Origin of Numbers

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Speaker 5 Hello, hello.

Speaker 1 Today's show is about mathematics. By a rather incredible coincidence, today's Infinite Monkey Cage is the third episode of series 673 in the year 2019.

Speaker 1 And what is amazing amazing is that number 2019 is only divisible by 3 and 673, so it's very nearly a prime number. That means it's almost a prime number.

Speaker 7 You can't have almost a prime number, though, can you?

Speaker 7 And also, isn't the 673rd series.

Speaker 1 Wouldn't it be good if it was, though?

Speaker 1 Wouldn't that be a coincidence? Except we've had to make up the coincidence.

Speaker 7 It's the 19th series.

Speaker 1 Right, anyway, so this is the problem with science-based pedantry: it often gets in the way of some of my mystical beliefs, such as numerology.

Speaker 1 In fact, the other day I went to see my Roman numerologist, and I was worried because she just seemed, oh, like, cross, cross, cross.

Speaker 1 She's 30. So,

Speaker 1 actually, I thought my hexadecimal numerologist was very cross with me the other day, but it turned out she was a

Speaker 9 not as good, that one, not as good, is it?

Speaker 1 So, we're going to give you a lot of choices here.

Speaker 7 Hexadecimal.

Speaker 7 Yeah, so you didn't pronounce hexadecimal. I did say hexadecimal.

Speaker 6 Well, what did I pronounce then?

Speaker 8 You said something like that. See, everyone knows.

Speaker 1 Okay, let's do it again and see if it works a second time.

Speaker 7 I thought my hexadecimal. Think Brian blessed.

Speaker 5 I thought my hexadecimal numerologist was very cross with me the other day, but it turned out she was A.

Speaker 1 I was meant to see my binary numerologist the other day, but she's 111.

Speaker 1 Is that too young to be a numerologist?

Speaker 10 Okay.

Speaker 1 I often try to confess. I've skipped that one.

Speaker 5 I love that one. Oh, very pretty.

Speaker 1 I thought my complex numerologist was very cross with the other day, but I.

Speaker 1 See?

Speaker 1 That's only because they felt a level of threat from me.

Speaker 8 Which is obviously how comedy has always worked.

Speaker 1 I often try to confound my fractional numerologist, but she always gets one over on me.

Speaker 1 I went to see my imaginary numerologist the other day, but she's very negative.

Speaker 7 The square root of her is very negative.

Speaker 5 Oh.

Speaker 7 Yeah.

Speaker 5 It doesn't make sense.

Speaker 1 Well, no, it does make because the whole, it's merely reference.

Speaker 1 Right, here's the problem. If jokes make sense, three men walk into a bar, an Englishman, an Irishman, a Scotsman.

Speaker 8 They have a pint. They leave.

Speaker 11 Everything was fine.

Speaker 5 So.

Speaker 5 Yeah, but Mathematics.

Speaker 1 My doctor, I've got a tummy ache. Have you? It may well be trapped gas.
Thank you. Take charcoal pills.

Speaker 5 Knock, knock.

Speaker 1 Who's there? Gary. Oh, good.
Haven't seen you for ages.

Speaker 1 This is the problem we have.

Speaker 7 So mathematical jokes have to be precise. It doesn't work, does it?

Speaker 5 So

Speaker 1 what is an imaginary number? Tell me an imaginary number.

Speaker 7 But so the square root of minus one.

Speaker 1 Right, so I've that's fine. Imaginary numerologists.

Speaker 5 Right then.

Speaker 1 I went to see the square root of my imaginary numerologist.

Speaker 5 We'll leave that hanging.

Speaker 1 If anyone is looking for a numerologist, I recommend my exponential numerologist. She's keen to expand her practice.

Speaker 5 So

Speaker 1 that'll do for a show. Good night.

Speaker 7 Today we're looking at numbers, in fact, the origin of numbers. Is mathematics unique to human beings or can fish count? We're joined by a prime number of panelists, and they are.

Speaker 9 My name is Brian Butterworth. I'm in the Institute of Cognitive Neuroscience at University College London.

Speaker 9 Now, I first really fell in love with mathematics when I met a very attractive mathematician at university. And ever since then, I have been gripped by it.

Speaker 5 Oh.

Speaker 5 I say.

Speaker 3 Well, I am Dr. Hannah Fry.
I'm a mathematician and associate professor at University College London.

Speaker 3 And I think I first decided that I liked mathematics when I typed 58008 into a calculator.

Speaker 3 It's not true. It's not true.
I came out of the womb liking maths.

Speaker 6 My name is Matt Parker. I am dangerously underqualified, but I am the Public Engagement in Maths Fellow at Queen Mary University of London, as well as being a maths author,

Speaker 6 YouTuber, etc. And I've loved maths ever since when I was very young.

Speaker 6 Before I went to school, not straight out of the womb, but my dad would give me maths problems, like some exercises, to do as a treat. And I was too young to know otherwise.
And

Speaker 6 I mean, say what you want about brainwashing, it works. And so to this day, I enjoy maths.

Speaker 1 And this is our panel.

Speaker 1 Brian, before we get to the fish, can we start with humans? Have we always had the ability to count?

Speaker 9 As a species, probably.

Speaker 9 So the oldest words that you can reconstruct from

Speaker 9 current languages, you can kind of say

Speaker 9 what these words were like 10,000 years ago.

Speaker 9 This work has been done.

Speaker 9 The only words that are common to all known languages where the reconstruction has happened are counting words, one, two, three, four, five, up to about five.

Speaker 9 So, certainly, quite a long time ago, we were counting verbally. There are also marks on bones and stones, which suggests that humans living in caves were also able to enumerate things and record

Speaker 9 the number

Speaker 9 of objects that were relevant to them. And in fact, there's a theory that one of the things that our cave-dwelling ancestors were really interested in and counted were phases of the moon.

Speaker 9 So you can find quite a lot of marks on bones and stones with repeated thirties, which is more or less

Speaker 9 the phase of the moon. And

Speaker 9 it looks as though the phases of the moon are recorded in such a way that you can see when it's a a waxing gibbous and a waning gibbous.

Speaker 9 So when the moon's getting bigger, the moon's getting getting smaller. So it looks as though our cave-dwelling ancestors, at least in Europe, were interested in counting

Speaker 9 days, phases of the moon, and other perhaps other astronomical phenomena.

Speaker 7 There's a big difference, though, isn't there, Hannah, between

Speaker 7 counting. So I suppose it's very easy to understand

Speaker 7 why counting would be useful to our distant ancestors. But then when we say mathematics, we mean something

Speaker 7 way beyond counting as well. We mean this abstraction.
of numbers.

Speaker 7 So did you find

Speaker 7 I thought you said you were interested in maths from the moment you were born.

Speaker 7 When did you make that transition from just the counting and times tables and things to abstraction?

Speaker 7 Because I think that point is a thing that many people find difficult to move into algebra or trigonometry or calculus or whatever it is.

Speaker 7 And at some point people just say, right, that's too difficult now.

Speaker 3 So I like the analogy that mathematics is like a language, really, because I think that ultimately you have very simple words to describe very simple things, but the more that you learn of that language, the more ability you have to be able to describe lots of of other things.

Speaker 3 So, in some ways, I kind of think that there's I think that math, sort of the ability to do maths, goes beyond just being able to quantify things.

Speaker 3 I think it's about a particular way of thinking about the world. So, you know, a sort of clean way of viewing things, you know, about shapes and about patterns and about structure, that kind of stuff.

Speaker 3 But I think that, you know, that transition from

Speaker 3 talking about numbers to talking about calculus or talking about much more complicated things is just one of experience of kind of like earning that language, really.

Speaker 7 And do you feel that that's also innate? I think, Brian, you were suggesting that there's some facility with number that appears to be innate in most human beings, and it has been practiced on many.

Speaker 9 I was very interested in what Hannah said about coming out of the womb. And we know that in the first few days of life,

Speaker 9 human infants are able to make numerical dist distinctions, discriminations. So, for example, human infants, like human adults, get bored when they see the same thing over and over again.

Speaker 9 And if you show them different patterns of dots, let's say two dots, then a different two dots, then a different two dots, and they'll start to look away.

Speaker 9 But then you show them three dots, and they'll start to look back again because

Speaker 9 they've noticed that there's a change in number. In fact, we did this experiment with our first child, Amy.

Speaker 9 We put a

Speaker 9 well, the thing was, no,

Speaker 9 no, no, seriously for a moment.

Speaker 9 There was a study that just come out in America which showed that six-month-old infants were able to make these numerical discriminations.

Speaker 9 And I thought, well, if American babies can do it at six months, my baby

Speaker 9 can do it at one month.

Speaker 9 And so we put her in this... cardboard box so all she could see

Speaker 9 we're talking science here

Speaker 1 Brian's just old enough to have been before ethics panels were brought in. Just that.

Speaker 9 But we used a method which wasn't very common at the time, which was sucking habituation. So babies suck more when they see something new.

Speaker 9 So if you see two green squares, two green squares, two green squares, and then three green squares, will sucking rate go up.

Speaker 9 And it turns out that we got some really beautiful data from Amy, really great data.

Speaker 9 And then, but halfway through the series, and she had to do the whole series or else the statistics wouldn't work, she spat this teeth out of her mouth and refused to suck anymore.

Speaker 9 And so we never got the complete statistical analysis. We couldn't publish the data, and strangely, no one would lend us a baby to experiment on after that.

Speaker 9 The point of the story, and I think Hannah's interesting

Speaker 9 reflection here, is that even infants have a sense of number.

Speaker 1 Matt, as someone who, you know, it's a very important position in terms of the public understanding of mathematics,

Speaker 1 why would you put a baby in a box for a mathematical experiment?

Speaker 6 That's a great question.

Speaker 5 And

Speaker 6 what's interesting is

Speaker 6 out of the box, when we first emerge into the world, we get a few bits of built-in maths for free.

Speaker 6 Like we can compare the size of numbers, we can do very basic arithmetic looking at dots, and we get some geometry, a sense of space, so we can kind of navigate.

Speaker 6 But everything after that, we have to learn ourselves, and we forget how much is repurposing other parts of the brain and learning things that we were never meant to do intuitively.

Speaker 6 So, if you do ever get a young child, or you borrow one of someone else who has very few ethical qualms with experimenting on their offspring, or you find people who've never been in formal education, so the same experiments have been done on infants as

Speaker 6 tribes who have never gone through formal education. If you ask someone who's been to school what's halfway

Speaker 6 between like 0 and 10 or between 1 and 9, we would say, well, 5. 5 is in the middle, because 1 plus 4 gives you 5 and then 5 plus 4 gives you 9.

Speaker 6 But if you get someone to put three dots between 1 and 9 who's never been educated, they'll put 3 in the middle, not 5. And that's because 1 times 3 is 3, and then 3 times 3 is 9.

Speaker 6 And so out of the box, we have this logarithmic, we do it in terms of multiples, not in terms of adding.

Speaker 6 And it's only when we go to school and we get, you know, bullied by teachers that we switch to this

Speaker 6 adding sense of a number line as opposed to the logarithmic sense that we start with, right? And that's already we're repurposing.

Speaker 3 So I think that's that, you know, we experience the world a lot actually that way. I mean, if you think about how time seems to speed up as you get older, right,

Speaker 3 actually, it's sort of in a way, you're not thinking about a year as being a fixed number, you're not kind of adding up the years, you're thinking about a year as like a fraction of your life that has gone to like up until that point.

Speaker 3 So, actually, I think that we kind of innately do think of things in these kind of and we still have this problem with big numbers.

Speaker 6 So, we get small numbers, we get forced to learn this linear. But then, I had to go on BBC News the first time the debt in the UK went over a trillion pounds.

Speaker 6 They went, we need someone to come and say how big a trillion is.

Speaker 6 I was like, All right, and they go, Okay, so explain how big a trillion, here's Matt. I'm like, it's huge, back to you.

Speaker 6 But then I did the classic,

Speaker 6 how long is that many seconds? It's like a million seconds is just over 11 days. And a billion seconds is just over 31 years.
Make sure you celebrate your billionth second birthday.

Speaker 6 And then a trillion seconds is not until the year 33,707. And everyone's like amazed by that.
Which, by the way, from the recording date is the 13th of September, and it will be a Tuesday.

Speaker 6 I checked.

Speaker 6 But that makes sense, right?

Speaker 6 Because a trillion is a thousand times bigger than a billion, it's way bigger than a billion, but yet we still think a million to a billion is about the same as a billion to a trillion, because we've got this law.

Speaker 8 This is important.

Speaker 7 Your job, this public understanding of mathematics,

Speaker 7 that's an example, actually, isn't it, of the way if you don't know or you don't have a feel for a billion or 350 million a week, for example, or something like that, then

Speaker 7 it can cause problems

Speaker 7 in wider society.

Speaker 7 But it is something that, interestingly, in modern life, it is something that we need a sense of.

Speaker 6 One of my favorite examples of this was Pepsi of all places.

Speaker 6 Pepsi ran a promotion in the mid-90s, where if you collected points from Pepsi products, you could trade them in for like t-shirts and sunglasses and stuff.

Speaker 6 And in the commercial, they had a joke where you could trade in enough points to get a Harriet jump jet.

Speaker 6 And they showed a kid flying this jet to school because they traded in apparently 7 million Pepsi points.

Speaker 10 Ha ha ha.

Speaker 6 And I don't know what, no one in the advertising planning meeting said, well, hang on, how much would it cost to get 7 million Pepsi points given we let people buy as many as they want for 10 cents each?

Speaker 6 And a jump jet at the time cost over 20 million US dollars to get in the air, and you could just buy 700,000

Speaker 6 dollars worth of Pepsi points and get one for free. And that's exactly what John Leonard did.

Speaker 6 he actually got the money together wrote to Pepsi and said here's my check for the money plus ten dollars postage and handling

Speaker 6 which for a jump jet should be covered right and then Pepsi wrote back and we're like no

Speaker 6 and his lawyer was like yes

Speaker 6 genuine court case because advertisers just thought seven million sounded really big but didn't check how really big it was.

Speaker 7 What was the outcome of the case? He didn't get it.

Speaker 6 Pepsi had to argue that their commercial was technically a joke and so they got expert witnesses to say that it was they genuinely argued no school would provide parking space

Speaker 11 for a jump chair.

Speaker 6 The US military came in and were technically the ability to land vertically when you descend. That's military grade information.

Speaker 6 We would have to deactivate that were we to sell it as yeah, that's where the military drew the line on ridiculous.

Speaker 7 So it was obvious their defense was it was obviously a joke.

Speaker 6 Obviously a joke. And they redid the commercial for 700 million Pepsi points.

Speaker 8 Such a beautiful image, though, isn't it?

Speaker 1 Someone with a fighter plane and no teeth.

Speaker 1 Brian, it's interesting.

Speaker 1 This is the most lip-smacking, thirst-quenching war I've ever been in.

Speaker 1 Brian, I've been checking just because of something Hannah was mentioning there, and I suppose it just enlarges on Matt's point, again, which is if you're talking about a different part of the brain is dealing with numbers.

Speaker 1 So when we have to verbalise, when we have to try,

Speaker 1 always, I agree, that idea that when you see the word a billion, it immediately removes some of what it really means.

Speaker 1 Is there any way we're seeing where language to really

Speaker 8 express

Speaker 1 that kind of the enormity of numbers?

Speaker 9 Or sometimes the smallness of numbers. One of our great inventions, one of humankind's great inventions,

Speaker 9 number words.

Speaker 9 And And the great advantage of number words is that you can you can talk about very large numbers, whereas it's very hard to conceptualize them even visually. Very large

Speaker 9 I mean, can you imagine even say what thirty-six dots looks like, not to mention a thousand dots. But once you've got words and or other symbolic means, then you can go into very large numbers.

Speaker 9 And this is, if you like, the human advantage over fish. Being able to communicate about numbers is one of the ways in which the human race actually progresses and gets better at dealing with numbers.

Speaker 9 So it's certainly true that

Speaker 9 we can talk about very large numbers. What they mean in our heads, of course, is

Speaker 9 a whole different issue. Now, Matt talked about we have a kind of logarithmic representation in our head, at least when we're born.
I think this is controversial,

Speaker 9 but anyway, even if that were true, how we

Speaker 5 wow,

Speaker 6 that's a mass smackdown, if you're not familiar

Speaker 6 with rigorous scientific debate.

Speaker 9 We could have a rigorous scientific debate about it, but the question is: if you've got a very big number and

Speaker 9 your mental representation is logarithmic, right, then your very big number is going to be very, very tiny on this

Speaker 9 logarithmic mental line. So it's going to be very hard to tell a million from a billion from a trillion because they're all really squashed up at the end of your logarithmic curve.

Speaker 6 I can't tell if you're agreeing with me or making fun of me now.

Speaker 9 No, take your pick.

Speaker 7 Just because you mentioned it, we may as well deal with the title of this

Speaker 7 radio show. Brian, can fish count?

Speaker 8 Yes. Good.

Speaker 5 Here we go. Moving on.

Speaker 1 And now we return you to the test card. How do we.

Speaker 5 I suppose, how do we know?

Speaker 7 How do we know that fish can count? And what can they count to?

Speaker 9 It looks as though they've got two separate counting mechanisms, maybe even three separate counting mechanisms. They've got a mechanism for counting

Speaker 9 what they like to count are other fish, because for little fish, it's very important for them to swim in shoals because shoals reduce the risk of predation.

Speaker 9 So if you've got a predator coming and you're in a big shoal, then the predator is less likely to get you. It might get some of your friends, but it's less likely to get you.

Speaker 9 So it's very useful for fish to be able to join a larger shoal. So it must be able to tell which shoal is larger.
Now, is this really counting?

Speaker 9 Well, for a big shoal, probably not, because fish are all swimming around in the shoals.

Speaker 9 So the fish has to make a kind of a global estimate about how many fish there are here versus how many fish there are over there. But experiments that have been done, even by me,

Speaker 9 with small numbers, shows that fish can actually enumerate up to about seven or eight other fish, or indeed

Speaker 9 blobs on a screen.

Speaker 7 This really does strongly suggest that mathematics is not a human construct, which you often hear.

Speaker 7 It's a human construct.

Speaker 7 Astronomers often talk about, you know, could an alien civilization count or understand mathematics. Would this strongly suggest that there's something clearly about number that would be universal?

Speaker 9 Yeah, I mean, I think I would argue that. I mean, different species use numbers for different purposes.
So, fish use it to choose the larger shoal. It's a life or death decision, actually, sometimes.

Speaker 6 These things are things that animals have learnt to survive, though. Animals have evolved to process number different ways.
Same as humans. I think that's how we get that.

Speaker 6 But what I love about humans,

Speaker 6 some of my best friends are humans,

Speaker 6 is we've taken what we were given from evolution but then where we've gone from number to maths is we've abstracted it and we've gone beyond what we can do naturally and I would agree I would say aliens other intelligent organisms will have done the same thing they will have discovered the same abstractions as we have but is the fact that we can now do things using maths we have to start writing down numbers which get us beyond what we could originally do.

Speaker 6 I think that for me that's the phenomenal thing about mathematics. We've gone just beyond number and we can use incredible things with this abstract reasoning.

Speaker 1 There is something very that very: oh my god, the buffaloes are charging. Quick, work out Fermat's last theorem.

Speaker 5 Yeah, there is.

Speaker 7 Hannah, this is the

Speaker 7 debate, isn't it? There's a sort of platonic school of maths, isn't there, which thinks that all mathematics is out there to be discovered rather than invented.

Speaker 3 Yeah, yeah, totally. So,

Speaker 3 well, it kind of goes back to

Speaker 3 what Max was saying a second ago: of like other aliens would have come up with the same abstractions as we have. You know, would they really have?

Speaker 3 Would they really have come up with the same ideas as we have? And this idea, this is

Speaker 3 Plato's idea that there is this perfect mathematical world, right? Perfect circles, perfect spheres, perfect parallel lines. Everything is absolutely as mathematics wants it to be.

Speaker 3 And all we're doing is we're kind of tapping into that world, right?

Speaker 3 When we're doing mathematics, we're doing the best that we can with kind of like you know our human flaws and sort of fumbling around and coming up with language that that sort of approximates to that that perfect mathematical world.

Speaker 3 And that's how we describe the universe. And I think, really, I mean, you know, this is actually a really sort of tough philosophical question of whether that perfect mathematical world really exists

Speaker 3 or whether actually all of this stuff is kind of just in our own minds.

Speaker 7 Isn't it like being a mathematician? Like being a musician, where some musicians will say, I discovered a tune. I didn't invite a tune, I discovered it.

Speaker 7 So if you talk about Andrew Wiles, for example, Fermat's last theorem,

Speaker 7 does he discover a proof or does he invent a proof? Is that proof out there? Is there a set of proofs of Fermat's last theorem that any civilization across the universe would have access to?

Speaker 3 So he says that it's discovered. He says that he very much discovered it.

Speaker 3 And he said, actually, in fact, you know, because this is, you know, it took him seven years basically working on his own to try and come up with this proof.

Speaker 3 He says that he always knew that it was out there and he just had to find it. The answer was

Speaker 3 effectively out there. He was sort of searching around.

Speaker 3 And I think that actually, when you talk to pretty much all professional mathematicians, they feel like this stuff is just too good to be a figment of our imagination.

Speaker 3 I mean, like, you take an equation, you try and break it, right? You try and trick it, you try and get ahead of it, and you just can't because it knows where you're going to go before you get there.

Speaker 3 It is literally like discovery.

Speaker 3 But you know, whether that's really what the universe looks like,

Speaker 3 I don't know, right? I mean, the things like

Speaker 3 zero, for example, which has been incredibly useful. I mean, we can't imagine really having like a number system without the number zero.

Speaker 3 But whether nothingness actually exists in the universe, I don't know whether there

Speaker 3 I think it probably doesn't. Like true nothingness.
I mean, even in kind of deep space, there's always still something.

Speaker 7 Oh, the vacuum is fizzing with activity. Yeah.

Speaker 6 The problem is, maths tries to find obscure pure bits of mathematics. And then physics somehow finds a way.

Speaker 6 If you're unfamiliar with how physics works, you do experiments until you run out of theories, and then you pop over to the maths department and say, what have you guys got lying around recently oh matrices 4d shapes thanks

Speaker 6 and then so you think you have this obscure bit of abstract mathematics like higher dimensional shapes and then a physics theory will come along and just repurpose this bit of maths into such a glorious way you're like it would be a waste if the universe didn't use that incredible bit of math.

Speaker 1 I just love that image though.

Speaker 1 The physicists always find a use. This turns physicists into kind of junkyard scavengers.
Just go, what have you got there?

Speaker 1 Oh, well, I found the handles of a wheelbarrow, half a basketball, and a flip-flop. I bet I'll find some use for it.
Look, it's a collider. You know, there's something really to me.

Speaker 7 There's a great book by Kip Thorne, who's one of the great physicists, and he's just written a book called Modern Classical Physics.

Speaker 7 And in that line one is that physics is geometrical relationships between geometrical objects. That's what it says.

Speaker 7 So that tells you there's a link between mathematics and nature, because nature is geometric.

Speaker 1 Well, on the brain element, Brian, I wanted to ask you about that.

Speaker 1 There are a lot of people who believe they don't have mathematical brains.

Speaker 1 There are people who, you know, you get to a certain point in the education system where it seems to make sense, and then there is sometimes just that single maths lesson where there's a new level of complexity, where

Speaker 1 you properly get a kind of a brain freeze. You just go, now you've looked a lot into this.
So, this, you know, for those people who just feel that they, I'm just gonna, I can't do maths.

Speaker 7 You know,

Speaker 1 how true is that in terms of you know, hardware, software, what is going on there?

Speaker 9 Well, a lot of it's got to do with how

Speaker 9 appropriate your educational system is.

Speaker 9 So, if you've got a bad maths teacher, I had a bad maths teacher, so I was never very good at maths at school. I had to learn it sort of on the job when I became a scientist.
But

Speaker 9 that's one reason.

Speaker 9 Also, we know that if you don't get much much in the way of numerical experiences in in your home, we we did this study, then you start off at school at a disadvantage, and a disadvantage might lead to a kind of vicious circle, so you're always falling behind, unable to do what the other kids can do.

Speaker 9 And so, that's another reason why, you know, when things you know, when the last straw comes, it's going to be the thing that stops you. But

Speaker 9 the stuff that is really the hardware problem is dyscalculia, And there's now quite good evidence that the part of the brain that deals with numbers is actually different in dyscalculics than

Speaker 9 in people who are not dyscalculic.

Speaker 9 And it looks as though we've got some evidence that there's a genetic component to this abnormality in what we've called the intraparietal sulcus, a bit of the brain just above your left ear, actually, and sometimes of the right ear as well.

Speaker 1 So,

Speaker 9 you know, if you're born like this, it's going to be very difficult to do arithmetic.

Speaker 9 Now, I've met mathematicians, really well-known mathematicians, I won't mention any names, who I suspect are discalculic. They really can't do calculations, numerical calculations.

Speaker 9 They're not in number theory, they're in things like geometry. And

Speaker 9 so, you know, they can

Speaker 9 no, you don't think so.

Speaker 6 Rohan and I are both laughing because number theorists are the worst at adding

Speaker 7 because they haven't defined it yet

Speaker 3 exactly I said there are no rigorous axioms for splitting this restaurant bill I don't know a single mathematician who's who would say that they were good at mental arithmetic I I've I've

Speaker 9 you are not a single one well but so they've survived school math school arithmetic in order to get on to stuff that they're really good at.

Speaker 9 And yes, you're right. I mean the standard joke is don't let a mathematician divide up the restaurant bill.
So

Speaker 9 yeah.

Speaker 7 This is tremendously interesting from the perspective of this

Speaker 7 show

Speaker 7 because we started talking about numbers.

Speaker 7 And really, I think what you're saying is that there's a distinction between mathematics and numbers, which actually might be very deep indeed, in that you can be a brilliant mathematician and not be able to add up.

Speaker 9 Yeah,

Speaker 9 I say I might have met some who will be nameless. I might tell you who they were after the show.
But that's right. I mean, we've evolved,

Speaker 9 as Galileo said, the language of the universe is written in mathematics. And

Speaker 9 in order to succeed in the universe, any creature has to be able to extract numerical information from its environment. And so we've evolved to extract that information.

Speaker 9 Not only fish, which can do it, but even insects. There's some very nice cases of, for example, bees, some very beautiful work by Lars Chitkerd at Matz University,

Speaker 5 where

Speaker 9 he's shown that bees count landmarks

Speaker 9 between the hive and the food source in order to be able to find their way back to the hive.

Speaker 9 And ants may count their steps as well. There's a very horrible experiment I'm not going to tell you about.
But

Speaker 9 I was just.

Speaker 8 You really know how to flirt with people, don't you?

Speaker 1 I may tell you the names of those mathematicians a little bit later on.

Speaker 8 There's something I know about ants, but I won't tell you now.

Speaker 9 I'm happy to tell you, but I just want to say one other thing.

Speaker 7 They're good at their six times table, but not their five times table, is what you're saying, isn't it? Or their four times table, and so on.

Speaker 9 Well, if they're counting,

Speaker 9 let me just say this: if they're counting their steps, and if you like, they're multiplying the number of steps by the length of their leg,

Speaker 9 you can see how you can manipulate this particular process by manipulating the length of their legs. I will say no more.
But

Speaker 9 I just want to point out.

Speaker 1 And there the flirting ended.

Speaker 7 We're going to get letters. Is there an ants protection society?

Speaker 9 I just want to point out that there's one area

Speaker 10 where

Speaker 9 another creature is actually better than us

Speaker 9 at a numerical task. And these are chimpanzees.
Chimps are the champs when it comes to numbers. Chimps can learn the digits.

Speaker 9 And they can learn to, for example, to match the digit seven with seven dots.

Speaker 9 I mean, there's not very many chimps that actually have this opportunity, but those that have had this opportunity can be very good at it.

Speaker 9 They also can learn the sequence of digits from one up to ten, or twelve even.

Speaker 9 And so they so these chimps will know, for example, that seven refers not only to an array of seven objects, but they will also know that seven is the digit after six and before eight.

Speaker 9 And what they can do better than us is that they can match digits to arrays of dots quicker and more accurately than we can do.

Speaker 9 But even more impressive is that at least one chimp, I mean when I say chimps,

Speaker 9 I mean one chimp, this chimp called Ayumu, trained by Tetsura Matsuzawa in Japan, what this chimp can do is it can see a sequence of digits random on the screen, say digits one to nine on the screen, and then

Speaker 9 the digit positions are masked, so it can only see the positions, but it has to remember what's under those masks.

Speaker 9 And it can do this up to with an exposure of 200 milliseconds, a fifth of a second, it can then touch those masks in the order of the numbers that were underneath them. And humans cannot do this.

Speaker 7 One chimp can do that.

Speaker 9 One chimp can do that.

Speaker 6 So chimps are better at humans than spotting numbers, but humans are better from extrapolating from a single data point.

Speaker 5 Good point.

Speaker 3 I want to pick up on what you said about ants, actually, because I think that ants are a really good example of how actually animals can often behave in very mathematical ways that aren't necessarily to do with them counting.

Speaker 3 So ants, if you put, there's lots of experiments where you put ants in a maze, right?

Speaker 3 You put a food source at one end, the ants in at the beginning, and between them, they're going to kind of strategize in this mathematically optimal way.

Speaker 3 So, they all go around and sort of walk around randomly.

Speaker 3 And then, when one of them finds the food source, they sort of retrace their steps, laying a different pheromone trail so the other ants can follow it.

Speaker 3 And actually, you know, you can do these run these mathematical simulations which demonstrate that they're really sort of them and lots of other creatures are acting in a mathematically optimal way.

Speaker 6 Well, I think that goes back to what Brian was saying, where, because I get annoyed when people say, if you catch a ball,

Speaker 6 you're solving quadratic equations. And you're like, well, you're not.
You've learned to do that. But we can now show why that is how you catch a ball.

Speaker 6 And so I think things, there's animals doing maths, but there's animals doing things incredibly well.

Speaker 6 And now we have the mathematics to explain and explore why that was the optimal solution that they ended up on.

Speaker 1 I like the fact that, because mathematicians, I work with you, and one thing's much like me, they're not great at sport, But I like the fact that they found out, oh, I might not be able to catch a ball, but I can explain how you did.

Speaker 1 Now, that to me is a great get-out clause.

Speaker 1 We've asked the audience a question: What do you think is the most terrifying number and why?

Speaker 1 Nine, because it's what that scary angler Merkel always says to me. Theresa May.

Speaker 5 Oh, terra.

Speaker 5 You see?

Speaker 7 Yes. Seven, because it's the average life expectancy of a strawberry.
That's tremendous.

Speaker 7 Have any of you ever listened to the infinite monkey cage?

Speaker 1 This is four, because in Japanese the sound of four is the same as death.

Speaker 5 Yes.

Speaker 1 Not all punchlines, sometimes learning.

Speaker 7 I like this one.

Speaker 7 Ropin ins or ropine ins. Spell R O P

Speaker 10 N.

Speaker 7 Ropine ins.

Speaker 7 Because it goes on forever without repeat. Yep.

Speaker 1 The 42, because it's the meaning of life, and I haven't figured out what that is yet.

Speaker 1 1997, because things did not get better.

Speaker 7 I don't get this one. Someone can explain this.
3.141592, because I'm gluten intolerant.

Speaker 5 Hi. Hi.
Aye.

Speaker 5 Hi.

Speaker 1 Does not compute brain. Oh, thank you, Mr.
Data, for reading the jokes.

Speaker 1 Thank you very much to our panel, Brian Butterworth, Matt Parker and Hannah Fry.

Speaker 7 Next week, we are asking, are humans still evolving? And if so, should they?

Speaker 1 Are we about to see the dawn of a new superbeing with shiny hair and the brain the size of the planet? Or will humanity shrivel into a strange bald creature in knitwear?

Speaker 1 And we'll also ask if I should have been more suspicious where Brian said, you pop out and get coffee, I'll just write a nice ending.

Speaker 1 Good night.

Speaker 1 In the infinite multi-cage.

Speaker 6 Till now, nice again.

Speaker 8 Be our guest at Disney's enchanting musical, Beauty and the Beast. Fill your heart with joy and Disney magic.
Brought to life like never before.

Speaker 8 Coming to the Orpheum Theater July 14th through August 9th. Tickets at BroadwaySF.com.