Why we're all connected by fewer than six people

HostIt happens to almost everyone. You meet a stranger in a different city and realize you both know the same person. We usually just call it a small world and move on, but there's actually a lot of math behind why that happens.

HostBack in the sixties, there was a famous study where people had to send a physical folder across the country to someone they had never met. How could they possibly know who to send it to?

GuestIt sounds like a needle in a haystack. A researcher named Stanley Milgram wanted to see just how many handshakes it takes to link any two people in the country. He started with a group of regular folks out in Nebraska and Kansas. He gave each of them a folder and a target person: a stockbroker who lived all the way in Boston. The rule was that they couldn't mail the folder straight to the broker. They had to mail it to someone they knew personally on a first-name basis who they thought might be just a bit closer to that guy in Boston. Then that next person would do the same thing.

HostThat sounds like a total shot in the dark. If someone handed me a folder today and told me to get it to a guy in a city I have never visited, I would've no clue which friend to pick. Did those folders actually make it?

GuestA lot of them did not. There were plenty of dead ends where the chain just stopped and the folder sat on a desk somewhere. But for the folders that did reach the stockbroker in Boston, the results were wild. The middle number of people it took to get the folder from a random person in the Midwest to that one specific guy in the East was only about five. That's where we get the famous phrase six degrees of separation. Even before the internet, it turned out we were all much closer than we thought.

HostI have to wonder about those dead ends, though. If a lot of the folders got lost, does that five or six number really tell the whole story? It feels like the folders that made it might have just been lucky.

GuestThe dead ends happen because people lose interest, but the paths are still there. There's a deep reason why these chains are so short, and it's something called the strength of weak ties. Think about your best friends. You all probably hang out in the same spots and know the same people. In terms of reaching the wider world, your close friends are kind of overlapping. The real power comes from people you just sort of know. Maybe it's someone you see at a coffee shop or an old classmate.

HostSo the people I barely know are actually more important for this than my actual friends? That feels backwards.

GuestIt does, but those people you only sort of know are the ones who act as bridges. Your best friend might not know anyone in Boston, but that guy you worked with once five years ago might have moved there. These people allow a message to jump from a small group of friends in one state to a whole different circle in another city in just one or two steps. They're the shortcuts that collapse the distance of the entire human population. They take you out of your own little bubble and link you to a different one.

HostOkay, but even with these bridges, the world is huge. There are billions of us. It's hard to wrap my head around the idea that some simple math can make every single person reachable in just six steps.

GuestTwo mathematicians looked at this in the late nineties and found it's actually bound to happen. They showed that in any big web, whether it's a power grid or the way nerves are wired up in a worm, you only need a tiny few of these random, long-distance links to make the gap between any two points shrink. Even if almost everyone you know lives in your own town, one person you know who moved to London makes everyone in London reachable to your entire town in just a couple of hops. This small world structure is just how complex systems set themselves up to be fast.

HostI can see how that works for a country, but it still feels like the number six is a bit low for the whole planet. Does this actually hold up when you look at billions of people across different countries?

GuestIt turns out that six was a very safe guess. When scientists finally got to look at data from hundreds of millions of people on Facebook, they found the world had become even smaller. In 2011, the gap between any two people on the site was about four point seven. By 2016, as more people got online and we all became more linked, that number dropped again. Now, the middle number of steps between you and any stranger on Earth is only about three and a half.

GuestThe average gap between any two people on the planet is now just three or four handshakes, which means you're likely connected to almost any stranger on the globe through just a few people.

HostThe folders from Nebraska had a long way to go in the mail, but the invisible path between those people was already much shorter than they ever realized.