What about the Six Degrees of Kevin Bacon?
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As u/tdscanuck stated there is some basic math that says it’s likely that two people have connections in less than X steps where X usually is about six.
In practice it’s a little trickier in the sense that pretty clearly it’s not true that everyone is connected, there are many uncontacted tribes for example if you take “everyone in the world” literally.
The famous experiment that most people vaguely know about is Milgram’s small world experiment. Basically what he did was send letters to random people in one city and say basically “hey do you know Cheatersfive in Boston? If you do, send this letter to him. If you don’t, send it on to someone who you think might know him”. Then he counted the number of jumps it took. On average, it took about six jumps. The big caveat being that it took six jumps for the ones that made it. Most of them never returned. There are various recreations of this. You can look up “small world experiments” and find a bunch.
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