Prediction The Code


Prediction

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For as long as human beings have walked upon earth,

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we've tried to make sense of our world

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and predict what the future will bring.

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Yet today,

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our lives seem more complicated and unpredictable than ever.

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And half the population of the planet

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now live in busy, sprawling cities.

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Every day throws up thousands of different encounters.

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A mass of interactions and forces that seem beyond our control.

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WOMAN LAUGHS

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It's hard to see how any of this could be connected.

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BABY CRIES

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Yet when we start to look closely at all this complexity,

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surprising patterns begin to emerge.

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It's these patterns that I believe point to an underlying Code

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at the very heart of existence

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that controls not only our world and everything in it, but even us.

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As a mathematician, I'm fascinated by the patterns we see all around us.

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Patterns that reflect the hidden connections between everything.

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From the movement of rush hour crowds...

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..to the shifting shape of a flock of starlings.

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The cacophony of a billion Internet searches...

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and the vagaries of the weather.

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THUNDER ROLLS

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CHEERING

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Together, these patterns and connections make up the Code.

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A model of our world that describes not only how it works,

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but can also predict what our future holds.

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Around 500 years ago, a ship was caught in a terrible storm.

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As rain lashed the decks

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and gale force winds tore through the rigging,

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the ship began to take on water.

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The captain had no choice but to run his ship aground and wait for help.

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But help never arrived, and the natives were hostile.

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After eight long months, and with his crew facing certain starvation,

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the captain came up with an ingenious plan.

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He summoned the local chief and told him his God was angry.

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So angry, in fact, that if they didn't bring supplies within three days,

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God would swallow the moon.

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And sure enough, as the moon rose on the third night, it had already begun to disappear.

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Terrified, the locals ran from all directions towards the ship,

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laden with provisions.

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The year was 1504, and the captain?

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Christopher Columbus.

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And the reason he was apparently able to command the heavens

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was because he had something like this.

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It's a set of lunar tables.

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And each one of these numbers represents a lunar eclipse.

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Today's date is June 15th, and it says that in about five hours' time

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the same thing is going to happen to the moon here in Cyprus.

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During a lunar eclipse, the earth passes between the sun and the moon,

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casting its shadow across the lunar surface.

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And there it goes.

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The moon has been swallowed up by the shadow of the Earth.

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But the amazing thing is actually the moon doesn't completely disappear, cos...

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there's a kind of... red, ghostly moon up there.

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And that's because the light from the sun is being refracted around the Earth.

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Really quite spooky.

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I can imagine how terrified the islanders would have been when they saw that 500 years ago.

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And the only explanation for them would have been that the gods really were angry with them.

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We now know that the movement of the planets is incredibly predictable.

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By understanding the Code, we can model their orbits far back into the past.

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And see thousands of years into the future.

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It's thanks to the Code that we're no longer frightened by an eclipse.

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In fact, the Code is such a powerful thing

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that I'm even prepared to entrust my life to it.

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This strange contraption is five and a half metres high.

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Using the force of gravity,

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a 30-kilogram ball will hurtle down the ramp and fire off the end.

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And when it does, I will be sitting directly in its path.

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If I get my sums wrong, I'll be killed outright.

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To calculate how far the ball's going to go,

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I need some key measurements about the ramp.

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Little h is 0.98 metres.

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The angle is 49.1 degree.

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So gravity, I know, on the Earth...

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is 9.8 metres per second squared.

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Interestingly, you don't have to know the weight of the ball, the mass of the ball.

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That's not relevant to how far the thing's going to go.

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Two times gravity, times the height, 5.5,

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multiplied by the speed, divided by 49.1,

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take the cosine...

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That will give me a distance of 9.95 metres.

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But we've got air resistance, there's friction on the... the ramp as well.

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What about the wind today? 9.16.

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OK, so the predicted distance is going to be 5.6 metres.

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That's where I think the ball is going to land.

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Which means if I set up my deckchair here, I should be able to watch the whole thing in complete safety.

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OK, release the ball.

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And that is the power of the Code.

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We can do this again and again and again...

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..and the numbers mean the ball is going to land in the same place each time.

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If everything in the world behaved according to equations that give definite answers,

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we'd be able to predict the future with absolute certainty.

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But unfortunately things aren't quite that simple.

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The natural world often appears so complex

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it's hard to imagine we could write equations to describe it.

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Even though we might glimpse what we think are patterns,

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they seem almost impossible to understand.

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I've come to witness a mysterious phenomenon

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that happens here in Denmark for a few short weeks every year.

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WINGS FLUTTER

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BIRDS TWITTER

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WINGS FLUTTER

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First few appearing, I think.

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These are starlings,

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making their annual migration between southern Europe and Scandinavia.

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A single flock can contain a million birds or more.

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Their dance obscures the fading evening light,

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giving the formation its eerie name -

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The Black Sun.

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There's another massive group coming in.

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Oh!

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There are thousands of them up there.

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It's not really clear why they do this.

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It's maybe like, kind of, safety in numbers.

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The whole shape looks quite intimidating.

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It looks like one large, black beast,

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frightening off any predators

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that might be looking for a bit of dinner before sunset.

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Look at that.

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Ah.

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It's almost hypnotic.

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It's amazing. There are so many of them,

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it's a wonder they don't smash into each other

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and sort of knock some out of the sky. But they don't seem to.

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Incredible synchronisation.

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Oh!

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You're never quite sure what it's going to do next.

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'It's an almost impossible achievement.

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'How can each bird predict the movements of thousands of others?'

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That's extraordinary?

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As strange as it seems, by reducing each starling to numbers,

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we can model what's happening on a computer.

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We start with a flock of virtual starlings,

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all flying at different speeds and in different directions.

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And then we give them some simple rules.

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The first is for each bird to fly at the same speed.

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The second rule is to stay close to your neighbours.

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And finally, if you see a predator nearby, get out of the way.

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Three simple rules are all it takes to create something

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that looks uncannily like the movement of a real flock of starlings.

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Oh, here they come.

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Oh!

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HE LAUGHS

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In fact, a recent study has shown

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that even in a flock of hundreds of thousands of birds,

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each starling only has to keep track of its seven nearest neighbours.

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And then...they've all gone.

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The sky's clear again.

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Who'd have thought that something so extraordinarily complex

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as a constantly shifting flock of thousands of birds in flight

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can have at its heart such a simple and elegant Code?

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WOMAN LAUGHS

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CHILD LAUGHS

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BABY CRIES

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It seems inconceivable that human beings

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could ever be reduced to a mathematical model like starlings.

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CLOCK TICKS

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But Iain Couzin studies how animals behave in groups,

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and his research has revealed some surprising parallels.

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How can you possibly begin to understand something like this huge mass of people?

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Even when you look at the crowd for a few seconds,

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you realise there's so many complicated factors at play.

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I started my research looking at simple organisms,

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organisms like ant swarms, schooling fish.

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And remarkably, our insights from studying those systems

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led to new insights in studying human crowds.

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But people are much more complicated than a...a fish or an ant.

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Exactly, but that's almost the beauty of this,

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is we're thinking about more interesting things

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when we're walking through crowds than, "How do I avoid that person and that obstacle?"

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You know, we're thinking about what we're going to cook for dinner or what our friends are doing.

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And so, in actual fact, we're almost on auto-pilot,

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and we're actually using very simple rules of interaction

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just like the schooling fish and the swarming ants.

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So can we learn things from the ants?

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We could learn an huge amount from the ants.

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Ants don't suffer from problems such as congestion.

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Because they're not selfish. And I'm afraid to say we are.

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We want to minimise our own travel time,

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but we don't necessarily care whether we do so at the expense of other individuals.

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Of all the animals Iain has studied,

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human beings are, in some ways, the most predictable.

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We walk at an optimum speed of 1.3 metres per second,

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and prefer to walk in straight lines to get to our destination.

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What happens is you will naturally fall

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into the slipstream of someone moving in the same direction as you.

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And so without you even knowing it, you're forming a lane.

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Similarly, pedestrians moving in the other direction will also form lanes,

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very much like the ants do.

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These lanes help us to avoid collisions.

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However, in a large open space,

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like the concourse at Grand Central Station,

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the lanes inevitably cross each other,

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which could lead to congestion.

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But when you put an obstacle - like this information desk -

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in the middle of the crowd, rather than getting in the way,

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it acts like a roundabout

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and increases the flow through the station by as much as 13%.

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These rules are so effective at predicting what we'll do,

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they can even be used to simulate crowds of people.

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Each individual is actually described by a set of numbers

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as they move through an environment.

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Exactly. We're capturing the average type of behaviour of pedestrians.

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We're capturing these simple and local rules that people use within crowds

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to then make predictions as to how the whole crowd

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is going to flow through different environments.

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We can use this underlying Code of the crowd

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to design buildings that are more efficient and safer.

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Simulations like these are able to accurately predict

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how quickly a building can be evacuated,

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even before it has been built.

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As a crowd, people are incredibly predictable.

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There are simple rules that we follow without being aware of it.

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But most of the time, we don't live on autopilot.

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And when the crowd disperses, so too do the rules of group behaviour.

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SIREN BLARES

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As individuals with our own free will, we're much harder to predict.

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Or so we think.

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Before we gets started, I would like to mention the rules.

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They are very simple.

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There are three throws and there are only three throws.

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We use a three-prime shoot, which means you go one, two, three

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and you release your throw on four.

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A throw of rock is a closed fist.

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You can throw it any way you want as long as it is a closed fist.

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Your paper must be horizontal.

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Your scissors must be vertical.

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That will be foul.

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The game of rock, paper, scissors is known all over the world.

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And some people take it very seriously.

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For those of you who don't know, and there should be very few,

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the throw of paper covers the throw of rock.

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The throw of scissors cuts the throw of paper,

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and the throw of rock crushes the throw of scissors.

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In Philadelphia, the Rock, Paper, Scissors League

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competes four times a week.

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The people in this room are fighting

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to go to the world championship in Las Vegas

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and the chance to win 10,000.

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Sweetji in the lead. Rock versus scissors for Sweetji.

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You're on the verge of elimination, Drew Bag.

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Third and final set, winner moves on.

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THE CROWD CHANTS AND CLAPS

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Rock versus scissors.

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And what a match, to take us down to the final four.

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The intriguing thing about this game is that it should be impossible

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to predict what your opponent's going to do next.

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In rock, paper, scissors, they're all pretty much equivalent.

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So each throw beats one and loses to another,

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so essentially it's a game of even odds.

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A bit like a flip of a coin.

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But if the game is entirely random,

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every player would be evenly matched.

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And yet some people win time and time again.

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It is match point, Sweetji.

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B-Pac has no points here in round number two.

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He will need two straight throws.

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Can he get through number one?

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No. Sweetji!

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So now our final match of the night.

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Sweetji, you're going to play dOGulas.

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The more we play, the more we're influenced by our past throws.

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Begin.

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And that creates patterns that can be exploited to win the game.

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Sweetji came fifth in the league last year,

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and this season looks set to do even better.

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dOGulas!

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Rock crushes scissors.

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Sweetji still has point...

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Rock crushes scissors!

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SHE SCREAMS

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Sweetji, Philadelphia Rock, Paper, Scissors City League Champion here at the Raven Lounge.

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-Congratulations.

-Thank you.

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So that was five consecutive wins.

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-What was the key to your success, do you think?

-I try to read people.

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-Yeah, you do, yeah?

-Or at least try to think what they're thinking.

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-You're looking for their patterns then?

-Yeah, a little bit like...

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Their patterns, and they'll be trying to learn mine and go against that.

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Rock, paper, scissors reveals a fundamental truth

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about human nature.

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We are so addicted to patterns

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that we let them seep into almost everything we do.

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And these patterns are the key

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to predicting many aspects of our behaviour.

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Even the darkest parts of our nature.

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SCREAMS

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Deceased. Female, five foot two.

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Complexion, dark. Eyes, brown. Hair, brown.

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When you see this much activity in such a small geographic area

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in such a tight time frame,

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that's a warning bell that something's going on,

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we have a predator operating.

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Kim Rossmo has 20 years' experience as a Detective Inspector.

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He specialises in hunting down serial killers.

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The victim's body was found here in the corner

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by a police officer that came in shortly after the crime had occurred.

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The prime crime scene would be...

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But Rossmo is no ordinary cop,

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because he's got a PhD

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and uses mathematics to understand the patterns criminals leave behind.

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There's a logic in how the offender hunted for the victim

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and the location where he committed the crime.

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If we can decode that and if we can understand that pattern,

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we can use that information to help us focus a criminal investigation.

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The reason it's so hard to catch serial killers is because there's often no link to their crimes.

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They kill random strangers

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in locations they have no obvious connection to.

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It's very common in the investigation of a serial murder case

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to have hundreds, thousands, even tens of thousands of suspects.

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It's a needle-in-a-haystack problem.

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Where do you start?

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In 1888, the most notorious serial killer of all, Jack the Ripper,

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killed five women in London's East End.

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Since then, countless people have tried to solve the mystery of the Ripper's identity.

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But Rossmo thinks he could have tracked him down

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without seeing a scrap of evidence.

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Because he's worked out where Jack the Ripper most likely lived.

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Based only on the location of the crimes.

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Flower and Dean Street should have been the epicentre of their search.

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And all he used to do it is an equation.

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Inherently, we're all lazy,

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and criminals just as much as anyone else.

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They want to accomplish their goals close to home rather than further away,

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because it involves too much effort, too much time, too much travel.

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The first half of Rossmo's equation

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models what's known as the least-effort principle.

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It means that the crime locations

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are statistically more likely the nearer they are to where the offender lives.

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If you have a choice of going to the corner store for a loaf of bread

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or one that's seven miles down the road, you'll pick the corner store.

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It seems a bit gruesome to apply the same thing to a serial killer

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as to going and buying a loaf of bread or milk.

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Well, actually, if we can get over the horrible nature of these crimes

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and recognise that these are human beings like the rest of us,

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we can, because we understand ourselves,

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maybe bet some understanding of these individuals.

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The second half of the equation

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describes something called the buffer zone.

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Criminals avoid committing crimes too close to home,

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for fear of drawing attention to themselves.

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It's the interaction of these two behaviours that allows Rossmo

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to calculate the most probable location of the criminal.

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These individuals have to not only obtain their target -

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or capture a victim -

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but avoid apprehension by the police and identification by witnesses.

0:26:100:26:15

The technique, known as geographic profiling,

0:26:180:26:21

is now used by police all over the world.

0:26:210:26:25

Police are examining the possibility that a small explosion

0:26:300:26:34

near a branch of Barclays Bank in West London

0:26:340:26:36

was the work of an extortionist.

0:26:360:26:38

Police believe the demand

0:26:380:26:40

came from the blackmailer known as Mardi Gra.

0:26:400:26:42

In the late '90s, Rossmo was called in by Scotland Yard

0:26:440:26:48

to help catch the notorious Mardi Gra bomber,

0:26:480:26:52

who for three years waged a campaign of terror

0:26:520:26:55

against banks and supermarkets.

0:26:550:26:58

A 17-year-old man is recovering in hospital after being injured

0:26:580:27:01

in an explosion at a Sainsbury's store in South London.

0:27:010:27:04

'Police are advising the public to be vigilant.

0:27:040:27:06

'In truth, they can only wait to see what Mardi Gra does next.'

0:27:060:27:10

How many bombs did he let off during that time?

0:27:160:27:19

Total, 36 known linked offences.

0:27:190:27:23

So you can see, they range from the north of Cambridge,

0:27:230:27:26

all the way down to the strait of Dover.

0:27:260:27:29

But most of them are in Greater London.

0:27:290:27:31

So this is a map showing the locations of all the bombs that were set off?

0:27:310:27:35

-That's right.

-There's certainly a concentration on London,

0:27:350:27:39

but it looks pretty randomly scattered.

0:27:390:27:42

So now you're feeding those locations into the equation?

0:27:420:27:45

Right. And what we have here now is the geo-profile.

0:27:450:27:49

And that's going to show us the most likely location

0:27:490:27:52

where the offender lived.

0:27:520:27:54

With dark orange being the most likely or the most probable.

0:27:540:27:58

So we can see that the major focus is around the Chiswick area.

0:27:580:28:02

In fact, in the report we prepared for Scotland Yard,

0:28:020:28:05

we even prioritised postcodes for that.

0:28:050:28:07

And how successful was it in this case?

0:28:070:28:09

Well, let me show you the locations...

0:28:090:28:12

of the two brothers, Edgar and Ronald Pearce.

0:28:120:28:15

-Right, that is really in the hot zone, isn't it?

-Yes.

0:28:150:28:19

Edgar's home is in the top 0.8%

0:28:190:28:21

of the area of the crimes in Greater London.

0:28:210:28:24

-So less than 1%.

-That's extraordinary.

0:28:240:28:27

Edgar Pearce had demanded £10,000 a day from Barclays.

0:28:310:28:35

And when he and his brother tried to collect it from a cash point in Chiswick,

0:28:350:28:39

the police were waiting.

0:28:390:28:41

Two bothers in their 60s were remanded in custody by magistrates

0:28:410:28:44

in connection with the so-called Mardi Gra bombings.

0:28:440:28:47

Ronald and Edgar Pearce, both from Chiswick in West London,

0:28:470:28:51

each face three conspiracy charges.

0:28:510:28:54

Based on the apparently random location of 36 bombs,

0:28:540:28:58

Rossmo's geographic profile narrowed the location of the Mardi Gra bomber

0:28:580:29:04

from 300 square miles to a postcode in Chiswick.

0:29:040:29:07

Although his bother, Ronald, was acquitted,

0:29:100:29:13

Edgar Pearce pleaded guilty and was jailed for 21 years.

0:29:130:29:18

So do you think the bomber was aware that he was creating these patterns?

0:29:180:29:22

No, he wasn't. But it's very difficult for humans

0:29:220:29:25

to engage in completely random behaviour.

0:29:250:29:28

Very few of us are aware of the patterns we leave behind.

0:29:340:29:38

WOMAN LAUGHS

0:29:380:29:40

From the way we move in a crowd...

0:29:400:29:43

..to the choices we make in a game...

0:29:460:29:48

Paper covers rock!

0:29:480:29:50

The victim's body was found here...

0:29:500:29:53

..or even how we commit murder.

0:29:530:29:55

In reality, these crimes are not random...

0:29:550:29:59

None of it is random.

0:29:590:30:01

It's all part of the Code.

0:30:010:30:05

There are always tell-tale patterns.

0:30:050:30:08

And if we're able to decode them,

0:30:080:30:11

we can use those patterns to model our behaviour.

0:30:110:30:15

And this leads to the intriguing possibility

0:30:150:30:19

that if we can reduce human beings to numbers, we might be able to predict our future

0:30:190:30:25

in the same way as we can predict the movement of the planets or the trajectory of a ball.

0:30:250:30:30

But the course of our lives never seems to run entirely smoothly,

0:30:390:30:44

and the future rarely turns out exactly as we'd planned.

0:30:440:30:49

I may have a good idea what I'm going to be doing tomorrow, or even next week,

0:30:490:30:53

but as the weeks turn into months and months to years, our future becomes less certain.

0:30:530:30:58

Every decision we make, every situation we encounter,

0:31:020:31:06

every person we meet, sends our life down a different path.

0:31:060:31:11

As you watch each stick floating off downstream, there's no sure way of predicting their fate.

0:31:120:31:17

I might be able to hazard a guess where a stick will be in two minutes.

0:31:170:31:22

But what about two hours? Two days?

0:31:220:31:25

'..Turn into years, our future becomes far less certain.'

0:31:250:31:29

Life sometimes seems so unpredictable that we think of it as being random.

0:31:290:31:35

But in fact it isn't random at all.

0:31:350:31:38

Simply a sequence of cause and effect.

0:31:380:31:40

A freak accident.

0:31:400:31:44

I'm so sorry.

0:31:440:31:45

A slight delay.

0:31:450:31:47

A missed bus.

0:31:470:31:49

A broken promise.

0:31:490:31:51

There are millions of factors that intervene to affect our journey through life,

0:31:510:31:58

and the tiniest shift in any one of these can completely change its future course.

0:31:580:32:04

The white one's caught in a dam, but the red one's fast.

0:32:050:32:07

I think this'd be a good finishing line.

0:32:190:32:23

And here comes the white. It's way ahead of the red.

0:32:230:32:27

And white's the winner.

0:32:280:32:32

Right, let's give it another go.

0:32:320:32:33

The truth is, our lives are controlled by the strangest code of all...

0:32:330:32:40

the code of chaos.

0:32:400:32:42

Our lives aren't random, they're chaotic,

0:32:460:32:49

a tangled web of cause and effect in which insignificant moments

0:32:490:32:54

can escalate into events that change our lives forever.

0:32:540:32:59

Any difference, no matter how small, can have a huge effect on the outcome.

0:32:590:33:05

It's this incredible sensitivity to even the slightest change

0:33:050:33:09

which is one of the defining features of chaos.

0:33:090:33:12

Because chaotic systems appear so random, it's often difficult to see a pattern.

0:33:180:33:23

And that has led us to sometimes misinterpret our world in a spectacular manner.

0:33:250:33:31

'In this land of many mysteries, it's a strange fact

0:33:370:33:40

'that large legends seem to collect around the smallest creatures.

0:33:400:33:44

'One of these is a mousy little rodent called the lemming.

0:33:440:33:49

'Here's an actual living legend, for it's said of this tiny animal

0:33:490:33:53

''that it commits mass suicide by rushing into the sea in droves.

0:33:530:33:57

This film from 1958

0:33:570:34:00

set out to explain the wildly fluctuating population

0:34:000:34:03

of these tiny rodents.

0:34:030:34:05

'Ahead lies the Arctic shore, and beyond, the sea. And still the little animals surge forward.

0:34:110:34:19

'Their frenzy takes them tumbling down the terraced cliffs,

0:34:210:34:25

'creating tiny avalanches of sliding soil and rocks.'

0:34:250:34:29

The legend of suicidal lemmings

0:34:330:34:35

was the accepted explanation for why the Arctic can be overrun with them one year

0:34:350:34:39

and completely empty the next.

0:34:390:34:41

'They reach the final precipice.

0:34:410:34:45

'This is the last chance to turn back.

0:34:450:34:48

'Yet over they go, casting themselves bodily out into space.'

0:34:520:34:56

This film popularised the belief that lemmings are stupid, reckless and suicidal.

0:35:010:35:07

The very word "lemming" has come to mean as much.

0:35:070:35:10

The trouble is, though, it isn't true.

0:35:150:35:18

In fact, it's been claimed that the whole thing was faked.

0:35:180:35:22

The film-makers apparently flew in hundreds of captive-bred lemmings

0:35:260:35:30

and drove them over the cliffs and out to sea.

0:35:300:35:33

'Soon the Arctic Sea is dotted with tiny bobbing bodies.

0:35:370:35:40

'And so is acted out the legend of mass suicide.'

0:35:430:35:48

Now, as appalling as this sounds, the reason for the alleged lemming abuse stems not so much

0:35:480:35:53

from ignoring the moral code,

0:35:530:35:55

but rather an ignorance of the mathematical one.

0:35:550:35:58

What no-one knew at the time was that the incredible fluctuation

0:35:580:36:04

in lemming numbers has nothing to do with mass suicide.

0:36:040:36:08

It's all because of chaos.

0:36:090:36:12

And there's a simple equation at its heart.

0:36:120:36:15

So, if I want to know how many lemmings there'll be next year,

0:36:170:36:22

what I need to do is take this year's population, "P",

0:36:220:36:26

and multiply that by the growth rate "R".

0:36:260:36:29

But not all lemmings will survive,

0:36:290:36:31

so there's a bit of the equation which tells me how many lemmings will die during the year.

0:36:310:36:36

So that's R times P times P.

0:36:360:36:39

So we can rewrite this equation

0:36:390:36:42

as the growth rate R times P times one minus P.

0:36:420:36:47

Now, this equation isn't specific to lemmings,

0:36:470:36:50

it actually applies to any animal population.

0:36:500:36:52

And the interesting part of the equation is this number R, the growth rate.

0:36:520:36:57

Because when we choose different values for R,

0:36:570:37:00

we get a very different behaviour for the population growth.

0:37:000:37:03

The growth rate determines how quickly a population expands.

0:37:040:37:08

For most species of mammal, this is usually below 2.

0:37:080:37:12

With a growth rate in this range, the equation predicts

0:37:120:37:16

that a population will rise until it stabilises at a fixed value.

0:37:160:37:20

But it turns out lemmings are one of the fastest-reproducing mammals on the planet.

0:37:200:37:26

Let's take R equals 3.1.

0:37:260:37:30

The lemmings don't stabilise now, but ping-pong between two different values.

0:37:300:37:35

So the population is high, then low, and back to high again, low again.

0:37:350:37:40

But when the growth rate reaches a value just over 3.57

0:37:400:37:44

then something incredibly unexpected happens.

0:37:440:37:49

Rather than levelling off at a fixed number,

0:37:490:37:52

or fluctuating between two values, their population erupts into chaos.

0:37:520:37:58

A plague of almost biblical proportions one year can plummet to near extinction the next.

0:37:580:38:04

It's almost impossible to predict how many lemmings you're going to have.

0:38:040:38:09

In fact, there doesn't seem to be any pattern to this at all.

0:38:090:38:12

And of course, this is exactly what's seen in reality.

0:38:120:38:16

Unpredictable boom-and-bust lemming populations.

0:38:160:38:20

Lemmings are one of the few creatures on Earth that breed so quickly

0:38:210:38:25

their growth rate can sometimes exceed this tipping point.

0:38:250:38:29

It's such an odd phenomenon that mass suicide seems like a plausible answer.

0:38:320:38:37

But the real explanation comes from the Code.

0:38:370:38:41

From this equation.

0:38:410:38:42

The problem is we can never know exactly how many lemmings are born or how many die.

0:38:480:38:53

And just the smallest difference in the growth rate R, produces a totally different answer.

0:38:530:39:00

And this is true of all equations that model chaos.

0:39:000:39:04

Although they can explain how something happens,

0:39:040:39:08

they're almost useless at predicting the future.

0:39:080:39:11

I can use an equation to calculate where this ball will land,

0:39:190:39:22

because even if I'm slightly out in any of my measurements,

0:39:220:39:25

it will only make a small difference to the final result.

0:39:250:39:28

The ball will be released from the ramp at 49.1 degrees.

0:39:280:39:34

But if this ball behaved according to the laws of chaos,

0:39:340:39:37

the tiniest shift in the ball's position

0:39:370:39:40

or the angle of release could dramatically alter its trajectory.

0:39:400:39:45

I'd have no idea whether it would just simply fall harmlessly

0:39:470:39:50

off the end of the ramp.

0:39:500:39:52

Or be sent into orbit.

0:39:550:39:58

I'd have no idea where to put my deckchair.

0:40:020:40:06

It turns out that much of the world is chaotic,

0:40:080:40:12

making it almost impossible to predict.

0:40:120:40:15

But that doesn't stop us trying.

0:40:170:40:20

Knowing whether the sun is going to shine

0:40:240:40:27

or the heavens are going to open, is a British obsession.

0:40:270:40:30

But trying to plan our lives around the vagaries of the weather

0:40:300:40:34

seems almost futile.

0:40:340:40:36

Even though we have precise equations that can describe how clashing air masses interact

0:40:420:40:48

to create clouds, wind and rainfall,

0:40:480:40:50

it doesn't really help us very much with our predictions.

0:40:500:40:56

THUNDER CRASHES

0:40:560:40:59

That's because we can never know the exact speed of every air particle.

0:40:590:41:05

The precise temperature at every point in space,

0:41:050:41:08

or the pressure across the whole planet.

0:41:080:41:11

And just a small variation in any one of these

0:41:110:41:14

can produce a vastly different forecast.

0:41:140:41:16

This is a map of how the weather looks right now.

0:41:220:41:26

The blue lines represent cold fronts and the red lines represent warm fronts.

0:41:260:41:31

In order to make a prediction

0:41:310:41:33

what we do is to take the mathematical equations for the weather

0:41:330:41:36

and create a model.

0:41:360:41:38

Now the trouble is, I can't know the precise atmospheric conditions,

0:41:380:41:43

so I take as much data as possible.

0:41:430:41:45

Then I make small variations in the data and run the model again

0:41:450:41:50

and again and again and what I get is different predictions according to those slight variations.

0:41:500:41:56

So for the weather tomorrow, the predictions are petty similar.

0:41:560:42:00

We've got a lot of blue lines together predicting a cold front.

0:42:000:42:05

A lot of red lines together predicting a warm front.

0:42:050:42:08

But look what happens when I look a little bit further ahead.

0:42:080:42:11

So two days, three days ahead...

0:42:110:42:15

so you can see these different predictions are beginning to spread out.

0:42:150:42:20

You can still see some sort of pattern in the weather

0:42:200:42:23

but if I move a week ahead...

0:42:230:42:26

..and I couldn't hazard a guess as to what the weather's going to be.

0:42:270:42:31

There are red and blue lines all over the place.

0:42:310:42:33

One prediction says it's going to be hot, the other says cold,

0:42:330:42:37

and if I go ten days ahead,

0:42:370:42:40

it just looks like a scrambled mess of spaghetti.

0:42:400:42:44

There's absolutely no way to make any prediction that far in advance.

0:42:440:42:49

And that's why beyond just a few days,

0:42:490:42:52

the weather forecast can be so spectacularly wrong.

0:42:520:42:55

Once we understand that the atmosphere is chaotic,

0:43:000:43:03

we can appreciate that the smallest change in the initial conditions

0:43:030:43:08

can dramatically alter what will happen.

0:43:080:43:11

The movement of just one molecule of air can be magnified over time

0:43:140:43:18

to have a huge effect on the weather as a whole.

0:43:180:43:21

We refer to this phenomenon as the "butterfly effect".

0:43:240:43:28

The idea that something as small as the flap of a butterfly's wings

0:43:280:43:33

might create changes in the atmosphere

0:43:330:43:36

that could ultimately lead to a tornado on the other side of the world.

0:43:360:43:40

CRASHING THUNDER

0:43:400:43:43

As a crowd, the patterns we make are incredibly predictable.

0:43:580:44:03

Even as individuals our actions are controlled by the Code.

0:44:040:44:09

And by untangling chaotic systems like the weather,

0:44:130:44:16

we've uncovered evidence of the Code in what we once thought of

0:44:160:44:21

as impossibly complex.

0:44:210:44:24

When we look at things from a different angle,

0:44:260:44:28

surprising patterns emerge.

0:44:280:44:31

Patterns that can reveal defining truths about ourselves and our future.

0:44:330:44:39

In 1906, an unfortunate cow laid down its life

0:44:470:44:51

for a place in mathematical history.

0:44:510:44:54

One.

0:44:540:44:55

Ten.

0:44:550:44:57

264.

0:44:570:44:59

417.

0:44:590:45:01

'The cow was the subject of a guess-the-weight competition at a village fare.

0:45:010:45:06

'The lucky person who came closest

0:45:060:45:09

'would win the slaughtered animal's meat.'

0:45:090:45:12

1,020.

0:45:130:45:14

2,137.

0:45:160:45:17

'The amazing thing was nobody guessed correctly.'

0:45:170:45:20

..570.

0:45:200:45:21

'And yet everybody got it right.'

0:45:210:45:24

4,510.

0:45:260:45:28

To show you how they did it,

0:45:300:45:32

I'm not going to use a cow, I'm going to use a jar of jelly beans.

0:45:320:45:36

450?

0:45:400:45:41

800?

0:45:410:45:43

12,000.

0:45:430:45:44

7,000.

0:45:440:45:45

How many jellybeans do you think there are in this jar?

0:45:450:45:48

Um,

0:45:480:45:50

50...

0:45:500:45:52

80 thousand.

0:45:520:45:54

80 thousand?

0:45:540:45:55

No, actually 50,000.

0:45:550:45:58

50,000. OK, yeah.

0:45:580:46:00

It's incredibly difficult for anyone to guess how many jellybeans there are.

0:46:040:46:09

I asked 160 people and most were way off the mark.

0:46:100:46:15

Everything from 400 right up to 50,000 beans.

0:46:150:46:20

In fact only four people got anywhere near the correct answer of 4,510.

0:46:200:46:27

Plus 1,500, plus 3,217, plus 83... .

0:46:270:46:36

If I add all the answers together and take the average, I get the combined guess of the entire group.

0:46:360:46:43

Plus, 4,000, plus 5,000,

0:46:430:46:46

463,

0:46:460:46:48

Plus 853, plus 1,000,

0:46:480:46:52

plus 5,000...

0:46:520:46:55

Which gives a grand total

0:46:550:46:58

of 722,383.5.

0:46:580:47:04

Somebody thought there was half a bean in there.

0:47:040:47:06

Now there are 160 guesses made, so let's see how close they are collectively.

0:47:060:47:13

Wow, that's extraordinary.

0:47:130:47:16

You remember there were 4,510.

0:47:160:47:20

The average guess to the nearest bean is 4,515.

0:47:200:47:26

I thought it would be close, but I didn't think it would be THAT close.

0:47:260:47:30

That is ridiculous.

0:47:300:47:31

Though we had guesses that were all over the place, up in 30,000s right down in the 400s,

0:47:310:47:36

collectively we get something which is just 0.1% away

0:47:360:47:40

from the real number of beans in there.

0:47:400:47:43

So as individuals the guesses are just that, guesses.

0:47:430:47:47

But when you take them collectively they become something else entirely.

0:47:470:47:52

-5,000.

-1,450.

-9,200.

0:47:520:47:57

What tends to happen is that more or less as many people

0:47:570:48:01

will underestimate the number of jellybeans as overestimate it.

0:48:010:48:05

-1,763...

-6,000.

0:48:050:48:08

A few people will be way off the mark either way, but that doesn't matter.

0:48:080:48:13

Provided you ask enough people, the errors should cancel each other out.

0:48:130:48:19

-1,000.

-1,275.

-700?

0:48:190:48:24

The accuracy of the group is far greater than the individual.

0:48:240:48:28

We call it "the wisdom of the crowd".

0:48:280:48:31

160 people is a powerful tool for working out how many jellybeans there are in the jar.

0:48:310:48:40

But imagine what you could do with a crowd of millions.

0:48:400:48:44

That's exactly what they use here at Google.

0:48:470:48:50

With access to over two billion web searches a day,

0:48:520:48:55

Google have found a way of tapping into the wisdom of the biggest crowd on Earth.

0:48:550:49:00

And by doing so,

0:49:000:49:02

they've been able to reveal the forces that control our lives,

0:49:020:49:07

and harness them to make predictions about us.

0:49:070:49:11

'Think of the things that people search for on a daily basis.

0:49:110:49:14

'Think of the things that YOU search for on a daily basis.'

0:49:140:49:17

I searched for cities in Mexico and films in Hackney today.

0:49:170:49:23

Lots of people may be searching for the similar...

0:49:230:49:26

a similar thing, movies in Hackney, for example.

0:49:260:49:29

And if you look at that query over the past three years,

0:49:290:49:33

um, what the pattern of searches for that term looks like.

0:49:330:49:36

Google had a hunch they could use all our searches

0:49:400:49:43

to make predictions about our lives.

0:49:430:49:46

They wanted to see if they could match the pattern of certain searches

0:49:470:49:51

with events in the real world.

0:49:510:49:53

Google began by seeing if they could predict outbreaks of flu.

0:49:550:49:59

So flu has a nice seasonal pattern

0:50:010:50:04

and because it has that pattern every year over many years,

0:50:040:50:09

we're able to...to take that trend

0:50:090:50:12

and say which search queries match that pattern.

0:50:120:50:16

So we built a database that included over 50 million different search terms.

0:50:160:50:21

50 million?

0:50:210:50:22

-Yes.

-Wow, yeah.

0:50:220:50:24

We didn't only include things that may be related to flu.

0:50:240:50:27

We included things like Britney Spears or...

0:50:270:50:29

Everything people search for would be included.

0:50:290:50:32

When Google looked back over the past five years of data,

0:50:350:50:38

there were certain search terms whose popularity exactly matched

0:50:380:50:43

the pattern of flu cases.

0:50:430:50:45

So people were searching for things like "symptoms"

0:50:450:50:49

or "medications" or "sore throat".

0:50:490:50:52

There are other things like complications.

0:50:520:50:56

So you're saying that the sort of number of search terms for flu-related things

0:50:560:51:01

-almost exactly mirrors the actual cases of flu that we see in the population?

-That's true.

0:51:010:51:07

It is an indicator of flu activity just based on lots of people searching for these terms.

0:51:070:51:12

We were amazed by this finding.

0:51:120:51:14

As soon as they see this pattern of search terms

0:51:190:51:22

Google can predict there will be an outbreak of flu.

0:51:220:51:26

Often before people had even gone to the doctor.

0:51:260:51:29

This is the extraordinary power of the Code.

0:51:310:51:36

But it's just the tip of the iceberg.

0:51:380:51:42

The searches we make can be used to predict

0:51:420:51:44

where we'll go on holiday.

0:51:440:51:46

What model of car we're going to buy.

0:51:460:51:48

Or how we're going to vote,

0:51:480:51:50

often before we know ourselves.

0:51:500:51:53

It's even been possible to forecast the movement of the Stock Market

0:51:550:51:59

from the number of negative words used on Twitter.

0:51:590:52:02

Analysing such vast amounts of data, doesn't just allow us to make predictions.

0:52:060:52:12

It can also tell us something fundamental about ourselves.

0:52:120:52:17

You look out at a city like this and it looks like, you know, some arbitrary jumbled mess.

0:52:200:52:26

Yet the city IS people.

0:52:260:52:30

It's not the buildings and the streets.

0:52:300:52:32

They're the stage upon which the real actors

0:52:320:52:36

are playing out the story of civilisation.

0:52:360:52:39

Geoffrey West is a physicist who's spent his life trying to see meaningful patterns in the universe.

0:52:420:52:48

And how he's turned his attention to the dynamics of human life in cities.

0:52:480:52:55

So you can see there's all kinds of infrastructure here.

0:52:590:53:03

There's the obvious, the roads, the electrical lines, the sewer lines.

0:53:030:53:09

They're an extraordinary network that is sustaining New York City.

0:53:090:53:13

You know, coming at it as a physicist,

0:53:130:53:16

I had this hunch that there is an underlying code to all this.

0:53:160:53:21

West amassed data about cities all over the world.

0:53:240:53:29

And the patterns he found mean that for any given population size,

0:53:290:53:33

he can predict the amount of roads,

0:53:330:53:35

electrical wiring or office space that city has.

0:53:350:53:40

But he also discovered something much more surprising.

0:53:430:53:46

One of the most interesting results we discovered was that, um...

0:53:500:53:56

Wages scale in a very systematic way

0:53:560:54:00

and the rule that came out was that if you doubled the size of the city,

0:54:000:54:04

you get this marvellous 15% increase in the wages.

0:54:040:54:08

-If you live in a large city, you're going to earn more?

-Yes.

0:54:080:54:13

So what, if there are two mathematicians

0:54:130:54:15

in two different cities - one twice the size - doing the same job,

0:54:150:54:19

-one will have a bigger income?

-On the average, that is what the data say.

0:54:190:54:24

-Was that a surprise to you to see that?

-A huge surprise.

0:54:240:54:26

I thought there was something wrong with the data.

0:54:260:54:29

And then it was like, "Of course! That's why cities exist."

0:54:290:54:35

Incredibly, it's not just people's salaries that increase.

0:54:400:54:43

When a city doubles in size, every measure of social and economic activity

0:54:430:54:49

goes up by 15% per person.

0:54:490:54:52

That's 15% more restaurants to choose from.

0:54:520:54:56

15% more art galleries to visit. 15% more shops to go to.

0:54:560:55:00

In short, life gets 15% better.

0:55:010:55:05

You know it looks like it's a magic formula

0:55:110:55:13

that we as social human beings have discovered...

0:55:130:55:17

..this 15% bonus, so to speak, is, I believe, the reason

0:55:200:55:25

that people are attracted to cities

0:55:250:55:28

and why there has been this continuous migration

0:55:280:55:32

from the countryside and into the cities.

0:55:320:55:35

And at some deeper level, actually drive our civilisation.

0:55:350:55:40

According to Geoffrey West, humankind has an ultimate number.

0:55:430:55:48

It's this extra 15%

0:55:480:55:51

or 1.15.

0:55:510:55:53

He believes it's the most important driving force in humanity.

0:55:530:55:58

This single number, 1.15,

0:56:000:56:03

predicts our future.

0:56:030:56:05

It will bring us together in ever expanding cities

0:56:060:56:10

and shape our destiny for as long as human beings exist.

0:56:100:56:14

Five hundred years ago, when faced with an eclipse,

0:56:250:56:29

many of us would have believed it was the work of an angry god.

0:56:290:56:33

But as we've unearthed the language of the Code,

0:56:330:56:35

we've discovered that the apparent mysteries of our world

0:56:350:56:39

can be understood without invoking the supernatural.

0:56:390:56:43

And this for me is what's so remarkable.

0:56:430:56:46

That despite the incredible complexity of the world we live in,

0:56:460:56:50

it can all, ultimately, be explained by numbers.

0:56:500:56:54

Just like the orbit of the planets, life too follows a pattern.

0:56:570:57:02

And it can all be reduced to cause and effect.

0:57:040:57:07

In the end, even the flip of a coin

0:57:110:57:13

is determined by how fast it's spinning

0:57:130:57:16

and how long it takes to hit the ground.

0:57:160:57:18

The ultimate symbol of chance isn't random at all.

0:57:180:57:23

It only appears that way.

0:57:230:57:26

When we don't understand the Code,

0:57:280:57:31

the only way we can make sense of our world is to make up stories.

0:57:310:57:36

But the truth is far more extraordinary.

0:57:370:57:40

Everything has mathematics at its heart.

0:57:420:57:46

When everything is stripped away all that remains is the Code.

0:57:470:57:52

Find clues to help you solve the Code's treasure hunt at...

0:57:570:58:05

Plus get a free set of mathematical puzzles and a treasure hunt clue

0:58:050:58:10

when you follow the links to the Open University.

0:58:100:58:14

Or call 0845 366 8026.

0:58:140:58:19

Subtitles by Red Bee Media Ltd

0:58:320:58:35

E-mail [email protected]

0:58:350:58:38

Marcus du Sautoy continues his exploration of the hidden numerical code that underpins all nature. This time it's the strange world of what happens next. Professor du Sautoy's odyssey starts with the lunar eclipse - once thought supernatural, now routinely predicted through the power of the code. But more intriguing is what the code can say about our future.

Along the path to enlightenment, Marcus overturns the lemming's suicidal reputation, avoids being crushed to death, reveals how to catch a serial killer and discovers that the answer to life the universe and everything isn't 42 after all - it's 1.15.


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