Maths QI


Maths

Similar Content

Browse content similar to Maths. Check below for episodes and series from the same categories and more!

Transcript


LineFromTo

CHEERING AND APPLAUSE

0:00:240:00:25

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

0:00:320:00:35

good evening, good evening, and welcome to QI,

0:00:350:00:37

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

0:00:370:00:41

Let's meet our mathematical masterminds.

0:00:410:00:43

The irrational Aisling Bea.

0:00:440:00:46

APPLAUSE

0:00:460:00:48

The recurring Susan Calman.

0:00:500:00:53

APPLAUSE

0:00:530:00:54

A prime example, Sandi Toksvig.

0:00:570:00:59

APPLAUSE

0:00:590:01:00

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

0:01:040:01:06

LAUGHTER AND APPLAUSE

0:01:060:01:07

So, let's get their numbers.

0:01:120:01:14

Susan goes:

0:01:140:01:15

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

0:01:150:01:18

Aisling goes:

0:01:180:01:19

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

0:01:190:01:21

-Sandi goes:

-# Five-seven-oh-five! #

0:01:210:01:25

And Alan goes:

0:01:250:01:27

-CHILD:

-'Two twos are six!

0:01:270:01:28

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

0:01:280:01:32

LAUGHTER

0:01:320:01:33

Well done.

0:01:330:01:35

It's getting worse, you know.

0:01:370:01:39

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

0:01:390:01:43

This man being the man sitting down with the crown.

0:01:440:01:47

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

0:01:470:01:50

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

0:01:500:01:52

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

0:01:520:01:55

It looks like that.

0:01:550:01:56

-AISLING:

-Is the man in the middle Jesus?

0:01:560:01:58

I know that face from somewhere.

0:02:000:02:02

-We're in the Old Testament.

-Oh, are we?

-Well...

0:02:020:02:04

The man in the middle is Daniel.

0:02:040:02:07

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

0:02:070:02:10

He was in prison and he was released from prison

0:02:100:02:12

because he had the ability to interpret?

0:02:120:02:15

-Dreams.

-Dreams.

-Dreams.

0:02:150:02:17

And the King whose dreams he interpreted was?

0:02:170:02:21

Happy.

0:02:210:02:22

LAUGHTER

0:02:220:02:23

-Asleep.

-N, N, N...

0:02:230:02:26

Nestafarius.

0:02:260:02:27

-Nebuchadnezzar.

-Nebuchadnezzar.

0:02:270:02:30

-Oh, I was close.

-Yes, yes.

0:02:300:02:31

Nebuchadnezzar, who was king of?

0:02:310:02:33

All things around him.

0:02:330:02:34

-Babylon.

-He was.

0:02:360:02:38

-Yes.

-And the Babylonians were very good

0:02:380:02:40

at doing what with their fingers?

0:02:400:02:42

Gardening. The Hanging Gardens of Babylon.

0:02:420:02:44

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

-Green-fingered.

0:02:440:02:48

-Babylon is...

-What's the theme of our show tonight?

0:02:480:02:50

-Babylon is where...

-Adding up, adding up.

0:02:500:02:52

-Maths.

-Yeah.

-Maths.

0:02:520:02:53

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

0:02:530:02:56

but they had a counting system on their fingers which was

0:02:560:02:59

different from ours.

0:02:590:03:00

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

0:03:000:03:03

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

0:03:030:03:06

And therefore, because of that...

0:03:060:03:08

-Decimal, decimal.

-We have a decimal system, based on ten.

0:03:080:03:10

But they have a different system,

0:03:100:03:12

they counted on their fingers differently.

0:03:120:03:14

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

0:03:140:03:16

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

-They went the JOINTS of the fingers.

0:03:160:03:19

-Yeah, the joints.

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

0:03:190:03:23

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

0:03:230:03:26

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

0:03:260:03:28

22, 23, 24.

0:03:280:03:30

Put their finger up.

0:03:300:03:31

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

0:03:310:03:36

After that you'd need another person.

0:03:360:03:38

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

0:03:380:03:41

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

0:03:410:03:45

Why is that important and influential?

0:03:450:03:48

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

0:03:480:03:50

Hours of the day, 60 minutes in an hour.

0:03:500:03:53

60 seconds in a minute.

0:03:530:03:54

But the 24 divides into more than any other number,

0:03:540:03:57

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

0:03:570:03:59

-Oh, Alan, you're on fire!

-..and 12.

0:03:590:04:01

LAUGHTER AND APPLAUSE

0:04:010:04:02

-Yeah! Absolutely right.

-Good boy!

0:04:090:04:11

We also have 360...

0:04:110:04:13

Degrees.

0:04:130:04:14

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

0:04:140:04:19

-12 is so much more pleasing, I think.

-It is.

0:04:190:04:21

Well, it's factorisable,

0:04:210:04:23

and therefore it's a much more natural way.

0:04:230:04:25

I've got a question.

0:04:250:04:27

Yeah?

0:04:270:04:28

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

0:04:280:04:31

-You know, across a room.

-Yeah.

0:04:310:04:34

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

0:04:340:04:36

Do you have to go like that?

0:04:360:04:38

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

0:04:420:04:45

It's a very interesting question.

0:04:450:04:47

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

0:04:470:04:49

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

0:04:490:04:51

It's very confusing.

0:04:510:04:52

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

-There you are, that's it.

0:04:520:04:55

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

0:04:550:04:59

What are the chances? What?

0:04:590:05:02

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

-No, no.

0:05:040:05:07

-Yeah, no, it's fine.

-No, no, I misunderstood, I misunderstood.

0:05:070:05:10

It's completely fine.

0:05:100:05:12

Two coins at the same time?

0:05:120:05:13

Yeah, a coin here, a coin there.

0:05:130:05:15

I just want to know what the odds are.

0:05:150:05:17

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

0:05:170:05:19

Well, what...

0:05:190:05:21

KLAXON

0:05:210:05:22

-SUSAN:

-It's seven in 94.

0:05:250:05:27

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

-Yeah.

0:05:280:05:31

There are four possible outcomes.

0:05:310:05:33

There's heads-heads.

0:05:330:05:35

Heads-tails.

0:05:350:05:36

Yeah.

0:05:360:05:37

Tails-tails.

0:05:370:05:39

-And tails-heads.

-Tails-heads.

0:05:390:05:40

-Tails-heads. Yeah.

-Yeah. So it's one in four.

0:05:400:05:43

-One in four.

-One in four.

-It's one in four.

0:05:430:05:44

Does it have anything to do with whether you normally toss

0:05:440:05:48

with your right hand, or toss with your left hand?

0:05:480:05:51

That's assuming it's an equal toss.

0:05:510:05:53

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

0:05:530:05:57

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

0:05:570:06:03

60% of MPs got it wrong.

0:06:030:06:07

Did that include the Chancellor of the Exchequer?

0:06:080:06:10

Well, there was a split on party lines.

0:06:100:06:12

47% of the Tories got it wrong.

0:06:120:06:15

And 77% of Labour MPs got it wrong.

0:06:160:06:19

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

0:06:210:06:23

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

0:06:230:06:27

No, I understand.

0:06:270:06:28

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

0:06:280:06:32

a physicist, and I was phobic about maths.

0:06:320:06:35

-Yeah.

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

0:06:350:06:38

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

-Oh, now I love it.

0:06:380:06:42

-I wish one could be turned on to it.

-Yeah.

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

0:06:420:06:45

All right.

0:06:450:06:46

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

0:06:460:06:49

-Yeah.

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

0:06:490:06:53

I'm not counting which coin does a thing.

0:06:530:06:55

I'm still sticking with three.

0:06:550:06:57

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

0:06:570:06:59

And you're still wrong.

0:06:590:07:00

On the subject of probability, I've got this,

0:07:020:07:04

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

0:07:040:07:07

You want a pack of cards each.

0:07:070:07:08

-I can't catch.

-Oh, well caught.

-Well held.

0:07:100:07:12

We've got some for you. All right.

0:07:120:07:13

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

0:07:130:07:16

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

0:07:160:07:18

I've just shuffled them.

0:07:180:07:19

Beautifully done.

0:07:240:07:26

Sandi's, Sandi's, Sandi's been doing it, look her, she's like a croupier.

0:07:260:07:31

Jesus!

0:07:310:07:32

Yeah. Very good.

0:07:340:07:35

Oh, no.

0:07:350:07:36

Very good.

0:07:360:07:38

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

-Yeah.

0:07:380:07:40

-I'm not a gambler.

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

0:07:400:07:44

Oh, all right, then.

0:07:440:07:45

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

0:07:450:07:48

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

0:07:480:07:50

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

0:07:500:07:53

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

0:07:530:07:55

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

0:07:550:07:59

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

0:07:590:08:02

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

0:08:020:08:04

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

0:08:040:08:06

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

0:08:070:08:10

All right, so you take one card out.

0:08:100:08:12

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

0:08:120:08:15

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

0:08:150:08:16

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

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

0:08:160:08:19

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

0:08:190:08:23

That's not your chest, darling.

0:08:230:08:25

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

0:08:250:08:27

when you reveal it, it's camera height.

0:08:270:08:29

-Oh, right.

-That's all it is.

0:08:290:08:31

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

0:08:310:08:34

-Magic.

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

0:08:340:08:39

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

0:08:390:08:42

The first card you choose, it could be anything.

0:08:420:08:45

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

0:08:450:08:49

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

0:08:490:08:52

and so on and so on.

0:08:520:08:54

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

0:08:540:08:57

is about one in two billion.

0:08:570:09:00

Now there is a possibility,

0:09:000:09:03

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

0:09:030:09:06

-OK.

-So Sandi, you'll reveal your card.

0:09:060:09:09

-Yours is the six of clubs, all right.

-Me?

0:09:110:09:13

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

0:09:130:09:15

Oh!

0:09:150:09:17

Now Alan. Oh! You reveal yours.

0:09:190:09:20

Oh, no, surely not.

0:09:200:09:21

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

0:09:210:09:25

Oh, there you go!

0:09:250:09:26

APPLAUSE

0:09:260:09:27

Funny, how can that happen?

0:09:270:09:28

There it is.

0:09:300:09:31

-Burn him!

-He's a witch.

0:09:310:09:33

Yeah. There you are. OK.

0:09:330:09:35

-He's a witch.

-That's a very good trick.

0:09:350:09:36

-Thank you very much.

-That's very good.

-That's terribly good.

0:09:360:09:39

-All right, there we are.

-Fantastic, honestly.

0:09:450:09:47

-That was really good.

-Oh, you're sweet, thank you.

0:09:470:09:49

It was like Paul Daniels was in the room.

0:09:490:09:51

If only he was in the bag.

0:09:510:09:53

LAUGHTER

0:09:530:09:54

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

0:09:550:10:00

the cards the same and it just happened, this evening.

0:10:000:10:03

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

0:10:030:10:07

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

0:10:080:10:12

-They count very much, in that sense.

-They count.

0:10:120:10:16

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

0:10:160:10:18

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

0:10:180:10:23

Yes, you're right.

0:10:230:10:24

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

-Yeah.

0:10:240:10:28

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

0:10:280:10:30

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

-Yeah.

-You don't hear them fighting.

0:10:300:10:33

Have you any thoughts on this side of the room?

0:10:330:10:36

Well, I can imagine a monkey can count.

0:10:360:10:38

Surely.

0:10:380:10:39

There must be a rhesus monkey with an accountancy degree,

0:10:390:10:42

-there must be.

-Yeah.

0:10:420:10:43

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

0:10:430:10:47

Apparently chicks when they hatch,

0:10:470:10:48

can show some propensity towards being able to count.

0:10:480:10:51

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

0:10:510:10:53

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

0:10:530:10:57

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

0:10:570:10:59

spotted counting.

0:10:590:11:01

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

0:11:010:11:06

monkeys and apes.

0:11:060:11:07

Have all been seen to count, add and subtract.

0:11:070:11:12

Rhesus monkeys - funny you should mention them,

0:11:120:11:14

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

0:11:140:11:19

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

0:11:190:11:21

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

-Yeah, you're right.

0:11:210:11:26

Crows and parrots can count up to five or six.

0:11:260:11:28

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

0:11:280:11:31

They take seven fish back to the nest.

0:11:310:11:33

-Not quite that.

-Something like that.

0:11:330:11:35

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

0:11:350:11:38

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

0:11:380:11:41

so that they can't swallow fish themselves.

0:11:410:11:44

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

0:11:440:11:48

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

0:11:480:11:53

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

0:11:530:11:57

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

0:11:570:12:00

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

0:12:000:12:03

was fed biscuits by the general public.

0:12:030:12:06

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

0:12:060:12:08

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

0:12:080:12:11

Yes, that's it.

0:12:110:12:12

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

0:12:120:12:15

It's brilliant.

0:12:150:12:16

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

0:12:160:12:19

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

0:12:190:12:21

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

0:12:210:12:25

Yes, yeah.

0:12:250:12:26

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

0:12:260:12:29

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

0:12:290:12:33

and we were forever trying to get baby ducks to join back up

0:12:330:12:37

with mother, who'd just gone off.

0:12:370:12:38

She was off down to Battersea.

0:12:380:12:40

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

0:12:400:12:43

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

0:12:430:12:47

I suffer from a fatal condition, Aisling,

0:12:470:12:49

which is posh voice, no money.

0:12:490:12:51

LAUGHTER AND APPLAUSE

0:12:510:12:53

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

0:12:580:13:01

Anyway, now, what do moon-starers do,

0:13:030:13:06

and why might they call themselves that?

0:13:060:13:09

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

0:13:090:13:11

Yeah.

0:13:110:13:13

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

0:13:130:13:17

-Yeah.

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

0:13:170:13:21

Yay! Points to you.

0:13:210:13:23

-Good work!

-That was damn fast.

0:13:270:13:28

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

0:13:280:13:32

-Oh!

-You're right, yeah.

0:13:320:13:34

I'll never win, Sandi Toksvig, never!

0:13:340:13:36

What's an aptagram, Sandi?

0:13:360:13:38

An aptagram is an anagram that, where the word

0:13:380:13:40

means roughly the same.

0:13:400:13:42

Like Apple Macintosh and laptop machines.

0:13:420:13:45

Yeah. Semolina - is no meal.

0:13:450:13:48

Yeah.

0:13:480:13:49

Yes, moon-starer is an anagram of astronomer.

0:13:490:13:51

In what time in history was that a relevant thing?

0:13:510:13:55

The idea of anagrams and astronomers?

0:13:550:13:59

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

0:13:590:14:02

It was indeed, the early 17th century.

0:14:020:14:04

But he wouldn't have spoken English,

0:14:040:14:06

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

0:14:060:14:09

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

0:14:090:14:11

Oh!

0:14:110:14:12

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

0:14:120:14:15

Gree...Latin.

0:14:160:14:18

Latin, very good. There he is.

0:14:180:14:22

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

0:14:220:14:26

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

-And ars magna is?

0:14:260:14:28

-And then magna is...

-Is an anagram of anagrams.

0:14:280:14:31

ALL: Oh.

0:14:320:14:33

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

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

0:14:330:14:37

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

0:14:370:14:40

I like his very casual approach to the telescope.

0:14:400:14:43

-He's just sort of...

-Yeah.

0:14:430:14:44

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

0:14:440:14:47

Was it just to make the whole thing more fun?

0:14:470:14:49

If only it was that.

0:14:490:14:51

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

0:14:510:14:54

So if you discovered something

0:14:540:14:56

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

0:14:560:14:58

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

0:14:580:15:03

Oh, it's like codes at school.

0:15:030:15:04

Yes, it is. Exactly that, yeah.

0:15:040:15:05

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

0:15:050:15:08

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

0:15:080:15:11

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

0:15:110:15:13

Who was his great rival and friend?

0:15:130:15:15

Is it an anagram?

0:15:150:15:17

I'm going to say Copernicus.

0:15:170:15:18

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

0:15:180:15:21

And he sent him an anagram

0:15:210:15:22

because he had discovered the rings of Saturn in 1610.

0:15:220:15:26

ALAN CHORTLES

0:15:260:15:27

No, not Saturn, that's Uranus!

0:15:270:15:29

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

0:15:290:15:32

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

-I knew one of them was funny.

0:15:350:15:38

And he sent Kepler this.

0:15:380:15:40

-Oh, my!

-Ah, "smaismrm..."

0:15:420:15:44

-Oh. Yeah.

-Yes.

0:15:440:15:45

-"Nugttauriras..."

-Great.

0:15:450:15:47

Stick that where the sun don't shine.

0:15:470:15:49

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

-Yeah.

0:15:490:15:52

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

0:15:520:15:54

I have discovered the rings of Saturn.

0:15:540:15:56

Yes, it is that. Altissimum planetam tergeminum observavi.

0:15:560:16:02

-OK.

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

0:16:020:16:04

-Seen it.

-I know.

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

0:16:040:16:09

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

0:16:090:16:12

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

0:16:120:16:14

It must have been so thrilling, just that one moment

0:16:140:16:17

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

0:16:170:16:20

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

0:16:200:16:23

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

0:16:230:16:26

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

0:16:260:16:29

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

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

0:16:290:16:32

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

-Yeah.

0:16:320:16:34

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

-Oh.

0:16:340:16:37

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

0:16:370:16:40

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

0:16:400:16:42

the government would turn out all the street lighting

0:16:420:16:45

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

0:16:450:16:49

-And people would go outside.

-Oh, brilliant.

0:16:490:16:50

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

0:16:500:16:54

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

-That is brilliant.

0:16:540:16:59

-Yeah.

-Yeah, I love that.

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

0:16:590:17:02

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

0:17:020:17:07

See if you can.

0:17:070:17:09

Uh?

0:17:090:17:10

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

0:17:100:17:12

-Yes.

-And you can do it.

0:17:120:17:14

-Can you?

-Yes.

-Yep.

-Yes, you can, it is a limerick.

0:17:140:17:17

-OK. OK.

-Right.

0:17:170:17:18

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

0:17:180:17:21

-They have some other...

-A dozen and 12 dozen.

0:17:210:17:23

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

0:17:230:17:25

A gross.

0:17:250:17:27

So a dozen, a gross, a score,

0:17:270:17:31

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

0:17:310:17:35

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

0:17:350:17:38

Plus five.

0:17:380:17:40

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

0:17:400:17:43

Yes!

0:17:430:17:44

Are you all right?

0:17:470:17:48

The episode of QI where Stephen just slaps me.

0:17:480:17:51

So say it again as a limerick.

0:17:510:17:53

-You can do it now.

-OK. Yes, yes.

0:17:530:17:55

-Go on.

-Go on, then Susan.

0:17:550:17:56

A dozen, a gross and a score,

0:17:580:18:00

plus three times the square root of four,

0:18:000:18:04

divided by seven plus five times 11

0:18:040:18:07

equals nine squared plus not a bit more.

0:18:070:18:10

There you are. Well done.

0:18:100:18:12

APPLAUSE

0:18:120:18:13

It was a guy called Leigh Mercer who came up with that.

0:18:180:18:20

And it's rather good. 12 plus one equals, 11 plus two?

0:18:200:18:23

Yes. It does.

0:18:230:18:24

Yeah, but in what other ways does 12 plus one equals 11 plus two?

0:18:240:18:28

Oh, is it an anagram, then?

0:18:280:18:29

They're anagrams of each other.

0:18:290:18:30

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

0:18:300:18:34

Eleven plus two.

0:18:340:18:36

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

0:18:360:18:38

These were worked out by Nelson Mandela on Robben Island.

0:18:380:18:42

I think they're rather fabulous, so there.

0:18:430:18:46

-They are rather. They're marvellous.

-All right, OK.

0:18:460:18:49

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

0:18:490:18:53

Hmm.

0:18:530:18:54

Oh, I say.

0:18:540:18:55

Oh, now, it's got to be a miscalculation or something.

0:18:550:18:58

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

0:18:580:19:00

"Yeah. Aah..."

0:19:000:19:01

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

0:19:010:19:04

-Lead poisoning? Sucking on the lead?

-"Steady."

0:19:040:19:06

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

0:19:060:19:09

No, it's astonishing.

0:19:090:19:10

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

0:19:100:19:12

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

0:19:120:19:14

-I'll tell you exactly...

-All right, Stephen?

0:19:140:19:16

Is that the pencil there?

0:19:160:19:18

Yeah. Just testing...

0:19:180:19:19

Were you miscalculating with a pencil there, sir?

0:19:190:19:22

I eased it in.

0:19:230:19:24

I eased it in and it was all fine.

0:19:260:19:29

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

0:19:290:19:31

In 1998, there was a problem with pencils. "Problem with pencils."

0:19:330:19:36

"Problem with pencils."

0:19:360:19:38

"A pencil problem," basically, yeah.

0:19:380:19:40

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

0:19:400:19:43

It was pencils given to children.

0:19:430:19:45

Ah, drugs. Was it the one...

0:19:450:19:47

Time for drugs!

0:19:470:19:49

I know what it was they printed, for children,

0:19:510:19:53

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

0:19:530:19:56

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

0:19:560:19:59

-Oh, you've dropped one.

-Ah.

0:19:590:20:00

-You're right.

-Very good, very good.

0:20:000:20:02

-Here they are.

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

0:20:020:20:05

On, they say here, "Too cool to do drugs."

0:20:050:20:09

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

0:20:090:20:11

"Cool to do drugs."

0:20:110:20:13

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

0:20:130:20:16

-Yes!

-Do drugs.

-There you are.

0:20:160:20:18

It was a bit of a mistake,

0:20:180:20:21

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

0:20:210:20:25

the Arkansas legislature accidentally repealed all their laws at once.

0:20:250:20:30

With a pencil?

0:20:300:20:31

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

0:20:310:20:36

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

0:20:360:20:41

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

0:20:410:20:47

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

0:20:470:20:51

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

0:20:510:20:56

She died in 777.

0:20:570:21:00

Never having paid for her licence!

0:21:010:21:04

No. It didn't stop them asking.

0:21:040:21:06

And then in the Australian Morning Bulletin,

0:21:060:21:08

which of course is called The Bully,

0:21:080:21:11

they said there was an error

0:21:110:21:14

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

0:21:140:21:18

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

0:21:180:21:22

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

0:21:220:21:26

Actually, what the owner of the piggery said was,

0:21:260:21:29

that "30 sows and pigs".

0:21:290:21:32

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

0:21:370:21:40

So, now, why did a failure to sell mirrors

0:21:400:21:43

massively improve modern media?

0:21:430:21:46

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

0:21:460:21:48

Is that it?

0:21:480:21:49

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

0:21:490:21:52

-A medieval version of selfies, at least.

-Medieval?

0:21:520:21:56

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

0:21:560:21:59

-People used to go on..?

-Pilgrimages.

0:21:590:22:01

Pilgrimages.

0:22:010:22:03

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

0:22:030:22:08

Sandwiches.

0:22:080:22:09

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

0:22:090:22:12

-Some kind of shrine or something.

-Shrine, a shrine, relics.

0:22:120:22:15

-Shrine. Oh, relics.

-Relics.

-I love a good relic.

0:22:150:22:17

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

0:22:170:22:20

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

0:22:200:22:23

-Porn.

-Yeah.

-And they were so popular that you might go there

0:22:230:22:26

and you couldn't even get close to it.

0:22:260:22:28

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

0:22:280:22:30

It wouldn't be a selfie stick.

0:22:300:22:32

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

0:22:320:22:36

And the mirror would see the relic.

0:22:360:22:39

And the beams and the rays would hit the mirror

0:22:390:22:42

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

0:22:420:22:45

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

0:22:450:22:50

-Did it, really?

-Seriously, one of the best pieces

0:22:500:22:53

-of medieval marketing I've ever heard.

-Yeah.

0:22:530:22:55

Yes. And this particular man was making mirrors.

0:22:550:22:59

And he made these mirrors for Aachen,

0:22:590:23:02

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

0:23:020:23:06

It had Jesus's swaddling clothes.

0:23:060:23:07

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

0:23:070:23:11

after he was decapitated.

0:23:110:23:13

The loincloth Jesus wore on the cross.

0:23:130:23:15

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

0:23:150:23:19

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

0:23:190:23:23

So he went back to his home town of Mainz,

0:23:230:23:26

and in 1450, he produced something that changed the world forever.

0:23:260:23:33

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

0:23:330:23:39

-Print...

-And it was stamped.

-Postcards.

0:23:390:23:41

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

0:23:410:23:43

- Souvenir mugs. - No.

0:23:430:23:45

He created printing. He created the printed word.

0:23:450:23:47

-MAN IN AUDIENCE:

-Johan Gutenberg.

-Thank you, audience.

0:23:470:23:50

APPLAUSE

0:23:500:23:51

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

0:23:540:23:57

and then other books he created.

0:23:570:23:59

-Oh, yes.

-It changed the world totally.

0:23:590:24:01

But unfortunately, the mistake was he went to basically

0:24:010:24:03

a kind of Dragons' Den, who funded him.

0:24:030:24:07

He took a wine press,

0:24:070:24:08

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

0:24:080:24:12

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

0:24:120:24:15

-But his investors...

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

0:24:150:24:19

-"No. I'm out."

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

0:24:190:24:22

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

0:24:220:24:28

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

0:24:280:24:30

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

0:24:300:24:34

-Yes, he was.

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

0:24:340:24:36

-There's a society, a Wynkyn society.

-Wynkyn society, yeah.

0:24:360:24:38

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

0:24:380:24:41

But, yeah.

0:24:410:24:42

Before he invented the printing press,

0:24:420:24:44

Gutenberg was a failed mirror-maker.

0:24:440:24:46

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

0:24:460:24:50

call General Ignorance.

0:24:500:24:52

And, given the show's theme,

0:24:520:24:55

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

0:24:550:24:58

Ooh!

0:24:580:25:00

Yeah, you'll be impressed with that.

0:25:000:25:02

Ooh.

0:25:020:25:03

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

0:25:030:25:06

LAUGHTER

0:25:060:25:08

-It does a bit, doesn't it?

-Yeah.

0:25:080:25:09

-It's lovely.

-But what is it, Stephen?

0:25:090:25:12

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

0:25:120:25:15

that this model demonstrates.

0:25:150:25:17

-Pythagoras.

-Pythagoras.

0:25:170:25:18

KLAXON

0:25:180:25:20

Oh!

0:25:200:25:21

My grandfather, who was from Hungary,

0:25:240:25:26

always pronounced it "Peeta-goras."

0:25:260:25:29

"So that at school doing the mathematics,

0:25:290:25:32

"are you studying Peeta-goras?"

0:25:320:25:34

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

0:25:340:25:36

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

0:25:360:25:40

-Oh.

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

0:25:400:25:44

A squared equals B squared plus C squared.

0:25:440:25:46

-Yeah, yeah, it's...

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

0:25:460:25:49

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

0:25:490:25:52

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

0:25:520:25:55

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

0:25:550:25:57

These are its two sides.

0:25:570:25:59

And these are the squares of the two sides,

0:25:590:26:01

they are literally geometrically expressed as squares,

0:26:010:26:04

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

0:26:040:26:08

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

0:26:080:26:11

And there's Y squared.

0:26:110:26:13

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

0:26:130:26:16

the longest side, the hypotenuse.

0:26:160:26:18

Because here's the right angle, here.

0:26:180:26:20

These are not right angles, obviously.

0:26:200:26:22

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

0:26:220:26:25

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

0:26:250:26:28

Drumroll, please.

0:26:280:26:30

Oh, yes.

0:26:300:26:31

THEY BANG THE DESKS

0:26:310:26:33

All right, let's go.

0:26:330:26:34

Ooh.

0:26:360:26:37

Oh, that's very clever.

0:26:380:26:40

There it goes, pouring into the first square.

0:26:400:26:42

-Wow!

-Expensive.

-Is it going to fill it up?

0:26:420:26:44

-Wow.

-Shut the front door!

0:26:440:26:47

-Oh, Well, it definitely equals X squared.

-Yes.

0:26:470:26:49

Does it equal Y squared as well?

0:26:490:26:51

I need to go to the toilet.

0:26:510:26:53

LAUGHTER

0:26:530:26:54

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

0:26:550:26:57

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

0:26:570:27:00

Hurray!

0:27:000:27:01

APPLAUSE

0:27:010:27:03

Isn't that satisfactory?

0:27:040:27:05

Highly satisfactory.

0:27:080:27:09

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

0:27:090:27:12

It's Pythagoras's theorem by name,

0:27:120:27:14

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

0:27:140:27:18

it to build buildings and Euclid demonstrated it before him.

0:27:180:27:22

But we give it the name of Pythagoras.

0:27:220:27:24

Who is Euclid, then? He was even before?

0:27:240:27:26

-He's the father of mathematics.

-Euclid?

0:27:260:27:29

-Oh, was he?

-Yeah.

-Yeah.

-Oh, Euclid, yes.

0:27:290:27:31

Before him, nothing.

0:27:310:27:32

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

0:27:320:27:35

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

0:27:350:27:38

APPLAUSE

0:27:380:27:39

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

0:27:440:27:46

Oh, my actual, oh, my actual.

0:27:460:27:49

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

0:27:490:27:52

it's Aisling Bee!

0:27:520:27:54

Oh!

0:27:540:27:55

APPLAUSE

0:27:550:27:56

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

0:27:590:28:04

APPLAUSE

0:28:040:28:05

A more than respectable minus six, Susan Calman.

0:28:080:28:10

APPLAUSE

0:28:100:28:12

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

0:28:160:28:19

Alan Davies.

0:28:190:28:20

APPLAUSE

0:28:200:28:22

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

0:28:280:28:31

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

0:28:310:28:35

My favourite dictator.

0:28:350:28:37

"The people who cast the votes decide nothing.

0:28:370:28:41

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

0:28:410:28:46

CHEERING AND APPLAUSE

0:28:460:28:47

Download Subtitles

SRT

ASS