Six degrees of separation?
In light of the estimated world population passing 6,666,666,666 a couple of days ago, and partially inspired by the inter-character linkages in the movie Love Actually, which I just happened to watch again last night, I got to thinking about the mathematical possibility of the six degrees of separation concept.
So, let's pretend for a moment, that every person on the planet has the same number of unique distinct people that they are "in contact" with. Let's define α to be that number. So if we let n be the number of degrees of separation, then the upper-bound of the total number of people within n degrees can be given by:
αn = α × α × ... × α = αn