3. Eugénie Hunsicker and Jorge Sofo
    Hunsicker, E., Nistor, V., and Sofo, J.O., "Analysis of periodic Schrödinger operators: regularity and approximation of eigenfunctions", J. Math. Phys. 49, 083501 (2008)

    4. Jorge Sofo and Milton Cole
    Kim, H.Y., Sofo, J.O., Velegol, D., Cole, M.W., and Mukhopadhyay, G., "Static polarizabilities of dielectric nanoclusters", Phys. Rev. A 72, 053201 (2005)

    5. Milton Cole and Nathan Urban
    Urban, N.M., Gatica, S.M., Cole, M.W., and Riccardo, J.L., "Thermodynamic properties and correlation functions of Ar films on the surface of a bundle of nanotubes", Phys. Rev. B 71, 245410 (2005)

  3. @scienceinthesky: I suppose you can call this shenanigans but I disagree. One of the reasons that Erdös is the person every uses as a focal mathematician is that he was prolific in writing in collaborations. Before his time, most mathematical papers were single author papers. He is an archetype of this new trend in mathematics. Today, the new trend in science is "big science" which also means big collaborations. So, using a connection with many other co-authors is within the spirit of the Erdös Number. It is also in-line with the spirit of Small World Experiment.

    An interesting consequence is that anyone who has ever published on a LIGO Scientific Collaboration paper will have an Erdös of at most 5.

    However, there are proponents who agree with you. So I figured out that my Erdös Number is at most 6 when including only short author list papers:

    1. Charles Kam-tai Chui & Paul Erdös
    2. Francis J. Narcowich & Charles Kam-tai Chui
    3. Robert M. Wald & Francis J. Narcowich
    4. Curt J. Culter & Robert M. Wald
    5. Lee Samuel Finn & Curt J. Culter
    6. Amber Stuver & Lee Samuel Finn

  4. @Nathan Urban: I was wondering if the Chandrasekhar biography should count too. However if the AMS says it does, I'm not about to argue with them. You know, you are the one who gave me this connection chain :)

  5. Amber, your Erdős number is ≤4 via Bruce Allen → Theodore A. Jacobsen → Mark Kac → Paul Erdős.

  6. @Nick: THANK YOU!!! This is great! I suspected that there was someone in the vast LIGO collaboration that could lower my number, but I only checked a few of the higher ups. This is great! I will have to make another post with thanks to you!