Maths QI XL

This programme contains some strong language

CHEERING AND APPLAUSE

Go-oo-oo-od evening, good evening, good evening, good evening,

good evening, good evening, and welcome to QI,

where tonight we're doing the maths and making the money.

Let's meet our mathematical masterminds.

The irrational Aisling Bea.

APPLAUSE

The recurring Susan Calman.

APPLAUSE

A prime example, Sandi Toksvig.

APPLAUSE

And the square root of f-all, Alan Davies.

LAUGHTER AND APPLAUSE

So, let's get their numbers.

Susan goes:

# One, two, three, four... #

Aisling goes:

# Two, four, six, eight... #

-Sandi goes:

-# Five-seven-oh-five! #

And Alan goes:

-CHILD:

-'Two twos are six!

'Two threes are seven. Two fours are 24.'

LAUGHTER Well done.

It's getting worse, you know.

Now, before we start, we've already done a little market research

to see if many heads are better than one.

We've asked a random selection of our studio audience to guess

how many sweets are in this jar,

and we want each member of the panel to do the same, right?

So you can write down your thoughts.

I'll come back to you at the end of the show

and ask you for your best guesses.

The winner will get to call themselves Smarty-Pants.

Can I just check that they are actually sweets first of all?

Oh, yes, they really are individual chocolate beans.

-I've done it already.

-Wow!

-Done.

You can put it away till the end of the show.

Now, what was this man very good at doing with his fingers?

This man being the man sitting down with the crown.

He kind of looks like he's doing the Macarena,

but I don't think they used to do that.

Is it a card trick? Is it a "nothing up my sleeves", is it one of those?

It looks like that.

-AISLING:

-Is the man in the middle Jesus?

I know that face from somewhere.

-We're in the Old Testament.

-Oh, are we?

-Well...

The man in the middle is Daniel.

He was in a lion's den, if you remember.

He was in prison and he was released from prison

because he had the ability to interpret...?

-Dreams.

-Dreams.

-Dreams.

And the King whose dreams he interpreted was?

Happy.

LAUGHTER

-Asleep.

-N, N, N...

Nestafarius.

-Nebuchadnezzar.

-Nebuchadnezzar.

-Oh, I was close.

-Yes, yes.

Nebuchadnezzar, who was king of?

All things around him.

-Babylon.

-He was.

-Yes.

-And the Babylonians were very good

at doing what with their fingers?

Gardening. The Hanging Gardens of Babylon.

-What's the theme... Yes, no, you're right. What's...

-Green-fingered.

-Babylon is...

-What's the theme of our show tonight?

-Babylon is where...

-Adding up, adding up.

-Maths.

-Yeah.

-Maths.

Babylonians, I won't say they invented mathematics, exactly,

but they had a counting system on their fingers which was

different from ours.

How's our counting system work? One, two, three, four, five...

One, two, three, four, five, six, seven, eight, nine, ten. Phew!

And therefore, because of that...

-Decimal, decimal.

-We have a decimal system, based on ten.

But they have a different system,

they counted on their fingers differently.

- Oh, they did the... - One, two, three...

-They went one, two, three, four...

-They went the JOINTS of the fingers.

-Yeah, the joints.

-Yes. One, two, three. Four, five, six. Seven, eight, nine, Ten, 11, 12.

And then they'd put their thumb up. 13, 14, 15.

16, 17, 18, 19, 20, 21,

22, 23, 24.

Put their finger up.

And so on, until they got to 60, which is five iterations of 12.

After that you'd need another person.

Yes, exactly. Just as we would need another person after ten.

That's the point. And they had a very successful system.

Why is that important and influential?

Well, it's the hours of the day, is it?

Hours of the day, 60 minutes in an hour.

60 seconds in a minute.

But the 24 divides into more than any other number,

divides by two, three, four, six, eight...

-Oh, Alan, you're on fire!

-..and 12.

LAUGHTER AND APPLAUSE

-Yeah! Absolutely right.

-Good boy!

We also have 360...

Degrees.

..degrees in a full circle. 12 inches to a foot.

-12 is so much more pleasing, I think.

-It is.

Well, it's factorisable,

and therefore it's a much more natural way.

It seems like it was some chap with more time on his hands.

Ten is easy - you look and think, "There's ten," straight away.

He's thinking, "But we could be more creative," and he's working out...

-Isn't he? He's got more time.

-But they didn't have the internet.

They were just looking at their hands, going,

"I wish I had a Game Boy. May as well count my knuckles."

I've got a question.

Yeah?

When you want to say to someone, just one, I just want one.

-You know, across a room.

-Yeah.

Get me two, get me two. How do you do that?

Do you have to go like that?

If you go like that it means three, you get three of everything.

It's a very interesting question.

I'm only going to tell you this three more times.

If you were Roman, that would be five, wouldn't it?

It's very confusing.

-Yeah, the Romans, that's five. Yeah.

-There you are, that's it.

Now, last night, I tossed two heads at the same time.

What are the chances? What?

-I don't understand, what are you doing? No, no, what?

-No, no.

-Yeah, no, it's fine.

-No, no, I misunderstood, I misunderstood.

It's completely fine.

Two coins at the same time?

Yeah, a coin here, a coin there.

I just want to know what the odds are.

Because I'm tempted to say one in three, but I bet it's not.

Well, what...

KLAXON

-SUSAN:

-It's seven in 94.

-No, you've got two coins, right.

-Yeah.

There are four possible outcomes.

There's heads-heads.

Heads-tails.

Yeah.

Tails-tails.

-And tails-heads.

-Tails-heads.

-Tails-heads. Yeah.

-Yeah. So it's one in four.

-One in four.

-One in four.

-It's one in four.

Does it have anything to do with whether you normally toss

with your right hand or toss with your left hand?

That's assuming it's an equal toss.

The thing is, it's not that difficult a thing to understand mathematically,

but this was given to Members of Parliament as a question in 2012.

60% of MPs got it wrong.

Did that include the Chancellor of the Exchequer?

Well, there was a split on party lines.

47% of the Tories got it wrong.

And 77% of Labour MPs got it wrong.

Now, listen, can I...? I should have said this at the beginning,

I have to be very honest, I am phobic about maths.

No, I understand.

I was like you, I was also... My father's a mathematician,

a physicist, and I was phobic about maths.

-Yeah.

-I always said, "Oh, no, I'm allergic to maths, I can't do it."

-But, actually, it's very beautiful, isn't it, it's really...

-Oh, now I love it.

-I wish one could be turned on to it.

-Yeah.

-I'm going to get turned on tonight to maths.

All right.

My thinking, Stephen, is if it's a head and a tail, that's one outcome.

-Yeah.

-And then a tail and a tail and a head and a head.

I'm not counting which coin does a thing.

I'm still sticking with three.

Ah, then you think it's one in three.

And you're still wrong.

But I'd give them a break, though,

because if I was in parliament and I was like,

"Listen, I know you said you're going to fix the housing system

"and you're going to sort my benefits,

"but the big question is - I've got two coins.

"I've got really good hands, I can flip them at the same time.

"What's the probability of each hand?"

Like, if he could pull that out and go, "You're a witch!"

and then... You wouldn't trust them.

Do you know the story of the professor of mathematics

at the University of Warwick, Jeffrey Hamilton,

giving a lecture in the 1970s on this topic?

He was talking about probabilities

and about it either coming down heads or coming down tails

and how you could calculate that it was going to be either one

or the other, and he tossed the coin in the air

and it fell from his hand and it rolled across the lecture theatre

and ended up exactly on its edge.

So I like the fact there is a chance element in all these things.

Always, absolutely. Yeah.

And of course, ordinary people who are not MPs are just as fallible.

In fact, 74% got it wrong - only 3% more stupid than the Labour MPs.

-At least then they're representing the common man.

-Yeah.

There was a third-pound burger, the A&E company, the rival to McDonalds.

People preferred it to the McDonalds version, but it failed.

When people were asked why they didn't buy it, they said,

well, it was a con.

Oh, they thought it was less than a quarter pound?

They thought you got less meat.

AMERICAN ACCENT: It's only a third, it's not a quarter!

And three is a smaller number than four,

therefore a third of a pound must be less than a quarter of a pound.

-Oh, my God.

-And this is the most powerful nation on Earth.

LAUGHTER

This is also the nation where nine out of ten high school graduates

-think that Joan of Arc is Noah's wife, so...

-Yes.

LAUGHTER

But on the subject of probability, I've got this.

It's really interesting, it's a probability issue.

You want a pack of cards each.

-I can't catch.

-Oh, well caught.

-Well held.

We've got some for you. All right.

I want you to take the cards out and give them a good shuffle,

good shuffle. I'm going to do the same.

I've just shuffled them.

LAUGHTER

Beautifully done.

Sandi's, Sandi's, Sandi's... Look at her, she's like a croupier.

Jesus!

Yeah. Very good.

Oh, no.

Very good.

-Yes, I've shuffled, I've riffle shuffled.

-Yeah.

-I'm not a gambler.

-OK. OK, so can you shove your cards in here?

Oh, all right, then.

All right. Thank you. I'll give it a good shake.

Is this going to be one of those Derren Brown ones where we

all can't eat for a week, or something like that?

No, nothing like that. There you are. There you go.

All right. It's just about probability, it's not a big deal.

Is there anything you can't turn your hand to, Stephen? Now it's magic.

You haven't seen me turn my hand to anything yet.

OK. And I'll put my cards in, as well.

There we go. All right. And give it all a good shake.

All right, so you take one card out.

Don't look, and if you can put it close to your chest,

but not, no, no, don't look.

-I've looked, I know what it is.

-Well, it doesn't matter. All right.

The point is to shove it close to your chest so that that's where you're going to...

That's not your chest, darling.

The reason to shove it close to your chest is so that

when you reveal it, it's camera height.

-Oh, right.

-That's all it is.

All right. So take one out, feel it, yeah, random. All right.

-Magic.

-Yeah, very good, very good. All right. I'll do the same. All right. All right.

I'll do the same. OK, so the point is it's about probability.

The first card you choose, it could be anything.

The second card, the probability it's going to be the same card is quite small.

And it's even less likely that three cards will be the same,

and so on and so on.

The chances that you'd get all the cards the same

is about one in two billion.

Now there is a possibility,

but a very unlikely possibility, that two of the cards will be the same.

-OK.

-So Sandi, you'll reveal your card.

-Yours is the six of clubs, all right.

-Me?

OK, and you reveal yours. Oh, my God!

Oh!

Now Alan. Oh! You reveal yours.

Oh, no, surely not.

No, oh, my God! And mine as well!

Oh, there you go!

APPLAUSE Funny, how can that happen?

There it is.

-Burn him!

-He's a witch.

Yeah. There you are. OK.

-He's a witch.

-That's a very good trick.

-Thank you very much.

-That's very good.

-That's terribly good.

APPLAUSE

-All right, there we are.

-Fantastic, honestly.

-That was really good.

-Oh, you're sweet, thank you.

It was like Paul Daniels was in the room.

If only he was in the bag.

LAUGHTER

So the chances were about one in two billion that you'd get all

the cards the same and it just happened this evening.

I'm amazed. So, tell me now, do animals count?

Do you mean in life, in a sort of sociological...?

-They count very much, in that sense.

-They count.

But do they count in the sense of actually...?

From what I know, there are some animals that can count.

Yes, you're right.

-They all lined up for Noah. I'm just saying.

-Yeah.

Yeah, and that's a fact story, a true fact story.

-That's a fact story, so...

-Yeah.

-You don't hear them fighting.

Have you any thoughts on this side of the room?

Well, I can imagine a monkey can count.

Surely.

There must be a rhesus monkey with an accountancy degree,

-there must be.

-Yeah.

But you're spot on. Not only monkeys, but monkeys certainly are.

Apparently chicks when they hatch

can show some propensity towards being able to count.

One, two, three, four, five, chicks.

Because you can see their heads counting, can't you, they're like one, two, three, four.

Well, let me give you a list of some of the animals that have been

spotted counting.

Pigeons, parrots, raccoons, ferrets, rats, salamanders, honeybees,

monkeys and apes

have all been seen to count, add and subtract.

Rhesus monkeys - funny you should mention them -

at Columbia University have shown they can arrange up to nine objects in the correct numerical sequence.

It's always rhesus monkeys. Do you not feel sorry for them?

-They're always saying, oh, let's teach them to speak French, or...

-Yeah, you're right.

Crows and parrots can count up to five or six.

Cormorants can count up to seven. Now how do you know that?

They take seven fish back to the nest.

-Not quite that.

-Something like that.

Actually, Chinese fishermen have trained them to catch fish for them.

And what they do is they put a ring round their throat,

so that they can't swallow fish themselves.

So they catch the fish, but dump them on the deck of the boat.

And how they've trained them is that once they get past seven, on

the eighth they get rid of the ring and the cormorant can catch its own.

I love that, when they make up their own mind.

There used to be a bear at Regent's Park Zoo in the 1920s

that was fed biscuits by the general public.

And on Mondays it was half price and so they got a lot more biscuits.

And so on Tuesdays the bear used to take day the off.

Yes, that's it.

He counted days, or she counted days - ursine calendar.

It's brilliant.

But I suppose it's when in need, like you wouldn't be needing

to count up stuff if you're a bear, like, you're not...

But sometimes you'll see, maybe they need to count how many kids they have.

Yes, yeah.

And they can tell if one of them has gone missing.

Although ducks are rubbish at that, they are. I live on a house boat for many, many years,

and we're forever trying to get baby ducks to join back up

with Mother, who'd just gone off.

She was off down to Battersea.

Sandi, loads of your stories of what you do for entertainment are like,

we used to try and convince ducks to hang out with each other...

I suffer from a fatal condition, Aisling,

which is posh voice, no money.

LAUGHTER AND APPLAUSE

That sounds absolutely awful, I would hate to have that.

What's funny about this, though, is that birds have got tiny,

-tiny brains. Really, you would expect nothing of a bird.

-Mmm.

And yet some of the primates have got quite big brains.

You'd think they'd be more than counting and yet

they don't seem to be doing more than count to five, like the birds.

I don't think it's anything to do with the brain

because I remember being in the desert in Africa

and there were ants I was shown who apparently work out their shadow

and the angle of the sun in order to get their path back home.

Now, really, that's kind of trigonometry, isn't it?

And you wouldn't think an ant would be doing it.

But they actually use their own shadow to work out...

to calculate their route.

Yes, and there are mosquito fish, which is a kind of carp,

and they are able to count, it seems.

If they are harassed by a male they take refuge in a shoal

of other mosquito fish.

They can count on their female...

Yeah, but they detect the difference between just one or two or

two or three or three or four. They can't tell

the difference between four or five, so, you know, it's basically

a small amount they can tell and they hide in the largest number.

It may be because the male mosquito fish has the largest penis

-of any fish relative to its body.

-Oh, God.

It's 70% of its length.

And it's barbed.

I don't think it's possible to come on this programme

and not discuss the penis.

No, it isn't. Not while I've got a breath in my body, Sandi!

LAUGHTER AND APPLAUSE

Now, why don't bankers give a damn what people think of them?

Because they're psychopaths and they lack empathy.

Something like one in ten people who work on Wall Street have

-psychopathic tendencies. Apparently.

-Yes, it's true, yes.

-But that leaves 90% perfectly fine, doesn't it?

-Yeah.

It must be because in their world it all seems fine, what they do.

That's probably true. But there's a funny thing about money.

Are you aware of that Hollywood phrase?

I think it was William Goldman - "follow the money".

You follow the money when you watch a movie.

So if you see a movie and someone, you know,

has a suitcase of money, everyone...

You can register it, watch their eyes move -

people watch the money. You can't help it, it's very human.

You know, the first time you get a load of cash in your hand,

-which occasionally I have, it's just...

-That's the point.

You know that scene in...

What's the one where Demi Moore rolls around the bed on the money?

Indecent Proposal. And she puts... I've done that...

LAUGHTER

-Which William Goldman was...

-..with 40 quid. But it does feel...

-If you get a...

-In change.

And that's the point of our...

That's the point of our question.

The physical proximity to money changes the way you feel.

It seems that you can prove that being close to money makes you

care less about what people think of you.

That must be quite a new thing, cos money's quite new.

There used to be like... You used to, when you had a good night,

come home and throw chickens on yourself

because that was how you...

But now it's cash.

But let me take you through the experiment.

Test subjects were asked who they wanted to work with.

They were told randomly either that everyone else wanted to work

with them or they were told that nobody did.

So half the subjects felt rejected by their peers, half felt reinforced.

Now, some of the subjects had been previously exposed to money

and they were just told it was a test for manual dexterity -

could you count out this money very fast?

And the other half were asked the same question,

but it was bits of blank paper.

The ones who had handled the money were not offended

when told that nobody wanted to work with them.

The ones that had handled the paper were offended.

I've got a Scottish fiver.

Coming here, trying to buy England!

LAUGHTER AND APPLAUSE

-It's a status thing, maybe it makes you feel more important.

-Exactly.

-I think it can make you feel safer.

-Even if it isn't yours, yeah.

Because you can buy your way out of any trouble, as we all know.

It's just, you just buy your way out, as I... Yep.

-So it makes you feel, erm, safer, I think, perhaps.

-Yeah.

It's weird, isn't it?

And they also used money to test people feigning blindness.

If someone says, "I'm blind,"

they go, "All right, let's test your blindness."

"Can't see anything." "Read this." "Can't see it."

Then you wave a £50 note in front of them, they go, "Oh, wow."

A £5 doesn't work,

but a £50 note is almost impossible for you not to look at it.

This is clearly a test not done by the NHS, who don't have a £50 note.

Well, there was an ophthalmic optician who didn't, so instead

he put a Post-it Note on his forehead saying "go fuck yourself".

And similarly, people couldn't help looking at it.

Now, what illegal substance can be found in the pockets

of most of our audience?

-How did it get there?

-Cocaine.

Cos it's on banknotes.

-Is the right answer.

-Yes!

-Yes, absolutely.

APPLAUSE

Most of our audience...

Most of our audience have residue of cocaine in their...

I can see everyone shuffling around...

They're licking their money.

More than 99% of banknotes in circulation have detectable cocaine.

-What?!

-Yes.

It's why drug dogs sometimes have difficulty in identifying.

Cos I get the sleeper train home and there's always a drug dog there.

Not for me, it's just a... It's because it's a good way

of smuggling drugs up to... up north, the sleeper train.

You don't want to go on the train. You want to get an actual mule.

Nobody is going to expect somebody to have drugs on a mule

because it's too obvious, isn't it?

I'd love somebody arriving into Glasgow on a mule.

-On a mule.

-Nothing to see.

-AISLING:

-All right, lads?

SHE IMITATES HOOVES

-Can you clean it off? I mean, I don't want it.

-Not really, no.

-Paper.

-Put a hairdryer over it and you can blow the dust off, maybe.

-That won't do it.

-There used to be a hotel, Stephen,

in New York, where the concierge was famous for washing the coins.

If you didn't like the coins in your pocket, I believe

he would put them in a jar and wash them for you.

I can't think which one it was.

Are there hotels where they don't do that?

LAUGHTER

I don't know, I have no money, I have no idea.

Now, let's leave the filthy moolah.

What do moon-starers do,

and why might they call themselves that?

Well, the clue would appear to be in the question.

Yeah.

It's too obvious, I'd say they watch bare arses all the time.

-Yeah.

-Well, moon-starers is an anagram of astronomers.

-Yay! Points to you.

-Good work.

APPLAUSE

-Good work!

-That was damn fast.

It's not an anagram, it's an aptagram. Sorry.

-Oh!

-You're right, yeah.

I'll never win, Sandi Toksvig, never!

What's an aptagram, Sandi?

An aptagram is an anagram that, where the word

means roughly the same.

Like Apple Macintosh and laptop machines.

Yeah. Semolina - is no meal.

Yeah.

Yes, moon-starer is an anagram of astronomer.

In what time in history was that a relevant thing,

the idea of anagrams and astronomers?

Well, it must have been around the time of Galileo, surely.

It was indeed, the early 17th century.

But he wouldn't have spoken English,

so why would he have changed his name to moon-starer?

Yeah, this is an example of an anagram. He...

Oh!

He didn't use English anagrams, he used...?

Gree...Latin.

Latin, very good. There he is.

Why would they have used ars magna, great art, in that?

-Oh, and that's moon is the ars.

-And ars magna is?

-And then magna is...

-Is an anagram of anagrams.

ALL: Oh.

-So, yes. But anyway, why...

-Well, because the Church took a dim view of...

Not because of the Church, although the Church did take a dim view of what he did.

I like his very casual approach to the telescope.

-He's just sort of...

-Yeah.

Now I'm going to have a cigarette and now I'm going to look again.

Was it just to make the whole thing more fun?

If only it was that.

In fact, even in his day, there was scientific rivalry.

So if you discovered something

and you wanted to tell a friend about it and you didn't want

anyone else to intercept the news, you gave it in anagram form.

Oh, it's like codes at school.

Yes, it is. Exactly that, yeah.

Do you think they ever used to, like, rub around the telescope with

ink and then run away and then he'll go, "Oh, what's that?

"Oh, no, my eye! Oh, that's trickery."

Who was his great rival and friend?

Is it an anagram?

I'm going to say Copernicus.

No, no, it wasn't Copernicus. It was Kepler.

And he sent him an anagram

because he had discovered the rings of Saturn in 1610.

ALAN CHORTLES

No, not Saturn, that's Uranus!

Oh, yeah. Sorry, I'm laughing at the wrong one.

-It's not the right planet, but it's still funny.

-I knew one of them was funny.

And he sent Kepler this.

-Oh, my!

-Ah, "smaismrm..."

-Oh. Yeah.

-Yes.

-"Nugttauriras..."

-Great.

Stick that where the sun don't shine.

-It's pretty obvious what he's putting there.

-Yeah.

-That's...

-I feel embarrassed asking you to say what it is.

I feel bad.

It's more important that the audience work it out.

-Yeah, you're right.

-I don't want to spoil the joy for them all.

You're right.

It's a Latin phrase, it actually is an anagram...

I have discovered the rings of Saturn.

Yes, it is that. Altissimum planetam tergeminum observavi.

-OK.

-"I have observed the highest planet to be triplets."

-Seen it.

-I know.

-Does he mean he's seen the moons of it, or something? What does he mean by triplets?

He thought they were moons, but in fact we now know them to be rings.

That must have been so exciting. Do you not think?

It must have been so thrilling, just that one moment

when that suddenly has happened and nobody else has seen it.

I think it's quite clever, but they worked out they're planets

because they were moving across the sky and the stars weren't.

I think it was just the first thing that made them think something was afoot.

-Oh, I know, and that's what...

-That one's moved. Why has that star moved?

-It's not a star, it's Jupiter.

-Yeah.

-And planet is from the Greek for wanderer, it means a wanderer.

-Oh.

They do this thing, I don't know if they're still doing it,

but they did it for a long time, once a month in Reykjavik,

the government would turn out all the street lighting

and there would be a lecture on the public radio about the stars.

-And people would go outside.

-Oh, brilliant.

And they got rid of all the ambient light and you could look up and listen to the lecture

-about what you were looking at. Do you not think that would be a wonderful thing?

-That is brilliant.

-Yeah.

-Yeah, I love that.

-But in terms of anagrams, this isn't an anagram, it's actually

a limerick composed by someone, which I invite you to recite to me.

See if you can.

Uh?

Yes. That's a shock, isn't it?

-Yes.

-And you can do it.

-Can you?

-Yes.

-Yep.

-Yes, you can, it is a limerick.

-OK. OK.

-Right.

You have to ask yourself what these number are, in fact.

-They have some other...

-A dozen and 12 dozen.

Ah! Yeah, 12, but 144 is also called a...?

A gross.

So a dozen, a gross, a score,

plus three times the square root of four... SUSAN LAUGHS HYSTERICALLY

..divided by seven. You're all right, you're doing well.

Plus five.

Well, calm down. I might have to slap you.

Yes!

Are you all right?

The episode of QI where Stephen just slaps me.

It's not enough to be a limerick, it has to be true.

What's nine squared?

-81.

-Yeah.

And as you know, 12 + 144 + 20 + 3...

x the square root of four ¸ 7 + 5 x 11 is 81.

-136.

-81.

No, 81. So, say it again now as a limerick. You can do it now.

-Yes, yes.

-Go on.

-Go on, then, Susan.

-Argh!

A dozen... A dozen...

A dozen, a gross and a score

Plus three times the square root of four

Divided by seven

Plus five times eleven

Equals nine squared plus not a bit more.

There you are, well done!

APPLAUSE

It was a guy called Leigh Mercer who came up with that. It's rather good.

-12 + 1 = 11 + 2.

-It does.

Yeah, but in what other ways does 12 + 1 = 11 + 2?

-Oh, is it an anagram, then?

-They're anagrams of each other.

"Twelve plus one" written out is an anagram of "eleven plus two".

Wow, you really have had too much time on your hands.

These were worked out by Nelson Mandela on Robben Island.

-I think they're rather fabulous, so there.

-They're marvellous.

All right, OK.

Now, what's the biggest mistake anyone's ever made with a pencil?

Hmm.

Oh, I say.

Oh, no, it's got to be a miscalculation or something.

Well, ah, you'd... "Ah, aah..."

"Yeah. Aah..."

MORE IMPRESSION: "Aah, aah, now, now..."

-Lead poisoning? Sucking on the lead?

-"Steady."

It's not a, it's not a historical miscalculation?

No, it's astonishing.

It took place in New York... HE GRUNTS LOUDLY

..in the '90s, I think it was.

-I'll tell you exactly...

-All right, Stephen?

Was that a pencil there?

Yeah. Just testing...

Were you miscalculating with a pencil there, sir?

I eased it in.

I eased it in and it was all fine.

Chapter four, I eased it in and it was all fine.

In 1998, there was a problem with pencils.

-"Problem with pencils."

-"Problem with pencils."

"A pencil problem," basically, yeah.

There's no reason for you to guess what it was.

I went to the Pencil Museum in Keswick. What a museum that is!

-Ah.

-No, it's seriously...

They've got a hall of fame of famous people that have visited.

-Phill Jupitus is on it.

-I've been there.

-It is a very good museum.

-It's a fabulous place.

-Ah, fabulous. It's not that.

It was pencils given to children.

Ah, drugs. Was it the one...?

Time for drugs!

I know what it was, they printed, for children,

pencils that said "do not use drugs" on them,

and when they sharpened them, eventually it said "use drugs."

-Oh, you've dropped one.

-Ah.

-You're right.

-Very good, very good.

-Here they are.

-That's "hil-ah-rious".

They say here, "Too cool to do drugs."

You shave it and it goes, "cool to do drugs."

"Cool to do drugs."

And then you shave it again and it goes, "do drugs."

-Yes!

-Do drugs.

-There you are.

It was a bit of a mistake,

but well done, Sandi. So, other mistakes include, in 1945,

the Arkansas legislature accidentally repealed all their laws at once.

With a pencil?

No, they had an act with the words - "All laws and parts of laws,

"and particularly Act 33 of the Acts of 1941, are hereby repealed."

They just meant the particular one, but it legally meant all their laws.

And then in 2003, the German agency responsible for TV licences

sent a series of reminders to St Walpurga, to pay her licence fee.

She died in 777.

Never having paid for her licence!

No. It didn't stop them asking.

And then in the Australian Morning Bulletin,

which of course is called The Bully,

they said there was an error

printed in a story titled Pigs Float Down The Dawson, on page

11 of yesterday's Bully. The story, by reporter Daniel Burdon, said

that "more than 30,000 pigs were floating down the Dawson River."

Actually, what the owner of the piggery said was,

that "30 sows and pigs".

LAUGHTER

"We'd like to apologise for the error."

Rather tragically, a group of volunteers in 1992 in France,

who had volunteered to get rid of graffiti in the caves.

-And they had a great big scrub away at a cave and...

-Oh...

Oh, no, not ancient cave paintings!

-..got rid of a 15,000-year-old bison painting.

-Oh, no!

Exactly!

-You'd be really kicking yourself after that.

-Yeah. Oops! Yeah.

I was telling you about the law in Ireland recently.

There were two within the one week.

-The first one was where drugs were legal for 48 hours.

-Oh, yes.

And people, like, just went nuts. Well, they didn't go nuts.

The said, "We're going to go nuts, but we won't really,

"just in case we get in trouble."

And then the other one was the translation of the Marriage Act

-in English, the translation in Gaelic...

-Mmm.

..technically, because of the way it was worded,

forbid marriage between a man and a woman.

It said "marriage is between men or women,

"but it's not between men and women."

So it technically made all marriage illegal.

They had to twist that one as well.

So, now, why did a failure to sell mirrors

massively improve modern media?

Because you can't put a mirror on a selfie stick.

Is that it?

Well, selfies, oddly enough, are rather close to it.

-A medieval version of selfies, at least.

-Medieval?

We're going back to the mid-15th century.

-People used to go on...?

-Pilgrimages.

Pilgrimages.

And a pilgrimage was a visit to a holy place, where there would be...

Sandwiches.

There would be sandwiches, but what were you going to see?

-Some kind of shrine or something.

-Shrine, a shrine, relics.

-Shrine. Oh, relics.

-Relics.

-I love a good relic.

Bones, material, bits of beard, bits of body,

bits of the true cross, bits of all kinds of stuff.

-Porn.

-Yeah.

-And they were so popular that you might go there

and you couldn't even get close to it.

So you'd hold up a selfie stick, as it were.

It wouldn't be a selfie stick.

It would be a box with a lid and the lid was a mirror.

And the mirror would see the relic.

And the beams and the rays would hit the mirror

and go down into the box and you'd close the box and you'd go home

and it contained the images, in your head at least, of the holy relics.

-Did it, really?

-Seriously, one of the best pieces

-of medieval marketing I've ever heard.

-Yeah.

Yes. And this particular man was making mirrors.

And he made these mirrors for Aachen,

and Aachen had Mary's robe from the night Jesus was born.

It had Jesus' swaddling clothes.

It had the cloth in which John the Baptist's head was wrapped,

after he was decapitated.

The loincloth Jesus wore on the cross.

So this person we're talking about made mirrors for pilgrims to

go to Aachen, but unfortunately he didn't sell any.

So he went back to his home town of Mainz,

and in 1450 he produced something that changed the world for ever.

A print, a stamp, a print version, Stephen, of what they'd see in...

-Print...

-And it was stamped.

-Postcards.

No, Sandi, that's kind of my idea. No.

- Souvenir mugs. - No.

He created printing. He created the printed word.

-MAN IN AUDIENCE:

-Johan Gutenberg.

-Thank you, audience.

APPLAUSE

He's Johannes Gutenberg. In 1450, he created the Gutenberg Bible,

and then other books he created.

-Oh, yes.

-It changed the world totally.

But unfortunately, the mistake was he went to basically

a kind of Dragons' Den, who funded him.

He took a wine press,

he converted the wine press into a letter press, to create books.

And then he had a Duncan Bannatyne character, "I'm out. Out."

-But his investors...

-"Don't like it, never take off, I liked your mirrors better.

-"No. I'm out."

-Well, they, unfortunately they took all the money, the investors,

the dragons took all the money. He died destitute in 1468. Very sad.

The most influential figure of his age, in those terms.

One of the first printers in Britain was called Wynkyn de Worde.

-Yes, he was.

-Don't you think that's so delightful?

-There's a society, a Wynkyn society.

-Wynkyn society, yeah.

And then, of course, Caxton was the other great one.

But, yeah.

Before he invented the printing press,

Gutenberg was a failed mirror-maker.

And so we enter the mad world of mangled misconceptions that we

call General Ignorance.

And, given the show's theme,

we've even spent a bit of money on a mathematical machine.

Ooh!

Yeah, you'll be impressed with that.

Ooh.

It looks like a happy face that's taken a lot of drugs.

LAUGHTER

-It does a bit, doesn't it?

-Yeah.

-It's lovely.

-But what is it, Stephen?

Well, I just want to know who first proved the theorem

that this model demonstrates.

-Pythagoras.

-Pythagoras.

KLAXON

Oh!

My grandfather, who was from Hungary,

always pronounced it "Peeta-goras."

"So that at school doing the mathematics,

"are you studying Peeta-goras?"

And I thought this man, Peter Goras, who was Peter?

No, it wasn't Peter Goras who first proved it.

-Oh.

-What is it, the theorem that needs to be discussed here?

A squared equals B squared plus C squared.

-Yeah, yeah, it's...

-The sum of the two, the squared of two smaller sides.

The sum on the two squares is equal to the sum on the hypotenuse, exactly.

Yeah, that big one should go into the other two.

So you can see here, the yellow, that's the triangle.

These are its two sides.

And these are the squares of the two sides,

they are literally geometrically expressed as squares,

rather than just mathematically, as if that was, say, X,

it's just not X squared, but it is literally the square, there.

And there's Y squared.

And it's supposedly equal to Z squared, which is

the longest side, the hypotenuse.

Because here's the right angle, here.

These are not right angles, obviously.

And there's that. How can we show they're equal?

Well, there are all kinds of ways, but here's one way.

Drumroll, please.

Oh, yes.

THEY BANG THE DESKS

All right, let's go.

Ooh.

Oh, that's very clever.

There it goes, pouring into the first square.

-Wow!

-Expensive.

-Is it going to fill it up?

-Wow.

-Shut the front door!

-Oh, Well, it definitely equals X squared.

-Yes.

Does it equal Y squared as well?

I need to go to the toilet.

LAUGHTER

There's Y squared, it's filling up, it's filling up,

it's filling up, it's full. And there it is.

Hurray!

APPLAUSE

Isn't that satisfactory?

Highly satisfactory.

It's the first theorem most people learn at school.

It's Pythagoras's theorem by name,

but it wasn't, it was used many, many years before him - people used

it to build buildings and Euclid demonstrated it before him.

But we give it the name of Pythagoras.

Who is Euclid, then? He was even before?

-He's the father of mathematics.

-Euclid?

-Oh, was he?

-Yeah.

-Yeah.

-Oh, Euclid, yes.

Before him, nothing.

The greatest. Yeah, well done to Euclid, we love Euclid.

So, let's take this model away. Let's hear it for him.

APPLAUSE

Now, by the end of Elizabeth I's reign, there was

a really extraordinary number of English dukes.

Five points for every one you can name.

-OK.

-Norfolk.

KLAXON

-Cambridge.

-Cambridge?

KLAXON

Erm, Hazzard. Dukes Of Hazzard.

Hazzard?

KLAXON

APPLAUSE

Is it some devilish trick and there aren't any at all?

I said it was an extraordinary number.

-The extraordinary number is none, exactly.

-Ah! Well done.

No dukes.

Can't believe I fell for that one.

By the end of her reign, there were certainly no royal dukes

because royal dukes are the issue of the monarch, essentially, and there

weren't any because Queen Elizabeth was a virgin queen and didn't marry.

And there were also no other dukes.

Are dukes always the children of the queen or king?

Royal dukes are, but other dukes aren't.

We have dukes of Marlborough, dukes of Buccleuch and so on.

And they were always into music

and that's where you get the duke box, which is...?

-I think you've understood it 100%.

-Yep.

There weren't very many peers by the time Queen Elizabeth died.

There was one marquess, 18 earls and 37...

Wigan Pier.

That hadn't been built yet, so even that didn't exist.

I know, it was a shocking thing, but, yeah.

The best peerage joke connected to Queen Elizabeth I

was told by John Aubrey, whose diaries are fantastic.

This involves the Earl of Oxford,

who some people think wrote the plays of Shakespeare.

He didn't.

He wrote this - "this Earl of Oxford, making his low obeisance to

"Queen Elizabeth, happened to let a fart, at which he was

"so abashed and ashamed that he went to travel seven years.

"On his return, the queen welcomed him home and said,

"'My Lord, I had forgot the fart.'"

Well, there you are. Yeah, good.

In the early 17th century, there were no dukes in England at all.

And that is very nearly all we have time for. However, we still

have to see if the QI audience has solved the sweet-jar challenge.

Because what we wanted to do was to take their average.

The idea is that we would arrive at the wisdom of crowds.

It was a man called Francis Galton who first came up with that phrase.

He went to a fair where there was weighing the pig

and no-one individually got it right,

but he noticed that if you added up all the guesses

-and divided them to get the average it was exactly on the weight.

-Wow.

We're hoping we'll get that here. So, reveal yourselves.

What have you come up with?

1,500.

6,024,000.

I've put 1,000 underneath,

though, cos I realised I'd really miscalculated when I saw Sandi's.

-Right.

-So 1,000 is my answer.

-1,966. 12.

-Yeah, just in case.

Just in case what?

Just in case what I see isn't what it appears to be.

Or...

Ah, clever!

Clever, clever, clever.

OK, so, the average of the audience's guess is 2,412.

The actual number of Smarties in that jar is 3,890.

So, the audience are the closest. Congratulations.

APPLAUSE

And that concerns the wisdom of crowds.

So, the time has come to tally up the scores.

Oh, my actual, oh, my actual.

So, in first place, with a magnificent two points,

it's Aisling Bea!

Oh!

APPLAUSE

And with an earth-shattering zero, it's Sandi Toksvig.

APPLAUSE

A more than respectable minus six, Susan Calman.

APPLAUSE

And on his terms, really quite handsome, minus 43,

Alan Davies.

APPLAUSE

So, it's goodnight from Susan, Sandi, Aisling, Alan and me.

And I'll leave you with this dark observation from Joseph Stalin.

My favourite dictator.

"The people who cast the votes decide nothing.

"The people who count the votes decide everything." Goodnight.

CHEERING AND APPLAUSE