Erdos numbers:

In the comments to my post on Bacon numbers below, I noted that my Erdős number was 8, but then revised it to 6. Here's what I previously thought my chain was:

  1. P. Erdos, C.D. Godsil, S.G. Krantz & T.D. Parsons, Intersection graphs for families of balls in R^n, European J. Combin. 9 (1988), no. 5, 501-505.

  2. Steven G. Krantz & Norberto Salinas, Proper holomorphic mappings and the Cowen-Douglas class, Proc. Amer. Math. Soc. 117 (1993), no. 1, 99-105.

  3. Gregory T. Adams, Paul J. McGuire, Norberto Salinas & Allen R. Schweinsberg, Analytic finite band width reproducing kernels and operator weighted shifts, J. Operator Theory 51 (2004), no. 1, 35-48.

  4. Ariel Pakes & Paul McGuire, Stochastic algorithms, symmetric Markov perfect equilibrium, and the "curse" of dimensionality, Econometrica 69 (2001), no. 5, 1261-1281.

  5. Laurence J. Kotlikoff, & Ariel Pakes, Looking for the news in the noise. Additional stochastic implications of optimal consumption choice, Ann. Econom. Statist. 1988, no. 9, 29-46.

  6. Laurence J. Kotlikoff & Lawrence H. Summers, Tax incidence, Handbook of public economics, Vol. II, 1043-1092, Handbooks in Econom., 4, North-Holland, Amsterdam, 1987.

  7. B. De Long, A. Shleifer, L. Summers & R. Waldmann, Noise Trader Risk in Financial Markets, Journal of Political Economy, August 1990, reprinted in Richard H. Thaler, ed., Advances in Behavioral Finance, Russell Sage Foundation, 1993.

  8. Juan Carlos Botero, Rafael La Porta, Florencio López-de-Silanes, Andrei Shleifer & Alexander Volokh, Judicial Reform, World Bank Research Observer 18 (2003), no. 1, pp. 61-88.

This took us through my industrial organization professor Ariel Pakes, former Harvard president Larry Summers, and my adviser Andrei Shleifer. But yesterday I discovered a new chain, of length 6 instead of 8, through Shechao Charles Feng, my one-time co-author on an L.A. Times op-ed on affirmative action, later reprinted in the Journal of Blacks in Higher Education, once of the UCLA Physics Department:

  1. P. Erdős, A. Rényi & V.T. Sós, On a problem of graph theory, Studia Sci. Math. Hungar. 1 (1966), pp. 215-235.

  2. Christian Borgs, Jennifer Chayes, László Lovász, Vera T. Sós & Katalin Vesztergombi, Counting graph homomorphisms, Algorithms Combin. 26 (2006), pp. 315-371.

  3. J.T. Chayes, L. Chayes, Daniel S. Fisher & T. Spencer, Finite-Size Scaling and Correlation Lengths for Disordered Systems, Phys. Rev. Letters 57 (1986), no. 24, pp. 2999-3002.

  4. Daniel S. Fisher & Patrick A. Lee, Relation between conductivity and transmission matrix, Phys. Rev. B 23 (1981), no. 12, pp. 6851-6854.

  5. Shechao Feng & Patrick A. Lee, Mesoscopic Conductors and Correlations in Laser Speckle Patterns, Science 251 (9 Feb. 1991), pp. 633-639.

  6. Alexander Volokh & Shechao Charles Feng, How Race Adds Up for UCLA Entry, L.A. Times (18 July 1995), partly reprinted in Journal of Blacks in Higher Education 9 (Autumn 1995), p. 94.

And just today I accidentally discovered an even shorter chain, again going through economists -- through my adviser Shleifer and my former economics professors Oliver Hart and Eric Maskin -- which gives me an Erdős number of 5!

  1. Paul Erdős, Peter Fishburn & Zoltán Füredi, Midpoints of diagonals of convex n-gons, SIAM J. Discrete Math. 4 (1991), no. 3, pp. 329-341

  2. Peter C. Fishburn, William V. Gehrlein & Eric Maskin, A progress report on Kelly's majority conjectures, Econom. Lett. 2 (1979), no. 4, pp. 313-314.

  3. Sanford J. Grossman, Oliver D. Hart & Eric S. Maskin, Unemployment with Observable Aggregate Shocks, J. Polit. Econ. 91 (1983), no. 6, pp. 907-928.

  4. Oliver Hart, Andrei Shleifer & Robert W. Vishny, The Proper Scope of Government: Theory and an Application to Prisons, Q.J. Econ. 112 (1997), no. 4, pp. 1127-1161.

  5. Juan Carlos Botero, Rafael La Porta, Florencio López-de-Silanes, Andrei Shleifer & Alexander Volokh, Judicial Reform, World Bank Research Observer 18 (2003), no. 1, pp. 61-88.

I know what you're thinking: What's Eugene's Erdős number? If you consider the blog to be a co-authored work, then Eugene could be a 6. On the other hand, if you consider the blog to be a journal where each post is a separate article -- so Eugene and I haven't co-authored anything -- then Eugene might be a 7, because I've co-authored with Judge Kozinski (The Appeal, 103 Mich. L. Rev. 1391 (2005)), and so has Eugene (Lawsuit, Shmawsuit, 103 Yale L.J. 463 (1993)). Or Eugene's number might be lower through his co-authorship with, say, Larry Lessig.

Sophist:
Correct me if I am wrong, but I believe Erdos numbers are for collaboration in mathematical research, not Op-Eds, blogs, or baseballs.
6.14.2007 11:41am
Sasha Volokh (mail) (www):
Baseballs, I agree, because I think that's more similar to an issue of a journal with many articles. Blogs, I would tend to agree.

However, why not op-eds? And why only mathematical research?

I think the proper idea should be collaboration on any written work, in any discipline -- mathematical work will still be privileged because most or all Erdos collaborators are mathematicians, and mathematicians usually collaborate with other mathematicians. And there should be no requirement that it be original research or whatever, because that leads to difficult line-drawing problems.
6.14.2007 11:46am
dimitrir:
Actually, you Bacon number is 2, as he lives accross the street from me (in NYC) and I see him regularly, and I am an infrequent poster on this blog.
6.14.2007 11:48am
Stephen Philbrick (mail):
I believe my Erdos number is three.

I co-authored a paper on Dynamic Financial Analysis with John Burkett. After we submitted the paper, he remarked that, as an undergrad, he had co-authored a paper with wit math advisor, who once c-authored with Erdos.

I realize I need to track down the retails to take full credit, something I really should do. (But it doesn't come up in conversation all that often.)
6.14.2007 11:54am
Sasha Volokh (mail) (www):
Stephen Philbrick:

MR1295263 (95g:41016)
Burkett, John(1-FL); Varma, A. K.(1-FL)
Lacunary spline interpolation. (English summary)
Proceedings of the Second International Conference in Functional Analysis and Approximation Theory (Acquafredda di Maratea, 1992).
Rend. Circ. Mat. Palermo (2) Suppl. No. 33 (1993), 219--228.
41A15 (65D07)


MR0836404 (87f:26017)
Erdös, P.(H-AOS); Varma, A. K.(1-FL)
An extremum problem concerning algebraic polynomials.
Acta Math. Hungar. 47 (1986), no. 1-2, 137--143.
26D05 (26D15)
6.14.2007 12:01pm
Sophist:

However, why not op-eds? And why only mathematical research?

I think the proper idea should be collaboration on any written work, in any discipline [. . .]


My first impulse was that by definition (viz., the definition of an Erdos number as given by the Erdos Number Project as well as Wikipedia) only mathematical collaboration counts. The Erdos Number Project claims to study "research collaboration among mathematicians."

This definition may be arbitrary and improper, but I think there are some good reasons to limit the amount of people with finite Erdos numbers in this way. One reason would be that the motivation for the study was Erdos' immense number of publications, many co-authored, in mathematics. The study would be limited to publication in mathematics because it would then be a more accurate indicator of the reach, across disciplines and countries, of his work.
6.14.2007 12:06pm
Sophist:
By disciplines, I meant disciplines within mathematics (discrete, group theory, etc.)
6.14.2007 12:08pm
Jody (mail):
Sophist:

From the Erdos Number Project's Compute your Erdos Number page

People in other sciences or even social sciences may also have small Erdös numbers. My brother (a physician with only one publication) has an Erdös number of at most 9.


So it appears that Sasha's interpretation is correct.
6.14.2007 12:13pm
Sophist:
Yes, there's also this in the same paragraph:


An author in the MathSciNet database, Mutt, is a computer with an Erdös number of 2. We’ve even heard about a horse who claimed to have an Erdös number of 3. For more on the whimsical side of this (after all, what you want to count as a joint publication is a matter of subjective judgment), see also this site, which carries it to a ridiculous extreme
6.14.2007 12:21pm
Sophist:
here is the site which carries the numbering to a ridiculous extreme.
6.14.2007 12:25pm
ys:
Besides a predicative definition, the official Erdös site also lists its primary and secondary sources, which by the fact of listing become another definition of at least a sufficient inclusion property.


Here are the procedures, rules, conventions, and assumptions we used in creating these lists. In most cases, our source is the database of the American Mathematical Society’s Mathematical Reviews (MR). Secondary sources include Zentralblatt, the Electronic Research Archive for Mathematics Jahrbuch Database, the Computer Science Bibliography (DBLP), and the hypertext bibliography project in theoretical computer science (HBP, which seems to be no longer active). In some cases we have used obituary articles in mathematical journals or similar sources. Finally, we thank the countless mathematicians, especially the coauthors of Paul Erdös, for providing information for this site.

As you can see, some sources on computer science are explicitly included, but nothing else (yes there is also a treatise on how signing a peace appeal with Einstein provided Bertrand Russell with an otherwise lacking Erdos number). Incidentally, a search on Volokh in DBLP database brought up a citation for Eugene (it was a publication in ACM), but not for Alexander, while the purely math db's brought up only a completely different Volokh (K.Volokh). I did not check obituaries in math journals. In an aside, I was gratified to see that a citation linking me with an Erdos 2 fellow comes up in DBLP.
6.14.2007 12:57pm
r78:
I have an Erdos number of 2 since I once had sex with a woman who served him coffee once.
6.14.2007 1:36pm
Sasha Volokh (mail) (www):
ys: Ethan Bolker?
6.14.2007 1:59pm
Warren Beatty:
But what is your Eros number?
6.14.2007 2:47pm
John Armstrong (mail) (www):
Despite what some commenters here say, I don't know of any actual mathematician who would count a non-mathematical paper as an arc in the graph.

And for added pedantry, Sasha is the only one here to actually spell the man's name right: Erdős. It's a double-acute accent, not a diaeresis.
6.14.2007 3:46pm
Ron Hardin (mail) (www):
I seem to have an Erdos number of 2. Time to update the CV.
6.14.2007 6:18pm