Frank Ramsey is all kinds of awesome. A mathematician who died far too young … but honestly, I really can’t begin a post like this without mentioning the fact that Frank Ramsey’s brother became the Archbishop of Canterbury.
I’m glad I got that out of the way.
Now, Ramsey is responsible for this branch of discrete math that is best exampled I think by the following problem – it also serves as a very nice example of the probabilistic method.
To begin with – next time you’re at a party or a bit of a get together, it probably goes down something like this. You walk in, say hello to the host, grab some drinks, wander, pet the dog, smile at people you think you’re supposed to know, brush the dog hair off your pants, then you see a group of people you know, and you wander over and chat with them for a bit. Note though that this is a mathematically ideal party, in that we assume if you know someone, they also know you : )
Of course, if you look around, you’re likely to see many such groups, of varying sizes, groups of mutual friends all saying nasty things about the people in your group.
Cliques, in a word.
The issue at hand is the -size- of the groups.
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