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00:11This is a film about one very simple question.
00:16How did we get here?
00:25These are the elements and compounds from which all humans are made.
00:30They're incredibly, almost embarrassingly common.
00:33In fact, almost 99% of the human body is a mixture of air, water, coal and chalk,
00:40with traces of other slightly more exotic elements like iron, zinc, phosphorus and sulphur.
00:48In fact, I've estimated that the elements which make up the average human cost at most a few pounds.
00:56But somehow, trillions of these very ordinary atoms conspire miraculously
01:02to organise themselves into thinking, breathing, living human beings.
01:08How the wonders of creation are assembled from such simple building blocks
01:13is surely the most intriguing question we can ask.
01:17You may think that answering it is beyond the realm of science.
01:22But that's changing.
01:24For the first time, I believe, science has pushed past religion and philosophy
01:30in daring to tackle this most fundamental of questions.
01:39This film is the story of a series of bizarre and interconnected discoveries
01:44that revealed a hidden face of nature.
01:49that woven into its simplest and most basic laws
01:53is a power to be unpredictable.
01:57It's about how inanimate matter with no purpose or design
02:02can spontaneously create exquisite beauty.
02:07It's about how the same laws that make the universe chaotic and unpredictable
02:12can turn simple dust into human beings.
02:18It's about the discovery that there is a strange and unexpected relationship
02:23between order and chaos.
02:59The natural world really is one great, blooming, buzzing confusion.
03:06It's a mess of quirky shapes and blotches.
03:09What patterns there are are never quite regular
03:12and never seem to repeat exactly.
03:19The idea that all this mayhem, all this chaos, is underpinned,
03:24indeed determined, by mathematical rules
03:27and that we can work out what those rules might be
03:30runs counter to our most dearly held intuitions.
03:40So, not surprisingly, the first man to really take on the momentous task
03:46of unravelling nature's mysterious mathematics
03:49had a very special and unusual mind.
03:53He was both a great scientist and a tragic hero.
03:58He was born in 1912 in London.
04:00His name was Alan Turing.
04:07Alan Turing was a remarkable man,
04:09one of the greatest mathematicians who ever lived.
04:12He discovered many of the fundamental ideas
04:14that underpin the modern computer.
04:17Also, during the Second World War, he worked here at Bletchley Park,
04:21just outside today's Milton Keynes,
04:23in what was then a secret government project called Station X,
04:27which was set up to crack the German military codes.
04:33The Station X codebreakers proved highly effective
04:37and Turing's contribution was crucial.
04:39The work he personally did to crack German naval codes
04:44saved thousands of Allied lives and was a turning point in the war.
04:48But codebreaking was just one aspect of Turing's genius,
04:54just one part of his uncanny ability to see patterns
04:57that are hidden from the rest of us.
05:00For Turing, the natural world offered up the ultimate codes.
05:03And over the course of his life, he'd come tantalisingly close to cracking them.
05:09Turing was a very original person.
05:13And he had realised that there was this possibility
05:17that simple mathematical equations might describe aspects of the biological world.
05:22And no-one had thought of that before.
05:26Of all nature's mysteries, the one that fascinated Turing most
05:30was the idea that there might be a mathematical basis to human intelligence.
05:37Turing had very personal reasons for believing in this.
05:42It was the death of this young man, Christopher Morecambe,
05:45who Alan Turing, well, he was gay,
05:47and it had been a great emotional thing of his life at that point.
05:52Christopher Morecambe suddenly died.
05:54And Alan Turing was very...
05:56Obviously, he was very emotionally disturbed by this,
05:59but you can see that he wanted to put this in an intellectual context,
06:03a scientific context.
06:05And the question he wanted to put into context was,
06:07what happens to the mind? What happens to it? What is it?
06:14Turing became convinced that mathematics could be used to describe biological systems,
06:20and ultimately, intelligence.
06:24This fascination would give rise to the modern computer,
06:27and later in Turing's life, an even more radical idea.
06:32The idea that a simple mathematical description
06:35could be given for a mysterious process
06:38that takes place in an embryo.
06:44The process is called morphogenesis, and it's very puzzling.
06:53At first, all the cells in the embryo are identical.
06:59Then, as this footage of a fish embryo shows,
07:02the cells begin to clump together,
07:05and also become different from each other.
07:09How does this happen?
07:11With no thought, no central coordination.
07:16How do cells that start off identical know to become, say, skin,
07:23while others become part of an eye?
07:31Morphogenesis is a spectacular example of something called self-organisation.
07:38And before Turing, no-one had a clue how it worked.
07:48Then, in 1952, Turing published this,
07:52his paper with the world's first mathematical explanation for morphogenesis.
07:58The sheer chutzpah of this paper was staggering.
08:05In it, Turing used a mathematical equation
08:08of the kind normally seen in papers on astronomy or atomic physics
08:13to describe a living process.
08:17No-one had done anything like this.
08:23Crucially, Turing's equations did, for the first time,
08:27describe how a biological system could self-organise.
08:32They showed that something smooth and featureless can develop features.
08:38One of the astonishing things about Turing's work
08:41was that, starting with a description of really very simple processes,
08:46that were governed by very simple equations,
08:49by putting these together, suddenly, complexity emerged.
08:53The pattern suddenly came out as a natural consequence.
08:56And I think, in many ways, this was very, very unexpected.
09:04In essence, Turing's equations described something quite familiar,
09:09but which no-one had thought of in the context of biology before.
09:19Think of the way a steady wind blowing across sand creates all kinds of shapes.
09:26The grains self-organise into ripples, waves and dunes.
09:33This happens even though the grains are virtually identical
09:36and have no knowledge of the shapes they become part of.
09:44Turing argued that, in a very similar way,
09:47chemicals seeping across an embryo might cause its cells
09:51to self-organise into different organs.
10:01These are Turing's own very rough scribblings of how this might work.
10:13They show how a completely featureless chemical soup
10:16can evolve these strange blobs and patches.
10:23In his paper, he refined his sketches
10:26to show how his equations could spontaneously create markings
10:30similar to those on the skins of animals.
10:37Turing went around showing people pictures, saying,
10:39doesn't this look a bit like the patterns on a cow?
10:41And everyone sort of went, what is this man on about?
10:44But actually, he knew what he was doing.
10:46Because, yeah, indeed, they did look like the patterns on a cow,
10:49and that's one of the reasons why cows have this sort of dappled pattern
10:52or whatever.
10:54So, an area where mathematics had never been used before,
10:58pattern formation in biology, animal markings.
11:02Suddenly, the door was opened,
11:04and we could see that mathematics might be useful in that sort of area.
11:10So, even though Turing's exact equations are not the full story,
11:14they are the first piece of mathematical work
11:19that showed there was any possibility of doing this kind of thing.
11:27Of course, we now know that morphogenesis is much more complicated
11:32than the process Turing's equations describe.
11:36In fact, the precise mechanism of how DNA molecules in our cells
11:41interact with other chemicals is still fiercely debated by scientists.
11:47But Turing's idea that whatever is going on
11:50is deep down a simple mathematical process was truly revolutionary.
11:57Well, I think Alan Turing's paper is probably the cornerstone
12:02in the whole idea of how morphogenesis works.
12:05What it does is it provides us with a mechanism,
12:08something that Darwin didn't for how pattern emerges.
12:11Darwin, of course, tells us that once you have a pattern
12:14and it is coded for in the genes,
12:17that may or may not be passed on depending on circumstances.
12:20But what it doesn't do is explain where that pattern comes from in the first place.
12:24That's the real mystery.
12:26And so what Turing had done was to subtly provide an accessible chemical mechanism for doing this.
12:33That was amazing.
12:37Turing was onto a really big, bold idea.
12:42But sadly, we can only speculate how his extraordinary mind would have developed his idea.
12:50Because shortly after his groundbreaking paper on morphogenesis,
12:54a dreadful and completely avoidable tragedy destroyed his life.
13:04After his work breaking codes at Bleshly Park,
13:08you might well have assumed that Turing would have been honoured by the country he did so much to protect.
13:14This couldn't be further from the truth.
13:17What happened to him after the war was a great tragedy,
13:20and one of the most shameful episodes in the history of British science.
13:26The same year Turing published his morphogenesis paper,
13:30he had a brief affair with a man called Arnold Murray.
13:34The affair went sour and Murray was involved in a burglary at Turing's house.
13:39But when Turing reported this to the police, they arrested him as well as Murray.
13:48In court, the prosecution then argued that Turing, with his university education,
13:54had led Murray astray.
13:58He was convicted of gross indecency.
14:02The judge then offered Turing a dreadful choice.
14:08He could either go to prison or sign up to a regime of female hormone injections
14:13to cure him of his homosexuality.
14:16He chose the latter, and it was to send him into a spiral of depression.
14:21On the 8th of June, 1954, Turing's body was found by his cleaner.
14:27He died the day before by taking a bite from an apple he'd laced with cyanide,
14:31ending his own life.
14:36Alan Turing died aged just 41.
14:40The loss to science is incalculable.
14:45Turing would never know that his ideas would inspire an entirely new mathematical approach to biology,
14:51and that scientists would find equations like his really do explain many of the shapes
14:57that appear on living organisms.
15:02Looking back, we now know Turing had really grasped the idea
15:07that the wonders of creation are derived from the simplest of rules.
15:12He had, perhaps unexpectedly, taken the first step to a new kind of science.
15:35The next step in this story was just as unexpected, and in many ways just as tragic as Turing's.
15:46In the early 1950s, around the time of Turing's seminal paper on morphogenesis,
15:53a brilliant Russian chemist by the name of Boris Belusov
15:56was beginning his own investigations into the chemistry of nature.
16:00Deep behind the Iron Curtain, in a lab at the Soviet Ministry of Health,
16:06he was beginning to investigate the way our bodies extract energy from sugars.
16:14Just like Turing, Belusov was working on a personal project,
16:19having just finished a distinguished career as a scientist in the military.
16:24In his lab, Belusov had formulated a mixture of chemicals
16:28to mimic one part of the process of glucose absorption in the body.
16:33The mix of chemicals sat on the lab bench in front of him,
16:37clear and colourless while being shaken.
16:40As he mixed in the final chemical, the whole solution changed colour.
16:46Now, this isn't particularly remarkable.
16:49If we mix ink into water, it changes colour.
16:52But then something happened that made no sense at all.
16:57The mixture began to go clear again.
17:07Belusov was astounded.
17:09Chemicals can mix together and react,
17:12but they shouldn't be able to go back on themselves
17:14to apparently unmix without intervention.
17:18You can change from a clear mixture to a coloured mixture, fine,
17:23but surely not back again.
17:27And it got weirder.
17:30Belusov's chemicals didn't just spontaneously go into reverse.
17:34They oscillated.
17:36They switched back and forth from coloured to clear,
17:39as if they were being driven by some sort of hidden chemical metronome.
17:46With meticulous care, Belusov repeated his experiments again and again.
17:52It was the same every time.
17:54His mixture would cycle from clear to coloured and back again, repeatedly.
18:00He discovered something that was almost like magic,
18:03a physical process that seemed to violate the laws of nature.
18:10Convinced he'd discovered something of great importance,
18:13Belusov wrote up his findings, keen to share his discovery with the wider world.
18:19But when he submitted his paper to a leading Russian scientific journal,
18:23he received a wholly unexpected and damning response.
18:28The editor of the journal told Belusov that his findings in the lab
18:33were quite simply impossible.
18:35They contravened the fundamental laws of physics.
18:38The only explanation was that Belusov had made a mistake in his experiment.
18:44And the work was simply not fit for publication.
18:52The rejection crushed Belusov.
18:55Deeply insulted by the suggestion his work had been botched,
18:59he abandoned his experiments.
19:02Soon he gave up science altogether.
19:06The tragic irony was that divided as they were by the Iron Curtain,
19:11Belusov never encountered Turing's work.
19:14For if he had, he would have been completely vindicated.
19:20It turns out that Belusov's oscillating chemicals, far from contravening the laws of physics,
19:26were actually a real-world example of precisely the behaviour Turing's equations predicted.
19:44While the connection might not appear obvious at first sight,
19:48other scientists showed that if you left a variation of Belusov's chemicals unstirred in a petri dish,
19:56instead of simply oscillating, they self-organise into shapes.
20:00In fact, they go beyond Turing's simple blobs and stripes,
20:05to create stunningly beautiful structures and patterns.
20:09Out of nowhere.
20:21The amazing and very unexpected thing about the BZ reaction
20:25is that someone had discovered a system which essentially reproduces the Turing equations.
20:31And so, from what looks like a very, very bland solution,
20:35emerge these astonishing patterns of waves and scrolls and spirals.
20:45Now, this is emphatically not abstract science.
20:48The way Belusov's chemicals move as coordinated waves is exactly the way our heart cells are coordinated as they beat.
21:01Animal skins and heartbeats.
21:04Self-organisation seems to operate all over the natural world.
21:14So why were the scientific community in Turing and Belusov's day so uninterested,
21:21or even hostile, to this astonishing and beautiful idea?
21:29Well, the reason was all too human.
21:34Mainstream scientists simply didn't like it.
21:38To them, it seemed to run counter to science and all that it had achieved.
21:51To change that view would require a truly shocking and completely unexpected discovery.
22:02In essence, by the beginning of the 20th century,
22:06scientists saw the universe as a giant, complicated, mechanical device.
22:12Kind of a supersized version of this orrery.
22:20The idea was that the universe is a huge and intricate machine
22:25that obeys orderly mathematical rules.
22:29If you knew the rules of how the machine was configured to start with,
22:33as you turn the handle over and over again,
22:36it would behave in an entirely predictable way.
22:42Back in the times of Isaac Newton, when people were discovering the laws that drove the universe,
22:48they came up with this kind of metaphor of a clockwork universe.
22:51The universe looked like a machine which had been set going at the instant of creation
22:56and just followed the rules and ticked along,
22:59and it was a complicated machine, and therefore complicated things happened.
23:03But once you set it going, it would only do one thing.
23:08And the message that people drew from this was that anything describable by mathematical rules
23:14must actually basically be fairly simple.
23:21Find the mathematics that describes a system, and you can then predict how that system will unfold.
23:28That was the big idea.
23:30It began with Newton's law of gravity, which can be used to predict how a planet moves around the sun.
23:38Scientists soon found many other equations just like it.
23:44Newtonian physics seemed like the ultimate crystal ball.
23:48It held up the tantalising possibility that the future could in principle be known.
23:54The more careful your measurements are today, the better you can predict what will happen tomorrow.
24:05But Newtonianism had a dangerous consequence.
24:09If a nice mathematical system that worked in a similar way to my orrery did sometimes become unpredictable,
24:17scientists assumed some malign outside force was causing it.
24:22Perhaps dirt had got in, perhaps the cogs were wearing out,
24:26or perhaps someone had tampered with it.
24:29Basically, we used to think if you saw very irregular behaviour in some problem you were working on,
24:36this must be the result of some sort of random outside influences.
24:40It couldn't be internally generated.
24:43It wasn't an intrinsic part of the problem.
24:45It was some other thing impacting on it.
24:51Looked at from this point of view, the whole idea of self-organisation
24:56seemed absurd.
24:57The idea that patterns of the kind Turing and Belusov had found
25:01could appear of their own accord without any outside influence
25:06was a complete taboo.
25:08Six, five, four, three...
25:12The only way for self-organisation to be accepted
25:16was for the domineering Newtonian view to collapse.
25:20But that seemed very unlikely.
25:25After all, by the late 60s, it had delivered all the wonders of the modern age.
25:31Terrible, dear.
25:32Is it something?
25:34Magnificent desolation.
25:39But then, at the same time as the Moon mission,
25:42a small group of scientists, all ardent Newtonians,
25:47quite unexpectedly found something wasn't right.
25:52Not right at all.
25:58During the second half of the 20th century,
26:01a devil was found in the detail.
26:03A devil that would ultimately shatter the Newtonian dream
26:07and plunge us literally into chaos.
26:20Ironically, the event that forced scientists to take self-organisation seriously
26:26was the discovery of a phenomenon known as chaos.
26:32Chaos is one of the most overused words in English,
26:35but in science, it has a very specific meaning.
26:40It says that a system that is completely described by mathematical equations
26:45is more than capable of being unpredictable
26:49without any outside interference whatsoever.
26:54There's a widespread misapprehension that chaos is just somehow saying
26:59the very familiar fact that everything's complicated.
27:02I mean, the nitwit chaoticist in Jurassic Park was under that confusion.
27:07It's something much simpler and yet much more complicated than that.
27:12It says some very, very simple rules or equations
27:17with nothing random in them, completely determined.
27:21We know everything about the rule,
27:23can have outcomes that are entirely unpredictable.
27:30Chaos is one of the most unwelcome discoveries in science.
27:36The man who forced the scientific community to confront it
27:41was an American meteorologist called Edward Lorenz.
27:45In the early 1960s, he tried to find mathematical equations
27:49that could help predict the weather.
27:55Like all his contemporaries, he believed that, in principle,
27:59the weather system was no different to my orrery,
28:03a mechanical system that could be described and predicted mathematically.
28:09But he was wrong.
28:15When Lorenz wrote down what looked like perfectly simple mathematical equations
28:20to describe the movement of air currents,
28:23they didn't do what they were supposed to.
28:26They made no useful predictions whatsoever.
28:32It was as if the lightest breath of wind one day could make the difference a month later
28:38between a snowstorm and a perfectly sunny day.
28:45How can a simple system that works in the regular clockwork manner of my orrery become unpredictable?
28:54It's all down to how it's configured, how the gears are connected.
28:58In essence, under certain circumstances, the tiniest difference in the starting positions of the cogs,
29:06differences that are too small to measure, can get bigger and bigger with each turn of the handle.
29:14With each step in the process, the system then moves further and further away from where you thought it was
29:21going.
29:23Lorenz captured this radical idea in an influential talk he gave,
29:28called Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?
29:39It was a powerful and evocative image and within months a new phrase had entered our language,
29:46the butterfly effect.
29:49And the butterfly effect, the hallmark of all chaotic systems, started turning up everywhere.
30:00In the early 70s, a young Australian called Robert May was investigating a mathematical equation
30:07that modelled how animal populations changed over time.
30:11But here too lurked the dreaded butterfly effect.
30:16Immeasurably small changes to the rate at which the animals reproduced
30:20could sometimes have huge consequences on their overall population.
30:25Numbers could go up and down wildly for no obvious reason.
30:30The idea that a mathematical equation gave you the power to predict how a system will behave was dead.
30:40In some sense, this is the end of the Newtonian dream.
30:44When I was a graduate student, the belief was, as we got more and more computer power,
30:52we'd be able to solve ever more complicated sets of equations.
30:57But this said, that's not necessarily true.
31:00You could have the simplest equations you can think of, with nothing random in them.
31:05You know everything.
31:07And yet, if they have behaviour that gives you chaotic solutions,
31:15then you can never know the starting point accurately enough.
31:23Centuries of scientific certainty dissolved in just a few short years.
31:29The truth of the clockwork universe turned out to be just an illusion.
31:33Something which had seemed a logical certainty revealed itself merely as an act of faith.
31:40And what's worse, the truth had been staring us in the face all the time,
31:44because chaos is everywhere.
31:51It seemed unpredictability was hard-wired into every aspect of the world we live in.
32:00The global climate could dramatically change in the course of a few short years.
32:06The stock market could crash without warning.
32:10We could be wiped from the face of the planet overnight,
32:13and there is nothing anyone could do about it.
32:23Unfortunately, I have to tell you that all of this is true.
32:28And yet, to be scared of chaos is pointless.
32:32It's woven into the basic laws of physics.
32:37And we really all have to accept it as a fact of life.
32:41The idea of chaos really did have a big impact over a period of about 20 or 30 years,
32:47because it changed the way everyone thought about what they were doing in science.
32:52It changed it to the point that they forgot that they'd ever believed otherwise.
32:55What chaos did was to show us that the possibilities inherent in the simple mathematics are much broader and much
33:06more general than you might imagine.
33:08And so a clockwork universe can nonetheless behave in the rich, complex way that we experience.
33:18The discovery of chaos was a real turning point in the history of science.
33:23As it tore down the Newtonian dream, scientists began to look more favourably at Turing and Belusov's work on spontaneous
33:32pattern formation.
33:33And perhaps more importantly, as they did so, they realised something truly astonishing.
33:40That there was a very deep and unexpected link, a truly cosmic connection between nature's strange power to self-organise
33:50and the chaotic consequences of the butterfly effect.
33:54Between them, Turing, Belusov, May and Lorenz had all discovered different faces of just one really big idea.
34:07They discovered that the natural world could be deeply, profoundly unpredictable.
34:14But the very same things that make it unpredictable also allow it to create pattern and structure.
34:21Order and chaos.
34:23It seems the two are more deeply linked than we could have ever imagined.
34:29So how is this possible?
34:32What do phenomena as apparently different as the patterns in Belusov's chemicals and the weather have in common?
34:42First, though both systems behave in very complicated ways, they are both based on surprisingly simple mathematical rules.
34:56Secondly, these rules have a unique property, a property that's often referred to as coupling or feedback.
35:10To show you what I mean, to show you both order and chaos can emerge on their own from a
35:16simple system with feedback,
35:18I'm going to do what seems at first glance like a rather trivial experiment.
35:29This screen behind me is connected up to the camera that's filming me.
35:34But the camera in turn is filming me with the screen.
35:38This creates a loop with multiple copies of me appearing on the screen.
35:47This is a classic example of a feedback loop.
35:50We get a picture in a picture in a picture.
35:54At first it seems fairly predictable.
35:57But as we zoom the camera in, some pretty strange things begin to happen.
36:04The first thing I notice is that the object I'm filming stops bearing much resemblance to what now appears on
36:11the screen.
36:17Small changes in the movement of the match become rapidly amplified as they loop round from the camera to the
36:24screen and back to the camera.
36:30So even though I can describe each step in the process mathematically, I still have no way of predicting how
36:37tiny changes in the flickering of the flame will end up in the final image.
36:46This is the butterfly effect in action.
36:55But now here comes the spooky bit.
37:00This is the butterfly effect.
37:01With just a slight tweak to the system, these strange and rather beautiful patterns begin to emerge.
37:10The same system, one that's based on simple rules with feedback, produces chaos and order.
37:26The same mathematics is generating chaotic behaviour and pattern behaviour.
37:33This changes completely how you think about all of this.
37:37The idea that there are regularities in nature and then totally separately from them are irregularities and these are just
37:45two different things.
37:47It's just not true.
37:48These are two ends of a spectrum of behaviour which can be generated by the same kind of mathematics.
37:54And it's the closest thing we have at the moment to the kind of true mathematics of nature.
38:01I think one of the great take home messages from Turing's work and from the discoveries in chemistry and biology
38:08and so on,
38:09is that ultimately pattern formation seems to be woven very, very deeply into the fabric of the universe.
38:15And it actually takes some very, very simple and familiar processes like diffusion, like the rates of chemical reactions,
38:21and the interplay between them naturally gives rise to pattern.
38:26So pattern is everywhere. It's just waiting to happen.
38:32From the 70s on, more and more scientists began to embrace the concept that chaos and pattern are built into
38:40nature's most basic rules.
38:43But one scientist more than any other brought a fundamentally new understanding to this astonishing and often puzzling idea.
38:53He was a colourful character and something of a maverick.
38:57His name is Benoit Mandelbrot.
39:03Benoit Mandelbrot wasn't an ordinary child.
39:06He skipped the first two years of school.
39:09And as a Jew in war-torn Europe, his education was very disrupted.
39:14He was largely self-taught or tutored by relatives.
39:17He never formally learned the alphabet or even multiplication beyond the five times table.
39:26But like Alan Turing, Mandelbrot had a gift for seeing nature's hidden patterns.
39:32He could see rules where the rest of us see anarchy.
39:36He could see form and structure, where the rest of us just see a shapeless mess.
39:42And above all, he could see that a strange new kind of mathematics underpinned the whole of nature.
39:52Mandelbrot's lifelong quest was to find a simple mathematical basis for the rough and irregular shapes of the real world.
40:04Mandelbrot was working for IBM and he was not in the normal academic environment.
40:10And he was working on a whole pile of different problems about irregularities in nature, in the financial markets, all
40:17over the place.
40:18And I think at some point it dawned on him that everything he was doing seemed to be really parts
40:23of the same big picture.
40:25And he was a sufficiently original and unusual person that he realised that pursuing this big picture was what he
40:32really wanted to do.
40:35To Mandelbrot, it seemed perverse that mathematicians have spent centuries contemplating idealised shapes like straight lines or perfect circles,
40:44and yet had no proper or systematic way of describing the rough and imperfect shapes that dominate the real world.
40:54Take this pebble.
40:57Is it a sphere or a cube? Or maybe a bit of both?
41:03And what about something much bigger?
41:06Look at the arch behind me.
41:08From a distance, it looks like a semi-circle.
41:11But up close, we see that it's bent and crooked.
41:16So what shape is it?
41:23Mandelbrot asked if there's something unique that defines all the varied shapes in nature.
41:28Do the fluffy surfaces of clouds, the branches in trees and rivers, the crinkled edges of shorelines share a common
41:37mathematical feature?
41:39Well, they do.
41:42Underlying nearly all the shapes in the natural world is a mathematical principle known as self-similarity.
41:50This describes anything in which the same shape is repeated over and over again at smaller and smaller scales.
42:01A great example are the branches of trees.
42:14The same branching principle applies in the structure of our lungs and the way our blood vessels are distributed throughout
42:22our bodies.
42:24It even describes how rivers split into ever smaller streams.
42:29And nature can repeat all sorts of shapes in this way.
42:35Look at this Romanesco broccoli.
42:38Its overall structure is made up of a series of repeating cones at smaller and smaller scales.
42:47Mandelbrot realised self-similarity was the basis of an entirely new kind of geometry.
42:54And he even gave it a name.
42:57Fractal.
42:59Now that's a pretty neat observation.
43:02But what if you could represent this property of nature in mathematics?
43:07What if you could capture its essence to draw a picture?
43:10What would that picture look like?
43:12Could you use a simple set of mathematical rules to draw an image that didn't look man-made?
43:20The answer would come from Mandelbrot, who had taken a job at IBM in the late 1950s to gain access
43:27to its incredible computing power and pursue his obsession with the mathematics of nature.
43:34Armed with a new breed of supercomputer, he began investigating a rather curious and strangely simple looking equation that could
43:44be used to draw a very unusual shape.
43:48What I'm about to show you is one of the most remarkable mathematical images ever discovered.
43:55Epic doesn't really do it justice.
43:59This is the Mandelbrot set.
44:02It's been called the thumbprint of God.
44:06And when we begin to explore it, you'll understand why.
44:17Just as with the tree or the broccoli, the closer you study this picture, the more detail you see.
44:28Each shape within the set contains an infinite number of smaller shapes, baby Mandelbrots, that go on forever.
44:42Yet all this complexity stems from just one incredibly simple equation.
44:48This equation has a very important property.
44:52It feeds back on itself.
44:56Like a video loop, each output becomes the input for the next go.
45:04This feedback means that an incredibly simple mathematical equation can produce a picture of infinite complexity.
45:30The really fascinating thing is that the Mandelbrot set isn't just a bizarre mathematical quirk.
45:37Its fractal property of being similar at all scales mirrors a fundamental ordering principle in nature.
45:51Turing's patterns, Belusov's reaction and Mandelbrot's fractals are all signposts pointing to a deep underlying natural principle.
46:05When we look at complexities in nature, we tend to ask, where did they come from?
46:09There is something in our heads that says complexity does not arise out of simplicity.
46:15It must arise from something complicated.
46:17We conserve complexity.
46:19But what the mathematics in this whole area is telling us is that very simple rules naturally give rise to
46:25very complex objects.
46:26And so if you look at the object, it looks complex, and you think about the rule that generates it,
46:31it's simple.
46:32So the same thing is both complex and simple from two different points of view.
46:36And that means we have to rethink completely the relation between simplicity and complexity.
46:45Complex systems can be based on simple rules.
46:49That's the big revelation.
46:52And it's an astonishing idea.
46:56It seems to apply all over our world.
47:09Look at a flock of birds.
47:11Each bird obeys very simple rules.
47:14But the flock as a whole does incredibly complicated things, avoiding obstacles, navigating the planet with no single leader or
47:25even conscious plan.
47:28But amazing though this flock's behaviour is, it's impossible to predict how it will behave.
47:35It never repeats exactly what it does, even in seemingly identical circumstances.
47:44It's just like the Belusov reaction.
47:47Each time you run it, the patterns produced are slightly different.
47:52They may look similar, but they are never identical.
47:56The same is true of video loops and sand dunes.
48:01We know they'll produce a certain kind of pattern, but we can't predict the exact shapes.
48:11The big question is, can nature's ability to turn simplicity into complexity in this mysterious and unpredictable way explain why
48:23life exists?
48:25Can it explain how a universe full of simple dust can turn into human beings?
48:32How inanimate matter can spawn intelligence?
48:38At first, you might think that this is beyond the remit of science.
48:42If nature's rules are really unpredictable, should we simply give up?
48:48Absolutely not. In fact, quite the opposite.
48:53Fittingly, the answer to this problem lies in the natural world.
48:58All around us, there exists a process that engineers these unpredictable, complex systems and hones them to perform almost miraculous
49:08tasks.
49:10The process is called evolution.
49:17Evolution has built on these patterns, it's taken them as the raw ingredients, it's combined them together in various ways,
49:26experimented to see what works and what doesn't, kept the things that do work, and then built on that.
49:33It's a completely unconscious process, but basically that's what's happening.
49:38Everywhere you look, you can see evolution using nature's self-organising patterns.
49:44Our hearts use Belousov-type reactions to regulate how they beat.
49:50Our blood vessels are organised like fractals.
49:53Even our brain cells interact according to simple rules.
49:59The way evolution refines and enriches complex systems is one of the most intriguing ideas in recent science.
50:11My interest in my PhD research in complex systems was to see how complex systems interact with evolution.
50:17So, on the one hand, you have systems that almost organise themselves as complex systems, so they exhibit order that
50:24you wouldn't expect.
50:26But on the other hand, you still have to have evolution interact with that to create something that is truly
50:31adapted to the environment.
50:34Evolution's mindless yet creative power to develop and shape complex systems is indeed incredible.
50:43But it operates on a cosmic timescale.
50:47From the first life on Earth to us walking about, took in the region of three and a half billion
50:53years.
50:56But we now have in our hands a device that can mimic this process on a much shorter timescale.
51:04What is the invention I'm talking about?
51:07Well, there's a good chance you've been sitting in front of one all day.
51:12It is, of course, the computer.
51:21Computers today can churn through trillions of calculations per second.
51:26And that gives them the power to do something very special.
51:30They can simulate evolution.
51:34More precisely, computers can use the principles of evolution to shape and refine their own programs.
51:41In the same way the natural world uses evolution to shape and refine living organisms.
51:49And today, computer scientists find that this evolved software can solve problems that would be beyond the smartest of humans.
52:00One thing that we found, particularly in our original research, is how powerful evolution is as a system, as an
52:06algorithm to create something that is very complex and create something that is very adaptive.
52:11Torsten and his team's goal was nothing less than to use computerized evolution to create a virtual brain that would
52:21control a virtual body.
52:23To begin with, they created 100 random brains. As you can see, they weren't up to much.
52:32Evolution then took over.
52:35The computer selected the brains that were slightly better at moving their bodies and got them to breed.
52:45The algorithm then takes those individuals that do the best and allows them to create offspring.
52:52The best movers of the next generation were then bred together and so on and on.
53:00Amazingly, after just ten generations, although they are still a bit unsteady, the figures could walk.
53:08Eventually, miraculously, you actually end up with something that works.
53:13The scary thing is you don't know why it works and how it works.
53:16You look at that brain and you have no idea actually what's going on because evolution has optimized it automatically.
53:26In 20 generations, evolution has turned this into this.
53:35But these evolved computer beings soon went far beyond just walking.
53:44They evolved to do things that really are impossible to program conventionally.
53:52They react realistically to unexpected events.
53:57Like being hit or falling over.
54:03Even though we program these algorithms, what actually then happens when it unfolds live, we don't control anymore.
54:10And things happen that we never expected.
54:12And it's quite a funny feeling that you create these algorithms but then they do their own thing.
54:23An unthinking process of evolutionary trial and error has created these virtual creatures that can move and react in real
54:33time.
54:38What we're seeing here is fantastic experimental evidence for the creative power of systems based on simple rules.
54:48How many people can't create these algorithms?
54:57Watching how computers can unconsciously evolve programs to do things that no human could consciously program is a fantastic example
55:07of the power of self-organization.
55:10It demonstrates that evolution is itself just like the other systems we've encountered,
55:17one based on simple rules and feedback, from which complexity spontaneously emerges.
55:25Think about it.
55:27The simple rule is that the organism must replicate with a few random mutations now and again.
55:34The feedback comes from the environment, which favours the mutations that are best suited to it.
55:43The result is ever-increasing complexity, produced without thought or design.
55:51The interesting thing is that one can move up to a higher level of organisation.
55:56Once you have organisms that actually have patterns on them,
56:00these can be selected for or selected against by processes which are essentially feedbacks.
56:07And so evolution itself, the whole Darwinian scheme,
56:10is in a sense Turing again with feedbacks happening through different processes.
56:18And that's the essence of this story.
56:21Unthinking simple rules have the power to create amazingly complex systems without any conscious thought.
56:30In that sense, these computer beings are self-organised systems,
56:36just like the one Belusov observed happening in his chemicals.
56:41Just like the ones in sand dunes and the Mandelbrot set.
56:46In our lungs, our hearts, in weather and in the geography of our planet.
56:53Design does not need an active, interfering designer.
56:59It's an inherent part of the universe.
57:06One of the things that makes people so uncomfortable about this idea of, if you will,
57:10spontaneous pattern formation, is that somehow or other, you don't need a creator.
57:15But perhaps a really clever designer, what he would do is to kind of treat the universe like a giant
57:22simulation,
57:23where you set some initial condition and just let the whole thing spontaneously happen in all of its wonder and
57:31all of its beauty.
57:33The mathematics of pattern formation shows that the same kind of pattern can show up in an enormous range of
57:41different physical, chemical, biological systems.
57:44Somewhere deep down inside, it's happening for the same mathematical reason.
57:48Implicit in those facts are these beautiful patterns that we see everywhere.
57:54You know, this, I think, is a mind-blowing thought.
58:07So, what is the ultimate lesson we can take from all this?
58:11Well, it's that all the complexity of the universe, all its infinite richness, emerges from mindless, simple rules, repeated over
58:22and over again.
58:23But remember, powerful though this process is, it's also inherently unpredictable.
58:30So, although I can confidently tell you that the future will be amazing,
58:35I can also say, with scientific certainty, that I have no idea what it holds.
58:47And there's more science here on BBC4 next week, with a volatile history of chemistry that starts at nine on
58:55Thursday.
58:56Tonight, though, from the hallowed halls of Cambridge University to the cages of the US fighting circuit,
59:02Storyville meets the UK's most successful female cage fighters next.
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