WEBVTT 00:00:01.000 --> 00:00:04.074 Subtitles downloaded from www.OpenSubtitles.org 00:00:06.760 --> 00:00:08.960 BOY: 'One for sorrow 00:00:08.960 --> 00:00:11.000 'Two for mirth 00:00:13.440 --> 00:00:15.280 GIRL: 'Three for a wedding 00:00:15.280 --> 00:00:16.880 'And four for death 00:00:16.880 --> 00:00:18.520 BOY: 'Nine for hell.' 00:00:21.560 --> 00:00:23.800 GIRL: '666.' 00:00:26.880 --> 00:00:31.520 Hidden within this cathedral are clues to a mystery, 00:00:31.520 --> 00:00:34.400 something that could help answer 00:00:34.400 --> 00:00:37.080 one of humanity's most enduring questions... 00:00:38.480 --> 00:00:42.080 ..why is the world the way it is? 00:00:43.800 --> 00:00:47.160 The 13th-century masons who constructed this place 00:00:47.160 --> 00:00:49.400 had glimpsed a deep truth 00:00:49.400 --> 00:00:52.680 and they built a message into its very walls 00:00:52.680 --> 00:00:56.480 in the precise proportions of this magnificent cathedral. 00:01:01.080 --> 00:01:03.240 To the medieval clergy, 00:01:03.240 --> 00:01:06.880 these divine numbers were created by God. 00:01:09.320 --> 00:01:12.800 But to me, they're evidence of something else, 00:01:12.800 --> 00:01:16.440 a hidden code that underpins the world around us, 00:01:16.440 --> 00:01:21.440 a code that has the power to unlock the laws that govern the universe. 00:01:48.720 --> 00:01:52.400 As a mathematician, I'm fascinated by the numbers 00:01:52.400 --> 00:01:54.800 and patterns we see all around us... 00:02:04.440 --> 00:02:08.000 ..numbers and patterns that connect everything 00:02:08.000 --> 00:02:10.720 from fish to circles 00:02:10.720 --> 00:02:13.480 and from our ancient past 00:02:13.480 --> 00:02:15.920 to the far future. 00:02:20.160 --> 00:02:21.600 INDISTINCT COMMENT 00:02:28.120 --> 00:02:30.840 Together they make up the Code... 00:02:33.200 --> 00:02:36.040 ..an abstract world of numbers... 00:02:37.640 --> 00:02:43.960 ..that has given us the most detailed description of our world we've ever had. 00:02:56.360 --> 00:03:01.040 For centuries, people have seen significant numbers everywhere... 00:03:02.680 --> 00:03:08.120 ..an obsession that's left its mark in the stones of this medieval cathedral. 00:03:19.320 --> 00:03:23.200 In the 12th century, religious scholars here in Chartres 00:03:23.200 --> 00:03:27.920 became convinced these numbers were intrinsically linked to the divine... 00:03:32.120 --> 00:03:35.520 ..an idea that dates back to the dawn of Christianity. 00:03:37.960 --> 00:03:41.520 The fourth-century Algerian cleric St Augustine believed 00:03:41.520 --> 00:03:45.920 that seven was so special that it represented the entire universe. 00:03:45.920 --> 00:03:49.560 He described how seven embraced all created things 00:03:49.560 --> 00:03:52.240 and ten was beyond even the universe 00:03:52.240 --> 00:03:55.920 because it was seven plus the three aspects of the Holy Trinity - 00:03:55.920 --> 00:03:58.920 Father, Son and Holy Ghost. 00:04:04.000 --> 00:04:11.720 12 was also hugely important, not simply because there are 12 tribes of Israel or 12 disciples of Jesus, 00:04:11.720 --> 00:04:19.240 but because 12 is divisible by one, two, three, four, six and 12 itself, 00:04:19.240 --> 00:04:21.480 more than any other number around it. 00:04:21.480 --> 00:04:24.920 For St Augustine, numbers had to come from God 00:04:24.920 --> 00:04:28.360 because they obey laws that no man can change. 00:04:32.000 --> 00:04:36.080 Around 800 years after St Augustine, 00:04:36.080 --> 00:04:40.520 the 12th-century Chartres School also recognised their significance. 00:04:44.120 --> 00:04:48.000 It's thought that, under their influence, sacred numbers 00:04:48.000 --> 00:04:52.400 were built into the structure of this majestic building. 00:04:55.400 --> 00:05:00.320 Numbers, they believed, held the key to the mystery of creation. 00:05:07.280 --> 00:05:11.040 I've spent my entire working life studying numbers, 00:05:11.040 --> 00:05:14.680 and for me they're more than just abstract entities. 00:05:14.680 --> 00:05:16.920 They describe the world around us. 00:05:16.920 --> 00:05:19.960 Although I don't share their religious beliefs, I can't help 00:05:19.960 --> 00:05:23.400 feeling something in common with the people who built this place. 00:05:23.400 --> 00:05:26.760 I share their awe and wonder at the beauty of numbers. 00:05:26.760 --> 00:05:32.360 For them, those numbers brought them closer to God, but I think they're important for another reason, 00:05:32.360 --> 00:05:36.600 because I believe they're the key to making sense of our world. 00:05:41.960 --> 00:05:47.640 Numbers have given us an unparalleled ability to understand our universe. 00:05:50.440 --> 00:05:55.080 And in places, this code literally emerges from the ground. 00:06:01.600 --> 00:06:04.200 Rural Alabama, 00:06:04.200 --> 00:06:07.240 spring 2011. 00:06:09.280 --> 00:06:12.360 Warm, lush and peaceful. 00:06:18.600 --> 00:06:21.560 But this year, there's a plague coming. 00:06:29.600 --> 00:06:32.080 While some locals are moving out, 00:06:32.080 --> 00:06:36.760 Dr John Cooley has driven thousands of miles to be here. 00:06:40.480 --> 00:06:44.440 He's on the trail of one of the area's strangest residents. 00:06:51.400 --> 00:06:56.440 We have been driving around looking for the emergences for about three and a half weeks. 00:06:56.440 --> 00:07:01.400 I've driven 7,200 miles since Good Friday trying to figure out where these things are. 00:07:06.600 --> 00:07:11.320 What makes these insects so remarkable is their bizarre lifecycle. 00:07:13.960 --> 00:07:19.160 For 12 whole years, they live hidden underground, in vast numbers. 00:07:23.160 --> 00:07:26.080 Then, in their 13th year... 00:07:26.080 --> 00:07:28.920 at precisely the same time... 00:07:30.600 --> 00:07:34.640 ..they all burrow out from the earth to breed. 00:07:40.760 --> 00:07:46.600 At the full part of the emergence, there will be millions of insects out per acre. They'll be everywhere. 00:07:46.600 --> 00:07:48.560 It really is insect mayhem. 00:07:55.120 --> 00:07:59.400 This is the periodical cicada. 00:08:01.040 --> 00:08:03.680 This one is a male... 00:08:05.320 --> 00:08:08.120 ..and you know that because on the abdomen, 00:08:08.120 --> 00:08:10.440 there's a pair of organs called timbles, 00:08:10.440 --> 00:08:12.760 and they're sound-producing organs. 00:08:12.760 --> 00:08:15.680 It's a little membrane that's vibrated, it makes a sound. 00:08:15.680 --> 00:08:18.720 Oh, yeah. I don't have to be frightened of these, do I? 00:08:18.720 --> 00:08:22.440 No, no, they're absolutely harmless. They make wonderful pets. Really? 00:08:22.440 --> 00:08:25.240 Mm-hm. They're quite ticklish. It's a harmless insect. 00:08:25.240 --> 00:08:28.720 It doesn't bite, it doesn't sting, nothing of that sort. 00:08:28.720 --> 00:08:31.600 Its only defence is safety in numbers. 00:08:33.880 --> 00:08:38.200 By emerging in such vast numbers, each individual cicada 00:08:38.200 --> 00:08:40.920 minimises its risk of being eaten. 00:08:40.920 --> 00:08:43.440 Because there are so many of them, 00:08:43.440 --> 00:08:47.120 their predators simply can't eat them fast enough. 00:08:48.320 --> 00:08:51.560 Well, you can certainly hear the cicadas. 00:08:51.560 --> 00:08:54.680 Yes, you can. There are probably millions of them up there. 00:08:54.680 --> 00:09:00.160 Millions? Yeah, millions. What you probably don't realise is you're only hearing half the population. 00:09:00.160 --> 00:09:02.000 Only the males make these loud sounds. 00:09:02.000 --> 00:09:04.640 There are just as many females up there as well. 00:09:04.640 --> 00:09:08.280 And it's extraordinary to think that if we came here next year, 00:09:08.280 --> 00:09:11.960 we wouldn't hear this sound at all? You'll have to come back in 13 years. 00:09:11.960 --> 00:09:16.200 So 2024 is when you'll hear the forest singing like this again? 00:09:16.200 --> 00:09:18.600 That's right. That's amazing. 00:09:25.480 --> 00:09:30.840 Why have the cicadas evolved with this 13-year lifecycle as opposed to any other number? 00:09:30.840 --> 00:09:36.120 Well, you have to remember that these cicadas require large numbers to survive predators, 00:09:36.120 --> 00:09:41.360 and so we think that these long lifecycles in some way help them maintain large populations. 00:09:46.680 --> 00:09:50.720 John believes that, by appearing every 13 years, 00:09:50.720 --> 00:09:54.040 the cicadas minimise their chances of emerging at the same time 00:09:54.040 --> 00:09:57.480 as other cicadas with different lifecycles... 00:09:59.880 --> 00:10:05.160 ..because if they were to interbreed, it could have disastrous consequences. 00:10:07.800 --> 00:10:11.520 The offspring would have unusual lifecycles. 00:10:11.520 --> 00:10:17.000 They're going to emerge a little bit here, a little bit there, some this year and some that year in small 00:10:17.000 --> 00:10:21.800 numbers, and that's key because if they emerge in small numbers, the predators eat them. 00:10:33.520 --> 00:10:38.560 The cicadas' survival depends on avoiding other broods. 00:10:53.840 --> 00:10:58.480 Imagine you've got a brood of cicadas that appears every six years. 00:11:10.800 --> 00:11:13.520 Now, let's suppose there's another brood 00:11:13.520 --> 00:11:16.880 which wants to try and avoid the red cicadas. 00:11:16.880 --> 00:11:21.760 One way to do that would be to appear less often in the forest, and that actually works. 00:11:21.760 --> 00:11:25.160 So let's suppose this brood appears every nine years. 00:11:33.480 --> 00:11:36.920 So if the green cicada appears every nine years, 00:11:36.920 --> 00:11:40.720 then it only coincides with the red cicada every 18 years. 00:11:41.840 --> 00:11:46.320 But, rather surprisingly, a smaller number, seven, works even better. 00:11:57.240 --> 00:12:01.560 Coming out every seven years instead of every nine 00:12:01.560 --> 00:12:04.760 means the cicadas appear together much less often. 00:12:07.240 --> 00:12:11.480 Now they only coincide every 42 years. 00:12:12.480 --> 00:12:15.320 That's just twice every century. 00:12:18.600 --> 00:12:20.920 And for the real cicadas, 00:12:20.920 --> 00:12:26.960 a 13-year lifecycle has exactly the same effect as seven does here 00:12:26.960 --> 00:12:31.760 because they both belong to a special series of numbers. 00:12:31.760 --> 00:12:35.520 Like 13, seven is a prime number. 00:12:35.520 --> 00:12:40.920 Unlike other numbers, primes can only be divided by themselves and one, 00:12:40.920 --> 00:12:45.200 and it's this property that means that numbers that are separated by primes 00:12:45.200 --> 00:12:49.000 are far less likely to coincide with multiples of other numbers. 00:12:50.600 --> 00:12:55.160 Because 13 is a prime number, a 13-year lifecycle 00:12:55.160 --> 00:12:59.800 makes the cicadas much less likely to coincide with other groups. 00:13:02.240 --> 00:13:06.200 Up in Georgia, there is another brood of periodical cicada 00:13:06.200 --> 00:13:09.040 and they, too, have a prime number lifecycle. 00:13:09.040 --> 00:13:11.840 They come out every 17 years. 00:13:11.840 --> 00:13:16.080 Because 13 and 17 are both prime numbers, 00:13:16.080 --> 00:13:22.440 the two broods only emerge together once every 221 years. 00:13:29.920 --> 00:13:34.760 Prime numbers are intimately linked to the cicadas' survival 00:13:34.760 --> 00:13:36.600 and, intriguingly, 00:13:36.600 --> 00:13:41.280 they're one of the most important elements of the Code, 00:13:41.280 --> 00:13:45.920 because the Code is a mathematical world, 00:13:45.920 --> 00:13:49.160 built from numbers. 00:13:49.160 --> 00:13:53.920 Just as atoms are the indivisible units that make up every physical object, 00:13:53.920 --> 00:13:58.480 so prime numbers are the indivisible building blocks of the Code. 00:14:03.360 --> 00:14:07.280 Prime numbers are indivisible, which means they can't be made 00:14:07.280 --> 00:14:10.640 by multiplying any other numbers together. 00:14:12.280 --> 00:14:17.200 But every non-prime number can be created by multiplying primes together. 00:14:20.560 --> 00:14:23.720 It's impossible to make any numbers without them. 00:14:29.760 --> 00:14:33.280 And if any primes are missing, 00:14:33.280 --> 00:14:36.920 there will always be some numbers you can't create. 00:14:44.040 --> 00:14:48.520 For me, the fact that the most fundamental units of mathematics 00:14:48.520 --> 00:14:50.880 can be found woven into the natural world 00:14:50.880 --> 00:14:55.400 is not only compelling evidence that the Code exists, 00:14:55.400 --> 00:14:59.160 but also that numbers underpin everything... 00:15:00.520 --> 00:15:04.080 ..including our own biology. 00:15:34.200 --> 00:15:37.280 This is an innately human characteristic. 00:15:37.280 --> 00:15:43.560 Music is one of the things which defines who we are, and each culture has its own particular style. 00:15:43.560 --> 00:15:46.400 These guys make it seem so effortless, as if the notes 00:15:46.400 --> 00:15:50.560 are just thrown together, but that's simply an illusion. 00:15:54.000 --> 00:15:57.160 MUSIC ENDS, APPLAUSE 00:15:58.400 --> 00:16:02.440 Because, just as numbers govern the cicadas' lives, 00:16:02.440 --> 00:16:05.280 so they determine how WE hear sound. 00:16:26.520 --> 00:16:28.240 That's a C. 00:16:28.240 --> 00:16:31.400 And using this oscilloscope, I can get a picture of that note. 00:16:32.480 --> 00:16:36.160 So I can actually SEE the sound wave. 00:16:36.160 --> 00:16:40.040 Now, the height of the wave corresponds to how loudly I'm playing the note, 00:16:40.040 --> 00:16:42.760 so if I play the note very quietly... 00:16:42.760 --> 00:16:47.560 play it very loudly...I suddenly get a huge wave on the screen. 00:16:47.560 --> 00:16:51.400 The more important thing is the distance between the peaks of the wave, 00:16:51.400 --> 00:16:54.840 because that's determined by the pitch or frequency of the note. 00:16:55.840 --> 00:16:57.400 'The higher the note... 00:16:58.960 --> 00:17:02.960 'the shorter the distance between the peaks.' 00:17:09.240 --> 00:17:11.680 Now, look what happens when I play a C... 00:17:13.840 --> 00:17:17.600 ..and compare that with the same note, a C, but an octave higher. 00:17:20.520 --> 00:17:24.040 Something rather surprising emerges, 00:17:24.040 --> 00:17:27.760 because now you can see that the higher note has twice 00:17:27.760 --> 00:17:29.720 as many peaks as the lower note, 00:17:29.720 --> 00:17:35.480 which means the frequency of the high C is twice that of the low C. 00:17:35.480 --> 00:17:38.120 And this happens whatever two notes you choose. 00:17:38.120 --> 00:17:44.000 Provided they're an octave apart, then their frequencies are going to be in this one-to-two ratio. 00:17:48.880 --> 00:17:53.480 Two notes which are an octave apart just sound nice together, and they're actually the most 00:17:53.480 --> 00:17:56.560 harmonious combination of notes that you can have. 00:17:56.560 --> 00:18:02.560 And that's because one to two is the simplest possible frequency relationship, and that's what 00:18:02.560 --> 00:18:09.160 music is all about, because it's these simple whole-number ratios that sound so good to the ear. 00:18:09.160 --> 00:18:11.720 A perfect fifth... 00:18:11.720 --> 00:18:14.440 is a frequency ratio of three to two. 00:18:14.440 --> 00:18:16.400 A perfect fourth... 00:18:16.400 --> 00:18:17.920 is four to three. 00:18:17.920 --> 00:18:21.560 And a slightly more complex sound, a minor sixth... 00:18:23.240 --> 00:18:26.840 ..that's a frequency ratio of five to eight. 00:18:28.720 --> 00:18:34.480 Every combination of notes used in music is defined by simple ratios. 00:18:36.360 --> 00:18:40.960 Although we might not be aware of it, these numerical rules underpin 00:18:40.960 --> 00:18:46.360 everything from the simplest song to the most elaborate symphony. 00:18:46.360 --> 00:18:50.240 They're so deeply ingrained that when they're broken, 00:18:50.240 --> 00:18:53.040 we intuitively know something is wrong. 00:19:05.800 --> 00:19:09.520 Professor Judy Edworthy understands this more than most. 00:19:14.040 --> 00:19:20.080 She spends her time subjecting people to some of most unpleasant noises imaginable. 00:19:21.080 --> 00:19:22.520 Hi, Judy. 00:19:22.520 --> 00:19:24.560 Ah, hello. Marcus. 00:19:24.560 --> 00:19:28.800 'Her research investigates the psychological effects of sound. 00:19:33.400 --> 00:19:41.640 'And by using complex ratios instead of simple ones, the noises she creates are nothing like music.' 00:19:41.640 --> 00:19:45.600 You can see just by looking at it it's not going to sound nice. 00:19:45.600 --> 00:19:47.360 The wave looks a mess. 00:19:47.360 --> 00:19:49.920 The wave is a mess. It's very difficult to see a pattern. 00:19:49.920 --> 00:19:54.200 CONSTANT DRONE 00:19:54.200 --> 00:19:56.440 OK. It sounds really quite odd now. 00:19:56.440 --> 00:20:01.240 It doesn't have any pitch. It sounds harsh and I could make it louder and that would make it harsher. 00:20:01.240 --> 00:20:05.200 When the various frequencies aren't simple multiples of one another, 00:20:05.200 --> 00:20:08.000 there's no common pattern for the ear to respond to, 00:20:08.000 --> 00:20:12.280 and the more complex you make the ratios, the more dissonant and harsh the sound will get. 00:20:16.040 --> 00:20:20.400 By monitoring her victims' reactions to these appalling noises, 00:20:20.400 --> 00:20:23.960 Professor Edworthy has found they have a very different effect 00:20:23.960 --> 00:20:25.440 on our minds than music. 00:20:25.440 --> 00:20:27.480 ALARM BEEPS 00:20:27.480 --> 00:20:30.160 HONKING 00:20:30.160 --> 00:20:31.200 WHIRRING 00:20:31.200 --> 00:20:33.880 They're so unpleasant... HAMMERING 00:20:33.880 --> 00:20:37.080 ..they shock our brains into action. 00:20:37.080 --> 00:20:38.960 For example, a siren. 00:20:38.960 --> 00:20:42.720 HIGH-PITCHED SIREN BLARES 00:20:45.840 --> 00:20:50.480 That's quite a harsh sound, but it's designed for a purpose - to get you out of the way. 00:20:50.480 --> 00:20:54.000 Sometimes you find these sounds in the animal world as well. 00:20:54.000 --> 00:20:56.960 So this, for example, this is a chimpanzee and an orang-utan. 00:20:56.960 --> 00:21:00.360 INTERMITTENT SCREECHING 00:21:03.480 --> 00:21:07.560 OK, these animals are obviously quite bothered by something. 00:21:07.560 --> 00:21:11.840 You don't need to know what that sound means to know that that animal's not happy 00:21:11.840 --> 00:21:17.680 and also that the other animals in that environment and us, for example, should just get out of the way. 00:21:17.680 --> 00:21:20.040 SHORT SCREECH 00:21:20.040 --> 00:21:23.200 So it's interesting that we really hear pattern, 00:21:23.200 --> 00:21:27.560 and when it isn't there, it creates an effect in all of us. 00:21:27.560 --> 00:21:30.480 LOW-PITCHED SCREECH 00:21:37.200 --> 00:21:41.280 Remarkably, it's numerical patterns in the Code 00:21:41.280 --> 00:21:45.080 that dictate the combinations of sounds we hear as music... 00:21:45.080 --> 00:21:47.360 RUSTLING 00:21:47.360 --> 00:21:51.000 ..and those we hear simply as noise. CHIRPING, SIREN 00:21:51.000 --> 00:21:54.120 BELL TOLLS 00:21:54.120 --> 00:21:58.840 And perhaps stranger still, it's these same numbers 00:21:58.840 --> 00:22:02.160 that are built into the walls of this medieval cathedral. 00:22:08.440 --> 00:22:12.600 Two notes which are an octave apart are going be in this one-to-two ratio. 00:22:20.240 --> 00:22:23.960 The width of the nave here is twice the distance between 00:22:23.960 --> 00:22:30.360 each of the columns that run up its length - a ratio of two to one. 00:22:30.360 --> 00:22:34.680 The most harmonious combination of notes from a pair. 00:22:34.680 --> 00:22:38.520 The altar divides the nave into a ratio of eight to five. 00:22:40.280 --> 00:22:42.560 A minor sixth... 00:22:42.560 --> 00:22:44.000 eight to five. 00:22:47.960 --> 00:22:49.680 A perfect fifth... 00:22:49.680 --> 00:22:51.920 three to two. 00:22:51.920 --> 00:22:55.440 A perfect fourth is four to three. 00:22:55.440 --> 00:22:57.600 Major third, five to four. 00:23:00.720 --> 00:23:04.360 And that's what music is all about. 00:23:04.360 --> 00:23:09.000 St Augustine believed these ratios were used by God to construct the universe 00:23:09.000 --> 00:23:13.040 and that that was why they produced harmony in music. 00:23:18.480 --> 00:23:22.240 By constructing their cathedral using the same ratios, 00:23:22.240 --> 00:23:26.280 the clergy at Chartres hoped to echo God's creation. 00:23:26.280 --> 00:23:29.800 This entire place is a symphony set in stone. 00:23:33.440 --> 00:23:38.440 Using the Code's numbers has created a building of awe-inspiring beauty. 00:23:52.760 --> 00:23:54.480 The only truth there is... 00:23:54.480 --> 00:23:56.960 Seemingly significant numbers... 00:24:03.240 --> 00:24:06.680 By searching for divine meaning in numbers, 00:24:06.680 --> 00:24:11.560 12th-century scholars had stumbled across elements of the Code. 00:24:11.560 --> 00:24:14.280 It's very difficult to see a pattern. 00:24:16.960 --> 00:24:21.920 Mysterious numbers and patterns that seem to be written into our biology. 00:24:22.960 --> 00:24:25.560 Its only defence is safety in numbers. 00:24:27.880 --> 00:24:34.200 And as we've looked closer, we haven't simply found more numbers - 00:24:34.200 --> 00:24:41.600 we've begun to uncover their strangest properties and started to see deep connections between them. 00:24:45.720 --> 00:24:49.760 Back in the distant past, in Neolithic times, 00:24:49.760 --> 00:24:55.160 around 4,000 years ago, an ancient people brought these stones here 00:24:55.160 --> 00:24:57.680 and arranged them like this. 00:24:57.680 --> 00:25:02.480 This is Sunkenkirk stone circle in Cumbria and it's one of around 1,000 00:25:02.480 --> 00:25:07.360 such structures that our ancient ancestors built across the UK. 00:25:13.840 --> 00:25:17.400 Stretching back into the mists of time, 00:25:17.400 --> 00:25:21.000 the circle has been steeped in mysticism. 00:25:24.720 --> 00:25:27.760 But whether the people who built this structure knew it or not, 00:25:27.760 --> 00:25:31.800 there is deep significance hidden inside this circle. 00:25:31.800 --> 00:25:36.080 OK, so I need to start by measuring the diameter 00:25:36.080 --> 00:25:41.360 of my circle, so that's the distance from one edge to the other. 00:25:43.600 --> 00:25:46.200 I need to go roughly through the centre. 00:25:48.640 --> 00:25:51.480 So that's 27 and 90. 00:25:55.480 --> 00:25:58.680 Right, so now I'm going to measure the circumference 00:25:58.680 --> 00:26:01.120 of the circle. So off we go. 00:26:01.120 --> 00:26:03.480 So around the outside. 00:26:05.520 --> 00:26:08.320 Oh, I've never got so much exercise doing maths before! 00:26:10.680 --> 00:26:13.440 And that's the circumference. 00:26:13.440 --> 00:26:17.880 So I've got 91 metres 00:26:17.880 --> 00:26:20.760 and 70 centimetres. 00:26:23.000 --> 00:26:28.160 I'm going to do a little calculation. I'm going to divide the circumference 00:26:28.160 --> 00:26:32.120 of the circle by the diameter. 00:26:32.120 --> 00:26:36.160 So 917 divided by 279. 00:26:36.160 --> 00:26:38.440 So that's roughly three... 00:26:38.440 --> 00:26:42.320 Bit of, er, mental arithmetic, not a mathematician's strongest point. 00:26:42.320 --> 00:26:45.040 OK, two lots of 279, 00:26:45.040 --> 00:26:46.600 so... 00:26:46.600 --> 00:26:49.400 not far out from what I was hoping for. 00:26:49.400 --> 00:26:54.840 So when I do that, I get roughly 3.2 as the answer. 00:27:00.000 --> 00:27:03.280 My measurements weren't very precise... 00:27:04.920 --> 00:27:10.320 ..but my answer is close to a mysterious number hidden within every circle. 00:27:15.000 --> 00:27:19.840 So, for example, let's take this circular plate here. 00:27:19.840 --> 00:27:21.880 I'm going to measure its diameter. 00:27:21.880 --> 00:27:25.120 26.4 centimetres. Now its circumference. 00:27:27.160 --> 00:27:29.080 That's a bit trickier. 00:27:29.080 --> 00:27:31.640 82.9 centimetres. 00:27:31.640 --> 00:27:35.640 Divide the circumference by the diameter, I get 3.14. 00:27:35.640 --> 00:27:38.560 Now let's take another circle. Measure its diameter. 00:27:38.560 --> 00:27:40.880 12.8 centimetres. 00:27:42.360 --> 00:27:47.200 So the circumference is 40.2 centimetres. 00:27:47.200 --> 00:27:52.160 Divide the circumference by the diameter and I get 3.14. 00:27:52.160 --> 00:27:56.240 In fact, whatever circle I take, divide the circumference 00:27:56.240 --> 00:28:01.080 by the diameter and you're going to get a number which starts 3.14. 00:28:01.080 --> 00:28:04.320 This is a number we call pi. 00:28:09.440 --> 00:28:13.920 No matter where the circles are, no matter how big or small... 00:28:15.480 --> 00:28:17.920 ..they will always contain pi. 00:28:20.200 --> 00:28:26.680 It's this universality of the number pi which tells you you've identified a piece of true Code. 00:28:26.680 --> 00:28:28.720 In fact, if you get another number, 00:28:28.720 --> 00:28:30.840 it means that you haven't got a circle. 00:28:30.840 --> 00:28:34.000 In some sense, pi is the essence of circleness, 00:28:34.000 --> 00:28:36.840 distilled into the language of the Code. 00:28:37.880 --> 00:28:43.440 And because circles and curves crop up again and again in nature, 00:28:43.440 --> 00:28:47.560 pi can be found all around us. 00:28:51.280 --> 00:28:54.480 It's in the gentle curve of a river... 00:28:55.720 --> 00:28:58.360 ..the sweep of a coast line... 00:29:00.440 --> 00:29:04.240 ..and the shifting patterns of the desert sands. 00:29:07.120 --> 00:29:12.960 Pi seems written into the structures and processes of our planet. 00:29:18.800 --> 00:29:22.160 But, strangely, pi also appears in places 00:29:22.160 --> 00:29:25.640 that seem to have nothing to do with circles. 00:29:31.400 --> 00:29:35.560 I started fishing Brighton in 1972. 00:29:35.560 --> 00:29:39.200 I've been a fisherman 40 years, catching Dover sole. 00:29:41.400 --> 00:29:45.480 That's the main target species for the English Channel. 00:29:46.520 --> 00:29:48.520 How many fish do you think you get a day? 00:29:48.520 --> 00:29:51.000 300 some days, 150 other days, 00:29:51.000 --> 00:29:53.040 so I'd say 200 would be average. 00:29:53.040 --> 00:29:58.080 And you've got me some Dover sole today so I can have a weigh of what you've caught today. 00:29:58.080 --> 00:29:59.920 Yeah, you can play with them! OK! 00:30:02.360 --> 00:30:06.600 What's remarkable is that, with just a small amount of information... 00:30:06.600 --> 00:30:08.840 It's 180 grams. 00:30:09.840 --> 00:30:11.880 ..and by weighing a few fish... 00:30:11.880 --> 00:30:13.120 That's a whopper. 00:30:13.120 --> 00:30:14.520 ..I can use the Code 00:30:14.520 --> 00:30:17.360 to tell me things about not just today's catch... 00:30:17.360 --> 00:30:21.320 360 grams. 50 grams. 110 grams. 00:30:22.000 --> 00:30:25.280 ..but about all the Dover sole Sam's ever fished... 00:30:25.280 --> 00:30:28.040 Whoa, jeez, come back! 00:30:28.040 --> 00:30:30.640 ..I can even get an estimate for the largest sole 00:30:30.640 --> 00:30:33.440 that Sam is likely to have caught during his career. 00:30:33.440 --> 00:30:34.800 Right... 00:30:34.800 --> 00:30:41.320 First , I need to work out what the average weight of a fish is, 00:30:41.320 --> 00:30:45.560 so 140 plus 190 00:30:45.560 --> 00:30:48.080 plus 150... 00:30:48.080 --> 00:30:53.040 So now I need to work out the standard deviation, so that's 140 minus square that... 00:30:53.040 --> 00:30:55.560 Bear with me, all right? Almost there. 00:30:55.560 --> 00:31:00.800 So he said he fished for 40 years, 00:31:00.800 --> 00:31:06.000 and eight weeks during the year, six days out of the week 00:31:06.000 --> 00:31:10.280 and 200 sole each day, 00:31:10.280 --> 00:31:14.160 so that gives you a total of 384,000 fish. 00:31:15.880 --> 00:31:19.600 Using these numbers, I can calculate that the largest one 00:31:19.600 --> 00:31:22.800 out of those 384,000 fish 00:31:22.800 --> 00:31:27.880 should be about 1.3 kilograms, which is roughly three pounds. 00:31:30.000 --> 00:31:34.400 So what's the largest Dover sole that you've caught in your career? 00:31:34.400 --> 00:31:37.160 We call them door mats, the large ones, 00:31:37.160 --> 00:31:40.480 and you maybe get four or five a season. 00:31:40.480 --> 00:31:45.240 The largest, I'd say, was three to three and a half pounds. 00:31:45.240 --> 00:31:49.800 An average Dover Sole is that sort of size 00:31:49.800 --> 00:31:51.240 and these... 00:31:51.240 --> 00:31:54.520 Wow, that's huge! Yeah! 00:31:54.520 --> 00:31:58.400 It's a whopper. It's always nice to catch big stuff, you know. 00:31:58.400 --> 00:32:00.960 Well, I think it is anyway. HE CHUCKLES 00:32:05.360 --> 00:32:08.520 Using the Code, it's possible to estimate the size 00:32:08.520 --> 00:32:11.560 of the biggest fish Sam's ever caught, 00:32:11.560 --> 00:32:16.280 despite not weighing a single fish anywhere near that size. 00:32:21.120 --> 00:32:27.520 Now, the reason this calculation is possible is because the distribution of the weights of fish, 00:32:27.520 --> 00:32:32.840 in fact the distribution of lots of things like the height of people in the UK or IQ, 00:32:32.840 --> 00:32:35.720 is given by this formula. 00:32:35.720 --> 00:32:38.760 'This is the normal distribution equation, 00:32:38.760 --> 00:32:42.160 'one of the most important bits of mathematics 00:32:42.160 --> 00:32:46.480 'for understanding variation in the natural world.' 00:32:46.480 --> 00:32:51.360 The most remarkable thing about this formula isn't so much what it does 00:32:51.360 --> 00:32:53.680 as this term here, pi. 00:32:53.680 --> 00:32:55.840 It seems totally bizarre 00:32:55.840 --> 00:32:59.640 that a bit of the Code that has something to do with the geometry of a circle 00:32:59.640 --> 00:33:02.120 can help you to calculate the weight of fish. 00:33:02.120 --> 00:33:07.080 Pi shouldn't have anything to do with fish, yet there it is. 00:33:15.320 --> 00:33:19.800 Just as the circle appears everywhere in nature, 00:33:19.800 --> 00:33:24.200 so pi crops up again and again in the mathematical world. 00:33:25.840 --> 00:33:31.600 It's an astonishing example of the interconnectedness of the Code. 00:33:31.600 --> 00:33:36.880 A glimpse into a world where numbers don't just have strange connections, 00:33:36.880 --> 00:33:40.520 they have deeply puzzling properties of their own. 00:33:43.960 --> 00:33:46.840 Pi is what's known as an irrational number. 00:33:49.040 --> 00:33:53.120 Written as a decimal, it has an infinite number of digits 00:33:53.120 --> 00:33:56.520 arranged in a sequence that never repeats. 00:33:58.200 --> 00:34:02.720 And it's thought that any number you can possibly imagine 00:34:02.720 --> 00:34:07.360 will appear in pi somewhere, from my birthday 00:34:07.360 --> 00:34:11.080 to the answer to life, the universe and everything. 00:34:14.120 --> 00:34:17.240 Because they go on for ever, we can never know all the digits 00:34:17.240 --> 00:34:18.880 that make up pi. 00:34:18.880 --> 00:34:22.600 But, luckily, we only need the first 39 00:34:22.600 --> 00:34:28.040 to calculate the circumference of a circle the size of the entire observable universe, 00:34:28.040 --> 00:34:31.480 accurate to the radius of a single hydrogen atom. 00:34:38.440 --> 00:34:43.440 But as strange as Pi is, it does at least describe a physical object. 00:34:44.680 --> 00:34:48.200 Some numbers don't make any sense in real world, 00:34:48.200 --> 00:34:51.400 despite the fact we use them all the time. 00:34:51.400 --> 00:34:54.240 Numbers, like negative numbers. 00:34:56.920 --> 00:35:01.320 It's impossible to trade anything, stocks, shares, currency, 00:35:01.320 --> 00:35:04.200 even fish, without negative numbers. 00:35:04.200 --> 00:35:06.240 Most of us are comfortable them. 00:35:06.240 --> 00:35:09.240 Even though we may not like it, we understand what it means 00:35:09.240 --> 00:35:11.520 to have a negative bank balance. 00:35:11.520 --> 00:35:13.760 But when you start to think about it, 00:35:13.760 --> 00:35:17.400 there's something deeply strange about negative numbers, 00:35:17.400 --> 00:35:21.240 cos they don't seem to correspond to anything real at all. 00:35:23.760 --> 00:35:28.920 The deeper we look into the Code, the more bizarre it becomes. 00:35:33.640 --> 00:35:40.160 It's easy to imagine one fish or two fish, or no fish at all. 00:35:40.160 --> 00:35:44.520 It's much harder to imagine what minus-one fish looks like. 00:35:44.520 --> 00:35:49.440 Negative numbers are so odd that if I have minus-one fish and you give me a fish, 00:35:49.440 --> 00:35:53.320 then all you can be certain of is that I've got no fish at all. 00:36:00.880 --> 00:36:06.680 Numbers, can exist regardless of whether they make any sense in the physical world. 00:36:11.040 --> 00:36:15.680 And if you think that's odd, some numbers are so strange 00:36:15.680 --> 00:36:18.720 they don't even seem to make sense as numbers. 00:36:19.960 --> 00:36:24.080 Now, this is one of the most basic facts of mathematics. 00:36:24.080 --> 00:36:28.520 A positive number multiplied by another positive number is a positive number. 00:36:28.520 --> 00:36:34.800 So for example, one times one is one. 00:36:34.800 --> 00:36:38.200 A negative number multiplied by another negative number 00:36:38.200 --> 00:36:41.200 also gives a positive number. 00:36:41.200 --> 00:36:47.400 So for example, minus-one times minus-one is plus-one. 00:36:47.400 --> 00:36:53.080 'It's not only a rule, it's a proven truth of multiplication. 00:36:53.080 --> 00:36:57.120 'Whenever the signs are the same, the product is always positive.' 00:36:57.120 --> 00:36:59.160 From this, it's obvious 00:36:59.160 --> 00:37:01.840 if I take any number and multiply it by itself, 00:37:01.840 --> 00:37:04.360 then the answer is going to be positive. 00:37:04.360 --> 00:37:06.680 However, in the Code, 00:37:06.680 --> 00:37:09.480 there's a special number which breaks this rule. 00:37:09.480 --> 00:37:13.400 When I multiply it by itself, it gives the answer minus-one. 00:37:13.400 --> 00:37:17.160 It's impossible to imagine what this number could be, 00:37:17.160 --> 00:37:21.120 because there simply is no number 00:37:21.120 --> 00:37:24.960 that when multiplied by itself, gives minus-one. 00:37:24.960 --> 00:37:29.240 This isn't a number I can calculate. I can't show you this number. 00:37:29.240 --> 00:37:31.720 Nevertheless, we've given this number a name. 00:37:31.720 --> 00:37:35.040 It's called "i", and it's part of a whole class of new numbers 00:37:35.040 --> 00:37:36.520 called imaginary numbers. 00:37:38.240 --> 00:37:42.800 Calculating with imaginary numbers is the mathematical equivalent 00:37:42.800 --> 00:37:44.880 of believing in fairies. 00:37:46.080 --> 00:37:50.560 But even these strangest elements of the Code turn out to have 00:37:50.560 --> 00:37:53.440 some very practical applications. 00:37:58.040 --> 00:38:01.720 The ground's close, will you call me, please, 1-1-9 next... 00:38:04.360 --> 00:38:09.440 Runway 25, clear to land. Surface is 1-3-0, less than five minutes. 00:38:09.440 --> 00:38:12.080 'Especially on a day like this.' 00:38:15.560 --> 00:38:21.040 8-5 Foxtrot, thank you, vacate next right and park yourself 1-3 short. 00:38:21.040 --> 00:38:25.040 '8-5 Foxtrot, 8-2-0, both making approach down direct and right, 2-5.' 00:38:25.040 --> 00:38:27.520 So where's this one coming from? 00:38:27.520 --> 00:38:31.680 That is from Barcelona. It's an Easyjet flight, EZZ6402. 00:38:31.680 --> 00:38:35.440 Don't know how many people are on board, but it seats about 190. 00:38:35.440 --> 00:38:37.880 And here he is. He's getting pretty close now. 00:38:37.880 --> 00:38:40.120 Just less than two miles till he lands. 00:38:40.120 --> 00:38:43.760 What information is the radar giving you about the aeroplanes? 00:38:43.760 --> 00:38:47.240 The first and most important thing is the position of the aircraft. 00:38:47.240 --> 00:38:50.520 The yellow slash there is where the aircraft is. 00:38:50.520 --> 00:38:54.600 You've got the blue trail, the history of where the aircraft's been. 00:38:54.600 --> 00:38:59.240 From that you get two things - you get its rough heading, where he's going, and its speed. 00:38:59.240 --> 00:39:02.040 The longer the trail, the faster the aircraft's going. 00:39:07.840 --> 00:39:11.040 Radar works by sending out a pulse of radio waves 00:39:11.040 --> 00:39:14.840 and analysing the small fraction of the signal that's reflected back. 00:39:19.040 --> 00:39:23.000 Complex computation is then needed to distinguish moving objects, 00:39:23.000 --> 00:39:26.800 like planes, from the stationary background. 00:39:26.800 --> 00:39:29.880 RADIO COMMUNICATION 00:39:29.880 --> 00:39:36.160 At the heart of that analysis lies "i", the number that cannot exist. 00:39:37.800 --> 00:39:42.560 Imaginary numbers are useful for working out the complex way 00:39:42.560 --> 00:39:44.920 radio waves interact with each other. 00:39:44.920 --> 00:39:48.600 It seems to be the right language to describe their behaviour. 00:39:48.600 --> 00:39:51.800 Now, you could do these calculations with ordinary numbers. 00:39:51.800 --> 00:39:53.600 But they're so cumbersome, 00:39:53.600 --> 00:39:57.480 by the time you've done the calculation the plane's moved to somewhere else. 00:39:57.480 --> 00:40:02.000 Attitude 6,000 on a squawk of 7-7-1-5. 00:40:02.000 --> 00:40:05.040 Using imaginary numbers makes the calculation simpler 00:40:05.040 --> 00:40:07.680 that you can track the planes in real time. 00:40:07.680 --> 00:40:12.880 In fact without them, radar would be next to useless for Air Traffic Control. 00:40:16.640 --> 00:40:20.680 It's kind of amazing that this abstract idea lands planes. 00:40:20.680 --> 00:40:23.520 It's a bit surprising, you're talking about imaginary numbers 00:40:23.520 --> 00:40:26.120 and this isn't imaginary, this is real. This is very real. 00:40:26.120 --> 00:40:30.000 I'm surprised at the fact that something so abstract 00:40:30.000 --> 00:40:32.040 is being used in such a concrete way. 00:40:46.560 --> 00:40:49.720 As strange as it may seem, the code provides us 00:40:49.720 --> 00:40:53.760 with an astonishingly successful description of our world. 00:40:59.680 --> 00:41:04.360 Its most ethereal numbers have starkly real applications. 00:41:04.360 --> 00:41:10.400 Its patterns can explain one of the most profound processes in nature - 00:41:10.400 --> 00:41:13.880 how living things grow. 00:41:16.720 --> 00:41:19.840 This is a picture of something I've been fascinated by 00:41:19.840 --> 00:41:22.000 ever since I became a mathematician. 00:41:22.000 --> 00:41:26.480 It's an X-ray of a marine animal called a nautilus. 00:41:26.480 --> 00:41:31.160 And this spiral here is one of the iconic images of mathematics. 00:41:31.160 --> 00:41:34.400 Now, while I've seen pictures like this hundreds of times, 00:41:34.400 --> 00:41:37.080 I've never actually seen the animal for real. 00:41:40.520 --> 00:41:45.240 'At Brooklyn College, biologist Jennifer Basil keeps five of these aquatic denizens, 00:41:45.240 --> 00:41:49.080 'for her research into the evolution of intelligence.' 00:41:51.280 --> 00:41:56.120 We keep the animals in these tall tanks because they're naturally active at night 00:41:56.120 --> 00:41:59.360 and they like darkness, they live in deep water. 00:41:59.360 --> 00:42:01.680 They also like to go up and down in the water column, 00:42:01.680 --> 00:42:03.840 that kind of makes them happy. OK! 00:42:03.840 --> 00:42:06.720 We give them the five-star treatment here. Right... 00:42:08.440 --> 00:42:11.400 This is Number Five. Ah, wow. Yeah. 00:42:11.400 --> 00:42:12.760 Gosh, big eyes. 00:42:12.760 --> 00:42:16.560 They have huge eyes, great for seeing in low light conditions. Right. 00:42:17.680 --> 00:42:20.000 So, here's that beautiful shell. Yeah. 00:42:20.000 --> 00:42:23.360 And the striping pattern helps them hide where they live. 00:42:40.000 --> 00:42:44.680 I've never seen the animal before inside the shell, what is it? 00:42:44.680 --> 00:42:47.520 They're related to octopuses, squids and cuttlefish. 00:42:47.520 --> 00:42:50.480 It's a little bit like an octopus with a shell 00:42:50.480 --> 00:42:54.240 and what's amazing about them is that their lineage 00:42:54.240 --> 00:42:58.120 is hundreds of millions of years old and they haven't changed very much 00:42:58.120 --> 00:43:00.520 in all that time. We call them a living fossil. 00:43:00.520 --> 00:43:05.200 It's a great opportunity to look at an ancient brain and behaviour 00:43:05.200 --> 00:43:08.800 and they're a wonderful way to study the evolution of intelligence. 00:43:08.800 --> 00:43:11.320 So are these guys intelligent, then? 00:43:11.320 --> 00:43:15.760 Some are smarter than others, like that's Number Four, 00:43:15.760 --> 00:43:18.400 he outperforms everybody in all the memory tests. 00:43:18.400 --> 00:43:21.560 He's quite active all the time, he's quite engaging. 00:43:21.560 --> 00:43:23.880 If you put your in the water he comes up to you, 00:43:23.880 --> 00:43:27.160 whereas Number Three, who happens to be a teenager, 00:43:27.160 --> 00:43:30.320 is I'd guess you'd say more shy and you put him in a new place 00:43:30.320 --> 00:43:34.440 and he sort of just attaches to the wall and sits there. 00:43:34.440 --> 00:43:37.480 I'm interested in the shell as a mathematician, 00:43:37.480 --> 00:43:40.080 but what does the nautilus use the shell for? 00:43:40.080 --> 00:43:42.440 I think the most obvious use is protection. 00:43:43.600 --> 00:43:45.840 They also use it for buoyancy. 00:43:45.840 --> 00:43:47.880 They only live in the front chamber 00:43:47.880 --> 00:43:50.240 and all the other chambers are filled with gas 00:43:50.240 --> 00:43:51.520 and with some fluid. 00:43:51.520 --> 00:43:56.560 By regulating that, they can gently and passively move up and down 00:43:56.560 --> 00:43:58.600 in the water like a submarine. 00:43:58.600 --> 00:44:00.920 The really cool thing they can do 00:44:00.920 --> 00:44:04.320 is they can actually survive on the oxygen in the chambers, 00:44:04.320 --> 00:44:08.600 if there's a period where the oxygen goes down in the oceans. 00:44:08.600 --> 00:44:12.840 It's one of the reasons why they've lived for millions of years. 00:44:12.840 --> 00:44:15.680 It's a really great adaptation. The shell is really amazing. 00:44:18.120 --> 00:44:22.560 But perhaps even more remarkably, the rules this ancient creature 00:44:22.560 --> 00:44:24.240 uses to construct its home 00:44:24.240 --> 00:44:28.280 are written in the language of the Code. 00:44:28.280 --> 00:44:30.600 HORNS BLARE 00:44:38.120 --> 00:44:42.520 The nautilus shell is one of the most beautiful and intricate structures in nature. 00:44:42.520 --> 00:44:45.760 Here you can see the chambers. This is the one where it lives 00:44:45.760 --> 00:44:48.200 and these are the ones it uses for buoyancy. 00:44:48.200 --> 00:44:51.640 Now, at first sight, this looks like a really complex shape, 00:44:51.640 --> 00:44:54.240 but if I measure the dimensions of these chambers 00:44:54.240 --> 00:44:57.080 a clear pattern begins to emerge. 00:45:10.800 --> 00:45:15.000 Now there doesn't seem to be any connection between these numbers, 00:45:15.000 --> 00:45:17.840 but look what happens when I take each number 00:45:17.840 --> 00:45:20.680 and divide it by the previous measurement. 00:45:20.680 --> 00:45:26.360 If I take 3.32 and divide by 3.07, 00:45:26.360 --> 00:45:28.400 I get 1.08. 00:45:28.400 --> 00:45:31.920 Divide 3.59 by 3.32 00:45:31.920 --> 00:45:35.120 and I get 1.08. 00:45:35.120 --> 00:45:38.760 Take 3.88 and divide by 3.59 and I get, again, 1.08. 00:45:40.960 --> 00:45:45.120 So every time I do this calculation, I get the same number. 00:45:45.120 --> 00:45:47.920 So although it's not clear by looking at the shell, 00:45:47.920 --> 00:45:52.560 this tells us that the nautilus is growing at a constant rate. 00:45:52.560 --> 00:45:56.240 Everytime the nautilus builds a new room, the dimensions of that room 00:45:56.240 --> 00:46:00.080 are 1.08 times the dimensions of the previous one. 00:46:00.080 --> 00:46:03.160 And it's just by following this simple mathematical rule 00:46:03.160 --> 00:46:06.800 that the nautilus builds this elegant spiral. 00:46:09.640 --> 00:46:13.080 And because many living things grow in a similar way, 00:46:13.080 --> 00:46:16.520 these spirals are everywhere. 00:46:18.600 --> 00:46:24.000 The rules nature uses to create its patterns are found in the Code. 00:46:51.320 --> 00:46:56.360 Behind the world we inhabit, there's a strange and wonderful mathematical realm. 00:46:56.360 --> 00:47:00.200 They're actually related to octopus, squids and cuttlefish. 00:47:00.200 --> 00:47:01.840 They're quite ticklish. 00:47:05.680 --> 00:47:11.360 The numbers and connections at its heart describe the processes we see all around us. 00:47:11.360 --> 00:47:12.760 Bear with me, all right? 00:47:17.480 --> 00:47:22.160 But the Code doesn't just contain the rules that govern our planet - 00:47:22.160 --> 00:47:28.040 its numbers also describe the laws that control the entire universe. 00:47:40.520 --> 00:47:45.800 For centuries, we've gazed out into the night's sky 00:47:45.800 --> 00:47:50.160 and tried to make sense of the patterns we see in the stars. 00:48:08.280 --> 00:48:13.320 To take a closer look, I've come to Switzerland's Sphinx Observatory, 00:48:13.320 --> 00:48:18.600 perched precariously on the Jungfrau mountain. 00:48:31.240 --> 00:48:38.280 At nearly 3,600 metres, it's one of the highest peaks in the Alps. 00:48:43.200 --> 00:48:46.840 And after the sun has sunk below the horizon... 00:48:49.080 --> 00:48:52.080 ..it's a great place to gaze at the stars. 00:49:00.680 --> 00:49:05.520 Well, it's a really clear night, so you can see loads of stars. 00:49:05.520 --> 00:49:08.920 There's Sirius over here, the brightest star in the night sky 00:49:08.920 --> 00:49:14.000 and right here a really recognisable constellation, which is Orion. 00:49:14.000 --> 00:49:16.120 Have people always picked out Orion 00:49:16.120 --> 00:49:18.560 as a significant pattern in the night sky? 00:49:18.560 --> 00:49:22.360 It seems like different cultures all picked out that group 00:49:22.360 --> 00:49:23.880 as being a significant one. 00:49:23.880 --> 00:49:26.280 They all have different legends about it. 00:49:26.280 --> 00:49:29.720 The Egyptians associated it with Osiris, their god of death and rebirth 00:49:29.720 --> 00:49:32.560 Other cultures group them together. 00:49:32.560 --> 00:49:35.360 A native American tribe called the three stars of the belt, 00:49:35.360 --> 00:49:38.000 the three footprints of the flee god. 00:49:38.000 --> 00:49:42.560 One group of the Aborigines in Australia called it the canoe. 00:49:47.600 --> 00:49:52.320 Today, we don't need legends to explain the patterns in the stars 00:49:52.320 --> 00:49:56.880 because we know their precise positions in space. 00:50:00.200 --> 00:50:03.440 And we don't just know where they are now, 00:50:03.440 --> 00:50:06.680 we know where they were yesterday and where they'll be 00:50:06.680 --> 00:50:09.600 millions of years into the future. 00:50:10.720 --> 00:50:15.440 So the Sun and all the stars in our galaxy, including the stars in Orion, 00:50:15.440 --> 00:50:18.680 are all moving in orbits around the centre of the galaxy, 00:50:18.680 --> 00:50:23.160 but like a swarm of bees, although they're all moving in roughly the same direction, 00:50:23.160 --> 00:50:27.360 they all follow their own paths and that means that their positions will change, 00:50:27.360 --> 00:50:29.640 as thousands of years tick by. 00:50:29.640 --> 00:50:33.200 And now we're two-and-a-half million years in the future 00:50:33.200 --> 00:50:37.760 and the constellation of Orion has completely gone. 00:50:38.880 --> 00:50:44.440 In fact, thousands of years ago our ancestors would have seen different patterns in the sky 00:50:44.440 --> 00:50:49.800 and our descendants, millions of years in the future, will also see different patterns. 00:50:58.200 --> 00:51:03.160 The reason we can predict how the stars will move into the far future 00:51:03.160 --> 00:51:06.360 is because we've uncovered the rules that govern their behaviour. 00:51:08.080 --> 00:51:12.880 And we've found these rules not in the heavens, but in numbers. 00:51:19.440 --> 00:51:24.600 It's only through the Code that we can understand the laws that govern the universe. 00:51:49.160 --> 00:51:52.680 Laws that describe everything from the motion of the planets 00:51:52.680 --> 00:51:55.400 to the flight of projectile. 00:51:56.560 --> 00:51:59.640 When you watch the fireball fly through the air 00:51:59.640 --> 00:52:02.240 then it appears in the first part of its flight, 00:52:02.240 --> 00:52:04.160 when it's just left the trebuchet, 00:52:04.160 --> 00:52:08.320 that it's accelerating upwards and then it begins to slow down, 00:52:08.320 --> 00:52:10.440 before it stops just above me 00:52:10.440 --> 00:52:14.800 and then, finally, accelerates back down towards the ground. 00:52:19.120 --> 00:52:22.000 But if you analyse the flight using numbers, 00:52:22.000 --> 00:52:24.360 it reveals something rather surprising. 00:52:26.440 --> 00:52:30.560 When you plot a graph of the projectile's vertical speed 00:52:30.560 --> 00:52:32.680 against time... 00:52:33.760 --> 00:52:36.760 ..you then you get a graph which looks like this. 00:52:41.080 --> 00:52:44.160 To start with, the projectile is moving upwards 00:52:44.160 --> 00:52:47.960 so it's vertical speed is positive, but decreasing. 00:52:49.200 --> 00:52:53.040 As it reaches the top of its arc, the vertical speed becomes negative 00:52:53.040 --> 00:52:58.360 as the fireball turns round and falls back to Earth. 00:53:01.800 --> 00:53:05.920 Because the graph is going like this, it means that the projectile, 00:53:05.920 --> 00:53:10.360 from the moment it leaves the trebuchet, is actually slowing down. 00:53:10.360 --> 00:53:14.800 So at no point during the flight is it ever accelerating upwards. 00:53:21.080 --> 00:53:26.160 Throughout its flight, the fireball is accelerating downwards 00:53:26.160 --> 00:53:29.040 towards the Earth at a constant rate. 00:53:30.840 --> 00:53:34.040 Something you would never realise simply by watching it 00:53:34.040 --> 00:53:36.280 fly through the air. 00:53:39.120 --> 00:53:41.400 And this is a profound truth 00:53:41.400 --> 00:53:44.480 about one of the fundamental forces of nature... 00:53:46.400 --> 00:53:48.160 ..gravity. 00:53:49.320 --> 00:53:52.600 Drop, throw, fire or launch anything you like - 00:53:52.600 --> 00:53:55.760 a rock, a bullet, a ball or even a pot plant 00:53:55.760 --> 00:53:58.880 and it will accelerate towards the ground at a constant rate 00:53:58.880 --> 00:54:02.600 of 9.8 metres per second, per second. 00:54:02.600 --> 00:54:06.200 This is a fundamental law of gravity on our planet. 00:54:06.200 --> 00:54:11.040 But it's only revealed by changing the flight path of the object into numbers. 00:54:16.760 --> 00:54:21.000 Appreciating this simple fact about how gravity works on Earth 00:54:21.000 --> 00:54:26.160 is the first step towards understanding gravity everywhere. 00:54:39.680 --> 00:54:45.160 It's the foundation stone of Newton's Law of Universal Gravitation. 00:54:46.400 --> 00:54:51.280 A mathematical theory that can describe the orbits of the planets, 00:54:51.280 --> 00:54:56.160 predict the passage of the stars into the distant future... 00:54:59.000 --> 00:55:04.640 ..and has even enabled human kind to step foot on the Moon. 00:55:08.920 --> 00:55:14.280 The laws that command the heavens are written in the Code. 00:55:26.000 --> 00:55:29.840 'We call them the door mats, the large ones. 00:55:29.840 --> 00:55:32.560 'Two-and-a-half million years in the future... 00:55:32.560 --> 00:55:35.200 'This isn't imaginery, this is real! 00:55:39.520 --> 00:55:44.120 'You don't need to know what that means to know that animal's not happy. 00:55:44.120 --> 00:55:45.920 'Whatever circle I take, 00:55:45.920 --> 00:55:48.880 'you're going to get a number which starts 3.14.' 00:55:53.040 --> 00:55:57.680 It's an incredible thought that the only way we can really make sense of our world 00:55:57.680 --> 00:56:00.960 is by using the abstract world of numbers. 00:56:00.960 --> 00:56:05.400 And yet those numbers have allowed us to take our first tentative steps off our planet. 00:56:05.400 --> 00:56:10.240 They've also given us the technology to transform our surroundings. 00:56:12.320 --> 00:56:15.120 'A hidden Code underpins the world around us. 00:56:18.320 --> 00:56:21.840 'A Code that has the power to unlock the rules that cover the universe.' 00:56:25.520 --> 00:56:30.000 This place was constructed to satisfy a spiritual need. 00:56:30.000 --> 00:56:34.240 But we couldn't have built it without the power of the Code. 00:56:34.240 --> 00:56:39.920 For me, it's an exquisite example of the beauty and potency of mathematics. 00:56:51.120 --> 00:56:53.880 From the patterns and numbers all around us, 00:56:53.880 --> 00:56:57.160 we've deciphered a hidden code. 00:57:11.000 --> 00:57:15.240 We've revealed a strange and intriguing numerical world, 00:57:15.240 --> 00:57:16.960 totally unlike our own. 00:57:18.720 --> 00:57:24.840 Yet it's a Code that also describes our world with astonishing accuracy. 00:57:30.800 --> 00:57:34.200 And has given us unprecedented power to describe... 00:57:37.600 --> 00:57:39.200 ..control... 00:57:41.640 --> 00:57:43.880 ..and predict our surroundings. 00:57:56.920 --> 00:58:01.280 The fact that the Code provides such a successful description of nature 00:58:01.280 --> 00:58:04.160 is for many one of the greatest mysteries of science. 00:58:05.240 --> 00:58:08.600 I think the only explanation that makes sense for me 00:58:08.600 --> 00:58:11.360 is that by discovering these connections, 00:58:11.360 --> 00:58:15.000 we have in fact uncovered some deep truth about the world. 00:58:15.000 --> 00:58:18.240 That perhaps, the Code is THE truth of the universe 00:58:18.240 --> 00:58:22.880 and it's numbers that dictate the way the world must be. 00:58:29.520 --> 00:58:31.120 Go to... 00:58:34.280 --> 00:58:37.360 ..to find clues to help you solve the Code's treasure hunt. 00:58:37.360 --> 00:58:41.000 Plus, get a free set of mathematical puzzles and a treasure hunt clue 00:58:41.000 --> 00:58:43.520 when you follow the links to The Open University 00:58:43.520 --> 00:58:46.160 or call 0845 366 8026. 00:59:00.880 --> 00:59:03.920 Subtitles by Red Bee Media Ltd 00:59:03.920 --> 00:59:06.960 E-mail subtitling@bbc.co.uk 00:59:07.000 --> 00:59:10.117 Download Movie Subtitles Searcher from 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