Maths

Download Subtitles

Transcript

0:00:24 > 0:00:25CHEERING AND APPLAUSE

0:00:32 > 0:00:35Go-oo-oo-od evening, good evening, good evening, good evening,

0:00:35 > 0:00:37good evening, good evening, and welcome to QI,

0:00:37 > 0:00:41where tonight we're doing the maths and making the money.

0:00:41 > 0:00:43Let's meet our mathematical masterminds.

0:00:44 > 0:00:46The irrational Aisling Bea.

0:00:46 > 0:00:48APPLAUSE

0:00:50 > 0:00:53The recurring Susan Calman.

0:00:53 > 0:00:54APPLAUSE

0:00:57 > 0:00:59A prime example, Sandi Toksvig.

0:00:59 > 0:01:00APPLAUSE

0:01:04 > 0:01:06And the square root of f-all, Alan Davies.

0:01:06 > 0:01:07LAUGHTER AND APPLAUSE

0:01:12 > 0:01:14So, let's get their numbers.

0:01:14 > 0:01:15Susan goes:

0:01:15 > 0:01:18# One, two, three, four... #

0:01:18 > 0:01:19Aisling goes:

0:01:19 > 0:01:21# Two, four, six, eight... #

0:01:21 > 0:01:25- Sandi goes: - # Five-seven-oh-five! #

0:01:25 > 0:01:27And Alan goes:

0:01:27 > 0:01:28- CHILD:- 'Two twos are six!

0:01:28 > 0:01:32'Two threes are seven. Two fours are 24.'

0:01:32 > 0:01:33LAUGHTER

0:01:33 > 0:01:35Well done.

0:01:37 > 0:01:39It's getting worse, you know.

0:01:39 > 0:01:43Now, what was this man very good at doing with his fingers?

0:01:44 > 0:01:47This man being the man sitting down with the crown.

0:01:47 > 0:01:50He kind of looks like he's doing the Macarena,

0:01:50 > 0:01:52but I don't think they used to do that.

0:01:52 > 0:01:55Is it a card trick? Is it a "nothing up my sleeves", is it one of those?

0:01:55 > 0:01:56It looks like that.

0:01:56 > 0:01:58- AISLING:- Is the man in the middle Jesus?

0:02:00 > 0:02:02I know that face from somewhere.

0:02:02 > 0:02:04- We're in the Old Testament. - Oh, are we?- Well...

0:02:04 > 0:02:07The man in the middle is Daniel.

0:02:07 > 0:02:10He was in a lion's den, if you remember.

0:02:10 > 0:02:12He was in prison and he was released from prison

0:02:12 > 0:02:15because he had the ability to interpret?

0:02:15 > 0:02:17- Dreams.- Dreams.- Dreams.

0:02:17 > 0:02:21And the King whose dreams he interpreted was?

0:02:21 > 0:02:22Happy.

0:02:22 > 0:02:23LAUGHTER

0:02:23 > 0:02:26- Asleep.- N, N, N...

0:02:26 > 0:02:27Nestafarius.

0:02:27 > 0:02:30- Nebuchadnezzar. - Nebuchadnezzar.

0:02:30 > 0:02:31- Oh, I was close. - Yes, yes.

0:02:31 > 0:02:33Nebuchadnezzar, who was king of?

0:02:33 > 0:02:34All things around him.

0:02:36 > 0:02:38- Babylon.- He was.

0:02:38 > 0:02:40- Yes.- And the Babylonians were very good

0:02:40 > 0:02:42at doing what with their fingers?

0:02:42 > 0:02:44Gardening. The Hanging Gardens of Babylon.

0:02:44 > 0:02:48- What's the theme, yes, no, you're right. What's...- Green-fingered.

0:02:48 > 0:02:50- Babylon is...- What's the theme of our show tonight?

0:02:50 > 0:02:52- Babylon is where... - Adding up, adding up.

0:02:52 > 0:02:53- Maths.- Yeah.- Maths.

0:02:53 > 0:02:56Babylonians, I won't say they invented mathematics, exactly,

0:02:56 > 0:02:59but they had a counting system on their fingers which was

0:02:59 > 0:03:00different from ours.

0:03:00 > 0:03:03How's our counting system work? One, two, three, four, five...

0:03:03 > 0:03:06One, two, three, four, five, six, seven, eight, nine, ten. Phew!

0:03:06 > 0:03:08And therefore, because of that...

0:03:08 > 0:03:10- Decimal, decimal.- We have a decimal system, based on ten.

0:03:10 > 0:03:12But they have a different system,

0:03:12 > 0:03:14they counted on their fingers differently.

0:03:14 > 0:03:16- Oh, they did the... - One, two, three...

0:03:16 > 0:03:19- They went one, two, three, four... - They went the JOINTS of the fingers.

0:03:19 > 0:03:23- Yeah, the joints.- Yes. One, two, three. Four, five, six. Seven, eight, nine, Ten, 11, 12.

0:03:23 > 0:03:26And then they'd put their thumb up. 13, 14, 15.

0:03:26 > 0:03:2816, 17, 18, 19, 20, 21,

0:03:28 > 0:03:3022, 23, 24.

0:03:30 > 0:03:31Put their finger up.

0:03:31 > 0:03:36And so on, until they got to 60, which is five iterations of 12.

0:03:36 > 0:03:38After that you'd need another person.

0:03:38 > 0:03:41Yes, exactly. Just as we would need another person after ten.

0:03:41 > 0:03:45That's the point. And they had a very successful system.

0:03:45 > 0:03:48Why is that important and influential?

0:03:48 > 0:03:50Well, it's the hours of the day, is it?

0:03:50 > 0:03:53Hours of the day, 60 minutes in an hour.

0:03:53 > 0:03:5460 seconds in a minute.

0:03:54 > 0:03:57But the 24 divides into more than any other number,

0:03:57 > 0:03:59divides by two, three, four, six, eight...

0:03:59 > 0:04:01- Oh, Alan, you're on fire! - ..and 12.

0:04:01 > 0:04:02LAUGHTER AND APPLAUSE

0:04:09 > 0:04:11- Yeah! Absolutely right. - Good boy!

0:04:11 > 0:04:13We also have 360...

0:04:13 > 0:04:14Degrees.

0:04:14 > 0:04:19Degrees in a full circle. 12 inches to a foot.

0:04:19 > 0:04:21- 12 is so much more pleasing, I think.- It is.

0:04:21 > 0:04:23Well, it's factorisable,

0:04:23 > 0:04:25and therefore it's a much more natural way.

0:04:25 > 0:04:27I've got a question.

0:04:27 > 0:04:28Yeah?

0:04:28 > 0:04:31When you want to say to someone, just one, I just want one.

0:04:31 > 0:04:34- You know, across a room. - Yeah.

0:04:34 > 0:04:36Get me two, get me two. How do you do that?

0:04:36 > 0:04:38Do you have to go like that?

0:04:42 > 0:04:45If you go like that it means three, you get three of everything.

0:04:45 > 0:04:47It's a very interesting question.

0:04:47 > 0:04:49I'm only going to tell you this three more times.

0:04:49 > 0:04:51If you were Roman, that would be five, wouldn't it.

0:04:51 > 0:04:52It's very confusing.

0:04:52 > 0:04:55- Yeah, the Romans, that's five. Yeah. - There you are, that's it.

0:04:55 > 0:04:59Now, last night, I tossed two heads at the same time.

0:04:59 > 0:05:02What are the chances? What?

0:05:04 > 0:05:07- I don't understand, what are you doing? No, no, what?- No, no.

0:05:07 > 0:05:10- Yeah, no, it's fine.- No, no, I misunderstood, I misunderstood.

0:05:10 > 0:05:12It's completely fine.

0:05:12 > 0:05:13Two coins at the same time?

0:05:13 > 0:05:15Yeah, a coin here, a coin there.

0:05:15 > 0:05:17I just want to know what the odds are.

0:05:17 > 0:05:19Because I'm tempted to say one in three, but I bet it's not.

0:05:19 > 0:05:21Well, what...

0:05:21 > 0:05:22KLAXON

0:05:25 > 0:05:27- SUSAN:- It's seven in 94.

0:05:28 > 0:05:31- No, you've got two coins, right. - Yeah.

0:05:31 > 0:05:33There are four possible outcomes.

0:05:33 > 0:05:35There's heads-heads.

0:05:35 > 0:05:36Heads-tails.

0:05:36 > 0:05:37Yeah.

0:05:37 > 0:05:39Tails-tails.

0:05:39 > 0:05:40- And tails-heads. - Tails-heads.

0:05:40 > 0:05:43- Tails-heads. Yeah. - Yeah. So it's one in four.

0:05:43 > 0:05:44- One in four.- One in four. - It's one in four.

0:05:44 > 0:05:48Does it have anything to do with whether you normally toss

0:05:48 > 0:05:51with your right hand, or toss with your left hand?

0:05:51 > 0:05:53That's assuming it's an equal toss.

0:05:53 > 0:05:57The thing is, it's not that difficult a thing to understand mathematically,

0:05:57 > 0:06:03but this was given to Members of Parliament as a question, in 2012.

0:06:03 > 0:06:0760% of MPs got it wrong.

0:06:08 > 0:06:10Did that include the Chancellor of the Exchequer?

0:06:10 > 0:06:12Well, there was a split on party lines.

0:06:12 > 0:06:1547% of the Tories got it wrong.

0:06:16 > 0:06:19And 77% of Labour MPs got it wrong.

0:06:21 > 0:06:23Now, listen, can I, I should have said this at the beginning,

0:06:23 > 0:06:27I have to be very honest, I am phobic about maths.

0:06:27 > 0:06:28No, I understand.

0:06:28 > 0:06:32I was like you, I was also... my father's a mathematician,

0:06:32 > 0:06:35a physicist, and I was phobic about maths.

0:06:35 > 0:06:38- Yeah.- I always said, Oh, no, I'm allergic to maths, I don't, I can't do it.

0:06:38 > 0:06:42- But actually it's very beautiful, isn't it, it's really... - Oh, now I love it.

0:06:42 > 0:06:45- I wish one could be turned on to it. - Yeah.- I'm going to get turned on tonight to maths.

0:06:45 > 0:06:46All right.

0:06:46 > 0:06:49My thinking, Stephen, is if it's a head and a tail, that's one outcome.

0:06:49 > 0:06:53- Yeah.- And then a tail and a tail and a head and a head.

0:06:53 > 0:06:55I'm not counting which coin does a thing.

0:06:55 > 0:06:57I'm still sticking with three.

0:06:57 > 0:06:59Ah, then you think it's one in three.

0:06:59 > 0:07:00And you're still wrong.

0:07:02 > 0:07:04On the subject of probability, I've got this,

0:07:04 > 0:07:07it's really interesting, it's a probability issue.

0:07:07 > 0:07:08You want a pack of cards each.

0:07:10 > 0:07:12- I can't catch. - Oh, well caught.- Well held.

0:07:12 > 0:07:13We've got some for you. All right.

0:07:13 > 0:07:16I want you to take the cards out and give them a good shuffle,

0:07:16 > 0:07:18good shuffle. I'm going to do the same.

0:07:18 > 0:07:19I've just shuffled them.

0:07:24 > 0:07:26Beautifully done.

0:07:26 > 0:07:31Sandi's, Sandi's, Sandi's been doing it, look her, she's like a croupier.

0:07:31 > 0:07:32Jesus!

0:07:34 > 0:07:35Yeah. Very good.

0:07:35 > 0:07:36Oh, no.

0:07:36 > 0:07:38Very good.

0:07:38 > 0:07:40- Yes, I've shuffled, I've riffle shuffled.- Yeah.

0:07:40 > 0:07:44- I'm not a gambler.- OK. OK, so can you shove your cards in here?

0:07:44 > 0:07:45Oh, all right, then.

0:07:45 > 0:07:48All right. Thank you. I'll give it a good shake.

0:07:48 > 0:07:50Is this going to be one of those Derren Brown ones where we

0:07:50 > 0:07:53all can't eat for a week, or something like that?

0:07:53 > 0:07:55No, nothing like that. There you are. There you go.

0:07:55 > 0:07:59All right. It's just about probability, it's not a big deal.

0:07:59 > 0:08:02Is there anything you can't turn your hand to, Stephen? Now it's magic.

0:08:02 > 0:08:04You haven't seen me turn my hand to anything yet.

0:08:04 > 0:08:06OK. And I'll put my cards in as well.

0:08:07 > 0:08:10There we go. All right. And give it all a good shake.

0:08:10 > 0:08:12All right, so you take one card out.

0:08:12 > 0:08:15Don't look, and if you can put it close to your chest,

0:08:15 > 0:08:16but not, no, no, don't look.

0:08:16 > 0:08:19- I've looked, I know what it is. - Well, it doesn't matter. All right.

0:08:19 > 0:08:23The point is to shove it close to your chest so that that's where you're going to...

0:08:23 > 0:08:25That's not your chest, darling.

0:08:25 > 0:08:27The reason to shove it close to your chest is so that

0:08:27 > 0:08:29when you reveal it, it's camera height.

0:08:29 > 0:08:31- Oh, right. - That's all it is.

0:08:31 > 0:08:34All right. So take one out, feel it, yeah, random. All right.

0:08:34 > 0:08:39- Magic.- Yeah, very good, very good. All right. I'll do the same. All right. All right.

0:08:39 > 0:08:42I'll do the same. OK, so the point is it's about probability.

0:08:42 > 0:08:45The first card you choose, it could be anything.

0:08:45 > 0:08:49And the second card, the probability it's going to be the same card is quite small.

0:08:49 > 0:08:52And it's even less likely that three cards will be the same,

0:08:52 > 0:08:54and so on and so on.

0:08:54 > 0:08:57The chances that you'd get all the cards the same

0:08:57 > 0:09:00is about one in two billion.

0:09:00 > 0:09:03Now there is a possibility,

0:09:03 > 0:09:06but a very unlikely possibility, that two of the cards will be the same.

0:09:06 > 0:09:09- OK.- So Sandi, you'll reveal your card.

0:09:11 > 0:09:13- Yours is the six of clubs, all right.- Me?

0:09:13 > 0:09:15OK, and you reveal yours. Oh, my God!

0:09:15 > 0:09:17Oh!

0:09:19 > 0:09:20Now Alan. Oh! You reveal yours.

0:09:20 > 0:09:21Oh, no, surely not.

0:09:21 > 0:09:25No, oh, my God! And mine as well!

0:09:25 > 0:09:26Oh, there you go!

0:09:26 > 0:09:27APPLAUSE

0:09:27 > 0:09:28Funny, how can that happen?

0:09:30 > 0:09:31There it is.

0:09:31 > 0:09:33- Burn him!- He's a witch.

0:09:33 > 0:09:35Yeah. There you are. OK.

0:09:35 > 0:09:36- He's a witch. - That's a very good trick.

0:09:36 > 0:09:39- Thank you very much.- That's very good.- That's terribly good.

0:09:45 > 0:09:47- All right, there we are. - Fantastic, honestly.

0:09:47 > 0:09:49- That was really good. - Oh, you're sweet, thank you.

0:09:49 > 0:09:51It was like Paul Daniels was in the room.

0:09:51 > 0:09:53If only he was in the bag.

0:09:53 > 0:09:54LAUGHTER

0:09:55 > 0:10:00So the chances were about one in two billion that you'd get all

0:10:00 > 0:10:03the cards the same and it just happened, this evening.

0:10:03 > 0:10:07I'm amazed. So, tell me now, do animals count?

0:10:08 > 0:10:12Do you mean in life, in a sort of sociological...?

0:10:12 > 0:10:16- They count very much, in that sense. - They count.

0:10:16 > 0:10:18But do they count in the sense of actually...?

0:10:18 > 0:10:23Well, from what I know, there are some animals that can count.

0:10:23 > 0:10:24Yes, you're right.

0:10:24 > 0:10:28- They all lined up for Noah. I'm just saying.- Yeah.

0:10:28 > 0:10:30Yeah, and that's a fact story, a true fact story.

0:10:30 > 0:10:33- That's a fact story, so... - Yeah.- You don't hear them fighting.

0:10:33 > 0:10:36Have you any thoughts on this side of the room?

0:10:36 > 0:10:38Well, I can imagine a monkey can count.

0:10:38 > 0:10:39Surely.

0:10:39 > 0:10:42There must be a rhesus monkey with an accountancy degree,

0:10:42 > 0:10:43- there must be.- Yeah.

0:10:43 > 0:10:47But you're spot on. Not only monkeys, but monkeys certainly are.

0:10:47 > 0:10:48Apparently chicks when they hatch,

0:10:48 > 0:10:51can show some propensity towards being able to count.

0:10:51 > 0:10:53One, two, three, four, five, chicks.

0:10:53 > 0:10:57Because you can see their heads counting, can't you, they're like one, two, three, four.

0:10:57 > 0:10:59Well, let me give you a list of some of the animals that have been

0:10:59 > 0:11:01spotted counting.

0:11:01 > 0:11:06Pigeons, parrots, raccoons, ferrets, rats, salamanders, honeybees,

0:11:06 > 0:11:07monkeys and apes.

0:11:07 > 0:11:12Have all been seen to count, add and subtract.

0:11:12 > 0:11:14Rhesus monkeys - funny you should mention them,

0:11:14 > 0:11:19at Columbia University, have shown they can arrange up to nine objects in the correct numerical sequence.

0:11:19 > 0:11:21It's always rhesus monkeys. Do you not feel sorry for them?

0:11:21 > 0:11:26- They're always saying, oh, let's teach them to speak French, or... - Yeah, you're right.

0:11:26 > 0:11:28Crows and parrots can count up to five or six.

0:11:28 > 0:11:31Cormorants can count up to seven. Now how do you know that?

0:11:31 > 0:11:33They take seven fish back to the nest.

0:11:33 > 0:11:35- Not quite that. - Something like that.

0:11:35 > 0:11:38Actually, Chinese fishermen have trained them to catch fish for them.

0:11:38 > 0:11:41And what they do is they put a ring round their throat,

0:11:41 > 0:11:44so that they can't swallow fish themselves.

0:11:44 > 0:11:48So they catch the fish, but dump them on the deck of the boat.

0:11:48 > 0:11:53And how they've trained them is, that once they get past seven, on

0:11:53 > 0:11:57the eighth they get rid of the ring and the cormorant can catch its own.

0:11:57 > 0:12:00I love that, when they make up their own mind.

0:12:00 > 0:12:03There used to be a bear at Regent's Park Zoo in the 1920s that

0:12:03 > 0:12:06was fed biscuits by the general public.

0:12:06 > 0:12:08And on Mondays it was half price and so they got a lot more biscuits.

0:12:08 > 0:12:11And so on Tuesdays the bear used to take day the off.

0:12:11 > 0:12:12Yes, that's it.

0:12:12 > 0:12:15He counted days, or she, counted days - ursine calendar.

0:12:15 > 0:12:16It's brilliant.

0:12:16 > 0:12:19But I suppose it's when in need, like you wouldn't be needing

0:12:19 > 0:12:21to count up stuff if you're a bear, like, you're not...

0:12:21 > 0:12:25But sometimes you'll see, maybe they need to count how many kids they have.

0:12:25 > 0:12:26Yes, yeah.

0:12:26 > 0:12:29And they can tell if one of them has gone missing.

0:12:29 > 0:12:33Although ducks are rubbish at that, they are. I lived on a house boat for many, many years,

0:12:33 > 0:12:37and we were forever trying to get baby ducks to join back up

0:12:37 > 0:12:38with mother, who'd just gone off.

0:12:38 > 0:12:40She was off down to Battersea.

0:12:40 > 0:12:43Sandi, loads of your stories of what you do for entertainment are like,

0:12:43 > 0:12:47we used to try and convince ducks to hang out with each other...

0:12:47 > 0:12:49I suffer from a fatal condition, Aisling,

0:12:49 > 0:12:51which is posh voice, no money.

0:12:51 > 0:12:53LAUGHTER AND APPLAUSE

0:12:58 > 0:13:01That sounds absolutely awful, I would hate to have that.

0:13:03 > 0:13:06Anyway, now, what do moon-starers do,

0:13:06 > 0:13:09and why might they call themselves that?

0:13:09 > 0:13:11Well, the clue would appear to be in the question.

0:13:11 > 0:13:13Yeah.

0:13:13 > 0:13:17It's too obvious, I'd say they watch bare arses all the time.

0:13:17 > 0:13:21- Yeah.- Well, moon-starers is an anagram of astronomers.

0:13:21 > 0:13:23Yay! Points to you.

0:13:27 > 0:13:28- Good work! - That was damn fast.

0:13:28 > 0:13:32It's not an anagram, it's an aptagram. Sorry.

0:13:32 > 0:13:34- Oh!- You're right, yeah.

0:13:34 > 0:13:36I'll never win, Sandi Toksvig, never!

0:13:36 > 0:13:38What's an aptagram, Sandi?

0:13:38 > 0:13:40An aptagram is an anagram that, where the word

0:13:40 > 0:13:42means roughly the same.

0:13:42 > 0:13:45Like Apple Macintosh and laptop machines.

0:13:45 > 0:13:48Yeah. Semolina - is no meal.

0:13:48 > 0:13:49Yeah.

0:13:49 > 0:13:51Yes, moon-starer is an anagram of astronomer.

0:13:51 > 0:13:55In what time in history was that a relevant thing?

0:13:55 > 0:13:59The idea of anagrams and astronomers?

0:13:59 > 0:14:02Well, it must have been around the time of Galileo, surely.

0:14:02 > 0:14:04It was indeed, the early 17th century.

0:14:04 > 0:14:06But he wouldn't have spoken English,

0:14:06 > 0:14:09so why would he have changed his name to moon-starer?

0:14:09 > 0:14:11Yeah, this is an example of an anagram. He...

0:14:11 > 0:14:12Oh!

0:14:12 > 0:14:15He didn't use English anagrams, he used..?

0:14:16 > 0:14:18Gree...Latin.

0:14:18 > 0:14:22Latin, very good. There he is.

0:14:22 > 0:14:26Why would they have used ars magna, great art, in that?

0:14:26 > 0:14:28- Oh, and that's moon is the ars. - And ars magna is?

0:14:28 > 0:14:31- And then magna is... - Is an anagram of anagrams.

0:14:32 > 0:14:33ALL: Oh.

0:14:33 > 0:14:37- So, yes. But anyway, why... - Well, because the Church took a dim view of...

0:14:37 > 0:14:40Not because of the Church, although the Church did take a dim view of what he did.

0:14:40 > 0:14:43I like his very casual approach to the telescope.

0:14:43 > 0:14:44- He's just sort of... - Yeah.

0:14:44 > 0:14:47Now I'm going to have a cigarette and now I'm going to look again.

0:14:47 > 0:14:49Was it just to make the whole thing more fun?

0:14:49 > 0:14:51If only it was that.

0:14:51 > 0:14:54In fact, even in his day, there was scientific rivalry.

0:14:54 > 0:14:56So if you discovered something

0:14:56 > 0:14:58and you wanted to tell a friend about it and you didn't want

0:14:58 > 0:15:03anyone else to intercept the news, you gave it in anagram form.

0:15:03 > 0:15:04Oh, it's like codes at school.

0:15:04 > 0:15:05Yes, it is. Exactly that, yeah.

0:15:05 > 0:15:08Do you think they ever used to like rub around the telescope with

0:15:08 > 0:15:11ink and then run away and then he'll go, "Oh, what's that?

0:15:11 > 0:15:13"Oh, no, my eye! Oh, that's trickery."

0:15:13 > 0:15:15Who was his great rival and friend?

0:15:15 > 0:15:17Is it an anagram?

0:15:17 > 0:15:18I'm going to say Copernicus.

0:15:18 > 0:15:21No, no, it wasn't Copernicus. It was Kepler.

0:15:21 > 0:15:22And he sent him an anagram

0:15:22 > 0:15:26because he had discovered the rings of Saturn in 1610.

0:15:26 > 0:15:27ALAN CHORTLES

0:15:27 > 0:15:29No, not Saturn, that's Uranus!

0:15:29 > 0:15:32Oh, yeah. Sorry, I'm laughing at the wrong one.

0:15:35 > 0:15:38- It's not the right planet, but it's still funny. - I knew one of them was funny.

0:15:38 > 0:15:40And he sent Kepler this.

0:15:42 > 0:15:44- Oh, my!- Ah, "smaismrm..."

0:15:44 > 0:15:45- Oh. Yeah.- Yes.

0:15:45 > 0:15:47- "Nugttauriras..."- Great.

0:15:47 > 0:15:49Stick that where the sun don't shine.

0:15:49 > 0:15:52- It's pretty obvious what he's putting there.- Yeah.

0:15:52 > 0:15:54It's a Latin phrase, it actually is an anagram...

0:15:54 > 0:15:56I have discovered the rings of Saturn.

0:15:56 > 0:16:02Yes, it is that. Altissimum planetam tergeminum observavi.

0:16:02 > 0:16:04- OK.- "I have observed the highest planet to be triplets."

0:16:04 > 0:16:09- Seen it.- I know.- Does he mean he's seen the moons of it, or something? What does he mean by triplets?

0:16:09 > 0:16:12He thought they were moons, but in fact we now know them to be rings.

0:16:12 > 0:16:14That must have been so exciting. Do you not think?

0:16:14 > 0:16:17It must have been so thrilling, just that one moment

0:16:17 > 0:16:20when that suddenly has happened and nobody else has seen it.

0:16:20 > 0:16:23I think it's quite clever, but they worked out they're planets

0:16:23 > 0:16:26because they were moving across the sky and the stars weren't.

0:16:26 > 0:16:29I think it was just the first thing that made them think something was afoot.

0:16:29 > 0:16:32- Oh, I know, and that's what... - That one's moved. Why has that star moved?

0:16:32 > 0:16:34- It's not a star, it's Jupiter. - Yeah.

0:16:34 > 0:16:37- And planet is from the Greek for wanderer, it means a wanderer.- Oh.

0:16:37 > 0:16:40They do this thing, I don't know if they're still doing it,

0:16:40 > 0:16:42but they did it for a long time, once a month in Reykjavik,

0:16:42 > 0:16:45the government would turn out all the street lighting

0:16:45 > 0:16:49and there would be a lecture on the public radio about the stars.

0:16:49 > 0:16:50- And people would go outside. - Oh, brilliant.

0:16:50 > 0:16:54And they got rid of all the ambient light and you could look up and listen to the lecture

0:16:54 > 0:16:59- about what you were looking at. Do you not think that would be a wonderful thing?- That is brilliant.

0:16:59 > 0:17:02- Yeah.- Yeah, I love that. - But in terms of anagrams, this isn't an anagram, it's actually

0:17:02 > 0:17:07a limerick composed by someone, which I invite you to recite to me.

0:17:07 > 0:17:09See if you can.

0:17:09 > 0:17:10Uh?

0:17:10 > 0:17:12Yes. That's a shock, isn't it?

0:17:12 > 0:17:14- Yes.- And you can do it.

0:17:14 > 0:17:17- Can you?- Yes.- Yep. - Yes, you can, it is a limerick.

0:17:17 > 0:17:18- OK. OK.- Right.

0:17:18 > 0:17:21You have to ask yourself what these number are, in fact.

0:17:21 > 0:17:23- They have some other... - A dozen and 12 dozen.

0:17:23 > 0:17:25Ah! Yeah, 12, but 144 is also called a..?

0:17:25 > 0:17:27A gross.

0:17:27 > 0:17:31So a dozen, a gross, a score,

0:17:31 > 0:17:35plus three times the square root of four... SUSAN LAUGHS HYSTERICALLY

0:17:35 > 0:17:38..divided by seven. You're all right, you're doing well.

0:17:38 > 0:17:40Plus five.

0:17:40 > 0:17:43Well, calm down. I might have to slap you.

0:17:43 > 0:17:44Yes!

0:17:47 > 0:17:48Are you all right?

0:17:48 > 0:17:51The episode of QI where Stephen just slaps me.

0:17:51 > 0:17:53So say it again as a limerick.

0:17:53 > 0:17:55- You can do it now. - OK. Yes, yes.

0:17:55 > 0:17:56- Go on.- Go on, then Susan.

0:17:58 > 0:18:00A dozen, a gross and a score,

0:18:00 > 0:18:04plus three times the square root of four,

0:18:04 > 0:18:07divided by seven plus five times 11

0:18:07 > 0:18:10equals nine squared plus not a bit more.

0:18:10 > 0:18:12There you are. Well done.

0:18:12 > 0:18:13APPLAUSE

0:18:18 > 0:18:20It was a guy called Leigh Mercer who came up with that.

0:18:20 > 0:18:23And it's rather good. 12 plus one equals, 11 plus two?

0:18:23 > 0:18:24Yes. It does.

0:18:24 > 0:18:28Yeah, but in what other ways does 12 plus one equals 11 plus two?

0:18:28 > 0:18:29Oh, is it an anagram, then?

0:18:29 > 0:18:30They're anagrams of each other.

0:18:30 > 0:18:34"Twelve plus one", written out, is an anagram of "eleven plus two".

0:18:34 > 0:18:36Eleven plus two.

0:18:36 > 0:18:38Wow, you really have had too much time on your hands.

0:18:38 > 0:18:42These were worked out by Nelson Mandela on Robben Island.

0:18:43 > 0:18:46I think they're rather fabulous, so there.

0:18:46 > 0:18:49- They are rather. They're marvellous. - All right, OK.

0:18:49 > 0:18:53Now, what's the biggest mistake anyone's ever made with a pencil?

0:18:53 > 0:18:54Hmm.

0:18:54 > 0:18:55Oh, I say.

0:18:55 > 0:18:58Oh, now, it's got to be a miscalculation or something.

0:18:58 > 0:19:00Well, ah, you'd... "Ah, aah..."

0:19:00 > 0:19:01"Yeah. Aah..."

0:19:01 > 0:19:04MORE IMPRESSION: "Aah, aah, now, now..."

0:19:04 > 0:19:06- Lead poisoning? Sucking on the lead? - "Steady."

0:19:06 > 0:19:09It's not a, it's not a historical miscalculation?

0:19:09 > 0:19:10No, it's astonishing.

0:19:10 > 0:19:12It took place in New York... HE GRUNTS LOUDLY

0:19:12 > 0:19:14..in the '90s, I think it was.

0:19:14 > 0:19:16- I'll tell you exactly... - All right, Stephen?

0:19:16 > 0:19:18Is that the pencil there?

0:19:18 > 0:19:19Yeah. Just testing...

0:19:19 > 0:19:22Were you miscalculating with a pencil there, sir?

0:19:23 > 0:19:24I eased it in.

0:19:26 > 0:19:29I eased it in and it was all fine.

0:19:29 > 0:19:31Chapter four, I eased it in and it was all fine.

0:19:33 > 0:19:36In 1998, there was a problem with pencils. "Problem with pencils."

0:19:36 > 0:19:38"Problem with pencils."

0:19:38 > 0:19:40"A pencil problem," basically, yeah.

0:19:40 > 0:19:43There's no reason for you to guess what it was.

0:19:43 > 0:19:45It was pencils given to children.

0:19:45 > 0:19:47Ah, drugs. Was it the one...

0:19:47 > 0:19:49Time for drugs!

0:19:51 > 0:19:53I know what it was they printed, for children,

0:19:53 > 0:19:56pencils that said "do not use drugs" on them,

0:19:56 > 0:19:59and when they sharpened them, eventually it said "use drugs."

0:19:59 > 0:20:00- Oh, you've dropped one.- Ah.

0:20:00 > 0:20:02- You're right. - Very good, very good.

0:20:02 > 0:20:05- Here they are. - That's "hil-ah-rious".

0:20:05 > 0:20:09On, they say here, "Too cool to do drugs."

0:20:09 > 0:20:11You shave it and it goes, "cool to do drugs."

0:20:11 > 0:20:13"Cool to do drugs."

0:20:13 > 0:20:16And then you shave it again and it goes, "do drugs."

0:20:16 > 0:20:18- Yes!- Do drugs. - There you are.

0:20:18 > 0:20:21It was a bit of a mistake,

0:20:21 > 0:20:25but well done, Sandi. So, other mistakes include, in 1945,

0:20:25 > 0:20:30the Arkansas legislature accidentally repealed all their laws at once.

0:20:30 > 0:20:31With a pencil?

0:20:31 > 0:20:36No, they had an act with the words - "All laws and parts of laws,

0:20:36 > 0:20:41"and particularly Act 33 of the Acts of 1941, are hereby repealed."

0:20:41 > 0:20:47They just meant the particular one, but it legally meant all their laws.

0:20:47 > 0:20:51And then in 2003, the German agency responsible for TV licences

0:20:51 > 0:20:56sent a series of reminders to St Walpurga, to pay her licence fee.

0:20:57 > 0:21:00She died in 777.

0:21:01 > 0:21:04Never having paid for her licence!

0:21:04 > 0:21:06No. It didn't stop them asking.

0:21:06 > 0:21:08And then in the Australian Morning Bulletin,

0:21:08 > 0:21:11which of course is called The Bully,

0:21:11 > 0:21:14they said there was an error

0:21:14 > 0:21:18printed in a story titled Pigs Float Down The Dawson, on page

0:21:18 > 0:21:2211 of yesterday's Bully, the story, by reporter Daniel Burdon, said

0:21:22 > 0:21:26that "more than 30,000 pigs were floating down the Dawson River."

0:21:26 > 0:21:29Actually, what the owner of the piggery said was,

0:21:29 > 0:21:32that "30 sows and pigs".

0:21:37 > 0:21:40"We'd like to apologise for the error."

0:21:40 > 0:21:43So, now, why did a failure to sell mirrors

0:21:43 > 0:21:46massively improve modern media?

0:21:46 > 0:21:48Because you can't put a mirror on a selfie stick.

0:21:48 > 0:21:49Is that it?

0:21:49 > 0:21:52Well, selfies, oddly enough, are rather close to it.

0:21:52 > 0:21:56- A medieval version of selfies, at least.- Medieval?

0:21:56 > 0:21:59We're going back to the mid-15th century.

0:21:59 > 0:22:01- People used to go on..? - Pilgrimages.

0:22:01 > 0:22:03Pilgrimages.

0:22:03 > 0:22:08And a pilgrimage was a visit to a holy place, where there would be...

0:22:08 > 0:22:09Sandwiches.

0:22:09 > 0:22:12There would be sandwiches, but what were you going to see?

0:22:12 > 0:22:15- Some kind of shrine or something. - Shrine, a shrine, relics.

0:22:15 > 0:22:17- Shrine. Oh, relics.- Relics. - I love a good relic.

0:22:17 > 0:22:20Bones, material, bits of beard, bits of body,

0:22:20 > 0:22:23bits of the true cross, bits of all kinds of stuff.

0:22:23 > 0:22:26- Porn.- Yeah.- And they were so popular that you might go there

0:22:26 > 0:22:28and you couldn't even get close to it.

0:22:28 > 0:22:30So you'd hold up a selfie stick, as it were.

0:22:30 > 0:22:32It wouldn't be a selfie stick.

0:22:32 > 0:22:36It would be a box with a lid and the lid was a mirror.

0:22:36 > 0:22:39And the mirror would see the relic.

0:22:39 > 0:22:42And the beams and the rays would hit the mirror

0:22:42 > 0:22:45and go down into the box and you'd close the box and you'd go home

0:22:45 > 0:22:50and it contained the images, in your head at least, of the holy relics.

0:22:50 > 0:22:53- Did it, really?- Seriously, one of the best pieces

0:22:53 > 0:22:55- of medieval marketing I've ever heard.- Yeah.

0:22:55 > 0:22:59Yes. And this particular man was making mirrors.

0:22:59 > 0:23:02And he made these mirrors for Aachen,

0:23:02 > 0:23:06and Aachen had Mary's robe from the night Jesus was born.

0:23:06 > 0:23:07It had Jesus's swaddling clothes.

0:23:07 > 0:23:11It had the cloth in which John the Baptist's head was wrapped,

0:23:11 > 0:23:13after he was decapitated.

0:23:13 > 0:23:15The loincloth Jesus wore on the cross.

0:23:15 > 0:23:19So this person we're talking about made mirrors for pilgrims to

0:23:19 > 0:23:23go to Aachen, but unfortunately he didn't sell any.

0:23:23 > 0:23:26So he went back to his home town of Mainz,

0:23:26 > 0:23:33and in 1450, he produced something that changed the world forever.

0:23:33 > 0:23:39A print, a stamp, a print version, Stephen, of what they'd see in...

0:23:39 > 0:23:41- Print... - And it was stamped.- Postcards.

0:23:41 > 0:23:43No, Sandi, that's kind of my idea. No.

0:23:43 > 0:23:45- Souvenir mugs. - No.

0:23:45 > 0:23:47He created printing. He created the printed word.

0:23:47 > 0:23:50- MAN IN AUDIENCE:- Johan Gutenberg. - Thank you, audience.

0:23:50 > 0:23:51APPLAUSE

0:23:54 > 0:23:57He's Johannes Gutenberg. In 1450, he created the Gutenberg Bible,

0:23:57 > 0:23:59and then other books he created.

0:23:59 > 0:24:01- Oh, yes. - It changed the world totally.

0:24:01 > 0:24:03But unfortunately, the mistake was he went to basically

0:24:03 > 0:24:07a kind of Dragons' Den, who funded him.

0:24:07 > 0:24:08He took a wine press,

0:24:08 > 0:24:12he converted the wine press into a letter press, to create books.

0:24:12 > 0:24:15And then he had a Duncan Bannatyne character, "I'm out. Out."

0:24:15 > 0:24:19- But his investors... - "Don't like it, never take off, I liked your mirrors better.

0:24:19 > 0:24:22- "No. I'm out."- Well, they, unfortunately they took all the money, the investors,

0:24:22 > 0:24:28the dragons took all the money. He died destitute in 1468. Very sad.

0:24:28 > 0:24:30The most influential figure of his age, in those terms.

0:24:30 > 0:24:34One of the first printers in Britain was called Wynkyn de Worde.

0:24:34 > 0:24:36- Yes, he was.- Don't you think that's so delightful?

0:24:36 > 0:24:38- There's a society, a Wynkyn society. - Wynkyn society, yeah.

0:24:38 > 0:24:41And then, of course, Caxton was the other great one.

0:24:41 > 0:24:42But, yeah.

0:24:42 > 0:24:44Before he invented the printing press,

0:24:44 > 0:24:46Gutenberg was a failed mirror-maker.

0:24:46 > 0:24:50And so we enter the mad world of mangled misconceptions that we

0:24:50 > 0:24:52call General Ignorance.

0:24:52 > 0:24:55And, given the show's theme,

0:24:55 > 0:24:58we've even spent a bit of money on a mathematical machine.

0:24:58 > 0:25:00Ooh!

0:25:00 > 0:25:02Yeah, you'll be impressed with that.

0:25:02 > 0:25:03Ooh.

0:25:03 > 0:25:06It looks like a happy face that's taken a lot of drugs.

0:25:06 > 0:25:08LAUGHTER

0:25:08 > 0:25:09- It does a bit, doesn't it?- Yeah.

0:25:09 > 0:25:12- It's lovely. - But what is it, Stephen?

0:25:12 > 0:25:15Well, I just want to know who first proved the theorem

0:25:15 > 0:25:17that this model demonstrates.

0:25:17 > 0:25:18- Pythagoras.- Pythagoras.

0:25:18 > 0:25:20KLAXON

0:25:20 > 0:25:21Oh!

0:25:24 > 0:25:26My grandfather, who was from Hungary,

0:25:26 > 0:25:29always pronounced it "Peeta-goras."

0:25:29 > 0:25:32"So that at school doing the mathematics,

0:25:32 > 0:25:34"are you studying Peeta-goras?"

0:25:34 > 0:25:36And I thought this man, Peter Goras, who was Peter?

0:25:36 > 0:25:40No, it wasn't Peter Goras who first proved it.

0:25:40 > 0:25:44- Oh.- What is it? The theorem that needs to be discussed here?

0:25:44 > 0:25:46A squared equals B squared plus C squared.

0:25:46 > 0:25:49- Yeah, yeah, it's...- The sum of the two, the squared of two smaller sides.

0:25:49 > 0:25:52The sum on the two squares is equal to the sum on the hypotenuse, exactly.

0:25:52 > 0:25:55Yeah, that big one should go into the other two.

0:25:55 > 0:25:57So you can see here, the yellow, that's the triangle.

0:25:57 > 0:25:59These are its two sides.

0:25:59 > 0:26:01And these are the squares of the two sides,

0:26:01 > 0:26:04they are literally geometrically expressed as squares,

0:26:04 > 0:26:08rather than just mathematically, as if that was, say, X,

0:26:08 > 0:26:11it's just not X squared, but it is literally the square, there.

0:26:11 > 0:26:13And there's Y squared.

0:26:13 > 0:26:16And it's supposedly equal to Z squared, which is

0:26:16 > 0:26:18the longest side, the hypotenuse.

0:26:18 > 0:26:20Because here's the right angle, here.

0:26:20 > 0:26:22These are not right angles, obviously.

0:26:22 > 0:26:25And there's that. How can we show they're equal?

0:26:25 > 0:26:28Well, there are all kinds of ways, but here's one way.

0:26:28 > 0:26:30Drumroll, please.

0:26:30 > 0:26:31Oh, yes.

0:26:31 > 0:26:33THEY BANG THE DESKS

0:26:33 > 0:26:34All right, let's go.

0:26:36 > 0:26:37Ooh.

0:26:38 > 0:26:40Oh, that's very clever.

0:26:40 > 0:26:42There it goes, pouring into the first square.

0:26:42 > 0:26:44- Wow!- Expensive. - Is it going to fill it up?

0:26:44 > 0:26:47- Wow.- Shut the front door!

0:26:47 > 0:26:49- Oh, Well, it definitely equals X squared.- Yes.

0:26:49 > 0:26:51Does it equal Y squared as well?

0:26:51 > 0:26:53I need to go to the toilet.

0:26:53 > 0:26:54LAUGHTER

0:26:55 > 0:26:57There's Y squared, it's filling up, it's filling up,

0:26:57 > 0:27:00it's filling up, it's full. And there it is.

0:27:00 > 0:27:01Hurray!

0:27:01 > 0:27:03APPLAUSE

0:27:04 > 0:27:05Isn't that satisfactory?

0:27:08 > 0:27:09Highly satisfactory.

0:27:09 > 0:27:12It's the first theorem most people learn at school.

0:27:12 > 0:27:14It's Pythagoras's theorem by name,

0:27:14 > 0:27:18but it wasn't, it was used many, many years before him - people used

0:27:18 > 0:27:22it to build buildings and Euclid demonstrated it before him.

0:27:22 > 0:27:24But we give it the name of Pythagoras.

0:27:24 > 0:27:26Who is Euclid, then? He was even before?

0:27:26 > 0:27:29- He's the father of mathematics. - Euclid?

0:27:29 > 0:27:31- Oh, was he?- Yeah.- Yeah. - Oh, Euclid, yes.

0:27:31 > 0:27:32Before him, nothing.

0:27:32 > 0:27:35The greatest. Yeah, well done to Euclid, we love Euclid.

0:27:35 > 0:27:38So, let's take this model away. Let's hear it for him.

0:27:38 > 0:27:39APPLAUSE

0:27:44 > 0:27:46So, the time has come to tally-up the scores.

0:27:46 > 0:27:49Oh, my actual, oh, my actual.

0:27:49 > 0:27:52So, in first place, with a magnificent two points,

0:27:52 > 0:27:54it's Aisling Bee!

0:27:54 > 0:27:55Oh!

0:27:55 > 0:27:56APPLAUSE

0:27:59 > 0:28:04And with an earth-shattering zero, it's Sandi Toksvig.

0:28:04 > 0:28:05APPLAUSE

0:28:08 > 0:28:10A more than respectable minus six, Susan Calman.

0:28:10 > 0:28:12APPLAUSE

0:28:16 > 0:28:19And on his terms, really quite handsome, minus 43,

0:28:19 > 0:28:20Alan Davies.

0:28:20 > 0:28:22APPLAUSE

0:28:28 > 0:28:31So, it's goodnight from Susan, Sandi, Aisling, Alan and me.

0:28:31 > 0:28:35And I'll leave you with this dark observation from Joseph Stalin.

0:28:35 > 0:28:37My favourite dictator.

0:28:37 > 0:28:41"The people who cast the votes decide nothing.

0:28:41 > 0:28:46"The people who count the votes decide everything." Goodnight.

0:28:46 > 0:28:47CHEERING AND APPLAUSE