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This is a film about one very simple question. | 0:00:12 | 0:00:17 | |
How did we get here? | 0:00:17 | 0:00:19 | |
These are the elements and compounds from which all humans are made. | 0:00:26 | 0:00:30 | |
They're incredibly, almost embarrassingly common. | 0:00:30 | 0:00:34 | |
In fact, almost 99% of the human body is a mixture of air, water, | 0:00:34 | 0:00:39 | |
coal and chalk, with traces of other slightly more exotic elements | 0:00:39 | 0:00:43 | |
like iron, zinc, phosphorus and sulphur. | 0:00:43 | 0:00:47 | |
In fact, I've estimated that the elements | 0:00:47 | 0:00:51 | |
which make up the average human cost at most a few pounds. | 0:00:51 | 0:00:56 | |
But somehow, trillions of these very ordinary atoms conspire miraculously | 0:00:56 | 0:01:03 | |
to organise themselves into thinking, breathing, living human beings. | 0:01:03 | 0:01:07 | |
How the wonders of creation are assembled from such simple | 0:01:09 | 0:01:12 | |
building blocks, is surely the most intriguing question we can ask. | 0:01:12 | 0:01:18 | |
You may think that answering it is beyond the realm of science. | 0:01:18 | 0:01:22 | |
But that's changing. | 0:01:22 | 0:01:24 | |
For the first time, I believe science has pushed past religion | 0:01:24 | 0:01:29 | |
and philosophy in daring to tackle this most fundamental of questions. | 0:01:29 | 0:01:34 | |
This film is the story of a series of bizarre | 0:01:40 | 0:01:43 | |
and interconnected discoveries that reveal a hidden face of nature. | 0:01:43 | 0:01:48 | |
That woven into its simplest and most basic laws, | 0:01:50 | 0:01:54 | |
is a power to be unpredictable. | 0:01:54 | 0:01:57 | |
It's about how inanimate matter with no purpose or design, | 0:01:58 | 0:02:02 | |
can spontaneously create exquisite beauty. | 0:02:02 | 0:02:08 | |
It's about how the same laws that make the universe chaotic | 0:02:08 | 0:02:12 | |
and unpredictable, can turn simple dust into human beings. | 0:02:12 | 0:02:17 | |
It's about the discovery that there is a strange | 0:02:19 | 0:02:22 | |
and unexpected relationship between order and chaos. | 0:02:22 | 0:02:28 | |
The natural world really is one great, blooming, buzzing confusion. | 0:02:59 | 0:03:05 | |
It's a mess of quirky shapes and blotches. | 0:03:06 | 0:03:09 | |
What patterns there are, are never quite regular, | 0:03:09 | 0:03:13 | |
and never seem to repeat exactly. | 0:03:13 | 0:03:16 | |
The idea that all this mayhem, all this chaos, is underpinned, | 0:03:19 | 0:03:24 | |
indeed determined, by mathematical rules, | 0:03:24 | 0:03:27 | |
and that we can work out what those rules might be, | 0:03:27 | 0:03:30 | |
runs counter to our most dearly held intuitions. | 0:03:30 | 0:03:34 | |
So not surprisingly, the first man to really take on the momentous task | 0:03:41 | 0:03:46 | |
of unravelling nature's mysterious mathematics, | 0:03:46 | 0:03:50 | |
had a very special and unusual mind. | 0:03:50 | 0:03:54 | |
He was both a great scientist and a tragic hero. | 0:03:54 | 0:03:58 | |
He was born in 1912, in London. | 0:03:58 | 0:04:02 | |
His name was Alan Turing. | 0:04:02 | 0:04:04 | |
Alan Turing was a remarkable man, | 0:04:06 | 0:04:09 | |
one of the greatest mathematicians who ever lived. | 0:04:09 | 0:04:12 | |
He discovered many of the fundamental ideas | 0:04:12 | 0:04:15 | |
that underpin the modern computer. | 0:04:15 | 0:04:18 | |
Also, during the Second World War, | 0:04:18 | 0:04:20 | |
he worked here at Bletchley Park, just outside today's Milton Keynes, | 0:04:20 | 0:04:24 | |
in what was then a secret government project called Station X, | 0:04:24 | 0:04:28 | |
which was set up to crack the German military codes. | 0:04:28 | 0:04:32 | |
The Station X code breakers proved highly effective, | 0:04:32 | 0:04:37 | |
and Turing's contribution was crucial. | 0:04:37 | 0:04:40 | |
The work he personally did to crack German naval codes, | 0:04:40 | 0:04:44 | |
saved thousands of Allied lives and was a turning point in the war. | 0:04:44 | 0:04:50 | |
But code breaking was just one aspect of Turing's genius. | 0:04:50 | 0:04:54 | |
Just one part of his uncanny ability to see patterns | 0:04:54 | 0:04:58 | |
that are hidden from the rest of us. | 0:04:58 | 0:05:00 | |
For Turing, the natural world offered up the ultimate codes. | 0:05:00 | 0:05:04 | |
And over the course of his life | 0:05:04 | 0:05:06 | |
he'd come tantalisingly close to cracking them. | 0:05:06 | 0:05:10 | |
Turing was a very original person. | 0:05:10 | 0:05:12 | |
And he had realised that there was this possibility | 0:05:12 | 0:05:17 | |
that simple mathematical equations | 0:05:17 | 0:05:20 | |
might describe aspects of the biological world. | 0:05:20 | 0:05:23 | |
And no-one had thought of that before. | 0:05:23 | 0:05:25 | |
Of all nature's mysteries, the one that fascinated Turing most | 0:05:27 | 0:05:31 | |
was the idea that there might be a mathematical basis | 0:05:31 | 0:05:34 | |
to human intelligence. | 0:05:34 | 0:05:38 | |
Turing had very personal reasons for believing in this. | 0:05:38 | 0:05:42 | |
It was the death of this young man, Christopher Morcom, | 0:05:42 | 0:05:45 | |
who...Alan Turing, well, he was gay, | 0:05:45 | 0:05:48 | |
and it had been the great emotional thing of his life at that point. | 0:05:48 | 0:05:52 | |
Christopher Morcom suddenly died. | 0:05:52 | 0:05:54 | |
And, Alan Turing was obviously very emotionally disturbed by this. | 0:05:54 | 0:06:00 | |
But you can see that he wanted to put this | 0:06:00 | 0:06:02 | |
in an intellectual context, a scientific context. | 0:06:02 | 0:06:05 | |
And the question he wanted to put into context was | 0:06:05 | 0:06:08 | |
what happens to the mind? What is it? | 0:06:08 | 0:06:10 | |
Turing became convinced that mathematics could be used to describe | 0:06:14 | 0:06:19 | |
biological systems, and ultimately intelligence. | 0:06:19 | 0:06:24 | |
This fascination would give rise to the modern computer, | 0:06:24 | 0:06:28 | |
and later in Turing's life, an even more radical idea. | 0:06:28 | 0:06:31 | |
The idea that a simple mathematical description could be given | 0:06:31 | 0:06:36 | |
for a mysterious process that takes place in an embryo. | 0:06:36 | 0:06:41 | |
The process is called morphogenesis, and it's very puzzling. | 0:06:44 | 0:06:49 | |
At first, all the cells in the embryo are identical. | 0:06:54 | 0:06:58 | |
Then, as this footage of a fish embryo shows, | 0:06:59 | 0:07:03 | |
the cells begin to clump together, | 0:07:03 | 0:07:05 | |
and also become different from each other. | 0:07:05 | 0:07:08 | |
How does this happen? With no thought, | 0:07:10 | 0:07:14 | |
no central co-ordination? | 0:07:14 | 0:07:16 | |
How do cells that start off identical, know to become say, skin, | 0:07:17 | 0:07:23 | |
while others become part of an eye? | 0:07:23 | 0:07:27 | |
Morphogenesis is a spectacular example | 0:07:31 | 0:07:35 | |
of something called self-organisation. | 0:07:35 | 0:07:38 | |
And before Turing, no-one had a clue how it worked. | 0:07:39 | 0:07:44 | |
Then, in 1952, Turing published this, his paper | 0:07:48 | 0:07:53 | |
with the world's first mathematical explanation for morphogenesis. | 0:07:53 | 0:07:57 | |
The sheer chutzpah of this paper was staggering. | 0:07:59 | 0:08:02 | |
In it, Turing used a mathematical equation | 0:08:06 | 0:08:09 | |
of the kind normally seen in papers on astronomy or atomic physics, | 0:08:09 | 0:08:14 | |
to describe a living process. | 0:08:14 | 0:08:17 | |
No-one had done anything like this. | 0:08:18 | 0:08:21 | |
Crucially, Turing's equations did, for the first time, | 0:08:22 | 0:08:27 | |
describe how a biological system could self-organise. | 0:08:27 | 0:08:32 | |
They showed that something smooth and featureless can develop features. | 0:08:32 | 0:08:38 | |
One of the astonishing things about Turing's work | 0:08:39 | 0:08:42 | |
was that starting with the description | 0:08:42 | 0:08:44 | |
of really very simple processes | 0:08:44 | 0:08:46 | |
governed by very simple equations, by putting these together, | 0:08:46 | 0:08:51 | |
suddenly complexity emerged. | 0:08:51 | 0:08:53 | |
The pattern suddenly came out as a natural consequence. | 0:08:53 | 0:08:57 | |
And I think in many ways this was very, very unexpected. | 0:08:57 | 0:09:00 | |
In essence, Turing's equations described something quite familiar, | 0:09:05 | 0:09:10 | |
but which no-one had thought of in the context of biology before. | 0:09:10 | 0:09:14 | |
Think of the way a steady wind blowing across sand | 0:09:20 | 0:09:23 | |
creates all kinds of shapes. | 0:09:23 | 0:09:26 | |
The grains self-organise into ripples, waves and dunes. | 0:09:26 | 0:09:32 | |
This happens, even though the grains are virtually identical, | 0:09:33 | 0:09:37 | |
and have no knowledge of the shapes they become part of. | 0:09:37 | 0:09:41 | |
Turing argued that in a very similar way, | 0:09:44 | 0:09:47 | |
chemicals seeping across an embryo | 0:09:47 | 0:09:49 | |
might cause its cells to self-organise into different organs. | 0:09:49 | 0:09:55 | |
These are Turing's own very rough scribblings of how this might work. | 0:10:02 | 0:10:07 | |
They show how a completely featureless chemical soup, | 0:10:13 | 0:10:17 | |
can evolve these strange blobs and patches. | 0:10:17 | 0:10:21 | |
In his paper, he refined his sketches | 0:10:24 | 0:10:27 | |
to show how his equations could spontaneously create markings | 0:10:27 | 0:10:31 | |
similar to those on the skins of animals. | 0:10:31 | 0:10:34 | |
Turing went around showing people pictures saying, | 0:10:36 | 0:10:39 | |
"Doesn't this look a bit like the patterns on a cow?" | 0:10:39 | 0:10:42 | |
And everyone sort of went, "What is this man on about?" | 0:10:42 | 0:10:44 | |
But actually, he knew what he was doing. | 0:10:44 | 0:10:47 | |
They did look like the patterns of a cow, and that's one of | 0:10:47 | 0:10:50 | |
the reasons why cows have this dappled pattern or whatever. | 0:10:50 | 0:10:53 | |
So, an area where mathematics had never been used before, | 0:10:53 | 0:10:58 | |
pattern formation in biology, animal markings, | 0:10:58 | 0:11:02 | |
suddenly the door was opened and we could see | 0:11:02 | 0:11:06 | |
that mathematics might be useful in that sort of area. | 0:11:06 | 0:11:10 | |
So even though Turing's exact equations are not the full story, | 0:11:10 | 0:11:14 | |
they are the first piece of mathematical work that showed | 0:11:14 | 0:11:19 | |
there was any possibility of doing this kind of thing. | 0:11:19 | 0:11:22 | |
Of course, we now know that morphogenesis | 0:11:28 | 0:11:31 | |
is much more complicated than the process Turing's equations describe. | 0:11:31 | 0:11:36 | |
In fact, the precise mechanism of how DNA molecules in our cells interact | 0:11:36 | 0:11:42 | |
with other chemicals, is still fiercely debated by scientists. | 0:11:42 | 0:11:46 | |
But Turing's idea that whatever is going on is, deep down, | 0:11:48 | 0:11:52 | |
a simple mathematical process, was truly revolutionary. | 0:11:52 | 0:11:57 | |
I think Alan Turing's paper is probably the cornerstone | 0:11:58 | 0:12:02 | |
in the whole idea of how morphogenesis works. | 0:12:02 | 0:12:06 | |
What it does is it provides us with a mechanism, | 0:12:06 | 0:12:08 | |
something that Darwin didn't, for how pattern emerges. | 0:12:08 | 0:12:12 | |
Darwin, of course, tells us that once you have a pattern | 0:12:12 | 0:12:15 | |
and it is coded for in the genes, that may or may not be passed on, | 0:12:15 | 0:12:19 | |
depending on circumstances. But what it doesn't do | 0:12:19 | 0:12:22 | |
is explain where that pattern comes from in the first place. | 0:12:22 | 0:12:25 | |
That's the real mystery. | 0:12:25 | 0:12:26 | |
And so, what Turing had done was to suddenly provide | 0:12:26 | 0:12:30 | |
an accessible chemical mechanism for doing this. That was amazing. | 0:12:30 | 0:12:34 | |
Turing was onto a really big, bold idea. | 0:12:37 | 0:12:41 | |
But sadly, we can only speculate how his extraordinary mind | 0:12:43 | 0:12:47 | |
would have developed his idea. | 0:12:47 | 0:12:50 | |
Shortly after his groundbreaking paper on morphogenesis, | 0:12:51 | 0:12:55 | |
a dreadful and completely avoidable tragedy destroyed his life. | 0:12:55 | 0:13:00 | |
After his work breaking codes at Bletchley Park, | 0:13:04 | 0:13:08 | |
you might well have assumed that Turing would have been honoured | 0:13:08 | 0:13:12 | |
by the country he did so much to protect. | 0:13:12 | 0:13:14 | |
This couldn't be further from the truth. | 0:13:14 | 0:13:17 | |
What happened to him after the war was a great tragedy, | 0:13:17 | 0:13:20 | |
and one of the most shameful episodes in the history of British science. | 0:13:20 | 0:13:25 | |
The same year Turing published his morphogenesis paper, | 0:13:27 | 0:13:31 | |
he had a brief affair with a man called Arnold Murray. | 0:13:31 | 0:13:35 | |
The affair went sour | 0:13:35 | 0:13:36 | |
and Murray was involved in a burglary at Turing's house. | 0:13:36 | 0:13:40 | |
But when Turing reported this to the police, | 0:13:40 | 0:13:43 | |
they arrested him as well as Murray. | 0:13:43 | 0:13:46 | |
In court, the prosecution argued | 0:13:48 | 0:13:51 | |
that Turing, with his university education, had led Murray astray. | 0:13:51 | 0:13:56 | |
He was convicted of gross indecency. | 0:13:59 | 0:14:02 | |
The judge then offered Turing a dreadful choice. | 0:14:02 | 0:14:06 | |
He could either go to prison, or sign up to a regime of | 0:14:08 | 0:14:12 | |
female hormone injections to cure him of his homosexuality. | 0:14:12 | 0:14:16 | |
He chose the latter, and it was to send him into a spiral of depression. | 0:14:16 | 0:14:22 | |
On 8 June 1954, Turing's body was found by his cleaner. | 0:14:22 | 0:14:27 | |
He'd died the day before by taking a bite from an apple | 0:14:27 | 0:14:31 | |
he'd laced with cyanide, ending his own life. | 0:14:31 | 0:14:34 | |
Alan Turing died aged just 41. | 0:14:37 | 0:14:40 | |
The loss to science is incalculable. | 0:14:40 | 0:14:44 | |
Turing would never know that his ideas would inspire | 0:14:44 | 0:14:48 | |
an entirely new mathematical approach to biology, | 0:14:48 | 0:14:52 | |
and that scientists would find equations like his | 0:14:52 | 0:14:55 | |
really do explain many of the shapes that appear on living organisms. | 0:14:55 | 0:15:00 | |
Looking back, we now know Turing had really grasped the idea | 0:15:03 | 0:15:07 | |
that the wonders of creation are derived from the simplest of rules. | 0:15:07 | 0:15:12 | |
He had, perhaps unexpectedly, taken the first step | 0:15:12 | 0:15:18 | |
to a new kind of science. | 0:15:18 | 0:15:20 | |
The next step in the story was just as unexpected, | 0:15:36 | 0:15:40 | |
and in many ways, just as tragic as Turing's. | 0:15:40 | 0:15:44 | |
In the early 1950s, around the time of Turing's seminal paper | 0:15:46 | 0:15:51 | |
on morphogenesis, a brilliant Russian chemist by the name of | 0:15:51 | 0:15:55 | |
Boris Belousov was beginning his own investigations | 0:15:55 | 0:15:59 | |
into the chemistry of nature. | 0:15:59 | 0:16:01 | |
Deep behind the iron curtain, in a lab at the Soviet Ministry of Health, | 0:16:01 | 0:16:06 | |
he was beginning to investigate the way our bodies | 0:16:06 | 0:16:09 | |
extract energy from sugars. | 0:16:09 | 0:16:11 | |
Just like Turing, Belousov was working on a personal project, having | 0:16:15 | 0:16:20 | |
just finished a distinguished career as a scientist in the military. | 0:16:20 | 0:16:25 | |
In his lab, Belousov had formulated a mixture of chemicals | 0:16:25 | 0:16:29 | |
to mimic one part of the process of glucose absorption in the body. | 0:16:29 | 0:16:34 | |
The mix of chemicals sat on the lab bench in front of him, | 0:16:34 | 0:16:38 | |
clear and colourless while being shaken. | 0:16:38 | 0:16:41 | |
As he mixed in the final chemical, the whole solution changed colour. | 0:16:41 | 0:16:46 | |
Now this isn't particularly remarkable. | 0:16:46 | 0:16:49 | |
If we mix ink into water, it changes colour. | 0:16:49 | 0:16:52 | |
But then something happened that made no sense at all. | 0:16:52 | 0:16:58 | |
The mixture began to go clear again. | 0:16:58 | 0:17:02 | |
Belousov was astounded. | 0:17:07 | 0:17:09 | |
Chemicals can mix together and react. | 0:17:09 | 0:17:12 | |
But they shouldn't be able to go back on themselves, | 0:17:12 | 0:17:16 | |
to apparently unmix without intervention. | 0:17:16 | 0:17:19 | |
You can change from a clear mixture to a coloured mixture, fine. | 0:17:19 | 0:17:23 | |
But surely not back again? | 0:17:23 | 0:17:25 | |
And it got weirder. | 0:17:28 | 0:17:30 | |
Belousov's chemicals didn't just spontaneously go into reverse. | 0:17:30 | 0:17:34 | |
They oscillated. | 0:17:34 | 0:17:36 | |
They switched back and forth from coloured to clear, | 0:17:36 | 0:17:40 | |
as if they were being driven by some sort of hidden chemical metronome. | 0:17:40 | 0:17:46 | |
With meticulous care, he repeated his experiments again and again. | 0:17:46 | 0:17:52 | |
It was the same every time. | 0:17:52 | 0:17:55 | |
His mixture would cycle from clear to coloured and back again, repeatedly. | 0:17:55 | 0:18:00 | |
He'd discovered something that was almost like magic, | 0:18:00 | 0:18:03 | |
a physical process that seemed to violate the laws of nature. | 0:18:03 | 0:18:07 | |
'Convinced he'd discovered something of great importance, Belousov | 0:18:11 | 0:18:14 | |
'wrote up his findings, keen to share his discovery with the wider world. | 0:18:14 | 0:18:20 | |
'But when he submitted his paper to a leading Russian scientific journal, | 0:18:20 | 0:18:24 | |
'he received a wholly unexpected and damning response.' | 0:18:24 | 0:18:29 | |
The editor of the journal told Belousov that his findings in the lab | 0:18:29 | 0:18:33 | |
were quite simply impossible. | 0:18:33 | 0:18:36 | |
They contravened the fundamental laws of physics. | 0:18:36 | 0:18:39 | |
The only explanation was that Belousov had made a mistake | 0:18:39 | 0:18:43 | |
in his experiment, and the work was simply not fit for publication. | 0:18:43 | 0:18:48 | |
'The rejection crushed Belousov. | 0:18:53 | 0:18:56 | |
'Deeply insulted by the suggestion his work had been botched, | 0:18:56 | 0:19:00 | |
'he abandoned his experiments. | 0:19:00 | 0:19:02 | |
'Soon he gave up science altogether.' | 0:19:02 | 0:19:05 | |
The tragic irony was that, divided as they were by the Iron Curtain, | 0:19:07 | 0:19:11 | |
Belousov never encountered Turing's work. | 0:19:11 | 0:19:15 | |
For if he had, he would have been completely vindicated. | 0:19:15 | 0:19:20 | |
It turns out that Belousov's oscillating chemicals, | 0:19:20 | 0:19:24 | |
far from contravening the laws of physics, | 0:19:24 | 0:19:27 | |
were actually a real world example | 0:19:27 | 0:19:30 | |
of precisely the behaviour Turing's equations predicted. | 0:19:30 | 0:19:34 | |
While the connection might not appear obvious at first sight, | 0:19:45 | 0:19:49 | |
other scientists showed that if you left a variation | 0:19:49 | 0:19:52 | |
of Belousov's chemicals, unstirred in a Petri dish, | 0:19:52 | 0:19:56 | |
instead of simply oscillating, they self-organise into shapes. | 0:19:56 | 0:20:01 | |
In fact, they go beyond Turing's simple blobs and stripes | 0:20:01 | 0:20:05 | |
to create stunningly beautiful structures and patterns | 0:20:05 | 0:20:10 | |
out of nowhere. | 0:20:10 | 0:20:12 | |
The amazing and very unexpected thing about the BZ reaction | 0:20:22 | 0:20:26 | |
is that someone had discovered a system | 0:20:26 | 0:20:28 | |
which essentially reproduces the Turing equations. | 0:20:28 | 0:20:32 | |
And so, from what looks like a very, very bland solution | 0:20:32 | 0:20:36 | |
emerge these astonishing patterns of waves and scrolls and spirals. | 0:20:36 | 0:20:41 | |
Now this is emphatically not abstract science. | 0:20:45 | 0:20:49 | |
The way Belousov's chemicals move as co-ordinated waves | 0:20:49 | 0:20:53 | |
is exactly the way our heart cells are co-ordinated as they beat. | 0:20:53 | 0:20:58 | |
Animal skins and heart beats. | 0:21:01 | 0:21:04 | |
Self-organisation seems to operate all over the natural world. | 0:21:04 | 0:21:08 | |
So why were the scientific community in Turing and Belousov's day, | 0:21:15 | 0:21:20 | |
so uninterested, or even hostile to this astonishing and beautiful idea? | 0:21:20 | 0:21:25 | |
Well, the reason was all too human. | 0:21:29 | 0:21:33 | |
Mainstream scientists simply didn't like it. | 0:21:34 | 0:21:38 | |
To them it seemed to run counter to science, | 0:21:38 | 0:21:41 | |
and all that it had achieved. | 0:21:41 | 0:21:44 | |
To change that view would require a truly shocking | 0:21:52 | 0:21:56 | |
and completely unexpected discovery. | 0:21:56 | 0:21:59 | |
In essence, by the beginning of the 20th century, | 0:22:02 | 0:22:06 | |
scientists saw the universe as a giant, | 0:22:06 | 0:22:09 | |
complicated, mechanical device. | 0:22:09 | 0:22:12 | |
Kind of a super-sized version of this orrery. | 0:22:12 | 0:22:17 | |
The idea was that the universe is a huge and intricate machine | 0:22:21 | 0:22:26 | |
that obeys orderly mathematical rules. | 0:22:26 | 0:22:30 | |
If you knew the rules of how the machine was configured to start with, | 0:22:30 | 0:22:33 | |
as you turned the handle, over and over again, | 0:22:33 | 0:22:37 | |
it would behave in an entirely predictable way. | 0:22:37 | 0:22:40 | |
Back in the times of Isaac Newton | 0:22:43 | 0:22:44 | |
when people were discovering the laws that drove the universe, | 0:22:44 | 0:22:48 | |
they came up with this kind of metaphor of a clockwork universe. | 0:22:48 | 0:22:52 | |
The universe looked like a machine which had been set going at the | 0:22:52 | 0:22:56 | |
instant of creation and just followed the rules and ticked along. | 0:22:56 | 0:23:00 | |
And it was a complicated machine and therefore complicated things happen. | 0:23:00 | 0:23:04 | |
But once you set it going it would only do one thing, | 0:23:04 | 0:23:08 | |
and the message that people drew from this | 0:23:08 | 0:23:11 | |
was that anything describable by mathematical rules | 0:23:11 | 0:23:14 | |
must actually basically be fairly simple. | 0:23:14 | 0:23:17 | |
Find the mathematics that describes a system | 0:23:21 | 0:23:25 | |
and you can then predict how that system will unfold. | 0:23:25 | 0:23:28 | |
That was the big idea. | 0:23:28 | 0:23:30 | |
It began with Newton's law of gravity | 0:23:30 | 0:23:33 | |
which can be used to predict how a planet moves around the sun. | 0:23:33 | 0:23:37 | |
Scientists soon found many other equations just like it. | 0:23:37 | 0:23:42 | |
Newtonian physics seemed like the ultimate crystal-ball. | 0:23:44 | 0:23:49 | |
It held up the tantalising possibility | 0:23:49 | 0:23:51 | |
that the future could, in principle, be known. | 0:23:51 | 0:23:54 | |
The more careful your measurements are today, | 0:23:54 | 0:23:57 | |
the better you can predict what will happen tomorrow. | 0:23:57 | 0:24:00 | |
But Newtonianism had a dangerous consequence. | 0:24:05 | 0:24:10 | |
If a nice mathematical system, that worked in a similar way | 0:24:10 | 0:24:13 | |
to my orrery, did sometimes become unpredictable, scientists assumed | 0:24:13 | 0:24:19 | |
some malign outside force was causing it. Perhaps dirt had got in? | 0:24:19 | 0:24:24 | |
Perhaps the cogs were wearing out? | 0:24:24 | 0:24:26 | |
Or perhaps someone had tampered with it? | 0:24:26 | 0:24:30 | |
Basically we used to think, if you saw very irregular behaviour | 0:24:30 | 0:24:34 | |
in some problem you're working on, this must be the result of some sort | 0:24:34 | 0:24:39 | |
of random outside influences, it couldn't be internally generated. | 0:24:39 | 0:24:43 | |
It wasn't an intrinsic part of the problem, | 0:24:43 | 0:24:45 | |
it was some other thing impacting on it. | 0:24:45 | 0:24:47 | |
Looked at from this point of view, | 0:24:50 | 0:24:53 | |
the whole idea of self-organisation seemed absurd. | 0:24:53 | 0:24:57 | |
The idea that patterns of the kind Turing and Belousov had found | 0:24:57 | 0:25:02 | |
could appear of their own accord, | 0:25:02 | 0:25:04 | |
without any outside influence, was a complete taboo. | 0:25:04 | 0:25:09 | |
The only way for self-organisation to be accepted | 0:25:12 | 0:25:15 | |
was for the domineering Newtonian view to collapse. | 0:25:15 | 0:25:21 | |
But that seemed very unlikely. | 0:25:21 | 0:25:23 | |
After all, by the late '60s it had delivered | 0:25:26 | 0:25:28 | |
all the wonders of the modern age. | 0:25:28 | 0:25:32 | |
Beautiful, beautiful. | 0:25:32 | 0:25:34 | |
-Ain't that something? -Magnificent desolation. | 0:25:34 | 0:25:36 | |
But then, at the same time as the moon mission, | 0:25:39 | 0:25:43 | |
a small group of scientists, all ardent Newtonians, | 0:25:43 | 0:25:47 | |
quite unexpectedly found something wasn't right. | 0:25:47 | 0:25:52 | |
Not right at all. | 0:25:52 | 0:25:55 | |
During the second half of the 20th century, | 0:25:58 | 0:26:01 | |
a devil was found in the detail. A devil that would ultimately | 0:26:01 | 0:26:06 | |
shatter the Newtonian dream and plunge us literally into chaos. | 0:26:06 | 0:26:11 | |
Ironically, the events that forced scientists to take self-organisation | 0:26:20 | 0:26:25 | |
seriously was the discovery of a phenomenon known as chaos. | 0:26:25 | 0:26:31 | |
Chaos is one of the most over-used words in English, but in science | 0:26:33 | 0:26:37 | |
it has a very specific meaning. It says that a system that is completely | 0:26:37 | 0:26:43 | |
described by mathematical equations is more than capable | 0:26:43 | 0:26:48 | |
of being unpredictable without any outside interference whatsoever. | 0:26:48 | 0:26:53 | |
There's a widespread misapprehension that chaos is just somehow saying, | 0:26:55 | 0:26:59 | |
the very familiar fact, that everything's complicated. | 0:26:59 | 0:27:03 | |
I mean, the nitwit chaoticist in Jurassic Park, | 0:27:03 | 0:27:06 | |
was under that confusion. | 0:27:06 | 0:27:08 | |
It's something much simpler and yet much more complicated than that. | 0:27:08 | 0:27:12 | |
It says, some very, very simple rules or equations, | 0:27:12 | 0:27:17 | |
with nothing random in them, they're completely determined, | 0:27:17 | 0:27:21 | |
we know everything about the rule, | 0:27:21 | 0:27:23 | |
can have outcomes that are entirely unpredictable. | 0:27:23 | 0:27:29 | |
Chaos is one of the most unwelcome discoveries in science. | 0:27:31 | 0:27:37 | |
The man who forced the scientific community to confront it | 0:27:37 | 0:27:41 | |
was an American meteorologist called Edward Lorenz. | 0:27:41 | 0:27:45 | |
In the early 1960s he tried to find mathematical equations | 0:27:45 | 0:27:49 | |
that could help predict the weather. | 0:27:49 | 0:27:52 | |
Like all his contemporaries, he believed that in principle | 0:27:55 | 0:28:00 | |
the weather system was no different to my orrery. | 0:28:00 | 0:28:03 | |
A mechanical system that could be described | 0:28:03 | 0:28:06 | |
and predicted mathematically. | 0:28:06 | 0:28:09 | |
But he was wrong. | 0:28:10 | 0:28:11 | |
When Lorenz wrote down what looked like perfectly simple mathematical | 0:28:15 | 0:28:19 | |
equations to describe the movement of air currents, | 0:28:19 | 0:28:23 | |
they didn't do what they were supposed to. | 0:28:23 | 0:28:26 | |
They made no useful predictions whatsoever. | 0:28:26 | 0:28:30 | |
It was as if the lightest breath of wind one day could make the | 0:28:33 | 0:28:37 | |
difference a month later between a snowstorm and a perfectly sunny day. | 0:28:37 | 0:28:44 | |
How can a simple system that works in the regular clockwork manner | 0:28:46 | 0:28:51 | |
of my orrery become unpredictable? | 0:28:51 | 0:28:54 | |
It's all down to how it's configured. | 0:28:54 | 0:28:57 | |
How the gears are connected. | 0:28:57 | 0:28:59 | |
In essence, under certain circumstances, | 0:28:59 | 0:29:02 | |
the tiniest difference in the starting positions of the cogs, | 0:29:02 | 0:29:07 | |
differences that are too small to measure, | 0:29:07 | 0:29:10 | |
can get bigger and bigger with each turn of the handle. | 0:29:10 | 0:29:15 | |
With each step in the process the system then moves | 0:29:15 | 0:29:18 | |
further and further away from where you thought it was going. | 0:29:18 | 0:29:23 | |
Lorenz captured this radical idea in an influential talk he gave called, | 0:29:23 | 0:29:28 | |
"Does a flap of a butterfly's wings in Brazil set off a tornado in Texas?" | 0:29:28 | 0:29:35 | |
It was a powerful and evocative image | 0:29:40 | 0:29:42 | |
and within months a new phrase had entered our language. | 0:29:42 | 0:29:46 | |
"The butterfly effect." | 0:29:46 | 0:29:48 | |
And the butterfly effect, the hallmark of all chaotic systems, | 0:29:50 | 0:29:54 | |
started turning up everywhere. | 0:29:54 | 0:29:56 | |
In the early '70s, a young Australian called Robert May, | 0:30:00 | 0:30:04 | |
was investigating a mathematical equation | 0:30:04 | 0:30:07 | |
that modelled how animal populations changed over time. | 0:30:07 | 0:30:12 | |
But here too lurked the dreaded butterfly effect. | 0:30:12 | 0:30:16 | |
Immeasurably small changes to the rates at which the animals reproduced | 0:30:16 | 0:30:20 | |
could sometimes have huge consequences | 0:30:20 | 0:30:23 | |
on their overall population. | 0:30:23 | 0:30:25 | |
Numbers could go up and down wildly for no obvious reason. | 0:30:25 | 0:30:31 | |
The idea that a mathematical equation gave you the power | 0:30:31 | 0:30:35 | |
to predict how a system will behave, was dead. | 0:30:35 | 0:30:41 | |
In some sense this is the end of the Newtonian dream. | 0:30:41 | 0:30:44 | |
When I was a graduate student, the belief was, | 0:30:44 | 0:30:48 | |
as we got more and more computer power, | 0:30:48 | 0:30:52 | |
we'd be able to solve ever more complicated sets of equations. | 0:30:52 | 0:30:57 | |
But this said that's not necessarily true. | 0:30:57 | 0:31:00 | |
You could have the simplest equations you can think of, | 0:31:00 | 0:31:03 | |
with nothing random in them, you know everything. | 0:31:03 | 0:31:07 | |
And yet, if they have behaviour | 0:31:07 | 0:31:12 | |
that gives you chaotic solutions, | 0:31:12 | 0:31:15 | |
then you can never know the starting point accurately enough. | 0:31:15 | 0:31:20 | |
Centuries of scientific certainty dissolved in just a few short years. | 0:31:23 | 0:31:29 | |
The truth of the clockwork universe turned out to be just an illusion. | 0:31:29 | 0:31:34 | |
Something which had seemed a logical certainty, | 0:31:34 | 0:31:37 | |
revealed itself merely as an act of faith. | 0:31:37 | 0:31:40 | |
And what's worse, the truth had been staring us in the face all the time. | 0:31:40 | 0:31:44 | |
Because chaos is everywhere. | 0:31:44 | 0:31:47 | |
It seemed unpredictability was hard-wired | 0:31:51 | 0:31:55 | |
into every aspect of the world we live in. | 0:31:55 | 0:31:58 | |
The global climate could dramatically change | 0:32:00 | 0:32:04 | |
in the course of a few short years. | 0:32:04 | 0:32:07 | |
The stock markets could crash without warning. | 0:32:07 | 0:32:09 | |
We could be wiped from the face of the planet overnight | 0:32:09 | 0:32:14 | |
and there is nothing anyone could do about it. | 0:32:14 | 0:32:18 | |
Unfortunately, I have to tell you that all of this is true. | 0:32:23 | 0:32:28 | |
And yet to be scared of chaos is pointless. | 0:32:28 | 0:32:31 | |
It's woven into the basic laws of physics. | 0:32:33 | 0:32:37 | |
And we really all have to accept it as a fact of life. | 0:32:37 | 0:32:42 | |
The idea of chaos really did have a big impact over a period of about 20 | 0:32:42 | 0:32:47 | |
or 30 years, because it changed the way everyone thought about | 0:32:47 | 0:32:50 | |
what they were doing in science. | 0:32:50 | 0:32:52 | |
It changed it to the point | 0:32:52 | 0:32:53 | |
that they forgot that they'd ever believed otherwise. | 0:32:53 | 0:32:56 | |
What chaos did was to show us that the possibilities inherent | 0:32:56 | 0:33:02 | |
in the simple mathematics are much broader and much more general | 0:33:02 | 0:33:07 | |
than you might imagine. And so a clockwork universe can | 0:33:07 | 0:33:12 | |
nonetheless behave in the rich, complex way that we experience. | 0:33:12 | 0:33:17 | |
The discovery of chaos | 0:33:19 | 0:33:21 | |
was a real turning point in the history of science. | 0:33:21 | 0:33:24 | |
As it tore down the Newtonian dream, | 0:33:24 | 0:33:27 | |
scientists began to look more favourably at Turing and | 0:33:27 | 0:33:30 | |
Belousov's work on spontaneous pattern formation. | 0:33:30 | 0:33:34 | |
And perhaps more importantly, as they did so, | 0:33:34 | 0:33:38 | |
they realised something truly astonishing. | 0:33:38 | 0:33:41 | |
That there was a very deep and unexpected link. | 0:33:41 | 0:33:44 | |
A truly cosmic connection | 0:33:44 | 0:33:47 | |
between nature's strange power to self-organise | 0:33:47 | 0:33:51 | |
and the chaotic consequences of the butterfly effect. | 0:33:51 | 0:33:55 | |
Between them, Turing, Belousov, May and Lorenz, | 0:33:55 | 0:34:00 | |
had all discovered different faces of just one really big idea. | 0:34:00 | 0:34:05 | |
They discovered that the natural world could be deeply, | 0:34:08 | 0:34:12 | |
profoundly, unpredictable. But the very same things that make it | 0:34:12 | 0:34:16 | |
unpredictable also allow it to create pattern and structure. | 0:34:16 | 0:34:21 | |
Order and chaos. | 0:34:21 | 0:34:24 | |
It seems the two are more deeply linked | 0:34:24 | 0:34:26 | |
than we could have ever imagined. | 0:34:26 | 0:34:28 | |
So how is this possible? | 0:34:30 | 0:34:32 | |
What do phenomena as apparently different as the patterns in | 0:34:32 | 0:34:36 | |
Belousov's chemicals and the weather, have in common? | 0:34:36 | 0:34:40 | |
First, though both systems behave in very complicated ways, | 0:34:43 | 0:34:47 | |
they are both based on surprisingly simple mathematical rules. | 0:34:47 | 0:34:52 | |
Secondly, these rules have a unique property. | 0:34:56 | 0:35:00 | |
A property that's often referred to as coupling, or feedback. | 0:35:00 | 0:35:05 | |
To show you what I mean, to show you both order and chaos can emerge | 0:35:10 | 0:35:15 | |
on the their own from a simple system with feedback, I'm going to do | 0:35:15 | 0:35:20 | |
what seems at first glance like a rather trivial experiment. | 0:35:20 | 0:35:24 | |
This screen behind me is connected up to the camera that's filming me. | 0:35:29 | 0:35:35 | |
But the camera in turn is filming me with the screen. | 0:35:35 | 0:35:39 | |
This creates a loop with multiple copies of me | 0:35:39 | 0:35:43 | |
appearing on the screen. | 0:35:43 | 0:35:45 | |
This is a classic example of a feedback loop. | 0:35:46 | 0:35:51 | |
We get a picture, in a picture, in a picture. | 0:35:51 | 0:35:55 | |
At first it seems fairly predictable. | 0:35:55 | 0:35:57 | |
But as we zoom the camera in | 0:35:57 | 0:36:00 | |
some pretty strange things begin to happen. | 0:36:00 | 0:36:03 | |
The first thing I notice is that the object I'm filming | 0:36:05 | 0:36:08 | |
stops bearing much resemblance to what now appears on the screen. | 0:36:08 | 0:36:13 | |
Small changes in the movement of the match become rapidly amplified | 0:36:17 | 0:36:22 | |
as they loop round from the camera to the screen and back to the camera. | 0:36:22 | 0:36:27 | |
So even though I can describe each step in the process mathematically, | 0:36:30 | 0:36:35 | |
I still have no way of predicting how tiny changes | 0:36:35 | 0:36:39 | |
in the flickering of the flame will end up in the final image. | 0:36:39 | 0:36:42 | |
This is the butterfly effect in action. | 0:36:46 | 0:36:49 | |
But now here comes the spooky bit. | 0:36:55 | 0:36:58 | |
With just a slight tweak to the system, | 0:37:00 | 0:37:03 | |
these strange and rather beautiful patterns begin to emerge. | 0:37:03 | 0:37:09 | |
The same system, one that's based on simple rules with feedback, | 0:37:11 | 0:37:16 | |
produces chaos and order. | 0:37:16 | 0:37:19 | |
The same mathematics is generating chaotic behaviour | 0:37:27 | 0:37:31 | |
and patterned behaviour. | 0:37:31 | 0:37:34 | |
This changes completely how you think about all of this. | 0:37:34 | 0:37:38 | |
The idea that there are regularities in nature and then, | 0:37:38 | 0:37:41 | |
totally separately from them, | 0:37:41 | 0:37:44 | |
are irregularities, and these are just two different things, | 0:37:44 | 0:37:47 | |
is just not true. | 0:37:47 | 0:37:49 | |
These are two ends of a spectrum of behaviour | 0:37:49 | 0:37:51 | |
which can be generated by the same kind of mathematics. | 0:37:51 | 0:37:55 | |
And it's the closest thing we have at the moment to the kind of true mathematics of nature. | 0:37:55 | 0:38:00 | |
I think one of the great take home messages from Turing's work and from | 0:38:01 | 0:38:06 | |
the discoveries in chemistry and biology and so on, is that | 0:38:06 | 0:38:10 | |
ultimately, pattern formation seems to be woven, very, very deeply | 0:38:10 | 0:38:13 | |
into the fabric of the universe. And it actually takes some very simple | 0:38:13 | 0:38:17 | |
and familiar processes, like diffusion, | 0:38:17 | 0:38:20 | |
like the rates of chemical reactions, | 0:38:20 | 0:38:22 | |
and the interplay between them naturally gives rise to pattern. | 0:38:22 | 0:38:26 | |
So pattern is everywhere, it's just waiting to happen. | 0:38:26 | 0:38:30 | |
From the '70s on, more and more scientists | 0:38:32 | 0:38:36 | |
began to embrace the concept that chaos | 0:38:36 | 0:38:39 | |
and pattern are built into nature's most basic rules. | 0:38:39 | 0:38:44 | |
But one scientist more than any other brought a fundamentally new | 0:38:44 | 0:38:48 | |
understanding to this astonishing and often puzzling idea. | 0:38:48 | 0:38:52 | |
He was a colourful character and something of a maverick. | 0:38:54 | 0:38:58 | |
His name is Benoit Mandelbrot. | 0:38:58 | 0:39:01 | |
Benoit Mandelbrot wasn't an ordinary child. | 0:39:03 | 0:39:07 | |
He skipped the first two years of school | 0:39:07 | 0:39:09 | |
and as a Jew in war-torn Europe his education was very disrupted. | 0:39:09 | 0:39:14 | |
He was largely self-taught or tutored by relatives. | 0:39:14 | 0:39:18 | |
He never formally learned the alphabet, | 0:39:18 | 0:39:21 | |
or even multiplication beyond the five times table. | 0:39:21 | 0:39:24 | |
But, like Alan Turing, | 0:39:27 | 0:39:29 | |
Mandelbrot had a gift for seeing nature's hidden patterns. | 0:39:29 | 0:39:33 | |
He could see rules where the rest of us see anarchy. | 0:39:33 | 0:39:37 | |
He could see form and structure, | 0:39:37 | 0:39:39 | |
where the rest of us just see a shapeless mess. | 0:39:39 | 0:39:42 | |
And above all, he could see that a strange new kind of mathematics | 0:39:42 | 0:39:47 | |
underpinned the whole of nature. | 0:39:47 | 0:39:49 | |
Mandelbrot's lifelong quest was to find a simple mathematical basis | 0:39:53 | 0:39:57 | |
for the rough and irregular shapes of the real world. | 0:39:57 | 0:40:02 | |
Mandelbrot was working for IBM | 0:40:05 | 0:40:07 | |
and he was not in the normal academic environment. | 0:40:07 | 0:40:10 | |
And he was working on a pile of different problems | 0:40:10 | 0:40:13 | |
about irregularities in nature, in the financial markets, | 0:40:13 | 0:40:17 | |
all over the place. | 0:40:17 | 0:40:18 | |
And I think at some point it dawned on him that everything | 0:40:18 | 0:40:21 | |
he was doing seen to be really parts of the same big picture. | 0:40:21 | 0:40:25 | |
And he was a sufficiently original and unusual person that | 0:40:25 | 0:40:30 | |
he realised that pursuing this big picture was what | 0:40:30 | 0:40:34 | |
-he really wanted to do. -To Mandelbrot, it seemed perverse that | 0:40:34 | 0:40:37 | |
mathematicians had spent centuries contemplating idealised shapes | 0:40:37 | 0:40:42 | |
like straight lines or perfect circles. | 0:40:42 | 0:40:45 | |
And yet had no proper or systematic way of describing the rough | 0:40:45 | 0:40:49 | |
and imperfect shapes that dominate the real world. | 0:40:49 | 0:40:53 | |
Take this pebble. | 0:40:55 | 0:40:57 | |
Is it a sphere or a cube? | 0:40:58 | 0:41:01 | |
Or maybe a bit of both? | 0:41:01 | 0:41:03 | |
And what about something much bigger? Look at the arch behind me. | 0:41:03 | 0:41:08 | |
From a distance, it looks like a semi-circle. | 0:41:08 | 0:41:12 | |
But up close, we see that it's bent and crooked. | 0:41:12 | 0:41:15 | |
So what shape is it? | 0:41:17 | 0:41:19 | |
Mandelbrot asked if there's something unique | 0:41:23 | 0:41:25 | |
that defines all the varied shapes in nature. | 0:41:25 | 0:41:29 | |
Do the fluffy surfaces of clouds, the branches in trees and rivers, | 0:41:29 | 0:41:33 | |
the crinkled edges of shorelines, share a common mathematical feature? | 0:41:33 | 0:41:39 | |
Well, they do. | 0:41:39 | 0:41:42 | |
Underlying nearly all the shapes in the natural world is a mathematical | 0:41:42 | 0:41:47 | |
principle known as self-similarity. This describes anything in which the | 0:41:47 | 0:41:53 | |
same shape is repeated over and over again at smaller and smaller scales. | 0:41:53 | 0:42:00 | |
A great example are the branches of trees. | 0:42:02 | 0:42:04 | |
They fork and fork again, repeating that simple process | 0:42:04 | 0:42:08 | |
over and over at smaller and smaller scales. | 0:42:08 | 0:42:13 | |
The same branching principle applies in the structure of our lungs | 0:42:14 | 0:42:19 | |
and the way our blood vessels are distributed throughout our bodies. | 0:42:19 | 0:42:23 | |
It even describes how rivers split into ever smaller streams. | 0:42:25 | 0:42:30 | |
And nature can repeat all sorts of shapes in this way. | 0:42:30 | 0:42:33 | |
Look at this Romanesco broccoli. | 0:42:35 | 0:42:38 | |
Its overall structure is made up of a series of repeating cones | 0:42:38 | 0:42:42 | |
at smaller and smaller scales. | 0:42:42 | 0:42:46 | |
Mandelbrot realised self-similarity | 0:42:47 | 0:42:50 | |
was the basis of an entirely new kind of geometry. | 0:42:50 | 0:42:54 | |
And he even gave it a name - fractal. | 0:42:54 | 0:42:58 | |
Now, that's a pretty neat observation. | 0:43:00 | 0:43:03 | |
But what if you could represent this property of nature in mathematics? | 0:43:03 | 0:43:07 | |
What if you could capture its essence to draw a picture? | 0:43:07 | 0:43:11 | |
What would that picture look like? | 0:43:11 | 0:43:13 | |
Could you use a simple set of mathematical rules | 0:43:13 | 0:43:17 | |
to draw an image that didn't look man-made? | 0:43:17 | 0:43:20 | |
The answer would come from Mandelbrot. | 0:43:20 | 0:43:23 | |
Who had taken a job at IBM in the late 1950s | 0:43:23 | 0:43:26 | |
to gain access to its incredible computing power | 0:43:26 | 0:43:30 | |
and pursue his obsession with the mathematics of nature. | 0:43:30 | 0:43:35 | |
Armed with a new breed of super-computer, | 0:43:35 | 0:43:38 | |
he began investigating a rather curious | 0:43:38 | 0:43:42 | |
and strangely simple-looking equation | 0:43:42 | 0:43:44 | |
that could be used to draw a very unusual shape. | 0:43:44 | 0:43:48 | |
What I'm about to show you is one of the most remarkable | 0:43:48 | 0:43:52 | |
mathematical images ever discovered. Epic doesn't really do it justice. | 0:43:52 | 0:43:59 | |
This is the Mandelbrot set. | 0:43:59 | 0:44:03 | |
It's been called the thumbprint of God. | 0:44:03 | 0:44:07 | |
And when we begin to explore it, you'll understand why. | 0:44:07 | 0:44:10 | |
Just as with the tree or the broccoli, | 0:44:18 | 0:44:21 | |
the closer you study this picture, the more detail you see. | 0:44:21 | 0:44:25 | |
Each shape within the set | 0:44:29 | 0:44:31 | |
contains an infinite number of smaller shapes. | 0:44:31 | 0:44:34 | |
Baby Mandelbrots that go on for ever. | 0:44:34 | 0:44:37 | |
Yet all this complexity stems from just one incredibly simple equation. | 0:44:43 | 0:44:48 | |
This equation has a very important property. | 0:44:49 | 0:44:53 | |
It feeds back on itself. | 0:44:53 | 0:44:55 | |
Like a video loop, each output becomes the input for the next go. | 0:44:56 | 0:45:02 | |
This feedback means that an incredibly simple mathematical | 0:45:06 | 0:45:09 | |
equation can produce a picture of infinite complexity. | 0:45:09 | 0:45:14 | |
The really fascinating thing | 0:45:31 | 0:45:33 | |
is that the Mandelbrot set isn't just a bizarre mathematical quirk. | 0:45:33 | 0:45:38 | |
Its fractal property of being similar at all scales | 0:45:38 | 0:45:42 | |
mirrors a fundamental ordering principle in nature. | 0:45:42 | 0:45:46 | |
Turing's patterns, Belousov's reaction and Mandelbrot's fractals | 0:45:51 | 0:45:57 | |
are all signposts pointing to a deep underlying natural principle. | 0:45:57 | 0:46:02 | |
When we look at complexities in nature, we tend to ask, | 0:46:05 | 0:46:08 | |
"Where did they come from?" | 0:46:08 | 0:46:10 | |
There is something in our heads that says | 0:46:10 | 0:46:13 | |
complexity does not arise out of simplicity. | 0:46:13 | 0:46:15 | |
It must arise from something complicated. We conserve complexity. | 0:46:15 | 0:46:19 | |
But what the mathematics in this whole area is telling us | 0:46:19 | 0:46:22 | |
is that very simple rules naturally give rise to very complex objects. | 0:46:22 | 0:46:27 | |
And so if you look at the object, it looks complex, and you think about | 0:46:27 | 0:46:30 | |
the rule that generates it, it's simple. | 0:46:30 | 0:46:32 | |
So the same thing is both complex and simple | 0:46:32 | 0:46:35 | |
from two different points of view. And that means we have to rethink | 0:46:35 | 0:46:38 | |
completely the relation between simplicity and complexity. | 0:46:38 | 0:46:42 | |
Complex systems can be based on simple rules. | 0:46:45 | 0:46:50 | |
That's the big revelation. | 0:46:50 | 0:46:52 | |
And it's an astonishing idea. | 0:46:52 | 0:46:55 | |
It seems to apply all over our world. | 0:46:56 | 0:46:59 | |
Look at a flock of birds. Each bird obeys very simple rules. | 0:47:10 | 0:47:15 | |
But the flock as a whole does incredibly complicated things. | 0:47:15 | 0:47:19 | |
Avoiding obstacles, navigating the planet with no single leader | 0:47:19 | 0:47:25 | |
or even conscious plan. But amazing though this flock's behaviour is, | 0:47:25 | 0:47:31 | |
it's impossible to predict how it will behave. | 0:47:31 | 0:47:34 | |
It never repeats exactly what it does, | 0:47:36 | 0:47:39 | |
even in seemingly identical circumstances. | 0:47:39 | 0:47:42 | |
It's just like the Belousov reaction. | 0:47:45 | 0:47:48 | |
Each time you run it, the patterns produced are slightly different. | 0:47:48 | 0:47:53 | |
They may look similar, but they are never identical. | 0:47:53 | 0:47:56 | |
The same is true of video loops and sand dunes. | 0:47:56 | 0:48:01 | |
We know they'll produce a certain kind of pattern, | 0:48:01 | 0:48:05 | |
but we can't predict the exact shapes. | 0:48:05 | 0:48:08 | |
The big question is, can nature's ability to turn simplicity | 0:48:12 | 0:48:17 | |
into complexity in this mysterious and unpredictable way | 0:48:17 | 0:48:21 | |
explain why life exists? | 0:48:21 | 0:48:24 | |
Can it explain how a universe full of simple dust | 0:48:26 | 0:48:29 | |
can turn into human beings? | 0:48:29 | 0:48:32 | |
How inanimate matter can spawn intelligence? | 0:48:33 | 0:48:37 | |
At first, you might think that this is beyond the remit of science. | 0:48:39 | 0:48:43 | |
If nature's rules are really unpredictable, | 0:48:43 | 0:48:46 | |
should we simply give up? | 0:48:46 | 0:48:48 | |
Absolutely not. In fact, quite the opposite. | 0:48:48 | 0:48:51 | |
Fittingly, the answer to this problem lies in the natural world. | 0:48:54 | 0:48:58 | |
All around us, there exists a process that engineers | 0:48:58 | 0:49:03 | |
these unpredictable complex systems | 0:49:03 | 0:49:05 | |
and hones them to perform almost miraculous tasks. | 0:49:05 | 0:49:10 | |
The process is called evolution. | 0:49:12 | 0:49:15 | |
Evolution has built on these patterns. | 0:49:17 | 0:49:20 | |
It's taken them as the raw ingredients. | 0:49:20 | 0:49:22 | |
It's combined them together in various ways, | 0:49:22 | 0:49:26 | |
experimented to see what works and what doesn't, | 0:49:26 | 0:49:29 | |
kept the things that do work and then built on that. | 0:49:29 | 0:49:34 | |
It's a completely unconscious process, | 0:49:34 | 0:49:36 | |
but basically that's what's happening. | 0:49:36 | 0:49:38 | |
Everywhere you look, you can see evolution | 0:49:38 | 0:49:41 | |
using nature's self-organising patterns. | 0:49:41 | 0:49:45 | |
Our hearts use Belousov-type reactions to regulate how they beat. | 0:49:45 | 0:49:50 | |
Our blood vessels are organised like fractals. | 0:49:50 | 0:49:54 | |
Even our brain cells interact according to simple rules. | 0:49:54 | 0:50:00 | |
The way evolution refines and enriches complex systems | 0:50:00 | 0:50:05 | |
is one of the most intriguing ideas in recent science. | 0:50:05 | 0:50:09 | |
My interest in my PhD research in complex systems was to see | 0:50:12 | 0:50:15 | |
how complex systems interact with evolution. | 0:50:15 | 0:50:18 | |
So, on the one hand you have systems that almost organise themselves | 0:50:18 | 0:50:22 | |
as complex systems, so they exhibit order that you wouldn't expect, | 0:50:22 | 0:50:26 | |
but on the other hand, you still have to have evolution interact with | 0:50:26 | 0:50:30 | |
that to create something that is truly adapted to the environment. | 0:50:30 | 0:50:33 | |
Evolution's mindless, yet creative, power to develop | 0:50:33 | 0:50:38 | |
and shape complex systems is indeed incredible. | 0:50:38 | 0:50:42 | |
But it operates on a cosmic timescale. | 0:50:43 | 0:50:46 | |
From the first life on Earth, to us walking about, | 0:50:48 | 0:50:51 | |
took in the region of 3.5 billion years. | 0:50:51 | 0:50:55 | |
But we now have in our hands | 0:50:56 | 0:50:59 | |
a device that can mimic this process on a much shorter timescale. | 0:50:59 | 0:51:04 | |
What is the invention I'm talking about? | 0:51:04 | 0:51:08 | |
Well, there's a good chance you've been sitting in front of one all day. | 0:51:08 | 0:51:12 | |
It is, of course, the computer. | 0:51:13 | 0:51:16 | |
Computers today can churn through trillions of calculations per second. | 0:51:21 | 0:51:27 | |
And that gives them the power to do something very special. | 0:51:27 | 0:51:30 | |
They can simulate evolution. | 0:51:30 | 0:51:34 | |
More precisely, computers can use the principles of evolution to shape | 0:51:35 | 0:51:40 | |
and refine their own programs, in the same way the natural world | 0:51:40 | 0:51:44 | |
uses evolution to shape and refine living organisms. | 0:51:44 | 0:51:49 | |
And today, computer scientists find that this evolved software | 0:51:49 | 0:51:55 | |
can solve problems that would be beyond the smartest of humans. | 0:51:55 | 0:52:00 | |
One thing that we found particularly in our original research is how | 0:52:00 | 0:52:04 | |
powerful evolution is as a system, as an algorithm, to create something | 0:52:04 | 0:52:08 | |
that is very complex and to create something that is very adaptive. | 0:52:08 | 0:52:12 | |
Torsten and his team's goal was nothing less | 0:52:12 | 0:52:16 | |
than to use computerised evolution | 0:52:16 | 0:52:18 | |
to create a virtual brain that would control a virtual body. | 0:52:18 | 0:52:23 | |
To begin with, they created 100 random brains. | 0:52:24 | 0:52:29 | |
As you can see, they weren't up to much. | 0:52:29 | 0:52:31 | |
Evolution then took over. | 0:52:33 | 0:52:35 | |
The computer selected the brains that were slightly better | 0:52:35 | 0:52:40 | |
at moving their bodies and got them to breed. | 0:52:40 | 0:52:43 | |
The algorithm then takes those individuals that do the best | 0:52:45 | 0:52:49 | |
and it allows them to create offspring. | 0:52:49 | 0:52:51 | |
The best movers of the next generation | 0:52:53 | 0:52:56 | |
were then bred together and so on and on. | 0:52:56 | 0:52:59 | |
Amazingly, after just 10 generations, | 0:52:59 | 0:53:03 | |
although they're still a bit unsteady, the figures could walk. | 0:53:03 | 0:53:08 | |
Eventually, miraculously, you actually end up | 0:53:09 | 0:53:11 | |
with something that works. The slightly scary thing | 0:53:11 | 0:53:14 | |
is you don't know why it works and how it works. | 0:53:14 | 0:53:17 | |
You look at that brain and you have no idea actually what's going on | 0:53:17 | 0:53:20 | |
because evolution has optimised it automatically. | 0:53:20 | 0:53:23 | |
In 20 generations, evolution had turned this... | 0:53:26 | 0:53:31 | |
..into this. | 0:53:31 | 0:53:33 | |
But these evolved computer beings soon went far beyond just walking. | 0:53:36 | 0:53:41 | |
They evolved to do things | 0:53:44 | 0:53:46 | |
that really are impossible to program conventionally. | 0:53:46 | 0:53:49 | |
They react realistically to unexpected events. | 0:53:53 | 0:53:57 | |
Like being hit or falling over. | 0:53:57 | 0:54:00 | |
Even though we programmed these algorithms, what actually happens | 0:54:03 | 0:54:07 | |
when it unfolds live, we don't control any more | 0:54:07 | 0:54:10 | |
and things happen that we never expected. | 0:54:10 | 0:54:12 | |
And it's quite a funny feeling | 0:54:12 | 0:54:14 | |
that you create these algorithms but then they do their own thing. | 0:54:14 | 0:54:18 | |
An unthinking process of evolutionary trial and error | 0:54:24 | 0:54:28 | |
has created these virtual creatures that can move and react in real time. | 0:54:28 | 0:54:34 | |
What we're seeing here is fantastic experimental evidence | 0:54:39 | 0:54:43 | |
for the creative power of systems based on simple rules. | 0:54:43 | 0:54:47 | |
Watching how computers can unconsciously evolve programs | 0:54:57 | 0:55:02 | |
to do things that no human could consciously program | 0:55:02 | 0:55:05 | |
is a fantastic example of the power of self-organisation. | 0:55:05 | 0:55:11 | |
It demonstrates that evolution is itself | 0:55:11 | 0:55:14 | |
just like the other systems we've encountered. | 0:55:14 | 0:55:18 | |
One based on simple rules and feedback. | 0:55:18 | 0:55:21 | |
From which complexity spontaneously emerges. | 0:55:21 | 0:55:25 | |
Think about it. The simple rule is that the organism | 0:55:26 | 0:55:30 | |
must replicate with a few random mutations now and again. | 0:55:30 | 0:55:36 | |
The feedback comes from the environment | 0:55:36 | 0:55:39 | |
which favours the mutations that are best suited to it. | 0:55:39 | 0:55:43 | |
The result is ever-increasing complexity, | 0:55:43 | 0:55:47 | |
produced without thought or design. | 0:55:47 | 0:55:51 | |
The interesting thing is that one can move up | 0:55:52 | 0:55:55 | |
to a higher level of organisation. Once you have organisms | 0:55:55 | 0:55:58 | |
that actually have patterns on them, these can be selected for | 0:55:58 | 0:56:02 | |
or selected against by processes which are essentially feedbacks. | 0:56:02 | 0:56:07 | |
And so evolution itself, the whole Darwinian scheme, | 0:56:07 | 0:56:11 | |
is, in a sense, Turing again | 0:56:11 | 0:56:14 | |
with feedbacks happening through different processes. | 0:56:14 | 0:56:17 | |
And that's the essence of this story. | 0:56:19 | 0:56:21 | |
Unthinking, simple rules have the power to create | 0:56:21 | 0:56:26 | |
amazingly complex systems without any conscious thought. | 0:56:26 | 0:56:30 | |
In that sense, these computer beings are self-organised systems, | 0:56:31 | 0:56:36 | |
just like the one Belousov observed happening in his chemicals. | 0:56:36 | 0:56:41 | |
Just like the ones in sand dunes and the Mandelbrot sets, | 0:56:42 | 0:56:46 | |
in our lungs, our hearts, in weather | 0:56:46 | 0:56:51 | |
and in the geography of our planet. | 0:56:51 | 0:56:53 | |
Design does not need an active, interfering designer. | 0:56:53 | 0:56:58 | |
It's an inherent part of the universe. | 0:56:58 | 0:57:02 | |
One of the things that makes people so uncomfortable about this idea of, | 0:57:06 | 0:57:10 | |
if you will, spontaneous pattern formation, is that somehow or other | 0:57:10 | 0:57:15 | |
you don't need a creator. But perhaps a really clever designer, | 0:57:15 | 0:57:19 | |
what he would do, is to kind of treat the universe | 0:57:19 | 0:57:22 | |
like a giant simulation, where you set some initial condition | 0:57:22 | 0:57:26 | |
and just let the whole thing spontaneously happen | 0:57:26 | 0:57:30 | |
in all of its wonder and all of its beauty. | 0:57:30 | 0:57:32 | |
The mathematics of pattern formation shows that the same kind of pattern | 0:57:35 | 0:57:39 | |
can show up in an enormous range of different physical, | 0:57:39 | 0:57:42 | |
chemical, biological systems. Somewhere deep down inside, | 0:57:42 | 0:57:46 | |
it's happening for the same mathematical reason. | 0:57:46 | 0:57:49 | |
Implicit in those facts are these beautiful patterns | 0:57:49 | 0:57:53 | |
that we see everywhere. | 0:57:53 | 0:57:55 | |
This, I think, is a mind-blowing thought. | 0:57:55 | 0:57:58 | |
So, what is the ultimate lesson we can take from all this? | 0:58:07 | 0:58:12 | |
Well, it's that all the complexity of the universe, | 0:58:12 | 0:58:15 | |
all its infinite richness, | 0:58:15 | 0:58:18 | |
emerges from mindless simple rules, repeated over and over again. | 0:58:18 | 0:58:23 | |
But remember, powerful though this process is, | 0:58:23 | 0:58:27 | |
it's also inherently unpredictable. | 0:58:27 | 0:58:30 | |
So although I can confidently tell you that the future will be amazing, | 0:58:30 | 0:58:36 | |
I can also say, with scientific certainty, | 0:58:36 | 0:58:40 | |
that I have no idea what it holds. | 0:58:40 | 0:58:43 | |
Subtitles by Red Bee Media Ltd | 0:59:04 | 0:59:07 | |
E-mail [email protected] | 0:59:07 | 0:59:10 |