Wednesday, 3 September 2008

Bacon vs. Erdos - it's a numbers game

Remember movie star Kevin Bacon, who fought so bravely for our right to dance in Footloose?

His dance activism aside, Bacon is probably best known for spawning the trivia game Six degrees of Kevin Bacon. The game is based upon the assumption that all actors can be linked to Bacon through their film roles in six steps. For example, Brad Pitt starred with Bacon in Sleepers, so he is connected by one film and has what is known as a "Bacon number" of one. In Top Gun, Val Kilmer starred with Tom Cruise, who starred with Bacon in A Few Good Men, so he has a Bacon number of two.

This theory that every actor can be connected to Bacon within six steps concerns the mathematical field of small world phenomena. Stanley Milgram first suggested that everyone on Earth is connected by a surprisingly small number of people when working at Harvard University in 1967. He sent packages to 160 random people in Omaha, US and asked them to forward the package to a friend or acquaintance who they thought would bring the package closer to a set final individual, a Boston stockbroker. The letter stated, “If you do not know the target person on a personal basis, do not try to contact him directly. Instead, mail this folder to a personal acquaintance who is more likely than you to know the target person.”

Milgram’s theory was that everyone is connected by on average six people – that is, even the Prime Minister is connected to rickshaw drivers in Thailand by six people. Whilst this may seem astounding, think about how many people you come across during your lifetime. Whilst I have never met the Prime Minister, I have met my local member of parliament which means I am only two steps from Rudd. Imagine that my local member has a son who travelled the world and visited Thailand – now the rickshaw driver is connected to the PM in only three steps. You only need to meet one well-connected person to be connected to almost everyone!

The concept of the Bacon number sprung from a similar idea surrounding the mathematician Paul Erdos. Erdos was an immensely prolific Hungarian mathematician who worked on a variety of problems from number theory to probability. He collaborated with so many other scientists that mathematicians invented the "Erdos number". You have an Erdos number of one if you directly collaborated with Erdos on a paper, an Erdos number of two if you worked on a paper with someone who collaborated with Erdos, etc.

The amusing consequence of all this is the "Erdos–Bacon number" which is the sum of your Erdos number and Bacon number. You would think that these two numbers would be completely separate – not many Hollywood stars have authored mathematical papers. However, thanks to a few movie and TV cameos, astronomer Carl Sagan has an ErdÅ‘s–Bacon number of nine, whilst theoretical physicist Stephen Hawking’s is seven. And most interestingly, thanks to her authorship of psychology papers during her Harvard degree, actress Natalie Portman also has an Erdos–Bacon number of seven!

Thanks to the fact that I was in our high-school production of Grease with my brother James, who had a role as an extra in the Australian gritty crime show Wildside, which starred Rachael Blake, who was in with Jennifer Aniston, who was in Picture Perfect with Bacon, I have a Bacon number of 4.

There are probably a few ways I could track back my Erdos number, but the easiest way is through Plus which I co-edit with Marianne Freiberger, who has an Erdos number of 4, making mine 5. There is probably another route back to Erdos through my chemistry work, but that is hard to track.

Therefore, my Erdos-Bacon number is 9. See if yours is lower. Here are some links to help:

1. Do High School Productions really count towards Bacon Numbers??

2. Ha - it was the only way I could think of getting one! It gives you the same as me - and thanks to Handled the Ball, you have an Erdos number of 6.

3. Indeed it is a number game.
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4. I feel very grateful that I read this. It is very helpful and very informative and I really learned a lot from it.
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