(soft piano music)
- This is a film about one very simple question:
how did we get here?
These are the elements and compounds
from which all humans are made.
They're incredibly, almost embarrassingly, common.
In fact, almost 99% of the human body
is a mixture of air, water, coal, and chalk,
with traces of other slightly more exotic elements
like iron, zinc, phosphorous, and sulfur.
In fact, I've estimated that the elements which make up
the average human cost at most a few pounds.
But somehow trillions of these very ordinary atoms
conspire miraculously to organize themselves
into thinking, breathing, living human beings.
How the wonders of creation are assembled
from such simple building blocks
is surely the most intriguing question we can ask.
You may think that answering it
is beyond the realm of science.
But that's changing.
For the first time, I believe,
science has pushed past religion and philosophy
in daring to tackle this most fundamental of questions.
This film is the story of a series
of bizarre and interconnected discoveries.
It reveals a hidden safe of nature.
That woven into it's simplest and most basic laws
is a power to be unpredictable.
It's about how inanimate matter with no purpose or design
can spontaneously create exquisite beauty.
It's about how the same laws that make
the universe chaotic and unpredictable
can turn simple dust into human beings.
It's about the discovery that there is
a strange and unexpected relationship
between order and chaos.
(soft piano music)
The natural world really is one great,
blooming, buzzing confusion.
It's a mess of quirky shapes and blotches.
What patterns there are are never quite regular,
and never seem to repeat exactly.
The idea that all this mayhem, all this chaos
is underpinned, indeed determined, by mathematical rules,
and that we can work out what those rules might be
run counter to our most dearly held intuitions.
So not surprisingly, the first man to really
take on the momentous task of unraveling
nature's mysterious mathematics
had a very special and unusual mind.
He was both a great scientist
and a tragic hero.
He was born in 1912 in London.
His name was Alan Turing.
Alan Turing was a remarkable man;
one of the greatest mathematicians who ever lived.
He discovered many of the fundamental ideas
that underpin the modern computer.
Also, during the Second World War, he worked here
at Bletchley Park just outside today's Milton Keynes
in what was then a secret government project
called Station X, which was set up
to crack the German military codes.
The Station X code breakers proved highly effective,
and Turing's contribution was crucial.
The work he personally did to crack
German naval codes saved thousands of Allied lives
and was a turning point in the war.
But code breaking was just one aspect of Turing's genius.
Just one part of his uncanny ability
to see patterns that are hidden from the rest of us.
For Turing, the natural world offered up the ultimate codes.
And over the course of his life,
he'd come tantalizingly close to cracking them.
- Turing was a very original person.
And he had realized that there was this possibility
that simple mathematical equations
might describe aspects of the biological world,
and no one had thought of that before.
- [Jim] Of all nature's mysteries,
the one that fascinated Turing most
was the idea that there might be a mathematical basis
to human intelligence.
Turing had very personal reasons for believing in this.
- It was the death of this young man, Christopher Morton,
who Alan Turing, well, he was gay,
and he'd been a great
emotional thing of this life at that point.
Christopher Morton suddenly died.
And Alan Turing was very,
obviously, he was very emotionally disturbed by this.
But you can see is he wanted to put this
in a intellectual context, a scientific context.
And the question he wanted to put into context was
what happens to the mind?
What is it?
- [Jim] Turing became convinced that mathematics
could be used to describe biological systems
and, ultimately, intelligence.
This fascination would give rise to the modern computer,
and later in Turing's life, an even more radical idea.
The idea that the simple mathematical description
could be given for a mysterious process
that takes place in an embryo.
The process is called morphogenesis,
and it's very puzzling.
At first, all the cells in the embryo are identical.
Then, the cells begin to clump together
and also become different from each other.
How does this happen?
With no thought,
no central coordination,
how do cells that start off identical
know to become, say, skin,
while others become part of an eye.
Morphogenesis is a spectacular example
of something called self organization.
And before Turing,
no one had a clue how it worked.
Then in 1952, Turing published this.
His paper was the world's first mathematical
explanation for morphogenesis.
The sheer chutzpah of this paper was staggering.
In it, Turing used a mathematical equation
of the type normally seen in papers on astronomy
or atomic physics to describe a living process.
No one had done anything like this.
Crucially, Turing's equations did, for the first time,
describe how a biological system could self organize.
They showed that something smooth and featureless
can develop features.
- One of the astonishing things about Turing's work
was that starting with the description of
really very simple processes
that were governed by very simple equations,
by putting these together, suddenly
complexity emerged.
The pattern suddenly came out as a natural consequence.
And I think in many ways this was very, very unexpected.
- [Jim] In essence, Turing's equations
described something quite familiar,
but which no one had thought of
in the context of biology before.
Think of the way a steady wind flowing across sand
creates all kinds of shapes.
The grains self organize into ripples, waves, and dunes.
This happens even though the grains are virtually identical
and have no knowledge of the shape they become part of.
Turing argues that, in a very similar way,
chemicals seeping across an embryo
might cause its cells to self organize
into different organs.
These are Turing's own very rough scribblings
of how this might work.
They show how a completely featureless chemical soup
can evolve these strange mods and patches.
In his paper, he refined his sketches
to show how his equations could spontaneously
create markings similar to those
on the skins of animals.
- Turing went around showing people pictures, saying,
"Does this look a bit like the patterns on a cow?"
And everyone sort of, what is this man on about?
But actually, and he knew what he was doing,
because yes, indeed, they did like the patterns on a cow,
and that's one of the reasons have this
sort of duffle pattern order.
So an area where mathematics have never been used before,
pattern formation in biology, animal markings,
suddenly the door was opened and we could see that
mathematics might be useful in that sort of area.
So even though Turing's exact equations
are not the full story,
they are the first piece
of mathematical work that showed there was
any possibility of doing this kind of thing.
- [Jim] Of course, we now know
that morphogenesis is much more complicated
than the process Turing's equations describe.
In fact, the precise mechanism of how
DNA molecules in our cells
interacts with other chemicals
is still fiercely debated by scientists.
But Turing's idea that whatever is going
is deep down a simple mathematical process
was truly revolutionary.
- I think Alan Turing's paper is
probably the cornerstone in the whole idea
of how morphogenesis works.
What it does is it provides us with a mechanism,
something that Darwin didn't for how pattern emerges.
Darwin, of course, tells us that once you have a pattern
and it is coded for in the genes,
that may or may not be passed on
depending on circumstances.
But what it doesn't do is explain
where that pattern comes from in the first place.
That's the real mystery.
And so what Turing's had done
was to suddenly provide an accessible
chemical mechanism for doing this.
That was amazing.
- [Jim] Turing was onto a really big, bold idea.
But sadly, we can only speculate how his
extraordinary mind would have developed his idea.
Because shortly after his groundbreaking paper
on morphogenesis, a dreadful
and completely avoidable tragedy destroyed his life.
After his work breaking codes at Bletchley Park,
you might all have assumed that Turing
would have been by the country
he did so much to protect.
This couldn't be further from the truth.
What happened to him after the war
was a great tragedy,
and one of the most shameful episodes
in the history of British science.
The same year Turing published his morphogenesis paper,
he had a brief affair with a man called Arnold Murray.
The affair went sour, and Murray was involved
in a burglary at Turing's house.
But when Turing reported this to the police,
they arrested him as well as Murray.
In court, the prosecution then argued
that Turing, with his university education,
had led Murray astray.
He was convicted of gross indecency.
The judge then offered Turing a dreadful choice.
He could either go to prison
or sign up to a regime of female hormone injections
to cure him of his homosexuality.
He chose the latter, and it was to send him
into a spiral of depression.
On the 8th of June, 1954,
Turing's body was found by his cleaner.
He died the day before by taking a bite from an apple
he'd laced with cyanide, ending his own life.
(somber violin music)
Alan Turing died aged just 41.
The loss to science is incalculable.
Turing would never know that his ideas
would inspire an entirely new
mathematical approach to biology,
and that scientists would find equations like his
really do explain many of the shapes
that appear on living organisms.
Looking back, we now know Turing
had really grasped the idea that
the wonders of creation are derived
from the simplest of rules.
He had, perhaps unexpectedly,
taken the first step to a new kind of science.
The next step in this story
was just as unexpected,
and in many ways just as tragic as Turing's.
In the early 1950s,
around the time of Turing's seminal paper on morphogenesis,
a brilliant Russian chemist by the name of Boris Belousov
was beginning his own investigations into
the chemistry of nature.
Deep behind the iron curtain
in a lab at the Soviet Ministry of Health,
he was beginning to investigate the way our bodies
extract energy from sugars.
Just like Turing, Belousov was working on a personal project
having just finished a distinguished career
as a scientist in the military.
In his lab, Belousov had formulated a mixture of chemicals
to mimic one part of the process of glucose absorption
in the body.
The mix of chemicals sat on the lab bench in front of him,
clear and colorless while being shaken.
As he mixed in the final chemical,
the whole solution changed color.
Now this isn't particularly remarkable.
If we mix ink into water, it changes color.
But then something happened that made no sense at all.
The mixture began to go clear again.
Belousov was astounded.
Chemicals can mix together and react.
But they shouldn't be able to go back on themselves
to apparently unmix without intervention.
You can change from a clear mixture to a colored mixture
fine, but surely not back again.
And it got weirder.
Belousov's chemicals didn't just spontaneously
go into reverse.
They oscillated.
They switched back and forth from colored to clear
as if they were being driven by some sort of
hidden chemical metronome.
With meticulous care, Belousov repeated his experiment
again and again.
It was the same every time.
His mixture would cycle from clear
to colored and back again repeatedly.
He discovered something that was almost like magic,
a physical process that seemed to violate
the laws of nature.
Convinced he'd discovered something of great importance,
Belousov wrote up his findings,
keen to share his discover with the wider world.
But when he submitted his paper to leading
Russian scientific journal,
he received a wholly unexpected and damning response.
The editor of the journal told Belousov
that his findings in the lab were quite simply impossible.
They contravene the fundamental laws of physics.
The only explanation was that Belousov
had made a mistake in his experiments.
And the work was simply not fit for publication.
The rejection crushed Belousov.
Deeply insulted by the suggestion his work
had been botched,
he abandoned his experiments.
Soon he gave up science altogether.
The tragic irony was that, divided as they were
by the iron curtain,
Belousov never encountered Turing's work.
For if he had, he would have been completely vindicated.
It turns out that Belousov's oscillating chemicals,
far from contravening the laws of physics,
were actually a real-world example
of precisely the behavior Turing's equations predicted.
While the connection might not appear
obvious at first sight,
other scientists showed that if you left
a variation of Belousov's chemicals,
unstirred in a Petri dish,
instead of simply oscillating, they self organized
into shapes.
In fact, they go beyond Turing's simple blobs and stripes
to create stunningly beautiful structures and patterns
out of nowhere.
- The amazing and very unexpected thing
about the Bizet Reaction
is that someone had discovered a system
which essentially reproduces the Turing equations.
And so from what looks like a very, very bland solution
emerged these astonishing patterns of waves
and scrolls and spirals.
- [Jim] Now this is emphatically not abstract science.
The way Belousov's chemicals move as coordinated waves
is exactly the way our heart cells
are coordinated as they beat.
Animal skins and heart beats.
Self organization seems to operate
all over the natural world.
So why were the scientific community
in Turing and Belousov's day
so uninterested or even hostile
to this astonishing and beautiful idea?
Well the reason was all too human.
Mainstream scientists simply didn't like it.
To them, it seemed to run counter to science
and all that it had achieved.
To change that view would require
a truly shocking and completely unexpected discovery.
In essence, by the beginning of the 20th century,
scientists saw the universe as a giant
complicated mechanical device,
kind of a super-sized version of this orrery.
The idea was that the universe is a huge
and intricate machine that obeys orderly mathematical rules.
If you knew the rules of how the machine
was configured to start with,
as you turn the handle over and over again,
it will behave in an entirely predictable way.
- Back in the times of Isaac Newton
when people were discovering the laws
that drove the universe,
they came up with this kind of metaphor
of a clockwork universe.
The universe looked like a machine
which had been set going at the instant of creation,
and just followed the rules and ticked along.
And it was a complicated machine,
and therefore complicated things happen.
But once you set it going, it would only do one thing.
And the message that people drew from this
was that anything describable by mathematical rules
must actually basically be fairly simple.
- [Jim] Find the mathematics that describes the system,
and you can then predict how that system will unfold.
That was the big idea.
It began with Newton's law of gravity,
which can be used to predict how a planet
moves around the Sun.
Scientists soon found many other equations
just like it.
Newtonian physics seemed like the ultimate crystal ball.
It held up the tantalizing possibility that the future
could, in principle, be known.
The more careful your measurements are today,
the better you can predict what will happen tomorrow.
But Newtonianism had a dangerous consequence.
If a nice mathematical system
that worked in a similar way to my orrery
did sometimes become unpredictable,
scientists assumed some malign outside force
was causing it.
Perhaps dirt had got it.
Perhaps the cogs were wearing out.
Or perhaps someone had tampered with it.
- Basically, we used to think if you saw
very irregular behavior in some
problem you're working on,
this must be the result of some sort of
random outside influences.
It couldn't be internally generated.
It wasn't an intrinsic part of the problem.
It was some other thing impacting on it.
- [Jim] Looked at from this point of view,
the whole idea of self organization seemed absurd.
The idea that patterns of the kind
Turing and Belousov had found
could appear of their own accord
without any outside influence was a complete taboo.
- [Man] Six, five, four, three--
- [Jim] The only way for self organization to be accepted
was for the domineering Newtonian view to collapse.
But that seemed very unlikely.
After all, by the late 60s,
it had delivered all the wonders of the modern age.
- [Man On Radio] Beautiful, beautiful
- [Man On Radio] Isn't that something?
(mumbles)
- [Jim] But then at the same time as the moon mission,
a small group of scientists, all ardent Newtonians,
quite unexpectedly found something wasn't right;
not right at all.
During the second half of the 20th century,
a devil was found in the detail.
A devil that would ultimately shatter the Newtonian dream,
and plunge us literally into chaos.
(chaotic electrical sounds)
Ironically, the events that forced scientists
to take self organization seriously
was the discovery of a phenomenon known as chaos.
Chaos is one of the most overused words in English.
But in science, has a very specific meaning.
It says that a system that is completely described
by mathematical equations
is more than capable of being unpredictable
without any outside interference whatsoever.
- There's a widespread misapprehension
that chaos is just somehow saying
the very familiar fact that everything's complicated.
I mean, the nitwit chaos assist in Jurassic Park
was under that confusion.
It's something much simpler and yet
much more complicated than that.
It says some very, very simple rules or equations
with nothing random in them;
they're completely determined;
we know everything about the rule;
can have outcomes that are entirely unpredictable.
- [Jim] Hail is one of the most unwelcome
discoveries in science.
The man who forced the scientific community
to confront it was an American (mumbles) zoologist
called Edward Lorenz.
In the early 1960s, he tried to find
mathematical equations that could help predict the weather.
Like all his contemporaries, he believed that, in principle,
the weather system was no different to my orrery.
A mechanical system that could be described
and predicted mathematically.
But he was wrong.
When Lorenz wrote down what looked like
perfectly simple mathematical equations
to describe the movement of air currents,
they didn't do what they were supposed to.
They made no useful predictions whatsoever.
It was as if the lightest breath of wind one day
could make the difference a month later
between a snow storm and a perfectly sunny day.
How can a simple system that works
in the regular clockwork manner of my orrery
become unpredictable?
It's all down to how it's configured,
how the gears are connected.
In essence, under certain circumstances,
the tiniest difference in the starting positions
of the cogs, differences that are too small to measure,
can get bigger and bigger with each turn of the handle.
With each step in the process,
the system then moves further and further away
from where you thought it was going.
Lorenz captured this radical idea
in an influential talk he gave
called Does the Flap of a Butterfly's Wings
in Brazil Set Up a Tornado in Texas?
It was a powerful and evocative image,
and within months, a new phrase had entered our language:
the butterfly effect.
And the butterfly effect,
the hallmark of all chaotic systems,
started turning up everywhere.
In the early '70s, a young Australian called Robert May
was investigating a mathematical equation
that modeled how animal populations changed over time.
But here too lurked the dreaded butterfly effect.
Immeasurably small changes to the rate
at which the animals reproduced
could sometimes have huge consequences
on their overall population.
Numbers could go up and down wildly
for no obvious reason.
The idea that a mathematical equation
gave you the power to predict how a system will behave
was dead.
- In some sense, this is the end of the Newtonian dream.
When I was a graduate student,
the belief was
as we got more and more computer power,
we'd be able to solve ever more complicated
sets of equations.
But this said that's not necessarily true.
You could have the simplest equations you can think of,
with nothing random in them, you know everything.
And yet, if they have
behavior that gives you chaotic solutions,
then you can never know the starting point
accurately enough.
- [Jim] Centuries of scientific certainty
dissolved in just a few short years.
The truth of the clockwork universe
turned out to be just an illusion;
something which had seemed a logical certainty
revealed itself merely as an act of faith.
And what's worse, the truth had been staring us
in the face all the time,
because chaos is everywhere.
It seemed unpredictability was hardwired
into everywhere aspect of the world we live in.
The global climate could dramatically change
in the course of a few short years.
The stock market could crash without warning.
We could be wiped from the face of the planet overnight,
and there is nothing anyone could do about it.
Unfortunately, I have to tell you that all of this is true.
And yet to be scared of chaos is pointless.
It's woven into the basic laws of physics.
I mean, really all has to accept it as a fact of life.
- The idea of chaos really did have a big impact
over a period of about 20 or 30 years,
because it changed the way everyone
thought about what they were doing in science.
It changed into the point the point
that they forgot that they'd ever believed otherwise.
What chaos did was to show us
that the possibilities inherent in the simple mathematics
are much broader, are much more general
than you might imagine.
And so a clockwork universe
can nonetheless behave in the rich, complex way
that we experience.
- [Jim] The discovery of chaos was a real
turning point in the history of science.
As it tore down the Newtonian dream,
scientists began to look more favorably
at Turing and Belousov's work
on spontaneous pattern formation.
And perhaps more importantly, as they did so,
they realized something truly astonishing.
That there was a very deep and unexpected link,
a truly cosmic connection between nature's
strange power to self organize
and the chaotic consequences of the butterfly effect.
Between them, Turing, Belousov,
May, and Lorenz had all discovered
different faces of just one really big idea.
They discovered that the natural world
could be deeply, profoundly unpredictable.
But the very same things that make it unpredictable
also allow it to create pattern and structure,
order and chaos.
It seems the two are more deeply linked
than we could have ever imagined.
So how is this possible?
What do phenomena as apparently different
as a pattern in Belousov's chemicals
and the weather have in common?
First, though both systems behave
in very complicated ways,
they are both based on surprisingly simple
mathematical rules.
Secondly, these rules have a unique property.
A property that's often referred to as coupling,
or feedback.
To show you what I mean,
to show you both order and chaos can emerge on their own
from a simple system with feedback,
I'm going to do what seems at first glance
like a rather trivial experiment.
This screen behind me is connected
up to the camera that's filming me.
But the camera in turn is filming me with the screen.
This creates a loop with multiple copies of me
appearing on the screen.
This is a classic example of a feedback loop.
We get a picture in a picture in a picture.
At first it seems fairly predictable,
but as we zoom the camera in,
some pretty strange things begin to happen.
The first thing I notice is that the object I'm filming
stops bearing much resemblance to what
now appears on the screen.
Small changes in the movements of the match
become rapidly amplified as they loop around
from the camera to the screen and back to the camera.
So even though I can describe each step
in the process mathematically,
I still have no way of predicting
how tiny changes in the flickering of the flame
will end up in the final image.
This is the butterfly effect in action.
But now here comes the spooky bit.
With just a slight tweak to the system,
these strange and rather beautiful patterns
begin to emerge.
The same system, one that's based on simple rules
with feedback, produces chaos and order.
- The same mathematics is generating chaotic behavior
and patterned behavior.
This changes completely how you think about all of this.
The idea that there are regularities in nature
and then totally separately from them are irregularities,
and these are just two different things.
It's just not true.
These are two ends of the spectrum of behavior
which can be generated by the same kind of mathematics.
And it's the closest thing that we have at the moment
to the kind of true mathematics of nature.
- I think one of the great take-home messages
from Turing's work and from the discoveries
in chemistry and biology and so on,
is that, ultimately, pattern formation
seems to be woven very, very deeply
into the fabric of the universe.
And it actually takes some very, very simple
and familiar processes like diffusion,
like the rates of chemical reactions.
And the interplay between them naturally gives rise
to pattern.
So pattern is everywhere. It's just waiting to happen.
- [Jim] From the '70s on,
more and more scientists began to embrace
the concept that chaos and pattern
are built into nature's most basic rules.
But one scientist, more than any other,
brought this fundamentally new understanding
to this astonishing and often puzzling idea.
He was a colorful character and something of a maverick.
His name is Benoit Mandelbrot.
Benoit Mandelbrot wasn't an ordinary child.
He skipped the first two years of school.
And as a Jew in war-torn Europe,
his education was very disrupted.
He was largely self-taught
or tutored by relatives.
He never formally learned the alphabet
or even multiplication beyond the Five times table.
But like Alan Turing, Mandelbrot had a gift
for seeing nature's hidden patterns.
He could see rules where the rest of us see anarchy.
He could see form and structure
where the rest of us just see a shapeless mess.
And above all, he could see that a strange
new kind of mathematics underpin the whole of nature.
Mandelbrot's lifelong quest was to find
a simple mathematical basis for the rough
and irregular shapes of the real world.
- Mandelbrot was working for IBM,
and he was not in the normal academic environment.
And he was working on a whole pile of different
problems about irregularities in nature,
in the financial markets, all over the place.
And I think at some point it dawned on him
that everything he was doing seemed to be
really parts of the same big picture.
And he was a sufficiently original and unusual person
that he'd realized that pursuing this big picture
was what he really wanted to do.
- [Jim] To Mandelbrot, it seemed perverse
that mathematicians have spent centuries
contemplating idealized shapes like straight lines
or perfect circles, and yet had no proper
or systematic way of describing the rough
and imperfect shapes that dominate the real world.
Take this pebble.
Is it a sphere or a cube?
Or maybe a bit of both?
And what about something much bigger?
Look at the arch behind me.
From a distance, it looks like a semi-circle.
But up close, we'll see that it's bent and crooked.
So what shape is it?
Mandelbrot asked if there's something unique
that defines all the varied shapes in nature.
Do the fluffy surfaces of clouds,
the branches and trees and rivers,
the crinkled edges of shorelines
share a common mathematical feature?
Well, they do.
Underlying nearly all the shapes in the natural world
is a mathematical principle known as self similarity.
This describes anything in which the same shape
is repeated over and over again
at smaller and smaller scales.
A great example are the branches of trees.
They fork and fork again
repeating that simple process over and over
at smaller and smaller scales.
The same branching principles applied
in the structure of our lungs,
and the way our blood vessels are
distributed throughout our body.
It's even described how rivers
split into ever smaller streams.
And nature can repeat all sorts of shapes in this way.
Look at this Romanesco Broccoli.
It's overall structure is made up of a series
of repeating cones at smaller and smaller scales.
Mandelbrot realized self similarity was the basis
of an entirely new kind of geometry.
And he even gave it a name:
fractal.
Now that's a pretty neat observation.
But what if you could represent this property
of nature in mathematics?
What if you could capture its essence to draw a picture?
What would that picture look like?
Could you use a simple set of mathematical rules
to draw an image that didn't look man-made?
The answer would come from Mandelbrot,
who had take a job at IBM in the late 1950s
to gain access to its incredible computing power
and pursue his obsession with the mathematics of nature.
Armed with a new breed of supercomputer,
he began investigating a rather curious
and strangely simple-looking equation
that could be used to draw a very unusual shape.
What I'm about to show you
is one of the most remarkable mathematical images
ever discovered.
Epic doesn't really do it justice.
This is the Mandelbrot set.
It's been called the thumbprint of God.
And when we begin to explore it,
you'll understand why.
Just as with the tree or the broccoli,
the closer you study this picture,
the more detail you see.
Each shape within the step contains
an infinite number of smaller shapes,
baby Mandelbrots, that go on forever.
Yet all this complexity stems from
just one incredibly simple equation.
This equation has a very important property.
It feeds back on itself.
Like a video loop, each output
becomes the input for next set.
This feedback means that an incredibly simple
mathematical equation can produce
a picture of infinite complexity.
The really fascinating thing
is that the Mandelbrot set
isn't just a bizarre mathematical quirk.
Its fractal property of being similar at all scales
mirrors fundamental order, in principle, in nature.
Turing's patterns, Belousov's reactions,
and Mandelbrot's fractals are all signposts
pointing to a deep underlying natural principle.
- When we look at complexities in nature,
we tend to ask where did they come from.
There is something in our heads that says
complexity does not arise out of simplicity;
it must arise from something complicated
with conserved complexity.
But what the mathematics in this whole area
is telling us is that very simple rules
naturally give rise to very complex objects.
And so if you look at the object, it looks complex,
and you think about the rule that generates it,
it's simple.
So the same thing is both complex and simple
from two different points of view.
And that means we have to rethink completely
the relation between simplicity and complexity.
- [Jim] Complex systems can be based on simple rules.
That's the big revelation.
And it's an astonishing idea.
It seems to apply all over our world.
Look at the flock of birds.
Each bird obeys very simple rules.
But the flock as a whole
does incredibly complicated things.
Avoiding obstacles, navigating the planet
with no single leader or even conscious plan.
But amazing though this flock's behavior is,
it's impossible to predict how it will behave.
It never repeats exactly what it does,
even in seemingly identical circumstances.
It's just like the Belousov reaction.
Each time you run it, the patterns produced
are slightly different.
They may look similar but they are never identical.
The same is true of video loops and sand dunes.
We know they'll produce a certain kind of pattern,
but we can't predict the exact shapes.
The big question is can nature's ability
to turn simplicity into complexity
in this mysterious and unpredictable way
explain why life exists?
Can it explain how a universe full of simple dust
can turn into human beings?
How inanimate matter can spawn intelligence?
At first you might think that this is
beyond the remit of science.
If nature's rules are really unpredictable,
should we simply give up?
Absolutely not. In fact, quite the opposite.
Fittingly, the answer to this problem
lies in the natural world.
All around us there exists a process
that's engineered these unpredictable complex systems
and hones them to perform almost miraculous tasks.
The process is called evolution.
- Evolution has built on these patterns,
it's taken them as the raw ingredients.
It's combined them together in various ways,
experimented to see what works and what doesn't,
kept the things that do work,
and then built on that.
It's a completely unconscious process,
but basically that's what's happening.
- [Jim] Everywhere you look, you can see evolution
using nature's self organizing patterns.
Our hearts use the Belousov-type reactions
to regulate how they beat.
Our blood vessels are organized like fractals.
Even our brain cells interact according to simple rules.
The way evolution refines and enriches complex systems
is one of the most intriguing ideas in recent science.
- My interest in my Ph.D. research in complex systems
was to see how complex systems interact with evolution.
So on the one hand, you have systems that
almost organize themselves as complex systems.
So they exhibit order that you wouldn't expect.
But on the other hand, you still have to have evolution
interact with that to create something
that is truly adapted to the environment.
- [Jim] Evolution's mindless, yet creative, power
to develop and shape complex systems
is indeed incredible.
But it operates on a cosmic time scale.
From the first life on Earth to us walking about
took in the region of 3 1/2 billion years.
But we now have in our hands
a device that can mimic this process
on a much shorter timescale.
What is the invention I'm talking about?
Well there's a good chance you've been
sitting in front of one all day.
It is, of course, the computer.
Computers today can churn through
trillions of calculations per second.
And that gives them the power to do something very special.
They can simulate evolution.
More precisely, computers can use the principles
of evolution to shape and refine their own program
in the same way the natural world uses evolution
to shape and refine living organisms.
And today, computer scientists find that
this evolved software can solve problems
that would be beyond the smartest of humans.
- One thing that we found, and particularly in
our original research, is how powerful
evolution is as a system, as an algorithm
to create something that is very complex,
and to create something that is very adaptive.
- [Jim] Swarston and his team's goal
was nothing less than to use computerized evolution
to create a virtual brain that would control a virtual body.
To begin with, they created 100 random brains.
As you can see, they weren't up to much.
Evolution then took over.
The computer selected the brain
that was slightly better at moving their bodies,
and got them to breed.
- The algorithm then takes those individuals
that do the best, and then allows them to create offspring.
- [Jim] The best movers of the next generation
were then bred together, and so on and on.
Amazingly, after just 10 generations,
although they're still a bit unsteady,
the figures could walk.
- Eventually, miraculously,
you actually end up with something that works.
The slightly scary thing is you don't know
why it works and how it works.
You look at that brain,
and you have no idea actually what's going on,
because evolution has optimized it automatically.
- [Jim] In 20 generations,
evolution had turned this
into this.
But these evolved computer beings
soon went far beyond just walking.
They evolved to do things that really are
impossible to program conventionally.
They react realistically to unexpected events,
like being hit or falling over.
- Even though we programmed these algorithms,
what actually then happens when it unfolds live
we don't control anymore.
And things happen that we never expected.
And it's quite a funny feeling that you
create these algorithms, but they do their own thing.
- [Jim] An unthinking process of evolutionary
trial and error had created these virtual creatures
that can move and react in real time.
What we're seeing here is fantastic
experimental evidence for the creative power
of systems based on simple rules.
(soft piano music)
Watching how computers can unconsciously
evolve programs to do things that
no human could consciously program
is a fantastic example of the power
of self organization.
It demonstrates that evolution is itself
just like the other systems we've encountered;
one based on simple rules and feedback,
from which complexity spontaneously emerges.
Think about it.
The simple rule is that the organism must replicate
with a few random mutations now and again.
The feedback comes from the environment
which favors the mutations that are best suited to it.
The result is ever-increasing complexity,
produced without thought or design.
- The interesting thing is that we can move up
to a higher level of organization.
Once you have organisms that actually have patterns on them,
these can be selected for or selected against
by process which are essentially feedbacks.
And so evolution itself, the whole Darwinian scheme,
is in sense Turing again
with feedbacks happening through different processes.
- [Jim] And that's the essence of this story.
Unthinking, simple rules
have the power to create amazingly complex systems
without any conscious thought.
In that sense, these computer beings
are self-organized systems
just like the one Belousov observed
happening in his chemicals;
just like the ones in sand dunes
and the Mandelbrot sets,
in our lungs, our hearts,
in weather, and in the geography of our planet.
Design does not need an active interfering designer.
It's an inherent part of the universe.
- One of the things that makes people so uncomfortable
about this idea of, if you will,
spontaneous pattern formation
is that somehow or other you don't need a creator
but perhaps a really clever designer.
What you would do is to kind of treat the universe
like a giant simulation,
where you set some initial condition
and just let the whole thing spontaneously happen
in all of its wonder and all if its beauty.
- The mathematics of pattern formation
shows that the same kind of pattern can show up
in an enormous range of different physical,
chemical, biological systems.
Somewhere deep down inside, it's happening
for the same mathematical reason.
Implicit in those facts
are these beautiful patterns that we see everywhere.
This, I think, is a mind-blowing thought.
- So what is the ultimate lesson
we can take from all this?
Well, it's that all the complexity of the universe,
all its infinite richness,
emerges from mindless simple rules
repeated over and over again.
But remember, powerful though this process is,
it's also inherently unpredictable.
So, although I can confidently tell you
that the future will be amazing,
I can also say with scientific certainty
that I have no idea what it holds.
(soft piano music)