What is six degrees of separation?

0:47 Welcome to Mass is not boring by Kidopoly.com. I'm Mira! And I'm Finn! If you haven't already, tap follow wherever you're listening so you never miss an episode.

0:59 So, Mira, what strange and wonderful thing are we looking at today?

1:04 Finn, I want you to imagine picking a completely random person anywhere on Earth. Someone you have absolutely never met, maybe living in a tiny village halfway around the world, going about their daily life right now.

1:20 Okay, let me think. I'm picturing a fisherman in a little wooden boat hauling up a net somewhere off the coast of Japan. Or maybe someone baking bread in a tiny flower-covered bakery in a little town in Peru. Perfect!

1:35 Now, what if I told you that you actually know someone who knows someone who knows someone who knows that exact fisherman in Japan? Or that exact baker in Peru.

1:47 Wait, what? No way! I don't know anyone who knows a Japanese fisherman. I just go to school, play in my neighbourhood, and hang out with my friends.

1:58 You might not know them directly, but you are connected to them and to every single other person on the planet by just a few invisible handshakes. Today we are looking at the math of how tiny our gigantic world really is, and the hidden web that ties every human being together. It feels impossible, but it is entirely true.

2:22 The math proves that nobody is truly a stranger. We call this beautiful idea a small world network, which is part of a bigger area of math called graph theory. It is the math of how things link together to form systems.

2:37 Graph theory. So it's not about measuring the actual Earth with a giant ruler. Or about figuring out the fastest walking route to get to Japan.

2:46 Exactly. It is absolutely not about walking routes, bridges, or distances on a map. It is entirely about who knows whom. A graph in this kind of math is just a picture of dots connected by lines. The dots are people, and the lines are friendships or acquaintances.

3:05 That makes sense. I'm a dot, you're a dot, and because we know each other, there's an invisible line between us.

3:12 You've got it! And the first person to really see this hidden pattern clearly wasn't even a mathematician. Really? Who was it? It was a brilliant Hungarian writer named Friges Corinthi. In the year 1929, living in the bustling city of Budapest, he wrote a short story called Chains.

3:32 1929! That's almost a hundred years ago. They didn't even have the internet or smartphones back then to connect people.

3:41 Exactly. But Corinthi noticed that trains and telegraphs were making the world feel faster. In his story, some friends are talking about how close everyone is getting. So they make a friendly challenge. One person says, I challenge you to pick anyone out of the one and a half billion people on Earth, and I can connect myself to them using at most five friends.

4:08 That sounds like a really fun game to play. Like saying, I know a guy who knows a guy who knows the president.

4:15 Exactly. And Corinthi was the very first person to write down this idea. He pictured human connections like interlocking chains spreading out across oceans and borders, linking every single person together in a giant web.

4:31 Okay, but hold on, Mira. I can see how I might be connected to someone in the next town over, because my aunt lives there. But the whole entire world. That can't be mathematically right.

4:42 Let's picture it out loud together. Think about how many people you know really well. Friends, teachers, family?

4:51 Well, I know my classmates, my cousins, the neighbours. Maybe I know about 50 people pretty well.

4:58 That's a great number. Now imagine that each of those 50 people knows 50 other people that you don't know.

5:07 Oh wow, okay. So if I just go two steps out to the people they know, that is 2,500 people.

5:16 See how incredibly fast it grows. By the time you go three steps out, that becomes a staggering 125,000 people.

5:26 My brain is already spinning. That's a whole stadium full of people, just three handshakes away.

5:32 Exactly. But for decades, people just thought Corinthi's idea was a neat story, a fun piece of fiction. Nobody knew if it was actually true in real life, because you couldn't possibly check everyone's friends.

5:46 Yeah, you'd have to ask millions of people who they know. It would take forever.

5:51 Right. Until 1967. That is when an American scientist decided it was time to find out the truth.

6:00 What happened in 1967? Who was the scientist?

6:04 His name was Stanley Milgram. He was a researcher who didn't just want to guess. He wanted to set up a massive real-world experiment to trace these invisible lines.

6:15 Did he travel around the world making people shake hands with strangers?

6:19 No. He used something much simpler: the mail. He picked one specific target man, a stockbroker living in the big city of Boston, Massachusetts. Then, Milgram handed out folders to hundreds of random people far away in the Midwest, in Omaha, Nebraska, and Wichita, Kansas.

6:41 Nebraska and Kansas are right in the middle of the United States. That is really far from Boston. How were they supposed to get the folders to him?

6:50 Here was the brilliant rule. They absolutely could not mail the folder directly to the stockbroker in Boston. They had to hand it, or mail it, to someone they knew personally on a first name basis, who they thought might be closer to the target.

7:08 Oh, I love this. It is just like passing a secret note in class, but across the whole country. You give it to your uncle who lives in New York, because New York is closer to Boston. And then he gives it to a banker he knows, because the target is a stockbroker.

7:25 You are thinking exactly the way they did. People looked at their friends and thought, who do I know that might know a stockbroker in Boston? And here is where we have to be really honest about the math.

7:39 Uh-oh. Did they cheat?

7:42 No, they didn't cheat. But most of those folders never made it to Boston at all. The chains just broke. People got busy, or they forgot, or they just didn't bother passing the folder on, and it ended up in a drawer.

7:58 Oh man, that is a little sad. So the web was broken.

8:03 The web wasn't broken, people just stopped playing the game. But wait, Finn, some of the folders did arrive. Milgum looked at the ones that successfully made it to the stockbroker, and he counted how many people they had passed through. How many?

8:20 Was it hundreds?

8:22 On average, the chains that completed had taken just five or six steps.

8:28 Wait, so Corinthi was right way back in 1929. It really was about six handshakes.

8:35 Yes. Now, scientists insist we remember that six is just the average for the ones that actually arrived, not a strict law for everyone. But it showed this absolutely incredible pattern. Even though the United States was huge, a few really well-connected people linked everyone together.

8:58 That is honestly kind of beautiful. We are all walking around in this giant invisible web, passing right by people who are secretly connected to us.

9:08 That giant invisible web is exactly what network theory studies today. And the amazing thing about this small world pattern is that it isn't just for people sending letters in the mail.

9:19 Where else does this hidden math live?

9:22 It explains how anything spreads through a network. It is the exact same reason why a funny joke you hear at recess can be heard by kids in a totally different country just a few days later.

9:34 Oh, because I tell my cousin, and he tells his friends at Summer Camp, and one of them lives in Canada, and they tell their whole school.

9:43 Exactly. It is how catchy songs get popular so fast, or even how a common cold spreads through an entire school in just one week. A few kids who have a lot of friends act like super connectors, tying everyone together.

10:02 One day someone sneezes in the cafeteria, and on Friday, half the class is blowing their noses.

10:09 It's all the same small world math. And here is a mind-bending fact to show you the sheer power of multiplying those connections. If you tell a secret to just ten people, and the next day they each tell ten new people, and the next day those people tell ten new people, how long do you think it would take until a million people know your secret?

10:31 Hmm, if it's just ten people a day, maybe a whole month or a year? It would take just six days.

10:40 The connections multiply so unbelievably fast that it hits one million.

10:45 Whoa, just six days to reach a million people. That makes me dizzy. So one single person really can reach the entire world incredibly fast.

10:56 They really can. The world is huge, but the math of networks pulls us all close together.

11:03 I am never going to look at a crowded street full of strangers the same way again. They aren't really strangers at all. They're all just friends I haven't clicked with yet. Alright, Finn, quiz time. Let's see what you remember about our invisible web. I am so ready. Bring on the questions.

11:20 First question. Who was the Hungarian writer who first wrote about this idea in 1929? Next one. What was the name of his short story? Question 3. In 1967, which American scientist tested the idea with folders in the mail? Here's number four. What city did the target person, the stockbroker, live in? Last question.

12:03 For the folders that actually arrived, about how many steps did it take on average? Great job, let's see how you did. The first answer is Frigas Carinthi. For question two, the short story was called Chains. Number three, the answer is Stanley Milgram. Question four, the stockbroker lived in Boston. And the final answer is it took about five or six steps.

12:37 That web of connections really is extraordinary, isn't it?

12:40 It really is. It makes this gigantic world feel so much cosier and less lonely. I love knowing that we are all linked up, no matter where we live.

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13:02 And please tap follow on this show so you never miss an episode. Oh, and we have sister shows too. History, science and philosophy is not boring. Go give those a listen and a follow as well.

13:14 Want your name on the show? Send us an email at hello at kidopoly.com. See you next time on Maths Is Not Boring. Bye everyone. Keep looking for those invisible lines!