The Secret Life of Chaos Page #4

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

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