Secret Life of Chaos

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,
phosphorus and sulphur.
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 organise 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 that
reveal a hidden face of nature.
That woven into its 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.
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,
runs counter
to our most dearly held intuitions.
So not surprisingly, the first man
to really take on the momentous task
of unravelling
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 tantalisingly
close to cracking them.
Turing was a very original person.
And he had realised that there
was this possibility
that simple mathematical equations
might describe aspects of
the biological world.
And no-one
had thought of that before.
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 Morcom,
who...Alan Turing, well, he was gay,
and it had been the great emotional
thing of his life at that point.
Christopher Morcom suddenly died.
And, Alan Turing was obviously
very emotionally disturbed by this.
But you can see
that he wanted to put this
in an intellectual
context, a scientific context.
And the question he wanted
to put into context was
what happens to the mind?
What is it?
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 a 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, as this footage of a
fish embryo shows,
the cells begin to clump together,
and also become
different from each other.
How does this happen?
With no thought,
no central co-ordination?
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-organisation.
And before Turing,
no-one had a clue how it worked.
Then, in 1952,
Turing published this, his paper
with 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 kind 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-organise.
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
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.
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
blowing across sand
creates all kinds of shapes.
The grains self-organise
into ripples, waves and dunes.
This happens, even though the
grains are virtually identical,
and have no knowledge of the
shapes they become part of.
Turing argued
that in a very similar way,
chemicals seeping across an embryo
might cause its cells to
self-organise 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 blobs 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,
"Doesn't this look
a bit like the patterns on a cow?"
And everyone sort of went,
"What is this man on about?"
But actually,
he knew what he was doing.
They did look like the patterns
of a cow, and that's one of
the reasons why cows have this
dappled pattern or whatever.
So, an area where mathematics
had 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.
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 interact
with other chemicals, is still
fiercely debated by scientists.
But Turing's idea that whatever
is going on 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 had done
was to suddenly provide
an accessible chemical mechanism
for doing this. That was amazing.
Turing was onto a really big,
bold idea.
But sadly, we can only speculate
how his extraordinary mind
would have developed his idea.
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 well have assumed that
Turing would have been honoured
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 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 8 June 1954, Turing's
body was found by his cleaner.
He'd died the day before
by taking a bite from an apple
he'd laced with cyanide,
ending his own life.
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 the 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 colourless
while being shaken.
As he mixed in the final chemical,
the whole solution changed colour.
Now this isn't
particularly remarkable.
If we mix ink into water,
it changes colour.
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 coloured 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 coloured to clear,
as if they were being driven by some
sort of hidden chemical metronome.
With meticulous care, he repeated
his experiments again and again.
It was the same every time.
His mixture would cycle from clear to
coloured and back again, repeatedly.
He'd 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 discovery with the wider world.
'But when he submitted his paper to a
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 contravened
the fundamental laws of physics.
The only explanation
was that Belousov had made a mistake
in his experiment, 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 behaviour
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-organise 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 BZ 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
emerge these astonishing patterns
of waves and scrolls and spirals.
Now this is emphatically not
abstract science.
The way Belousov's chemicals
move as co-ordinated waves
is exactly the way our heart
cells are co-ordinated as they beat.
Animal skins and heart beats.
Self-organisation 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 turned the handle,
over and over again,
it would 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.
Find the mathematics
that describes a 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 tantalising 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 in?
Perhaps the cogs were wearing out?
Or perhaps someone
had tampered with it?
Basically we used to think,
if you saw very irregular behaviour
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.
Looked at from this point of view,
the whole idea of self-organisation
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.
The only way for self-organisation
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.
Beautiful, beautiful.
Ain't that something?
Magnificent desolation.
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.
Ironically, the events that forced
scientists to take self-organisation
seriously was the discovery
of a phenomenon known as chaos.
Chaos is one of the most over-used
words in English, but in science
it 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 chaoticist
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.
Chaos is one of the most
unwelcome discoveries in science.
The man who forced the
scientific community to confront it
was an American meteorologist
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
snowstorm 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 a flap of a butterfly's wings
in Brazil set off 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 modelled how animal
populations changed over time.
But here too lurked
the dreaded butterfly effect.
Immeasurably small changes to the
rates 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 behaviour
that gives you chaotic solutions,
then you can never know the
starting point accurately enough.
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 hard-wired
into every aspect
of the world we live in.
The global climate
could dramatically change
in the course
of a few short years.
The stock markets
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.
And we really all have
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 it to 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 and much more general
than you might imagine.
And so a clockwork universe can
nonetheless behave in the rich,
complex way that we experience.
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
favourably at Turing and
Belousov's work
on spontaneous pattern formation.
And perhaps more importantly,
as they did so,
they realised
something truly astonishing.
That there was a very deep
and unexpected link.
A truly cosmic connection
between nature's strange
power to self-organise
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 the patterns 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 the 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 movement of
the match become rapidly amplified
as they loop round 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 behaviour
and patterned behaviour.
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,
is just not true.
These are two ends of a spectrum of
behaviour
which can be generated
by the same kind of mathematics.
And it's the closest thing 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 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.
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 a fundamentally new
understanding to this astonishing
and often puzzling idea.
He was a colourful 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
underpinned 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 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 seen to be really
parts of the same big picture.
And he was a sufficiently
original and unusual person that
he realised that pursuing
this big picture was what
he really wanted to do. To
Mandelbrot, it seemed perverse that
mathematicians had spent centuries
contemplating idealised 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 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 in 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 principle applies
in the structure of our lungs
and the way our blood vessels are
distributed throughout our bodies.
It even describes how rivers
split into ever smaller streams.
And nature can repeat
all sorts of shapes in this way.
Look at this Romanesco broccoli.
Its overall structure is made up
of a series of repeating cones
at smaller and smaller scales.
Mandelbrot realised 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 taken 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 super-computer,
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 set
contains an infinite number
of smaller shapes.
Baby Mandelbrots
that go on for ever.
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 the next go.
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 a fundamental
ordering principle in nature.
Turing's patterns, Belousov's
reaction 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. We conserve 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.
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 a 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 behaviour 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 engineers
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.
Everywhere you look,
you can see evolution
using nature's
self-organising patterns.
Our hearts use Belousov-type
reactions to regulate how they beat.
Our blood vessels are
organised 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 PhD research
in complex systems was to see
how complex systems
interact with evolution.
So, on the one hand you have systems
that almost organise 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.
Evolution's mindless, yet creative,
power to develop
and shape complex systems
is indeed incredible.
But it operates on
a cosmic timescale.
From the first life on
Earth, to us walking about,
took in the region of
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 programs,
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 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.
Torsten and his team's goal
was nothing less
than to use computerised 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 brains
that were slightly better
at moving their bodies
and got them to breed.
The algorithm then takes those
individuals that do the best
and it allows them
to create offspring.
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
optimised it automatically.
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 happens
when it unfolds live,
we don't control any more
and things happen
that we never expected.
And it's quite a funny feeling
that you create these algorithms
but then they do their own thing.
An unthinking process of
evolutionary trial and error
has 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.
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-organisation.
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 favours the mutations
that are best suited to it.
The result is
ever-increasing complexity,
produced without thought or design.
The interesting thing
is that one can move up
to a higher level of organisation.
Once you have organisms
that actually have patterns on them,
these can be selected for
or selected against by processes
which are essentially feedbacks.
And so evolution itself,
the whole Darwinian scheme,
is, in a sense, Turing again
with feedbacks happening
through different processes.
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-organised 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 he 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 of 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.

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