1 00:00:05,920 --> 00:00:11,120 VARIOUS VOICES FADE IN AND OUT 2 00:00:11,120 --> 00:00:12,800 'I'm Alan Davies... 3 00:00:17,840 --> 00:00:20,480 'And this is a piece of string. 4 00:00:20,480 --> 00:00:24,520 'All I was asked to do is find out how long it is. 5 00:00:24,520 --> 00:00:27,120 'You'd think that would be a piece of cake.' 6 00:00:30,440 --> 00:00:33,000 You can only measure shiny flat things? 7 00:00:33,000 --> 00:00:36,520 'But little did I know that, by the end of the week, 8 00:00:36,520 --> 00:00:42,720 'a centimetre would hold a new meaning and I'd be starting to question the fabric of reality.' 9 00:00:42,720 --> 00:00:47,120 That piece of string could actually be infinite. 10 00:00:47,120 --> 00:00:50,520 Strings can be in more than one place at a time. 11 00:00:50,520 --> 00:00:53,840 Your string does not actually possess a length. 12 00:00:53,840 --> 00:00:57,720 Somehow, by measuring it, we create a length for the string. 13 00:00:57,720 --> 00:01:00,920 THEY LAUGH 14 00:01:00,920 --> 00:01:04,800 'All because I tried to measure string. 15 00:01:04,800 --> 00:01:08,640 VARIOUS VOICES FADE IN AND OUT 16 00:01:08,640 --> 00:01:12,080 'It doesn't look a length till you measure the length. 17 00:01:12,080 --> 00:01:15,160 'The more you measure it, the longer it gets.' 18 00:01:15,160 --> 00:01:18,800 How long is a piece of string? Should be simple. 19 00:01:43,480 --> 00:01:46,560 'Now, I was never a great science enthusiast. 20 00:01:46,560 --> 00:01:49,400 'In fact, at school, I wasn't very good at it. 21 00:01:49,400 --> 00:01:52,600 'But measuring a piece of string, that's something 22 00:01:52,600 --> 00:01:56,760 'I can do. It's just one step up from colouring in, isn't it? 23 00:01:56,760 --> 00:01:59,800 'That's always been a skill of mine.' 24 00:01:59,800 --> 00:02:02,760 I wonder if you can help. I need a piece of string. 25 00:02:02,760 --> 00:02:07,080 A piece of string? Yeah, just a piece. A piece? Say when. 26 00:02:07,080 --> 00:02:12,080 That's good, that is good. A piece of string. 27 00:02:12,080 --> 00:02:14,000 Have you got a ruler? 28 00:02:18,360 --> 00:02:21,600 Yeah, 32 centimetres. 29 00:02:21,600 --> 00:02:23,920 32 centimetres. 30 00:02:23,920 --> 00:02:26,440 That'll be the end of the programme, then. 31 00:02:26,440 --> 00:02:29,560 Thanks for solving that. That's pretty good. 32 00:02:29,560 --> 00:02:32,120 32 centimetres. 33 00:02:32,120 --> 00:02:35,000 Thanks a lot, see you, bye. Thank you. Bye. 34 00:02:35,000 --> 00:02:37,840 Unfortunately, I suspect it won't be that simple, 35 00:02:37,840 --> 00:02:42,160 as I am now about to visit the professor of mathematics. 36 00:02:42,160 --> 00:02:46,040 'Professor Marcus du Sautoy is a maths genius 37 00:02:46,040 --> 00:02:48,720 'but also rather foolish.' 38 00:02:48,720 --> 00:02:51,840 OK, Alan, let me take you into the fourth dimension. 39 00:02:51,840 --> 00:02:55,760 'Last year, he took it upon himself to try to teach me 40 00:02:55,760 --> 00:02:58,080 'some really complicated mathematics.' 41 00:02:58,080 --> 00:03:00,760 LAUGHTER 42 00:03:00,760 --> 00:03:03,080 You've sold me, Marcus. 43 00:03:03,080 --> 00:03:05,680 You've changed my view of the universe. 44 00:03:05,680 --> 00:03:07,920 That's fantastic! 45 00:03:07,920 --> 00:03:12,160 'So who better to help me solve a simple question about string?' 46 00:03:12,160 --> 00:03:16,960 Professor! Hello! Great to see you. How the devil are you? I'm good. How about you? I'm very well. 47 00:03:16,960 --> 00:03:20,760 All I want you to do for me is a simple task this time, shouldn't take long. 48 00:03:20,760 --> 00:03:24,040 OK. I just need to know how long is this piece of string. 49 00:03:24,040 --> 00:03:28,400 Oh... OK, you want the one-minute version? Yeah. 50 00:03:28,400 --> 00:03:33,000 Or the 60-minute version? Well, I've measured it, I know it's 32 centimetres long. 51 00:03:33,000 --> 00:03:37,440 You used a ruler where you bought this? Where did you buy this? The hardware shop. OK. 52 00:03:37,440 --> 00:03:41,040 They had a ruler on the desk, it's been measuring things for years. 53 00:03:41,040 --> 00:03:46,800 And what about this ruler? Do you think it's the same length? It's got centimetres on it, yeah. 54 00:03:46,800 --> 00:03:50,840 You want it in centimetres or inches or cubits? Centimetres, please. 55 00:03:50,840 --> 00:03:53,000 I'm... Or stadia? 56 00:03:53,000 --> 00:03:54,520 LAUGHTER 57 00:03:54,520 --> 00:03:57,880 The problem about measuring things and putting them against... 58 00:03:57,880 --> 00:04:02,080 'I knew he'd be like this. To me, it's a short piece of string. 59 00:04:02,080 --> 00:04:06,400 'But for Marcus, it's a major mathematical problem.' 60 00:04:06,400 --> 00:04:10,880 ..measure and make it standard. Measurement is really the beginning of mathematics. 61 00:04:10,880 --> 00:04:14,240 And new numbers arise out of trying to measure things like this, 62 00:04:14,240 --> 00:04:16,360 and the Greeks, they were obsessed... 63 00:04:16,360 --> 00:04:19,200 'Good god, he's giving me the history of geometry.' 64 00:04:19,200 --> 00:04:23,520 Your piece of string is really a fundamental mathematical object. 65 00:04:23,520 --> 00:04:26,440 I've spent the whole morning trying to measure things. 66 00:04:26,440 --> 00:04:30,280 This little Greek symbol here stands for measurement 67 00:04:30,280 --> 00:04:35,760 and it's measuring the size of this double coset - GSP 2 N QP. 68 00:04:35,760 --> 00:04:39,640 OK, tiger. Can I...? Hold on there. MARCUS LAUGHS 69 00:04:39,640 --> 00:04:43,280 I just need to how long this piece of string is. Go back to the string. 70 00:04:43,280 --> 00:04:48,120 There's interesting maths and physics behind the question of how long this piece of string is. 71 00:04:48,120 --> 00:04:50,920 It isn't just 32 centimetres. 72 00:04:50,920 --> 00:04:55,800 You're beginning a journey that mathematicians started 5,000 years ago. 73 00:05:07,600 --> 00:05:11,120 'I knew this wouldn't be as simple as it first appeared, 74 00:05:11,120 --> 00:05:13,960 'but things were going well at this point. 75 00:05:13,960 --> 00:05:19,240 'As far as I was concerned, 32 centimetres was close enough. 76 00:05:19,240 --> 00:05:23,520 'But Marcus wanted to take me somewhere very special, 77 00:05:23,520 --> 00:05:27,640 'a place that's dedicated to just one thing - measurement.' 78 00:05:27,640 --> 00:05:31,480 And that's why we're going to the National Physics Laboratory. 79 00:05:31,480 --> 00:05:35,000 Bits of the bodies were first used as a form of measurement, 80 00:05:35,000 --> 00:05:39,040 so the Egyptians, for example, they had something called a cubit - 81 00:05:39,040 --> 00:05:43,320 the distance from your elbow to the tip of your middle finger. 82 00:05:43,320 --> 00:05:46,240 It's quite a nice distance. Let's measure ours and see... 83 00:05:47,760 --> 00:05:51,760 Look, you've got a huge cubit. Famous for the size of my cubit. 84 00:05:51,760 --> 00:05:56,360 That's no good for measuring, because your house will be bigger or smaller than my house. 85 00:05:56,360 --> 00:06:00,440 It'll be bigger and that's fine. What will it be? Bigger or smaller? 86 00:06:00,440 --> 00:06:04,000 If we have the same number of cubits? It'll be bigger. You'll say, 87 00:06:04,000 --> 00:06:07,960 "My house is six cubits high and it'll be longer." Six cubits high! 88 00:06:07,960 --> 00:06:13,440 I won't be able to get in the door. Whatever. We need something which is gonna be the same for everybody. 89 00:06:13,440 --> 00:06:19,400 You don't really want it depending on whether people are tall or small, or how big things are. 90 00:06:19,400 --> 00:06:21,880 You want something which is gonna be standard. 91 00:06:21,880 --> 00:06:24,400 Do you mind if I ask you a question? Yeah, sure. 92 00:06:24,400 --> 00:06:28,400 How long is that piece of string? Nine inches. 93 00:06:28,400 --> 00:06:33,080 No, no, it's just 12 and a bit. Good guess, though, it's not bad. 94 00:06:33,080 --> 00:06:34,880 Nine inches. 95 00:06:34,880 --> 00:06:36,760 Cheers. Thank you. 96 00:06:36,760 --> 00:06:41,000 He's quite tall, so I bet his cubit is probably a bit bigger than our cubit. 97 00:06:41,000 --> 00:06:43,440 No way you can rely on anything that he says. 98 00:06:43,440 --> 00:06:46,480 Go and ask him how far it is to London. 99 00:06:46,480 --> 00:06:50,240 He thinks that's nine inches, he's 25% out! Yeah. 100 00:06:51,920 --> 00:06:55,440 'Body parts and Egyptian cubits are all very well, 101 00:06:55,440 --> 00:06:59,280 'but they aren't exactly what I had in mind for my string.' 102 00:06:59,280 --> 00:07:04,200 What's needed is some science, and that's what brings us 103 00:07:04,200 --> 00:07:08,920 to the National Physical Laboratory, the scientific home of measurement. 104 00:07:08,920 --> 00:07:13,200 'This is a place filled with priceless treasures carefully locked away.' 105 00:07:13,200 --> 00:07:16,400 It's got this special feet-cleaning sticky floor. 106 00:07:16,400 --> 00:07:17,960 We need to get this for home. 107 00:07:17,960 --> 00:07:20,320 We have to keep the room very, very clean. 108 00:07:20,320 --> 00:07:23,240 'They are the country's measurement standards, 109 00:07:23,240 --> 00:07:26,720 'objects that define the units we use to measure every day.' 110 00:07:26,720 --> 00:07:30,320 This is the UK's primary mass standard. 111 00:07:30,320 --> 00:07:33,720 'That's a kilo to you and me.' It's quite small. 112 00:07:33,720 --> 00:07:37,800 Yes, this little cylinder in here, that's a kilo? Yes. 113 00:07:37,800 --> 00:07:41,880 The size minimises the surface area. There's less to get contaminated. Ah. 114 00:07:42,920 --> 00:07:47,280 'Got them all here, replicas of the cubit.' Wow! 115 00:07:47,280 --> 00:07:50,360 You are an Egyptian man! LAUGHTER 116 00:07:50,360 --> 00:07:53,160 'The definitive yard.' 117 00:07:53,160 --> 00:07:56,160 It's 36 inches at 68 Fahrenheit. 118 00:07:56,160 --> 00:08:00,200 'And a 200-year-old original metre bar.' 119 00:08:00,200 --> 00:08:03,200 How do they decide which metal to make it from? 120 00:08:03,200 --> 00:08:08,000 Well, they commissioned a study to find out the most stable metal 121 00:08:08,000 --> 00:08:11,040 and, after a lot of experiments, decided that a mixture 122 00:08:11,040 --> 00:08:15,720 of 90% platinum and 10% iridium was the most stable material. 123 00:08:15,720 --> 00:08:18,840 This is 90% platinum! 90% platinum. That's quite valuable. 124 00:08:18,840 --> 00:08:22,440 I don't think you'll get that in your trousers. Watch me! 125 00:08:23,400 --> 00:08:28,720 'For hundreds of years, we defined measurements with rods of stone and metal.' 126 00:08:28,720 --> 00:08:31,240 18 fingers. 18 fingers. 127 00:08:31,240 --> 00:08:35,720 Your answer. Happy with that. It's quite cute. How long's a piece of string? 18 fingers. 128 00:08:35,720 --> 00:08:41,400 'But platinum is old hat when it comes to defining length. 129 00:08:41,400 --> 00:08:47,000 'At the NPL, the metre is defined by the speed of light.' 130 00:08:47,000 --> 00:08:53,760 I tell you, this is where we want, the Length Bar Interferometry department. 131 00:08:53,760 --> 00:08:57,880 Let's run out screaming. LAUGHTER 132 00:08:57,880 --> 00:09:01,720 MACHINE HISSES 133 00:09:04,080 --> 00:09:07,600 MARCUS LAUGHS This is really... I love the sound. 134 00:09:07,600 --> 00:09:12,360 I feel like Q in James Bond. Yeah... "Don't touch it, Bond." 135 00:09:12,360 --> 00:09:15,880 One of the problems when you want to measure things very accurately 136 00:09:15,880 --> 00:09:19,400 is keeping them still enough and that's why we have to minimise 137 00:09:19,400 --> 00:09:21,920 the vibration levels that we get in the room. 138 00:09:21,920 --> 00:09:25,880 So this table is floating on air and shining throughout this instrument 139 00:09:25,880 --> 00:09:29,680 is the laser beam that actually performs the measurement. 140 00:09:29,680 --> 00:09:34,960 'A laser! That's the kind of measurement technology I need.' 141 00:09:34,960 --> 00:09:39,000 So I think the amazing thing is that, today, a metre isn't defined 142 00:09:39,000 --> 00:09:43,360 by a piece of metal, but it's defined by light and in particular 143 00:09:43,360 --> 00:09:47,880 how far light will travel in a fraction of a second, 144 00:09:47,920 --> 00:09:51,040 and it's 1 over 299 million. 145 00:09:51,040 --> 00:09:57,880 792458. There you go. Of a second. Of a second, yeah. Yeah. 146 00:09:57,880 --> 00:10:03,840 In that fraction of a second, light will have travelled exactly a metre. 147 00:10:03,840 --> 00:10:05,560 OK. 148 00:10:05,560 --> 00:10:10,200 'If a metre is the distance light travels in three billionths of a second, 149 00:10:10,200 --> 00:10:13,080 'how long is my string in light speed?' 150 00:10:13,080 --> 00:10:15,880 So, Andrew, I was wondering 151 00:10:15,880 --> 00:10:20,240 if I can measure my string here in your interferometer? 152 00:10:20,240 --> 00:10:22,360 It would be a little bit difficult. 153 00:10:22,360 --> 00:10:27,320 I would need to have the ends of the string polished nice and shiny flat 154 00:10:27,320 --> 00:10:31,160 and so I don't think we could measure it in here... 155 00:10:31,160 --> 00:10:34,880 You only measure shiny flat things? In this particular instrument, 156 00:10:34,880 --> 00:10:38,400 but we have got something else which could have a go at measuring it. 157 00:10:38,400 --> 00:10:41,120 A stringometer? A stringometer. 158 00:10:42,640 --> 00:10:47,320 'When they say stringometer, what they mean is this little fellow - 159 00:10:47,320 --> 00:10:52,040 'the fully-automated tracking laser.' 160 00:10:52,040 --> 00:10:55,920 Are you interested in the length of a piece of string? 161 00:10:55,920 --> 00:10:58,360 Do you want us to go? 162 00:10:58,360 --> 00:11:00,960 LAUGHTER 163 00:11:00,960 --> 00:11:03,800 So what you're going to have to do is take your ball, 164 00:11:03,800 --> 00:11:07,840 position it accurately on the end of the piece of string, about there. 165 00:11:07,840 --> 00:11:13,400 Hold it stationary on that end, and tell Andrew when you're ready, he'll record the point. 166 00:11:13,400 --> 00:11:15,760 OK, Andrew. I'm ready. 167 00:11:15,760 --> 00:11:17,440 MACHINE BEEPS 168 00:11:17,440 --> 00:11:22,040 Move to the other end of the piece of string. I'll get out of the way. 169 00:11:22,040 --> 00:11:23,680 MACHINE BEEPS 170 00:11:23,680 --> 00:11:27,400 If he says 320 millimetres, I'm leaving. 171 00:11:27,400 --> 00:11:31,480 Well, according to the laser tracker, the distance between those two points 172 00:11:31,480 --> 00:11:38,280 you just selected is 319 millimetres and 442 micrometres. 173 00:11:38,280 --> 00:11:41,120 It's 319 and a half millimetres? 174 00:11:41,120 --> 00:11:43,640 Just a touch under. 175 00:11:45,720 --> 00:11:49,760 And do you know why it wasn't 320? I didn't add the little bit of fray. 176 00:11:52,360 --> 00:11:54,040 'I thought that was it. 177 00:11:54,040 --> 00:11:59,080 '319.442 millimetres seems a pretty definite length to me. 178 00:12:00,800 --> 00:12:03,280 'But Marcus doesn't agree. 179 00:12:03,280 --> 00:12:06,120 'He thinks we can get an even better measurement, 180 00:12:06,120 --> 00:12:09,520 'something more accurate than the laser can produce.' 181 00:12:09,520 --> 00:12:12,040 It's that long. Yes. 182 00:12:13,480 --> 00:12:17,520 'So we travelled 132.4 miles to the west, 183 00:12:17,520 --> 00:12:23,440 'because Marcus says that my string is actually a famous mathematical conundrum 184 00:12:23,440 --> 00:12:28,680 'and he seems to think that the way to solve it lies in measuring Cornwall.' 185 00:12:30,760 --> 00:12:36,520 Five...six... This could take a while, this is really complicated. 186 00:12:36,520 --> 00:12:39,720 You can do it a bit rough and ready to start with. Do it wrong? 187 00:12:39,720 --> 00:12:43,240 No, it's just quite hard to get inside of all of the little inlets. 188 00:12:43,240 --> 00:12:46,440 I'm prepared to make the effort. I can see you're trying. 189 00:12:46,440 --> 00:12:49,360 This might be the best bit of the show if I get this right. 190 00:12:49,360 --> 00:12:52,960 It could. On the other hand... You deliberately made me lose my place. 191 00:12:52,960 --> 00:12:57,160 Right start again, start again. 133, 143... 192 00:12:57,160 --> 00:13:00,000 'What Marcus wants to demonstrate is that 193 00:13:00,000 --> 00:13:04,440 'how I go about measuring something can change the result. 194 00:13:04,440 --> 00:13:08,600 'With a ruler, from Black Head to Looe is 42 centimetres.' 195 00:13:08,600 --> 00:13:12,760 Down to Looe... It's 42 centimetres. 196 00:13:12,760 --> 00:13:15,800 Now of course the problem you are finding using this is 197 00:13:15,800 --> 00:13:21,040 with a flat edge, it's really difficult to get into all of the inlets and things like that. 198 00:13:21,040 --> 00:13:23,280 What about using your piece of string? 199 00:13:23,280 --> 00:13:28,800 'My string was somewhat better, but produced a different result...' 200 00:13:28,800 --> 00:13:31,280 47 centimetres. 201 00:13:31,280 --> 00:13:35,000 Right, let's do 47. Seems to be growing. 202 00:13:36,040 --> 00:13:39,280 'Finally, a map measuring wheel.' 203 00:13:42,120 --> 00:13:46,360 Gosh, OK! Whoa! Look, this is, this is... 204 00:13:46,360 --> 00:13:49,400 centimetres round the side here. 65. 205 00:13:49,400 --> 00:13:54,000 We've got up to 65 centimetres using this one. So... 206 00:13:54,000 --> 00:13:59,960 with a ruler, we had 42 centimetres. 207 00:13:59,960 --> 00:14:04,040 With your piece of string, 47 centimetres. 208 00:14:04,040 --> 00:14:07,160 If we had an even more accurate way to measure the length here, 209 00:14:07,160 --> 00:14:09,680 we'd probably get the coast going up even more, 210 00:14:09,680 --> 00:14:13,800 because you'd be able to get into all the nooks and crannies. 211 00:14:13,800 --> 00:14:17,440 Each measuring device is effectively zooming in on the coast 212 00:14:17,440 --> 00:14:20,320 looking at in greater detail, 213 00:14:20,320 --> 00:14:24,320 and that reveals more twists and turns. 214 00:14:24,320 --> 00:14:28,640 Each new cove or inlet increases the overall length 215 00:14:28,640 --> 00:14:32,600 all the way down to individual grains of sand. 216 00:14:32,600 --> 00:14:36,520 And the more detail you reveal, the longer the length becomes. 217 00:14:36,520 --> 00:14:40,280 This'll have serious implications for measuring your piece of string, 218 00:14:40,280 --> 00:14:42,680 because this isn't a smooth piece of string. 219 00:14:42,680 --> 00:14:46,880 It's actually also got lots of crinkly bits inside it, 220 00:14:46,880 --> 00:14:51,560 so the length of this piece of string is going to depend on how accurately we measure it. 221 00:14:51,560 --> 00:14:53,440 Oh, boy! 222 00:14:53,440 --> 00:14:55,400 I knew this would happen. 223 00:14:55,400 --> 00:14:57,240 LAUGHTER 224 00:14:57,240 --> 00:14:59,880 So make sure he gets a good night's sleep, 225 00:14:59,880 --> 00:15:03,400 because tomorrow, we're going to find out how long he really is. 226 00:15:15,920 --> 00:15:19,040 'Studying Britain's crinkly coastline 227 00:15:19,040 --> 00:15:24,040 'has actually resulted in a whole new field of mathematics.' 228 00:15:24,040 --> 00:15:27,160 What I want to do is to measure out nine metres. 229 00:15:27,160 --> 00:15:30,840 That's the side of our triangle. 'It's the maths of fractals.' 230 00:15:30,840 --> 00:15:33,160 Excellent. 231 00:15:34,800 --> 00:15:38,640 Brilliant, so this triangle that we're building is 232 00:15:38,640 --> 00:15:41,040 a third the size of the larger triangle. 233 00:15:41,040 --> 00:15:44,200 Now we're going to add even smaller triangles on, 234 00:15:44,200 --> 00:15:48,400 we're going to make it even more complicated. Right. 235 00:15:48,400 --> 00:15:52,160 'Now I was wondering what on earth a fractal looked like. 236 00:15:53,920 --> 00:15:56,320 'But I wish I'd never asked Marcus, 237 00:15:56,320 --> 00:16:01,200 'because he has me drawing triangles in the sand over and over again.' 238 00:16:01,200 --> 00:16:04,720 Brilliant. The sticks are getting a little bit big, 239 00:16:04,720 --> 00:16:09,000 so I think it's chopsticks now. Come on, then. Race you? Race you! 240 00:16:11,600 --> 00:16:14,520 Nice little triangle. 241 00:16:14,520 --> 00:16:18,520 Wow, there you go! OK, shall we do another set of triangles? No. 242 00:16:18,520 --> 00:16:21,400 You got the point? OK. That's enough triangles! 243 00:16:21,400 --> 00:16:24,640 So what we have here is the beginning of a fractal 244 00:16:24,640 --> 00:16:29,400 and does it remind you of anything? Um... 245 00:16:29,400 --> 00:16:31,920 Ice... Dust... Snow. Snow. 246 00:16:31,920 --> 00:16:35,440 It's like a snow flake and in fact this is called the Koch snow flake. 247 00:16:35,440 --> 00:16:37,040 Nice(!) Yes, exactly! 248 00:16:37,040 --> 00:16:39,840 It's the name of the German who discovered the... 249 00:16:39,840 --> 00:16:43,360 EMPHASISING THE END OF THE WORD: The Koch! The Koch, yes, exactly. 250 00:16:44,520 --> 00:16:48,120 All this drawing is so Marcus can show me that fractals 251 00:16:48,120 --> 00:16:51,120 are mathematical shapes that look the same 252 00:16:51,120 --> 00:16:53,760 no matter how zoomed in on they are. 253 00:16:55,760 --> 00:17:00,480 Their shape is repeated over and over and over again. 254 00:17:02,320 --> 00:17:06,320 And he thinks it's the same for my string. 255 00:17:06,320 --> 00:17:10,640 The closer you look at it, the more crinkles appear. 256 00:17:10,640 --> 00:17:16,480 That makes calculating the length of the string a little tricky. 257 00:17:20,800 --> 00:17:24,480 How long do you think the fractal is that we drew here? 258 00:17:24,480 --> 00:17:28,720 How long was the triangle, the big triangle we drew at the beginning? 259 00:17:28,720 --> 00:17:32,560 27 metres. Three times nine. Yeah, nine metres each side, 260 00:17:32,560 --> 00:17:35,160 so we had a triangle which was 27 metres long 261 00:17:35,160 --> 00:17:38,680 and then what we did was to add a smaller triangle on the side 262 00:17:38,680 --> 00:17:43,920 so actually, the length of this has gone up by four-thirds by adding these new triangles, 263 00:17:43,920 --> 00:17:50,680 so every time I add on more triangles, each time, the length increases by four-thirds. 264 00:17:50,680 --> 00:17:55,720 You add one third, but to do the sum, you have to multiply by four and divide by three. Yes. 265 00:17:55,720 --> 00:17:59,680 You've got 27, the original length, and we're adding a third on again 266 00:17:59,680 --> 00:18:04,120 each time we add another triangle. Multiply by four-thirds. Exactly. Now do that again, 267 00:18:04,120 --> 00:18:08,920 add an extra third on by adding more triangles, so maybe you can see what's happening. 268 00:18:08,920 --> 00:18:13,480 Every time I add smaller and smaller triangles on, the length increases 269 00:18:13,480 --> 00:18:17,120 by another factor of four-thirds, and potentially, 270 00:18:17,120 --> 00:18:22,360 the lengths of this fractal... will actually be infinite. 271 00:18:23,880 --> 00:18:28,680 So we've drawn an infinite line in the sand 272 00:18:28,680 --> 00:18:33,800 and because your piece of string is a bit crinkly, a bit fractal-like, 273 00:18:33,800 --> 00:18:37,720 that piece of string could actually be infinite in length. 274 00:18:40,480 --> 00:18:44,800 Right. You've been carrying around infinity in your pocket 275 00:18:44,800 --> 00:18:47,640 all these days without knowing it. 276 00:18:47,640 --> 00:18:52,360 Well, you say that, but look there's the beginning and there's the end. 277 00:18:52,360 --> 00:18:54,640 This is quite theoretical, if you ask me! 278 00:18:54,640 --> 00:19:00,240 You're right, I mean, this is a shape in the beautiful, pure world of mathematics and you're right. 279 00:19:00,240 --> 00:19:05,720 If we kept on adding triangles into the sand, at some point, you're going to hit a grain of sand, 280 00:19:05,720 --> 00:19:09,560 the atom, and you won't be able to divide any further. Yeah, yeah, so! 281 00:19:09,560 --> 00:19:15,000 OK, you're right, but I love this pure world of mathematic where you can just keep on dividing off 282 00:19:15,000 --> 00:19:18,680 into infinity and produce this beautiful fractal thing. 283 00:19:29,120 --> 00:19:32,160 'When I asked Marcus to help me measure my string, 284 00:19:32,160 --> 00:19:35,400 'I thought he would definitely have an answer. 285 00:19:35,400 --> 00:19:38,320 'Instead, he proposes fractals, 286 00:19:38,320 --> 00:19:41,880 'theoretical objects that are infinite. 287 00:19:41,880 --> 00:19:45,640 'But I want a length that works in the real world and that means 288 00:19:45,640 --> 00:19:48,880 'I'm gonna have to leave Marcus and his equations behind.' 289 00:19:51,720 --> 00:19:54,760 My watch says 8:52. What time's it going down? 290 00:19:54,760 --> 00:19:56,800 Doesn't this say when the sun sets? 291 00:19:59,400 --> 00:20:02,440 Yeah, this is the classic 21st-century life. 292 00:20:02,440 --> 00:20:07,000 We're so busy looking at what time the sun sets, we missed the sunset. 293 00:20:07,000 --> 00:20:11,200 LAUGHTER We actually... Oh, it's gone. 294 00:20:11,200 --> 00:20:15,800 It says it's still up at the moment. Oh, does it?! Good, good. 295 00:20:19,880 --> 00:20:22,480 Beautiful sunset. Yeah. 296 00:20:25,880 --> 00:20:30,400 'I've still got my measurement of 319.442 millimetres, 297 00:20:30,400 --> 00:20:35,400 'which is pretty good, but I must be able to do better than that. 298 00:20:35,400 --> 00:20:40,920 'What I need to do is measure it in the smallest units possible 299 00:20:40,920 --> 00:20:44,440 'and surely, that means measuring in atoms. 300 00:20:49,320 --> 00:20:54,440 'So...I guess I'll have to get to grips with some physics. 301 00:20:57,600 --> 00:21:00,160 'Just one problem. 302 00:21:00,160 --> 00:21:04,200 'When it comes to physics, I have a little secret.' 303 00:21:04,200 --> 00:21:06,560 I've been sent back to school to do physics, 304 00:21:06,560 --> 00:21:10,080 which I'm not proud to admit 305 00:21:10,080 --> 00:21:13,640 that I deliberately failed my mock O-level 306 00:21:13,640 --> 00:21:16,160 to get a U, so that I could drop it. 307 00:21:16,160 --> 00:21:19,040 I've been slightly anxious about a physics teacher, 308 00:21:19,040 --> 00:21:23,040 but got my string and actually I'm finding it quite comforting. 309 00:21:23,040 --> 00:21:25,240 SCHOOL BELL RINGS 310 00:21:27,120 --> 00:21:30,640 'This is the Simon Langton School for Boys 311 00:21:30,640 --> 00:21:36,080 'and I'm here to meet one of the country's best physics teachers - 312 00:21:36,080 --> 00:21:37,600 'Becky Parker.' 313 00:21:45,160 --> 00:21:50,120 Hi there! Hi! Are you Becky? Yeah, welcome to the Langton. Nice to meet you. Lovely to meet you. 314 00:21:50,120 --> 00:21:55,760 I've got a bit of a problem - I've been trying to measure the length of this piece of string. 315 00:21:55,760 --> 00:22:00,400 Right, and you want a straightforward simple answer to this one? Wow! Is there one? 316 00:22:00,400 --> 00:22:05,440 When you get down to the really tiny scale, things get complicated 317 00:22:05,440 --> 00:22:10,880 and that's why your problem of measuring really accurately that length of string 318 00:22:10,880 --> 00:22:15,920 is not just straightforward. I need to take you on a bit of a journey through 319 00:22:15,920 --> 00:22:20,760 lots of quite wonderful ideas, which I think you'll find quite mind-blowing. 320 00:22:20,760 --> 00:22:22,800 I had a feeling there'd be a journey. 321 00:22:27,720 --> 00:22:30,960 'This is exactly what I was afraid of - 322 00:22:30,960 --> 00:22:35,160 'being locked in a dark room with a physics teacher.' 323 00:22:35,160 --> 00:22:39,480 'Any minute now, she'll ask me for my homework.' 324 00:22:39,480 --> 00:22:45,720 There you go, just need to get it completely dark... Oh, now, hold on a minute. 325 00:22:45,720 --> 00:22:49,240 SHE IMITATES A FANFARE AND PRESSES A SWITCH Bang... 326 00:22:49,240 --> 00:22:51,600 Oh! Electricity, that's what you need. 327 00:22:51,600 --> 00:22:55,000 Hey, hey, we have light! 328 00:22:55,000 --> 00:22:58,960 Now we're going to try and do some experiments 329 00:22:58,960 --> 00:23:03,120 to understand what's going to happen and it is quite amazing, 330 00:23:03,120 --> 00:23:07,640 almost magical in a way, to see the weird effects which happen 331 00:23:07,640 --> 00:23:13,200 down in this atomic world, but what do you understand the atom as being? 332 00:23:13,200 --> 00:23:17,720 I bet you've probably done that at school? I have a vague recollection of it, yes. 333 00:23:17,720 --> 00:23:20,880 Have you got any picture of what that atom might look like? 334 00:23:20,880 --> 00:23:22,640 Something might come to me. 335 00:23:22,640 --> 00:23:25,720 Would you like to draw a model of the atom on the board? 336 00:23:25,720 --> 00:23:27,760 Why certainly! 337 00:23:30,920 --> 00:23:33,520 Draw an atom. Yeah. 338 00:23:33,520 --> 00:23:35,480 Right... 339 00:23:35,480 --> 00:23:38,320 Well, all I really remember, I remember from school, 340 00:23:38,320 --> 00:23:40,240 I remember there was... 341 00:23:40,240 --> 00:23:43,480 There's something very, very small in the middle. Yeah. 342 00:23:43,480 --> 00:23:47,720 And then, is there not something going round and round it? 343 00:23:47,720 --> 00:23:51,240 Yeah, definitely. Spinning round and round. 344 00:23:51,240 --> 00:23:54,760 So, in the middle, there's protons. Yeah. 345 00:23:54,760 --> 00:23:58,000 And neutrons. Yeah, absolutely brilliant. 346 00:23:58,000 --> 00:24:03,320 And then, what's the thing that's going round? Electrons. Electrons. 347 00:24:03,320 --> 00:24:06,520 That's it. That's all I remember. Yeah. 348 00:24:06,520 --> 00:24:09,880 I mean, this is how the atom is portrayed, 349 00:24:09,880 --> 00:24:13,360 a bit like a little mini solar system that you've got this thing 350 00:24:13,360 --> 00:24:16,880 which is pulling the electrons. An orbit thing. Yeah yeah. 351 00:24:16,880 --> 00:24:24,360 It gives an idea of how tiny this nucleus is with the protons and neutrons compared to the electron. 352 00:24:24,360 --> 00:24:28,960 Most of the atom is nothing. So if you collapsed - here's a question - 353 00:24:28,960 --> 00:24:32,080 if you collapsed, all of what you are as matter, 354 00:24:32,080 --> 00:24:35,320 the whole of the human race into just the massive stuff, 355 00:24:35,320 --> 00:24:39,160 which is the protons and neutrons, what would be the size of...? 356 00:24:39,160 --> 00:24:41,840 If you just took the actual stuff that we're made of 357 00:24:41,840 --> 00:24:44,920 and took the space out, we'd shrink down dramatically. 358 00:24:44,920 --> 00:24:49,040 I mean, I'd come down to just a little bit of... Yeah. ..a crumb. 359 00:24:49,040 --> 00:24:52,560 You be careful, cos you wouldn't see you, you'd be microscopic. 360 00:24:52,560 --> 00:24:56,720 The whole of the human race would be in the volume of a sugar cube. 361 00:24:56,720 --> 00:24:58,400 Everybody? Yeah. 362 00:24:58,400 --> 00:25:03,920 So the matter of everybody in the world amounts to one sugar cube? 363 00:25:03,920 --> 00:25:06,880 Yeah, if you got rid of... The rest is just space? Yeah. 364 00:25:06,880 --> 00:25:12,720 And so, we're all made up of these just tiny little fundamental things. 365 00:25:14,200 --> 00:25:16,760 'Talk about making someone feel inadequate! 366 00:25:16,760 --> 00:25:21,360 'We're all made up of space, of nothing at all. 367 00:25:23,120 --> 00:25:27,520 'At least I've managed to pass my first physics test. 368 00:25:27,520 --> 00:25:30,120 'Quite pleased with my atom.' 369 00:25:31,400 --> 00:25:35,000 The only trouble is, if the atom was like that, 370 00:25:35,000 --> 00:25:39,160 then the actual electrons, if they were accelerating round 371 00:25:39,160 --> 00:25:43,200 orbiting the protons and neutrons, they would lose energy 372 00:25:43,200 --> 00:25:46,120 and so they would actually spiral into the nucleus 373 00:25:46,120 --> 00:25:50,160 and that would mean that all matter would just collapse. 374 00:25:50,160 --> 00:25:54,440 Now we know that matter doesn't. So that's wrong? The only thing I remember. 375 00:25:54,440 --> 00:25:57,280 I know, because that's what you've always been taught 376 00:25:57,280 --> 00:26:02,040 then you have to re-learn it and think that's not a very good model cos it doesn't work at all. 377 00:26:02,040 --> 00:26:04,800 So sorry about that! That's what often happens. 378 00:26:04,800 --> 00:26:10,040 You have to sort of, you know, refine your thinking as you understand more and more. 379 00:26:10,040 --> 00:26:13,560 Atoms aren't what I thought they were, 380 00:26:13,560 --> 00:26:17,880 not neat little solar systems with particle planets. 381 00:26:17,880 --> 00:26:21,720 According to Becky, they're much weirder than that. 382 00:26:21,720 --> 00:26:26,800 So weird, they have their own branch of physics - quantum mechanics. 383 00:26:28,520 --> 00:26:32,440 'And that is a big problem, because in quantum physics, 384 00:26:32,440 --> 00:26:36,720 'the particles in my string can be in two places at once. 385 00:26:38,200 --> 00:26:42,680 'And that makes working out where they are really hard.' 386 00:26:44,480 --> 00:26:49,880 So...the thing about why actually it's important is 387 00:26:49,880 --> 00:26:55,480 when it comes to footballs, for example, which, obviously, are particle-like... Mm-hm. 388 00:26:55,480 --> 00:27:00,760 ..they're smeared out, so in the quantum world, they wouldn't just be here. 389 00:27:00,760 --> 00:27:06,640 It'd be all over the place and around and you wouldn't necessarily be able to tell where it was. 390 00:27:06,640 --> 00:27:12,320 So if I throw it at you, in the quantum world, you wouldn't be actually sure where... 391 00:27:12,320 --> 00:27:17,200 A bit like somebody trying to save a penalty, you wouldn't know which way to go. 392 00:27:17,200 --> 00:27:20,880 Oh, there you are, you see. But that was a terrible penalty. 393 00:27:20,880 --> 00:27:26,480 But say, in the quantum world, we wouldn't know exactly in which position the ball was. 394 00:27:26,480 --> 00:27:29,520 It could even be behind me or over your head. 395 00:27:30,640 --> 00:27:35,120 So is this ball that ball? Yeah, exactly. It can be in two places at once? Yeah. 396 00:27:35,120 --> 00:27:38,640 'This is a fundamental tenet of quantum physics. 397 00:27:38,640 --> 00:27:44,520 It's not a weird by-product, but a reality that explains how the smallest objects behave. 398 00:27:44,520 --> 00:27:48,440 The whole question of actually defining where the atoms, 399 00:27:48,440 --> 00:27:52,280 where the footballs are becomes quite a serious measurement problem. 400 00:27:52,280 --> 00:27:57,560 That's the last thing I wanted was a serious measurement problem. It's the nature of the quantum world. 401 00:27:57,560 --> 00:28:01,680 I wanted a simple measurement solution. It's not straightforward, 402 00:28:01,680 --> 00:28:08,520 because you can never be exactly sure at what point your string ends. 403 00:28:08,520 --> 00:28:10,040 Oh, no! 404 00:28:10,040 --> 00:28:12,000 LAUGHTER 405 00:28:12,000 --> 00:28:14,800 'I find it hard to accept 406 00:28:14,800 --> 00:28:18,720 'that particles can be in two places at once, 407 00:28:18,720 --> 00:28:22,760 'not just two places at once, but many places at once. 408 00:28:27,400 --> 00:28:30,440 'Unfortunately, to see this miraculous behaviour 409 00:28:30,440 --> 00:28:33,080 'takes a lot more than a bag of footballs. 410 00:28:35,000 --> 00:28:40,760 'To prove to me that my string can be in many places at once, we need a real physics lab. 411 00:28:44,000 --> 00:28:47,520 'At Imperial College in London, they have the equipment 412 00:28:47,520 --> 00:28:52,280 'to see individual particles and watch how they behave.' 413 00:29:00,800 --> 00:29:04,720 All these flashing lights... A centre for cold matters. 414 00:29:04,720 --> 00:29:08,200 Is that the fridge? SHE LAUGHS 415 00:29:18,200 --> 00:29:22,280 Johnny! Hi, great to see you. Hi. Thanks for seeing us. 416 00:29:22,280 --> 00:29:27,000 Dr Johnny Hudson, Alan Davis. Hello! Hi, good to meet you. 417 00:29:27,000 --> 00:29:31,560 'Becky and Johnny have chosen one of the most common things in the universe 418 00:29:31,560 --> 00:29:35,560 'to provide evidence that objects can be in two places at once. 419 00:29:35,560 --> 00:29:39,800 'It's something that surrounds us all the time - light.' 420 00:29:39,800 --> 00:29:45,480 We'll shine a laser beam through two very narrow slits. Can you see them? 421 00:29:45,480 --> 00:29:50,000 Can you see two? OK. Just. Yes, yes, I can. 422 00:29:50,000 --> 00:29:56,200 They're about the size of a human hair each and they're spaced by about the same amount. OK. 423 00:29:56,200 --> 00:29:58,440 What you can see over on the far wall 424 00:29:58,440 --> 00:30:03,680 are the stripes from the waves coming from each slit interfering. 425 00:30:04,680 --> 00:30:07,200 'Right, let's just stop it there. 426 00:30:07,200 --> 00:30:11,920 'In a minute, I will to see something that was to turn my world upside down. 427 00:30:11,920 --> 00:30:18,240 'But to properly understand it, Becky needed to explain a simple concept. 428 00:30:18,240 --> 00:30:22,160 'It's all to do with how light works.' 429 00:30:22,160 --> 00:30:24,680 Firing laser light at two slits 430 00:30:24,680 --> 00:30:28,440 doesn't create two shafts of light, as you'd think. 431 00:30:30,000 --> 00:30:32,800 It creates stripes. 432 00:30:32,800 --> 00:30:35,360 That's because light is a wave. 433 00:30:35,360 --> 00:30:39,280 The waves of light pass through both slits 434 00:30:39,280 --> 00:30:42,720 and then interfere with each other. 435 00:30:42,720 --> 00:30:49,280 Some add up to give bright bands, others cancel out, leaving darkness. 436 00:30:49,280 --> 00:30:53,880 Becky calls this an interference pattern 437 00:30:53,880 --> 00:30:57,400 and she says it's telltale evidence that the light 438 00:30:57,400 --> 00:31:01,280 has passed through both slits at the same time. 439 00:31:01,280 --> 00:31:03,960 But Johnny is only going to send through 440 00:31:03,960 --> 00:31:08,160 a single particle of light, called a photon, at a time. 441 00:31:08,160 --> 00:31:11,680 Of course, you'd have thought that would just create a dot, 442 00:31:11,680 --> 00:31:13,560 but that wouldn't be quantum. 443 00:31:17,600 --> 00:31:21,360 OK. So what we can see here 444 00:31:21,360 --> 00:31:25,960 is each of these little green splodges of light 445 00:31:25,960 --> 00:31:29,440 is a single photon. 446 00:31:32,040 --> 00:31:36,960 OK, so this is now averaging those successive frames together, 447 00:31:36,960 --> 00:31:41,880 laying them on each other as if you printed them and put them in a stack then held them up to the light. 448 00:31:41,880 --> 00:31:45,400 Where you get more photon impacts, you see a brighter green colour. 449 00:31:45,400 --> 00:31:48,920 Where there are fewer, you see a darker colour. And you can see that? 450 00:31:48,920 --> 00:31:53,920 It's amazing. Stripes. Completely amazing. It's definitely stripes. 451 00:31:53,920 --> 00:31:58,280 'If only one photon at a time goes through the slits, 452 00:31:58,280 --> 00:32:00,800 'how does it create an interference pattern?' 453 00:32:00,800 --> 00:32:05,800 So you've got your photons, they're going through two slits. 454 00:32:05,800 --> 00:32:11,160 And they, they're passing through them, one photon goes through both, 455 00:32:11,160 --> 00:32:15,600 it has to go through both to create the wave effect. Yeah. 456 00:32:15,600 --> 00:32:20,000 But it's one photon. Yes. So it has to be in two places at once? Yes. 457 00:32:20,000 --> 00:32:23,040 It has to be in both slits at once? Yeah, effectively. 458 00:32:24,600 --> 00:32:28,680 It's adding up to a bright band, cancelling out to give nothing... 459 00:32:28,680 --> 00:32:33,200 But the photon's something that... That's as small as you can get. 460 00:32:33,200 --> 00:32:36,480 You can't split it in half and re-form it? 461 00:32:36,480 --> 00:32:42,320 Well, that's because you can't then have that picture of it being a single particle. 462 00:32:42,320 --> 00:32:46,560 It seems to then act as a wave when it goes through the slits. 463 00:32:46,560 --> 00:32:50,680 The thing is, position isn't a good idea any more. 464 00:32:50,680 --> 00:32:53,960 Position is something that's useful for big things. 465 00:32:53,960 --> 00:32:59,040 But when you talk about the smallest things, position is not a good idea any more. 466 00:32:59,040 --> 00:33:01,960 You mean where things are? Yeah, they're not in a place. 467 00:33:01,960 --> 00:33:06,920 They don't really have a position as such, which is surprising, right? 468 00:33:11,040 --> 00:33:16,320 'I thought that Johnny would have a big fancy machine that would count the atoms in the string. 469 00:33:16,320 --> 00:33:20,200 'It's a tricky task, but at least understandable. 470 00:33:20,200 --> 00:33:23,720 'Alas, the real world just isn't like that. 471 00:33:23,720 --> 00:33:27,560 'It turns out, in reality, the fundamental building blocks 472 00:33:27,560 --> 00:33:31,240 'of the universe don't have a fixed position. 473 00:33:31,240 --> 00:33:35,400 'Well, if that's the case, how am I ever going to measure my string?' 474 00:33:37,600 --> 00:33:41,200 I think the philosophical understanding 475 00:33:41,200 --> 00:33:46,520 of how we understand reality has got a long way to go, I think. 476 00:33:47,560 --> 00:33:53,040 Really, we probably need a whole new way of thinking about the world. 477 00:33:53,040 --> 00:33:55,680 Yeah, it's quite difficult to get your head round, 478 00:33:55,680 --> 00:33:59,280 except it turns out out it is possible to get your head round it, 479 00:33:59,280 --> 00:34:02,160 because your head could be in two places at once. Ha-ha! 480 00:34:02,160 --> 00:34:05,680 Yes, so your head could be here and then it would understand. 481 00:34:05,680 --> 00:34:10,920 Yeah, it's getting your head round the fact that you could get your head round it. That's the trouble. 482 00:34:12,080 --> 00:34:15,600 Wow, this whole measuring thing turned out to be 483 00:34:15,600 --> 00:34:18,720 so much more complicated than I thought. 484 00:34:23,520 --> 00:34:26,840 FAIRGROUND MUSIC PLAYS 485 00:34:30,480 --> 00:34:34,680 'Measurement should be easy. I do it all the time 486 00:34:34,680 --> 00:34:39,240 'but according to quantum mechanics, it's an almost impossible challenge. 487 00:34:42,720 --> 00:34:45,480 'Worse than that, it's a science that declares 488 00:34:45,480 --> 00:34:48,880 'that the world is mysterious and confusing. 489 00:34:48,880 --> 00:34:50,880 'I knew that already.' 490 00:34:53,280 --> 00:34:58,840 It sounds like a cop-out to have a theory which says that you can't work out the answer. 491 00:34:58,840 --> 00:35:04,800 Well, Alan, yeah, like you, Einstein grappled with this and never... 492 00:35:04,800 --> 00:35:07,400 I like that sentence. Yeah, you and Einstein. 493 00:35:07,400 --> 00:35:11,720 Like me, Einstein grappled with the laws of physics. No, you did! 494 00:35:11,720 --> 00:35:15,000 Einstein and I have many of the same concerns. 495 00:35:15,000 --> 00:35:18,520 Yeah. You know, people like you and Einstein 496 00:35:18,520 --> 00:35:21,760 expect to be able to understand the world and have it... 497 00:35:21,760 --> 00:35:28,040 We do, we both do. Yeah, have it completely clear exactly what reality is. 498 00:35:28,040 --> 00:35:30,160 You... 499 00:35:30,160 --> 00:35:34,600 You don't get an absolute, definitive answer. 500 00:35:34,600 --> 00:35:38,080 You get probabilities and likely to be here, 501 00:35:38,080 --> 00:35:41,320 and most probable to be there. 502 00:35:41,320 --> 00:35:45,800 I'm gonna go back to 320 millimetres. 503 00:35:53,720 --> 00:35:55,680 'Becky has been trying to help... 504 00:35:58,280 --> 00:36:01,600 'But I think she might've scrambled my mind.' 505 00:36:01,600 --> 00:36:03,400 'Position is not a good idea...' 506 00:36:03,400 --> 00:36:06,920 'I thought she'd give me real world answers,' 507 00:36:06,920 --> 00:36:12,440 'Turns out the real world is stranger than I imagined. 508 00:36:13,120 --> 00:36:15,640 'Now I'm more confused than ever. 509 00:36:20,040 --> 00:36:23,560 'But what does this mean for me and my string? 510 00:36:23,560 --> 00:36:25,840 'We're all made of atoms and particles. 511 00:36:25,840 --> 00:36:28,920 'Does that mean we're also blurry at the edges? 512 00:36:31,800 --> 00:36:35,320 'Can I be in many places at once? VOICE ECHOES 513 00:36:37,240 --> 00:36:40,800 'If I'm here, where else am I? VOICE ECHOES 514 00:36:42,680 --> 00:36:44,720 'I want answers.' 515 00:36:51,520 --> 00:36:55,960 'Quite an amazing journey right right down into the tiniest stuff 516 00:36:55,960 --> 00:36:59,000 'which I think you'll find quite mind-blowing.' 517 00:37:10,440 --> 00:37:14,680 'To find them, I've arranged to meet a professor of quantum physics, 518 00:37:14,680 --> 00:37:17,200 'a man called Seth Lloyd. 519 00:37:19,600 --> 00:37:22,120 'Seth is a master of the quantum. 520 00:37:22,120 --> 00:37:29,080 'He works with particles and atoms all the time and can bend them to his will. 521 00:37:29,080 --> 00:37:34,240 'Seth's the man to bring sense to this quantum madness. 522 00:37:38,200 --> 00:37:43,480 'But I'm not entirely sure why he wants to meet me in a taxidermist's.' 523 00:37:46,640 --> 00:37:51,680 Seth! Oh, Alan! Hello. Good to meet you. 524 00:37:51,680 --> 00:37:56,200 Nice to meet you too. Thanks for inviting me to this place. 525 00:37:56,200 --> 00:38:00,480 You're probably wondering why I asked you down here today. It has crossed my mind. 526 00:38:00,480 --> 00:38:04,920 You have nothing to fear. Good! LAUGHTER 527 00:38:04,920 --> 00:38:09,720 In fact, I brought you here to introduce you to Fluffy. 528 00:38:09,720 --> 00:38:13,640 What a beautiful cat. She WAS a beautiful cat. 529 00:38:13,640 --> 00:38:15,680 LAUGHTER 530 00:38:15,680 --> 00:38:20,240 First, let me ask you a question. Do you think this cat is alive? 531 00:38:20,240 --> 00:38:24,280 No, I think, I think it's stuffed. You think it's stuffed? Yeah. 532 00:38:26,080 --> 00:38:31,840 Now it may not seem to begin with that cats have much to do with measuring string, 533 00:38:31,840 --> 00:38:35,600 but in fact, they have everything to do with measuring string. 534 00:38:35,600 --> 00:38:41,240 About 70 years ago, the German physicist, Erwin Schrodinger, 535 00:38:41,240 --> 00:38:44,320 came up with a thought experiment about a cat, 536 00:38:44,320 --> 00:38:48,360 a thought experiment which I'm now going to ask you to go through. 537 00:38:48,360 --> 00:38:50,560 OK. I'm ready. OK. 538 00:38:50,560 --> 00:38:55,160 So Schrodinger imagined that you had a cat. 539 00:38:55,160 --> 00:38:59,200 But then, as a result of a radioactive decay, 540 00:38:59,200 --> 00:39:03,240 where an atom would decay and emit a photon, 541 00:39:03,240 --> 00:39:08,400 this photon would be absorbed by a detector and, if the photon was absorbed by the detector, 542 00:39:08,400 --> 00:39:13,400 then a small amount of poison would be put in the cat's milk. 543 00:39:13,400 --> 00:39:17,160 The cat would drink the milk and then die. 544 00:39:19,720 --> 00:39:22,720 Right. At the level of quantum mechanics, 545 00:39:22,720 --> 00:39:26,680 a particle isn't in one place or another, 546 00:39:26,680 --> 00:39:32,240 so the photon in some funny sense is both detected and it's somewhere else where it's not detected 547 00:39:32,240 --> 00:39:37,760 and that means that the poison is being put in the milk and not being put in the milk at the same time. 548 00:39:37,760 --> 00:39:42,600 So if a photon can be here and there at the same time, then a cat 549 00:39:42,600 --> 00:39:46,600 can be alive and dead at the same time. 550 00:39:48,000 --> 00:39:52,240 'I was hoping Seth would make things seem less weird, 551 00:39:52,240 --> 00:39:55,280 'but now, things aren't just in two places at once. 552 00:39:55,280 --> 00:39:58,920 'They're also dead and alive at the same time.' 553 00:39:58,920 --> 00:40:02,600 I'm picking up the thought experiment and I get the theory, 554 00:40:02,600 --> 00:40:07,240 but in reality, we're alive, the cat's dead. 555 00:40:08,640 --> 00:40:13,760 The string is a certain length. Well, that's what Einstein would've liked to have thought. 556 00:40:13,760 --> 00:40:18,040 This is why Einstein didn't like quantum mechanics. Right. So what's going on? 557 00:40:18,040 --> 00:40:22,600 How can a cat be alive and dead? We never see the cat alive and dead. 558 00:40:22,600 --> 00:40:25,320 This has to do with observation, crucially. 559 00:40:25,320 --> 00:40:29,360 Looking at the cat is an act of measurement and if the cat is, 560 00:40:29,360 --> 00:40:33,920 in this funny sense, alive and dead at the same time, and we look at it or measure it, 561 00:40:33,920 --> 00:40:38,160 it effectively has to have become either alive or dead, 562 00:40:38,160 --> 00:40:40,200 but not both. 563 00:40:44,080 --> 00:40:47,600 LAUGHTER 564 00:40:48,680 --> 00:40:53,920 I'm getting it, but I just feel as though, even if I don't see it, it's still dead. 565 00:40:53,920 --> 00:40:57,920 Yeah, so it's important here to, to think about what we mean by observation. 566 00:40:57,920 --> 00:41:03,280 Most human beings when they say, "We observe something," it means we're there to see it. 567 00:41:03,280 --> 00:41:08,320 But you have to think that, as every particle of light bounces off this cat, 568 00:41:08,320 --> 00:41:14,640 it's effectively observing it, so if there's anything there to detect whether the cat is alive or dead, 569 00:41:14,640 --> 00:41:18,600 then it's either alive or dead and not alive and dead at the same time. 570 00:41:18,600 --> 00:41:21,200 CAT PURRS 571 00:41:22,280 --> 00:41:25,800 So big things don't show up being two places at once 572 00:41:25,800 --> 00:41:29,320 or cats don't show up being dead and alive at the same time, 573 00:41:29,320 --> 00:41:32,200 cos they're big and interact with their surroundings. 574 00:41:32,200 --> 00:41:36,120 Every interaction with the surroundings is effectively an observation. 575 00:41:36,120 --> 00:41:38,160 The environment observes the cat. 576 00:41:38,160 --> 00:41:41,680 And this is very important for your length of string, 577 00:41:41,680 --> 00:41:46,080 because, just in the same way the photons can be here and there at the same time, 578 00:41:46,080 --> 00:41:49,920 the string can have multiple lengths at one time. 579 00:41:49,920 --> 00:41:53,840 'This isn't the news I was hoping for. 580 00:41:53,840 --> 00:41:56,640 'In fact, it's an utter disaster.' 581 00:41:56,640 --> 00:41:59,800 Your string does not actually possess a length. 582 00:41:59,800 --> 00:42:04,200 Somehow, by measuring it, we create a length for the string. 583 00:42:04,200 --> 00:42:07,320 It hasn't got a length till you measure the length? 584 00:42:07,320 --> 00:42:11,320 It doesn't, and then its length is what you measure it to be. 585 00:42:11,320 --> 00:42:17,040 Then it goes back to not having a length again? It's not even really there until you measure it. 586 00:42:17,040 --> 00:42:20,240 That's what Einstein hated about quantum mechanics, 587 00:42:20,240 --> 00:42:24,600 that things aren't there until you actually look at them. 588 00:42:24,600 --> 00:42:30,440 So reality, in some sense, doesn't exist unless we're actually observing it 589 00:42:30,440 --> 00:42:34,640 and it's our act of observation that makes things real. 590 00:42:35,840 --> 00:42:37,560 Oh, no! 591 00:42:39,120 --> 00:42:41,560 'Right, so let me get this straight. 592 00:42:41,560 --> 00:42:48,360 'My string doesn't have a length until it's observed, and then its length is created. 593 00:42:50,320 --> 00:42:52,840 'But it IS observed, it's in my pocket. 594 00:42:52,840 --> 00:42:56,520 'The last time I looked, it was about 320 millimetres.' 595 00:42:58,640 --> 00:43:02,920 I'm enjoying the theory and the thought experiments. 596 00:43:02,920 --> 00:43:08,040 I can see things and where things are and I'm not really getting the relevance to the real world. 597 00:43:08,040 --> 00:43:10,760 It doesn't really matter. 598 00:43:10,760 --> 00:43:15,120 This is all just theory that isn't really relevant, 599 00:43:15,120 --> 00:43:18,680 because we are observed by the environment, so does it...? 600 00:43:18,680 --> 00:43:22,440 Who are you - Einstein?! Does it really matter? What's your problem(?) 601 00:43:22,440 --> 00:43:27,120 I feel more and more like Einstein every day, which I previously thought was a good thing. 602 00:43:27,120 --> 00:43:32,920 You think that quantum mechanics doesn't matter in a really important way for living things. 603 00:43:32,920 --> 00:43:37,240 Come with me, I'll show you how it matters. Don't knock quantum mechanics, baby! 604 00:43:37,240 --> 00:43:39,680 LAUGHTER 605 00:43:47,160 --> 00:43:50,680 'Seth doesn't need a laser or a lab to demonstrate 606 00:43:50,680 --> 00:43:55,360 'that quantum mechanics isn't only relevant to invisible particles. 607 00:43:56,880 --> 00:44:00,000 'All he needs is a greenhouse. 608 00:44:02,160 --> 00:44:06,200 'He's brought me to Kew Gardens, cos the latest scientific research 609 00:44:06,200 --> 00:44:08,840 'has uncovered a surprising truth. 610 00:44:08,840 --> 00:44:13,120 'That all life on Earth relies on quantum physics.' 611 00:44:14,840 --> 00:44:20,080 You say you don't believe that quantum mechanics is really important at a basic scale. 612 00:44:20,080 --> 00:44:24,440 So what would you say if I told you that every single plant here 613 00:44:24,440 --> 00:44:27,960 is using quantum mechanics in a fundamental fashion in order 614 00:44:27,960 --> 00:44:32,680 to turn light into energy, and to build itself up from scratch? 615 00:44:34,200 --> 00:44:40,040 Nature effectively discovered how to use the same kind of quantum weirdness that allows 616 00:44:40,040 --> 00:44:42,240 particles to be in two places at once 617 00:44:42,240 --> 00:44:48,040 and that underlies Schrodinger's cat in order to make all this happen. 618 00:44:48,040 --> 00:44:53,800 Things have to be in two places at once or there's no plant life? 619 00:44:53,800 --> 00:44:56,400 That's right, exactly. 620 00:44:56,400 --> 00:44:59,080 How do the plants know that? 621 00:45:02,720 --> 00:45:07,360 Even I know that plants turn sunlight, air and water into food 622 00:45:07,360 --> 00:45:10,960 in a process called photosynthesis, 623 00:45:10,960 --> 00:45:17,000 but according to Seth, this relies on quantum physics. 624 00:45:18,840 --> 00:45:24,320 The way that photosynthesis works is that a photon particle of light from the sun comes in, 625 00:45:24,320 --> 00:45:30,160 gets absorbed in a gigantic molecule like a chlorophyll and it creates 626 00:45:30,160 --> 00:45:35,080 an energy state called an exciton, an excited state of electron. 627 00:45:35,080 --> 00:45:39,640 Now this exciton has got to get from this side of the molecule where it's been created 628 00:45:39,640 --> 00:45:45,480 to this side of the molecule where it can be turned into chemical energy and photosynthesis is incredibly 629 00:45:45,480 --> 00:45:49,240 efficient in this energy transfer process, like 99% efficient. 630 00:45:50,760 --> 00:45:56,000 And that's very hard to understand because you can understand if it were maybe, like, 50% efficient, 631 00:45:56,000 --> 00:45:57,640 so if half the energy got there, 632 00:45:57,640 --> 00:46:02,600 but it's quite crazy that 99% of the energy gets from where it's absorbed 633 00:46:02,600 --> 00:46:05,480 to where it actually gets turned into chemical energy. 634 00:46:07,120 --> 00:46:13,280 And the way that these organisms figured out how to make it efficient is by using this wacky quantum state 635 00:46:13,280 --> 00:46:16,320 where you go through all possible paths at once of the molecule 636 00:46:16,320 --> 00:46:19,360 so it's in many, many, many different places at once. 637 00:46:19,360 --> 00:46:23,040 That way it can do it without dissipating all this energy that it's got. 638 00:46:23,040 --> 00:46:24,840 We've gone past two places at once. 639 00:46:24,840 --> 00:46:27,520 We've gone into thousands, millions of places. 640 00:46:27,520 --> 00:46:30,640 Millions of places at once, yeah. Hey! Hey. 641 00:46:34,000 --> 00:46:36,200 It's almost like this quantum process 642 00:46:36,200 --> 00:46:39,240 is trying to find a path through a maze, 643 00:46:39,240 --> 00:46:43,080 and the energy takes every possible path at the same time 644 00:46:43,080 --> 00:46:45,800 but having arrived at the centre, 645 00:46:45,800 --> 00:46:49,960 it appears to have only taken the quickest route. 646 00:46:49,960 --> 00:46:55,240 Without this quantum weirdness that allows plants to be so energy-efficient, 647 00:46:55,240 --> 00:46:58,000 life on earth would be very different. 648 00:47:00,440 --> 00:47:04,120 So without plant life discovering this ability to transfer energy 649 00:47:04,120 --> 00:47:08,200 in that way, there's no dinner on the table, there's no anything? 650 00:47:08,200 --> 00:47:09,920 There's no barley for the beer. 651 00:47:12,640 --> 00:47:14,720 I have new respect for plants now. 652 00:47:14,720 --> 00:47:18,320 The question really is do they have new respect for you? 653 00:47:18,320 --> 00:47:20,360 THEY LAUGH 654 00:47:29,880 --> 00:47:35,040 Quantum physics isn't restricted just to plant life. 655 00:47:35,040 --> 00:47:37,520 It's everywhere. It's even in me. 656 00:47:41,840 --> 00:47:47,000 Apparently quantum physics is going on between my ears. 657 00:47:47,000 --> 00:47:51,240 Alas, not in my brain but up my nose. 658 00:47:51,240 --> 00:47:53,360 Smell that. Very nice. 659 00:47:53,360 --> 00:47:57,200 You couldn't smell if quantum mechanics weren't there to help you. 660 00:48:00,000 --> 00:48:02,520 The role of quantum mechanics in the way we smell 661 00:48:02,520 --> 00:48:06,920 is not yet fully understood, but a research group, 662 00:48:06,920 --> 00:48:11,080 led by Professor Marshall Stoneham, are just beginning to uncover it. 663 00:48:11,080 --> 00:48:13,160 Dr Simon Gain. Hi, there. 664 00:48:13,160 --> 00:48:16,680 The question is what happens when you actually get a smell. 665 00:48:16,680 --> 00:48:23,120 But what we believe is happening is the smell molecule has to pass through various mucus layers 666 00:48:23,120 --> 00:48:27,600 and so forth and it ends up at a receptor, and you have 350 different receptors. 667 00:48:27,600 --> 00:48:30,440 And they're all sitting there waiting to be triggered? 668 00:48:30,440 --> 00:48:33,920 That's right, and only perhaps a dozen of those will be triggered by 669 00:48:33,920 --> 00:48:40,320 any one scent molecule, and then the mixture of those signals is what tells your brain which smell it is. 670 00:48:40,320 --> 00:48:46,560 And if it was a bad egg that you've just opened, then you'd get that effect of the bad egg smell 671 00:48:46,560 --> 00:48:51,080 about a millisecond, about a thousandth of a second after things had gone in. 672 00:48:51,080 --> 00:48:54,440 We can show you because it doesn't happen everywhere in your nose. 673 00:48:54,440 --> 00:48:58,640 It only happens in a specific bit right up at the top between your eyes 674 00:48:58,640 --> 00:49:01,520 and in, just behind the bones of your nose. 675 00:49:01,520 --> 00:49:05,840 So if you're interested, we can put a camera up there and have a look. 676 00:49:05,840 --> 00:49:07,760 And what does this camera look like? 677 00:49:07,760 --> 00:49:09,000 This is the camera. 678 00:49:09,000 --> 00:49:10,600 Holy smoke! 679 00:49:12,320 --> 00:49:14,360 Better you than me, is all I can say. 680 00:49:14,360 --> 00:49:16,000 Yeah, yeah. 681 00:49:16,000 --> 00:49:22,560 To see where the quantum physics is happening, required numbing my nose and face. 682 00:49:28,640 --> 00:49:32,720 And placing a camera just below my brain. 683 00:49:32,720 --> 00:49:37,480 So that's called the nasal vestibule, the hair-bearing part. 684 00:49:40,960 --> 00:49:45,760 Looking into the nose now with the septum on the 685 00:49:45,760 --> 00:49:50,240 right of the picture, we're looking right up just below your brain. 686 00:49:52,720 --> 00:49:56,000 Right here at the top of my nose is a gap in the skull 687 00:49:56,000 --> 00:50:00,920 that allows the smell receptors to connect directly to my brain. 688 00:50:00,920 --> 00:50:05,840 And that's where the lining of your nose changes from the respiratory mucosa 689 00:50:05,840 --> 00:50:07,280 to the olfactory mucosa 690 00:50:07,280 --> 00:50:13,400 which has the nerve endings that bear the receptor that we think works by quantum methods. 691 00:50:16,120 --> 00:50:18,680 Just seeing if you left any equipment. 692 00:50:18,680 --> 00:50:20,560 THEY ALL LAUGH 693 00:50:20,560 --> 00:50:22,560 Thank you! 694 00:50:32,400 --> 00:50:37,480 As a scent molecule travels up the nose, it finds its way to a receptor. 695 00:50:39,000 --> 00:50:45,000 To distinguish different smells, the receptors have to send a signal to the brain. 696 00:50:45,000 --> 00:50:49,160 That signal is triggered by an electron. 697 00:50:49,160 --> 00:50:52,000 The only way for the electron to signal the brain 698 00:50:52,000 --> 00:50:55,400 is to go through the solid scent molecule 699 00:50:55,400 --> 00:50:58,440 though this should be an impenetrable barrier, 700 00:50:58,440 --> 00:51:01,960 but when the right molecule hits the right receptor, 701 00:51:01,960 --> 00:51:05,280 the electron can magically pass through the molecule 702 00:51:05,280 --> 00:51:07,560 and begin its journey to the brain. 703 00:51:08,600 --> 00:51:13,720 This seemingly impossible process is called quantum tunnelling. 704 00:51:17,480 --> 00:51:20,000 What's remarkable, I think, about this is that, 705 00:51:20,000 --> 00:51:22,840 we've known about quantum mechanics for 100 years now 706 00:51:22,840 --> 00:51:25,720 but only in the last few years has it become clear 707 00:51:25,720 --> 00:51:29,920 that nature actually discovered all this quantum weirdness 708 00:51:29,920 --> 00:51:35,000 a billion years before human beings even came on the scene. 709 00:51:35,000 --> 00:51:39,760 You would expect it to be very interesting to go from what seemed to be a purely theoretical 710 00:51:39,760 --> 00:51:44,280 experimental side to something that's actually day to day life. 711 00:51:44,280 --> 00:51:51,000 So are you willing to accept now that quantum mechanics is more important to life than just dead cats? 712 00:51:51,000 --> 00:51:52,640 Yes, I can accept that. 713 00:51:54,920 --> 00:51:57,720 The smell of success! 714 00:51:59,160 --> 00:52:00,880 Yes, I get it. 715 00:52:08,200 --> 00:52:11,960 Quantum physics underlies everything in the world, 716 00:52:11,960 --> 00:52:16,360 and gives us a glimpse of what reality is actually like. 717 00:52:16,360 --> 00:52:23,120 It's amazing and I'm very pleased that smart people like Seth are working all this stuff out 718 00:52:23,120 --> 00:52:26,120 but I just think we've taken a bit of a detour. 719 00:52:29,840 --> 00:52:32,240 I set out to measure a piece of string 720 00:52:32,240 --> 00:52:35,280 and I can't believe that 0.442 of a millimetre 721 00:52:35,280 --> 00:52:36,960 is as accurate as I can get. 722 00:52:36,960 --> 00:52:41,720 Surely, there's a way to go beyond that to get a better length. 723 00:52:41,720 --> 00:52:43,800 So Seth, 724 00:52:43,800 --> 00:52:45,320 come on! 725 00:52:47,520 --> 00:52:50,640 You've shown me a lot of particles and waves and... 726 00:52:50,640 --> 00:52:57,600 I know a bit about quantum mechanics now but I don't know the length of my piece of string. 727 00:52:57,600 --> 00:52:59,880 Fair enough. 728 00:52:59,880 --> 00:53:02,120 Isn't science always like that? 729 00:53:02,120 --> 00:53:03,840 It's turning out that way. 730 00:53:03,840 --> 00:53:07,720 It answers lots of questions but not the one you want to know the answer to. 731 00:53:07,720 --> 00:53:09,720 How long is a piece of string? 732 00:53:09,720 --> 00:53:11,320 Absolutely. 733 00:53:11,320 --> 00:53:16,080 Well, let's look at how accurately you could possibly measure your string. Yes, let's. 734 00:53:16,080 --> 00:53:19,520 All right, so you know that if you can measure your string very 735 00:53:19,520 --> 00:53:25,600 accurately within a millionth of a metre by counting the number of wave lengths of light that go along it. 736 00:53:25,600 --> 00:53:28,520 And then you say hey, I can measure it more accurately 737 00:53:28,520 --> 00:53:31,840 by putting in light with a shorter wavelength, so if the light 738 00:53:31,840 --> 00:53:36,560 has half the wavelength, I can measure it to twice the accuracy. 739 00:53:36,560 --> 00:53:40,600 This is what they were talking about at the National Physical Laboratory, 740 00:53:40,600 --> 00:53:45,160 using the wavelength of laser light to measure my string. 741 00:53:45,160 --> 00:53:50,880 Despite the uncertainties of quantum physics, it's the best way to measure length. 742 00:53:52,400 --> 00:53:58,240 Theoretically, there is almost no limit to how well you can measure with it. 743 00:53:58,240 --> 00:54:04,440 In principle you could actually by making a light wiggle up and down really, really, really, really fast, 744 00:54:04,440 --> 00:54:08,280 you would think, "I can measure my string to any degree of accuracy I want." 745 00:54:08,280 --> 00:54:13,160 Which would make you happy. Yes. 746 00:54:13,160 --> 00:54:16,920 But there's one slight hitch. Yeah, I thought there'd be a "but" after it. 747 00:54:16,920 --> 00:54:19,520 Yeah, yeah, I know. 748 00:54:19,520 --> 00:54:22,560 I know. It's always this way, right? 749 00:54:22,560 --> 00:54:24,680 Yeah. So... Go on then, what is it? 750 00:54:24,680 --> 00:54:28,760 OK, the hitch is that if the light is wiggling up and down faster, 751 00:54:28,760 --> 00:54:34,040 each photon has more and more energy 752 00:54:34,040 --> 00:54:38,400 so if it wiggles up and down twice as fast, you double the energy of the photon. 753 00:54:38,400 --> 00:54:44,200 That's OK, we just put in more energy but we get a better measurement of your piece of string. 754 00:54:44,200 --> 00:54:51,160 But what Einstein taught us is that energy effectively has mass, 755 00:54:51,160 --> 00:54:55,600 and mass gives us gravity, but there's actually a limit 756 00:54:55,600 --> 00:55:01,080 to how densely you can pack a bunch of energy into a sub-class. 757 00:55:01,080 --> 00:55:03,440 What's the limit? 758 00:55:03,440 --> 00:55:06,400 Do the words, "Black hole" ring a bell? 759 00:55:06,400 --> 00:55:10,040 I can make a black hole with my string? Well, you can. 760 00:55:10,040 --> 00:55:12,480 Measuring leads to black holes? 761 00:55:12,480 --> 00:55:15,840 To measure you need to put in energy. Energy causes gravitation. 762 00:55:15,840 --> 00:55:18,360 Excess of gravitation causes black holes. 763 00:55:22,160 --> 00:55:24,280 Oh, that's a terrible disappointment. 764 00:55:31,720 --> 00:55:33,800 I'm going with the black hole, Seth. 765 00:55:33,800 --> 00:55:35,680 You wanted to know the answer. 766 00:55:35,680 --> 00:55:37,200 I don't care any more. 767 00:55:39,360 --> 00:55:42,200 Thanks for everything but... 768 00:55:42,200 --> 00:55:43,720 kaboom! 769 00:55:43,720 --> 00:55:46,200 THEY LAUGH 770 00:55:47,400 --> 00:55:50,240 I've learnt something. 771 00:55:55,120 --> 00:55:59,440 I just thought at the beginning of this, a group of men in white coats 772 00:55:59,440 --> 00:56:02,680 would point a laser at the string and da-da, you'd get a length. 773 00:56:05,080 --> 00:56:07,160 But it turns out that trying to measure 774 00:56:07,160 --> 00:56:12,040 something as simple as string is actually a philosophical journey. 775 00:56:12,040 --> 00:56:15,720 'The whole of the human race would be in the volume of a sugar cube.' 776 00:56:15,720 --> 00:56:18,040 'Everybody in the world?' 777 00:56:18,040 --> 00:56:24,040 It's led me to discover the fundamental building blocks of everything defy reality. 778 00:56:24,040 --> 00:56:28,560 We're only scratching the surface of what's really going on in the world. 779 00:56:28,560 --> 00:56:31,640 'The length of this piece of string is going to depend....' 780 00:56:31,640 --> 00:56:34,840 'It's a simple task, this time, shouldn't take long.' 781 00:56:34,840 --> 00:56:37,240 'The more you measure it, the longer it gets.' 782 00:56:38,920 --> 00:56:41,160 How long is this piece of string? 783 00:56:41,160 --> 00:56:43,920 Right, and you want a simple answer to this one? 784 00:56:44,920 --> 00:56:49,320 319 millimetres and 442 micrometers. 785 00:56:49,320 --> 00:56:54,160 That piece of string could actually be infinite in length. 786 00:56:54,160 --> 00:56:57,440 'Things aren't there until you actually look at them.' 787 00:56:57,440 --> 00:56:59,960 VOICES ECHO 788 00:56:59,960 --> 00:57:01,800 32 centimetres. 789 00:57:01,800 --> 00:57:04,560 That'll be the end of the programme, then. 790 00:57:06,520 --> 00:57:09,520 But after all this maths and physics, 791 00:57:09,520 --> 00:57:11,480 how long is my piece of string? 792 00:57:11,480 --> 00:57:15,440 Well, I promised to tell Marcus the answer. 793 00:57:23,760 --> 00:57:27,120 Hello, how are you! I'm good, how about you? 794 00:57:27,120 --> 00:57:29,120 I'm fine, I'm fine. 795 00:57:29,120 --> 00:57:31,840 My head is full of string now. 796 00:57:31,840 --> 00:57:37,560 So ultimately what's the answer? How long is your piece of string, Alan? 797 00:57:37,560 --> 00:57:39,560 It's 320 millimetres. 798 00:57:39,560 --> 00:57:42,240 That's what you said right at the beginning. 799 00:57:42,240 --> 00:57:46,000 But every time I asked someone how long is it, they took me further and further 800 00:57:46,000 --> 00:57:50,240 down into it and they said, really you can't measure it. 801 00:57:50,240 --> 00:57:53,560 How long's a piece of string? We just don't know. 802 00:57:53,560 --> 00:57:58,160 I think your piece of string might deserve a drink after its long journey. 803 00:57:58,160 --> 00:58:01,040 Shall we take it for a pint? OK. 804 00:58:01,040 --> 00:58:05,760 I still don't really know, though, why I had a six inch needle stuffed up my nose. 805 00:58:05,760 --> 00:58:09,320 I still don't really understand that bit. 806 00:58:24,120 --> 00:58:26,160 Subtitles by Red Bee Media Ltd 807 00:58:26,160 --> 00:58:28,200 E-mail subtitling@bbc.co.uk