My Friend Erdös..

After one of my  lectures a few weeks ago, a student came up to me and asked whether I had an Erdős number and, if so, what it was.  I didn’t actually know what he was talking about but was yesterday reminded of it, so tried to find out.

In case you didn’t know, Paul Erdős (who died in 1996) was an eccentric Hungarian mathematician who wrote more than 1000 mathematical papers during his life but never settled in one place for any length of time. He travelled between colleagues and conference, mostly living out of a suitcase, and showed no interest at all in property or possessions. His story is a fascinating one, and his contributions to mathematics were immense and wide-ranging.  The Erdős number is a tiny part of his legacy, but one that seems to have taken hold. Some mathematicians appear to take it very seriously, but most treat it with tongue firmly in cheek, as I certainly do.

So what is the Erdős number?

It’s actually quite simple to define. First, Erdős himself is assigned an Erdős number of zero. Anyone who co-authored a paper with Erdős has an Erdős number of 1. Then anyone who wrote a paper with someone who wrote a paper with Erdős has an Erdős number of 2, and so on. The Erdős number is thus a measure of “collaborative distance”, with lower numbers representing closer connections.

I say it’s quite easy to define, but it’s rather harder to calculate. Or it would be were it not for modern bibliographic databases. In fact there’s a website run by the American Mathematical Society which allows you to calculate your Erdős number as well as a similar measure of collaborative distance with respect to any other mathematician.

A list of individuals with very low Erdős numbers (1, 2 or 3) can be found here.

Given that Erdős was basically a pure mathematician, I didn’t expect first to show up as having any Erdős number at all, since I’m not really a mathematician and I’m certainly not very pure. However, his influence is clearly felt very strongly in  physics and a surprisingly large number of physicists (and astronomers) have a surprisingly small Erdős number. According to the AMS website, mine is 5 – much lower than I would have expected. The path from me to Erdős in this case goes through G.F.R. Ellis, a renowned expert in the mathematics of general relativity (as well as a ridiculous number of other things!). I wrote a paper and a book with George Ellis some time ago.

However, looking at the list I realise that I have another route to Erdős, through the great Russian mathematician Vladimir Arnold, who has an Erdős number of 3. Arnold wrote a paper with Sergei Shandarin with whom I wrote a paper some time ago. That gives me another route to an Erdős number of 5, but I can’t find any paths  shorter than that.

I guess many researchers will have links through their PhD supervisors, so I checked mine – John D. Barrow. It turns out he also has an Erdős number of 5 so a path through him doesn’t lower my number.

I used to work in the School of Mathematical Sciences at Queen Mary, University of London, and it is there that I found some people I know well who have lower Erdős numbers than me. Reza Tavakol, for example, has an Erdős number of 3 but although I’ve known him for 20 years, we’ve never written a paper together. If we did, I could reduce my Erdős number by one. You never know….

This means that anyone I’ve ever written a paper with has an Erdős number no greater than 6. I doubt if it’s very important, but it definitely qualifies as Quite Interesting.

22 Responses to “My Friend Erdös..”

1. Anton Garrett Says:

Why do you say he’s eccentric Peter? His behaviour sounds wholly routine for a mathematician. Witness the current furore over Perelman:

http://news.bbc.co.uk/1/hi/world/europe/8585407.stm

2. telescoper Says:

What’s normal for mathematicians is often eccentric for the rest of us…

3. My Erdös number is NaN according to the AMS website. I guess their bibliographical database doesn’t include much astronomy literature.

BTW, the “author distance” is used by http://www.arxivsorter.org/ which writes: “Arxivsorter uses the network of co-authorship to estimate a proximity between people. It then ranks a list of publications using a friends-of-friends algorithm”. I find it useful.

4. Anton and telescoper, your comments are offensive. Mathematicians, and scientists, are normal people. There are weird/eccentric/crazy mathematicians just as there are astronomers, authors, politicians, or mail carriers. But we’re mostly normal and I personally don’t appreciate the perpetuation of that particular myth.

• telescoper Says:

Ahava,

As someone who is himself openly eccentric, I can assure you no offence was intended.

Peter

5. anisotropie Says:

I think you’ll be happy yo know that yours is lower, given that mine is 4 via Tegmark that has 2, and we both published with someone connected to Tegmark.

6. telescoper Says:

anisotropie,

Interesting. The link with Tegmark could be via Cooray but, strictly speaking, those papers aren’t published yet. Unless it’s someone else.

I don’t know who you are, though, so I can’t check.

Peter

7. Anton Garrett Says:

Ahava,

Like Peter I meant no offence. In fact I have delivered an examinable lecture course in a university mathematics department and published mathematical work without any physics applications attached, and I believe that people are entitled to lampoon themselves. The mathematician and lampoon Tom Lehrer always got a laugh with his line about mathematicians.

Anton

• telescoper Says:

Yes, I worked in a mathematics department for the best part of a decade. Some of the folks there were quite eccentric, but most of them wouldn’t mind being described by that word. Neither would I. Normality (whatever it is) is highly overrated.

8. It’s certainly possible yours is lower Peter. The AMS route isn’t perfect. I had no idea what my number was, but plugged my name into the site and it came back with 4. However, the path it gave took me first through my advisor and then through one of his other students. Since that person and I published together anyway, it could have avoided going through my advisor at all, but it missed it. So my number is at most 3, which was quite unexpected. Now, if I could only make it 2…

• telescoper Says:

Mark,

I have had quite a few emails about this. There are a lot of missing links in the AMS database. I’m pretty sure now that mine is 4 – it certainly is if you count papers in the press. I’m also pretty sure John Barrow’s is less than 5 too…

Peter

9. Anton Garrett Says:

This routine is unlikely ever to be perfect. Is it Erdos-specific or can it trace a likely shortest path between any two reasonably prolific scientific authors?
Anton

10. Didn’t someone recently auction on Ebay an opportunity to obtain a rather low Erdös number?

I don’t know if Erdös was the first with such a number. Fans of the folk-rock group Fairport Convention talk of Pegg numbers, Dave Pegg being FC’s bass player. So your Pegg number is 1 if you’ve recorded or toured with Pegg etc. I suspect most FC fans have never heard of the Erdös number. (Though, continuing the theme, FC guitarist and singer Simon Nicol once toured with Art Garfunkel, who has a degree in mathematics. (I read once that he was at some point a professor of geometry, but can’t find a reference in a quick search.))

Basically, this is just another aspect of six degrees of separation, as is six degrees of Kevin Bacon.

Another aspect involves sexually transmitted diseases. I think the first case of a human with AIDS was traced back to a flight attendant, with not that many steps between an average victim and the first one.

More interesting is perhaps the Erdös-bacon number, or even a combination of that and the Pegg number.

Of course, Kibo introduced the concept of a Kibo number, it being 1 if you have gotten email from Kibo etc.

• telescoper Says:

Philip,

What are you trying to say with your statement

I think the first case of a human with AIDS was traced back to a flight attendant…

That flight attendants are not human or that the person the flight attendant caught it from wasn’t human?

Peter

11. verystrangedave Says:

A study of mathematically gifted Icelanders demonstrated an increased risk of mental illness in their ranks. (4 times the normal rate!) Google “relation of mathematical ability to psychosis in iceland” … “feynman fredkin wolfram” … “erdos eccentricity”

12. Anton Garrett Says:

Phillip,

I remember some years ago when pathology specimens of people who had died mysteriously of everything, before the 1980s, were retested for AIDS and the date of first fatality got pushed ever farther back. Genetic mutation rates now suggest that AIDS jumped from monkeys to people in West/Central Africa – most likely when an infected animal was butchered – about a century ago; see

http://en.wikipedia.org/wiki/History_of_AIDS

which also shows that the flight attendant often mentioned in this connection, while infecting many people, was far from being the first.

Anton

13. “That flight attendants are not human or that the person the flight attendant caught it from wasn’t human?”

On re-reading it, I do admit that it sounds a bit confusing (probably due to watching both Swedish and Norwegian television last week while on holiday, simultaneously reading a book in English and talking to my son in German).

What I meant was: Several years ago, I read an article about the spread of AIDS where, through interviews etc, it was determined from whom various people caught the disease, then the sources of their infection were tracked down etc, leading back to the first person infected, who IIRC was a flight attendant (perhaps not relevant, or perhaps relevant in that this led to more widespread infections (back when people didn’t even know that AIDS existed, much less whether they were infected)). The “six degrees of separation” rule applies here too.

This hadn’t crossed my mind in a while but the idea of Erdös numbers brought it back.

Googling for “aids first case flight attendant” gives this as the first hit:

http://www.avert.org/origin-aids-hiv.htm

Towards the bottom of the page, one can read:

Much was made in the early years of the epidemic of a so-called ‘Patient Zero’ who was the basis of a complex “transmission scenario” compiled by Dr. William Darrow and colleagues at the Centre for Disease Control in the US. This epidemiological study showed how ‘Patient O’ (mistakenly identified in the press as ‘Patient Zero’) had given HIV to multiple partners, who then in turn transmitted it to others and rapidly spread the virus to locations all over the world. A journalist, Randy Shilts, subsequently wrote a book21 based on Darrow’s findings, which named Patient Zero as a gay Canadian flight attendant called Gaetan Dugas. For several years, Dugas was vilified as a ‘mass spreader’ of HIV and the original source of the HIV epidemic among gay men. However, four years after the publication of Shilts’ article, Dr. Darrow repudiated his study, admitting its methods were flawed and that Shilts’ had misrepresented its conclusions.

While Gaetan Dugas was a real person who did eventually die of AIDS, the Patient Zero story was not much more than myth and scaremongering. HIV in the US was to a large degree initially spread by gay men, but this occurred on a huge scale over many years, probably a long time before Dugas even began to travel.

So, my dimly remembered version of the story is perhaps more of an urban legend, though some aspects of it are true.

It does appear though that at some point in the past AIDS did indeed pass from non-human to human (see the text near the picture of the chimpanzee at the link above).

14. […] After one of my  lectures a year or so ago, a student came up to me and asked whether I had an Erdős number and, if so, what it was.  I didn’t actually know what he was talking about but  tried to find out and eventually posted about it. […]

15. Roronoazoro Zoro Says:

I just discovered that if our paper gets accepted, I will have erdos number 4, which is pretty cool. By the way, in your last paragraph, you must have meant “no less” not “no greater”

• telescoper Says:

I don’t think so. Friends might have a number less than 6 because of some other connection, but it can’t be greater than six because of mine.

• Roronoa Zoro Says:

Yes, you’re right. I got it backwards, I was thinking “no less” than 4 (assuming you’re 5), so the difference has to be 1… Anyways, thanks for correcting my (attempt) to correct you.