Aug 19, 2010

A Very Lucky Wind

Laura Buxton, an English girl just shy of ten years old, didn't realize the strange course her life would take after her red balloon was swept away into the sky. It drifted south over England, bearing a small label that said, "Please send back to Laura Buxton." What happened next is something you just couldn't make up - well, you could, but you'd be accused of being absolutely, completely, appallingly unrealistic.

On a journey to find out how we should think about Laura's story, and luck and chance more generally, Jad and Robert join Deborah Nolan to perform a simple coin-toss experiment. And Jay Koehler, an expert in the role of probability and statistics in law and business, demystifies some of Jad and Robert's miraculous misconceptions.

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JAD ABUMRAD: We're gonna start the show today with a truly remarkable story, which begins with this girl right here.


LAURA BUXTON: Hello. I'm Laura Buxton.


JAD: Laura Buxton is her name. Remember that name. And Laura, let's do this like a movie, okay?


LAURA BUXTON: Like a movie.


JAD: Yeah.




JAD: Okay, it's June, 2001.




ROBERT KRULWICH: Where are we?


JAD: We're in a little town in northern England called ...


LAURA BUXTON: Stoke-on-Trent.


ROBERT: Stoke-on-Trent.


JAD: Yep. And there is Laura Buxton standing in her front yard. She is 10 years old.


LAURA BUXTON: Yeah. Well, almost 10.


JAD: Whatever. She's a tall girl.


LAURA BUXTON: Pretty tall for my age.


JAD: Pigtails. And in her hand, she's holding a balloon. A red balloon. You with me so far?




JAD: She has written her name on the balloon.


LAURA BUXTON: It just said, 'Please return to Laura Buxton.' And then on the other side, it had my address.


ROBERT: Mm-hmm.


JAD: So there she is, standing in her front yard with her balloon.


LAURA BUXTON: It's very windy.


JAD: And she holds her balloon up to the sky, to the heavens.


LAURA BUXTON: And I just let it go.


JAD: Phew!


LAURA BUXTON: And the wind took it.


ROBERT: [laughs]


LAURA BUXTON: We were laughing and joking because we just thought it would get stuck in a tree a bit further down the road somewhere.


JAD: That's not what happened. The balloon kept going.


JAD: All right. Now, I'm looking at a map here of England and Stoke-on-Trent is at the top.




JAD: So the balloon would have had to go south. Like, down, down, down. Past Stratford.




JAD: Past Walsall, past Wolverhampton. Then past Birmingham. Past Kidderminster. Past Worcester.




JAD: Past millions of people.


JAD: Past Cheltenham.




JAD: People with different lives, different names.


JAD: Past Glou-chester?


LAURA BUXTON: Gloucester.


JAD: Gloucester.


JAD: And all in all, the red balloon goes about 140 miles south.


LAURA BUXTON: Exactly. Against the prevailing wind.


JAD: Oh, really?


LAURA BUXTON: Which is a southwesterly.


JAD: Okay. So finally, when this balloon is all the way on the other side of the country it begins to descend. Down, down, down. And of all the places it could have landed, you know, in a river and a factory parking lot, in the sea, instead the balloon touches down in the yard of this girl.


GIRL: I live -- I live in the countryside in a little village called Milton Lilbourne.


JAD: Just so you're not confused, this is a different girl than the first one. They do sound the same, but they live on opposite ends of the country.


GIRL: The balloon got stuck in our hedge, but our next door neighbor found it and he thought it was just a bit of rubbish and he collected it up so the cows wouldn't eat it, because he didn't want the cows to, like, choke on the rubbish. And he was about to put it in the bin. Like, literally. And then he saw the label saying, 'Please send back to Laura Buxton,' and he was like, "Oh, my God!"


ROBERT: Why? Why would he say, "Oh, my God?"


JAD: Okay, so check this out. Remember how I told you how the first girl who sent the balloon was 10?




JAD: The second girl who received it?


GIRL: I'm 10 years old.


JAD: She's 10. Okay?




JAD: No, wait. There's more.


ROBERT: Better be.


JAD: Remember how I told you the first girl's name was Laura Buxton?




JAD: Well, girl number two, can you introduce yourself?


LAURA BUXTON 2: Okay. Hi, I'm Laura Buxton.




JAD: Girl number one.


LAURA BUXTON 1: Hello, I'm Laura Buxton.


JAD: Girl number two.


LAURA BUXTON 2: Hello, I'm Laura Buxton.


ROBERT: They're both Laura Buxton?


JAD: Yeah.




JAD: Yes!


ROBERT: Both named Laura Buxton.


JAD: Yes. You heard me right. A 10-year-old girl named Laura Buxton lets go of a balloon. That balloon floats 140 miles and lands in the yard of another 10-year-old girl named Laura Buxton.


ROBERT: This is for real.


JAD: Yes. I think it might be the strangest thing I've ever heard in my life.


LAURA BUXTON 1: It's pretty weird.


JAD: So weird we had to get them both into a studio.


STUDIO ENGINEER: Hello, New York. This is London. Can you hear me?


LAURA BUXTON 1: So, like, we're going to hear Americans through these?


JAD: This balloon thing happened about eight years ago. So both Lauras are now 18, and they've actually become really good friends. Anyhow, back to the story.


LAURA BUXTON 2: Yeah, I got the balloon.


JAD: That's Laura number two.


JAD: What did you think at that point?


LAURA BUXTON 2: Well, I -- I was quite young so I didn't really know what to think. I was just like, I'd better write the letter because, you know, there's someone else out there called Laura Buxton. I must see them!


JAD: So Laura number two wrote a letter to Laura number one.


LAURA BUXTON 2: "Dear Laura," I think I put. "I'm 10 years old and I live in Milton. I found your balloon and the thing is that my name is Laura Buxton as well. So lots of love from Laura Buxton.


JAD: Laura number one.




JAD: You get the note.


LAURA BUXTON 1: Got it through the post.


JAD: Do you remember reading it?


LAURA BUXTON 1: I remember reading because I was so -- I opened up while I was in the kitchen, and it was really quite confusing, actually.


JAD: Okay, a short while later the two Lauras meet.






JAD: And at that moment, things get even weirder. They realize when they see each other for the first time, oh my God, not only do we have the same name and are the same age, but we look the same. Same height ...


LAURA BUXTON 2: Skinny and tall.


JAD: Same color hair.


LAURA BUXTON 2: Brown-ish hair. And I remember the weirdest thing was that we were wearing really similar clothes.




LAURA BUXTON 2: Which I always thought was so weird.


JAD: Wait. What were you wearing, do you remember?


LAURA BUXTON 2: Pink jumpers and jeans.




JAD: So you both had on pink jumpers and jeans?


LB1 and LAURA BUXTON 2: Yeah. [laughs]


JAD: And as they started to talk, it just kept getting weirder.


LAURA BUXTON 1: Well, we both got a three-year-old black Labrador.


LAURA BUXTON 2: We've both got a gray rabbit. We've both got guinea pigs.


ROBERT: Really?


JAD: Yeah, yeah. And they both brought their guinea pigs with them that day.


LAURA BUXTON 1: I remember Laura took hers out of its cage and I had mine on my lap and we were like, "Oh my God!"


LAURA BUXTON 2: They were identical.


LAURA BUXTON 1: They were both brown with a sort of beige-y orange patch on their bum. Like, completely the same.


LAURA BUXTON 2: I was just like, "Oh my gosh! How is this happening?"


JAD: Do you believe in miracles? Either of you?


LAURA BUXTON 1: I don't know. Would you call this a miracle?


LAURA BUXTON 2: I'm not sure. I mean, I guess it could be, but I think it's more of a case of fate.


LAURA BUXTON 1: Yeah, I'd say it's more fate than a miracle.


JAD: So you don't think that wind the blew the balloon was just wind?


LAURA BUXTON 2: Well, if it was just the wind it was a very, very lucky wind. The chance is just so unlikely, there must be some kind of reason.


JAD: What kind of reason?


LAURA BUXTON 2: Maybe we were meant to meet? I don't know.


JAD: But meant by who? Or what?


LAURA BUXTON 1: Who knows, really?


LAURA BUXTON 2: I mean, only time will tell. It could actually be, like, preparing us for something else later in life, who knows?


LAURA BUXTON 1: Maybe when we're old grannys.


LAURA BUXTON 2: We'll find out.


ROBERT: Oh, Jad. I mean, look what you -- you know what you are?


JAD: What?


ROBERT: You're a destiny bully.


JAD: Did you call me a destiny's bully?




JAD: Sounds like a pop band or something.


ROBERT: No, it's what you're doing to those girls. You want them to act like they are somehow the subject of a miracle.


JAD: No, I wasn't trying to force God on them, if that's what you mean.


ROBERT: Yes. You -- you're the one who says, "Oh, who's behind this?"


JAD: No! The question I was trying to get at is, like, how should we think about that story? Do we live in a world where there's magic and meaning, or is it all just chance?


ROBERT: In fact, that's what we're going to do for this whole hour on Radiolab. We're going to discuss the role the chance plays in so many things.


JAD: Things like lottery tickets, sports, coin flips, even the cells inside our own body.


ROBERT: You know what, actually? We could upgrade the whole thing and give the show a fancier name. I've got a five-syllable word that means randomness.


JAD: Bring it.


ROBERT: Very Latinate. Stochasticity.


JAD: Stochasticity! I'm Jad Abumrad.


ROBERT: I'm Robert Krulwich.


JAD: Stay with us.


ROBERT: So let's start with a very basic question.


JAD: Let's.


ROBERT: Random sounds like it means random. That is anything can happen at the next turn of the wheel.




JAD: Like your phone ringing, for example.


ROBERT: Oh, God.


JAD: Random.


ROBERT: Sorry, Sorry, sorry.


JAD: Although it's happened so many times, that it's no longer random. It's completely predictable.


ROBERT: But it does have a very nice kind of lilt to it, don't you think? I'm going to sing with it now. [HUMS TO CELLPHONE MELODY]




ROBERT: [laughs]


JAD: [laughs]


ROBERT: And now back to our regularly-scheduled program. So let's say that something remarkable happens.


JAD: Like the Lauras.


ROBERT: Like the Lauras. Can you tell whether this is just the random act of -- of an indifferent universe, or is there something truly miraculous and wonderful about it?


JAD: Excellent question.


ROBERT: Thank you very much.


JAD: And it's a question that took us to Berkeley, California.


DEBORAH NOLAN: I'm Deborah Nolan. I'm a Professor of Statistics at the University of California, Berkeley.


JAD: The reason we'd come to see Deb Nolan at Berkeley is because we'd heard that she plays this game.


DEBORAH NOLAN: I like to incorporate lots of classroom activities and demos.


JAD: One in particular has to do with randomness.




JAD: It's a game that helps her students understand what real randomness actually looks like. And it doesn't look like what you would think. In any case, she takes us into her classroom. Us and a few students.




ROBERT: And she sits us down. We all sit down.


ROBERT: Should we sit in a semi-circle?


DEBORAH NOLAN: That sounds good.


JAD: And then she explains.


DEBORAH NOLAN: Okay, I'm gonna divide the group up into two, and I'm gonna divide it right here.


JAD: She splits us up so that group one is three of her students.


JOE CHANG: I'm Joe Chang.


RICHARD LIANG: Richard Liang.


MARGARET TAUBE: Margaret Taube.


JAD: And group two ...


JAD: Jad Abumrad.


ROBERT: And Robert Krulwich.


JAD: Is us.


DEBORAH NOLAN: And the group here ...


ROBERT: She's pointing at us.


DEBORAH NOLAN: I'm gonna give you a penny and I'm gonna ask you to flip the coin a hundred times. And the three of you ...


ROBERT: She points to her students.


DEBORAH NOLAN: Your job is to pretend to flip a coin.


JAD: Meaning they just have to flip the coin in their heads. Kind of guess.


DEBORAH NOLAN: How do you think that coin might land? Produce a hundred fake coin flips.


ROBERT: And then Deb leaves the room. So her students start whipping through their imaginary fake flips.














MARGARET TAUBE: How many is that?


ROBERT: While we actually flipped the coin a hundred times.


JAD: Heads.


ROBERT: Heads.


JAD: Tails.


ROBERT: Tails.


JAD: Tails.


ROBERT: Tails.


JAD: Tails. Heads. Tails.


ROBERT: This is exhausting!


ROBERT: But eventually, we did finish and both groups then put our strings of H and Ts up right there on the blackboard. And then Deb came back.


DEBORAH NOLAN: Hello. Here they are, huh? Let's have a look.


JAD: Okay. So on the board, you've got two sets of Hs and Ts which look pretty much the same. To us.


ROBERT: But she looked at their list.


JAD: The fakers.


ROBERT: And then she looked at our list. And right away she says, pointing at our list ...


DEBORAH NOLAN: This is the real one.


JAD: We were like, "Wow! How did she do that?" Well, amazingly the way she knew had to do with one particular moment.


ROBERT: Right. Roll the tape back to a moment right at the beginning of our coin flip.


JAD: Tails. Tails. Tails. Three in a row. Another tails. I feel like we have way too many tails.


ROBERT: [laughs]


ROBERT: Seven tails in a row!


JAD: It was really spooky.


ROBERT: Completely.


JAD: Like, at any moment a unicorn was gonna come galloping in. That's how weird it was.


ROBERT: But as magical and un-random as it felt to us?


JAD: That's how she knew that we were the real flippers.


DEBORAH NOLAN: As soon as I saw the seven tails and then I looked over to the other board and there weren't any longer than four, I think.


JAD: That's how she knew. And when we asked one of the guys on the other team, "Why didn't you put more streaks in your flips?"




JAD: Well, he said what I think we'd all say.


JOE CHANG: I was thinking if we did that too much maybe she would recognize that we were actually doing it on purpose.


JAD: In other words, those streaks just feel wrong. And that's the thing about randomness: real randomness when you see it, it just doesn't feel random enough.


ROBERT: But, says Deb, the truth is ...


DEBORAH NOLAN: Strange things do happen by chance.


ROBERT: But why is it so hard for us to emotionally accept this? Well, it finally made sense to us when we spoke to this guy.


JAY KOEHLER: Hi, Jad. Hi, Robert.


ROBERT: That's Jay Koehler.


JAY KOEHLER: And I'm a professor of finance and professor of law at Arizona State University.


JAD: So here's how the epiphany happened. We were explaining to Jay the unicorn experience in Deb's classroom.


ROBERT: We got one tail. Then we got a second, then we got a third.




ROBERT: And then we got a seventh.


JAD: And somewhere in the conversation, we started to do the math. Like, okay, what actually are the odds?


JAY KOEHLER: Let me see. Was it heads in a row or tails in a row?


ROBERT: Tails.


JAY KOEHLER: Seven tails in a row. That's one-half raised to the seventh power.


JAD: So we started to do the calculations, and at first it looked pretty good.


JAY KOEHLER: Point zero zero -- a little more than one percent.


JAD: Just over one percent chance.




JAD: So it seemed at first that what had happened in Deb's class was super unlikely.


ROBERT: Right.


JAD: But then Soren.




JAD: Our producer.


ROBERT: Soren.


JAD: Had to go and say this.


SOREN WHEELER: You know, to be fair you should tell him that you actually flipped the coin a hundred times.


JAY KOEHLER: Oh, ho ho, now you -- wait, wait. Did you -- you were holding back on me.


ROBERT: Wait, wait. We're too stupid to know that. That's why we have Soren here.


JAY KOEHLER: Are you saying that somewhere in the hundreds flips you got a run of seven?


ROBERT: That's what we're saying.


JAY KOEHLER: That's not a particularly good coincidence. I'm sorry to burst the bubble.


JAD: What do you mean?


JAD: And then Jay explained it to us. If you're just doing seven flips then yeah, getting seven in a row is really unlikely. But if you're doing multiple sets of seven ...


JAY KOEHLER: Fourteen of those sets of seven.


JAD: Which we were, because we were doing a hundred. Then the probabilities start to add up. And we start small, like one percent. But then that one becomes two, which becomes four, which becomes eight, until when it's all said and done, the chances of getting seven tails in a row somewhere in a set of a hundred is -- don't hold your breath.


JAY KOEHLER: About one in six chance.


JAD: One in six. That's it.


JAY KOEHLER: That you would've gotten a string of seven.


JAD: So what felt spooky and almost Twilight Zone-ish in the moment is actually ...


ROBERT: It's not that improbable.


JAD: Oh.


ROBERT: See, that's why you don't want to know it. It doesn't confirm your goosebumps.


JAD: No, I think the goosebumps are dead now.


JAY KOEHLER: Oh, I'm sorry to do that. I still enjoy life.


JAD: The problem says Jay, is that we were so focused on those seven flips in a row that we'd forgotten about the other 93 that weren't seven in a row. We'd forgotten about what he calls the background. We were too zoomed in.


JAY KOEHLER: So you've got to back the camera up and pan around and look at the complete sample space.


JAD: And when you do that, he says what you will realize is that the thing that felt so special ...


JAY KOEHLER: Suddenly you see that it's not so odd in its real context.


JAD: And this sad lesson goes way beyond coins. He gave us this example.


JAY KOEHLER: In 1985 and 1986, Evelyn Adams of New Jersey wins the lottery twice.


JAD: Back-to-back years. Crazily improbable, right?


ROBERT: Right.


JAD: So if you zoom in, all the way in, there she is. Evelyn Adams, standing outside of a convenience store somewhere in New Jersey.


EVELYN ADAMS: I just won it again! I just won the lottery for a second time!


JAD: She is completely blown away for good reason.


JAY KOEHLER: The odds that those two particular tickets would become winning lottery tickets are one in 17.3-trillion.


JAD: Wow!


ROBERT: [laughs]


JAD: But, Jay would say, if you pan the camera back away from Evelyn. If you look at the whole world of people buying lottery tickets, at this vantage point you can begin to ask a different question.


JAY KOEHLER: What are the odds that somebody somewhere ...


JAD: Somebody somewhere.


JAY KOEHLER: Would win the lottery twice? And in fact, the answer to that is it would be very surprising if it didn't happen repeatedly. And it has happened repeatedly.


JAD: Really?


ROBERT: For instance ...


JAY KOEHLER: In Connecticut, employees of a place called the Shuttle Meadow Country Club they won twice. A man in Pennsylvania, he won twice a few years later. A California retiree won a Fantasy 5 and the Super Lotto in the same day. The odds of that were calculated at one in 23.5-trillion.


JAD: That's 'trillion' with a T.


JAY KOEHLER: One way I think to think about this whole thing, I think one example is sort of brings it all home, at least it did for me when I thought about the blade in the grass paradox. The golfer hits the ball down the fairway and the ball lands on a particular blade of grass. If the blade of grass could talk, you know, the blade of grass would say, "Wow! Oh my God, what are the odds that that ball out of all the billions of blades of grass ..."


ROBERT: Then it went to the right. On me. It lands on me.


JAY KOEHLER: "How did it come to be that it just landed on me?


ROBERT: I don't know. It's sort of like a miracle, really.


JAY KOEHLER: And it is sort of miraculous. But what we know is that it was gonna land on some blade of grass somewhere. So it's nearly a hundred percent chance that some blade of grass was gonna say, "Wow. What are the odds of that ball was going to land on me?"


ROBERT: And if I were that blade of guess I'd feel so special and chosen.


SOREN: And crushed.


ROBERT: And crushed! [laughs]


JAD: Soren! The real lesson here, according to Jay Koehler and also Deb Nolan before him, is that if you don't see past yourself you fall prey to, you know, superstition.


DEBORAH NOLAN: Right. Or magical thinking. You have to be careful that you're not finding meaning here when -- when it's just coincidence.


JAD: But there are some things, like the Lauras ...




JAD: That will never feel like just coincidence.


LAURA BUXTON 2: Well, if it was just wind, it was a very, very lucky wind.


ROBERT: So we had to ask Jay.


ROBERT: I ask you sir, is this a miracle?


JAY KOEHLER: This is not a miracle. It's a good story. But, you know, there's lots of little things I could pick at in the story, you know?


JAD: Like what?


ROBERT: Oh, yeah. Pick -- pick away.


JAY KOEHLER: Well, I mean, you know, Laura Buxton didn't find the balloon. Somebody else who knew a Laura Buxton found the balloon. And you selected out the features that match. And trust me, somebody checked to see if she was an identical twin and said, "No, no. That's not a good one. Skip the twin. Okay, how many brothers and sisters? Oh, not the same number? Skip that. Ah, they both have a rabbit. Let's put that one in the story."


JAD: To be totally honest, he's -- he's right.


ROBERT: What? What do you mean?


JAD: Well, I -- when I was interviewing the Lauras, I asked them a bunch of questions kind of scouting for similarities.


JAD: What's your favorite color, both of you?






JAD: Scrap that.


JAD: And what do you guys study in school?


LAURA BUXTON 1: Biology, chemistry and geography.


LAURA BUXTON 2: Whereas I'm doing English and history and classical civilization.


JAD: Hmm. Scrap that.


JAY KOEHLER: What people do is they try to make the story better by showing more similarities.


JAD: So you're saying that somebody -- I couldn't imagine who -- doctored the story?


JAY KOEHLER: By the way, I don't want to spoil anything and this is a trivial comment, but I believe that one of the girls was actually nine.


LAURA BUXTON 1: Well, almost 10.


JAY KOEHLER: And the other one was 10.


ROBERT: [laughs] Oh well, that's the story then. Never mind.


JAY KOEHLER: I'm sorry to be your most depressing guest.


JAD: Nonetheless, I will continue to tell the Laura story every chance I get, on the air, at parties, wherever. Because, you know, damn the statistics, it just makes me feel good.


ROBERT: I think Jay would agree with you.


JAY KOEHLER: Well, it -- first of all, we love stories. It connects us. It makes -- it gives us insight into our own lives. And I think it also gives us a feeling that life is magical.


JAD: And maybe we don't have to call it magic to enjoy the experience. In fact, I was talking to the Lauras and I asked them, "What if a statistician were to walk in the room right now and say to you, ''This was bound to happen. Statistically, this was gonna happen sometime to someone.'"


LAURA BUXTON 1: That's fair enough, really. Because it just happens to be us in those statistics. So ...


LAURA BUXTON 2: Yeah. I mean, if that's what the statistician thinks I mean, yeah. Fair game to him.


JAD: They don't really care. The way they see it, whatever was in that wind, whether it was fate or just wind, it doesn't matter. It brought them together. And now they're friends.


[LAURA BUXTON 1: Hello, my name is Laura Buxton. Radiolab is funded in part by the Alfred P. Sloan Foundation.]


[JAY KOEHLER: Corporation for Public Broadcasting and the National Science Foundation.]


[LAURA BUXTON 1: Radiolab is produced by WNYC and distributed by National Public Radio. Thank you. Bye.]