Six degrees of separation is the theory that everyone and everything is six or fewer steps away, by way of introduction, from any other person in the world, so that a chain of "a friend of a friend" statements can be made to connect any two people in a maximum of six steps.
For me, I had been dating my first ever boyfriend for about six months. I have no idea how we got on the subject, but I mentioned my mother and her maiden name which he kind of looked at me weird and said that it sounded familiar to him. He calls me later and he's like I know where I've heard that name. He asked his mom and turns out his mom and my aunt were both roommates and sorority sisters in college who had remained good friends.
Also in middle school I asked one of my really good friends to come and pick me up from my house for the first time. Gave him the address, and he's like, oh, you know what, I actually know very well where you live. Turns out his uncle lived right across the street from me longer than I'd actually known my friend.
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Well, I attended a pretty small high school in a different city than where I live (I commuted by train) and it just so happened that the guy I always used to ride the train with in my first year was the son of a couple who were old friends of my parents. My parents and that guy's parents had been hanging out a lot in their early and mid 20s. It was quite remarkable that this guy and I were not only in the same grade but also in the same class (in Switzerland we only have one fix class, you're always together with the same people rather than meeting different people depending on whether you're having a math lesson or a history lesson). And we even rode the train together... so that was kinda cool.
However, generally speaking I don't believe in this six-steps idea. For example I got to know my girlfriend through an absolutely incredible coincidence when she spent one year in my country Switzerland as an exchange student. She was born and lived all her life in South Korea. I have no idea how she and I could possibly be connected through 6 or less steps. None of her friends or family members have ever been to Switzerland. In fact, some of them have never been to Europe at all. As far as I know, they also don't have any European/western friends or acquaintances (at least her family members don't). It doesn't seem very likely that you could somehow find a connection of only 6 steps between her and me... except maybe if you include stuff like "that waitress at the airport restaurant I once had a 1-minute chat with 15 years ago).1