George Szirtes mentions that Frigyes Karinthy was the first proponent of the concept of six degrees of separation (as confirmed by Wikipedia).
I thought about this once. Let's imagine two farmers, each of whom lives far out in the country in two different very large countries that are on opposite sides of the world from each other. Now, we can't be sure that each of these farmers knows the mayor of a town near where the farmer lives, but it's safe to assume that each farmer knows somebody who knows such a mayor. So we've got farmer-somebody-mayor on each end.
Now, we can't be sure that the mayor of a small town in the country in a large country knows the president of that country, but we can be pretty sure that said mayor knows some politician who knows the president. So now we've got farmer-somebody-mayor-politician-president on each end.
And the two presidents may not know each other, but each president knows his or her ambassador to the other country. So even with these two completely rural farmers (who may never go further than a few miles from their farms, say), the longest chain from one to the other is farmer-somebody-mayor-politician-president-ambassador, and then back down: president-politician-mayor-somebody-farmer.
So, six degrees of separation, perhaps. But you don't need more than ten degrees of separation to get from yourself to anybody else on earth.