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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 “š”, 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. |
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