Friends and Strangers

This is a post for all you Facebook users out there...

At one time or another, you've probably heard of the so-called birthday paradox. Roughly put, if you grab 23 random strangers off the street, there's a 50% chance that 2 of them will have exactly the same birthday. It's an interesting property about the world. You can observe it yourself by looking through the birthdays of your friends on social networking sites like Facebook.

Perhaps more interesting is a cute theorem I read about today, similar to the birthday paradox. I found it after trawling a mathematics webcomic (yes, they exist), then linking to a page on Ackermann's function, then linking to Graham's number, then linking to Ramsey theory, and finally linking to the theorem on friends and strangers. This theorem says that "if you take 6 random people off the street, you can guarantee that either 3 are mutual acquaintances, or 3 are mutual strangers". Think of that next time you do a triple-date organised by a friend. No matter who else attends, you are guaranteed that 3 people there have never seen each other before, or that 3 people already know each other. Or both.

I will now return to my regular schedule of self-inflicted thesis pains...

P.S. You may have noticed the six-degrees of connection in the above text. I swear that was completely unintentional. ;)