[RADIOLAB INTRO]

JAD ABUMRAD: Three, two, one. Hey, I'm Jad Abumrad.

ROBERT KRULWICH: I'm Robert Krulwich.

JAD: This is Radiolab.

ROBERT: And this ...

ALEX BELLOS: This. Like this?

ROBERT: This is Alex Bellos.

ALEX BELLOS: Okay.

ROBERT: He's a writer. He's written a lot about sports—particularly about Brazilian soccer, but also math or he likes to say, "maths."

ALEX BELLOS: And when I wrote my first math book, Here's Looking at Euclid, I went and gave loads of talks. And at the end of the talks, there always would be someone who would put their hand up and they'd say "What's your favorite number?" And this used to just irritate me because I myself don't have a favorite number.

ROBERT: You don't have a favorite number?

ALEX BELLOS: No, I think it's stupid. Well no, that's actually incorrect. I—I did think it was stupid, I just didn't have one.

ROBERT: Okay.

JAD: Wait, and why would the question annoy him? Well, it seems to me it's the most normal question you could ask.

ROBERT: Well, but this is—remember, this is a—this is—he's talking about a math book to math enthusiasts. "What's your favorite number?" It's like sort of a—it's like it's too silly. Or maybe it's like they're making fun of him.

ALEX BELLOS: I got so infuriated that once—I think I was a bit tired, it was like, I don't know where the gig was, and I just said, "What's your favorite number?" Just turning it back at the person in the audience, and they said "Um, oh, 12."

ALEX BELLOS: And I was shocked, and I said, "What? You—you weren't asking me because you were kind of taking the piss out of the math there, you were—actually really wanted to know because you wanted to share your own favorite number." And he's like, "Oh, yeah." And then the person sitting next to them were like, "Oh, yeah. Like, mine's eight." And then, "Mine's seven." And I thought this is interesting! And I can remember asking the audience as well, "Who here has got a favorite number?" And at least half the people put their hands up. And in a way that you go from being a smoker and when you stop smoking to being like a rabid anti-smoker, I went from being, you know, favorite number agnostic to being obsessed with favorite numbers.

ROBERT: He started a website.

ALEX BELLOS: Favouritenumber.net.

ROBERT: You know, just asking people the question.

ALEX BELLOS: And I put it out there.

ROBERT: And I helped him out on my blog.

ALEX BELLOS: And I had, within the first few weeks, actually, more than 30,000 people.

[ARCHIVE CLIP, woman: Hello?]

[ARCHIVE CLIP, woman: Hello.]

[ARCHIVE CLIP, woman: Hi.]

ALEX BELLOS: From all over the world.

[ARCHIVE CLIP, woman: This is Jenny from Round Lake, New York.]

[ARCHIVE CLIP, man: My name is Zatar from Dubai.]

[ARCHIVE CLIP, man: Darren Sker, Sydney, Australia.]

[ARCHIVE CLIP, woman: Montevideo, Uruguay.]

[ARCHIVE CLIP, man: Oslo, Norway.]

ALEX BELLOS: Telling their favorite numbers.

[ARCHIVE CLIP, man: My favorite number is definitely eight.]

[ARCHIVE CLIP, man: 30.]

[ARCHIVE CLIP, woman: 29.]

[ARCHIVE CLIP, woman: 11.]

ALEX BELLOS: And the reasons why.

[ARCHIVE CLIP, woman: The reason it's four is because my favorite card is the ace of spades, and it's commonly called the Death Card.]

[ARCHIVE CLIP, woman: My birth date is 4, 14, 59. So 5 from 9 is 4.]

[ARCHIVE CLIP, child: My favorite number is 100 because it has two zeros.]

ROBERT: Okay, so here's what's fascinating about this—at least to me. First of all, the volume of responses. He got about 30,000 submissions from all over the planet. We put out a call on our app, which are the voices you're listening to here, and ...

JAD: We got 30,000?

ROBERT: No, we got 100.

JAD: All right.

ROBERT: But that's good for us. Okay. And clearly, people want to talk about their favorite numbers and about their reasons, which are from the heart.

[ARCHIVE CLIP, woman: The number five was always a friend.]

[ARCHIVE CLIP, woman: Because it feels like home and family, and it's kind of whole and balanced.]

ROBERT: People talked about it in emotional terms. There's this warmness, coolness, standoffishness, invitingness. It's a—there's a whole emotional landscape sitting here under the numbers. It has nothing to do with the numbers, really, but it's just there. It was there from the very start.

JAD: Okay.

ROBERT: First of all, where do numbers come from? Who invented them?

ALEX BELLOS: Well, it depends what you mean by "numbers." If by numbers you mean this idea that we can tell the difference between two things and three things, well, then we've had that ever since, you know, humans existed. And you can test animals and they do it too.

ROBERT: But if you're talking about symbols and words, abstractions to designate specific numbers ...

ALEX BELLOS: This is probably only about 5,000 years old, and was an invention of the Sumerians, which is basically Iraq.

ROBERT: And Alex says from the moment they came up with these symbols, they then added sort of extra layers of utterly un-number-y stuff.

ALEX BELLOS: Right.

ROBERT: Like, let's take the Sumerian word for "one."

ALEX BELLOS: And apologies for my accent in Sumerian. [laughs]

ROBERT: I could not be able to fault you. I'm—my Sumerian's been very rough.

ALEX BELLOS: I think it's "ges."

ROBERT: That's the word for "one."

ALEX BELLOS: And that is also the word for "fast."

ROBERT: Huh.

ALEX BELLOS: And the word for two is "min,"

ROBERT: Min.

ALEX BELLOS: Which is also the word for "woman." And one can only really speculate that there are—you know, why one is "man" and two is "woman." It could be ...

ROBERT: It could be they had some sort of Adam and Eve notion in mind. Like ...

ALEX BELLOS: Me first, you second. [laughs] Or could be our distinguishing feature is that we have one of what makes us a man, and the woman has two breasts.

JAD: What?

ROBERT: But look, whatever they were thinking, they were not the only ones to be thinking along these lines. You go forward 3,000 years, 3,000 years later, you get to Pythagoras, right?

ROBERT: The Pythagorean theorum guy?

ALEX BELLOS: Yes, so Pythagoras repeated the "one is male, two is female" thing by saying that odd numbers were masculine and even numbers were feminine.

ROBERT: Even tried to justify it by saying, "Look, do the—do the calculations here."

ALEX BELLOS: Because when you add even to odd ...

ROBERT: Say, three plus two.

ALEX BELLOS: You get odd.

ROBERT: Five.

ALEX BELLOS: Which means that when you add man to woman you get man. So man is kind of stronger than—than woman.

STEVE STROGATZ: By that logic, odd plus odd makes even.

ROBERT: Right.

STEVE STROGATZ: So what is that? Two males make a female?

ROBERT: [laughs]

STEVE STROGATZ: I mean, the whole thought is a little far-fetched to me.

ROBERT: So that is Steve Strogatz.

STEVE STROGATZ: Professor of math at Cornell.

ROBERT: A regular on our show.

STEVE STROGATZ: Friend of Radiolab.

ROBERT: Hater of the Pythagorean way of thinking about numbers—except for the triangle thing, which he loves. But—but here's what's weird is that, you know, go 5,000 years after the Sumerians and right up to the present time, when Alex does this worldwide survey, the what's-your-favorite-number thing, hears something weirdly familiar.

ALEX BELLOS: I will just read you, for example, some of the adjectives in reasons why people prefer the number one: strong.

[ARCHIVE CLIP, man: Strong. Bold.]

ALEX BELLOS: Independent.

[ARCHIVE CLIP, woman: Independent.]

ALEX BELLOS: Honest.

[ARCHIVE CLIP, man: Brave.]

ALEX BELLOS: Brave.

[ARCHIVE CLIP, man: Different.]

ALEX BELLOS: Pioneering.

[ARCHIVE CLIP, man: Lonesome.]

ALEX BELLOS: Lonely.

ROBERT: Cowboys! Those are cowboy words.

ALEX BELLOS: [laughs] Exactly.

[ARCHIVE CLIP, woman: I picture the number one as a man in a really nicely-tailored Italian suit. He's got dark hair. [laughs] I don't know why.]

JAD: It's like Marcello Mastroianni rather than John Wayne.

ROBERT: Exactly.

ALEX BELLOS: Two. Cautious. Wise. Pretty.

[ARCHIVE CLIP, man: Soft. Nurturing. Old.]

ALEX BELLOS: Fragile.

[ARCHIVE CLIP, woman: Very personal, unintimidating.]

ALEX BELLOS: Open.

[ARCHIVE CLIP, woman: Uh, friendly?]

[ARCHIVE CLIP, man: Relational.]

ALEX BELLOS: Sympathetic.

[ARCHIVE CLIP, man: Complimentary.]

ALEX BELLOS: Quiet.

[ARCHIVE CLIP, man: Easy to understand.]

ALEX BELLOS: Flexible.

[ARCHIVE CLIP, man: Makes more sense.]

ALEX BELLOS: They're kind of feminine.

ROBERT: They're kind of feminine.

JAD: Well, stereotypically feminine.

ROBERT: And these are both men and women contributing these descriptors for these two numbers.

ALEX BELLOS: Yes. Yes. That was really striking to me, and it made me think you know what? We could all laugh at Pythagoras and the Sumerians and all the kind of ancient people saying well, one is male and two is female, but some fragments of that remain.

JAD: Wait, this is not like a scientific study.

ROBERT: Well ...

JAD: It's just a survey.

ROBERT: ... actually ...

ALEX BELLOS: The more that you look, there's kind of some science behind it.

ROBERT: In fact, there's a guy and a study in Indiana. A place you know.

JAD: [laughs]

JAMES WILKIE: Uh, yes.

ROBERT: This guy.

JAMES WILKIE: James Wilkie, assistant professor of the University of Notre Dame.

ROBERT: So James and his team, here's what they do.

ALEX BELLOS: They take a baby that's just been born, only a few weeks old. Impossible to say just with the face whether it's a boy or girl. So you have to go 50/50.

ROBERT: They show people pictures of these androgynous little babies, and buried over on the side—you would hardly notice them ...

JAMES WILKIE: Are strings of four- or five-digit numbers.

ROBERT: Numbers happen to be either all even or all odd.

JAMES WILKIE: Right.
ROBERT: And James' guys say don't worry about those. They're there for the storage.

JAMES WILKIE: These are tracking numbers. Go ahead and ignore these.

ROBERT: Just focus on the babies in the pictures and tell us ...

ALEX BELLOS: Male or female?

ROBERT: Just look at the face and tell us whether it's a male or a female?

ALEX BELLOS: Mm-hmm. And it turns out that if a baby is next to odd digits, you're more likely to say that it's a boy than if the baby is next to even digits.

JAD: Really?

JAMES WILKIE: Yes.

JAD: Wait, how much more likely?

ROBERT: By a lot, or by a teeny bit?

JAMES WILKIE: By a statistically significant amount, not a landslide.

ROBERT: Do you yourself assign any gender to either one? Do you find odd a little more male in some ...?
ALEX BELLOS: No, not at all.

ROBERT: Not at all.

ALEX BELLOS: I've never felt that at all. I've known that they were a bit different because they sort of feel different.

ROBERT: So he decided to investigate.

ALEX BELLOS: Just to see if there's anything behind it. Yeah, why not?

ROBERT: Which led him—and us—to a guy named Greg Rowland.

GREG ROWLAND: Okay.

ROBERT: Okay, this is Robert.

GREG ROWLAND: Hi, Robert. How are you?

ANDY MILLS: This is Andy. I'm a producer working with Robert.

GREG ROWLAND: Hi, Andy.

ROBERT: So first of all, can you just tell us, like, what—you have a peculiar job, I guess. At least peculiar to me. Like, what do you do?

GREG ROWLAND: Well, I founded a company called The Semiotic Alliance.

ROBERT: Which is a business, right?

GREG ROWLAND: It is a consultancy, yeah.

ALEX BELLOS: So Greg is paid very good money by some of the biggest brands in the world ...

ROBERT: Coca-Cola, Ford, IBM ...

ALEX BELLOS: ... to give them advice about how their brands would go down.

GREG ROWLAND: We look at people's emotional responses to culture symbols and ideas. On the basis of this we can help companies with packaging, advertising.

ROBERT: And often, he says, what that means is helping companies harness the symbolic power of numbers.

JAD: [laughs]

GREG ROWLAND: I think one of the most exciting encounters with mathematics for me was with KFC.

[ARCHIVE CLIP, advertisement: 11 herbs and spices.]

GREG ROWLAND: With the 11 herbs and spices.

[ARCHIVE CLIP, advertisement: [singing] Serenade.]

GREG ROWLAND: Eleven, which is Kabbalistic in its—in its secrecy. Such a strange number!

ROBERT: [laughs] Well, I thought that Colonel Saunders was in his experimental kitchen, and just—and he just happened to ...

ANDY: It's "Sanders."

ROBERT: Oh, Sanders.

ANDY: He's Southern.

ROBERT: Oh, Sanders.

ANDY: Sanders.

ROBERT: Colonel Sanders was in his kitchen, and he was just fiddling around and he came up with 11 herbs—we call them herbs here—and spices.

GREG ROWLAND: Well, that's one version of the truth, but the symbolic truth is far more interesting and potent. 11 has, you know, enormous mystical potential simply because it's not 10 or 12 or five. It's not a sensible number.

ROBERT: What's wrong with 10? Like, if I say, "With my 10 herbs and spices?"

GREG ROWLAND: Because with 10, you're implying that you have a decimal balance at work. It's gonna be very hard to engage people emotionally with—with 10. 10 feels ordered, it feels highly rational.

ROBERT: Greg says it may have something to do with the fact that you have only 10 fingers. I mean, look at them. That's it. 10.

GREG ROWLAND: So 11, just is that extra one that has made Colonel Sanders uncopyable.

ROBERT: And the same thing might be happening with 501 jeans. Like, you know, why is it 501, Jad?

JAD: Hmm.

ROBERT: And not 500?

GREG ROWLAND: 501 again, has just gone one beyond the place you would expect to get to.

JAD: But wait a second. What if you don't want that? What if you want a product where you need to play it safe?

GREG ROWLAND: Well ...

ROBERT: Then you can stick with multiples of 10, which is really useful when you're trying to be practical or scientific.

GREG ROWLAND: Absolutely.

ROBERT: For example ...

[ARCHIVE CLIP, advertisement: Mayday! Mayday! I'm being attacked by dirt! Oxy 10, we're winning the war against zits.]

ROBERT: Take the acne cream Oxy 10, which viewing your face I know you're not entirely unfamiliar with.

JAD: [laughs]

GREG ROWLAND: The 10 there is obviously, you know, that's where we get to a solution. That's where our—the fingers on our hands run out, so there is a sense of completion there that says we've gone through the process and we're gonna come out okay. And of course, that's why 11 is interesting because you're—you're embarking into the infinite at that point. You're going beyond the human finger count.

ROBERT: Oh, interesting!

JAD: Mm-hmm.

ROBERT: 11 herbs and spices.

GREG ROWLAND: That's right.

ROBERT: Now—you say that as if you want to taste the thing.

STEVE STROGATZ: I do. Like, I used to love getting that as a kid.

ROBERT: But did not—did the 11—did the number 11 tickle you in any way?

STEVE STROGATZ: Yes, definitely. Would not buy it with 10 herbs and spices. That sounds very solid and Stalinist.

ROBERT: [laughs] Really?

STEVE STROGATZ: No. I'm yanking—I'm yanking—I'm yanking your wishbone.

ROBERT: Oh really? I was kind of hoping you meant it.

STEVE STROGATZ: No. No, I don't mean it. No, come on.

JAD: I gotta agree with Steve. Like, the—the idea that 11 is mystical because it's one more than 10? Meh. Although with 10, I think he has a point.

STEVE STROGATZ: It is boring. I agree.

ROBERT: Here's just a fact: big companies with large checkbooks call Greg up all the time for advice.

GREG ROWLAND: I think the thing about numbers is that because they are so rational, so abstract, for that very reason they are to us in some way bizarre.

ROBERT: Hmm.

GREG ROWLAND: I think human beings have an absolute need to invest emotion—love, hate, fear—to invest the non-rational into things which seem almost obscenely rational.

[ARCHIVE CLIP, woman: My magic number is number eight. I turned age 18 on October the 18, 1988.]

[ARCHIVE CLIP, woman: Number four because I won a swimming race in lane four as a child.]

[ARCHIVE CLIP, man: My favorite number is three because to me it recalls to mind the Trinity.]

ROBERT: Now however you feel about all this stuff, one thing that seemed pretty interesting to us— and to Alex—is you'd expect if you were asking the world to give you a favorite number, there'd be a huge difference from one culture to the next. 13 is an unlucky number. You don't have a 13th floor in America. In Korea, they don't have a fourth floor because it's unlucky four over there.

JAD: Really?

ROBERT: Yeah. But here's something interesting: the entire planet—all the continents and everyone in all the continents—came to a kind of consensus around one number.

ALEX BELLOS: Yeah.

ROBERT: So tell me, Alex, what was the world's favorite number?

ALEX BELLOS: I hope you got some good audio of a drumroll coming up. Maybe I'll do it myself. [drum roll] Seven.

[ARCHIVE CLIP, woman: It's seven.]

[ARCHIVE CLIP, woman: My favorite number is seven.]

[ARCHIVE CLIP, woman: I like the number seven.]

[ARCHIVE CLIP, woman: My favorite number is number seven.]

ROBERT: And we heard pretty much the same thing.

ROBERT: Boo!

ALEX BELLOS: In second place was three, and then third place was eight.

ROBERT: Yeah, but it was a big win for seven: 30 percent ahead of three.

ALEX BELLOS: I became really interested in seven because yes, we all know it's a favorite number, but why is it the people's favorite number? And when did that begin? And ...

ROBERT: I have one.

ALEX BELLOS: Oh great. I love reasons.

ROBERT: Holes in your head.

ALEX BELLOS: [laughs]

ROBERT: Ears, two and two. One and one. Nostrils, three and four. Five. Yeah, eyes six and seven. Yeah, yeah. Seven. Seven holes in your head.

JAD: There's no way that can be true.

ROBERT: Well, then look up at the night sky and be a Mesopotamian. So you don't have a telescope. What do you see? The sun, the moon and five planets. Seven. You spent the whole night looking at seven.

JAD: Yeah, all right.

ROBERT: Course, that's not what you hear from people.

[ARCHIVE CLIP, man: The number seven just looks beautiful.]

ROBERT: What you hear from people is about how beautiful it is.

[ARCHIVE CLIP, woman: I like the way it looks when I write it.]
JAD: It is a good-looking number.

ROBERT: Or how it sounds.

[ARCHIVE CLIP, man: It sounds beautiful. It sounds perfect.]

ROBERT: A lot of people came in about the sound.

[ARCHIVE CLIP, woman: The sound of seven.]

JAD: I'd get on that train. I think seven comes out of your mouth real nicely. Seven! Sept!

[ARCHIVE CLIP, woman: I just feel like the number seven belongs to me, I guess.]

JAD: Sabea! It even sounds good in Arabic.

ROBERT: Yeah.

JAD: Sabea.

ROBERT: In Hebrew it's sheva.

JAD: Really?

ROBERT: Very similar. Siete.

JAD: Oh, it sounds great in Spanish.

ROBERT: Oh!

STEVE STROGATZ: This—this makes me feel a little sad, not to get silly on you, but there's a certain pleasure that people are getting that I'm not getting from numbers.

ROBERT: Ever?

STEVE STROGATZ: Because I feel like a—like, if someone says eight is curvy, part of me feels you're talking about the shape of the way that we draw the—the number eight as a numeral. That has nothing to do with the number eight.

ROBERT: What are you talking about? It's the way I see—you say "eight" to me, I see—I don't see eight apples, I see that curve—I see the two circles, one on top of the other resting comfortably.

STEVE STROGATZ: Makes me—that makes me sad. That makes me feel like you're missing the reality of the number eight, which is that eight has intrinsic properties. That's really dry speak, but eight—eight is a—I mean, like 10? Okay, 10 to me is much more like when you go to the bowling alley and the 10 pins are lined up in that triangle pattern.

ROBERT: Yeah.

STEVE STROGATZ: You know what I'm talking about?

ROBERT: Yeah.

STEVE STROGATZ: There's the one then the two then the three then the four. That is a gorgeous way to think about 10. 10 is about this magnificent symmetry that can make a triangle. But seven is a disaster as a mathematical object.

ROBERT: [laughs]

STEVE STROGATZ: I mean, it doesn't have nice symmetries. If I tried to put bowling pins down with seven, it's ugly however you arrange it. To me. So it makes me feel left out that I can't have the same fun that other people are having.

ROBERT: Okay, but if you ask Alex why is seven the world's favorite number, he says ...

ALEX BELLOS: It's because seven is arithmetically unique. It is the only digit of the first 10 numbers that can neither be multiplied or divided within the group. So one, two, three, four, five, we can double them.

ROBERT: And they stay under 10.

ALEX BELLOS: In the group. You've got to keep them in the group. Six. What's left? So okay, we have six, eight and 10. Those you can halve them. And the ones left are seven and nine, and nine you can divide by three. So seven is unique.

ROBERT: So you think that there's enough arithmetic in everybody that without having worked it out as painfully as you just did, people will still find that there's something unusual about seven mathematically? Not about memories, not about culture, not about shape, just about the math itself?

ALEX BELLOS: You cannot separate the math from all of those things. The way we understand numbers is to do with their arithmetic, and that it's the arithmetic has been absorbed by culture. And sort of the greatest example of that is the predominance of seven as the most special religious mystical number that there is.

JAD: Oh, so he thinks it's not so much that the culture has gotten in the math, it's the other way around, that the math actually was there first and that that got into the culture.

ROBERT: Yeah.

ALEX BELLOS: I mean, zero is the obvious loop and its loop shape is part of why zero is zero. When I was a kid, I used to think, oh zero, it's just like a hole with nothing in it. But actually zero was chosen by the Indians as kind of reflecting the eternal cycles of the faces of heaven.

[ARCHIVE CLIP, Laguardia Arts High School singers: Something in nothing ...]

ALEX BELLOS: The Romans and the Greeks and the—and the Jews, we didn't have a zero. We just had, you know, start, everything started at one. And one reason why we didn't is that we were kind of afraid of the void.

[ARCHIVE CLIP, Laguardia Arts High School singers: The void ...]

JAD: Afraid of the void? What, like the ...

ROBERT: Well, I mean, how would you describe something ...

[ARCHIVE CLIP, Laguardia Arts High School singers: Something.]

ROBERT: ... that isn't there?

[ARCHIVE CLIP, Laguardia Arts High School singers: Nothing.]

ROBERT: There's nothing to say.

JAD: And that's scary somehow?

ROBERT: Yeah, it's an emptiness and a nothingness and it means you're so alone, you don't even know where you are.

ALEX BELLOS: And so this sort of was a psychological barrier to us grasping this zero. But in India, everything and nothing was the same thing. They had this very sort of fluidity and they grasped this idea that nothingness was something.

ROBERT: And oddly enough, the way they decided to represent the nothing was they—they took a little piece of nothing and they drew a circle around it, which turns the nothing into a something.

ALEX BELLOS: And it's a loop.

ROBERT: And it's a loop.

[ARCHIVE CLIP, Laguardia Arts High School singers: Something in nothing, nothing in something, something in nothing.]

ALEX BELLOS: So this idea of eternity and continuity and infinity is actually contained with the—our numeral for zero.

[ARCHIVE CLIP, Laguardia Arts High School singers: God.]

ALEX BELLOS: I mean, I kind of love the idea that actually here is kind of the most mystical, kind of magical, spiritual digit of them all. You know, and it's—we use it every day.

JAD: Would you like to thank somebody?
ROBERT: I would. I'd like to thank Steve Strogatz once again for joining us whenever we call him. And I'd like to thanks Alex Bellos, whose book is called The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life.

[LISTENER: This is Christine Quintana from Vancouver, BC. Radiolab is supported in part by the National Science Foundation, and by the Alfred P Sloan Foundation, enhancing public understanding of science and technology in the modern world. More information about Sloan at www.sloan.org.]

LATIF: Hi!

LULU MILLER: Hello! I have to find your window. Hi. Are you tired?

LATIF: No. No, I'm all right.

LULU: Oh.

LATIF: How are you?

LULU: Oh, good. I'm good. I'm excited for this random little thing.

LATIF: Hey, I'm Latif Nasser.

LULU: I'm Lulu Miller.

LATIF: This is Radiolab.

LULU: Okay, well some—a mystery guest is going to appear momentarily.

LATIF: Mm-hmm.

LULU: Oh, we see you!

LATIF: Hey!

KARIM ANI: I can hear you both.

LATIF: Perfect!

LULU: Yay, we can hear you!

KARIM ANI: It worked!

LATIF: Hi.

LULU: Well, okay, so Karim, Latif.

LATIF: Hi!

KARIM ANI: It's very nice to meet you.

LATIF: My pleasure. Where are you?

KARIM ANI: I'm in Alexandria, outside of DC.

LULU: Okay, so I guess the best way to set you up is that Karim is here because he has broken one of the most forbidden rules of the universe.

LATIF: Are you a cannibal? Is that what I'm about to learn?

KARIM ANI: [laughs] I haven't broken anything. It's the question of ...

LULU: You haven't yet.

KARIM ANI: No, no, no. Well, that's the question. It's the question of whether to break it and how to break it. What are the consequences of breaking it?

LULU: Yeah. Could you break it?

KARIM ANI: Should I? Should I try to?

LULU: Yeah. Should you?

LATIF: Whoa! You seem like you're on a precipice.

KARIM ANI: Brother ...

LATIF: [laughs]

LULU: Okay, so what is this rule that ...?

KARIM ANI: The rule ...

LULU: Yeah, what's the rule?

KARIM ANI: ... in mathematics, you're allowed to do everything for the most part. You can multiply, you can divide. But as you may recall from school, there's one thing in mathematics you're not allowed to do. Do you remember?

LATIF: Is it dividing by zero?

KARIM ANI: Dividing by zero.

LATIF: [gasps]

KARIM ANI: We have this entire structure of mathematics that is incredibly useful, it's incredibly powerful, but it all kind of hinges upon our agreeing to not go through this one door that has on it—there is a sign on this door that says, "Division by zero. Don't open this door." Because what's on the other side of this door is ...

[ARCHIVE CLIP: To infinity ...]

KARIM ANI: ... all sorts of craziness.

[ARCHIVE CLIP: … and beyond!]

[ARCHIVE CLIP: An infinite loop.]

[ARCHIVE CLIP: To see a world in a grain of sand.]

[ARCHIVE CLIP: Where everything is the same.]

[ARCHIVE CLIP: Note this down.]

[ARCHIVE CLIP: Don't divide by zero.]

[ARCHIVE CLIP: When you make the two into one, and when you make the inner like the outer, then you will enter the kingdom.]

LATIF: It's like—it's like the sign you hang on the elevator that's not working, you know? Like, it's like, "Out of order." Like, please, do not—do not go through here.

KARIM ANI: Well, here's the thing, though. It isn't that the elevator is out of order. It's that the elevator goes to a dimension that is so problematic to our way of thinking in this dimension that as long as you agree to not go into that kind of elevator shaft wormhole, we're good. You can have your airplanes, you can have your computers.

LULU: So today we've got a story about a paper that Karim Ani wrote almost 20 years ago about dividing by zero. I happened across it about 10 years ago, and it really tickled something in me. Over the years, I would think about it, I'd wonder whatever happened to this guy who wanted to divide by zero. I'd wonder if there were consequences for math, I'd wonder if there were real consequences for reality—for my reality, for his reality. I didn't know, but I thought that as we ourselves are rounding the clock of the calendar year, passing through zero to start anew, I thought now might be a nice time to call him up and try to understand. So my friends, leave your calculators at the door because we are going to try to enter a new kind of math. Here we go!

KARIM ANI: Well, I think what a mainstream—what a mathematician would say is ...

LATIF: Yeah.

KARIM ANI: By all means ...

LATIF: Are you a mathematician?

LULU: Yeah, sorry. We should say who you are, by the way. Who are you, Karim? What do you do? Like, what do you do?

KARIM ANI: So I'm the founder of Citizen Math. And what we do is we write lessons for middle and high school classrooms around real issues. So students are using mathematics to discuss should the federal government increase the minimum wage? Or why do airlines oversell their flights? Using mathematics as a tool for discussing and analyzing the world around us.

LATIF: Love it!

KARIM ANI: But coming back to this idea of division by zero ...

LULU: Yeah. Okay, so maybe we just start with why can't you divide by zero? Like, why is that such a hard and fast rule?

KARIM ANI: Okay. Well, so one reason is because it violates a mathematical principle that every operation needs to be undoable. Anything you do, you need to be able to undo.

LATIF: Okay.

KARIM ANI: So let's say you start with 10 and you divide by five. And so now you're at ...

LULU: Two.

KARIM ANI: Now you need to be able to get back to 10, though. And so you can go from two and multiply it by five to get back to 10. 10 divided by five gets you to two, two times five gets you back to 10. But if you now try that with zero ...

LATIF: Okay.

KARIM ANI: 10 divided by zero is—I don't know, some number. Well, to go backwards, now that some number times zero, how can that get you back to 10? So it violates ...

LULU: Because zero times anything is zero.

KARIM ANI: It's kind of sucked into the black hole of zeroness.

LULU: Right.

LATIF: Right.

KARIM ANI: So that's the—it violates this custom, let's say, or law.

LULU: Because there would be no thing you can multiply by zero to get to the number 10.

KARIM ANI: You—exactly. Once you ...

LULU: Right.

KARIM ANI: Right.

LULU: So mathematicians created this rule, this kind of barricaded door that basically says "Do not try to divide by zero because the answer is undefined. There is no answer. You can't do it."

KARIM ANI: However, there have been people who have gone through that door.

STEVE STROGATZ: Hi there.

LULU: Hi Steve!

STEVE STROGATZ: Lulu, I don't think we've ever done this together.

LULU: I know. Isn't that wild? I have never actually gotten to meet you. This is so nice.

STEVE STROGATZ: Well, it's nice. Yeah, hi.

LULU: Okay, this is Steve.

STEVE STROGATZ: Steve Strogatz, and I'm a mathematician and a math professor at Cornell University.

LULU: And Steve has not walked through the door of dividing by zero, but he says that these sorts of rules, these sorts of barricades, in math it's always been important to break them.

STEVE STROGATZ: Exactly. That's actually some of the most fruitful parts of math, that when you try to do something that seems impossible, it often leads to the creation of whole new universes.

LULU: So for example, Steve was like, okay, let's think about square roots. So if you take a number like the number three ...

STEVE STROGATZ: So—okay, so three times three, that would be, in the jargon, three squared. Three times three, three squared, is nine. So the undoing of that is that the square root of nine is three.

LULU: But now let's say that you wanted to take the square root of negative nine.

STEVE STROGATZ: You know, your first thought would be negative three, maybe, is the square root of negative nine, but it doesn't work. If you do negative three times negative three, you get positive nine, not negative nine.

LULU: Because in math—and we're not gonna go into why—if you multiply two negative numbers you get a—boom!—positive number.

STEVE STROGATZ: So you can't do it. You can't take the square root of negative nine. There is no number that will work.

LULU: So a long, long time ago, mathematicians were like, "Okay, there is a rule. No square roots of negative numbers." But then in, like, the late 1500s, a bunch of new, rambunctious upcoming disobedient mathematicians said, "Well, what if we just broke that rule, and to make the math work, we just invented a whole universe of new numbers?"

STEVE STROGATZ: That is so bizarre that mathematicians called these "imaginary numbers."

LULU: Numbers that are not technically negative and they're not technically positive.

STEVE STROGATZ: They were sometimes called "fictitious numbers."

LULU: But they allow the math to work in such a way that you can start doing square roots of negative numbers.

STEVE STROGATZ: Because you just wish it to be so.

LULU: Just invent some new numbers?

STEVE STROGATZ: Yeah, it's invention. Exactly, it's invention in the artistic sense. You can invent something that didn't previously exist.

LULU: But was anyone like, "No! We have a rule. You can't take a square root of a negative number!"

STEVE STROGATZ: Yes, absolutely. It's like anything else that human beings do—there are always reactionaries. There are always people who say, "You're muddying the waters. You're messing up the pristine and beautiful world of math with your ugly ideas." Because these ideas have a lot at stake intellectually, and there's always resistance. But that's where the breakthroughs happen. You take something that earlier generations say was impossible and you say, "What if?" And then you try it and you figure out a way to do it. And that's where the progress happens.

LULU: But, like, what does, like, an imaginary number give us?

STEVE STROGATZ: Ooh! [laughs] That gives us the modern world!

LULU: Like concrete stuff?

STEVE STROGATZ: I'm gonna tell you.

LULU: Okay.

STEVE STROGATZ: I mean, imaginary numbers—okay, so if we fast forward to the 20th century—this is not why imaginary numbers are invented. They're invented much earlier than that, but in the 20th century, when the theory of the atom starts to be worked out, we learn how to describe what's going on with hydrogen atoms and helium and how light works. In other words, we invent—we, the collective of scientists in the 1920s, invent quantum mechanics. So it's our most accurate physical theory there is. It gives us, today, everything. It gives us what we're doing right now, talking over the internet. It gives us lasers, it gives us transistors, chips. Everything in the modern world has an underpinning in quantum theory and the electronic revolution that it made possible. The math of quantum theory is built on imaginary numbers.

LULU: Hmm.

STEVE STROGATZ: You can't do quantum mechanics without comfort with imaginary numbers. And it's crazy, in that what was thought to be imaginary, a few decades—or really more like a few centuries later—turns out to be the mathematics of reality.

LULU: And to Steve, this is sort of the beauty and the artistry of math.

STEVE STROGATZ: I mean that in math, we have creative freedom. We can do anything we want as long as it's logical.

KARIM ANI: Mathematics in many ways is a chronicle of humans' understanding of reality and logic, kind of a chronicle of how we think.

LULU: Like, it began with early humans coming up with the idea of what we call "natural numbers"—one, two, three, and so on. Then the Sumerians in Mesopotamia and the Mayans each independently came up with the idea of zero, which blows its way around the globe. And then a few thousand years later, in the third century in China, negative numbers show up and they too spread across the world. And math gets more and more complicated, and so we start to come up with rules, and then we try to break those rules. And in the wake of that breakage, we often invent new numbers, like imaginary numbers or irrational numbers or real numbers or complex numbers. We come up with all these different tools that we've invented by pushing at the rules, pushing at the boundaries of math that then help us to better understand the world around us.

KARIM ANI: But this is where division by zero is different, categorically different, because it's so beyond the—like, it leads to these results that would undermine all of mathematics.

STEVE STROGATZ: It would break math as we know it.

KARIM ANI: And this is where, for me, this becomes actually quite existential.

LULU: When we come back, we are stepping through the door!

LULU: Lulu.

LATIF: Latif.

LULU: Radiolab. We are back with Karim and ...

KARIM ANI: Dividing by zero.

LULU: All right, friends. It is time now to break the rule. We are going to divide by zero, we are going to grab our calculators and watch what happens when we do.

[ARCHIVE CLIP, YouTube: If divide by zero, does it catch fire?]

LULU: Because there are actually all these videos on YouTube ...

[ARCHIVE CLIP, YouTube: Trying to divide by zero is awesome and dangerous.]

LULU: ... where sweet ...

[ARCHIVE CLIP: Where we show the machine dividing by zero ...]

LULU: ... nerdy men ...

[ARCHIVE CLIP, YouTube: We're gonna watch as this calculator tries to divide by zero.]

LULU: ... will take these old mechanical calculators ...

[ARCHIVE CLIP, YouTube: I will just input a ...]

LULU: ... punch in some number ...

[ARCHIVE CLIP, YouTube: ... dividend of 1, 2, 3 ...]

[ARCHIVE CLIP, YouTube: Divide it by zero, we hit equals ...]

[ARCHIVE CLIP, YouTube: Oh, here we go.]

LULU: And what happens is the numbers on these calculators just keep rolling over and over and over ...

[ARCHIVE CLIP, YouTube: And what happens is that it gets into an infinite loop.]

LULU: ... and over.

[ARCHIVE CLIP, YouTube: And it will never stop. And I guess it heats up, so eventually it will catch fire.]

LULU: Like, the mechanisms driving that calculator just get stuck.

[ARCHIVE CLIP, YouTube: ... in an infinite loop. Loop-loop-loop-loop-loop ...]

LULU: And it is right here for Karim ...

KARIM ANI: Where this becomes actually quite existential.

LULU: Because, he explains, to understand what's driving that looping, you have to think about the math going on. He said, you know, take for example, the number 10.

KARIM ANI: If you take 10 and divide it by 10, you get one. 10 divided by five is two. 10 divided by half is 20. The smaller the number on the bottom, the number that you're dividing by, the larger the result. And so by that reasoning ...

LULU: If you divide by zero, the smallest nothingness number we can conceive of, then your answer ...

KARIM ANI: Would be infinity.

LULU: Why isn't it infinity? Infinity feels like a great answer.

KARIM ANI: Because infinity in mathematics isn't actually a number, it's a direction. It's a direction that we can move towards, but it isn't a destination that we can get to. And the reason is because if you allow for infinity then you get really weird results. For instance, infinity plus zero is ...

LATIF: Infinity.

LULU: Infinity. [laughs]

KARIM ANI: Infinity plus one is ...

LULU: Infinity.

LATIF: Infinity.

KARIM ANI: Infinity plus two is infinity. Infinity plus three is infinity. And what that would suggest is zero is equal to one, is equal to two, is equal to three, is equal to four ...

LULU: Oh!

STEVE STROGATZ: And that would break math as we know it.

LULU: Again, Steve Strogatz.

STEVE STROGATZ: Because then, as your friend says, all numbers would become the same number.

LULU: Which, you know, for math ...

STEVE STROGATZ: The whole vast, interconnected web of it ...

LULU: ... would be a problem.

STEVE STROGATZ: The world of fluid dynamics, calculus ...

LULU: Geometry, physics, all this stuff depends on numbers being individual, discrete things.

KARIM ANI: But if you allow for division by zero, that all goes away and you get into all of these strange consequences like one equaling zero equaling two equaling infinity equaling four.

LULU: And so in order to protect math and all the things we use it for, like making computers and planes and ...

STEVE STROGATZ: And all modern technology.

LULU: ... mathematicians said that when you try to divide by zero, the answer ...

KARIM ANI: Is undefined.

STEVE STROGATZ: It's undefined. There's no sensible definition.

LULU: And that's why they put up that barricaded door.

KARIM ANI: Because what's beyond the door is—it just seems impossible. It seems very difficult to get our heads around, because effectively what we're saying is everything is one thing.

LULU: Now Karim says ...

KARIM ANI: When I first started thinking about this 10 years ago or however long that was, it was something fun to think about, it was something fun to write a grad school paper about.

LULU: But he says more recently, he's had this feeling that's grown and grown.

KARIM ANI: Of this isn't complete. There's something else here.

LULU: Now maybe this is something you have felt at some point in your life, maybe you're even feeling it right now, that the daily stuff of it isn't all there is, that there's something else out there. And for Karim, he's like, look ...

KARIM ANI: I'm not religious.

LULU: He's devoted basically his whole life to math.

KARIM ANI: And mathematics is kind of a representative of one way of thinking about not just about the world, but one way of thinking about reality.

LULU: And so to Karim, it perplexes him, it sort of tugs at him to see math itself saying, when you actually follow out the operation of dividing by zero ...

KARIM ANI: You end up in a completely different realm.

LULU: Where one equals two, equals three, equals infinity.

KARIM ANI: That all of these numbers are one and the same. That everything is effectively one thing. Everything is equal to everything else. And this world of division—I don't mean political division, but that too—this world of duality, of differences, of things being discrete from one another, that all goes away.

LULU: And Karim can't help but to notice that's the sort of stuff you hear from ...

[ARCHIVE CLIP: Jesus said to them ...]

LULU: ... people like ...

KARIM ANI: Jesus.

[ARCHIVE CLIP: When you make the two into one ...]

KARIM ANI: And Buddha.

LULU: Or people who follow Daoism, or people who have done intense meditation, or intense hallucinogenics.

KARIM ANI: Oftentimes those people come back, and the thing that they say is, "I felt like I was one with everything."

LULU: So you see in these, like, religious texts—you see literally, like, the collapse of the integer system?

KARIM ANI: I'm seeing math being a way of thinking about reality and thinking about the nature of nature.

LULU: And to Karim, because the math itself leads to this undefined place where numbers work really differently ...

KARIM ANI: Where all of these numbers are one and the same ...

LULU: ... to him ...

KARIM ANI: ... that suggests that there is something else. And I'm not saying that's God or whatever it is. It's just there's something else here. And I can't—by definition, I cannot, on this side of the door, articulate, what is—what that reality would look like.

LULU: But ...

KARIM ANI: I'm middle-aged. [laughs]

LULU: Now that Karim is rolling into his mid-40s ...

KARIM ANI: I don't have children, a spouse.

LULU: ... he finds himself unable to stop wondering about what that something else could really look like.

KARIM ANI: I look at my life and I think, "Well, after 44 years, you're still not content with this. That must be a sign that either you're doomed to be discontented, or that's a sign that, like, you're not gonna find it here."

LULU: Hmm.

KARIM ANI: You need to go through the door, because honestly, what's your alternative?

LULU: But how do you actually do it? Like, how do—I don't get how you—how do you actually divide by zero and go through the door?

KARIM ANI: I don't know. Whatever that means, I have no idea what it would mean, practically, to divide by zero.

LULU: But he says he does know it would have to start with some pretty major changes, like he would definitely need to quit his job, he would need to leave behind his house in the DC 'burbs.

KARIM ANI: Look, I'm Arab. I feel this weird, like, attraction to the desert. [laughs]

LULU: Hmm.

KARIM ANI: Like, I would probably go—take camping gear and go find a desert and sit in the desert.

LULU: And then—well, he's not entirely sure. All he knows is that he would need to connect with that math-y part of his brain he has been using for decades, thinking about numbers as these discrete and different things—and then try to turn it off.

KARIM ANI: That is the thing that I will need to put down.

LULU: And then maybe if he listened really close, he could begin to hear or feel ...

KARIM ANI: The something else behind all of this.

STEVE STROGATZ: Now okay, so what's my personal reaction to that?

LULU: By the way, there's a guy named Steve Strogatz.

KARIM ANI: Yeah, sure.

LULU: And we talked to him about you.

KARIM ANI: Oh, really?

LULU: We went behind your back, and we talked to him about you, yup. And we told him about how you were thinking about trying to access a world where there are no differences in numbers.

KARIM ANI: Mm-hmm?

STEVE STROGATZ: I would say you can do that. If you want to do that, you can do it. You can make a universe in your mind where all numbers are the same number. Let me describe that universe.

LULU: Yeah.

STEVE STROGATZ: There's a universe I'm gonna call Zeroworld.

[ARCHIVE CLIP: Welcome to Zeroworld.]

LULU: [laughs] Okay.

STEVE STROGATZ: Where, in fact, there's only one number.

[ARCHIVE CLIP: Zero.]

STEVE STROGATZ: And here are the properties of the mathematical Zeroworld: zero plus zero equals zero. And that's true no matter how many times you add zero. You can't get any new numbers in this world because there are no additional numbers, there's only zero. Zero plus zero plus zero plus zero as far as the eye can see. And that's it. That's your universe. It's the universe of zero, all numbers are the same because they're all zero, and are you happy now?

LULU: [laughs]

KARIM ANI: [laughs]

LULU: He keeps—he keeps going. He says, "To me ..."

STEVE STROGATZ: That's, like, such a solipsistic, pathetic little universe. That is the ultimate in navel-gazing. That does nothing for anybody, but it's self-consistent. You can live in that universe if you want to pretend there's nothing but zero.

KARIM ANI: Oh. See, okay. And let me respond to that then.

LULU: Yeah.

KARIM ANI: Because it's a beaut—Steven Strogatz is a really smart dude, but that question, that first question of, "Are you happy now?"

LULU: Uh-huh?

KARIM ANI: I would say, "Well Steven, if you live in one world, or—where every number is distinct from one another, like, if you're happy in that world, great! I'm not, because I have this question in the back of my mind."

LULU: This question of what is actually on the other side of that door?

STEVE STROGATZ: To me, it is Zeroworld, and it's—I just find it incredibly stultifying. It's a very impoverished little self-contained logical place.

LULU: [laughs] Stultifying but mathematically sound?

STEVE STROGATZ: I think it is. It's defensible. You can have it, there's nothing wrong with it.

LULU: Yeah.

STEVE STROGATZ: It's just—it's just as minimal as a thing can be. It has no potential for anything beyond itself, but it's just a fine little solipsist looking at its own belly button. And I ...

LULU: But inside your belly button is everyone and everything.

STEVE STROGATZ: [laughs]

LULU: It's like—it's like—I don't know. I'm just trying to defend him because he's not here. I don't know if I want to go there, but ...

STEVE STROGATZ: You can try. I'm not buying it.

LULU: No, but it's like division. He kept saying, like, division goes away—political division, spiritual division, duality goes away.

STEVE STROGATZ: Well, that's right. Right, let me try to make the case for it, right? The case for it, I guess, is this is a noble impulse to see the unity. And it's also a productive impulse. Scientifically, looking for unified theories has historically been the way to great progress in physics. So to recognize that electricity and magnetism are actually two sides of the same coin that we now call electromagnetism, that was a great invention, a great breakthrough of the middle 1800s that gave us modern things like wireless and telegraphs and telephone.

STEVE STROGATZ: And then Einstein unifying space and time, matter and energy—this is a trend. We've been doing this unification program in physics for the past 150 years, and it's very, very successful, and it reveals these underlying deep commonalities among things that are superficially different.

STEVE STROGATZ: So the idea that there's great insight to be had by realizing that things that look different are actually deep down the same, that's a good move. That is historically a very good move much of the time. But there's also the move that, along with the unifying impulse, you also have to have the diversifying impulse. You have to realize that not all things are the same, that there is great abundance in the world—all kinds of diversity, whether of people or biological species or phenomena. And, you know, like, there are two kinds of scientists—or more than two, but I mean, there are unifiers and diversifiers. And there's a need for both.

LULU: Hmm.

STEVE STROGATZ: And I guess I want to argue for the happy middle that if you—if you're all about diversity, you won't see patterns. And if you're all about unity, you won't see richness. And I think both are blinkered visions of the world. I just don't believe in either extreme.

LULU: In some ways, talking to Steve and talking to Karim, I think the question we were really kicking around is: does your experience of the world feel fulfilling and complete—even true? And I think for Steve, there is a deep pleasure and joy and a benefit—like, a real tangible benefit to accepting math exactly as it is, and reveling in how it describes reality. And for Karim ...

KARIM ANI: Every day I sit at my computer.

LULU: ... there isn't.

KARIM ANI: Kind of rewriting our lessons to tighten things up. The one I was working on yesterday was about concert tickets and about all the fees and, like, are secondary ticket brokers discouraged or are they actually, like, correcting kind of a market failure?

LULU: That sounds interesting.

KARIM ANI: Oh, yeah. All of our lessons are interesting, I mean I think.

LULU: But that is so based on math. And it sounds like you're—every day you're staring at these things that you believe are confining you, these numbers. And you're literally not just staring at them, you're, like, working with them even more intimately than most people because you're trying to, like, fit them around the universe and explain that back to kids. Like, you're playing with these tools that sound like they have—you feel like are failing you, or maybe not failing you, but they aren't all that's there.

KARIM ANI: I sort of feel like I'm spinning my wheels needlessly. I feel like I'm ready for something. I feel like I'm ready for whatever is the next thing.

LULU: But—but what's crazy to me is, like—but to do that, because of the nature of what you do and what your passion has been, you have to turn your back on math, it sort of sounds like.

KARIM ANI: I mean, I think—look, I think we live our lives in phases, and that isn't—I'm not gonna put it down and then stomp all over it, right?

LULU: Yeah.

KARIM ANI: It's a gentle putting down. It's not throwing it on the ground. But I feel like I've sucked all the juice out of that orange, for me.

LULU: Okay, one last question. When you think about the world—when you think about Zeroworld mathematically ...

KARIM ANI: Mm-hmm.

LULU: Where one equals two equals zero equals infinity ...

KARIM ANI: Everything gets sucked into a black hole of zero.

LULU: Yeah. This place that you—it sounds like you yearn for, that you want to go experience and understand and feel, right? I mean, is that ...

KARIM ANI: Mm-hmm.

LULU: Okay. What does—has it—has thinking about it and spending time there theoretically, has it changed your understanding of numbers or math at all? Has it expanded math for you at all?

KARIM ANI: I respect math more by virtue of it writing the sign.

LULU: Writing the sign?

KARIM ANI: Yeah.

LULU: What does that mean?

KARIM ANI: Mathematics saying—mathematics saying there's something we can't account for.

LULU: [laughs]

KARIM ANI: I admire that.

LULU: Why? Why? Why?

KARIM ANI: Because everybody—I am Christian, this is the truth. There is no truth but for this. I am Muslim. This is the truth. There is no truth but for this. Mathematics is an incredibly powerful tool. And for the institution, for mathematics personified to say, "I'm an exceptionally powerful tool. If you master me and if you use me, you're gonna be able to do so much. But I'm not complete."

LULU: Hmm.

KARIM ANI: There is something I can't account for. I think that's humility, I really—I think that is enviable. When I first wrote that paper about division by zero, I was like, "Pfft. I'm really gonna stick it to math," you know? [laughs] And—and now it's more like what a wonderful gift for this powerful tool that we use to do so much to say, "But if you want to go further, you need to put me down now."

LULU: This episode was produced by Matthew Kielty with help from Ekedi Fausther-Keeys and Alyssa Jeong Perry. Mixing help from Arianne Wack. Fact-checking by Diane Kelly. It was edited by Pat Walters.

LULU: Steve Strogatz, by the way, also hosts a podcast all about math where he zips and zabbles through different puzzles and questions with all kinds of fun guests. It is called The Joy of Why. W-H-Y. The Joy of Why. And Karim wrote a book all about how to get kids talking about how math interplays with real-world puzzles. It's called Dear Citizen Math. And you can check out CitizenMath.com to see all sorts of neat lessons he and his team have dreamed up over the years for middle school and high school classrooms.

LULU: That'll do it for today. That will do it for this year. Thank you so much for listening to Radiolab. Hope you all get a little bit of Zeroworld over the break, like, where nothing is happening, just low stress, low thought, rest—dare we say rest? Bye!

[ARCHIVE CLIP: [laughs menacingly] Welcome back to Zeroworld, where there are no phones. Yes, your precious little phone is gone. Oh, no! No phone! Going somewhere? I don't think so. There are no cars. There's no planes, motorcycles, bicycles. None of it! Mm-mm. No money. Oh, how good! Freedom! No money! You can't even count here. There's nothing. Nothing but zero as far as the eye can see. [laughs]]

STEVE STROGATZ: Are you happy now?

[LISTENER: Hi. I'm Hazel and I'm from Silver Springs. Radiolab was created by Jad Abumrad and is edited by Soren Wheeler. Lulu Miller and Latif Nasser are our co-hosts. Dylan Keefe is our director of sound design. Our staff includes: Simon Adler, Jeremy Bloom, Becca Bressler, Ekedi Fausther-Keeys, W. Harry Fortuna, David Gebel, Maria Paz Gutiérrez, Sindhu Gnanasambandan, Matt Kielty, Annie McEwen, Alex Neason, Sarah Qari, Alyssa Jeong Perry, Sarah Sandbach, Arianne Wack, Pat Walters and Molly Webster. Our fact-checkers are Diane Kelly, Emily Krieger and Natalie Middleton. Thank you.]

[LISTENER: Hi, I'm Rahm from India. Leadership support for Radiolab's science programming is provided by the Gordon and Betty Moore Foundation, Science Sandbox, a Simons Foundation initiative, and the John Templeton Foundation. Foundational support for Radiolab was provided by the Alfred P. Sloan Foundation.]

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