Erdos-Bacon Numbers

Written for the Daily Telegraph, April 2002.

It’s the hottest newest game in Hollywood and top mathematicians are playing it too. The new world record holder is a professor from Columbia University, and there is speculation that Gwyneth Paltrow might be on the verge of becoming a major player who could steal the champion’s crown. Welcome to the exclusive world of the Erdos-Bacon number game.

I became aware of the game last month, when I met Professor Dave Bayer at a New York diner. We were meeting to discuss something else altogether, but he could not resist telling me about the Erdos-Bacon number game, having just matched the world record score.

The game has its origins in the 1960s and the work of Stanley Milgram, who showed that the world is a tightly knit community, because each person knows people, who know people, who know people, until the whole world is connected. He claimed that any two people in the world could be connected by six steps on average, giving rise to the expression ‘six degrees of separation’.

The theory inspired a huge amount of scientific research, ranging from how to build a telephone network to the interconnectivity of brain cells, and including studies on the transmission of sexual diseases. But the most famous spin-off has been Six Degrees of Kevin Bacon, a game invented by three students at Albright College, Pennsylvania, which involves linking people to Kevin Bacon via film appearances.

Building a bridge to Bacon can be done on the web, where there are specially designed databases with half a million actors. Most actors can reach Bacon within 3 links, and are said to have a Bacon number of 3. In fact, the average Bacon number is 2.920. But many major stars have lower Bacon numbers. For example, Keith Chegwin has a Bacon number of 2, because Cheggers was in “House!” with Miriam Margolyes, who was in “Balto” with Kevin Bacon.

Meanwhile, mathematicians were working out their Erdos numbers. Paul Erdos was a prolific mathematician who wrote academic papers with a total of 502 co-authors, more than twice as many co-authors as any other mathematician. So if you wrote a paper with Erdos, then you have an Erdos number of 1, and if you wrote a paper with someone who wrote a paper with Erdos then you have an Erdos number of 2, and so on. There are 337,000 mathematicians who can be linked to Erdos in this way.

But recently, following a spate of mathematical films such as “Good Will Hunting”, an elite group of people have emerged, namely those who have appeared in films and written mathematical papers, and therefore qualify for Erdos-Bacon numbers. For a long time, the physicist Brian Greene had a clear lead with score of 5. He appeared in “Frequency” with John Di Benedetto, who was in “”Sleepers” with Kevin Bacon. And he wrote a paper with Shing-Tung Yau, who wrote a paper with Ronald Graham, who wrote a paper with Erdos. This gives a combined number of 2 + 3 = 5.

There were rumours that Erdos appeared in “ð”, which would have given him an Erdos-Bacon number of 3, blowing away all competition. However, official sources can find no evidence for a movie credit for Erdos. Brian Greene’s only serious rival appeared this year, when Dave Bayer, mathematical consultant to “A Beautiful Mind”, was given a minor role in the film and equalled the record.

“In my scene, known as the ‘Pen Ceremony’ I say either “congratulations” or “a privilege, professor” depending on the cut,” says Bayer proudly. “I believe the latter was the final cut. I’m the third professor to lay down a pen before Russell Crowe.” Rance Howard was also in “A Beautiful Mind”, and he was in “Apollo 13” with Kevin Bacon, giving Bayer a Bacon number of 2, which he could add to his Erdos number of 3 to also give a total of 5.

And now there is speculation about who will be next to set a new Erdos-Bacon record. Although most bets are on a mathematician achieving this, it is worth considering the possibility of a Hollywood star stealing the honour. For example, Gwyneth Paltrow is about to appear at the Donmar Warehouse in “Proof”, a play involving mathematics. Acting in a mathematical play might inspire her co-author a paper.

In theory, she could achieve an Erdos number of 2 – it is too late to get an Erdos number of 1 because Erdos died some years ago. Already she has a Bacon number of 2, having appeared in “The Pallbearer” with Greg Grunberg, who was in “Hollow Man” with the omnipresent Mr Bacon. This would give her a combined number of 4. If, however, she could star alongside Kevin Bacon, then potentially she could achieve a combined number of 3.

The only actor who could beat 3 would be Kevin Bacon himself, who is in the privileged position of having a Bacon number of zero.

You can establish the Bacon and Erdos numbers of your favourite film stars and actors by visiting the following sites: