*Photo: Paul Erdős. (c) Topsy Kretts, CC BY 3.0*

*Warning: very nerdy.*

* *Sometimes I get distracted and go down a rabbithole. Sometimes the result is fun.

I’ve been lucky, over my career, to have a large number of coauthors (some of whom are good friends; but many of whom I’ve never even met). Coauthorhip makes my work better, but it has other benefits too. A somewhat abstract one is that it makes me feel that I’m part of something larger than my own research program, or even my own discipline. I belong (as we all do) to a global and cross-disciplinary network of collaborating scientists. And to prove it, I have an Erdős number.

Paul Erdős (1913-1996) was a Hungarian mathematician who published somewhere around 1,500 papers (in mostly pure-math fields including set theory and number theory) and had somewhere around 500 coauthors. He was a fascinating figure, and his biography *The Man Who Loved Only Numbers* is a great read. He was famous both for brilliance and for broad collaboration. Those two things in combination inspired mathematicians to invent the Erdős number as a metric of their collaborative closeness to Erdős. Here’s how it works: Erdős’s own Erdős number is E = 0; those who have coauthored research papers with Erdős have E = 1; those who have coauthored with an E = 1 scientist have, as a result, E=2, and so on.

What, I wondered, was my own Erdős number? I knew I probably had one, because an interesting property of networks is that given a surprisingly low degree of connectedness, there tend to be pathways from most nodes to most other nodes. I also knew it probably wasn’t that large: another interesting property of networks is that internodal paths are often surprisingly short. (If someone has an Erdős number at all, it’s normally less than about 10-15.) If you know me at all, you’ll be unsurprised that I wanted to pin this down.

Turns out, to my considerable surprise, that my Erdős number is 3.

To put that in perspective: Richard Feynman’s Erdős number is also 3; so is Andrew Wiles’s. Erwin Schrödinger, Francis Crick, Harry Kroto, Linus Pauling, and John Nash all have E = 4. George Smoot has E = 5, and Peter Higgs has a lovely boson and a lovely Nobel Prize, but an unimpressive E = 9. The *average* for Fields Medal winners is 3.2, and the *average *for Nobel Prize winners (excluding Peace) is 5.3.

And yes, I know this means absolutely nothing; but again, *my* Erdős number is 3.

So how on Earth did I acquire E = 3? Actually, this surprised me, because when I calculated my Erdős number I intended to cheat. Back in 2004, I coauthored a paper with Stephen Hawking. Yes, *that* Stephen Hawking; but no, not a *real* paper – it was a joke piece, with a huge author list, in the *Annals of Improbable Research* (you can read about it here). I figured if I bent the rules and counted this as a coauthored paper, I’d get myself a nice small Erdős number. Turns out, though, Hawking’s Erdős number is a good-but-not-awesome E = 4. But Steven Weinberg, the 1979 Physics Nobelist, was also a coauthor and has E = 3. That gave me E = 4, equalling Hawking, which made me pretty happy.

But then on a whim I plugged myself into the American Mathematical Society’s Erdős number calculator and discovered that I don’t have to cheat. Based on my *real* papers and coauthors, I have E = 3 because:

- In 2007 I coauthored a book chapter with Michael Blum
*(Mooers, AØ, LJ Harmon, MGB Blum, DHJ Wong, SB Heard. Some models of phylogenetic tree shape.*In*Reconstructing evolution, 149–170, Oxford Univ. Press, Oxford)*; and - In 2006, Michael Blum coauthored a paper with Svante Janson
*(Blum, MGB, O François, S Janson. The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance. Ann. Appl. Probab. 16: 2195–2214.)*; and - in 1996, Svante Janson coauthored a paper with Paul Erdős
*(Erdős, P, S Janson, T Łuczak, J Spencer. A note on triangle-free graphs. Random discrete structures. IMA Vol. Math. Appl., 76:117-119, Springer, New York).*

Again, this doesn’t *mean* anything; but it’s pretty cool (for a spectacularly nerdy definition of “cool”). And if you’ve ever coauthored with me*, then your Erdős number is at most 4 (and you’re welcome).

So: anybody got me beat? Are there E = 2’s in ecology and evolution (besides, of course, Michael Blum)? Who else can join me at E = 3?**

Now if only I had an Erdős-Bacon-Sabbath number. ** That** would be cool.

*© Stephen Heard January 8, 2018*

*^Or with Arne Mooers or Luke Harmon or Dennis Wong – but this post is *my* self-indulgence, not theirs.

**^ To find your own Erdős number, you can try the American Mathematical Society calculator, but its journal coverage outside math is badly incomplete. There are further computation tips at the Erdős Number Project home page.

jeffollertonJeez, you’re a distraction Prof. Heard! I’m supposed to be looking at a draft grant proposal……

So, seeing that you and I are co-authors, my Erdos number is 4 and I doubt whether I’ll improve on that, even if I write a paper with my cousin Richard Ollerton who is a mathematician with an Erdos number of 3, I’ve just discovered.

More pertinent to EEB, how many handshakes are you from Darwin? I can do it in five (proper handshake relationships, not just casual meetings at a conference, that is).

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ScientistSeesSquirrelPost authorOoh, handshakes from Darwin – I wouldn’t even know how to find out, but what an awesomely nerdy thing to spend time trying! I guess when we meet in person, that will put me at no worse than 6…

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jeffollertonYeah, you need to know about PhD supervisors and personal relationships back over time. Mine goes like this: my main PhD supervisor was Andrew Lack, son of David Lack. David was close to Julian Huxley, who in turn was close to his grandfather Thomas Henry Huxley, who was of course a very close friend of Darwin.

Interestingly I can also get there via my second supervisor, Denis Owen, who was a research assistant to David Lack for a while.

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sheardcatMine is 4, and I doubt it’s ever going to get lower. (My dad’s is 3, and for a while my mom was on my case to publish something with my dad so that I could get my Erdos number down from a 6, but I got there all by myself, thanks.) (Welcome to what academic families squabble about.)

I have a colleague with an Erdos-Bacon number of 8 (in her case, Bacon number 2, Erdos number 6). An actual movie credit, none of this “appearing as yourself” nonsense. Now that, I am jealous of.

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ScientistSeesSquirrelPost authorI am jealous of her Erdos-Bacon number too. Does she have a Sabbath number?

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jeffollertonI have a credit as scientific advisor on a Disney movie documentary called “Wings of Life” that was narrated by Meryl Streep. Mery Streep has a Bacon number of 1. Does that mean my Bacon number is 2? Or does it just apply to acting roles?

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ScientistSeesSquirrelPost authorSadly, strict Baconists would argue that it only applies to acting roles (https://oracleofbacon.org/help.php). Although I am still jealous.

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jeffollertonBoo 😦 Shame, I think I’d also have a Sabbath number from working with Radiohead’s old stage crew, but that’s probably outside of the rules too…

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sheardcatOh goodness, I don’t think so, but I’ll definitely ask her next time I see her!

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Daniel WeissmanThere are a good number of E=2s in the more math-y side of population genetics. Depending on how far you’re willing to stretch the boundaries of the field, Sam Karlin, JFC Kingman, RC Griffiths, Eran Halperin, Rick Durrett, Susan Holmes, Dan Gusfield, Julia Salzman, Steve Evans, Bernd Sturmfels, and Elchanan Mossel are all E=2.

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ScientistSeesSquirrelPost authorExcellent! That should give quite a few ecologists and evolutionary biologists a path to E=3.

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William Kenneth Wayne GodsoeI haven’t seen anyone on this thread post the xkcd on erdos numbers so just to avoid that tragedy, here it is: https://xkcd.com/599/ .

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ScientistSeesSquirrelPost authorHow on earth did I fail to link to that???? Thanks.

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