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00:30Hello, and welcome once again to Think of a Number.
00:38Now, has anybody noticed anything different?
00:41Glasses.
00:43Glasses, that's right.
00:44And they don't have to make your nose itch.
00:47Actually, there's no glass in these.
00:49There's no glass in these, but glass is what this programme is all about.
00:53Glasses, not glasses, glasses.
00:56I'm making a spectacle of myself.
00:57However, put those there.
01:00The programme's about a mixture of things, and I'm going to mix this with this.
01:04Now, I want four times as much as this as I have of this.
01:07So, to make sure we've got four times as much, we're going to count the grains as I pour them in.
01:12OK?
01:13So, count the grains.
01:14Ready?
01:15Go!
01:16Now, remember that total.
01:19And count the grains from this glass.
01:23Now, what are the two totals?
01:25They don't know.
01:27We'll have to hope it's right.
01:29But, I'll stir that all up.
01:31Mix it up.
01:32Now, I'm going to put some water in.
01:34Now, you can't count water, can you?
01:37I know.
01:38Perhaps if we counted the molecules of water as I poured it in.
01:41Do you think that would be possible?
01:42No.
01:43No, it's not really.
01:45Do you know why?
01:47Well, that's because there are quite a lot of molecules in a pint of water.
01:50In fact, if you poured water at the rate of a million molecules every second, to pour a pint of water would take 50 billion years.
02:03We haven't got that time, have we?
02:05Now, let's get the mixture cooking.
02:11Turn the gas.
02:13Yeah.
02:15Turn the gas up.
02:17There.
02:19Lid on.
02:19Now, 50 billion years.
02:27It's got a lot of noughts to it, hasn't it?
02:29And this has got some noughts.
02:30Can you see?
02:31Because it's around zero.
02:33And it's a thermometer.
02:35A centigrade thermometer.
02:36And the probe has been on a plate that's been very cold.
02:39I'm going to put it in here now.
02:42Put that on there.
02:43Right, and I would like a clock watcher.
02:47Will you come and watch?
02:49Sit there.
02:50And I want you to tell me when that dial gets up to 140 degrees centigrade.
02:57Okay?
02:58Shouldn't be long.
02:59Meanwhile, let's chat about our bottle of water.
03:04With all those molecules in it.
03:06You see, the amount of molecules in a pint of water,
03:09well, it's about 1 followed by 25 noughts.
03:17It's an incredibly large number.
03:19Now, do you think we could count a number like that on our fingers?
03:22Well, we could collectively.
03:24I'll show you what I mean.
03:26We'll take you first.
03:28How many fingers have we got?
03:2910.
03:30So why?
03:31What a coincidence.
03:32Right, so you could count from 1 to 10, couldn't you?
03:35But don't.
03:36Just count from 1 to 9.
03:37Because you're in the units column.
03:39You see?
03:40And that's why you've got that card.
03:41It says, no 10s.
03:43Just 1 to 9.
03:44Because your mate here, you can be in the 10s column.
03:48Can't you?
03:48And with your fingers, you can register all the 10s.
03:51That's why you've got a card that says 10 to the 1.
03:54It means every finger you put up is a 10.
03:57So if I say, represent 34, you put 3 fingers up and you put 4 fingers up.
04:02It's too easy, this.
04:03If I said, represent 30, you could put a 3 up and this, which says 10 to the 1, which
04:08means every one of your fingers stands for a 10.
04:11Simple.
04:12You've got a card that says 10 to the 2.
04:15That means two 10s multiplied together.
04:17Or 100.
04:19So you're in the 100s column.
04:20And you've all got cards getting slowly bigger and bigger.
04:23Come have a look.
04:25That's right.
04:26You see, because as numbers get bigger, so people tend to round them off.
04:30Politicians might say, and Hamas's government has decided to donate 3 million pounds to the
04:36Save the Johnny Ball Fund.
04:37I wish they would.
04:39I wish they would.
04:39Now, 3 million, that's a seven-figure number.
04:42So we'd need 1, 2, 3, 4, 5, 6, 7 people.
04:46But we really don't need those.
04:48For 3 million, you'd put three fingers up.
04:50Try it with that hand.
04:51And you'd put noughts up.
04:53But we don't need you because you've got this card.
04:55Because this card says 10 to the 6, which means 1 followed by 6 noughts, or 1 million.
05:01So the three fingers mean three times that, which is 3 million.
05:04So this system, with this system, you can represent large numbers.
05:10Now, all these small numbers above the tens are called exponents.
05:13And we're all exponents of something, or other.
05:16Some people say, I'm an exponent of television.
05:18Hmm.
05:19Yes.
05:20However, there are 84 of you in the audience.
05:22We counted you as you came in.
05:23And if you all had a card, the one right at the back, you'd have a card with 10 to the 84,
05:28which would mean 1 of 1 followed by 84 noughts.
05:31Do you think that's a big enough number for us to need if we were going to count lots of things?
05:37Hmm.
05:38It's a pretty big number.
05:38Have a look at this.
05:4310, 100, 1000, million, billion.
05:46That's the American billion, but it's the one that's generally used these days.
05:49Now, a lifetime of counting, if you counted every second from the day you were born until you were 80,
05:55you would only reach a 10-figure number, 1 followed by 9 noughts.
06:00The number of brain cells, it's only 10 to the 10.
06:05The number of stars in the Milky Way, only 10 to the 11.
06:09It's not a very big number, is it?
06:11There's a trillion.
06:12All the money in the world converted into pounds would work out at about an American quadrillion,
06:18or 1 followed by 15 noughts.
06:21The distance to the furthest star you can see with the naked eye, 1 followed by 18 noughts.
06:27Look at this.
06:28All the molecules in a pint of water, 1 followed by 25 noughts.
06:33And if you had a number with 84 noughts,
06:40that would represent all the molecules in all the stars and all the planets in the universe,
06:48as far as we know.
06:50So it's not likely that we'd need a bigger number than one with 84 noughts.
06:56How's the cooking going?
06:58Ready?
06:59Great.
07:00Thanks very much.
07:01You can go and sit down now.
07:03Lovely.
07:04The cooking's done.
07:05So, oh, turn the gas off first.
07:07And take this off.
07:10Whoa!
07:11Why should we let that there, I mean?
07:12Take that off there.
07:14There.
07:15That's safe.
07:16Now, here's our brew.
07:21Bobbin.
07:29Two blobs.
07:29And some more.
07:35There.
07:36That should be enough.
07:38Let's clean it out a little bit.
07:46Now, let that cool.
07:47It's still a bit warm.
08:03Now, let's see if I can get this piece off.
08:07This is much cooler.
08:11Whoops.
08:11There it goes.
08:15Here it comes.
08:16Here it comes.
08:16And it bends a little and it crinkles.
08:27Here it comes.
08:27Now, here we go.
08:35All the time it's cooling and getting stiffer.
08:39And who's got a tray?
08:40And it's just about set now.
08:43Although it's slightly bendy, it's almost set.
08:47And if I drop it, it breaks just like glass.
08:56There.
08:57Shattered again.
08:57Now, of course, you'd never play with glass as I'm playing with this.
09:02The thing about this is it isn't glass.
09:04It's sugar glass.
09:05And it's made with sugar.
09:07And glass, real glass, is not to be played with at all.
09:10Who wants to wear any specs?
09:12Okay.
09:13Have a look at this as it breaks.
09:16It really is still a bit springy.
09:18But it looks like glass.
09:20And tastes like sugar.
09:22Would you like it taste?
09:24Yeah.
09:24It's rather like barley sugar.
09:26Do you want some?
09:28All right?
09:30Mm.
09:31It makes you get very sticky.
09:34Now, the reason we've made sugar glass is because it's made with a similar process.
09:39Only instead of sugar to make glass, you would use sand.
09:43We couldn't do it in the studio because you'd need incredibly high temperatures.
09:47But glass, when you've made it, is a dangerous substance but also a very beautiful one.
09:52And the history of glass is quite something.
09:55The first glass appeared about 4000 BC in Egypt.
10:15Not as glass, but as glazing on pottery.
10:18And this piece of Egyptian pottery is at least 2000 years old.
10:23Then, the first jugs were formed by making a core of dung and wrapping the glass around the core and then taking the dung out later.
10:30Bowls like that were moulded and then decorated afterwards.
10:35And then, about the time of the birth of Christ, glass was first blown.
10:40And that flask there is a very early piece.
10:45As soon as they could blow glass, it became more plentiful.
10:48And when they, by blowing a big piece of glass and spinning it around, they could make windows.
10:52And here is the bullion.
10:57And this is spun in the middle to make the piece of glass.
11:01The Venetians were great craftsmen in glass.
11:06Lead was added to the glass about 1680.
11:09And it made it much stronger so that bottles could be made of glass from then on.
11:12Well, the first spectacles, well, the 13th century they appeared, which was very early.
11:23There's another type of glass, church glass, stained glass.
11:29In York Minster, there's over 25,000 square feet of stained glass, some of it very old.
11:36Look at this, modern piece of glass.
11:38It's one piece of glass on which has been etched the Magna Carta.
11:46You can see the lettering.
11:47It's etched into the glass with acid.
11:51And then, the etching is filled with gold leaf.
11:56And it's presented to the American people as part of the celebrations of their bicentennial.
12:02Absolutely beautiful.
12:03Now, the thing about glass is it's very fragile.
12:15As we'll show you over here.
12:21When glass is, when you have molten glass in a crucible, the last drop from the crucible is called a Rupert drop.
12:30And this is one here.
12:32And it's a drip with a long tail.
12:34Watch carefully.
12:42It's completely shattered.
12:44It's like dust.
12:46And that's because of the way glass is constructed.
12:48The molecules are hung together in such a way that one shockwave from a little bit breaking shatters the whole lot.
12:53And that's one of the reasons glass is very dangerous.
12:55Now, some glass is made to break in a certain way.
13:00Look at how...
13:01This, as you can see, is a fragmented windscreen.
13:06Has anybody been in a car on the motorway when the windscreen's gone?
13:10It's frightening, isn't it?
13:11Big bang!
13:11If you're in luck, it stays together like a mosaic.
13:15But sometimes, some of it drops into the car.
13:18But incredibly, it's not all that sharp.
13:23And it doesn't really cut.
13:25However, this kind of glass would be dangerous if you hit it with your head.
13:29And that's why, today, laminated glass is much safer.
13:33Two sheets of very hard glass with a piece of plastic sandwiched in between it.
13:39Now, if your glass can't be made too strong, then you must give it another property if you don't want it to break.
13:45You must allow it to bend.
13:50I've got a car here.
13:54And this car is powered by a glass spring.
13:56And just like any other spring, it's in one shape and wants to stay there.
14:02Even when it's bent, it springs back.
14:05When it's stretched, or when it's compressed, or when it's twisted.
14:13Now, a spring similar to this has been built into this car.
14:16And it's been coated in plastic so that you can see it.
14:20And if I wind the car up, you can see the chain pulling the spring round.
14:26Then, as I switch it on.
14:36Off it goes.
14:41Now, if you can't make bendy glass, and you don't want it to break,
14:44then you've got to make really tough glass.
14:48Glass perhaps as tough as this.
14:52Can you bring the blocks out, please?
14:56One about there, and one about there.
15:01Lovely. Thanks very much.
15:06Now, this glass is very, very tough.
15:11And I'll prove that...
15:13...by jumping on it.
15:17Now, there is no glass anywhere near your house that is anywhere near as strong as this,
15:24so you must never, ever try that kind of thing.
15:27The reason this glass is so tough is because it's made for an aircraft window.
15:32And when aircraft fly very high, the difference in pressure between the outside and the inside is incredible.
15:39So if a glass window was to break in an aircraft, the passengers will get sucked straight out.
15:44So this glass has to be really, really tough.
15:47Much tougher than domestic glass or any glass you would find around normally.
15:52This is so tough, you can hit it with a hammer.
15:57Not even the hammer broke.
16:00Now, you wouldn't expect the hammer to break, but this one might.
16:03Or might it?
16:04It's made of glass.
16:05Glass-reinforced cement.
16:08But glass is used for so many things.
16:10Fiberglass holes for ocean-going yachts.
16:12It's very tough.
16:13The battering of the waves doesn't seem to do it much harm.
16:16Even the nose cones of space rockets are made from glass.
16:22And they can withstand incredible pressures and changes in temperature.
16:26So just as you can make glass very tough,
16:30well, you can also make glass that's very delicate.
16:34So delicate that you can break it without even touching it at all.
16:41I'd like you to meet our special guest.
16:46Miss Angela Pressman, who is...
16:51A singer.
16:52A singer.
16:52Sorry, machine.
16:53Fine.
16:55But you are an opera singer, aren't you?
16:57And she's a very good singer with an incredible voice.
17:00Do you want your note?
17:01Yes, please.
17:03Me.
17:04No, me.
17:05Oh, you then.
17:06Hang on.
17:16I think we're ready.
17:22I think we're ready.
17:22I think we're ready.
17:24I think we're ready.
17:27I think we're ready.
17:40I think we're ready.
17:42Oh, wow!
17:46Incredible!
17:51I'm a smashing singer.
17:54Now, another property of glass is the way it affects light.
17:57Light normally travels through air in straight lines.
18:00But when it hits another medium like glass or water,
18:05it's bent.
18:09That's why you can see three pencils.
18:13Now, this bending is called refraction.
18:18But if the light hits the water, shall we say,
18:22at a very shallow angle, it doesn't actually enter the water.
18:25It bounces off.
18:26Similarly, if the light is inside the water
18:29and bounces on the undersurface at a shallow angle,
18:34it bounces. It's reflected.
18:37That's why you can see four eyes.
18:41Can you?
18:42Right.
18:43Oh, four eyes is back.
18:45Now, if you could get the light to bounce time and again inside the water,
18:49perhaps you could capture the light.
18:52Rather like this.
19:02You can see through this spout of water, the light is bouncing here.
19:06And then bouncing again here.
19:12And it bounces all the way down.
19:13And all the other spout bends, the light doesn't escape.
19:15As you can see, it's not shining on my hand.
19:18Unless I touch the water.
19:20And the light's travelling all the way down the spout
19:23and even entering the trough at the bottom.
19:27And actually illuminating the water.
19:31There.
19:32Now, if you use that principle of bouncing light in glass,
19:44then you've got the principle on which it's based on one of the new industries.
19:50Industry of fibre optics.
19:53Here we have what seems to be a rubber tube.
19:57It's quite bendy.
19:59There's light coming down it.
20:01It's not rubber inside.
20:03It's glass.
20:04Lots and lots of very thin strands of glass,
20:06which are actually tubes.
20:08And the light is coming down all those tubes.
20:11And even if I tie it in a knot,
20:13the light still comes out of the other end.
20:15But just as light is coming down the tube,
20:20so going up the tube,
20:22there's some more information.
20:24And that information produces a television picture.
20:28And with this, you can look just about anywhere.
20:31I wonder what I've got in my pockets.
20:34Let's have a look.
20:38There's the material.
20:42Copper coin.
20:43And two coins with milled edges.
20:47Three.
20:50However, let's prove I've got money in my pocket.
20:54There you are.
20:56Some coins including a 2p piece.
20:59But you could look anywhere with this.
21:01In my mouth, do you think?
21:03People of a nervous disposition I should switch off now.
21:07Here we go.
21:13Okay.
21:14Yes.
21:19It's very difficult to talk when you've got a television camera in your mouth.
21:20it's very difficult to talk when you've got a television camera in your mouth
21:37however obviously these things are called endoscopes and they're used by surgeons
21:42they don't have to cut people up they can look inside also they're used in industry
21:46because you can make them much finer than this and you can look into very intricate machinery
21:50right inside and see just what's wrong and what's going on so once more glass is coming to the fore
21:57it's another use of glass and there are so many uses of glass when you think about it
22:01it's such simple stuff made of sand and in america they've got a new use for glass
22:12at coney island the beach keeps getting eroded by the sea and they had to keep bringing more
22:18sand in but now they've got the answer instead of bringing sand in they use glass and grind
22:23it up to make sand let's have a trick this is a victorian trick see and i have this ring looks
22:35expensive but it's a glass ring i'm gonna put this glass tumbler over the top and then make
22:41it disappear watch very carefully do you think it's gone yet have another look there's the ring
22:54there's the glass and now concentrate look very deeply i have to say sim talabim yaka bakaka
23:06and it's gone the ring's still there but the glass has disappeared you see it's a kind of trick
23:17and if you know how i did it i'm sure you agree but if you don't know how i did it drop me a line
23:22and i'll tell you johnny ball think of a number bbc television london w1a1a but think about glass
23:29it's incredible stuff you know it's got so many uses when you think about it we're almost totally
23:34surrounded by glass it's a bit like being in a museum isn't it hope you're looking next week
23:51so
24:03so
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24:11so
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