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TVTranscript
00:30Well, hello, hello, and welcome once again to Think of a Number.
00:34I'm Johnny Ball.
00:36You probably all know your names.
00:38What we need today is someone who's good at adding up.
00:43Do you think you could help?
00:44What's one and one?
00:45Two.
00:46Correct!
00:47That's 100% right.
00:49Come out, that's fine.
00:50Now, I wonder if you talk nicely, because you're going to be on the telly, you see.
00:54We'll see how you talk.
00:54Can you tell me how you say the word T-W-O?
01:00Two.
01:00Very good.
01:01And how do you say the word T-O-O?
01:04Two.
01:05That's marvellous.
01:06And how do you say the second day of the week?
01:08Monday.
01:09Monday!
01:10I thought you were going to say Tuesday and fools.
01:12Never mind.
01:13Out you come.
01:14That's very clever.
01:14If you stand there, and don't look bored, because I've got a board here for you.
01:21Monday indeed.
01:24Board here for you.
01:26There we are.
01:27Now, what I want you to do is to enter some numbers, but first of all, I'll get a calculator.
01:33Because that's what we need.
01:34Anybody here own a pocket calculator?
01:37Oh, could any opponent get it?
01:39Now, hang on.
01:40You there.
01:40You come out and help, because I've got in here a calculator.
01:46Which is designed for big pockets.
01:54Here they are.
01:55I'll just shut the door.
01:56Now, do you think you could work this calculator?
01:59Right, get in.
02:00I'll find the door.
02:01You could fit in it, couldn't you?
02:03I'll switch it on.
02:03Well, that's fine.
02:06Now, hear the noises.
02:11That's a man inside winding the handle.
02:13Try it.
02:14Just add two numbers.
02:15Say nine and six together and see what we get.
02:17Nine plus six equals 15.
02:23Is that right?
02:24Yes!
02:25So it's good enough.
02:26Okay.
02:27These two are going to write some numbers down in this column here.
02:30And I want you to put them all in there with a plus sign between each one so that we add the total up.
02:34Okay.
02:35Now, you two think of a number between one and five.
02:38It doesn't have to be a big number, because you've a lot of adding up to do.
02:41You think of yours and put it opposite the number one.
02:48And you think of yours and put it opposite the number two.
02:54Right?
02:55Now, if you'll add the two of them together, put that opposite number three.
03:01And if you will add the last two only, and put that opposite number four.
03:06The last two numbers.
03:09And if you will add the last two, and put that opposite number five.
03:12And continue like that, adding just the last two.
03:15While they're doing that, in this show, we're going to discuss why trees are so tremendous.
03:21We'll try and get rid of a boomerang, because it's difficult.
03:24There's the key coming back.
03:25We'll put nylon in an endless spin, and try to turn a fossil back into a dinosaur,
03:31with the aid of an element that never forgets.
03:34But first, let's see how they're going on.
03:36Have you finished?
03:39That was lightning.
03:40Now, I know a few of the numbers.
03:42I saw a few there, but I don't know them all.
03:44And I'm going to try to add them up as quickly as I can.
03:48Let's see if I can do it.
03:51The answer is five, one, seven.
03:55I hope, press the answer on the calculator, equals five, one, seven.
04:00How about that?
04:04Amazing.
04:05Lovely.
04:06Now, you weren't really clapping me.
04:08You were clapping our helpers, because they were marvellous.
04:11Thanks ever so much.
04:12That really is terrific.
04:14Now, you're all wondering how this is done.
04:17Well, really, it's simplicity itself, when you know how to do the trick.
04:21When you have a series like this, where you get two numbers,
04:24and add them together to make the third,
04:26and then you add the last two to make that number,
04:28the last two to make that number, and so on, all the way down.
04:31When you've done ten of them, to add them up,
04:34you simply multiply the seventh one by eleven.
04:39And eleven forty-sevens are five, one, seven.
04:44That's the answer.
04:45Now, why are we taking all this time to show you such an elaborate sum?
04:50Well, if we started that series with a nought and a one,
04:55we'd have got this series of numbers.
05:01Which goes on forever.
05:06We've got it to go that far.
05:08There you are.
05:08Nought plus one is one.
05:10One and one equals two.
05:12And so on.
05:13Three plus five is eight.
05:15Thirteen and twenty-one is thirty-four.
05:18And so on, and so on.
05:19This series of numbers is known as the Fibonacci series,
05:23because it was discovered by a man called Leonardo Fibonacci,
05:27who lived some eight hundred years ago.
05:29But he wasn't the first person to use this series of numbers.
05:32The first person was Mother Nature.
05:35Here we have a picture of...
05:40Oh, oh.
05:41Oh, I'm sorry.
05:42Oh, wrong side.
05:44Half a lick.
05:44Here we have half an apple.
05:46Who's got the other half?
05:48Lots of you.
05:49You've got halves of apples.
05:51Look at your apple, look at the middle,
05:52and you'll say,
05:53Caw.
05:57There are five pockets for seeds.
06:00Is that right?
06:01Yes.
06:02Every apple has got five pockets for seeds.
06:05Five is a number on the Fibonacci series.
06:09Now here we have the head of a sunflower seed.
06:14All these seeds are spread all over the head,
06:16but if you look at them,
06:18you might see a pattern.
06:23If you look closely,
06:25the seeds are in whorls.
06:27Can you see?
06:28Going out.
06:29And they're also in whorls coming this way.
06:32Lots of whorls.
06:34Now, it's very difficult to count them,
06:37but if you do count those whorls,
06:38you'll find that you get numbers,
06:41different numbers each way,
06:43but two numbers that are always very close
06:45to numbers in the Fibonacci series.
06:49And you can try that with rubber plants.
06:51Their leaves grow in fives.
06:53And with daisies and petals,
06:55you get Fibonacci numbers.
06:57Perhaps even with hairs on a guzgog.
07:00Two trees.
07:01Six.
07:01No, no, no, no.
07:03Two trees.
07:04This one here has got one trunk,
07:07which splits into two,
07:08then the brown splits into four,
07:10then to eight,
07:11then to 16,
07:12and so on.
07:13And it looks quite nice.
07:17This tree here has got one trunk,
07:19which splits into two,
07:21then three,
07:22then five,
07:23then eight,
07:24and continues.
07:25Numbers in the Fibonacci series.
07:28And some trees,
07:29under ideal conditions,
07:31actually do grow using this system.
07:35Now, man has got a great affinity with trees.
07:37Some scientists believe that we all come from monkeys.
07:41That's not true.
07:41Some of us come from whales.
07:44However,
07:45some people do believe that long before man walked on the earth,
07:49he was rather like a monkey,
07:51and perhaps somewhere in the world,
07:52some of them lived in trees.
07:55We've got a man here today who thinks we should be living in trees now.
07:58So, stand by for a partly satirical broadcast on behalf of the Tree Society.
08:04Hello.
08:11Hello.
08:12I represent the Total World in Tree Society,
08:15or TWITS for short.
08:18Friends,
08:19do you look forward,
08:20do you look forward to going up in the world?
08:22Do you want people to look up to you?
08:24The best thing is live up a tree.
08:26Last year, TWITS held a pole.
08:30I shinned up the pole into the tree,
08:32and I've been there ever since.
08:34We at TWITS get lots of ladders.
08:36Uh, letters.
08:37We get ladders as well, actually.
08:39We need those to help us to get up the trees
08:41when we've no TWITS to hold the poles.
08:42But we get lots of letters
08:44complaining about the falling standards of education.
08:48We say,
08:49put the schools up in trees.
08:50Ha ha!
08:51You'd have immediate higher education.
08:54You might suffer from the odd dropout,
08:56but don't worry.
08:57You see,
08:58it's a high old life in a tree.
09:00There's nothing quite like waking up in the morning
09:01and listening to the birds coughing,
09:04or perhaps listening to the chapinch's
09:06first early morning sound.
09:09Is it cheap, you ask?
09:10No,
09:10it's more of a quack.
09:13The great thing about living in trees
09:15is, apart from leaves,
09:16there are no overheads.
09:18It's ideal for stargazers.
09:20They're nearer the sky.
09:21Some people say
09:22they don't fancy having their furniture
09:24on higher perches.
09:26Well, you get used to it.
09:28In fact,
09:28after a while,
09:29even the creepy crawlies
09:31begin to grow on you.
09:34So,
09:34put your money in a tree
09:36and watch it grow.
09:38It's a hedge against inflation.
09:40Why,
09:40even if you get the chop,
09:41you may feel cut up about it,
09:43but there are lots of shavings
09:45to be made.
09:46So take a leaf
09:47out of my book.
09:50Go out on a limb
09:51and buy a tree.
09:53See your branch manager today.
09:56I remember the twits' motto.
09:57Trees
09:58are tremendous!
09:59Trees
10:00are tremendous!
10:06Well, one thing's certain.
10:07We couldn't live in trees
10:08unless we were cuckoo.
10:11Another thing that's even more certain
10:12is that we could not live without trees.
10:15Or, to be more precise,
10:16we couldn't live without wood.
10:18Just 150 years ago,
10:20everything that was made practically
10:21had to be made out of wood.
10:22Our furniture,
10:23boats and ships,
10:25carts were made of wood
10:26with wooden wheels,
10:27otherwise I wouldn't go.
10:29Throughout history,
10:31wood has been the most important
10:33design material
10:34that man has known.
10:36And when you're making a thing,
10:37there are two things to remember.
10:39The material you make it with
10:40and the design.
10:42And here is probably
10:44the greatest designer
10:45that ever lived.
10:47His name?
10:52Leonardo da Vinci.
10:54He was born
10:55in 1452.
10:58This is a self-portrait of him,
10:59which he painted himself.
11:01You usually do with self-portraits,
11:03don't you?
11:03Not only was he a great artist,
11:05he was also
11:06a great designer,
11:08a great military engineer,
11:09an architect,
11:10and a brilliant inventor.
11:13He invented
11:13this.
11:21And this
11:21is the very first
11:24flying machine.
11:27Now,
11:28he designed it to be made
11:29out of wood
11:30covered in a sort of canvas.
11:32And it would have been quite heavy.
11:33In fact,
11:34it's doubtful
11:35that it would actually have flown.
11:37But that doesn't matter
11:38because it wasn't even built
11:39in Leonardo's lifetime.
11:41But he was so confident
11:42that man would one day
11:43be able to fly
11:44that he also designed
11:46this.
11:50The very first parachute.
11:54Neither of them
11:55were built
11:56in his lifetime.
11:57But that
11:58isn't the important thing.
12:01The important thing
12:02was
12:03that he designed them.
12:04He was the first.
12:06And that was the first step
12:07on man's long road
12:09to achieving
12:09his dream
12:10to be able to fly
12:12like the birds.
12:14Now,
12:15wood and canvas
12:16weren't a very good material.
12:18But a by-product of wood
12:20would have been excellent.
12:24Paper.
12:24I've got some paper aeroplanes
12:27because
12:27building model flying machines
12:29has been a craze
12:30ever since
12:31Leonardo da Vinci
12:32invented his first
12:34flying machine.
12:35This is very simple.
12:36Two hoops
12:37joined together
12:37with a straw.
12:39And it flies
12:40quite well.
12:41Let me show you.
12:44It loses height
12:45all the time
12:45but it
12:46flies quite a long way
12:47in a gradual
12:50descend.
12:52now.
12:54All you people
12:54with hoops
12:55all got hoops.
12:56Hoop hoop.
12:57Hooray.
12:57Are you ready?
12:59Launch them
12:59now.
13:04Hoopless.
13:05Never mind.
13:07This is another design
13:08and this won an award
13:09in an international
13:10model
13:11plane
13:13making
13:13competition.
13:14and does it
13:16remind you of anything?
13:18Concorde.
13:19Concorde, doesn't it?
13:19And yes,
13:20yes, it's very simple
13:21and it flies very well.
13:23Won the award
13:23for flying the furthest.
13:25See how far this will fly.
13:27Not bad.
13:29Over here
13:29we've got lots of those.
13:31Are you ready?
13:31Not yet.
13:32See if you can reach me.
13:34Ready?
13:34Go!
13:35They all nose dived.
13:40In fact,
13:41one nearly dived
13:42on my nose.
13:43However,
13:44paper is great
13:45at making
13:45model flying machines.
13:47You can use wood.
13:48These are made out of wood.
13:51Boomerang.
13:51And boomerangs,
13:52if you throw them right,
13:53come back to you.
13:54I won't throw this
13:54because it'll knock
13:55your heads off.
13:57But this is my boomerang.
13:58I made this one.
14:01You're laughing,
14:02but the secret
14:02is in the throwing.
14:03If you know how to throw it,
14:04it'll come back to you.
14:05Ready?
14:06Steady.
14:09Hang on.
14:11You get the wood.
14:12You can make boomerangs
14:13out of paper.
14:14And you can make
14:15your own designs.
14:17And they fly really well.
14:18Watch this.
14:19A four-pronged one.
14:23Hang on.
14:24A five-pronged one.
14:27Whee!
14:30A six-pronged one.
14:34A four-pronged squiggly one.
14:42Are they lovely?
14:43This one's from
14:43the Isle of Man.
14:49Came back.
14:49This one,
14:50from British Rail.
14:54Came back.
14:55Lovely.
14:55And this one
14:56was a design
14:57used by American Indians
14:59for hunting.
15:01It flies
15:01usually quite well.
15:05There.
15:06Now,
15:07we can't leave
15:08flying
15:09models
15:10without looking
15:12at a model
15:13aeroplane.
15:14Look at this.
15:14Now,
15:20this is the
15:21lightest
15:22model
15:22aeroplane
15:23that we could
15:23have built
15:24that would
15:25fly
15:25in the studio.
15:27And it weighs
15:28just two and a half
15:30grams.
15:32Watch it fly.
15:33I think that was
15:38me then.
15:39Here we go
15:39again.
15:43Oh!
15:44I'll see if I can
15:45fly it again.
15:46It's just
15:47stalling a little
15:47bit.
15:53Go on then.
15:54Go on.
15:56There it goes.
15:57It's so light
16:22and it had a bit
16:22of difficulty
16:23flying at first
16:24because
16:25it's so hot
16:26in here
16:26and there's
16:27turbulence
16:28with all the
16:28people about
16:29so it finds
16:30difficulty to
16:30fly.
16:31But you can
16:31build a model
16:33aircraft
16:34one-tenth
16:35of the weight
16:37of this one.
16:39Wouldn't fly
16:40in here
16:40but this is
16:41what the wing
16:42looks like.
16:51It's made
16:52out of
16:53microfilm
16:54that is
16:55six millionths
16:56of an inch
16:57of an inch
16:57thick
16:57and I'll take
16:59the lid off
16:59and we'll see
17:00what happens.
17:09The heat
17:10and the turbulence
17:10in here
17:11this delicate
17:13thing
17:13couldn't fly
17:16it would break
17:20it would break
17:20and it would break
17:20up.
17:21Oh.
17:24You see it's
17:25broken.
17:30Isn't it delicate?
17:31So this is the ultimate
17:34in model aeroplanes
17:37and it's made
17:38out of microfilm
17:39as opposed to one
17:40made out of paper
17:41and that is what's
17:42happening all the time.
17:44Paper and wood
17:45are being conserved
17:47and we're using more
17:49and more synthetic
17:50materials like
17:51plastics,
17:52like cellophane,
17:54like fiberglass.
17:55and all these
17:57things are made
17:58from fossil fuels,
17:59coal and oil
18:01basically.
18:02Just a minute,
18:04our fossil fuels
18:04were
18:05300 million years
18:07ago
18:08actually trees
18:09growing
18:10on earth
18:11which means
18:13that we're
18:13conserving our
18:14trees today
18:15by using up
18:16trees that grew
18:17300 million
18:18years ago
18:19to make things
18:21like this.
18:26Now most
18:27synthetic materials
18:28are made
18:29by mixing
18:30two liquids
18:32together
18:32like this.
18:36Put those
18:36together in there
18:37and give it
18:38a good stir.
18:45And pour it
18:46in there.
18:49that's our
18:51cake
18:52and that can
18:55be cooking
18:55while we have
18:57a look
18:57at this.
19:00A rubber
19:00ball
19:00and a synthetic
19:02rubber ball.
19:03What do you think
19:03it'll bounce
19:03the highest?
19:07Synthetic ones
19:08bounce like
19:08mad,
19:09don't they?
19:09The rubber
19:10one bounces
19:11quite well.
19:12It's very heavy
19:13and big.
19:14This one
19:14bounces and
19:16spins.
19:19Back to our
19:22cookery.
19:23We have
19:23here a piece
19:25of plastic
19:26that was
19:27moulded into
19:29a shape
19:29and then
19:30a ray was
19:32shone on it
19:32to fasten
19:34the shape
19:35into its
19:36memory so
19:37that it
19:37remembered that
19:38shape.
19:38Then it was
19:39pressed into
19:39this shape.
19:41Let's see
19:42what happens
19:42when it's
19:43dropped in
19:44boiling water.
19:46While that's
19:46cooking,
19:47let's get back
19:47to these
19:48two liquids.
19:49Look at the
19:49loaf!
19:50Look at the
19:50loaf!
19:51This is the
19:51way expanded
19:52polystyrene
19:53is made.
19:54These two
19:54liquids I've
19:55got to mix
19:55and try
19:56not to
19:57mix them
20:00too much.
20:02You see
20:02what I mean?
20:04He-he.
20:07One liquid
20:08is sitting
20:08on top of
20:08the other,
20:09rather like
20:09oil on water.
20:11And where
20:11they've
20:12touched,
20:13they've
20:14formed
20:14skin,
20:15like skin
20:15on a rice
20:16pudding.
20:17And if I
20:19lift that
20:19skin out,
20:20nothing much
20:21happens.
20:22Hang on,
20:23I'll try
20:23again.
20:26I get a
20:26lot of
20:27gunge.
20:27I'll take
20:28all that
20:28out,
20:28that's too
20:29much.
20:30You see?
20:31Now,
20:32see if I
20:33can get
20:33some more.
20:34Here we
20:35go.
20:37Now it's
20:37broken.
20:39It's very
20:39difficult to
20:40get this to
20:41run, but
20:41you can
20:41sometimes get
20:44a long,
20:44thin thread.
20:47there it
20:48is.
20:54Whittle up
20:55the weight
20:55will make
20:57it spin.
20:58Oh,
20:58it's just
20:59broken.
20:59Don't mind.
21:01Come on,
21:02then.
21:02Come on.
21:04Anyone
21:05know what
21:05this is?
21:07It's
21:07nylon.
21:08It's nylon.
21:08This back
21:12wheel's a bit
21:13dirty now,
21:13so it might
21:14not run,
21:15which is a
21:15pity, but
21:16that's how
21:17nylon is made.
21:18I'd like to
21:19see somebody
21:19knit a pair
21:19of tights
21:20after this
21:21stuff.
21:21Let's see
21:22how our
21:22cooking's
21:23do.
21:23Look at
21:23the loaf!
21:23Look at
21:24the loaf!
21:26Isn't that
21:26incredible?
21:27And look at
21:28our cooking,
21:29because the
21:30plastic piece,
21:30it was like
21:31that.
21:32There's now
21:32like that.
21:38So it's
21:41turned into
21:42a dinosaur,
21:43which was
21:44the shape
21:44that was
21:45put into
21:46it in the
21:46first place.
21:47And that
21:48reminds us
21:48that all
21:49these things
21:50are made
21:50of fossil
21:50fuels,
21:51which 300
21:52million years
21:53ago were
21:53actually trees
21:54growing on
21:55Earth.
21:56That's when
21:57dinosaurs
21:57roamed the
21:58Earth.
21:59You're all
21:59looking puzzles,
22:00so we'll
22:00have a
22:01puzzle with
22:02some cars,
22:03which are
22:03made out of
22:04paper and
22:05plastic covering.
22:07So it's a bit
22:07of each.
22:08So who would
22:08like to help
22:09with the
22:09card trick?
22:09Who would
22:09like to
22:10help?
22:10Would you
22:10come and
22:11help?
22:11Fine.
22:12I'll tell you
22:12what to do.
22:13I want you to
22:14take some
22:15cards while my
22:16backs turn and
22:17count them.
22:18Take some
22:18cards.
22:18Don't let me
22:19see how many.
22:20Have you
22:20taken some?
22:21Count them,
22:22and I'll take
22:22some and count
22:23mine.
22:33Right?
22:34Now, I don't
22:34know how many
22:35you've got,
22:35but I think
22:37I've got as
22:37many as you've
22:38got, plus
22:39four more,
22:42plus enough
22:43to make yours
22:44up to 15.
22:46Okay?
22:47How many have
22:47you got?
22:48Nine.
22:48Nine.
22:49So, I think
22:50I've got
22:50one, two,
22:52three, four,
22:53five, six,
22:54seven, eight,
22:55nine, plus
22:56four.
22:58One, two,
22:59three, four.
23:01Have you put
23:01your nine down
23:02there?
23:03That's enough to
23:03make the nine up
23:04to 15.
23:05Nine, ten,
23:0611, 12,
23:0713, 14,
23:0915.
23:11Amazing.
23:14Thanks very much.
23:14That's lovely.
23:17Thanks ever so much
23:18for helping me with that
23:19trick.
23:19That's lovely.
23:20If you'd like to know
23:20how that trick's done,
23:21drop us a line,
23:22think of a number,
23:22but please include
23:23a stamped address
23:24envelope,
23:25and we'll see you
23:26next week.
23:26Don't think.
23:27Man has learnt to
23:28build machines that
23:29fly, but he can't
23:30yet fly himself.
23:32Who knows?
23:32Perhaps one day,
23:33he'll be able to just
23:34flap his arms and fly.
23:35I doubt it,
23:36but you never know,
23:37do you?
23:38Bye!
23:39Woo!
23:40CHEERING
23:41APPLAUSE
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