The Secret Life of Chaos


The Secret Life of Chaos

Jim Al-Khalili shows how chaos theory can answer a question that mankind has asked for millennia - how does a universe that starts off as dust end up with intelligent life?


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Transcript


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This is a film about one very simple question.

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How did we get here?

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These are the elements and compounds from which all humans are made.

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They're incredibly, almost embarrassingly common.

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In fact, almost 99% of the human body is a mixture of air, water,

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coal and chalk, with traces of other slightly more exotic elements

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like iron, zinc, phosphorus and sulphur.

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In fact, I've estimated that the elements

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which make up the average human cost at most a few pounds.

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But somehow, trillions of these very ordinary atoms conspire miraculously

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to organise themselves into thinking, breathing, living human beings.

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How the wonders of creation are assembled from such simple

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building blocks, is surely the most intriguing question we can ask.

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You may think that answering it is beyond the realm of science.

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But that's changing.

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For the first time, I believe science has pushed past religion

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and philosophy in daring to tackle this most fundamental of questions.

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This film is the story of a series of bizarre

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and interconnected discoveries that reveal a hidden face of nature.

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That woven into its simplest and most basic laws,

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is a power to be unpredictable.

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It's about how inanimate matter with no purpose or design,

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can spontaneously create exquisite beauty.

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It's about how the same laws that make the universe chaotic

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and unpredictable, can turn simple dust into human beings.

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It's about the discovery that there is a strange

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and unexpected relationship between order and chaos.

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The natural world really is one great, blooming, buzzing confusion.

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It's a mess of quirky shapes and blotches.

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What patterns there are, are never quite regular,

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and never seem to repeat exactly.

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The idea that all this mayhem, all this chaos, is underpinned,

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indeed determined, by mathematical rules,

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and that we can work out what those rules might be,

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runs counter to our most dearly held intuitions.

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So not surprisingly, the first man to really take on the momentous task

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of unravelling nature's mysterious mathematics,

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had a very special and unusual mind.

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He was both a great scientist and a tragic hero.

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He was born in 1912, in London.

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His name was Alan Turing.

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Alan Turing was a remarkable man,

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one of the greatest mathematicians who ever lived.

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He discovered many of the fundamental ideas

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that underpin the modern computer.

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Also, during the Second World War,

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he worked here at Bletchley Park, just outside today's Milton Keynes,

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in what was then a secret government project called Station X,

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which was set up to crack the German military codes.

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The Station X code breakers proved highly effective,

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and Turing's contribution was crucial.

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The work he personally did to crack German naval codes,

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saved thousands of Allied lives and was a turning point in the war.

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But code breaking was just one aspect of Turing's genius.

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Just one part of his uncanny ability to see patterns

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that are hidden from the rest of us.

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For Turing, the natural world offered up the ultimate codes.

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And over the course of his life

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he'd come tantalisingly close to cracking them.

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Turing was a very original person.

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And he had realised that there was this possibility

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that simple mathematical equations

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might describe aspects of the biological world.

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And no-one had thought of that before.

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Of all nature's mysteries, the one that fascinated Turing most

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was the idea that there might be a mathematical basis

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to human intelligence.

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Turing had very personal reasons for believing in this.

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It was the death of this young man, Christopher Morcom,

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who...Alan Turing, well, he was gay,

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and it had been the great emotional thing of his life at that point.

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Christopher Morcom suddenly died.

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And, Alan Turing was obviously very emotionally disturbed by this.

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But you can see that he wanted to put this

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in an intellectual context, a scientific context.

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And the question he wanted to put into context was

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what happens to the mind? What is it?

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Turing became convinced that mathematics could be used to describe

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biological systems, and ultimately intelligence.

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This fascination would give rise to the modern computer,

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and later in Turing's life, an even more radical idea.

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The idea that a simple mathematical description could be given

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for a mysterious process that takes place in an embryo.

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The process is called morphogenesis, and it's very puzzling.

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At first, all the cells in the embryo are identical.

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Then, as this footage of a fish embryo shows,

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the cells begin to clump together,

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and also become different from each other.

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How does this happen? With no thought,

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no central co-ordination?

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How do cells that start off identical, know to become say, skin,

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while others become part of an eye?

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Morphogenesis is a spectacular example

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of something called self-organisation.

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And before Turing, no-one had a clue how it worked.

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Then, in 1952, Turing published this, his paper

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with the world's first mathematical explanation for morphogenesis.

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The sheer chutzpah of this paper was staggering.

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In it, Turing used a mathematical equation

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of the kind normally seen in papers on astronomy or atomic physics,

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to describe a living process.

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No-one had done anything like this.

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Crucially, Turing's equations did, for the first time,

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describe how a biological system could self-organise.

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They showed that something smooth and featureless can develop features.

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One of the astonishing things about Turing's work

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was that starting with the description

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of really very simple processes

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governed by very simple equations, by putting these together,

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suddenly complexity emerged.

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The pattern suddenly came out as a natural consequence.

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And I think in many ways this was very, very unexpected.

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In essence, Turing's equations described something quite familiar,

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but which no-one had thought of in the context of biology before.

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Think of the way a steady wind blowing across sand

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creates all kinds of shapes.

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The grains self-organise into ripples, waves and dunes.

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This happens, even though the grains are virtually identical,

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and have no knowledge of the shapes they become part of.

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Turing argued that in a very similar way,

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chemicals seeping across an embryo

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might cause its cells to self-organise into different organs.

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These are Turing's own very rough scribblings of how this might work.

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They show how a completely featureless chemical soup,

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can evolve these strange blobs and patches.

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In his paper, he refined his sketches

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to show how his equations could spontaneously create markings

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similar to those on the skins of animals.

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Turing went around showing people pictures saying,

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"Doesn't this look a bit like the patterns on a cow?"

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And everyone sort of went, "What is this man on about?"

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But actually, he knew what he was doing.

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They did look like the patterns of a cow, and that's one of

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the reasons why cows have this dappled pattern or whatever.

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So, an area where mathematics had never been used before,

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pattern formation in biology, animal markings,

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suddenly the door was opened and we could see

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that mathematics might be useful in that sort of area.

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So even though Turing's exact equations are not the full story,

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they are the first piece of mathematical work that showed

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there was any possibility of doing this kind of thing.

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Of course, we now know that morphogenesis

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is much more complicated than the process Turing's equations describe.

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In fact, the precise mechanism of how DNA molecules in our cells interact

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with other chemicals, is still fiercely debated by scientists.

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But Turing's idea that whatever is going on is, deep down,

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a simple mathematical process, was truly revolutionary.

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I think Alan Turing's paper is probably the cornerstone

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in the whole idea of how morphogenesis works.

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What it does is it provides us with a mechanism,

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something that Darwin didn't, for how pattern emerges.

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Darwin, of course, tells us that once you have a pattern

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and it is coded for in the genes, that may or may not be passed on,

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depending on circumstances. But what it doesn't do

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is explain where that pattern comes from in the first place.

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That's the real mystery.

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And so, what Turing had done was to suddenly provide

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an accessible chemical mechanism for doing this. That was amazing.

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Turing was onto a really big, bold idea.

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But sadly, we can only speculate how his extraordinary mind

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would have developed his idea.

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Shortly after his groundbreaking paper on morphogenesis,

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a dreadful and completely avoidable tragedy destroyed his life.

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After his work breaking codes at Bletchley Park,

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you might well have assumed that Turing would have been honoured

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by the country he did so much to protect.

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This couldn't be further from the truth.

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What happened to him after the war was a great tragedy,

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and one of the most shameful episodes in the history of British science.

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The same year Turing published his morphogenesis paper,

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he had a brief affair with a man called Arnold Murray.

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The affair went sour

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and Murray was involved in a burglary at Turing's house.

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But when Turing reported this to the police,

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they arrested him as well as Murray.

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In court, the prosecution argued

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that Turing, with his university education, had led Murray astray.

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He was convicted of gross indecency.

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The judge then offered Turing a dreadful choice.

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He could either go to prison, or sign up to a regime of

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female hormone injections to cure him of his homosexuality.

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He chose the latter, and it was to send him into a spiral of depression.

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On 8 June 1954, Turing's body was found by his cleaner.

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He'd died the day before by taking a bite from an apple

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he'd laced with cyanide, ending his own life.

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Alan Turing died aged just 41.

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The loss to science is incalculable.

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Turing would never know that his ideas would inspire

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an entirely new mathematical approach to biology,

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and that scientists would find equations like his

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really do explain many of the shapes that appear on living organisms.

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Looking back, we now know Turing had really grasped the idea

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that the wonders of creation are derived from the simplest of rules.

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He had, perhaps unexpectedly, taken the first step

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to a new kind of science.

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The next step in the story was just as unexpected,

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and in many ways, just as tragic as Turing's.

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In the early 1950s, around the time of Turing's seminal paper

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on morphogenesis, a brilliant Russian chemist by the name of

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Boris Belousov was beginning his own investigations

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into the chemistry of nature.

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Deep behind the iron curtain, in a lab at the Soviet Ministry of Health,

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he was beginning to investigate the way our bodies

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extract energy from sugars.

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Just like Turing, Belousov was working on a personal project, having

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just finished a distinguished career as a scientist in the military.

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In his lab, Belousov had formulated a mixture of chemicals

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to mimic one part of the process of glucose absorption in the body.

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The mix of chemicals sat on the lab bench in front of him,

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clear and colourless while being shaken.

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As he mixed in the final chemical, the whole solution changed colour.

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Now this isn't particularly remarkable.

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If we mix ink into water, it changes colour.

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But then something happened that made no sense at all.

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The mixture began to go clear again.

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Belousov was astounded.

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Chemicals can mix together and react.

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But they shouldn't be able to go back on themselves,

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to apparently unmix without intervention.

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You can change from a clear mixture to a coloured mixture, fine.

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But surely not back again?

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And it got weirder.

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Belousov's chemicals didn't just spontaneously go into reverse.

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They oscillated.

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They switched back and forth from coloured to clear,

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as if they were being driven by some sort of hidden chemical metronome.

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With meticulous care, he repeated his experiments again and again.

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It was the same every time.

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His mixture would cycle from clear to coloured and back again, repeatedly.

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He'd discovered something that was almost like magic,

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a physical process that seemed to violate the laws of nature.

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'Convinced he'd discovered something of great importance, Belousov

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'wrote up his findings, keen to share his discovery with the wider world.

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'But when he submitted his paper to a leading Russian scientific journal,

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'he received a wholly unexpected and damning response.'

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The editor of the journal told Belousov that his findings in the lab

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were quite simply impossible.

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They contravened the fundamental laws of physics.

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The only explanation was that Belousov had made a mistake

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in his experiment, and the work was simply not fit for publication.

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'The rejection crushed Belousov.

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'Deeply insulted by the suggestion his work had been botched,

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'he abandoned his experiments.

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'Soon he gave up science altogether.'

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The tragic irony was that, divided as they were by the Iron Curtain,

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Belousov never encountered Turing's work.

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For if he had, he would have been completely vindicated.

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It turns out that Belousov's oscillating chemicals,

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far from contravening the laws of physics,

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were actually a real world example

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of precisely the behaviour Turing's equations predicted.

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While the connection might not appear obvious at first sight,

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other scientists showed that if you left a variation

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of Belousov's chemicals, unstirred in a Petri dish,

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instead of simply oscillating, they self-organise into shapes.

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In fact, they go beyond Turing's simple blobs and stripes

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to create stunningly beautiful structures and patterns

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out of nowhere.

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The amazing and very unexpected thing about the BZ reaction

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is that someone had discovered a system

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which essentially reproduces the Turing equations.

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And so, from what looks like a very, very bland solution

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emerge these astonishing patterns of waves and scrolls and spirals.

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Now this is emphatically not abstract science.

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The way Belousov's chemicals move as co-ordinated waves

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is exactly the way our heart cells are co-ordinated as they beat.

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Animal skins and heart beats.

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Self-organisation seems to operate all over the natural world.

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So why were the scientific community in Turing and Belousov's day,

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so uninterested, or even hostile to this astonishing and beautiful idea?

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Well, the reason was all too human.

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Mainstream scientists simply didn't like it.

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To them it seemed to run counter to science,

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and all that it had achieved.

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To change that view would require a truly shocking

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and completely unexpected discovery.

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In essence, by the beginning of the 20th century,

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scientists saw the universe as a giant,

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complicated, mechanical device.

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Kind of a super-sized version of this orrery.

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The idea was that the universe is a huge and intricate machine

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that obeys orderly mathematical rules.

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If you knew the rules of how the machine was configured to start with,

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as you turned the handle, over and over again,

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it would behave in an entirely predictable way.

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Back in the times of Isaac Newton

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when people were discovering the laws that drove the universe,

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they came up with this kind of metaphor of a clockwork universe.

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The universe looked like a machine which had been set going at the

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instant of creation and just followed the rules and ticked along.

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And it was a complicated machine and therefore complicated things happen.

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But once you set it going it would only do one thing,

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and the message that people drew from this

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was that anything describable by mathematical rules

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must actually basically be fairly simple.

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Find the mathematics that describes a system

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and you can then predict how that system will unfold.

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That was the big idea.

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It began with Newton's law of gravity

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which can be used to predict how a planet moves around the sun.

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Scientists soon found many other equations just like it.

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Newtonian physics seemed like the ultimate crystal-ball.

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It held up the tantalising possibility

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that the future could, in principle, be known.

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The more careful your measurements are today,

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the better you can predict what will happen tomorrow.

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But Newtonianism had a dangerous consequence.

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If a nice mathematical system, that worked in a similar way

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to my orrery, did sometimes become unpredictable, scientists assumed

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some malign outside force was causing it. Perhaps dirt had got in?

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Perhaps the cogs were wearing out?

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Or perhaps someone had tampered with it?

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Basically we used to think, if you saw very irregular behaviour

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in some problem you're working on, this must be the result of some sort

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of random outside influences, it couldn't be internally generated.

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It wasn't an intrinsic part of the problem,

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it was some other thing impacting on it.

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Looked at from this point of view,

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the whole idea of self-organisation seemed absurd.

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The idea that patterns of the kind Turing and Belousov had found

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could appear of their own accord,

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without any outside influence, was a complete taboo.

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The only way for self-organisation to be accepted

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was for the domineering Newtonian view to collapse.

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But that seemed very unlikely.

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After all, by the late '60s it had delivered

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all the wonders of the modern age.

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Beautiful, beautiful.

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-Ain't that something?

-Magnificent desolation.

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But then, at the same time as the moon mission,

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a small group of scientists, all ardent Newtonians,

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quite unexpectedly found something wasn't right.

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Not right at all.

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During the second half of the 20th century,

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a devil was found in the detail. A devil that would ultimately

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shatter the Newtonian dream and plunge us literally into chaos.

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Ironically, the events that forced scientists to take self-organisation

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seriously was the discovery of a phenomenon known as chaos.

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Chaos is one of the most over-used words in English, but in science

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it has a very specific meaning. It says that a system that is completely

0:26:370:26:43

described by mathematical equations is more than capable

0:26:430:26:48

of being unpredictable without any outside interference whatsoever.

0:26:480:26:53

There's a widespread misapprehension that chaos is just somehow saying,

0:26:550:26:59

the very familiar fact, that everything's complicated.

0:26:590:27:03

I mean, the nitwit chaoticist in Jurassic Park,

0:27:030:27:06

was under that confusion.

0:27:060:27:08

It's something much simpler and yet much more complicated than that.

0:27:080:27:12

It says, some very, very simple rules or equations,

0:27:120:27:17

with nothing random in them, they're completely determined,

0:27:170:27:21

we know everything about the rule,

0:27:210:27:23

can have outcomes that are entirely unpredictable.

0:27:230:27:29

Chaos is one of the most unwelcome discoveries in science.

0:27:310:27:37

The man who forced the scientific community to confront it

0:27:370:27:41

was an American meteorologist called Edward Lorenz.

0:27:410:27:45

In the early 1960s he tried to find mathematical equations

0:27:450:27:49

that could help predict the weather.

0:27:490:27:52

Like all his contemporaries, he believed that in principle

0:27:550:28:00

the weather system was no different to my orrery.

0:28:000:28:03

A mechanical system that could be described

0:28:030:28:06

and predicted mathematically.

0:28:060:28:09

But he was wrong.

0:28:100:28:11

When Lorenz wrote down what looked like perfectly simple mathematical

0:28:150:28:19

equations to describe the movement of air currents,

0:28:190:28:23

they didn't do what they were supposed to.

0:28:230:28:26

They made no useful predictions whatsoever.

0:28:260:28:30

It was as if the lightest breath of wind one day could make the

0:28:330:28:37

difference a month later between a snowstorm and a perfectly sunny day.

0:28:370:28:44

How can a simple system that works in the regular clockwork manner

0:28:460:28:51

of my orrery become unpredictable?

0:28:510:28:54

It's all down to how it's configured.

0:28:540:28:57

How the gears are connected.

0:28:570:28:59

In essence, under certain circumstances,

0:28:590:29:02

the tiniest difference in the starting positions of the cogs,

0:29:020:29:07

differences that are too small to measure,

0:29:070:29:10

can get bigger and bigger with each turn of the handle.

0:29:100:29:15

With each step in the process the system then moves

0:29:150:29:18

further and further away from where you thought it was going.

0:29:180:29:23

Lorenz captured this radical idea in an influential talk he gave called,

0:29:230:29:28

"Does a flap of a butterfly's wings in Brazil set off a tornado in Texas?"

0:29:280:29:35

It was a powerful and evocative image

0:29:400:29:42

and within months a new phrase had entered our language.

0:29:420:29:46

"The butterfly effect."

0:29:460:29:48

And the butterfly effect, the hallmark of all chaotic systems,

0:29:500:29:54

started turning up everywhere.

0:29:540:29:56

In the early '70s, a young Australian called Robert May,

0:30:000:30:04

was investigating a mathematical equation

0:30:040:30:07

that modelled how animal populations changed over time.

0:30:070:30:12

But here too lurked the dreaded butterfly effect.

0:30:120:30:16

Immeasurably small changes to the rates at which the animals reproduced

0:30:160:30:20

could sometimes have huge consequences

0:30:200:30:23

on their overall population.

0:30:230:30:25

Numbers could go up and down wildly for no obvious reason.

0:30:250:30:31

The idea that a mathematical equation gave you the power

0:30:310:30:35

to predict how a system will behave, was dead.

0:30:350:30:41

In some sense this is the end of the Newtonian dream.

0:30:410:30:44

When I was a graduate student, the belief was,

0:30:440:30:48

as we got more and more computer power,

0:30:480:30:52

we'd be able to solve ever more complicated sets of equations.

0:30:520:30:57

But this said that's not necessarily true.

0:30:570:31:00

You could have the simplest equations you can think of,

0:31:000:31:03

with nothing random in them, you know everything.

0:31:030:31:07

And yet, if they have behaviour

0:31:070:31:12

that gives you chaotic solutions,

0:31:120:31:15

then you can never know the starting point accurately enough.

0:31:150:31:20

Centuries of scientific certainty dissolved in just a few short years.

0:31:230:31:29

The truth of the clockwork universe turned out to be just an illusion.

0:31:290:31:34

Something which had seemed a logical certainty,

0:31:340:31:37

revealed itself merely as an act of faith.

0:31:370:31:40

And what's worse, the truth had been staring us in the face all the time.

0:31:400:31:44

Because chaos is everywhere.

0:31:440:31:47

It seemed unpredictability was hard-wired

0:31:510:31:55

into every aspect of the world we live in.

0:31:550:31:58

The global climate could dramatically change

0:32:000:32:04

in the course of a few short years.

0:32:040:32:07

The stock markets could crash without warning.

0:32:070:32:09

We could be wiped from the face of the planet overnight

0:32:090:32:14

and there is nothing anyone could do about it.

0:32:140:32:18

Unfortunately, I have to tell you that all of this is true.

0:32:230:32:28

And yet to be scared of chaos is pointless.

0:32:280:32:31

It's woven into the basic laws of physics.

0:32:330:32:37

And we really all have to accept it as a fact of life.

0:32:370:32:42

The idea of chaos really did have a big impact over a period of about 20

0:32:420:32:47

or 30 years, because it changed the way everyone thought about

0:32:470:32:50

what they were doing in science.

0:32:500:32:52

It changed it to the point

0:32:520:32:53

that they forgot that they'd ever believed otherwise.

0:32:530:32:56

What chaos did was to show us that the possibilities inherent

0:32:560:33:02

in the simple mathematics are much broader and much more general

0:33:020:33:07

than you might imagine. And so a clockwork universe can

0:33:070:33:12

nonetheless behave in the rich, complex way that we experience.

0:33:120:33:17

The discovery of chaos

0:33:190:33:21

was a real turning point in the history of science.

0:33:210:33:24

As it tore down the Newtonian dream,

0:33:240:33:27

scientists began to look more favourably at Turing and

0:33:270:33:30

Belousov's work on spontaneous pattern formation.

0:33:300:33:34

And perhaps more importantly, as they did so,

0:33:340:33:38

they realised something truly astonishing.

0:33:380:33:41

That there was a very deep and unexpected link.

0:33:410:33:44

A truly cosmic connection

0:33:440:33:47

between nature's strange power to self-organise

0:33:470:33:51

and the chaotic consequences of the butterfly effect.

0:33:510:33:55

Between them, Turing, Belousov, May and Lorenz,

0:33:550:34:00

had all discovered different faces of just one really big idea.

0:34:000:34:05

They discovered that the natural world could be deeply,

0:34:080:34:12

profoundly, unpredictable. But the very same things that make it

0:34:120:34:16

unpredictable also allow it to create pattern and structure.

0:34:160:34:21

Order and chaos.

0:34:210:34:24

It seems the two are more deeply linked

0:34:240:34:26

than we could have ever imagined.

0:34:260:34:28

So how is this possible?

0:34:300:34:32

What do phenomena as apparently different as the patterns in

0:34:320:34:36

Belousov's chemicals and the weather, have in common?

0:34:360:34:40

First, though both systems behave in very complicated ways,

0:34:430:34:47

they are both based on surprisingly simple mathematical rules.

0:34:470:34:52

Secondly, these rules have a unique property.

0:34:560:35:00

A property that's often referred to as coupling, or feedback.

0:35:000:35:05

To show you what I mean, to show you both order and chaos can emerge

0:35:100:35:15

on the their own from a simple system with feedback, I'm going to do

0:35:150:35:20

what seems at first glance like a rather trivial experiment.

0:35:200:35:24

This screen behind me is connected up to the camera that's filming me.

0:35:290:35:35

But the camera in turn is filming me with the screen.

0:35:350:35:39

This creates a loop with multiple copies of me

0:35:390:35:43

appearing on the screen.

0:35:430:35:45

This is a classic example of a feedback loop.

0:35:460:35:51

We get a picture, in a picture, in a picture.

0:35:510:35:55

At first it seems fairly predictable.

0:35:550:35:57

But as we zoom the camera in

0:35:570:36:00

some pretty strange things begin to happen.

0:36:000:36:03

The first thing I notice is that the object I'm filming

0:36:050:36:08

stops bearing much resemblance to what now appears on the screen.

0:36:080:36:13

Small changes in the movement of the match become rapidly amplified

0:36:170:36:22

as they loop round from the camera to the screen and back to the camera.

0:36:220:36:27

So even though I can describe each step in the process mathematically,

0:36:300:36:35

I still have no way of predicting how tiny changes

0:36:350:36:39

in the flickering of the flame will end up in the final image.

0:36:390:36:42

This is the butterfly effect in action.

0:36:460:36:49

But now here comes the spooky bit.

0:36:550:36:58

With just a slight tweak to the system,

0:37:000:37:03

these strange and rather beautiful patterns begin to emerge.

0:37:030:37:09

The same system, one that's based on simple rules with feedback,

0:37:110:37:16

produces chaos and order.

0:37:160:37:19

The same mathematics is generating chaotic behaviour

0:37:270:37:31

and patterned behaviour.

0:37:310:37:34

This changes completely how you think about all of this.

0:37:340:37:38

The idea that there are regularities in nature and then,

0:37:380:37:41

totally separately from them,

0:37:410:37:44

are irregularities, and these are just two different things,

0:37:440:37:47

is just not true.

0:37:470:37:49

These are two ends of a spectrum of behaviour

0:37:490:37:51

which can be generated by the same kind of mathematics.

0:37:510:37:55

And it's the closest thing we have at the moment to the kind of true mathematics of nature.

0:37:550:38:00

I think one of the great take home messages from Turing's work and from

0:38:010:38:06

the discoveries in chemistry and biology and so on, is that

0:38:060:38:10

ultimately, pattern formation seems to be woven, very, very deeply

0:38:100:38:13

into the fabric of the universe. And it actually takes some very simple

0:38:130:38:17

and familiar processes, like diffusion,

0:38:170:38:20

like the rates of chemical reactions,

0:38:200:38:22

and the interplay between them naturally gives rise to pattern.

0:38:220:38:26

So pattern is everywhere, it's just waiting to happen.

0:38:260:38:30

From the '70s on, more and more scientists

0:38:320:38:36

began to embrace the concept that chaos

0:38:360:38:39

and pattern are built into nature's most basic rules.

0:38:390:38:44

But one scientist more than any other brought a fundamentally new

0:38:440:38:48

understanding to this astonishing and often puzzling idea.

0:38:480:38:52

He was a colourful character and something of a maverick.

0:38:540:38:58

His name is Benoit Mandelbrot.

0:38:580:39:01

Benoit Mandelbrot wasn't an ordinary child.

0:39:030:39:07

He skipped the first two years of school

0:39:070:39:09

and as a Jew in war-torn Europe his education was very disrupted.

0:39:090:39:14

He was largely self-taught or tutored by relatives.

0:39:140:39:18

He never formally learned the alphabet,

0:39:180:39:21

or even multiplication beyond the five times table.

0:39:210:39:24

But, like Alan Turing,

0:39:270:39:29

Mandelbrot had a gift for seeing nature's hidden patterns.

0:39:290:39:33

He could see rules where the rest of us see anarchy.

0:39:330:39:37

He could see form and structure,

0:39:370:39:39

where the rest of us just see a shapeless mess.

0:39:390:39:42

And above all, he could see that a strange new kind of mathematics

0:39:420:39:47

underpinned the whole of nature.

0:39:470:39:49

Mandelbrot's lifelong quest was to find a simple mathematical basis

0:39:530:39:57

for the rough and irregular shapes of the real world.

0:39:570:40:02

Mandelbrot was working for IBM

0:40:050:40:07

and he was not in the normal academic environment.

0:40:070:40:10

And he was working on a pile of different problems

0:40:100:40:13

about irregularities in nature, in the financial markets,

0:40:130:40:17

all over the place.

0:40:170:40:18

And I think at some point it dawned on him that everything

0:40:180:40:21

he was doing seen to be really parts of the same big picture.

0:40:210:40:25

And he was a sufficiently original and unusual person that

0:40:250:40:30

he realised that pursuing this big picture was what

0:40:300:40:34

-he really wanted to do.

-To Mandelbrot, it seemed perverse that

0:40:340:40:37

mathematicians had spent centuries contemplating idealised shapes

0:40:370:40:42

like straight lines or perfect circles.

0:40:420:40:45

And yet had no proper or systematic way of describing the rough

0:40:450:40:49

and imperfect shapes that dominate the real world.

0:40:490:40:53

Take this pebble.

0:40:550:40:57

Is it a sphere or a cube?

0:40:580:41:01

Or maybe a bit of both?

0:41:010:41:03

And what about something much bigger? Look at the arch behind me.

0:41:030:41:08

From a distance, it looks like a semi-circle.

0:41:080:41:12

But up close, we see that it's bent and crooked.

0:41:120:41:15

So what shape is it?

0:41:170:41:19

Mandelbrot asked if there's something unique

0:41:230:41:25

that defines all the varied shapes in nature.

0:41:250:41:29

Do the fluffy surfaces of clouds, the branches in trees and rivers,

0:41:290:41:33

the crinkled edges of shorelines, share a common mathematical feature?

0:41:330:41:39

Well, they do.

0:41:390:41:42

Underlying nearly all the shapes in the natural world is a mathematical

0:41:420:41:47

principle known as self-similarity. This describes anything in which the

0:41:470:41:53

same shape is repeated over and over again at smaller and smaller scales.

0:41:530:42:00

A great example are the branches of trees.

0:42:020:42:04

They fork and fork again, repeating that simple process

0:42:040:42:08

over and over at smaller and smaller scales.

0:42:080:42:13

The same branching principle applies in the structure of our lungs

0:42:140:42:19

and the way our blood vessels are distributed throughout our bodies.

0:42:190:42:23

It even describes how rivers split into ever smaller streams.

0:42:250:42:30

And nature can repeat all sorts of shapes in this way.

0:42:300:42:33

Look at this Romanesco broccoli.

0:42:350:42:38

Its overall structure is made up of a series of repeating cones

0:42:380:42:42

at smaller and smaller scales.

0:42:420:42:46

Mandelbrot realised self-similarity

0:42:470:42:50

was the basis of an entirely new kind of geometry.

0:42:500:42:54

And he even gave it a name - fractal.

0:42:540:42:58

Now, that's a pretty neat observation.

0:43:000:43:03

But what if you could represent this property of nature in mathematics?

0:43:030:43:07

What if you could capture its essence to draw a picture?

0:43:070:43:11

What would that picture look like?

0:43:110:43:13

Could you use a simple set of mathematical rules

0:43:130:43:17

to draw an image that didn't look man-made?

0:43:170:43:20

The answer would come from Mandelbrot.

0:43:200:43:23

Who had taken a job at IBM in the late 1950s

0:43:230:43:26

to gain access to its incredible computing power

0:43:260:43:30

and pursue his obsession with the mathematics of nature.

0:43:300:43:35

Armed with a new breed of super-computer,

0:43:350:43:38

he began investigating a rather curious

0:43:380:43:42

and strangely simple-looking equation

0:43:420:43:44

that could be used to draw a very unusual shape.

0:43:440:43:48

What I'm about to show you is one of the most remarkable

0:43:480:43:52

mathematical images ever discovered. Epic doesn't really do it justice.

0:43:520:43:59

This is the Mandelbrot set.

0:43:590:44:03

It's been called the thumbprint of God.

0:44:030:44:07

And when we begin to explore it, you'll understand why.

0:44:070:44:10

Just as with the tree or the broccoli,

0:44:180:44:21

the closer you study this picture, the more detail you see.

0:44:210:44:25

Each shape within the set

0:44:290:44:31

contains an infinite number of smaller shapes.

0:44:310:44:34

Baby Mandelbrots that go on for ever.

0:44:340:44:37

Yet all this complexity stems from just one incredibly simple equation.

0:44:430:44:48

This equation has a very important property.

0:44:490:44:53

It feeds back on itself.

0:44:530:44:55

Like a video loop, each output becomes the input for the next go.

0:44:560:45:02

This feedback means that an incredibly simple mathematical

0:45:060:45:09

equation can produce a picture of infinite complexity.

0:45:090:45:14

The really fascinating thing

0:45:310:45:33

is that the Mandelbrot set isn't just a bizarre mathematical quirk.

0:45:330:45:38

Its fractal property of being similar at all scales

0:45:380:45:42

mirrors a fundamental ordering principle in nature.

0:45:420:45:46

Turing's patterns, Belousov's reaction and Mandelbrot's fractals

0:45:510:45:57

are all signposts pointing to a deep underlying natural principle.

0:45:570:46:02

When we look at complexities in nature, we tend to ask,

0:46:050:46:08

"Where did they come from?"

0:46:080:46:10

There is something in our heads that says

0:46:100:46:13

complexity does not arise out of simplicity.

0:46:130:46:15

It must arise from something complicated. We conserve complexity.

0:46:150:46:19

But what the mathematics in this whole area is telling us

0:46:190:46:22

is that very simple rules naturally give rise to very complex objects.

0:46:220:46:27

And so if you look at the object, it looks complex, and you think about

0:46:270:46:30

the rule that generates it, it's simple.

0:46:300:46:32

So the same thing is both complex and simple

0:46:320:46:35

from two different points of view. And that means we have to rethink

0:46:350:46:38

completely the relation between simplicity and complexity.

0:46:380:46:42

Complex systems can be based on simple rules.

0:46:450:46:50

That's the big revelation.

0:46:500:46:52

And it's an astonishing idea.

0:46:520:46:55

It seems to apply all over our world.

0:46:560:46:59

Look at a flock of birds. Each bird obeys very simple rules.

0:47:100:47:15

But the flock as a whole does incredibly complicated things.

0:47:150:47:19

Avoiding obstacles, navigating the planet with no single leader

0:47:190:47:25

or even conscious plan. But amazing though this flock's behaviour is,

0:47:250:47:31

it's impossible to predict how it will behave.

0:47:310:47:34

It never repeats exactly what it does,

0:47:360:47:39

even in seemingly identical circumstances.

0:47:390:47:42

It's just like the Belousov reaction.

0:47:450:47:48

Each time you run it, the patterns produced are slightly different.

0:47:480:47:53

They may look similar, but they are never identical.

0:47:530:47:56

The same is true of video loops and sand dunes.

0:47:560:48:01

We know they'll produce a certain kind of pattern,

0:48:010:48:05

but we can't predict the exact shapes.

0:48:050:48:08

The big question is, can nature's ability to turn simplicity

0:48:120:48:17

into complexity in this mysterious and unpredictable way

0:48:170:48:21

explain why life exists?

0:48:210:48:24

Can it explain how a universe full of simple dust

0:48:260:48:29

can turn into human beings?

0:48:290:48:32

How inanimate matter can spawn intelligence?

0:48:330:48:37

At first, you might think that this is beyond the remit of science.

0:48:390:48:43

If nature's rules are really unpredictable,

0:48:430:48:46

should we simply give up?

0:48:460:48:48

Absolutely not. In fact, quite the opposite.

0:48:480:48:51

Fittingly, the answer to this problem lies in the natural world.

0:48:540:48:58

All around us, there exists a process that engineers

0:48:580:49:03

these unpredictable complex systems

0:49:030:49:05

and hones them to perform almost miraculous tasks.

0:49:050:49:10

The process is called evolution.

0:49:120:49:15

Evolution has built on these patterns.

0:49:170:49:20

It's taken them as the raw ingredients.

0:49:200:49:22

It's combined them together in various ways,

0:49:220:49:26

experimented to see what works and what doesn't,

0:49:260:49:29

kept the things that do work and then built on that.

0:49:290:49:34

It's a completely unconscious process,

0:49:340:49:36

but basically that's what's happening.

0:49:360:49:38

Everywhere you look, you can see evolution

0:49:380:49:41

using nature's self-organising patterns.

0:49:410:49:45

Our hearts use Belousov-type reactions to regulate how they beat.

0:49:450:49:50

Our blood vessels are organised like fractals.

0:49:500:49:54

Even our brain cells interact according to simple rules.

0:49:540:50:00

The way evolution refines and enriches complex systems

0:50:000:50:05

is one of the most intriguing ideas in recent science.

0:50:050:50:09

My interest in my PhD research in complex systems was to see

0:50:120:50:15

how complex systems interact with evolution.

0:50:150:50:18

So, on the one hand you have systems that almost organise themselves

0:50:180:50:22

as complex systems, so they exhibit order that you wouldn't expect,

0:50:220:50:26

but on the other hand, you still have to have evolution interact with

0:50:260:50:30

that to create something that is truly adapted to the environment.

0:50:300:50:33

Evolution's mindless, yet creative, power to develop

0:50:330:50:38

and shape complex systems is indeed incredible.

0:50:380:50:42

But it operates on a cosmic timescale.

0:50:430:50:46

From the first life on Earth, to us walking about,

0:50:480:50:51

took in the region of 3.5 billion years.

0:50:510:50:55

But we now have in our hands

0:50:560:50:59

a device that can mimic this process on a much shorter timescale.

0:50:590:51:04

What is the invention I'm talking about?

0:51:040:51:08

Well, there's a good chance you've been sitting in front of one all day.

0:51:080:51:12

It is, of course, the computer.

0:51:130:51:16

Computers today can churn through trillions of calculations per second.

0:51:210:51:27

And that gives them the power to do something very special.

0:51:270:51:30

They can simulate evolution.

0:51:300:51:34

More precisely, computers can use the principles of evolution to shape

0:51:350:51:40

and refine their own programs, in the same way the natural world

0:51:400:51:44

uses evolution to shape and refine living organisms.

0:51:440:51:49

And today, computer scientists find that this evolved software

0:51:490:51:55

can solve problems that would be beyond the smartest of humans.

0:51:550:52:00

One thing that we found particularly in our original research is how

0:52:000:52:04

powerful evolution is as a system, as an algorithm, to create something

0:52:040:52:08

that is very complex and to create something that is very adaptive.

0:52:080:52:12

Torsten and his team's goal was nothing less

0:52:120:52:16

than to use computerised evolution

0:52:160:52:18

to create a virtual brain that would control a virtual body.

0:52:180:52:23

To begin with, they created 100 random brains.

0:52:240:52:29

As you can see, they weren't up to much.

0:52:290:52:31

Evolution then took over.

0:52:330:52:35

The computer selected the brains that were slightly better

0:52:350:52:40

at moving their bodies and got them to breed.

0:52:400:52:43

The algorithm then takes those individuals that do the best

0:52:450:52:49

and it allows them to create offspring.

0:52:490:52:51

The best movers of the next generation

0:52:530:52:56

were then bred together and so on and on.

0:52:560:52:59

Amazingly, after just 10 generations,

0:52:590:53:03

although they're still a bit unsteady, the figures could walk.

0:53:030:53:08

Eventually, miraculously, you actually end up

0:53:090:53:11

with something that works. The slightly scary thing

0:53:110:53:14

is you don't know why it works and how it works.

0:53:140:53:17

You look at that brain and you have no idea actually what's going on

0:53:170:53:20

because evolution has optimised it automatically.

0:53:200:53:23

In 20 generations, evolution had turned this...

0:53:260:53:31

..into this.

0:53:310:53:33

But these evolved computer beings soon went far beyond just walking.

0:53:360:53:41

They evolved to do things

0:53:440:53:46

that really are impossible to program conventionally.

0:53:460:53:49

They react realistically to unexpected events.

0:53:530:53:57

Like being hit or falling over.

0:53:570:54:00

Even though we programmed these algorithms, what actually happens

0:54:030:54:07

when it unfolds live, we don't control any more

0:54:070:54:10

and things happen that we never expected.

0:54:100:54:12

And it's quite a funny feeling

0:54:120:54:14

that you create these algorithms but then they do their own thing.

0:54:140:54:18

An unthinking process of evolutionary trial and error

0:54:240:54:28

has created these virtual creatures that can move and react in real time.

0:54:280:54:34

What we're seeing here is fantastic experimental evidence

0:54:390:54:43

for the creative power of systems based on simple rules.

0:54:430:54:47

Watching how computers can unconsciously evolve programs

0:54:570:55:02

to do things that no human could consciously program

0:55:020:55:05

is a fantastic example of the power of self-organisation.

0:55:050:55:11

It demonstrates that evolution is itself

0:55:110:55:14

just like the other systems we've encountered.

0:55:140:55:18

One based on simple rules and feedback.

0:55:180:55:21

From which complexity spontaneously emerges.

0:55:210:55:25

Think about it. The simple rule is that the organism

0:55:260:55:30

must replicate with a few random mutations now and again.

0:55:300:55:36

The feedback comes from the environment

0:55:360:55:39

which favours the mutations that are best suited to it.

0:55:390:55:43

The result is ever-increasing complexity,

0:55:430:55:47

produced without thought or design.

0:55:470:55:51

The interesting thing is that one can move up

0:55:520:55:55

to a higher level of organisation. Once you have organisms

0:55:550:55:58

that actually have patterns on them, these can be selected for

0:55:580:56:02

or selected against by processes which are essentially feedbacks.

0:56:020:56:07

And so evolution itself, the whole Darwinian scheme,

0:56:070:56:11

is, in a sense, Turing again

0:56:110:56:14

with feedbacks happening through different processes.

0:56:140:56:17

And that's the essence of this story.

0:56:190:56:21

Unthinking, simple rules have the power to create

0:56:210:56:26

amazingly complex systems without any conscious thought.

0:56:260:56:30

In that sense, these computer beings are self-organised systems,

0:56:310:56:36

just like the one Belousov observed happening in his chemicals.

0:56:360:56:41

Just like the ones in sand dunes and the Mandelbrot sets,

0:56:420:56:46

in our lungs, our hearts, in weather

0:56:460:56:51

and in the geography of our planet.

0:56:510:56:53

Design does not need an active, interfering designer.

0:56:530:56:58

It's an inherent part of the universe.

0:56:580:57:02

One of the things that makes people so uncomfortable about this idea of,

0:57:060:57:10

if you will, spontaneous pattern formation, is that somehow or other

0:57:100:57:15

you don't need a creator. But perhaps a really clever designer,

0:57:150:57:19

what he would do, is to kind of treat the universe

0:57:190:57:22

like a giant simulation, where you set some initial condition

0:57:220:57:26

and just let the whole thing spontaneously happen

0:57:260:57:30

in all of its wonder and all of its beauty.

0:57:300:57:32

The mathematics of pattern formation shows that the same kind of pattern

0:57:350:57:39

can show up in an enormous range of different physical,

0:57:390:57:42

chemical, biological systems. Somewhere deep down inside,

0:57:420:57:46

it's happening for the same mathematical reason.

0:57:460:57:49

Implicit in those facts are these beautiful patterns

0:57:490:57:53

that we see everywhere.

0:57:530:57:55

This, I think, is a mind-blowing thought.

0:57:550:57:58

So, what is the ultimate lesson we can take from all this?

0:58:070:58:12

Well, it's that all the complexity of the universe,

0:58:120:58:15

all its infinite richness,

0:58:150:58:18

emerges from mindless simple rules, repeated over and over again.

0:58:180:58:23

But remember, powerful though this process is,

0:58:230:58:27

it's also inherently unpredictable.

0:58:270:58:30

So although I can confidently tell you that the future will be amazing,

0:58:300:58:36

I can also say, with scientific certainty,

0:58:360:58:40

that I have no idea what it holds.

0:58:400:58:43

Subtitles by Red Bee Media Ltd

0:59:040:59:07

E-mail [email protected]

0:59:070:59:10

Chaos theory has a bad name, conjuring up images of unpredictable weather, economic crashes and science gone wrong. But there is a fascinating and hidden side to Chaos, one that scientists are only now beginning to understand.

It turns out that chaos theory answers a question that mankind has asked for millennia - how did we get here?

In this documentary, Professor Jim Al-Khalili sets out to uncover one of the great mysteries of science - how does a universe that starts off as dust end up with intelligent life? How does order emerge from disorder?

It's a mindbending, counterintuitive and for many people a deeply troubling idea. But Professor Al-Khalili reveals the science behind much of beauty and structure in the natural world and discovers that far from it being magic or an act of God, it is in fact an intrinsic part of the laws of physics. Amazingly, it turns out that the mathematics of chaos can explain how and why the universe creates exquisite order and pattern.

And the best thing is that one doesn't need to be a scientist to understand it. The natural world is full of awe-inspiring examples of the way nature transforms simplicity into complexity. From trees to clouds to humans - after watching this film you'll never be able to look at the world in the same way again.


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