The Erdos Number and social nets

31 December 2009

My friend Don – we’ve been pals since elementary school – has one of the strongest moral centers of anyone I know (here‘s an example of what I mean, and here’s another side to this guy). I can remember back in high school sitting around a camp fire having one of those “meaning of life” conversations, when he caught me up short with the simple, obvious, and still true question we’re all struggling to answer. The question, he said, was simply, “how to live.” What are the ethics of a life well lived, he was asking. I still think that’s the essential question, partly because it’s something we can actually do something about.

Which brings me to Paul Erdos.

The other day I was listening to a show about “Numbers” from my absolutely all-time favorite podcast, Radiolab. The show featured a story about Paul Erdos and something called Erdos Numbers. (Sidebar: walking Mingus the Super Dog up the hill and down the hill yesterday I was thinking about this post, and it occurred to me that – while they’re quite different – Radiolab’s the aural equivalent of my all-time favorite magazine, the late, lamented, wish-it-was-still-around Whole Earth Review aka Coevolution Quarterly. Why? Because both are rich in sideways thinking, bringing the unexpected together with the everyday in brilliant moments of insight.)

Erdos (pronounced “Eyrdish”) was a Hungarian Jew who, with two mathematicians for parents, lived and breathed numbers pretty much from birth (it was said he could calculate the number of seconds someone had lived, at the age of 3).

The day he was born, his two sisters died of scarlet fever; his mother was so terrified that Paul would get a fatal disease she didn’t let him leave the house til he was 11 – no going to school, no outside friends, nothing much except numbers. With the Nazi takeover of Hungary, Erdos’ father and four of his mother’s siblings were killed by the Nazis. Erdos left Hungary for good, eventually landing a teaching position at Princeton University.

Twenty-seven years old, disconnected from his Hungarian family and social world (and with an unusual relationship to that larger world to begin with), Erdos had no conventional friendships, and a noticeable lack of interest in accumulating worldly possessions. His only meaningful social relationships were through mathematics.

He could have gone completely insane; instead Erdos “turned this inwardness into making mathematics a joyous and social occasion” according to Paul Hoffman, who has written a biography of Erdos. He began traveling, visiting other mathematicians working on interesting projects. “My brain,” Erdos would announce on arrival, “is open.” He couldn’t cook, barely changed his clothes (and didn’t know how to tie his shoes til he was 11), drank copious amounts of coffee.

But people put him up, and put up with him. He was brilliant, generous – and prolific:  Erdos collaborated with more people and wrote more papers (1400 by one count) than any mathematician in history.

Which is what led to the Erdos number. Created by some of his fellow mathematicians to poke fun at Erdos while also honoring him, an “Erdos number” (so says Wikipedia) is “the “collaborative distance” between a person and Erdos, as measured by authorship of mathematical papers.

Erdos himself had an Erdos number of 0. If you published a paper with him you were assigned an Erdos number of 1 (there are about 500 of these, including ex-Atlanta Braves slugger Hank Aaron, who autographed the same baseball as Erdos when the two of them were awarded honorary degrees by Emory University). If you published a paper with one of his collaborators, you had an Erdos number of 2 (about 8,000). Erdos number 3: 34,000. Erdos number 4: 84,000. And so on. At this point, it’s estimated that some 200,000 mathematicians have an Erdos number, and that about 90 percent of active mathematicians have an Erdos number of 8 or lower.

Think about that: 200,000 people whose ideas are linked together with one another, and with this one, extraordinary man with Erdos number 0.

Listening to the Radiolab piece on Erdos, I thought to myself, well, all of us have our own Erdos number – rings of relationships built around ideas and passions. Our connections to family, partners, sons and daughters. People we’ve learned from in our work, study, or activism. People we’ve trained and mentored over the years.  And in the digital space, of course, the infinite network that fans out from the connections we know to the viral universe we don’t know.

I don’t know if Erdos knew how big his “Erdos number” community really was, or if he even cared about that. But that’s the point: we can’t really know the scale of repercussions of our own choices and words as they spread out over time and space (whether that’s real or digital). But there’s an ethics there that needs to be paid attention to. It’s not just about the technology.

And that’s my thought for the New Year.

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One Response to “The Erdos Number and social nets”


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