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00:00Thank you very much.
00:30Thank you very much. Thank you. Thank you.
00:32Hello, and welcome to Think of a Number.
00:36Number 27.
00:37Think of a number between 1 and 10.
00:404. Correct!
00:42Not only is that correct, being a number between 1 and 4,
00:45it's also the same number that I had written on this board,
00:49which is a complete fluke, you see?
00:51Which shows you, with all that luck, the show must go pretty well.
00:54My name's Johnny Ball.
00:55In this programme, we hope to show you the first hit numbers,
00:58the first record producers.
01:00We'll be having a party to get rid of all our energy,
01:02I'll be getting struck by lightning,
01:04and lots of other shocking things.
01:06The question is, why think of a number?
01:09Well, nearly everything scientific can be explained
01:12by a mathematical principle that's really quite basic.
01:16And mathematics, after all, is just a handful of numbers.
01:19So, every time you think of a number, it could lead anywhere.
01:24Now, I'm fascinated by numbers,
01:25but some people are a bit nervous with numbers.
01:28Hands up the people who like numbers and number puzzles
01:30and are quite happy with numbers at school.
01:33Hands up.
01:34Nearly all of you.
01:35Fantastic.
01:37The people who find numbers a bit worrying and are a bit nervous
01:40and a bit confused by numbers.
01:41Put your hands up.
01:43Somebody put a foot up there.
01:44They're very nervous.
01:46All right, don't worry.
01:46All of you can help with this.
01:48It's a little addition sum.
01:50It's very simple.
01:50I want you to add it up with me aloud,
01:53so we can all hear you.
01:551,000 plus 20 is...
01:581,020.
02:00Plus 30 is...
02:011,050.
02:02Plus 1,000 is...
02:042,050.
02:06Plus 1,030 is...
02:073,080.
02:09Plus 1,000 is...
02:114,080.
02:12Plus 20 is...
02:145,000.
02:17Well, congratulations, because you've all got it wrong.
02:19It's 4,100.
02:22You see?
02:23When you got to 80 here, you added 20,
02:25and instead of calling it 100,
02:26you carried the 1 over to the 1,000.
02:29I got it wrong the first time I tried it,
02:31which just shows that even people who are good at maths
02:34aren't always very good at maths.
02:36So we'd better start at the very beginning
02:38and ask, where did numbers come from?
02:40Well, there are two kinds of people.
02:42Doers and thinkers.
02:44And I think numbers were thought of by a thinker.
02:47Something like this.
02:49Picture the scene many thousands of years ago.
03:03Some cavemen killed a bison,
03:05dragged it back to the cave,
03:06and now are ripping ribs and legs off it
03:08and devouring it hungrily.
03:10The doers.
03:12In a darkened corner of the cave
03:14is our thinker sitting on a stalactite,
03:18which is very difficult,
03:19because there's the ones that hang down.
03:21He's sitting there, and he's thinking.
03:24He's thinking,
03:24if I don't get some of that bison,
03:27I'm going to starve.
03:28So he gets up to get himself a bison for.
03:30But as he goes across,
03:32they push him away.
03:33They say,
03:33get away, thinker,
03:34because you don't count.
03:37And he realises,
03:39and he'd better start counting soon,
03:40because he's losing weight quicker than the bison.
03:42So,
03:43he touches a small rock,
03:45and feeling a little bolder,
03:47he goes back
03:48to the gang
03:50that are chewing the bison.
03:51And he goes up
03:52to the big hefty one,
03:54who's a big brute
03:55called Grotto.
03:57It's his cave, you see.
03:59And this Grotto is chewing
04:00this leg of bison,
04:01and he says,
04:02OK, Grotto,
04:02let me have it.
04:03And Grotto goes,
04:04boom,
04:05and hits him.
04:06Oh, he says,
04:07I've got a leg to stand on,
04:09never mind chew on.
04:10I've lost,
04:11all because
04:12I don't count.
04:13And Grotto says,
04:14yes,
04:15you've lost,
04:16and I've won.
04:18And he thinks,
04:18one?
04:19It's a good name for a number.
04:21So,
04:21he then says to Grotto,
04:23he says,
04:23listen, Grotto,
04:23why don't you break your leg
04:24in two,
04:25in two,
04:26in two?
04:27And Grotto says,
04:28for what?
04:29And he says,
04:29for free,
04:30for free arrowheads.
04:32And he gives Grotto
04:33some arrowheads.
04:35And Grotto looks down
04:36and says,
04:37what are these for?
04:38And he says,
04:39for?
04:39And realises
04:40that he'd given him
04:41one too many,
04:41because he's nervous,
04:42you see.
04:42So,
04:43he says,
04:43they're for you,
04:44sort of a favour,
04:45you see,
04:45in exchange
04:46for a handful of meat.
04:47And Grotto says,
04:48if you want a handful of meat,
04:49take that,
04:50boom,
04:50and he hits him in the nose.
04:51Oh,
04:52he says,
04:52a bunch of fives.
04:55And he slinks back
04:56to his corner.
04:57I'm all at sixes
04:58and sevens,
04:59he says.
04:59Never mind.
05:01I ate yesterday.
05:02And nine times out of ten,
05:04they leave some scraps.
05:06So he sits down
05:07on his stalagmite.
05:08Oh,
05:09and it's sharp.
05:10And just then,
05:11a shadow looms over him
05:13and it's Grotto again
05:14who says,
05:15come on,
05:15thinker,
05:16we were a bit hard on you.
05:18Come with us.
05:19Make the number up.
05:21Make the number up.
05:22But I have made the numbers up.
05:25There was a one,
05:25and a two,
05:25and a three,
05:26and a four,
05:26and a five,
05:27and a six,
05:27and a seven,
05:28and an eight,
05:29and a nine,
05:29and a ten.
05:30Don't you realise,
05:31Grotto,
05:32at last,
05:32I'm beginning to count.
05:34I'm beginning to count.
05:38Hello!
05:38Oh, you've got the bones!
05:44Ready?
05:45Mush!
05:46Whoa!
05:47Off goes a hide,
05:48and the cave,
05:49caves in.
05:50Like this.
05:54And then,
05:57we are ready to carry on
06:00and say,
06:01now,
06:01our caveman
06:02has got his numbers.
06:04But he's got a lot to do.
06:05For instance,
06:06he's got to record the numbers.
06:08I don't mean on record players,
06:09because it was a long time
06:10before he had top 20s.
06:12How can he remember the numbers?
06:14Write them down.
06:15Well,
06:16cavemen started scratching
06:17with sticks.
06:20A bit like a loofah.
06:22No,
06:22they scratched in clay.
06:24And all the civilisations
06:25throughout the world
06:26started at different times
06:27and used different systems.
06:28The Mayans,
06:29in South America,
06:30used a system of dots.
06:32One dot for one,
06:32two dots for two,
06:33three dots for three.
06:38Four dots for four.
06:40By this time,
06:41it had driven them dotty,
06:42so they used a dash for five,
06:43and a dash dot for six,
06:45and so on.
06:46Now,
06:47the Babylonians
06:48and the Sumerians,
06:50they were very good at sums,
06:52Sumerians.
06:52they used a system of kites.
06:54One kite for one,
06:55two kites for two,
06:57three kites for three,
06:58little wedges,
06:59four for four,
07:01and so on,
07:02until they got to ten,
07:03and then they turned
07:04the wedge
07:05or the kite sideways.
07:07And when they got to 60,
07:08I don't know why 60,
07:09it was just the system they chose,
07:11they made a very deep one.
07:15For 70,
07:16well,
07:16that was like that,
07:17and 71
07:18was like that,
07:20and so on.
07:22Now,
07:22the Chinese
07:23and the Egyptians,
07:25when they wanted to write numbers,
07:26they used to dash off a few dashes.
07:28And it was the Egyptian system
07:29that was developed
07:31until it became the system
07:32we use today.
07:33For a start,
07:34they started to write the dashes
07:36much quicker.
07:37The one,
07:38they found,
07:39was easier to write quickly
07:40if they made it a downstroke.
07:42With the two,
07:43well,
07:43they made the two dashes,
07:44but writing it in a hurry,
07:46they joined them up.
07:47And three,
07:48they did the same.
07:49Two,
07:50three.
07:52And slowly but surely,
07:53they rounded them off
07:54until...
07:56Oops.
07:57Not very good.
07:58Until we got the numbers
08:00that we use today.
08:03Now,
08:04they wrote these numbers
08:05in clay
08:06on tablets
08:07which dried in the sun.
08:09The tablets,
08:09they eventually put on legs,
08:10called them tables,
08:11and because they counted on them,
08:13they called the tables
08:14counters.
08:15The problem was this,
08:17was
08:17these tablets are very heavy
08:20and difficult to move about.
08:21They just carry them on their heads.
08:23And two of these tablets
08:24would give you a headache
08:25rather than get rid of it.
08:26So,
08:27they had no paper,
08:29they had to have a system
08:30of making numbers
08:31transportable.
08:33So,
08:34they thought
08:34and thought
08:35and thought
08:36until one day
08:37it struck somebody.
08:39The very stick
08:40with which they had scratched
08:41could itself
08:42be scratched.
08:43So,
08:44this is what they did.
08:45They scratched notches
08:46in the stick
08:46with a knife
08:47which is much sharper
08:49than my finger.
08:50but once they'd scratched
08:51the notches
08:51they had a permanent record
08:53of the number.
08:54Not only that,
08:55if they split the stick
08:56down the middle
08:56they had two copies
08:59of the transaction.
09:00So,
09:01they could give one copy
09:01to one person
09:02and the other person
09:04could keep the master copy.
09:05these were called
09:07tally sticks.
09:08The age of the tally stick
09:09had arrived.
09:10It had taken thousands
09:11of years to develop
09:11and it lasted
09:12for thousands of years.
09:13In fact,
09:14tally sticks are still used today
09:15in some parts of the world
09:16and they were used
09:17in this country
09:18until 1826
09:20for certain tax purposes
09:22and they were stored
09:24in the cellars
09:25of the House of Lords.
09:27But in 1834
09:28somebody decided
09:29to get rid of them all
09:30so they sent some men
09:31to the cellars
09:32to burn them.
09:34Three o'clock
09:35in the afternoon
09:36a man looking round
09:38complained
09:38the floor was so hot
09:39he could feel it
09:39through his boots
09:40and there was so much smoke
09:41about
09:41that he couldn't even
09:42see the tapestries
09:43with his nose
09:44pressed up against them.
09:46And yet it wasn't
09:46until six o'clock
09:47that someone shouted
09:48fire!
09:49fire!
09:53The House of Lords
09:54was on fire.
09:55The whole of the City of London
09:57turned out to watch.
09:58Three regiments of soldiers
10:00had to fight
10:00to keep the crowds back
10:01when they could have been
10:02fighting the fire.
10:04The crowd cheered
10:05every time the flames went up.
10:07Nine o'clock
10:08the whole building
10:09was covered in smoke
10:11nobody could see a thing
10:11so they booed
10:12until the smoke cleared
10:13and then they cheered again
10:15because the House
10:15had come and to gun up as well.
10:17In fact,
10:17apart from Westminster Hall
10:19all the buildings
10:20were completely gutted
10:21and so the dream
10:23that Guy Fawkes had had
10:25some 150 years earlier
10:27had been achieved
10:29with the help
10:30of some negligent workmen
10:32and the last
10:33of the mighty
10:35Tally Sticks.
10:36the heat was a bit hot.
10:42Now heat
10:42is energy
10:43which is stored in fuel
10:44and released
10:45when you burn it.
10:46There are lots of ways
10:47of storing energy.
10:48This box
10:49is full of energy.
10:50Watch what happens
10:51when I release it.
10:52It scares me
10:57every time that happens.
10:58Now
10:58these
10:59pop-ups
11:01pop up
11:02because they've got
11:02an elastic band
11:03inside.
11:04Can you see?
11:04And the elastic band
11:05works rather like
11:07human muscles.
11:08It expands and contracts
11:09to provide the energy.
11:12And cavemen
11:13discovered how to
11:14store energy
11:15although they didn't know it
11:16when they discovered
11:17the bow.
11:17You see
11:18the energy
11:19is stored
11:20in the taut string
11:21and when you
11:22stretch that string
11:23you increase
11:24the energy
11:25that's stored
11:25and the energy
11:26increases and increases
11:28until you let it go
11:29and fire the bow.
11:32Should have really
11:32fired the arrow.
11:33Never mind.
11:34Once cavemen
11:35had invented the bow
11:36and arrow
11:36all he had to do
11:37was develop it
11:37and that's what he did
11:38with these weapons here.
11:40Can you come out
11:41and help?
11:42Please.
11:42Just three of you.
11:44Here are the weapons.
11:45I'll load this one up
11:46for you.
11:47All right.
11:48Ping pong balls.
11:49One, two, three.
11:52Hey, ready?
11:52Have a trial fire.
11:53Ready?
11:54Aim, fire!
11:55Boom, boom, doom.
11:57Ah, yours didn't go far
11:58did it?
11:59This one here
12:00is
12:01this one here
12:03was called
12:04a trebuchet
12:05or trebuchet
12:06and they were used
12:07in the time
12:08of the Crusades.
12:11Several tons of stone
12:12were lifted up
12:13at this end
12:13dropped suddenly
12:14and the thing fired.
12:16Fire it.
12:17Boom.
12:19Like that.
12:20Now, they weren't
12:20as good
12:21as a machine
12:22that was invented
12:23as a machine
12:25that was invented
12:25some thousands
12:26of years earlier.
12:28This was used
12:29by the Greeks
12:29and the Romans
12:30and was charged
12:31by pulling that back
12:33under great stress
12:34holding it there.
12:36There was a stop bar
12:38here
12:38so that when it was fired
12:39the arm stopped
12:40and the missile
12:41probably rocks
12:42would be fired.
12:44ready, aim, fire.
12:46Boing.
12:47It's a good one
12:48that, isn't it?
12:49But this one
12:49was even better.
12:51This was called
12:51the ballista
12:52and gave its name
12:54to the whole
12:54science of ballistics.
12:57And this was fired
12:58very, very similarly
13:00to a modern day gun
13:02in that
13:03it had a bolt action.
13:05Right, ready, aim, fire.
13:07And there you are.
13:09One last go.
13:10Load them up again.
13:12Ready.
13:16You got it?
13:18Aim.
13:19Fire.
13:19Boing.
13:21Oh, thanks a lot.
13:22All right, you're fired.
13:23There you go.
13:25You've got to see.
13:26Lovely.
13:27Now, apart from weapons
13:28being used to store energy
13:29there are other things
13:30that have been used
13:30to store energy.
13:32In the 16th century
13:33there was a monk
13:34called Dom Perignon
13:35who liked his wine
13:36with a bit of fizz in it.
13:37but it was physically impossible
13:39to keep the fizz
13:40in the bottle
13:41until he invented
13:42a corking mechanism
13:45that kept the fizz
13:46in the bottle.
13:47The wine was called
13:48champagne
13:49and Dom Perignon
13:50must have been
13:51the first physicist.
13:53Have you ever seen
13:53champagne fired?
13:57You have to undo the cork
13:59because it's held in
14:00with wire.
14:05You unscrew it.
14:06Loosen the wire
14:08and then
14:10let's see if I can hit
14:10that target on the wall
14:11over there.
14:12Ready?
14:13Aim.
14:14Fire.
14:15Bit short.
14:16Never mind.
14:17Anybody want a cup of froth?
14:19Here you are.
14:19Take the bottom cup.
14:20Pass the cups along.
14:22There you are.
14:22I don't know if they ever
14:24watch plays on television
14:26but you find that
14:28when they use champagne
14:29they always use this
14:29orange label champagne.
14:31That's because it's the
14:32finest vintage ginger ale.
14:34All right?
14:37Take the bottle
14:37have some yourself
14:38and pass it along
14:39because it's party time
14:40and we're having a party
14:41over here.
14:42Everybody's got balloons
14:43here.
14:45Can you all blow
14:46your balloons up?
14:47The people on the back row
14:48they've got balloons
14:49which are blown up
14:51attached to straws
14:52and threaded on strings.
14:54You see because balloons
14:55are absolutely full of energy
14:56when they're blown up.
14:57All you have to do
14:58is to release the energy
14:59by letting them go.
15:01So from the back
15:02over there
15:03when I say go
15:04let yours go
15:05one at a time
15:05and they should
15:06shoot down the line.
15:07Ready?
15:08Let go.
15:09One.
15:09Next one.
15:10Let go.
15:11Two.
15:11Next one.
15:12Let go.
15:12That's a good one.
15:13And the next one.
15:14Let go.
15:14Let go.
15:15Let go.
15:16Let go.
15:17Let go.
15:18Let go.
15:18Let go.
15:19Hey!
15:20Let go.
15:21All right.
15:21Everybody else
15:22let go of your balloons.
15:27Must be weather balloons.
15:37Have you ever thought
15:38have you ever thought
15:41how much energy
15:42there is stored
15:43in a thunderstorm?
15:45You see the clouds
15:46that surround the earth
15:47are completely full
15:48of energy
15:49and this energy
15:51is released
15:51in a thunderstorm.
15:52Now there are
15:5216 million thunderstorms
15:54every year
15:55on earth.
15:56In fact
15:56there are 1,800
15:58thunderstorms
15:58happening
15:59at this very minute.
16:01In thunderstorms
16:02you get lightning
16:03and the lightning flash
16:05is really two flashes
16:06one coming down
16:07at 100 to 1,000 miles
16:08per second
16:09which is answered
16:10by a flash going up
16:11at 87,000 miles
16:14per second
16:15which is half
16:16the speed of light.
16:17And about
16:17every million flashes
16:19you get a giant one
16:21and the heat
16:22achieved by a giant one
16:23is about
16:2430,000 degrees centigrade.
16:26which is hotter
16:28than the surface
16:30of the sun.
16:31shocking weather.
16:41Now lightning
16:42is really
16:43static electricity
16:44but we don't have
16:45to look to the clouds
16:46for static
16:46because it's all around us
16:47even in our own bodies.
16:49I'm sure you've all
16:49had a shock
16:50from a car
16:51door
16:52or perhaps
16:52when you've taken
16:53your shirt off
16:53it's crackled
16:54or perhaps
16:56you've had a shock
16:56from your nylon underwear
16:57oops
16:58there's one now
16:58when you comb your hair
17:01you'll sometimes find
17:03that it stands on end
17:04caused by a static
17:06and the same static
17:07in a comb
17:08will pick up
17:08pieces of tissue paper.
17:09let's try it again
17:15there we are
17:20I knew it would
17:21static
17:22is used
17:23in the home
17:24you get static
17:24clothes brushes
17:25static vacuum cleaners
17:26and even a machine
17:27now
17:28that removes
17:29smells
17:30from the kitchen
17:31by means of static
17:33here's a piece of perspex
17:35and some tissue paper
17:37underneath it
17:37watch what happens
17:38when I rub
17:39the perspex
17:40the tissue dances about
17:43let's get rid of it now
17:45because this
17:47is part of a machine
17:48called
17:49an electrophorus
17:50sounds like
17:52it should be in a zoo
17:52now
17:54rub some static into it
17:55and I have
17:56the other part
17:56of the machine here
17:57it's a brass plate
17:58place that on top
18:00press them together
18:01and the static should have
18:02transferred from that plate
18:03to that plate
18:04and it should now
18:05jump onto my hand
18:07and you might hear a crack
18:08a little spark
18:10of static
18:11our own lightning
18:13over here
18:15now
18:16not pawnbroker's equipment
18:18these
18:19are called
18:20van der graf machines
18:21this one here
18:22is worked by a crank
18:23not me
18:24no
18:24the crank's down here
18:26and it drives a belt
18:27which carries the static
18:28up into this ball
18:29where it gathers
18:30waiting to jump off
18:31if you hold
18:32anything close
18:33like this
18:34and you can see it
18:41jumping off
18:42with little sparks
18:44it might jump
18:46onto my palm
18:47even better
18:50you can definitely
18:52hear the crack
18:53this is a van der graf machine
18:58just the same
18:58as that one
18:59only
19:00instead of being
19:00worked by a crank
19:01it's worked
19:02by a motor
19:03and the sparks
19:12and the sparks
19:12are strong enough
19:12to rock the ball
19:14there we are
19:19now if you attach
19:20hair
19:22to the van der graf machine
19:24and turn it on
19:27find that the hair
19:32stands on end
19:33and it will discharge
19:36onto my finger
19:37drop down
19:39charge up again
19:40and come up again
19:41now when static
19:42jumps from point
19:43to point
19:44it doesn't make a spark
19:46that's why lightning
19:47conductors
19:47are sharp pointed
19:49metal things
19:49see
19:51jumps from point
19:53to point
19:54of course
19:55you always get
19:56lots of jumps
19:56at point to points
19:57don't you
19:58now
19:59this is a piece
20:00of neon
20:00which you might
20:01find outside the shop
20:02if you do find it
20:03outside the shop
20:03leave it there
20:04because it belongs
20:04to somebody
20:05but
20:06what happens
20:07when I turn
20:08on the machine
20:08the static
20:12lights up
20:13the neon
20:14can you see it
20:16flickering
20:16the light
20:25only goes
20:25as far as
20:26my hand
20:26you see
20:30there
20:35isn't that
20:35illuminating
20:36or are you all
20:39still in the dark
20:40all right
20:41let's have a puzzle
20:42writing things up
20:44in here
20:45we have
20:46a conundrum
20:51could you come
20:53and help
20:53by holding this
20:55there you are
20:55if you go over there
20:56and
20:57hold that there
20:58show the people
20:59and show them
21:01over there
21:01and
21:02you there
21:03if you take the slate
21:04and the chalk
21:05and select any animal
21:06you like
21:07from this diagram
21:08and write it down
21:09on the board
21:10and I'm going to try
21:11and find out
21:12which one he wrote
21:13could you come forward
21:14how am I going
21:16to do this
21:16well I'm going
21:16to touch him
21:17and absorb
21:18his static
21:19which will run
21:20through this pointer
21:21so that when I tap
21:22on the diagram
21:22I will find out
21:24which animal he's written
21:25all right
21:26don't let me see it
21:27just touch my hand
21:28electrify
21:31now I have the force
21:32now I want you to remember
21:34that word
21:35look at it
21:36don't look at the diagram
21:37and
21:38spell out the word
21:39one letter
21:40per tap
21:41as I tap
21:42when I
21:42when you get to the last letter
21:44say stop
21:44so it's one letter per tap
21:46you ready
21:47and spell it out
21:47in your head
21:48so I don't hear
21:49stop
21:58and you've written
21:59monkey
22:00it's amazing
22:02monkey is written
22:04a monkey I was pointing at
22:06thanks
22:06can you come and sit down
22:07there we are
22:10hold those
22:11all right I say
22:12but if you would like to know
22:13how that is done
22:14then drop me a line
22:15johnny ball
22:16think of a number
22:16bbc
22:17er
22:18london
22:19w12
22:208qt
22:21but please send a stamped
22:22addressed envelope
22:23otherwise all my wages
22:25will go in buying stamps
22:26to send you the replies
22:27and we'll be here next week
22:29with another programme
22:30we won't have any static
22:31but we will have
22:32quite a lot of
22:33hair raising experiments
22:36goodbye
22:40applause
Recommended
24:16
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