Speaker 1: Wait, wait, you're--
Robert Krulwich: All right.
Robert: All right.
Announcer: You are listening to Radiolab from WNYC and NPR.
Jad Abumrad: Yes.
Robert: Listen to this just for a second.
Jad: Is that Johnny Cash?
Robert: Yes, it's Johnny Cash and he sing a song about the deep importance of mathematics in your life.
Jad: There's no math here. What are you talking about?
Robert: No, there's a lot of math here because you see, what he's doing moving to his extinction it seems, but he's being very careful to calibrate.
Jad: Oh my God. We're going to go all the way to one? I feel I've listened to the song for three hours already. The numbers are making a tidy. If I were him, I'd lose the numbers.
Robert: Lose the numbers?
Jad: Yes, this is stress.
Robert: You can't lose the numbers. You cannot lose the numbers because numbers create order in your life.
Jad: I could lose the numbers. I could survive my whole life without them.
Robert: That's just completely ridiculous.
Jad: Please, try me. Try me.
Robert: All right, let me just ask you some very simple. You go to buy some M&M'S and you have $5 bill in your hand and you give it to the vendor and the vendor gives you back the M&M'S and what?
Jad: No numbers required. If I hand him the bill, he hands me some changes. I just go by trust.
Robert: You go by trust?
Robert: He asked you how old you are? What do you say?
Jad: Middle-aged, I tell him.
Robert: Listen to that. You hear that? It's a point that you're late for an appointment or something like that. You call up and you say, "I'm going to be three minutes late, five minutes, late, 10 minutes late."
Jad: I usually just wait for the call before I leave.
Robert: I know that.
Jad: Which you know it's true.
Robert: I know it's true.
Jad: Yes, don't need them. Don't need them.
Robert: Your test. You're taking the test in school. You get a 98, you get a 52. You don't care?
Jad: Pass, fail.
Robert: How much gas is in your car, Jad?
Jad: I wait for the light to come on.
Robert: [laughs] First you want to call me and you can't remember my phone number.
Jad: Two words.
Jad: Speed dial.
Robert: How many words?
Jad: Oh, crap, crap. Damn it.
Robert: You see, you got to use numbers.
Jad: Is that how it ends?
Jad: That's a great ending.
Robert: Ending made possible all thanks to the disciplined use of numbers and that's going to be our, what do numbers do to us and for us?
Jad: Or don't do for us. Forget the-- What do we have? We have a [crosstalk].
Robert: We're going to have a detective story. I love stories, some Nazis and lots of numbers.
Jad: I'm Jad Abumrad.
Robert: I'm Robert Krulwich.
Jad: This is Radiolab, stay with us.
Robert: Jad, do you want to introduce this person?
Jad: This is-- This is a little Amil.
Robert: Hi, Amil. How old is he?
Jad: He's hungry right now. He's about 30-- Karla, how old is he? 36?
Jad: At the time of this recording he is 36 days old.
Robert: Well, I've you must have wondered. Do you think he has any sense at all of numbers or quantities or anything?
Jad: What do you mean? Can he count? Is that what you're asking?
Robert: [unintelligible 00:04:31] count, but do you think he has a-- I don't know, a numeric sense at all?
Jad: Do I think he has a numeric? No. No, I don't think he knows that that is his hand that he's chewing.
I don't think there are any numbers in there. In fact, I'm pretty sure there aren't.
Robert: Lulu, you should introduce yourself to Amil.
Lulu: Hi, Amil.
Jad: Amil, this is our producer, Lulu Miller.
Robert: By the way, Jad, while you were on paternity leave, we sent Lulu on a little mission to ask, where does a number sense come from, and how soon does it arrive in a person.
Stanislas Dehaene: Hello
Lulu: This is the first guy I spoke to. His name is Stanislas Dehaene.
Robert: Who is he?
Lulu: He is a neuroscientist in Paris.
Stanislas: We've been brushing up my English for a few minutes.
Lulu: Currently, he's like the godfather, this research.
Lulu: He wrote a whole book called The Number Sense that talks all about what babies understand. He said that for a long time, people thought that babies came into the world just empty.
Stanislas: Piaget and many other thinkers so that there is what people have called the blank slate.
Lulu: That we could only learn numbers if we were taught them.
Jad: Yes, that's what I think.
Stanislas: Now we know it's just completely wrong.
Robert: How do they know this.
Lulu: Well experiments? Lots and lots of baby experiments.
Stanislas: The equipment we have is a set of little sponges which contain a very small electrode that you can place on the head of the baby. It's [unintelligible 00:06:00].
Lulu: These babies are how old?
Stanislas: : In this case it was babies of two or three months.
Lulu: He plunks the baby down in front of a computer screen. On the screen are a bunch of little pictures.
Stanislas: Like little ducks, for instance, it's always a set of eight of the same objects. You do eight ducks, eight ducks, eight ducks, eight ducks.
Lulu: What he sees is that at first, the baby's brain is a little excited about getting to see ducks, and then slowly the firing just kind of fizzles out.
Stanislas: Another eight ducks, another eight ducks. Then, at some point suddenly--
Lulu: He changes it to--
Stanislas: Eight trucks.
Lulu: He sees a spike in brain activity.
Stanislas: in the- What we call the temporal lobe--
Lulu: Meaning the baby can notice that change.
Robert: but that's not number.
Lulu: No, no, no, he's just getting started because Stan runs the whole thing again, starting out the same way, but then instead of changing the trucks, he just changes the number
Stanislas: eight ducks, eight ducks, eight ducks, 16 ducks.
Lulu: Once again, the baby notices the change, but now it's in a different part of the brain.
Stanislas: What we call the parietal lobe.
Lulu: The suggestion is according to Stan, that they're noticing that this is a different kind of change that in some sense, they're noticing this is a change in quantity.
Stanislas: Which is very important because it means that even in newborns, they have in their minds and in their brains an intuition of numbers.
Jad: Is he sure that they're seeing numbers or maybe they're just seeing a change in the pattern?
Stanislas: Some, some, some, some, some more.
Lulu: Well, sure. what they're good at is making these gross distinctions like eight versus 16.
Stanislas: Or say 10 and 20,
Lulu: As the difference in number gets smaller and smaller then they're not so good.
Stanislas: There is no baby that will ever know the difference between nine and 10. These numbers are too close together.
Lulu: It's not quite as simple as you think. According to Stan--
Stanislas: Which is most extraordinary I think--
Lulu: The way that they're actually experiencing quantities is not just a dumb-down version of what adults do. It's a completely different version of what adults do.
Stanislas: They seem to care about the logarithm of the number.
Jud: The what?
Stanislas: The logarithm of the number.
Robert: You mean logarithm?
Stanislas: Sorry. My English is getting really bad.
Lulu: No, logarithms.
Stanislas: I don't know if this will scare if you ever listen to this show--
Lulu: It scares me a little, but it's actually not that bad.
Stanislas: You can think of it in terms of live shows--
Lulu: First think about you.
Lulu: Us. How we think about numbers.
Lulu: Imagine in your head, the distance between one and two. What is that?
Lulu: Now imagine the distance between eight and nine
Robert: One also.
Lulu: They feel like the same distance from each other.
Lulu: That's because we think of numbers in these discrete ordered chunks.
Stanislas: One, two, three, four.
Lulu: Now if you were to think about it logarithmically--
Stanislas: Like the baby.
Lulu: The distance between one and two is huge. It's this vast space. The distance between eight and nine, tiny.
Robert: Why is that?
Lulu: Well, because one to two is doubling, but eight to nine--
Stanislas: it's a ratio of close to one. Only one point something.
Lulu: Now here's the spooky thing about this. You might think what must happen is that eventually as we grow up, we just naturally switch from logarithmic thinking to the numbers we all know now.
Stanislas: This is not true.
Lulu: According to Stan, if left to your own devices, you'd never switch.
Jad: What do you mean you mean?
Lulu: You would stay in this logarithmic world forever.
Stanislas: We've done these very funny experiments in the Amazon, with people from the Amazon who do not count. Basically, in their culture, they do not have number words beyond five and they don't recite these numbers. What we found is that these people still think of numbers in a logarithmic way even the adults. What that means is that if you give them a line and on the left, you place one object and on the right you place nine objects.
Lulu: You got that?
Lulu: He asked them, "What number is exactly between one and nine?"
Lulu: You'd say?
Lulu: Exactly but-
Stanislas: What they put in the middle is three.
Lulu: Wait, help me here a little bit. The-
Stanislas: The property of the logarithm is that each time you multiply the number, you move by a constant displacement in the--
Lulu: Okay, this is a bit tricky, but the gist is if you're thinking in ratios, and you're starting at one then you multiply by three to get to three, and then hey, hey we multiply by three again to get to nine.
Robert: I see.
Lulu: Those are equal jumps on either side.
Stanislas: 3:1 as 9:3.
Lulu: Get it?
Robert: Yes, well it's such a sophisticated way to go about thinking about it.
Lulu: Yes, to us but not to them. That feels intuitively simply like the middle. Dozens of people did this without hesitation. I mean this experiment gives me chills. These are the numbers that we all for want of a better word naturally feel.
Stanislas: Or at least that has been my [unintelligible 00:11:35] claim for many years.
Lulu: I don't quite know how to phrase this question but is there some-- Is it almost like the way we think about numbers with an equal distance between one, two, three, four, five, six, seven is wrong?
Stanislas: I wouldn't go too far.
Lulu: Then I talked to Susan Carey.
Susan: I'm a professor of psychology at Harvard University.
Lulu: She said that numbers as we think of them today are certainly made up.
Susan: Those are human constructions.
Lulu: Even somewhat at odds with how we feel numbers intuitively.
Susan: That's right they are. [laughs] There is the problem.
Lulu: Then how do we ever come to understand the numbers we know now?
Susan: That's a $64,000 question.
Lulu: She says it happens gradually.
Amanda: Okay, don't touch the microphone.
Lulu: Over a couple of years.
Amanda: Can you count?
Amanda: Let's hear it.
Mina: one, two, three.
Lulu: One more quick introduction, that is-
Lulu: -who you might remember from the Laughter Show.
Amanda Aronczyk: You've met Mina before.
Lulu: Her mother, producer Amanda Aronczyk.
Amanda: She will be two in a week.
Amanda: Yes. It's her birthday.
Lulu: We've called them in today because of an experiment.
Susan: An incredibly simple set of tasks.
Lulu: That Susan told me about.
Susan: If you have a two-year-old at home you can do these tasks.
Amanda: Honey, so we're going to play a game.
Susan: You put a bunch of pennies on the table.
Amanda: I'm going to give you some pennies okay?
Amanda: Just a second. Let mommy get them for you.
Susan: You say to the child, "Can you give me one penny?"
Amanda: Can I have one penny?
Susan: The child very carefully picks up one and hands it to you.
Amanda: That's right, that's one penny. Thank you.
Susan: Young two-year-olds almost all can do that. Then you ask for two pennies.
Amanda: Now can I have two pennies?
Amanda: No? Please can I have two?
Susan: It doesn't matter what you ask for they just pick up a handful and hand them to you. More than two pennies. You have like one, two, three, four. They've given you four pennies and you say, "Is that two?" They say--
Susan: [laughs] right. Then you say-
Amanda: Can you count how many pennies you have?
Susan: Can you count to make sure?
Amanda: How many pennies is that?
Susan: They go one, two, three, four and you say, "Is that two?" They say, "Yes."
Mina: Yes. More pennies.
Susan: Sometimes they count-
Amanda: How many pennies is that?
Susan: One, two, two, two-
Mina: One, two, two.
Susan: It's like they somehow know that all of their other words contrast with one and meaning. That is they're giving you a number and they're giving you a number more than one but they haven't the slightest idea what two is or three is or four is or five is. They don't know what two means for nine months.
Susan: They're in that stage for several months and then they become three knowers and then they become four knowers. That process takes a year and a half.
Lulu: In other words, even though it sounds like--
Mina: Seven, eight, nine, ten.
Lulu: Mina understands numbers like we do.
Amanda: Good job.
Lulu: She's probably still living in the land of that baby math.
Mina: One, two, ten.
Lulu: But, there does come a moment when they finally step away.
Amanda: Can you sing that song?
Lulu: It happens right when the kid's about three and a half years old.
Susan: What they do I think, this is speculative but--
Lulu: After years of everyone around them saying--
Amanda: Can you count how many pennies you have?
Susan: This is something parents do.
Amanda: One, two, three, four
Susan: They practice counting with children.
Amanda: Can you count to three?
Child: One, two, three.
Amanda: Can you do four, five?
Child: Two, one
Lulu: Even though the kid is baffled by these numbers and they don't know what five, or six, or seven means.
Lulu: At some point, after enough pressure, they just throw up their hands and believe the song.
Susan: That's a very bold leap that children must make. Now, what five means for the child is one more than four.
Child: Fives, six, seven.
Susan: What six means is one more than five, but now you've got integers.
Child: Eight, nine, ten.
Lulu: We're all relying on this song.
Susan: Yes, one, two, three.
Lulu: We just one day decided, "Okay. That means something."
Susan: That's right. This is a trick.
Robert: What does she mean by that, trick? Sounds almost like a dirty word.
Lulu: [laughs] She doesn't use it like a dirty word. She says, "It's a wonderful trick."
Susan: The point is, once you have that trick, you build on that.
Lulu: That opens up the whole world of mathematics to you and we can build buildings and launch rockets into space.
Susan: And no other animal has invented that trick.
Lulu: I can't help feeling there's something about this that's a little bit sad.
Lulu: Just the idea that to step into this world of numbers, we all had to leave something behind.
Robert: That you were born with.
Robert: It doesn't look what you get on the other side, though. You get to play and have a remarkably interesting-- If you like math, you get to play with deeply abstract and beautiful thoughts.
Lulu: Yes, and that's great, but--
Robert: All of a sudden you feel sad when somebody good at a trapeze work? No, that's just something that they're good at. They practice it and they learn it, just like different talents. That's all.
Jad: Robert, I think I know what Lulu is talking about. It's refreshing somehow to know that the numbers that we use day-to-day are somehow made up because sometimes the numbers for me, at least feel like these hard fussy, foreign things that don't feel real. They feel actually the opposite of real.
Robert: You're sure that real isn't just unfamiliar, a little strange?
Jad: Foreign. Yes, sure.
Robert: Because before you could walk, when you were just a crawler, toddling was unusual. Then toddling became an adventure and then that became usual.
Jad: Yes, but eventually you do walk. There's something about numbers where I feel like, personally, I never learned how to walk. I think there are a lot of people listening right now who probably feel that way about numbers.
Robert: What does that mean though?
Jad: We're just logarithmic people.
Robert: Come on.
Robert: Thank you very much for that lesson.
Jad: Luly, stay strong in your opposition to integers.
Robert: Yes. [laughs]
Robert: They'll be right back.
Amanda: Hello there. This is Amanda and Mina, and we are going to read the credits. Mina, you ready? Can you say, "Radiolab"?
Amanda: Radiolab is funded in part by the Alfred P. Sloan Foundation, the Corporation for Public Broadcasting, and the National Science Foundation. Mina, can you say, "National Science Foundation?"
Amanda: Radiolab is produced by WNYC and distributed by National Public Radio. Good job. Okay.
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