You have probably heard the phrase “six degrees of separation,” the idea that you’re connected to everyone else on Earth by a chain of just six people. It has inspired a Broadway play, a film nerd’s game, called “Six Degrees of Kevin Bacon”...and even a No Doubt song! But is it true? In the ‘90s, two mathematicians set out to discover just how connected we really are—and ended up launching a new field of science in the process.
GUESTS
- Duncan Watts, Principal Researcher at Microsoft Research, author of Six Degrees: The Science of a Connected Age
- Steven Strogatz, Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, author of Sync
- Andrew Leifer, Assistant Professor in the Department of Physics and the Princeton Neuroscience Institute at Princeton University
FOOTNOTES
- Read Duncan Watts’ and Steven Strogatz’s breakthrough 1998 Nature paper on small-world networks.
- Read Stanley Milgram’s 1967 article about his letter experiment in Psychology Today.
- Watch Duncan and Steve discuss the past and future of small-world networks at Cornell.
- Watch C. elegans' brain glow! And read more about the brain imaging work happening in Andrew Leifer’s lab.
- Browse the small-world network of C. elegans’ 302 neurons at wormweb.org.
- Read Facebook’s analysis of Facebook users’ “degrees of separation.”
- Just for funsies, a network analysis of Game of Thrones.
CREDITS
This episode of Undiscovered was reported and produced by Annie Minoff and Elah Feder. Editing by Christopher Intagliata. Fact-checking help by Michelle Harris. Original music by Daniel Peterschmidt. Additional music by Podington Bear and Lee Rosevere. Our theme music is by I am Robot and Proud. Art for this episode by Claire Merchlinsky. Story consulting by Ari Daniel. Engineering help from Sarah Fishman. Recording help from Alexa Lim. Thanks to Science Friday’s Danielle Dana, Christian Skotte, Brandon Echter, and Rachel Bouton.
EPISODE TRANSCRIPT
Undiscovered is produced for your ears! Whenever possible, we recommend listening to—not reading—our episodes. Important things like emotion and emphasis are often lost in transcripts. Also, if you are quoting from an Undiscovered episode, please check your text against the original audio as some errors may have occurred during transcription.
ELAH FEDER: I’m Elah.
ANNIE MINOFF: And I’m Annie. And you’re listening to Undiscovered, a podcast about the backstories of science.
ELAH FEDER: <<whispering>> Oh my god, is this Stanley Milgram’s writing?
ANNIE MINOFF: <<whispering>> I think so!
ANNIE MINOFF: So a few months ago, Elah, you and I took this trip to Yale University to root around in the archives of Stanley Milgram.
ELAH FEDER: We did, and we had to whisper, because you know, library.
ANNIE MINOFF: Rules.
ANNIE MINOFF: <<whispering>> He had really. Good. Handwriting.
ANNIE MINOFF: Stanley Milgram was a social scientist in the ‘60s and ‘70s. And if you know him, it’s probably for some pretty memorable research that he did with a fake shock machine.
ARCHIVAL AUDIO (MAN’S VOICE): Answer. <<buzzer>> Wrong! 150 volts!
ARCHIVAL AUDIO (SECOND MAN’S VOICE): Ahhh!
ANNIE MINOFF: Yeah. So Milgram was the guy who showed that we will totally shock strangers with what we think are a hundred fifty volts of electricity because someone in a lab coat asked us to.
ELAH FEDER: But not all of Milgram’s experiments were quite this disturbing.
ANNIE MINOFF: Not all that dark.
ELAH FEDER: Relatively speaking some of them were kind of warm and fuzzy! Like in the sixties, he got curious about how connected Americans were. So to find out, he writes a letter.
ANNIE MINOFF: <<whispering>> Oh here we go. Alright.
ELAH FEDER: <<whispering>> We are looking at the communications project mailing. This is what they sent out to people.
ANNIE MINOFF: And it says, “We need your help with an unusual scientific study…”
ANNIE MINOFF: Milgram picks some random people in Kansas. Sends them this kind of strange letter. And he gives them a challenge. Can they get this letter to a stranger halfway across the country?
ELAH FEDER: Right. And not just any stranger. Alice Mahan. Former schoolteacher, resident of Cambridge, Massachusetts.
ANNIE MINOFF: So the catch is that they can’t just send the letter to Alice. They have to send it to someone who they know personally. And like, first name basis personally. Because the idea is you’re sending it to someone who’s gonna help you get the letter to Alice through a chain of people.
ELAH FEDER: Right. So for example, I get the letter, I send it to my former landlord... who is very surprised to hear from me! <<laughing>>
ANNIE MINOFF: A little out of the blue...
ELAH FEDER: She sends it to her college roommate and so on, who sends it to Alice Mahan. That’s one way this could happen.
ELAH FEDER: <<whispering>> Your help is greatly appreciated. Sincerely, Stanley Milgram. Yeah, this, this looks like spam.
ANNIE MINOFF: June Shields in Wichita, Kansas does not think this is spam.
ELAH FEDER: <<whispering>> She decided to send it to Augusta in New York...
ELAH FEDER: Who sent it to Robert, who sent it to Meg…
ANNIE MINOFF: <<whispering>> Sent it to Florence...Manamaka.
ELAH FEDER: <<whispering>> Macnamara.
ANNIE MINOFF: Macnamara! <<laughs>>
ELAH FEDER: It looks like it took a chain of ten people to get this particular letter to Alice. But Milgram found that a lot of the time, the chains were shorter. Across the entire experiment, he found the average number of links between two randomly-selected Americans...was 6. 6 links.
ANNIE MINOFF: 6 degrees of separation. So maybe you haven’t heard of Stanley Milgram? I’m willing to bet you have heard of 6 degrees of separation. Because it’s kind of become this pop culture meme.
6 DEGREES MOVIE AUDIO: I read somewhere that everybody on this planet, is separated by only 6 other people. 6 degrees of separation…
ANNIE MINOFF: That is Stockard Channing. She is playing the upper-east-side sophisticate Ouisa Kittredge in the movie, 6 Degrees of Separation, based on the broadway play.
ELAH FEDER: There’s the film geek’s game, 6 degrees of Kevin Bacon...
ANNIE MINOFF: There’s actually a No Doubt song about this…
NO DOUBT SONG: <<singing>> Six degrees of separation, we all know someone else. It all comes full circle...
ANNIE MINOFF: And somewhere along the line, it’s like we forgot to ask. This whole 6 degrees thing—is it even true? I mean are we really gonna extrapolate from a few chain letters in the 1960s, to the entire world’s social connections?
ELAH FEDER: Today on the show: Do we live in a 6 degrees world. The people who figured this out were actually two mathematicians. They cracked this problem in a world before Myspace, before Linkedin, before Facebook. And not only did they figure this out, they created a new scientific field in the process.
ANNIE MINOFF: That’s all coming up, on Undiscovered.
NO DOUBT SONG: <<singing>> Six degrees of separation, we all know someone else. It all comes full circle…
****************
ELAH FEDER: So, it’s 1995. The 6 Degrees of Separation” movie had come out a few years earlier. I personally loved it. Didn’t make a lot of money <<laughing>> but most people did think Will Smith did a good job.
ANNIE MINOFF: And this summer, the summer of ‘95, a graduate student named Duncan Watts is in Ithaca New York. He’s studying math at Cornell. Duncan’s from Australia...
DUNCAN WATTS:….Grew up in a, in a small town in Queensland called Toowoomba.
ANNIE MINOFF: He moved to the U.S. not knowing anybody.
ELAH FEDER: And this is the dark ages. It’s 1995! Which means you can’t just Skype home.
DUNCAN WATTS: I used to write letters. I would type them up and then I would make, you know, thirty photocopies and then take them all to the post office, because the phone was over a dollar a minute.
ELAH FEDER: To make things worse, Duncan’s research, it doesn’t exactly lend itself to an active social life. In the summer of 1995, he’s studying a bug. Actually, the sound of a bug.
DUNCAN WATTS: I’ll do my best to to simulate it. It’s sort of a <<burrrp burrrp burrrp burrrp burrrp>>
ANNIE MINOFF: That is Duncan’s best snowy tree cricket. So snowy tree crickets have a reputation in the bug world, because they do one thing extremely well. They all chirp in perfect sync. Perfectly together.
<<crickets chirping in sync>>
ELAH FEDER: Duncan wanted to figure out how they achieve this perfect sync by measuring how the crickets space out their chirps. He actually has a stable of these little guys. These live crickets that he caught in the Cornell orchard….
ANNIE MINOFF: And named!
DUNCAN WATTS: Started calling them Hercules and Prometheus and Odysseus…
ANNIE MINOFF: Get it? Because Odysseus was from Ithaca, in Greece? Duncan’s in Ithaca, New York? That is a grad student joke.
ELAH FEDER: Mm-hm very good. So snowy tree crickets they only chirp at night. Which means that suddenly, Duncan’s spending a LOT of his evenings holed up in the lab with Odysseus, in this totally sound-proofed room, measuring cricket chirps.
DUNCAN WATTS: And some nights, nothing would happen. The cricket would, you know they get kinda freaked out sitting there by themselves in a soundproof chamber and so they wouldn't chirp.
ANNIE MINOFF: How long do you wait?
DUNCAN WATTS: I would wait for hours! You know I was just sitting there in the dark, by myself. <<Laughs>>
ELAH FEDER: Those nights, Duncan did a lot of thinking and one of the things he thought about was something his dad said on one of those calls to Australia.
DUNCAN WATTS: My dad just mentioned very much off the cuff, he said have you ever heard of this, this idea that you're only 6 handshakes away from the President of the United States? And I hadn’t heard of it, but he said you know you've shaken hands with someone, who's shaken hands with someone, who's shaken hands with someone, who's shaken hands with the president, and the claim is that that number is never more than 6.
ANNIE MINOFF: Duncan’s never heard of Stanley Milgram. He hasn’t seen the 6 degrees movie. He is totally captivated by this idea. Because it sounds like a math problem.
DUNCAN WATTS: I wonder if it’s true. I wonder if you could prove that it’s true. And I wonder if it matters?
ELAH FEDER: Is it true that we’re all 6 handshakes away from each other? And does that matter? That’s the question. And maybe it’s because Odysseus is right there in front of him, refusing to chirp. But to Duncan, these completely unrelated things—6 degrees, the crickets—They start to sound….related. Okay so here’s Duncan’s line of thought. And if this sounds a little nuts, just imagine yourself slowly unraveling, in a soundproofed room.
ANNIE MINOFF: So according to this 6 degrees idea, everybody on earth—and this is 1995 so we’re gonna round up, it’s gonna be 6 billion people—they are spread out across different continents and language groups. But that distance is actually deceptive. Because we’re really all just six handshakes away from each other. But then if you accept for just a second that that’s true for people, why couldn’t it be true for crickets?
<<cricket chirping>>
ELAH FEDER: Say, you’ve got a tree full of crickets, and they’re all chirping in sync. What if every cricket in that tree is just a few chirps away from any other cricket in that tree? Like a 6 degree cricket communication network? Is that the secret to how they sync up so well?
ANNIE MINOFF: And if humans and crickets might be organized in these 6-degree networks….What else might be?
DUNCAN WATTS: I thought, “Ok I’m going to tell Steve about this.” You know, “I got to tell him.”
STEVE STROGATZ: Duncan one day, banged on my door the way he used to do, and I was probably locked in my room in my office, playing chess on the internet <<laughs>> hoping he would go away! <<Laughs>> But he would bang very insistently, <<Steve does an Australian accent>> “Steve I know you're in there!”
ANNIE MINOFF: Steve is Steve Strogatz. He’s a Cornell math professor and Duncan’s PhD advisor. He is no stranger to Duncan’s kind of out-there ideas. And true to form, Duncan bursts in, and he’s like, “Steve! Have you heard this thing about how we’re all 6 handshakes away from the president?”
ELAH FEDER: And Steve’s like “Yeah, I saw the movie with Will Smith.”
ANNIE MINOFF: In fact, the whole idea of 6 degrees, it had stuck with Steve too!
STEVE STROGATZ: It was an astonishment to me. More than the movie which was fine, but this idea that was in the movie and on which the movie was based seemed... kind of tantalizing and incredible!
ANNIE MINOFF: He’d thought what Duncan had thought. 6 Degrees? That’s a math problem.
STEVE STROGATZ: Like why is the number so small, how does it work. And I thought that’s what he was suggesting but then he took it much farther than I had— I mean my vision was quite constricted compared to his.
ANNIE MINOFF: Because Duncan wasn’t just asking “Are we all 6 handshakes from the President?” He was asking a much bigger question. Is it a big, disconnected world, or is it a small, hyperconnected world?
ELAH FEDER: Not just for people,or crickets, or social relationships, but for all kinds of networks.
ANNIE MINOFF: Take banks for example. If banks borrow and lend in a 6 degrees network, does that explain how a financial crisis in Thailand bankrupts a hedge fund in Connecticut?
ELAH FEDER: Or take pandemics. If we live in a 6 degrees world, does that explain how a virus from Africa, crops up in Haiti, hits LA and New York, and becomes the global AIDS crisis.
ANNIE MINOFF: Could understanding 6 degrees actually lead to better disease models? The implications could be big.
ELAH FEDER: So now Steve’s excited too.
STEVE STROGATZ: This was a revolution in front of my eyes if it could be pulled off.
ANNIE MINOFF: But that’s a big if. For one thing, if you were gonna put money on who’s gonna discover the network theory of everything? You would not put it on Steve and Duncan.
ELAH FEDER: Steve’ll tell you himself—he’s not a network guy. This isn’t his area of math. His area is something called dynamical systems.
STEVE STROGATZ: I thought we’re gonna be out of our depth. He didn’t, Duncan didn’t— wasn’t even an expert in anything! He’s just a grad student, you know, very smart but...So I kind of wanted to take a chance on this, but I also knew that it verged on crackpot, you know, -ism <<laughs>>
ELAH FEDER: So Steve made a compromise. They’d work on 6 degrees, but they wouldn’t tell anybody. And if they ran into a brick wall? It was back to the soundproofed room, and little Odysseus.
ANNIE MINOFF: So putting aside crickets, and diseases, and banks for just a second. Just looking at people: Are we all connected by 6 degrees? Is it a small world, or is it a big world?
ELAH FEDER: And to figure that out, you need a map, right? You need a map of the world’s social connections. And today we have that for about a quarter of the world. It’s called Facebook.
ANNIE MINOFF: Ta-dah!
ELAH FEDER: But In January of 1996, Duncan and Steve, they don’t have Facebook. So they don’t have a map. Their first step is to change the question.
DUNCAN WATTS: So rather than asking “What does the actual world look like?” We said “Let’s imagine a whole universe of worlds.”
ELAH FEDER: Duncan and Steve decide to do a thought experiment. They’re gonna imagine—mathematically—every way that 6 billion people on earth could be networked together. And then they’ll say, “Hey. Do any of these networks look like that world Duncan’s dad was talking about. Where everyone is just six handshakes from the president?”
ANNIE MINOFF: And they started by imagining the two most extreme ways 6 billion people could be networked together. The theory is, you imagine the extreme ends of the spectrum, then you can ask what’s in the middle.
ELAH FEDER: Extreme world number 1? Was a place called ring world. Here’s Steve.
STEVE STROGATZ: So imagine the 6 billion people all gathered in some enormous playground. And the teacher has told them everybody stand in a circle and hold hands.
ANNIE MINOFF: So for some reason, when Steve was describing ring world, all I could think about was that seventies commercial “I’d like to Buy the World a Coke”? Which if you haven’t seen it it features these beautiful young people, they’re from all over the world, all nationalities. They’re gathered on this hillside, smiling and singing about Coca Cola…
<<Singing: I’d like to buy the world a Coke, and keep it company. That’s the real thing...>>
ANNIE MINOFF: And that’s sort of the idea with ring world. You gather all of humanity onto this one hillside, and everyone stands in a circle and holds hands.
ELAH FEDER: Right except this is everyone on Earth so the circle’s about a billion miles wide…
ANNIE MINOFF: It’s a thought experiment, okay?
ELAH FEDER: Okay.
ANNIE MINOFF: So, say you are one of these smiling young people in ring world in this big, big ring. Your network is the hundred people closest to you in this ring. So if you yell, the fifty people to your left are gonna hear you, the fifty people to your right, but no one else. So those hundred people— That’s everybody you know.
STEVE STROGATZ: And now you could ask, in the world like that, if the world were like that, would it have the 6 degrees of separation property. And the answer is clearly, no it will not.
ANNIE MINOFF: So so here’s how I think about it. If I am living in ring world, and I wanted to say “hi” to someone who’s like two hundred people to my left? The way that would work is I would yell “hi” to my fiftieth friend, like the furthest person who can hear me on the left. They would yell “hi” to their fiftieth friend, and it would keep going like that kind of like a game of telephone….
ELAH FEDER: So four times...
ANNIE MINOFF: Four times, until I got to person two hundred.
ELAH FEDER: Okay.
ANNIE MINOFF: That’s just four people right? That’s four degrees of separation. But say I wanted to say “hi” to the person ACROSS the ring from me, millions of miles away.
STEVE STROGATZ: <<chalk writing on blackboard>> seven...Which in plain language would be sixty million. Is that the number you also got?
ANNIE MINOFF: Yeah.
STEVE STROGATZ: Sixty million steps to the most distant person.
ANNIE MINOFF: That is sixty million degrees! So ring world is not a 6 degrees world. It is a sixty million degrees world.
ELAH FEDER: But that’s ok! Because we’ve got other options here that’s just one extreme of the spectrum.
ANNIE MINOFF: Right.
ELAH FEDER: On the other end, we’ve got another, equally bizarre option to consider. This is extreme world number 2. Welcome, friends, to random world.
STEVE STROGATZ: Let's just imagine it'd be sort of like you could do a lottery? And out of the 6 billion, you know, a hundred names are drawn out of one of those things with the ping pong balls that you see <<laugh>> every night on the news?
TV ANNOUNCER: All right America, we have the number eleven! <<ping pong balls jostling in a machine>>
STEVE STROGATZ: So they’re there! The hundred, you know, ping pong balls have come out and those are now your hundred friends and have fun with them. Ok!
ANNIE MINOFF: In random world, your best friend could be a tribesman in the Amazon. Maybe your mom is a nurse in Oslo. And your spouse is a magazine editor in Malaysia. And because all your connections are coming out of a pinball machine, the chances that any of these people know each other are just really really low. So random world might feel like this big, disconnected world.…
ELAH FEDER: I mean, your spouse is in Malaysia….
ANNIE MINOFF: True. But in degree terms? This world is actually small. It is is hyper-connected. Because it’s not like you know the ring world we just talked about where you’re just hanging out with your friends in your little corner of the ring. In random world, your connections span the globe. So you can hopscotch around this global network, and within a few links, you have reached….everybody.
ELAH FEDER: Think about it. In random world, If I have a hundred friends, and each of those friends has a hundred friends…
ANNIE MINOFF: So that’s like a hundred times a hundred…
ELAH FEDER: Right. So by the time that I’m looking at people who are 5 degrees away from me? My network is…
STEVE STROGATZ: Ten billion people! Which is more than the number of people on earth.
ELAH FEDER: Game over right? Steve and Duncan, they were trying to imagine a 6 degrees world, a world that is hyperconnected, where we’re all just a few handshakes away from each other.
ANNIE MINOFF: Game over!
ELAH FEDER: We’re done!....We’re not done.
ANNIE MINOFF: Just one problem.
DUNCAN WATTS: It’s just not true. It’s a ridiculous model of the world.
ANNIE MINOFF: Random world works fine as a thought experiment. You don’t live there.
ELAH FEDER: Random world assumes that none of your friends know each other. And that’s obviously not true. In fact, most of our social networks? Pretty ring world-y.
ANNIE MINOFF: Meaning they’re cliquish. Case in point. So I went to visit Steve, Duncan’s advisor, the math professor at Cornell. And he has this really nice office, it’s on the fifth floor of the math building. And if you think about it, the fifth floor is kind of like a little corner of ring world. Right like nobody’s holding hands, but all of these professors know every other professor on the hall. They teach the same students. They probably went to the same grad schools...
STEVE STROGATZ: We shop at the same places, we go to the farmers market together. Our dogs are in the same doggy daycare, and our kids <<laughing>> are in the same kiddie daycare!
ANNIE MINOFF: Because Ithaca is a small town. There are no small towns in random world!
ELAH FEDER: So the real question isn’t, “Can we imagine a 6 degrees world?”
ANNIE MINOFF: We just did.
ELAH FEDER: It’s “Can we imagine a 6 degrees world that actually LOOKS like ours?”
ANNIE MINOFF: That’s cliquish AND connected. So we’ve got our 2 extreme ends of the spectrum, right. We’ve got ringworld, where everyone’s kind of sweatily holding hands in this giant ring. Then we’ve got random world, where your spouse comes to you from the lottery, which is terrifying. <<Elah laughs>> All the worlds that can possibly exist, exist between these two extremes. So the question is….
DUNCAN WATTS: What do they look like in the middle?
ANNIE MINOFF: Duncan Watts.
DUNCAN WATTS: So you start with ring world, and then you say, I’m going to mess with it a little bit.
ANNIE MINOFF: Ring world exists as this list of network connections in Duncan’s computer. So he can tweak it, he can run computations on it. And Duncan and Steve tweak ring world. They give just a few people in that billion mile-wide ring a friend across the ring.
ELAH FEDER: So you can think of this as like an “out-of-network friend.” Like the nurse in Oslo. None of your friends actually know this person.
ANNIE MINOFF: And what happens when you give ring worlders just a few random friends?
STEVE STROGATZ: Well, the world effectively instantly became small.
ANNIE MINOFF: Suddenly Ringworld doesn’t have sixty million degrees of separation. More like 6.
STEVE STROGATZ: It was, you just needed to put in the slightest sprinkling of randomness and BAM, the world was suddenly small.
ANNIE MINOFF: This is Duncan and Steve’s discovery about small worlds: They can totally exist. All it takes is a few random connections. And we all have them. Including those math professors on the fifth floor.
MATHEMATICIAN 1: My friend Chandor is in software in Budapest, Hungary.
MATHEMATICIAN 2: My old college roommate…
MATHEMATICIAN 3: The midwife that delivered my first daughter…
MATHEMATICIAN 4: My uncle Art…
MATHEMATICIAN 5: Henrich
MATHEMATICIAN 6: Philip
MATHEMATICIAN 7: Nargis Khoshnood
MATHEMATICIAN 8: ...is an electrical engineer and judo enthusiast...
MATHEMATICIAN 4: ...a former truck driver...
MATHEMATICIAN 9: ...artist and gallerist...
MATHEMATICIAN 1: ...in Cape Town South Africa…
MATHEMATICIAN 2: ...Florida...
MATHEMATICIAN 5: ...in Warsaw.
ELAH FEDER: One hallway in Ithaca connects to Budapest, Cape Town, Warsaw...To Judo enthusiasts, midwives, and truck drivers. That’s just 1 degree of separation.
ANNIE MINOFF: Duncan and Steve proved mathematically—without any real world data—that these clique-ish, connected small worlds can exist. And today, we know they do. Last year, Facebook data scientists crunched the numbers. They found that on average, every Facebook user connects to every other Facebook user in about 5 degrees.
ELAH FEDER: The world of human social connections—of people on Facebook anyway?—It’s small. Really small. But for Duncan and Steve in 1996, Facebook is still twenty years away. So right now, all they’ve proven is that small worlds can exist. As a thought experiment.
ANNIE MINOFF: They can model a 6-degrees world. It is sitting in their computer. They can imagine it. Now? They have to FIND ONE. In the real world. Coming up, we find a small world network. And I mean really small.
ANDREW LEIFER: Like when I trim my beard?
ANNIE MINOFF: It's like smaller than the little hair bits?
ANDREW LEIFER: Yeah exactly.
ELAH FEDER: After the break.
***************
ANNIE MINOFF: So at this point, Duncan and Steve have modelled a 6 degrees world. This model is sitting in their computer. It is cliquish like ring world, it’s connected like random world….
ELAH FEDER: And it’s still totally theoretical. Duncan and Steve haven’t actually found one of these small world networks in the real world.
ANNIE MINOFF: But eventually, you know, they do. And if you live in New York City, you actually wanna see one of the small world networks that Steve and Duncan found—like look at it, visually—you don’t even have to go that far. I went to New Jersey! To Andrew Leifer’s lab, to look at some very tiny worm brains.
ANDREW LEIFER: So this is kind of the wet lab area…
ANNIE MINOFF: Andrew’s a neuroscientist at Princeton. The worms he’s about to show me are a kind of roundworm called C. elegans.
ANDREW LEIFER: They’re really small. Like when I trim my beard?
ANNIE MINOFF: It's like smaller than the little hair bits?
ANDREW LEIFER: Yeah exactly.
ANNIE MINOFF: C. elegans really does look like a little white beard shaving. It’s small, it’s transparent. And most important for Andrew’s purposes, its brain is stupid simple. Which makes it one of the easier brains to study.
ELAH FEDER: So if you compare it to your brain, which has about eighty-six billion neurons? C. elegans has exactly three-hundred and two.
ANNIE MINOFF: And in Andrew’s lab, those worm neurons, they come with a bonus feature. Thanks to a jellyfish gene, they glow!
ANDREW LEIFER: <<setting up microscope>> Go ahead and take a look.
ANNIE MINOFF: Under the microscope, C. elegans looks a little less like a beard hair and more like a worm.
ANDREW LEIFER: And you can zoom in if you like…
ANNIE MINOFF: And I’m focusing in on this big fat one, when Andrew flips off the microscope light.
ANDREW LEIFER: You shouldn’t see any head glowing? But now when I turn it off, now the neurons in the head should—
ANNIE MINOFF: Oh my God!—
ANDREW LEIFER: glow green.
ANNIE MINOFF: Everything goes dark, and where that worm’s head used to be, are these teeny tiny points of glowing green light against this of field of black. Three hundred and two of them. I am looking at C. elegans’ brain.
ANNIE MINOFF: Yeah….
ANDREW LEIFER: So so each green speck is a different neuron.
ANNIE MINOFF: It’s like a little, a little cosmos in there.
ANNIE MINOFF: These tiny green stars are individual neurons. And right now—incredibly—I am looking at Duncan and Steve’s discovery. Because C. elegans’ brain? It’s not just small. It’s a small world network.
ANNIE MINOFF: So do we know why this worm’s brain might be a small world network?
ANDREW LEIFER: Yeah so that's a really good question.
ELAH FEDER: Which is what scientists say when the answer is, “We don’t know.” And we don’t. Maybe it’s just chance.
ANNIE MINOFF: But Andrew did mention another possibility. So when I was looking at these worms through the microscope, they kept kind of wiggling unhelpfully out of the frame. Because apparently microscope lights are kinda hot and uncomfortable if you’re a worm. But just that little movement takes this network of sensory neurons talking to this network of motor neurons, saying, like, “Hey guys, this is kind of hot and uncomfortable! Let’s move away from that!” And that communication has to happen really fast.
ELAH FEDER: One of the ways that you get that fast, efficient communication? Small world networks.
ANDREW LEIFER: ...And so small world networks might be a really good balance between having local communications but then also syncing up with the, with the larger network.
ANNIE MINOFF: So the reason I went out to New Jersey to look at this particular worm’s brain is because back in 1996, Duncan and Steve didn’t have a network diagram for the world’s social connections. They couldn’t just crunch the numbers the way a Facebook data scientist could today. What they did have was the wiring diagram for C. elegans’ brain.
ELAH FEDER: Because it was sitting on a floppy disk in the Cornell library.
ANNIE MINOFF: And when they analyzed that network of neurons? It was clique-ish AND connected. Every one of those three hundred and two neurons was just a few synapses away from any other neuron in the brain.
ELAH FEDER: Which meant that small worlds weren’t just something Duncan and Steve conjured up in a computer. They actually existed in the real world. In fact, it turns out, they were everywhere.
ANNIE MINOFF: In June of 1998, Duncan and Steve reported their discovery in the journal Nature. And that’s when small worlds BLEW UP.
ANNIE MINOFF: I mean could you say that this paper was kind of one of the key papers in pushing networks to the fore in science?
STEVE STROGATZ: Well I can’t say that! <<laughing>> You can say that! But the truth is, leaving any modesty out the door, this paper started the network revolution.
ANNIE MINOFF: Soon researchers, they were finding small worlds in places Duncan and Steve hadn’t even imagined.
STEVE STROGATZ: This ranges from the boards of fortune five hundred companies, to food webs of who's eating who in some pond. You can look at structures of language and what words are connected through common associations. Even characters in comic books? So people have done silly kind of whimsical studies of the small world of the Game of Thrones...
ANNIE MINOFF: This was a new field. Network science. And it wasn’t just about spotting small worlds. It was about answering that question that Duncan had asked all those summers ago in ‘95. If we live in a 6 degrees world, does that matter?
ELAH FEDER: And the answer seems to be yes. It does matter. It mattered in 2014, during the ebola outbreak. In a small world, an outbreak anywhere has the potential to be an outbreak everywhere.
ANNIE MINOFF: That’s why epidemiologists, they’re actually using network science to design better disease models.
ELAH FEDER: And it matters in transportation, like figuring out how efficient a subway network is.
ANNIE MINOFF: It also matters to psychologists when they’re making diagnoses. In the small world of mental health symptoms, actually turns out some symptoms? More linked than others.
STEVE STROGATZ: These subjects are not going away. Networks are, the structural underpinning of everything being studied in science today, and you could say that all the major unsolved problems of science today—I think it's not an exaggeration!—essentially all of them, they're about networks at their core.
ANNIE MINOFF: So 6 degrees seems to be true. On average anyway. Maybe it’s not always 6 handshakes to the president. But chances are, the chain linking you to any other person on this planet? It’s probably pretty short.
ELAH FEDER: And that— that is just a massive idea to get your head around. I mean what do you do as a human being with this idea?
ANNIE MINOFF: I asked Duncan.
DUNCAN WATTS: You know I really thought that, this would— that when people understood this, it would change how they thought about the world. Right, that understanding that you're connected to people who otherwise seem very distant, should make you think differently about them. Right? That if an epidemic is only ever a few steps away from you, you should care about ebola in West Africa. You know you should care about unrest in the Middle East. That, that, you know, you should care about financial contagion in Southeast Asia. That all of these things have a way of showing up on your doorstep. And it's not enough, it's not good enough to say, “These people are far away, these people are different, I don't care.” That was always the message that I thought should come out of this work. And so, it's actually really disappointing that almost twenty years later, it doesn't seem like that message has sunk in.
STEVE STROGATZ: Mhm. He really, he did say that huh?
ANNIE MINOFF: He did!
STEVE STROGATZ: I’m surprised.
ANNIE MINOFF: Duncan’s advisor, Steve Strogatz.
ANNIE MINOFF: Was that your take home?
STEVE STROGATZ: No, it’s not.
ANNIE MINOFF: Yeah.
STEVE STROGATZ: I don’t feel that it’s changed my thinking much at all. <<Laughs>> Because part of the paradox of the small world is the difference between the small world of who we’re connected to through a short number of steps, and who we can influence through a short number of steps.
ANNIE MINOFF: In other words, there’s a big difference in the links between you and some other person existing, and actually being able to use them.
STEVE STROGATZ: And it’s even in the play…
ANNIE MINOFF: Stockard Channing, in the play and movie 6 Degrees of Separation, she gives this speech, where she says…
STEVE STROGATZ: That it’s torture…
OUISA (STOCKARD CHANNING): I also find it like Chinese water torture that we’re so close because you have to find the right 6 people to make the connection.
STEVE STROGATZ:...I, I know that I’m connected, but I have no way of finding the chain. You know that’s the mystery.
OUISA: Six degrees of separation. But…. To find the right 6 people...
ELAH FEDER: Stanley Milgram found this out the hard way in his letter experiment. Sure, a lot of his letters did make it across the country. But most didn’t. People didn’t send them. They couldn’t find the chain, or they didn’t care enough to.
ANNIE MINOFF: And sometimes, that’s ok.
STEVE STROGATZ: Part of what’s so paradoxical is that even though we know we’re connected, these people are so psychologically so distant from us as they have to be! What if they what if we did really feel truly connected in a psychological way to all 6 billion? I think that would be cognitive overload of a very great sort!
ELAH FEDER: So we’ve got two mathematicians, two takeaways about what it means to live in a small world.
ANNIE MINOFF: And I have to say, listening to Steve and Duncan, I was nodding—enthusiastically—both times. I was completely convinced both times. Because life in a small world means feeling connected to your friends and your family, and your fellow dentists, or computer programmers. But it’s also the moment that your city’s lights go out because of an equipment failure five states away. It’s browsing a college friend’s facebook page, and seeing your childhood babysitter in their friends list. It’s those moments when one of the billions of links connecting us becomes visible...just for a second. We’re ring world, with a dash of random.
***********
ANNIE MINOFF: Undiscovered is reported and produced by me, Annie Minoff.
ELAH FEDER: And me, Elah Feder. Our editor is Christopher Intagliata. Shoutout this week to Ari Daniel, our story consultant, and Alexa Lim for recording help.
ANNIE MINOFF: Thanks also to Danielle Dana, Christian Skotte, Brandon Echter, Rachel Bouton, and Sarah Fishman. We had fact-checking help from Michelle Harris. Original music is by Daniel Peterschmidt. Additional music is by Podington Bear and Lee Rosevere. I am Robot and Proud wrote our theme.
ELAH FEDER: Special thanks to our launch partner, the John Templeton Foundation. Find more Undiscovered at undiscovered podcast dot o-r-g or on Twitter at undiscovered pod.
ANNIE MINOFF: And if you liked this episode, let us know! Review us on Apple podcasts. Goatlady did. Thank you Goatlady.
ELAH FEDER: See you next week!
<<cricket chirping>>
ANNIE MINOFF: And very final question which is: Did you ever find out what was happening with the crickets?
DUNCAN WATTS: <<sigh>> No not really. <<laughing>> I mean we did— we did characterize the phase response curves and they were, you know, consistent with the sort of theory of synchronization. And then, you know I sort of went off on this tangent that I never came back from. So you know, if anyone’s listening now, you know, there’s a great experiment you could do with crickets. I’d be happy to talk to you about it! <<laughs>>
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