The Handshake Theory
Every time two people shake hands for the first time, they bring two people closer together, they are now one handshake away from eachother.
What makes it more interesting is that they bring numerous other people closer to eachother as well. I once shook hands with Jiang Zemin, and my wife Maja once shook hands with Zbigniew Boniek. This means that Jiang and Boniek would be three handshakes away from eachother (we assume that Maja and I shook hands already).
But maybe they are even closer, I could imagine that there is someone who shooks hands with both Jiang and Boniek, for example Lech Walesa or the Pope, who knows? If so, they are two handshakes away, I don't think that they ever met personally so let's forget about one handshake.
Isn't this interesting? Especially big handshakers, such as presidents, bring people closer together.
I would be surprised if there are many people in the USA who are more than three handshakes away from Clinton and therefore five from me (I shook hands with a couple of people who met Clinton, so that is two "shakes").
And how about the whole world? I would guess that 99% of the world's population is within 10 handshakes, and maybe even less. There are of course some exceptions
(courtesy of a Danish friend called Ivan Nielsen, with whom I lost contact more than 10 years ago)