"BOY: 'One for sorrow" "'Two for mirth" "GIRL: 'Three for a wedding" "'And four for death" "BOY: 'Nine for hell.'" "GIRL: '666.'" "Hidden within this cathedral are clues to a mystery, something that could help answer one of humanity's most enduring questions..." "..why is the world the way it is?" "The 13th-century masons who constructed this place had glimpsed a deep truth and they built a message into its very walls in the precise proportions of this magnificent cathedral." "To the medieval clergy, these divine numbers were created by God." "But to me, they're evidence of something else, a hidden code that underpins the world around us, a code that has the power to unlock the laws that govern the universe." "As a mathematician, I'm fascinated by the numbers and patterns we see all around us..." "..numbers and patterns that connect everything from fish to circles and from our ancient past to the far future." "INDISTINCT COMMENT" "Together they make up the Code... ..an abstract world of numbers..." "..that has given us the most detailed description of our world we've ever had." "For centuries, people have seen significant numbers everywhere... ..an obsession that's left its mark in the stones of this medieval cathedral." "In the 12th century, religious scholars here in Chartres became convinced these numbers were intrinsically linked to the divine..." "..an idea that dates back to the dawn of Christianity." "The fourth-century Algerian cleric St Augustine believed that seven was so special that it represented the entire universe." "He described how seven embraced all created things and ten was beyond even the universe because it was seven plus the three aspects of the Holy Trinity " "Father, Son and Holy Ghost." "12 was also hugely important, not simply because there are 12 tribes of Israel or 12 disciples of Jesus, but because 12 is divisible by one, two, three, four, six and 12 itself, more than any other number around it." "For St Augustine, numbers had to come from God because they obey laws that no man can change." "Around 800 years after St Augustine, the 12th-century Chartres School also recognised their significance." "It's thought that, under their influence, sacred numbers were built into the structure of this majestic building." "Numbers, they believed, held the key to the mystery of creation." "I've spent my entire working life studying numbers, and for me they're more than just abstract entities." "They describe the world around us." "Although I don't share their religious beliefs, I can't help feeling something in common with the people who built this place." "I share their awe and wonder at the beauty of numbers." "For them, those numbers brought them closer to God, but I think they're important for another reason, because I believe they're the key to making sense of our world." "Numbers have given us an unparalleled ability to understand our universe." "And in places, this code literally emerges from the ground." "Rural Alabama, spring 2011." "Warm, lush and peaceful." "But this year, there's a plague coming." "While some locals are moving out," "Dr John Cooley has driven thousands of miles to be here." "He's on the trail of one of the area's strangest residents." "We have been driving around looking for the emergences for about three and a half weeks." "I've driven 7,200 miles since Good Friday trying to figure out where these things are." "What makes these insects so remarkable is their bizarre lifecycle." "For 12 whole years, they live hidden underground, in vast numbers." "Then, in their 13th year... at precisely the same time..." "..they all burrow out from the earth to breed." "At the full part of the emergence, there will be millions of insects out per acre." "They'll be everywhere." "It really is insect mayhem." "This is the periodical cicada." "This one is a male... ..and you know that because on the abdomen, there's a pair of organs called timbles, and they're sound-producing organs." "It's a little membrane that's vibrated, it makes a sound." "Oh, yeah." "I don't have to be frightened of these, do I?" "No, no, they're absolutely harmless." "They make wonderful pets." "Really?" "Mm-hm." "They're quite ticklish." "It's a harmless insect." "It doesn't bite, it doesn't sting, nothing of that sort." "Its only defence is safety in numbers." "By emerging in such vast numbers, each individual cicada minimises its risk of being eaten." "Because there are so many of them, their predators simply can't eat them fast enough." "Well, you can certainly hear the cicadas." "Yes, you can." "There are probably millions of them up there." "Millions?" "Yeah, millions." "What you probably don't realise is you're only hearing half the population." "Only the males make these loud sounds." "There are just as many females up there as well." "And it's extraordinary to think that if we came here next year, we wouldn't hear this sound at all?" "You'll have to come back in 13 years." "So 2024 is when you'll hear the forest singing like this again?" "That's right." "That's amazing." "Why have the cicadas evolved with this 13-year lifecycle as opposed to any other number?" "Well, you have to remember that these cicadas require large numbers to survive predators, and so we think that these long lifecycles in some way help them maintain large populations." "John believes that, by appearing every 13 years, the cicadas minimise their chances of emerging at the same time as other cicadas with different lifecycles..." "..because if they were to interbreed, it could have disastrous consequences." "The offspring would have unusual lifecycles." "They're going to emerge a little bit here, a little bit there, some this year and some that year in small numbers, and that's key because if they emerge in small numbers, the predators eat them." "The cicadas' survival depends on avoiding other broods." "Imagine you've got a brood of cicadas that appears every six years." "Now, let's suppose there's another brood which wants to try and avoid the red cicadas." "One way to do that would be to appear less often in the forest, and that actually works." "So let's suppose this brood appears every nine years." "So if the green cicada appears every nine years, then it only coincides with the red cicada every 18 years." "But, rather surprisingly, a smaller number, seven, works even better." "Coming out every seven years instead of every nine means the cicadas appear together much less often." "Now they only coincide every 42 years." "That's just twice every century." "And for the real cicadas, a 13-year lifecycle has exactly the same effect as seven does here because they both belong to a special series of numbers." "Like 13, seven is a prime number." "Unlike other numbers, primes can only be divided by themselves and one, and it's this property that means that numbers that are separated by primes are far less likely to coincide with multiples of other numbers." "Because 13 is a prime number, a 13-year lifecycle makes the cicadas much less likely to coincide with other groups." "Up in Georgia, there is another brood of periodical cicada and they, too, have a prime number lifecycle." "They come out every 17 years." "Because 13 and 17 are both prime numbers, the two broods only emerge together once every 221 years." "Prime numbers are intimately linked to the cicadas' survival and, intriguingly, they're one of the most important elements of the Code, because the Code is a mathematical world, built from numbers." "Just as atoms are the indivisible units that make up every physical object, so prime numbers are the indivisible building blocks of the Code." "Prime numbers are indivisible, which means they can't be made by multiplying any other numbers together." "But every non-prime number can be created by multiplying primes together." "It's impossible to make any numbers without them." "And if any primes are missing, there will always be some numbers you can't create." "For me, the fact that the most fundamental units of mathematics can be found woven into the natural world is not only compelling evidence that the Code exists, but also that numbers underpin everything..." "..including our own biology." "This is an innately human characteristic." "Music is one of the things which defines who we are, and each culture has its own particular style." "These guys make it seem so effortless, as if the notes are just thrown together, but that's simply an illusion." "MUSIC ENDS, APPLAUSE" "Because, just as numbers govern the cicadas' lives, so they determine how WE hear sound." "That's a C." "And using this oscilloscope, I can get a picture of that note." "So I can actually SEE the sound wave." "Now, the height of the wave corresponds to how loudly I'm playing the note, so if I play the note very quietly... play it very loudly..." "I suddenly get a huge wave on the screen." "The more important thing is the distance between the peaks of the wave, because that's determined by the pitch or frequency of the note." "'The higher the note... 'the shorter the distance between the peaks.'" "Now, look what happens when I play a C... ..and compare that with the same note, a C, but an octave higher." "Something rather surprising emerges, because now you can see that the higher note has twice as many peaks as the lower note, which means the frequency of the high C is twice that of the low C." "And this happens whatever two notes you choose." "Provided they're an octave apart, then their frequencies are going to be in this one-to-two ratio." "Two notes which are an octave apart just sound nice together, and they're actually the most harmonious combination of notes that you can have." "And that's because one to two is the simplest possible frequency relationship, and that's what music is all about, because it's these simple whole-number ratios that sound so good to the ear." "A perfect fifth... is a frequency ratio of three to two." "A perfect fourth... is four to three." "And a slightly more complex sound, a minor sixth... ..that's a frequency ratio of five to eight." "Every combination of notes used in music is defined by simple ratios." "Although we might not be aware of it, these numerical rules underpin everything from the simplest song to the most elaborate symphony." "They're so deeply ingrained that when they're broken, we intuitively know something is wrong." "Professor Judy Edworthy understands this more than most." "She spends her time subjecting people to some of most unpleasant noises imaginable." "Hi, Judy." "Ah, hello." "Marcus." "'Her research investigates the psychological effects of sound." "'And by using complex ratios instead of simple ones, the noises she creates are nothing like music.'" "You can see just by looking at it it's not going to sound nice." "The wave looks a mess." "The wave is a mess." "It's very difficult to see a pattern." "CONSTANT DRONE" "OK." "It sounds really quite odd now." "It doesn't have any pitch." "It sounds harsh and I could make it louder and that would make it harsher." "When the various frequencies aren't simple multiples of one another, there's no common pattern for the ear to respond to, and the more complex you make the ratios, the more dissonant and harsh the sound will get." "By monitoring her victims' reactions to these appalling noises," "Professor Edworthy has found they have a very different effect on our minds than music." "ALARM BEEPS" "HONKING" "WHIRRING" "They're so unpleasant..." "HAMMERING" "..they shock our brains into action." "For example, a siren." "HIGH-PITCHED SIREN BLARES" "That's quite a harsh sound, but it's designed for a purpose - to get you out of the way." "Sometimes you find these sounds in the animal world as well." "So this, for example, this is a chimpanzee and an orang-utan." "INTERMITTENT SCREECHING" "OK, these animals are obviously quite bothered by something." "You don't need to know what that sound means to know that that animal's not happy and also that the other animals in that environment and us, for example, should just get out of the way." "SHORT SCREECH" "So it's interesting that we really hear pattern, and when it isn't there, it creates an effect in all of us." "LOW-PITCHED SCREECH" "Remarkably, it's numerical patterns in the Code that dictate the combinations of sounds we hear as music..." "RUSTLING" "..and those we hear simply as noise." "CHIRPING, SIREN" "BELL TOLLS" "And perhaps stranger still, it's these same numbers that are built into the walls of this medieval cathedral." "Two notes which are an octave apart are going be in this one-to-two ratio." "The width of the nave here is twice the distance between each of the columns that run up its length - a ratio of two to one." "The most harmonious combination of notes from a pair." "The altar divides the nave into a ratio of eight to five." "A minor sixth... eight to five." "A perfect fifth... three to two." "A perfect fourth is four to three." "Major third, five to four." "And that's what music is all about." "St Augustine believed these ratios were used by God to construct the universe and that that was why they produced harmony in music." "By constructing their cathedral using the same ratios, the clergy at Chartres hoped to echo God's creation." "This entire place is a symphony set in stone." "Using the Code's numbers has created a building of awe-inspiring beauty." "The only truth there is..." "Seemingly significant numbers..." "By searching for divine meaning in numbers, 12th-century scholars had stumbled across elements of the Code." "It's very difficult to see a pattern." "Mysterious numbers and patterns that seem to be written into our biology." "Its only defence is safety in numbers." "And as we've looked closer, we haven't simply found more numbers - we've begun to uncover their strangest properties and started to see deep connections between them." "Back in the distant past, in Neolithic times, around 4,000 years ago, an ancient people brought these stones here and arranged them like this." "This is Sunkenkirk stone circle in Cumbria and it's one of around 1,000 such structures that our ancient ancestors built across the UK." "Stretching back into the mists of time, the circle has been steeped in mysticism." "But whether the people who built this structure knew it or not, there is deep significance hidden inside this circle." "OK, so I need to start by measuring the diameter of my circle, so that's the distance from one edge to the other." "I need to go roughly through the centre." "So that's 27 and 90." "Right, so now I'm going to measure the circumference of the circle." "So off we go." "So around the outside." "Oh, I've never got so much exercise doing maths before!" "And that's the circumference." "So I've got 91 metres and 70 centimetres." "I'm going to do a little calculation." "I'm going to divide the circumference of the circle by the diameter." "So 917 divided by 279." "So that's roughly three..." "Bit of, er, mental arithmetic, not a mathematician's strongest point." "OK, two lots of 279, so... not far out from what I was hoping for." "So when I do that, I get roughly 3.2 as the answer." "My measurements weren't very precise... ..but my answer is close to a mysterious number hidden within every circle." "So, for example, let's take this circular plate here." "I'm going to measure its diameter." "26.4 centimetres." "Now its circumference." "That's a bit trickier." "82.9 centimetres." "Divide the circumference by the diameter, I get 3.14." "Now let's take another circle." "Measure its diameter." "12.8 centimetres." "So the circumference is 40.2 centimetres." "Divide the circumference by the diameter and I get 3.14." "In fact, whatever circle I take, divide the circumference by the diameter and you're going to get a number which starts 3.14." "This is a number we call pi." "No matter where the circles are, no matter how big or small... ..they will always contain pi." "It's this universality of the number pi which tells you you've identified a piece of true Code." "In fact, if you get another number, it means that you haven't got a circle." "In some sense, pi is the essence of circleness, distilled into the language of the Code." "And because circles and curves crop up again and again in nature, pi can be found all around us." "It's in the gentle curve of a river... ..the sweep of a coast line..." "..and the shifting patterns of the desert sands." "Pi seems written into the structures and processes of our planet." "But, strangely, pi also appears in places that seem to have nothing to do with circles." "I started fishing Brighton in 1972." "I've been a fisherman 40 years, catching Dover sole." "That's the main target species for the English Channel." "How many fish do you think you get a day?" "300 some days, 150 other days, so I'd say 200 would be average." "And you've got me some Dover sole today so I can have a weigh of what you've caught today." "Yeah, you can play with them!" "OK!" "What's remarkable is that, with just a small amount of information..." "It's 180 grams." "..and by weighing a few fish..." "That's a whopper." "..I can use the Code to tell me things about not just today's catch... 360 grams. 50 grams. 110 grams." "..but about all the Dover sole Sam's ever fished..." "Whoa, jeez, come back!" "..I can even get an estimate for the largest sole that Sam is likely to have caught during his career." "Right..." "First , I need to work out what the average weight of a fish is, so 140 plus 190 plus 150..." "So now I need to work out the standard deviation, so that's 140 minus square that..." "Bear with me, all right?" "Almost there." "So he said he fished for 40 years, and eight weeks during the year, six days out of the week and 200 sole each day, so that gives you a total of 384,000 fish." "Using these numbers, I can calculate that the largest one out of those 384,000 fish should be about 1.3 kilograms, which is roughly three pounds." "So what's the largest Dover sole that you've caught in your career?" "We call them door mats, the large ones, and you maybe get four or five a season." "The largest, I'd say, was three to three and a half pounds." "An average Dover Sole is that sort of size and these..." "Wow, that's huge!" "Yeah!" "It's a whopper." "It's always nice to catch big stuff, you know." "Well, I think it is anyway." "HE CHUCKLES" "Using the Code, it's possible to estimate the size of the biggest fish Sam's ever caught, despite not weighing a single fish anywhere near that size." "Now, the reason this calculation is possible is because the distribution of the weights of fish, in fact the distribution of lots of things like the height of people in the UK or IQ, is given by this formula." "'This is the normal distribution equation, 'one of the most important bits of mathematics 'for understanding variation in the natural world.'" "The most remarkable thing about this formula isn't so much what it does as this term here, pi." "It seems totally bizarre that a bit of the Code that has something to do with the geometry of a circle can help you to calculate the weight of fish." "Pi shouldn't have anything to do with fish, yet there it is." "Just as the circle appears everywhere in nature, so pi crops up again and again in the mathematical world." "It's an astonishing example of the interconnectedness of the Code." "A glimpse into a world where numbers don't just have strange connections, they have deeply puzzling properties of their own." "Pi is what's known as an irrational number." "Written as a decimal, it has an infinite number of digits arranged in a sequence that never repeats." "And it's thought that any number you can possibly imagine will appear in pi somewhere, from my birthday to the answer to life, the universe and everything." "Because they go on for ever, we can never know all the digits that make up pi." "But, luckily, we only need the first 39 to calculate the circumference of a circle the size of the entire observable universe, accurate to the radius of a single hydrogen atom." "But as strange as Pi is, it does at least describe a physical object." "Some numbers don't make any sense in real world, despite the fact we use them all the time." "Numbers, like negative numbers." "It's impossible to trade anything, stocks, shares, currency, even fish, without negative numbers." "Most of us are comfortable them." "Even though we may not like it, we understand what it means to have a negative bank balance." "But when you start to think about it, there's something deeply strange about negative numbers, cos they don't seem to correspond to anything real at all." "The deeper we look into the Code, the more bizarre it becomes." "It's easy to imagine one fish or two fish, or no fish at all." "It's much harder to imagine what minus-one fish looks like." "Negative numbers are so odd that if I have minus-one fish and you give me a fish, then all you can be certain of is that I've got no fish at all." "Numbers, can exist regardless of whether they make any sense in the physical world." "And if you think that's odd, some numbers are so strange they don't even seem to make sense as numbers." "Now, this is one of the most basic facts of mathematics." "A positive number multiplied by another positive number is a positive number." "So for example, one times one is one." "A negative number multiplied by another negative number also gives a positive number." "So for example, minus-one times minus-one is plus-one." "'It's not only a rule, it's a proven truth of multiplication." "'Whenever the signs are the same, the product is always positive.'" "From this, it's obvious if I take any number and multiply it by itself, then the answer is going to be positive." "However, in the Code, there's a special number which breaks this rule." "When I multiply it by itself, it gives the answer minus-one." "It's impossible to imagine what this number could be, because there simply is no number that when multiplied by itself, gives minus-one." "This isn't a number I can calculate." "I can't show you this number." "Nevertheless, we've given this number a name." "It's called "i", and it's part of a whole class of new numbers called imaginary numbers." "Calculating with imaginary numbers is the mathematical equivalent of believing in fairies." "But even these strangest elements of the Code turn out to have some very practical applications." "The ground's close, will you call me, please, 1-1-9 next..." "Runway 25, clear to land." "Surface is 1-3-0, less than five minutes." "'Especially on a day like this.'" "8-5 Foxtrot, thank you, vacate next right and park yourself 1-3 short." "'8-5 Foxtrot, 8-2-0, both making approach down direct and right, 2-5.'" "So where's this one coming from?" "That is from Barcelona." "It's an Easyjet flight, EZZ6402." "Don't know how many people are on board, but it seats about 190." "And here he is." "He's getting pretty close now." "Just less than two miles till he lands." "What information is the radar giving you about the aeroplanes?" "The first and most important thing is the position of the aircraft." "The yellow slash there is where the aircraft is." "You've got the blue trail, the history of where the aircraft's been." "From that you get two things - you get its rough heading, where he's going, and its speed." "The longer the trail, the faster the aircraft's going." "Radar works by sending out a pulse of radio waves and analysing the small fraction of the signal that's reflected back." "Complex computation is then needed to distinguish moving objects, like planes, from the stationary background." "RADIO COMMUNICATION" "At the heart of that analysis lies "i", the number that cannot exist." "Imaginary numbers are useful for working out the complex way radio waves interact with each other." "It seems to be the right language to describe their behaviour." "Now, you could do these calculations with ordinary numbers." "But they're so cumbersome, by the time you've done the calculation the plane's moved to somewhere else." "Attitude 6,000 on a squawk of 7-7-1-5." "Using imaginary numbers makes the calculation simpler that you can track the planes in real time." "In fact without them, radar would be next to useless for Air Traffic Control." "It's kind of amazing that this abstract idea lands planes." "It's a bit surprising, you're talking about imaginary numbers and this isn't imaginary, this is real." "This is very real." "I'm surprised at the fact that something so abstract is being used in such a concrete way." "As strange as it may seem, the code provides us with an astonishingly successful description of our world." "Its most ethereal numbers have starkly real applications." "Its patterns can explain one of the most profound processes in nature - how living things grow." "This is a picture of something I've been fascinated by ever since I became a mathematician." "It's an X-ray of a marine animal called a nautilus." "And this spiral here is one of the iconic images of mathematics." "Now, while I've seen pictures like this hundreds of times," "I've never actually seen the animal for real." "'At Brooklyn College, biologist Jennifer Basil keeps five of these aquatic denizens, 'for her research into the evolution of intelligence.'" "We keep the animals in these tall tanks because they're naturally active at night and they like darkness, they live in deep water." "They also like to go up and down in the water column, that kind of makes them happy." "OK!" "We give them the five-star treatment here." "Right..." "This is Number Five." "Ah, wow." "Yeah." "Gosh, big eyes." "They have huge eyes, great for seeing in low light conditions." "Right." "So, here's that beautiful shell." "Yeah." "And the striping pattern helps them hide where they live." "I've never seen the animal before inside the shell, what is it?" "They're related to octopuses, squids and cuttlefish." "It's a little bit like an octopus with a shell and what's amazing about them is that their lineage is hundreds of millions of years old and they haven't changed very much in all that time." "We call them a living fossil." "It's a great opportunity to look at an ancient brain and behaviour and they're a wonderful way to study the evolution of intelligence." "So are these guys intelligent, then?" "Some are smarter than others, like that's Number Four, he outperforms everybody in all the memory tests." "He's quite active all the time, he's quite engaging." "If you put your in the water he comes up to you, whereas Number Three, who happens to be a teenager, is I'd guess you'd say more shy and you put him in a new place" "and he sort of just attaches to the wall and sits there." "I'm interested in the shell as a mathematician, but what does the nautilus use the shell for?" "I think the most obvious use is protection." "They also use it for buoyancy." "They only live in the front chamber and all the other chambers are filled with gas and with some fluid." "By regulating that, they can gently and passively move up and down in the water like a submarine." "The really cool thing they can do is they can actually survive on the oxygen in the chambers, if there's a period where the oxygen goes down in the oceans." "It's one of the reasons why they've lived for millions of years." "It's a really great adaptation." "The shell is really amazing." "But perhaps even more remarkably, the rules this ancient creature uses to construct its home are written in the language of the Code." "HORNS BLARE" "The nautilus shell is one of the most beautiful and intricate structures in nature." "Here you can see the chambers." "This is the one where it lives and these are the ones it uses for buoyancy." "Now, at first sight, this looks like a really complex shape, but if I measure the dimensions of these chambers a clear pattern begins to emerge." "Now there doesn't seem to be any connection between these numbers, but look what happens when I take each number and divide it by the previous measurement." "If I take 3.32 and divide by 3.07," "I get 1.08." "Divide 3.59 by 3.32 and I get 1.08." "Take 3.88 and divide by 3.59 and I get, again, 1.08." "So every time I do this calculation, I get the same number." "So although it's not clear by looking at the shell, this tells us that the nautilus is growing at a constant rate." "Everytime the nautilus builds a new room, the dimensions of that room are 1.08 times the dimensions of the previous one." "And it's just by following this simple mathematical rule that the nautilus builds this elegant spiral." "And because many living things grow in a similar way, these spirals are everywhere." "The rules nature uses to create its patterns are found in the Code." "Behind the world we inhabit, there's a strange and wonderful mathematical realm." "They're actually related to octopus, squids and cuttlefish." "They're quite ticklish." "The numbers and connections at its heart describe the processes we see all around us." "Bear with me, all right?" "But the Code doesn't just contain the rules that govern our planet - its numbers also describe the laws that control the entire universe." "For centuries, we've gazed out into the night's sky and tried to make sense of the patterns we see in the stars." "To take a closer look, I've come to Switzerland's Sphinx Observatory, perched precariously on the Jungfrau mountain." "At nearly 3,600 metres, it's one of the highest peaks in the Alps." "And after the sun has sunk below the horizon... ..it's a great place to gaze at the stars." "Well, it's a really clear night, so you can see loads of stars." "There's Sirius over here, the brightest star in the night sky and right here a really recognisable constellation, which is Orion." "Have people always picked out Orion as a significant pattern in the night sky?" "It seems like different cultures all picked out that group as being a significant one." "They all have different legends about it." "The Egyptians associated it with Osiris, their god of death and rebirth" "Other cultures group them together." "A native American tribe called the three stars of the belt, the three footprints of the flee god." "One group of the Aborigines in Australia called it the canoe." "Today, we don't need legends to explain the patterns in the stars because we know their precise positions in space." "And we don't just know where they are now, we know where they were yesterday and where they'll be millions of years into the future." "So the Sun and all the stars in our galaxy, including the stars in Orion, are all moving in orbits around the centre of the galaxy, but like a swarm of bees, although they're all moving in roughly the same direction," "they all follow their own paths and that means that their positions will change, as thousands of years tick by." "And now we're two-and-a-half million years in the future and the constellation of Orion has completely gone." "In fact, thousands of years ago our ancestors would have seen different patterns in the sky and our descendants, millions of years in the future, will also see different patterns." "The reason we can predict how the stars will move into the far future is because we've uncovered the rules that govern their behaviour." "And we've found these rules not in the heavens, but in numbers." "It's only through the Code that we can understand the laws that govern the universe." "Laws that describe everything from the motion of the planets to the flight of projectile." "When you watch the fireball fly through the air then it appears in the first part of its flight, when it's just left the trebuchet, that it's accelerating upwards and then it begins to slow down," "before it stops just above me and then, finally, accelerates back down towards the ground." "But if you analyse the flight using numbers, it reveals something rather surprising." "When you plot a graph of the projectile's vertical speed against time..." "..you then you get a graph which looks like this." "To start with, the projectile is moving upwards so it's vertical speed is positive, but decreasing." "As it reaches the top of its arc, the vertical speed becomes negative as the fireball turns round and falls back to Earth." "Because the graph is going like this, it means that the projectile, from the moment it leaves the trebuchet, is actually slowing down." "So at no point during the flight is it ever accelerating upwards." "Throughout its flight, the fireball is accelerating downwards towards the Earth at a constant rate." "Something you would never realise simply by watching it fly through the air." "And this is a profound truth about one of the fundamental forces of nature..." "..gravity." "Drop, throw, fire or launch anything you like - a rock, a bullet, a ball or even a pot plant and it will accelerate towards the ground at a constant rate of 9.8 metres per second, per second." "This is a fundamental law of gravity on our planet." "But it's only revealed by changing the flight path of the object into numbers." "Appreciating this simple fact about how gravity works on Earth is the first step towards understanding gravity everywhere." "It's the foundation stone of Newton's Law of Universal Gravitation." "A mathematical theory that can describe the orbits of the planets, predict the passage of the stars into the distant future..." "..and has even enabled human kind to step foot on the Moon." "The laws that command the heavens are written in the Code." "'We call them the door mats, the large ones." "'Two-and-a-half million years in the future..." "'This isn't imaginery, this is real!" "'You don't need to know what that means to know that animal's not happy." "'Whatever circle I take, 'you're going to get a number which starts 3.14.'" "It's an incredible thought that the only way we can really make sense of our world is by using the abstract world of numbers." "And yet those numbers have allowed us to take our first tentative steps off our planet." "They've also given us the technology to transform our surroundings." "'A hidden Code underpins the world around us." "'A Code that has the power to unlock the rules that cover the universe.'" "This place was constructed to satisfy a spiritual need." "But we couldn't have built it without the power of the Code." "For me, it's an exquisite example of the beauty and potency of mathematics." "From the patterns and numbers all around us, we've deciphered a hidden code." "We've revealed a strange and intriguing numerical world, totally unlike our own." "Yet it's a Code that also describes our world with astonishing accuracy." "And has given us unprecedented power to describe..." "..control... ..and predict our surroundings." "The fact that the Code provides such a successful description of nature is for many one of the greatest mysteries of science." "I think the only explanation that makes sense for me is that by discovering these connections, we have in fact uncovered some deep truth about the world." "That perhaps, the Code is THE truth of the universe and it's numbers that dictate the way the world must be." "Go to..." "..to find clues to help you solve the Code's treasure hunt." "Plus, get a free set of mathematical puzzles and a treasure hunt clue when you follow the links to The Open University or call 0845 366 8026." "Subtitles by Red Bee Media Ltd" "E-mail subtitling@bbc.co.uk" "OVERLAPPING VOICES" "This is the Giant's Causeway at the northern tip of Northern Ireland, and it's famed for these strange angular rocks." "There are 40,000 of them crammed into this small area of coastline." "What makes them so striking is that they're so regular, so simple, they just don't seem to fit in to this rugged natural environment." "The mystery of these hexagonal rock formations has inspired storytellers and composers." "But their strange beauty is only the start of the story." "Because these stones tell of a hidden geometric force that underpins and pervades all nature." "And if we can uncover that force, it'll help us to explain the shape of everything... from the smallest microbe, to the construction of these stones and the formation of the world itself." "As a mathematician, I'm fascinated by the numbers and shapes we see all around us..." "..connecting everything, from bees to bubbles and the handwork of our distant ancestors to the imagination of our greatest modern artists." "These are the hidden connections that make up the Code..." "..an abstract, enigmatic world of numbers that has given us the most detailed description of our world we've ever had." "Ever since they settled here, over 30,000 years ago, people have tried to explain these remarkable hexagonal columns poking out of the Irish Sea." "Why are they the shape they are?" "And where did they come from in the first place?" "Legend has it that this peninsula was once home to a giant called Fionn mac Cumhaill." "One day the giant got into an argument with another giant called Benandonner who lived 80 miles away across the sea in Scotland." "The giants hurled insults at each other, swiftly followed by a few stones." "And things soon got out of hand." "Benandonner swore that if he was a better swimmer, he'd come straight over to sort Fionn out." "Fionn was so enraged that he started picking up huge clumps of earth and throwing them across the sea so he could create a pathway for the Scottish giant to come and face him." "And that, legend has it, is what I'm standing on now." "The handiwork of a giant." "It's a nice story, but the reality is even more extraordinary." "Because what's written into these rocks is a fundamental truth about the universe." "A truth that we can find written throughout the natural world." "These orchards in California, are the site of one of the largest animal migrations on the planet." "Every spring, billions of bees are brought here to help pollinate the almond trees." "Several thousand of these hives belong to Steve Godling." "You go ahead and smoke it when we get it open." "Yep." "Right there." "That's good." "Got this glued together very tight." "You want to try to get an outside one so as not to kill the queen." "You don't want to kill any of them but you particularly don't want to kill her." "If you kill the queen, you've killed the hive." "Wow!" "That's one of the wonders of the natural world." "It's beautiful." "'The bees' honeycomb is a marvel of natural engineering.'" "They've got plenty of honey." "'Everything they need is here." "'It's a place to raise their young and store their food." "'And it's all made from wax, 'a substance so labour intensive that the bees have to fly the equivalent 'of 12 times round the Earth to produce a single pound of it.'" "This almost looks man-made, manufactured." "Yeah." "It doesn't look like something from the natural world." "The precision, the fine straight lines that they've created is extraordinary." "Right." "It's an engineering wonder, for sure." "Look at the..." "It's perfect hexagons here." "Yeah." "It's amazing." "And the hexagon is a very strong structure." "'The bees have made an identical pattern to the columns 'on the Giant's Causeway." "'Each cell is exactly like the others - 'six walls meeting precisely at 120 degrees." "'And every honeybee, everywhere in the world, 'knows how to build these shapes." "'It's as if the hexagon is built into the bee's DNA.'" "You can see the bees going down inside the cell." "It's almost exactly the same size as their bodies." "Right." "Are they using their body like a ruler in some sense, to do the geometry?" "That's an accurate description." "I know different races have a smaller body and the cell size in their comb is smaller." "And each of the hexagons, how do they actually make a hexagon rather than some irregular shape?" "They've just done it for thousands of years." "They were born to do it, they just instinctively know that this is the shape of their home." "But there's more to the bees' behaviour than raw instinct." "There's another reason why they build in hexagons." "And to reveal that reason, we need to turn to the universal language of all nature." "Mathematics." "The bees' primary need is to store as much honey as they can while using as little precious wax as possible." "The bees' honeycomb is an amazing piece of engineering, but why have they evolved to produce this hexagonal pattern?" "They don't have too many choices." "If you try to put pentagons together, for example, they just don't fit together nicely." "Or circles leave lots of little gaps." "If they want to produce a network of regular shapes which fit together neatly then you've really only got three options." "You can do equilateral triangles, or you could do squares, or you can do the bees' hexagons." "But why of those three does the bee choose the hexagons?" "Well, it turns out that the triangles actually use much more wax than any of the other shapes." "Squares are a little better, but it's the hexagons which use the least amount of wax." "'It's a solution that was only mathematically proven a few years ago." "'The hexagonal array IS the most efficient storage solution 'the bees could have chosen." "'Yet with a little help from evolution, 'they worked it out for themselves millions of years ago.'" "This is nature's Code at work, and the bees are in tune with it." "It's easy to see why efficiency is important to the bees." "After all, it's hard work making wax." "But what could be the reason for the same pattern being permanently engraved in the rock of the Giant's Causeway?" "The geological processes that form these columns took place over thousands of years." "But to understand what happened, we need to look at structures that last for only a few seconds." "Soap films are mostly thinner than wavelengths of light." "About 20,000 times thinner than a human hair." "They're almost not here." "Probably the thinnest thing you've ever looked at and got information back from was a soap film." "Tom Noddy is one of the world's foremost exponents of bubble art." "The different colours on a bubble are different thickness of soap film." "So looking over the colours of a bubble, you're actually looking at a contour map of the surface of the bubble." "Bang." "So, like everything in nature, bubbles are just trying to economise, they're trying to get as small as they possibly can." "But in the case of bubbles, they can do it perfectly." "A single bubble in the air is always a sphere." "At first sight, it seems obvious that the bubble should be round." "But why is the sphere so special?" "The sphere is one surface, no corners, infinitely symmetrical." "Of all the shapes this bubble could be, the sphere is the one with the smallest surface area, which makes it the most efficient shape possible." "And it is because nature loves to use her resources effectively that we can see spheres everywhere we look." "The Earth is round because gravity pulls the planet's bulk into a ball around its core." "Water forms into spherical droplets - the shape minimises the amount of surface tension needed to hold the droplet together." "And a spherical shape gives simple life forms, like this Volvox plankton, optimal contact with their surrounding environment." "But not everything is spherical." "And because bubbles are so thin and flexible" "?" "we can use them to create other shapes." "So, a single bubble in the air is always a sphere." "But if they touch each other, they can save material for both of them by sharing a common wall." "And so they do." "If they can save surface area by taking advantage of their environment, they will." "So when you've got just one bubble, the sphere is the most efficient shape." "But as we add more bubbles, we see the geometry changing." "So, in this case, we've got four bubbles and you can see them meeting at a point." "But put a shape in the middle, we don't get a spherical bubble, we get, in fact, a little tetrahedron." "With four faces, they're not exactly flat, they're parts of spheres, but each time, the bubbles are trying to find the most efficient shape for the arrangement of bubbles." "So now we've got six bubbles, we've got a little cube appearing in the middle." "This is nature's laws at work." "The universe is always trying to find the most efficient solution it can." "And as we pop them, the bubbles change, finding the most efficient, until we're left with a sphere again." "It has no choice." "But what's most remarkable is that those solutions are so often neat, geometric shapes." "Wow!" "That's a dodecahedron." "That's fantastic." "And they're almost perfect pentagons." "That's really surprising." "They're not bulging really very much at all." "That's right." "So, 12 bubbles around make 12 faces and the most economical shape that they can make, the lowest energy, is the dodecahedron." "Yeah." "The soap bubble reveals something fundamental about nature." "It's lazy." "It tries to find the most efficient shape, the one using the least energy, the least amount of space." "And it appears there ARE fixed rules about how it finds these economic solutions." "The bubbles are incredibly dynamic, but each time one pops, they're always trying to assume the most efficient shape, the one that uses the least energy." "And what they're doing is trying to minimise the surface area across the whole bubble structure." "This beautifully illustrates one of the fundamental rules of bubbles, which is, three walls of a bubble will meet always at 120 degree angle." "Wherever you are in the foam, it's the same law." "But if we, in fact, made each of the bubbles the same size, a rather magical shape starts to appear." "The hexagon." "'And when you pack lots of hexagons together, 'the pattern that spontaneously emerges is the familiar sight 'of a tightly ordered honeycomb.'" "So when we see that pattern at the heart of the beehive, it's echoing some of the fundamental geometrical rules of the universe." "It's the principles we see in bubbles that help explain where all structure comes from." "And it's those same fundamental laws of shape that played out on the Giant's Causeway in the distant geological past." "50 million years ago, before there was any thought of warring giants, this area was very unstable." "There was a huge amount of volcanic activity." "The molten rock forces its way through the chalk bed beneath my feet and then spread out, forming a huge lava lake." "As it cooled, the lake contracted, and as it shrunk, it cracked." "And as the cracks spread, they sought out the most efficient path through the lava, which turned out to be this neat hexagonal pattern..." "..leaving this monument to the order and economy of nature." "'It's an engineering wonder, for sure.'" "The Code reveals itself where you would least expect it." "It defines the shape of honeycomb." "'They've just done it for thousands of years." "They were born to do it.'" "And it forms Ulster's epic coastline." "'..they just don't seem to fit in to this rugged natural environment.'" "'Fionn mac Cumhaill.'" "And it appears in the lazy efficiency of a soap film." "'About 20,000 times thinner than a human hair.'" "These natural codes are so fundamental that they've been appropriated by artists and architects to shape the modern world." "CHEERING" "So this is the Olympic stadium that was built in Munich in 1972, also scene of a rather famous victory for England." "A rare one, 5-1 to us against Germany." "It's really stunning but I'm quite surprised at how insubstantial it feels." "It feels as though it could blow away in the wind." "It's got those features you expect in nature, very elegant, but rather delicate feel to it." "So it's almost more like a cobweb than a man-made structure." "In 1972, which you have to remember is pre the computer age, it was very difficult to build structures like this." "The distribution of forces that's going on inside this roof are incredibly complicated." "It would be almost impossible to calculate by hand a shape like this that would be both stable and affordable." "But the revolutionary engineer Frei Otto realised that you don't have to do these calculations by hand." "Otto was desperate to find new shapes and forms to build, so he looked to nature, and the fundamental principles of the Code, for inspiration." "What Otto did was to make models like this one here." "It's constructed out of string, wires and these poles." "It doesn't look like much but when I dip the string inside the soap solution and pull it up, something rather surprising happens." "You start to see these beautiful shapes beginning to emerge inside a soap film." "And you can see that they're not just exact triangles, you get wonderful curves and arcs that Otto knew were inherently stable." "Oh, that's lovely, that one there." "The surface tension pulls the strings into the most sparing shape for each arrangement." "What results is a shape that's not only stable but remarkably striking too." "So he could make copies of these shapes, make small little models, which would then be used to construct the groundbreaking structures you see behind me." "Frei Otto started something of a revolution in architecture." "The sweeping curves of the Munich Stadium are echoed in countless modern structures." "And although Otto discovered the mathematical and aesthetic beauty of the Code in the 20th century, there's evidence that this obsession with form stretches back thousands of years." "These stone balls were found in Scotland and they date back to the Neolithic period, which is over 4,000 years ago." "They sit very beautifully in the hands." "They found hundreds of these balls." "But it's not really clear what they were used for." "It's a bit of a mystery." "But imagine the amount of work that's gone into making these shapes." "For example this one here has got four different faces arranged in a beautifully symmetrical manner." "This one here has six faces, a bit like a cube." "And you can see some of them are really intricate." "This ones got..." "I don't know how many nodules on there." "Some of them have got up to 160 different nodules." "But these stones really show an obsession with symmetry and regularity, already, thousands of years ago." "This obsession with shape isn't unique to the ancient Scots." "We find it in other cultures all over the world." "The Egyptians had their pyramids, of course." "But it was the Greeks who first took this innate fascination with shape and turned it into a subject of its own." "They believed that by understanding its principles, they could describe the whole world." "And they gave a name to this new idea." "One which meant measuring the Earth." "They called it geometry." "The mainstay of Greek geometry was a discovery of five perfect shapes, now called the Platonic Solids, after the Greek philosopher Plato, who believed these were the building blocks of nature." "So we've got the tetrahedron with its four faces, the cube with its six faces, the octahedron with its eight faces, the dodecahedron, 12 faces, and the most complicated shape of all, the icosahedron, with its 20 faces." "Today these are more commonly known as dice." "We're all used to the familiar six sided dice, but these four other shapes have also been used as dice for centuries." "What makes them perfect for the job is that they are so regular." "The faces of each are all the same shape." "All meet at the same angles." "It means that there's no way of telling one end from another, and that they are equally likely to land on any face." "But most surprisingly, these are the only five shapes like this that can possibly exist." "They're the only perfectly symmetrical solids." "It's this almost magical symmetry which made the Greeks believe that these shapes were so important." "They associated them with the building blocks of nature:" "air, fire, earth, the cosmos and water." "These five shapes built the natural world." "It's very easy to dismiss this approach as naive." "After all, it's clear the world around us isn't made out of just five neat geometric shapes." "But perhaps we should have more faith in this ancient intuition." "Because by laying out the laws of geometry the Greeks had in fact tapped straight into the Code that shapes all nature." "It turns out that the Greeks were right about their shapes, but they couldn't have known it, because the world that's governed by their laws of geometry was completely invisible to them." "We can find traces of it deep underground." "This is the Merkers potash mine, in the heart of what used to be East Germany." "It has long since stopped production, but you can still explore its 3,000 miles of tunnels." "That's stunning, my God." "I've never seen anything like this." "In fact I think this is the only one like this in the world." "It's absolutely amazing." "Just goes on and on down through the cave." "The cave is full of perfectly cubic crystals that mirror the geometric precision of the Platonic solids." "These cubes are amazing." "Look at that." "The surface is perfectly flat and if you run your finger down the edge here it's so sharp." "Comes down to this precise right angle." "An architect would be happy with that kind of precision." "Doesn't look real." "Even if you look inside you can see all the cracks are right angles and geometric shapes." "Totally surreal." "Actually, this isn't anything particularly special." "This is just sodium chloride which we know as salt." "This is what you stick on your chips." "But you don't generally see salt as big a cube as this one here." "How these crystals were able to form with such perfect precision was a mystery until just over 100 years ago, when X-rays were discovered." "Our understanding of our biology was transformed by being able to see inside the human body." "And when X-rays were shone through crystals, they uncovered another invisible world, one that was both mysterious and geometric." "This was the world of the atom." "And these neat symmetrical images, called diffraction patterns, can reveal how individual atoms were put together to form the crystals in this cave." "Essentially you've got to think of these a bit like shadows." "Just in the same way as an X-ray of my hand is a shadow of the bones underneath the skin, this is a shadow of the billions of atoms contained inside the crystal." "It's a little bit more complicated than that, but essentially, these are 2D projections of the 3D structure inside this crystal." "So now we can analyse these patterns and work out exactly how the atoms are arranged inside the salt." "And there is only one possible arrangement of these atoms that can produce patterns like these." "And it too, unsurprisingly, is a cube." "This is a model of the structure of salt, and these gold balls are the sodium atoms, and the green ones are the chlorine atoms." "And it's this atomic symmetry which explains why were seeing such symmetry in these huge crystals." "But instead of just three atoms lining themselves up in this model, we've got billions and billions of sodium and chlorine atoms arranging themselves rigidly to create these perfect cubes." "What makes this cave so special is that the perfect geometric arrangement of the atoms has been maintained in these huge crystals." "They're a window into nature, and how it's governed by the laws of geometry at the most fundamental atomic level." "But what's surprising is that we can find the same laws, not just in rocks and minerals, but deep inside ourselves." "I've come to the Department of Chemical and Structural Biology at Imperial College in London." "Steve Matthews studies how individual atoms are built up into living systems, like you and me." "X-rays are obviously very powerful, high energy radiation, so proteins are very delicate." "So we cool it down with a stream of liquid nitrogen gas blowing over the crystal." "In this tiny wire loop is another crystal, but this time, it's a crystal of protein, part of the machinery of living cells." "Just as it's possible to work out the atomic structure of the salt crystals with X-rays, we can deduce the shape of the protein molecules in the same way." "Though the results aren't quite so easy to interpret." "I'd be hard pushed to actually give a name to that shape mathematically." "It looks like a blob." "It doesn't have a shape but many of these blobs come together to form shapes." "There's a huge amount of structure and symmetry in this protein?" "Oh yes, definitely." "That's amazing." "We've got a cylinder now." "This is a real surprise to see geometry at work inside our bodies." "But evolution creates a very efficient process, so symmetry is a very efficient way of building these types of structures." "So by a process of evolution biology has discovered that..." "Before us, yes." "..that geometry gives us the best shapes?" "Right." "But if you really want symmetry we can move over to a virus particle." "I recognise that." "That's a icosahedron." "That's an icosahedron." "This is one of the shapes the Greeks were obsessed with." "Seems that viruses are too." "That's right." "It's very striking cos the physical world you somehow expect maybe salt crystals to be symmetric, but the biological world everyone considers rather a messy one." "But this is not messy at all." "This is beautiful." "The geometric shapes which you find at the heart of our cells are the most efficient that nature can produce." "It seems like the Greeks could have been right after all." "It's their shapes that build the word around us and produce its inherent beauty." "'An obsession with symmetry and regulatory.'" "The Code dictates some shapes through efficiency..." "'The building blocks of nature.'" "..and others by providing frameworks for the tiniest particles there are." "'This is nature's code at work.'" "'It fits beautifully in the hand.'" "What the Greeks discovered in mathematical theory is to be found at the heart of nature, from crystals to viruses." "It all seems very neat." "'Now I recognise that." "That's an icosahedron.'" "'The only one like it in the world.'" "But our world isn't filled with precise geometric shapes." "It seems random, disordered." "To find out why we need to look to the sky and the crystals that fall from it." "Snowflakes assemble themselves in the heart of frozen clouds and fall to earth in a dazzling display." "VOICES CHATTER INAUDIBLY" "And if there's one thing we know about snowflakes, it's that they're all perfectly symmetrical." "Wow." "Here we are." "It's the snow lab." "Physicist Kenneth Libbrecht has created a lab for growing and photographing these perfect crystals." "It's a cold chamber." "Its actually cold on the bottom, very cold, about minus 40 on the bottom and about plus 40 on top." "In a sense this machine is trying to replicate what happens inside a snow cloud." "In a sense, that's right." "It's not hard to grow ice crystals." "All you need is cold and water." "In the freezing conditions of the chamber, we should be able to see the inherent geometry of the world emerging in front of our eyes, as the crystals start to form." "Now, with any luck, we'll see some stars growing on the ends of those needles." "As the temperature drops, billions of water molecules coalesce out of the vapour, spontaneously arranging themselves into these six pointed patterns." "At least, that's the theory." "But the reality turns out to be very different." "As Ken found out, even in laboratory conditions, it's almost impossible to grow perfect snowflakes." "I don't think any of these are symmetrical." "Not a single one." "What's the chance of getting a perfectly symmetrical snowflake in here?" "PROFESSOR SIGHS" "The really beautiful snowflakes are about one in a million." "Really?" "Wow." "Sometimes they've got five sides or three sides." "Five sides?" "Oh no!" "Or three, or sometimes you get a blob." "It's a little hard to see but this mess here is one funny looking snowflake." "We do tend to think of the snowflake as something beautifully symmetrical, but actually that's just some idealised notion and the reality is that they're actually much more complex and irregular than we think they are." "If the molecular scale it's perfect, but as the crystal gets bigger, the atoms don't hook on in always exactly the right way, so when it grows, or how it grows depends on the environment," "the temperature and the humidity, so it starts growing one way, then moves to a different spot in the cloud and grows a different way and then a different way, so by the time the crystal hits the ground," "it's had a complex growth history, so it ends up as a complex crystal." "Ah, there it goes." "It seems you can only come so far in trying to describe the world with simple geometry." "You can see it at work in the salt crystals in the crystal cave." "But in truth, that's one of the very few places in the world where you'll find such crystals." "The bees use simple geometry to make their honeycomb, but they've evolved to perform that task over many thousands of years." "And it's only occasionally that you'll ever find a purely symmetrical snowflake." "Because although everything is formed from tidy geometry at the atomic level, that underlying order falls apart amid all the competing forces of our chaotic world." "Even the Giant's Causeway isn't really a neat hexagonal array." "It's almost there, but amongst the hexagons there are pentagons, seven-sided columns, even a few with eight sides." "That network of perfectly interlocking hexagons just doesn't exist." "The world clearly isn't just built from simple geometric shapes." "The movement of the sea and the flow of the waves are far too complicated to explain in these terms." "It's difficult to imagine how we could ever find a code to explain all this complexity." "But what if there are patterns in the chaos of nature?" "Patterns that we're not aware of, but that we're attuned to on a subconscious level." "This barn was home to one of the artistic revolutions of the 20th century." "The painter who worked here had become disillusioned with conventional painting techniques." "In fact he stopped painting altogether and started splattering." "He was as controversial as the art he produced." "An arrogant, self-destructive drunk." "And perhaps a visionary." "His name was Jackson Pollock." "The floor you can still see is covered in paint." "What Pollock would do is to lay a canvas out on the floor." "And then - often intoxicated - he would drip and flick the paint all over the surface." "He'd come back week after week, adding more and more layers, more and more colours." "The result was extraordinary." "They're a huge outburst of abstract expressionism." "Just covered in paint, scattered all over the place." "Pollock's paintings sent shockwaves through the art world." "No-one had ever seen anything like this before." "Life Magazine declared him, artist of the century." "Others derided his efforts as the substandard dross of a drunken lunatic." "But though Pollock's paintings courted controversy, they were incredibly influential." "Not least because the apparent random squiggles are strangely compelling." "Many people have tried to copy Pollock's techniques." "Some in homage, others in attempted forgeries." "But nobody seems to be able to reproduce that magic that Pollock brought to the originals." "Pollock's paintings seem to have captured something of the wildness of the natural world." "But for a long time no-one could define exactly what it was that made his work so appealing." "Until it came to the attention of artist and physicist, Richard Taylor." "His unique approach was to invent a machine that can mimic Pollock's eccentric painting style." "It's all based on this apparatus called the Pollockiser." "The Pollockiser?" "That's lovely." "No, what it is essentially though is what's called a kicked pendulum and as you know a basic pendulum is very, very regular like a clock, but at the top here what you've got is a little device that can actually knock the" "string as it's swinging around and that induces a very different type of motion called "chaotic motion."" "So this would be like Pollock's hand, this would be what he'd be trying to achieve with that sort of off balance, um, painting that we do?" "Absolutely, so they're very similar processes." "It's very effective." "By recreating his technique, the Pollockiser is able to mimic one particular aspect of the artist's work." "And that is that it appears more or less the same, no matter how closely you look." "You keep on seeing these patterns unfolding in front of you." "And with a Pollock painting, all of those patterns of different size scales look the same." "This is a property known as fractal." "So if I took pictures at these different scales and showed them to somebody, in some sense they wouldn't be able to tell which one was the close and which one was far away?" "Absolutely." "So as long as you can't see that canvas edge, then you have no idea whether you're standing 30 feet away or 2 feet away, they'll both have exactly the same level of complexity." "More than any other painter, Jackson Pollock was able to consistently repeat the same level of complexity at different scales throughout his paintings." "The fractal quality of his work appeals to us." "Because, despite seeming abstract, it actually mirrors the reality of the world around us." "When we started to actually analyse the buried patterns in there, this amazing thing emerged." "Deep down hidden in there is this level of mathematical structure." "So it's this really delicate interplay between something that looks messy and chaotic, but actually it has structure and some underlying code hidden inside it?" "Absolutely, and you can see it not only in his paintings, but you see it everywhere." "You know like a tree outside." "You look at the tree from far away you see this big trunk with a few branches going off." "Superficially they look cluttered and they look incredibly complex, but your eye can sense that there's a sort of underlying mathematical structure to all it." "Pollock was the first person to actually put it on canvas in a direct fashion that no other artist has ever done." "It really is the basic fingerprint of nature." "And that's what's most fascinating about Pollock's art." "In creating work devoid of conventional meaning, he had in fact stumbled across something fundamental." "Because fractals are how nature builds the world." "Clouds are fractal, because they display the same quality." "Giant clouds are identical to tiny ones." "And it's the same with rocks." "From appearances you can't tell if you're looking at an enormous mountain, or a humble bolder." "And then there are living fractals like this tree." "It's quite easy to see how fractal it is, because if you take one of the branches it looks remarkably like a small version of the tree itself." "If you look at the twigs coming off the branch, they have the same shape." "So you see the same pattern appearing again and again at smaller and smaller scales." "And trees also demonstrate the great powers of fractal systems." "Their great complexity stems from very simple rules." "Now the reason the tree makes this shape is because it wants to maximise the amount of sunlight it gets." "Very clever." "But also very simple, because you just need one rule to create this shape." "What the tree does is to grow, then divide." "Grow then divide." "And by using this one rule, we get this incredibly complex shape we call a tree." "This is the same pattern repeating itself at a smaller and smaller scale." "It's a rule that's easy to test." "Grow a bit, then branch." "Grow a bit then branch." "And before our eyes a mathematically perfect tree appears." "But just as you never get a perfect snowflake, you never get a perfect tree either." "But allow for some natural variability, different growing seasons, the wind, an occasional accident and the result is a very real looking tree." "And we find the same fractal branching system time and again throughout nature." "Deep down in there is this level of mathematical structure." "This idea that the patterns of nature may be inherently fractal was pioneered in the 1970s by French mathematician, Benoit Mandelbrot." "This is his most famous creation." "The Mandelbrot Set." "Its systems of circles and swirls repeats itself at smaller and smaller scales forever." "And this infinite complexity was created from just one very simple mathematical function." "Mandelbrot's quantum leap was to suggest that similar simple mathematical codes could describe not just trees, but many of the seemingly random shapes of much of the natural world." "INDISTINCT VOICES" "And the most powerful demonstration of that belief comes, not from maths or nature, but from make believe." "INDISTINCT VOICES" "A smart pencil..." "In the 1980s, a computer scientist working for the aircraft manufacturer Boeing was struggling to create computer-generated pictures of planes." "At Boeing, we discovered a method of making curved surfaces, very nice curved surfaces, so I was applying it to airplanes." "And Boeing publicity photos have mountains behind their planes and so I wanted to be able to put a mountain behind my airplane, but I had no idea of the mathematics or how to do that, not a clue." "So you wanted something that however far or near away you were, it would look like something natural?" "Yes, exactly, to show that these mountains were real and live, in the sense that you can move around them with a camera." "So the algorithm needed to be invented and so that's what I set my mind to doing was invent the algorithm that would produce the mountain pictures." "At the time, even creating a virtual cylinder was hard." "So generating the apparently random jaggedness of a realistic mountain range seemed impossible." "Then Loren found inspiration." "Coincidentally at that time, Mandelbrot's book came out." "He had pictures that showed what fractal mathematics could produce and so wow, all I have to do is find a way to implement this mathematics on my computer and I can make pictures of mountains." "Loren set to work to investigate how Mandelbrot's theories about the real world could be used to make virtual ones." "This is a little film I made in 1980." "And the landscape is constructed by me, by hand, of about 100 big triangles." "Yeah." "So that doesn't look very natural." "No, it's very pyramid-like." "So what we're going to do is take each of these big triangles and break it up into little triangle and break those little triangles up into littler triangles, until it gets down to the point where you can't see triangles any more." "What Loren had realised was that he could use the maths of fractals to turn just a handful of triangles into realistic virtual worlds." "We turn the fractal process loose and instantly it looks natural." "We went from about 100 triangles to about 5 million." "And there it is." "And then we jump off the cliff." "You feel that it's a real three-dimensional world." "And we're swooping over the landscape." "Yeah, we're going from ten miles away to ten feet away and all that detail was generated on the fly as we came in." "In a few seconds." "And here's that fractal quality, this infinite complexity at work." "It's exactly what I wanted." "Yeah." "By today's standards, this animation does not look like much." "But in the 1980s, no-one had ever seen anything like it." "If you did that by hand, to do that frame by frame, it would take you?" "100 years." "100 years and this took to generate?" "It took about 15 minutes per frame on a computer that's about 100 times slower than my phone." "That one short film changed the face of animation and revolutionised Hollywood." "Loren went on to co-found Pixar, one of the most successful film studios in the world." "Cars, monsters and, of course, toys owe their existence to the Code." "An empire built on the power of fractals." "Did you realise at the time the potential of the discovery you'd made?" "Well, I knew that, that within a half a second that it was a major discovery." "I've seen, you know, all the special effects, all the movies you can imagine, nothing was like that." "And my heart skipped." "And the power of fractals is still to be found hidden in the fabric of Pixar movies." "They use the rule of repetition and self-similarity to create the rocks, clouds and forests." "In fact, the realism and complexity of these virtual worlds is only possible using mathematics." "Fractals are everywhere in these movies." "They generate the texture of the rocks." "And they bring the jungle alive." "That these pretend worlds are so realistic, demonstrates the power of maths to describe the complexity of nature." "They're evidence that we have glimpsed the Code that governs the shape of the world." "But that Code is a complicated one." "If we want to understand the shape of the world, then we need to recognise the simple geometry of form at work at the most basic level." "INDISTINCT VOICES" "We need to understand that the universe is lazy." "And that it will always seek out the most efficient solution." "INDISTINCT VOICES" "That at the atomic level, the world is structured around strict geometric laws..." "INDISTINCT VOICES" "..that were first recognised by the Greeks thousands of years ago." "We also need to appreciate the complexity of that geometry playing out against the competing forces of the natural world." "And that means grasping how even the apparent randomness we see around us is underwritten by mathematical rules like fractals." "Rules that can explain the patterns in everything." "From the chaos of Jackson Pollock's paintings, to the structure of trees and the realism of virtual worlds." "And that's the beauty of the Code." "However complex we find our world, it provides a reason, an underlying explanation for why things look and behave as they do." "INDISTINCT VOICES" "This is nature's code of law." "Go to bbc.co.uk/code to find clues to help you solve the Code's treasure hunt." "Plus, get a free set of mathematical puzzles and a treasure hunt clue when you follow the links to the Open University." "Or call:" "Subtitles by Red Bee Media Ltd" "E-mail subtitling@bbc.co.uk" "For as long as human beings have walked upon earth, we've tried to make sense of our world and predict what the future will bring." "Yet today, our lives seem more complicated and unpredictable than ever." "And half the population of the planet now live in busy, sprawling cities." "Every day throws up thousands of different encounters." "A mass of interactions and forces that seem beyond our control." "WOMAN LAUGHS" "It's hard to see how any of this could be connected." "BABY CRIES" "Yet when we start to look closely at all this complexity, surprising patterns begin to emerge." "It's these patterns that I believe point to an underlying Code at the very heart of existence that controls not only our world and everything in it, but even us." "As a mathematician, I'm fascinated by the patterns we see all around us." "Patterns that reflect the hidden connections between everything." "From the movement of rush hour crowds... ..to the shifting shape of a flock of starlings." "The cacophony of a billion Internet searches... and the vagaries of the weather." "THUNDER ROLLS" "CHEERING" "Together, these patterns and connections make up the Code." "A model of our world that describes not only how it works, but can also predict what our future holds." "Around 500 years ago, a ship was caught in a terrible storm." "As rain lashed the decks and gale force winds tore through the rigging, the ship began to take on water." "The captain had no choice but to run his ship aground and wait for help." "But help never arrived, and the natives were hostile." "After eight long months, and with his crew facing certain starvation, the captain came up with an ingenious plan." "He summoned the local chief and told him his God was angry." "So angry, in fact, that if they didn't bring supplies within three days," "God would swallow the moon." "And sure enough, as the moon rose on the third night, it had already begun to disappear." "Terrified, the locals ran from all directions towards the ship, laden with provisions." "The year was 1504, and the captain?" "Christopher Columbus." "And the reason he was apparently able to command the heavens was because he had something like this." "It's a set of lunar tables." "And each one of these numbers represents a lunar eclipse." "Today's date is June 15th, and it says that in about five hours' time the same thing is going to happen to the moon here in Cyprus." "During a lunar eclipse, the earth passes between the sun and the moon, casting its shadow across the lunar surface." "And there it goes." "The moon has been swallowed up by the shadow of the Earth." "But the amazing thing is actually the moon doesn't completely disappear, cos... there's a kind of..." "red, ghostly moon up there." "And that's because the light from the sun is being refracted around the Earth." "Really quite spooky." "I can imagine how terrified the islanders would have been when they saw that 500 years ago." "And the only explanation for them would have been that the gods really were angry with them." "We now know that the movement of the planets is incredibly predictable." "By understanding the Code, we can model their orbits far back into the past." "And see thousands of years into the future." "It's thanks to the Code that we're no longer frightened by an eclipse." "In fact, the Code is such a powerful thing that I'm even prepared to entrust my life to it." "This strange contraption is five and a half metres high." "Using the force of gravity, a 30-kilogram ball will hurtle down the ramp and fire off the end." "And when it does, I will be sitting directly in its path." "If I get my sums wrong, I'll be killed outright." "To calculate how far the ball's going to go," "I need some key measurements about the ramp." "Little h is 0.98 metres." "The angle is 49.1 degree." "So gravity, I know, on the Earth... is 9.8 metres per second squared." "Interestingly, you don't have to know the weight of the ball, the mass of the ball." "That's not relevant to how far the thing's going to go." "Two times gravity, times the height, 5.5, multiplied by the speed, divided by 49.1, take the cosine..." "That will give me a distance of 9.95 metres." "But we've got air resistance, there's friction on the..." "the ramp as well." "What about the wind today?" "9.16." "OK, so the predicted distance is going to be 5.6 metres." "That's where I think the ball is going to land." "Which means if I set up my deckchair here, I should be able to watch the whole thing in complete safety." "OK, release the ball." "And that is the power of the Code." "We can do this again and again and again..." "..and the numbers mean the ball is going to land in the same place each time." "If everything in the world behaved according to equations that give definite answers, we'd be able to predict the future with absolute certainty." "But unfortunately things aren't quite that simple." "The natural world often appears so complex it's hard to imagine we could write equations to describe it." "Even though we might glimpse what we think are patterns, they seem almost impossible to understand." "I've come to witness a mysterious phenomenon that happens here in Denmark for a few short weeks every year." "WINGS FLUTTER" "BIRDS TWITTER" "WINGS FLUTTER" "First few appearing, I think." "These are starlings, making their annual migration between southern Europe and Scandinavia." "A single flock can contain a million birds or more." "Their dance obscures the fading evening light, giving the formation its eerie name " "The Black Sun." "There's another massive group coming in." "Oh!" "There are thousands of them up there." "It's not really clear why they do this." "It's maybe like, kind of, safety in numbers." "The whole shape looks quite intimidating." "It looks like one large, black beast, frightening off any predators that might be looking for a bit of dinner before sunset." "Look at that." "Ah." "Ah." "It's almost hypnotic." "It's amazing." "There are so many of them, it's a wonder they don't smash into each other and sort of knock some out of the sky." "But they don't seem to." "Incredible synchronisation." "Oh!" "You're never quite sure what it's going to do next." "'It's an almost impossible achievement." "'How can each bird predict the movements of thousands of others?" "'" "That's extraordinary?" "As strange as it seems, by reducing each starling to numbers, we can model what's happening on a computer." "We start with a flock of virtual starlings, all flying at different speeds and in different directions." "all flying at different speeds and in different directions." "And then we give them some simple rules." "The first is for each bird to fly at the same speed." "The second rule is to stay close to your neighbours." "And finally, if you see a predator nearby, get out of the way." "Three simple rules are all it takes to create something that looks uncannily like the movement of a real flock of starlings." "Oh, here they come." "Oh!" "HE LAUGHS" "In fact, a recent study has shown that even in a flock of hundreds of thousands of birds, each starling only has to keep track of its seven nearest neighbours." "And then...they've all gone." "The sky's clear again." "Who'd have thought that something so extraordinarily complex as a constantly shifting flock of thousands of birds in flight can have at its heart such a simple and elegant Code?" "WOMAN LAUGHS" "CHILD LAUGHS" "BABY CRIES" "It seems inconceivable that human beings could ever be reduced to a mathematical model like starlings." "CLOCK TICKS" "But Iain Couzin studies how animals behave in groups, and his research has revealed some surprising parallels." "How can you possibly begin to understand something like this huge mass of people?" "Even when you look at the crowd for a few seconds, you realise there's so many complicated factors at play." "I started my research looking at simple organisms, organisms like ant swarms, schooling fish." "And remarkably, our insights from studying those systems led to new insights in studying human crowds." "But people are much more complicated than a...a fish or an ant." "Exactly, but that's almost the beauty of this, is we're thinking about more interesting things when we're walking through crowds than, "How do I avoid that person and that obstacle?"" "You know, we're thinking about what we're going to cook for dinner or what our friends are doing." "And so, in actual fact, we're almost on auto-pilot, and we're actually using very simple rules of interaction just like the schooling fish and the swarming ants." "So can we learn things from the ants?" "We could learn an huge amount from the ants." "Ants don't suffer from problems such as congestion." "Because they're not selfish." "And I'm afraid to say we are." "We want to minimise our own travel time, but we don't necessarily care whether we do so at the expense of other individuals." "Of all the animals Iain has studied, human beings are, in some ways, the most predictable." "We walk at an optimum speed of 1.3 metres per second, and prefer to walk in straight lines to get to our destination." "What happens is you will naturally fall into the slipstream of someone moving in the same direction as you." "And so without you even knowing it, you're forming a lane." "Similarly, pedestrians moving in the other direction will also form lanes, very much like the ants do." "These lanes help us to avoid collisions." "However, in a large open space, like the concourse at Grand Central Station, the lanes inevitably cross each other, which could lead to congestion." "But when you put an obstacle - like this information desk - in the middle of the crowd, rather than getting in the way, it acts like a roundabout and increases the flow through the station by as much as 13%." "These rules are so effective at predicting what we'll do, they can even be used to simulate crowds of people." "Each individual is actually described by a set of numbers as they move through an environment." "Exactly." "We're capturing the average type of behaviour of pedestrians." "We're capturing these simple and local rules that people use within crowds to then make predictions as to how the whole crowd is going to flow through different environments." "We can use this underlying Code of the crowd to design buildings that are more efficient and safer." "Simulations like these are able to accurately predict how quickly a building can be evacuated, even before it has been built." "As a crowd, people are incredibly predictable." "There are simple rules that we follow without being aware of it." "But most of the time, we don't live on autopilot." "And when the crowd disperses, so too do the rules of group behaviour." "SIREN BLARES" "As individuals with our own free will, we're much harder to predict." "Or so we think." "Before we gets started, I would like to mention the rules." "They are very simple." "There are three throws and there are only three throws." "We use a three-prime shoot, which means you go one, two, three and you release your throw on four." "A throw of rock is a closed fist." "You can throw it any way you want as long as it is a closed fist." "Your paper must be horizontal." "Your scissors must be vertical." "That will be foul." "The game of rock, paper, scissors is known all over the world." "And some people take it very seriously." "For those of you who don't know, and there should be very few, the throw of paper covers the throw of rock." "The throw of scissors cuts the throw of paper, and the throw of rock crushes the throw of scissors." "In Philadelphia, the Rock, Paper, Scissors League competes four times a week." "The people in this room are fighting to go to the world championship in Las Vegas and the chance to win $10,000." "Sweetji in the lead." "Rock versus scissors for Sweetji." "You're on the verge of elimination, Drew Bag." "Third and final set, winner moves on." "THE CROWD CHANTS AND CLAPS" "Rock versus scissors." "And what a match, to take us down to the final four." "The intriguing thing about this game is that it should be impossible to predict what your opponent's going to do next." "In rock, paper, scissors, they're all pretty much equivalent." "So each throw beats one and loses to another, so essentially it's a game of even odds." "A bit like a flip of a coin." "But if the game is entirely random, every player would be evenly matched." "And yet some people win time and time again." "It is match point, Sweetji." "B-Pac has no points here in round number two." "He will need two straight throws." "Can he get through number one?" "No." "Sweetji!" "So now our final match of the night." "Sweetji, you're going to play dOGulas." "The more we play, the more we're influenced by our past throws." "Begin." "And that creates patterns that can be exploited to win the game." "Sweetji came fifth in the league last year, and this season looks set to do even better." "dOGulas!" "Rock crushes scissors." "Sweetji still has point..." "Rock crushes scissors!" "SHE SCREAMS" "Sweetji, Philadelphia Rock, Paper, Scissors City League Champion here at the Raven Lounge." "Congratulations." "Thank you." "So that was five consecutive wins." "What was the key to your success, do you think?" "I try to read people." "Yeah, you do, yeah?" "Or at least try to think what they're thinking." "You're looking for their patterns then?" "Yeah, a little bit like..." "Their patterns, and they'll be trying to learn mine and go against that." "Rock, paper, scissors reveals a fundamental truth about human nature." "We are so addicted to patterns that we let them seep into almost everything we do." "And these patterns are the key to predicting many aspects of our behaviour." "Even the darkest parts of our nature." "SCREAMS" "Deceased." "Female, five foot two." "Complexion, dark." "Eyes, brown." "Hair, brown." "When you see this much activity in such a small geographic area in such a tight time frame, that's a warning bell that something's going on, we have a predator operating." "Kim Rossmo has 20 years' experience as a Detective Inspector." "He specialises in hunting down serial killers." "The victim's body was found here in the corner by a police officer that came in shortly after the crime had occurred." "The prime crime scene would be..." "But Rossmo is no ordinary cop, because he's got a PhD and uses mathematics to understand the patterns criminals leave behind." "There's a logic in how the offender hunted for the victim and the location where he committed the crime." "If we can decode that and if we can understand that pattern, we can use that information to help us focus a criminal investigation." "The reason it's so hard to catch serial killers is because there's often no link to their crimes." "They kill random strangers in locations they have no obvious connection to." "It's very common in the investigation of a serial murder case to have hundreds, thousands, even tens of thousands of suspects." "It's a needle-in-a-haystack problem." "Where do you start?" "In 1888, the most notorious serial killer of all, Jack the Ripper, killed five women in London's East End." "Since then, countless people have tried to solve the mystery of the Ripper's identity." "But Rossmo thinks he could have tracked him down without seeing a scrap of evidence." "Because he's worked out where Jack the Ripper most likely lived." "Based only on the location of the crimes." "Flower and Dean Street should have been the epicentre of their search." "And all he used to do it is an equation." "Inherently, we're all lazy, and criminals just as much as anyone else." "They want to accomplish their goals close to home rather than further away, because it involves too much effort, too much time, too much travel." "The first half of Rossmo's equation models what's known as the least-effort principle." "It means that the crime locations are statistically more likely the nearer they are to where the offender lives." "If you have a choice of going to the corner store for a loaf of bread or one that's seven miles down the road, you'll pick the corner store." "It seems a bit gruesome to apply the same thing to a serial killer as to going and buying a loaf of bread or milk." "Well, actually, if we can get over the horrible nature of these crimes and recognise that these are human beings like the rest of us, we can, because we understand ourselves, maybe bet some understanding of these individuals." "The second half of the equation describes something called the buffer zone." "Criminals avoid committing crimes too close to home, for fear of drawing attention to themselves." "It's the interaction of these two behaviours that allows Rossmo to calculate the most probable location of the criminal." "These individuals have to not only obtain their target - or capture a victim - but avoid apprehension by the police and identification by witnesses." "The technique, known as geographic profiling, is now used by police all over the world." "Police are examining the possibility that a small explosion near a branch of Barclays Bank in West London was the work of an extortionist." "Police believe the demand came from the blackmailer known as Mardi Gra." "In the late '90s, Rossmo was called in by Scotland Yard to help catch the notorious Mardi Gra bomber, who for three years waged a campaign of terror against banks and supermarkets." "A 17-year-old man is recovering in hospital after being injured in an explosion at a Sainsbury's store in South London." "'Police are advising the public to be vigilant." "'In truth, they can only wait to see what Mardi Gra does next.'" "How many bombs did he let off during that time?" "Total, 36 known linked offences." "So you can see, they range from the north of Cambridge, all the way down to the strait of Dover." "But most of them are in Greater London." "So this is a map showing the locations of all the bombs that were set off?" "That's right." "There's certainly a concentration on London, but it looks pretty randomly scattered." "So now you're feeding those locations into the equation?" "Right." "And what we have here now is the geo-profile." "And that's going to show us the most likely location where the offender lived." "With dark orange being the most likely or the most probable." "So we can see that the major focus is around the Chiswick area." "In fact, in the report we prepared for Scotland Yard, we even prioritised postcodes for that." "And how successful was it in this case?" "Well, let me show you the locations... of the two brothers, Edgar and Ronald Pearce." "Right, that is really in the hot zone, isn't it?" "Yes." "Edgar's home is in the top 0.8% of the area of the crimes in Greater London." "So less than 1%." "That's extraordinary." "Edgar Pearce had demanded £10,000 a day from Barclays." "And when he and his brother tried to collect it from a cash point in Chiswick, the police were waiting." "Two bothers in their 60s were remanded in custody by magistrates in connection with the so-called Mardi Gra bombings." "Ronald and Edgar Pearce, both from Chiswick in West London, each face three conspiracy charges." "Based on the apparently random location of 36 bombs," "Rossmo's geographic profile narrowed the location of the Mardi Gra bomber from 300 square miles to a postcode in Chiswick." "Although his bother, Ronald, was acquitted," "Edgar Pearce pleaded guilty and was jailed for 21 years." "So do you think the bomber was aware that he was creating these patterns?" "No, he wasn't." "But it's very difficult for humans to engage in completely random behaviour." "Very few of us are aware of the patterns we leave behind." "WOMAN LAUGHS" "From the way we move in a crowd... ..to the choices we make in a game..." "Paper covers rock!" "The victim's body was found here... ..or even how we commit murder." "In reality, these crimes are not random..." "None of it is random." "It's all part of the Code." "There are always tell-tale patterns." "And if we're able to decode them, we can use those patterns to model our behaviour." "And this leads to the intriguing possibility that if we can reduce human beings to numbers, we might be able to predict our future in the same way as we can predict the movement of the planets or the trajectory of a ball." "But the course of our lives never seems to run entirely smoothly, and the future rarely turns out exactly as we'd planned." "I may have a good idea what I'm going to be doing tomorrow, or even next week, but as the weeks turn into months and months to years, our future becomes less certain." "Every decision we make, every situation we encounter, every person we meet, sends our life down a different path." "As you watch each stick floating off downstream, there's no sure way of predicting their fate." "I might be able to hazard a guess where a stick will be in two minutes." "But what about two hours?" "Two days?" "'.." "Turn into years, our future becomes far less certain.'" "Life sometimes seems so unpredictable that we think of it as being random." "But in fact it isn't random at all." "Simply a sequence of cause and effect." "A freak accident." "I'm so sorry." "A slight delay." "A missed bus." "A broken promise." "There are millions of factors that intervene to affect our journey through life, and the tiniest shift in any one of these can completely change its future course." "The white one's caught in a dam, but the red one's fast." "I think this'd be a good finishing line." "And here comes the white." "It's way ahead of the red." "And white's the winner." "Right, let's give it another go." "The truth is, our lives are controlled by the strangest code of all... the code of chaos." "Our lives aren't random, they're chaotic, a tangled web of cause and effect in which insignificant moments can escalate into events that change our lives forever." "Any difference, no matter how small, can have a huge effect on the outcome." "It's this incredible sensitivity to even the slightest change which is one of the defining features of chaos." "Because chaotic systems appear so random, it's often difficult to see a pattern." "And that has led us to sometimes misinterpret our world in a spectacular manner." "'In this land of many mysteries, it's a strange fact 'that large legends seem to collect around the smallest creatures." "'One of these is a mousy little rodent called the lemming." "'Here's an actual living legend, for it's said of this tiny animal" ""that it commits mass suicide by rushing into the sea in droves." "This film from 1958 set out to explain the wildly fluctuating population of these tiny rodents." "'Ahead lies the Arctic shore, and beyond, the sea." "And still the little animals surge forward." "'Their frenzy takes them tumbling down the terraced cliffs, 'creating tiny avalanches of sliding soil and rocks.'" "The legend of suicidal lemmings was the accepted explanation for why the Arctic can be overrun with them one year and completely empty the next." "'They reach the final precipice." "'This is the last chance to turn back." "'Yet over they go, casting themselves bodily out into space.'" "This film popularised the belief that lemmings are stupid, reckless and suicidal." "The very word "lemming" has come to mean as much." "The trouble is, though, it isn't true." "In fact, it's been claimed that the whole thing was faked." "The film-makers apparently flew in hundreds of captive-bred lemmings and drove them over the cliffs and out to sea." "'Soon the Arctic Sea is dotted with tiny bobbing bodies." "'And so is acted out the legend of mass suicide.'" "Now, as appalling as this sounds, the reason for the alleged lemming abuse stems not so much from ignoring the moral code, but rather an ignorance of the mathematical one." "What no-one knew at the time was that the incredible fluctuation in lemming numbers has nothing to do with mass suicide." "It's all because of chaos." "And there's a simple equation at its heart." "So, if I want to know how many lemmings there'll be next year, what I need to do is take this year's population, "P", and multiply that by the growth rate "R"." "But not all lemmings will survive, so there's a bit of the equation which tells me how many lemmings will die during the year." "So that's R times P times P." "So we can rewrite this equation as the growth rate R times P times one minus P." "Now, this equation isn't specific to lemmings, it actually applies to any animal population." "And the interesting part of the equation is this number R, the growth rate." "Because when we choose different values for R, we get a very different behaviour for the population growth." "The growth rate determines how quickly a population expands." "For most species of mammal, this is usually below 2." "With a growth rate in this range, the equation predicts that a population will rise until it stabilises at a fixed value." "But it turns out lemmings are one of the fastest-reproducing mammals on the planet." "Let's take R equals 3.1." "The lemmings don't stabilise now, but ping-pong between two different values." "So the population is high, then low, and back to high again, low again." "But when the growth rate reaches a value just over 3.57 then something incredibly unexpected happens." "Rather than levelling off at a fixed number, or fluctuating between two values, their population erupts into chaos." "A plague of almost biblical proportions one year can plummet to near extinction the next." "It's almost impossible to predict how many lemmings you're going to have." "In fact, there doesn't seem to be any pattern to this at all." "And of course, this is exactly what's seen in reality." "Unpredictable boom-and-bust lemming populations." "Lemmings are one of the few creatures on Earth that breed so quickly their growth rate can sometimes exceed this tipping point." "It's such an odd phenomenon that mass suicide seems like a plausible answer." "But the real explanation comes from the Code." "From this equation." "The problem is we can never know exactly how many lemmings are born or how many die." "And just the smallest difference in the growth rate R, produces a totally different answer." "And this is true of all equations that model chaos." "Although they can explain how something happens, they're almost useless at predicting the future." "I can use an equation to calculate where this ball will land, because even if I'm slightly out in any of my measurements, it will only make a small difference to the final result." "The ball will be released from the ramp at 49.1 degrees." "But if this ball behaved according to the laws of chaos, the tiniest shift in the ball's position or the angle of release could dramatically alter its trajectory." "I'd have no idea whether it would just simply fall harmlessly off the end of the ramp." "Or be sent into orbit." "I'd have no idea where to put my deckchair." "It turns out that much of the world is chaotic, making it almost impossible to predict." "But that doesn't stop us trying." "Knowing whether the sun is going to shine or the heavens are going to open, is a British obsession." "But trying to plan our lives around the vagaries of the weather seems almost futile." "Even though we have precise equations that can describe how clashing air masses interact to create clouds, wind and rainfall, it doesn't really help us very much with our predictions." "THUNDER CRASHES" "That's because we can never know the exact speed of every air particle." "The precise temperature at every point in space, or the pressure across the whole planet." "And just a small variation in any one of these can produce a vastly different forecast." "This is a map of how the weather looks right now." "The blue lines represent cold fronts and the red lines represent warm fronts." "In order to make a prediction what we do is to take the mathematical equations for the weather and create a model." "Now the trouble is, I can't know the precise atmospheric conditions, so I take as much data as possible." "Then I make small variations in the data and run the model again and again and again and what I get is different predictions according to those slight variations." "So for the weather tomorrow, the predictions are petty similar." "We've got a lot of blue lines together predicting a cold front." "A lot of red lines together predicting a warm front." "But look what happens when I look a little bit further ahead." "So two days, three days ahead... so you can see these different predictions are beginning to spread out." "You can still see some sort of pattern in the weather but if I move a week ahead..." "..and I couldn't hazard a guess as to what the weather's going to be." "There are red and blue lines all over the place." "One prediction says it's going to be hot, the other says cold, and if I go ten days ahead, it just looks like a scrambled mess of spaghetti." "There's absolutely no way to make any prediction that far in advance." "And that's why beyond just a few days, the weather forecast can be so spectacularly wrong." "Once we understand that the atmosphere is chaotic, we can appreciate that the smallest change in the initial conditions can dramatically alter what will happen." "The movement of just one molecule of air can be magnified over time to have a huge effect on the weather as a whole." "We refer to this phenomenon as the "butterfly effect"." "The idea that something as small as the flap of a butterfly's wings might create changes in the atmosphere that could ultimately lead to a tornado on the other side of the world." "CRASHING THUNDER" "As a crowd, the patterns we make are incredibly predictable." "Even as individuals our actions are controlled by the Code." "And by untangling chaotic systems like the weather, we've uncovered evidence of the Code in what we once thought of as impossibly complex." "When we look at things from a different angle, surprising patterns emerge." "Patterns that can reveal defining truths about ourselves and our future." "In 1906, an unfortunate cow laid down its life for a place in mathematical history." "One." "Ten." "264." "417." "'The cow was the subject of a guess-the-weight competition at a village fare." "'The lucky person who came closest 'would win the slaughtered animal's meat.'" "1,020." "2,137." "'The amazing thing was nobody guessed correctly.'" "..570." "'And yet everybody got it right.'" "4,510." "To show you how they did it," "I'm not going to use a cow, I'm going to use a jar of jelly beans." "450?" "800?" "12,000." "7,000." "How many jellybeans do you think there are in this jar?" "Um, 50... 80 thousand." "80 thousand?" "No, actually 50,000." "50,000." "OK, yeah." "It's incredibly difficult for anyone to guess how many jellybeans there are." "I asked 160 people and most were way off the mark." "Everything from 400 right up to 50,000 beans." "In fact only four people got anywhere near the correct answer of 4,510." "Plus 1,500, plus 3,217, plus 83... ." "If I add all the answers together and take the average, I get the combined guess of the entire group." "Plus, 4,000, plus 5,000, 463," "Plus 853, plus 1,000, plus 5,000..." "Which gives a grand total of 722,383.5." "Somebody thought there was half a bean in there." "Now there are 160 guesses made, so let's see how close they are collectively." "Wow, that's extraordinary." "You remember there were 4,510." "The average guess to the nearest bean is 4,515." "I thought it would be close, but I didn't think it would be THAT close." "That is ridiculous." "Though we had guesses that were all over the place, up in 30,000s right down in the 400s, collectively we get something which is just 0.1% away from the real number of beans in there." "So as individuals the guesses are just that, guesses." "But when you take them collectively they become something else entirely." "5,000. 1,450. 9,200." "What tends to happen is that more or less as many people will underestimate the number of jellybeans as overestimate it." "1,763... 6,000." "A few people will be way off the mark either way, but that doesn't matter." "Provided you ask enough people, the errors should cancel each other out." "1,000. 1,275. 700?" "The accuracy of the group is far greater than the individual." "We call it "the wisdom of the crowd"." "160 people is a powerful tool for working out how many jellybeans there are in the jar." "But imagine what you could do with a crowd of millions." "That's exactly what they use here at Google." "With access to over two billion web searches a day," "Google have found a way of tapping into the wisdom of the biggest crowd on Earth." "And by doing so, they've been able to reveal the forces that control our lives, and harness them to make predictions about us." "'Think of the things that people search for on a daily basis." "'Think of the things that YOU search for on a daily basis.'" "I searched for cities in Mexico and films in Hackney today." "Lots of people may be searching for the similar... a similar thing, movies in Hackney, for example." "And if you look at that query over the past three years, um, what the pattern of searches for that term looks like." "Google had a hunch they could use all our searches to make predictions about our lives." "They wanted to see if they could match the pattern of certain searches with events in the real world." "Google began by seeing if they could predict outbreaks of flu." "So flu has a nice seasonal pattern and because it has that pattern every year over many years, we're able to...to take that trend and say which search queries match that pattern." "So we built a database that included over 50 million different search terms." "50 million?" "Yes." "Wow, yeah." "We didn't only include things that may be related to flu." "We included things like Britney Spears or..." "Everything people search for would be included." "When Google looked back over the past five years of data, there were certain search terms whose popularity exactly matched the pattern of flu cases." "So people were searching for things like "symptoms"" "or "medications" or "sore throat"." "There are other things like complications." "So you're saying that the sort of number of search terms for flu-related things almost exactly mirrors the actual cases of flu that we see in the population?" "That's true." "It is an indicator of flu activity just based on lots of people searching for these terms." "We were amazed by this finding." "As soon as they see this pattern of search terms" "Google can predict there will be an outbreak of flu." "Often before people had even gone to the doctor." "This is the extraordinary power of the Code." "But it's just the tip of the iceberg." "The searches we make can be used to predict where we'll go on holiday." "What model of car we're going to buy." "Or how we're going to vote, often before we know ourselves." "It's even been possible to forecast the movement of the Stock Market from the number of negative words used on Twitter." "Analysing such vast amounts of data, doesn't just allow us to make predictions." "It can also tell us something fundamental about ourselves." "You look out at a city like this and it looks like, you know, some arbitrary jumbled mess." "Yet the city IS people." "It's not the buildings and the streets." "They're the stage upon which the real actors are playing out the story of civilisation." "Geoffrey West is a physicist who's spent his life trying to see meaningful patterns in the universe." "And how he's turned his attention to the dynamics of human life in cities." "So you can see there's all kinds of infrastructure here." "There's the obvious, the roads, the electrical lines, the sewer lines." "They're an extraordinary network that is sustaining New York City." "You know, coming at it as a physicist," "I had this hunch that there is an underlying code to all this." "West amassed data about cities all over the world." "And the patterns he found mean that for any given population size, he can predict the amount of roads, electrical wiring or office space that city has." "But he also discovered something much more surprising." "One of the most interesting results we discovered was that, um..." "Wages scale in a very systematic way and the rule that came out was that if you doubled the size of the city, you get this marvellous 15% increase in the wages." "If you live in a large city, you're going to earn more?" "Yes." "So what, if there are two mathematicians in two different cities - one twice the size - doing the same job, one will have a bigger income?" "On the average, that is what the data say." "Was that a surprise to you to see that?" "A huge surprise." "I thought there was something wrong with the data." "And then it was like, "Of course!" "That's why cities exist."" "Incredibly, it's not just people's salaries that increase." "When a city doubles in size, every measure of social and economic activity goes up by 15% per person." "That's 15% more restaurants to choose from." "15% more art galleries to visit." "15% more shops to go to." "In short, life gets 15% better." "You know it looks like it's a magic formula that we as social human beings have discovered..." "..this 15% bonus, so to speak, is, I believe, the reason that people are attracted to cities and why there has been this continuous migration from the countryside and into the cities." "And at some deeper level, actually drive our civilisation." "According to Geoffrey West, humankind has an ultimate number." "It's this extra 15% or 1.15." "He believes it's the most important driving force in humanity." "This single number, 1.15, predicts our future." "It will bring us together in ever expanding cities and shape our destiny for as long as human beings exist." "Five hundred years ago, when faced with an eclipse, many of us would have believed it was the work of an angry god." "But as we've unearthed the language of the Code, we've discovered that the apparent mysteries of our world can be understood without invoking the supernatural." "And this for me is what's so remarkable." "That despite the incredible complexity of the world we live in, it can all, ultimately, be explained by numbers." "Just like the orbit of the planets, life too follows a pattern." "And it can all be reduced to cause and effect." "In the end, even the flip of a coin is determined by how fast it's spinning and how long it takes to hit the ground." "The ultimate symbol of chance isn't random at all." "It only appears that way." "When we don't understand the Code, the only way we can make sense of our world is to make up stories." "But the truth is far more extraordinary." "Everything has mathematics at its heart." "When everything is stripped away all that remains is the Code." "Find clues to help you solve the Code's treasure hunt at..." "Plus get a free set of mathematical puzzles and a treasure hunt clue when you follow the links to the Open University." "Or call 0845 366 8026." "Subtitles by Red Bee Media Ltd" "E-mail subtitling@bbc.co.uk"