All language subtitles for Tails You Win The Science of Chance (2012)

(gentle instrumental music)

- All our lives, we are
pulled about and pushed around

by the mysterious workings of chance.

When chance seems cruel,
some call it fate.

And when chance is kind,
we might call it luck.

Scoring a big win,

being saved from disaster,

or meeting that special someone.

But what actually is chance?

Is it something fundamental
in the fabric of the universe?

Does chance have rules?

And does it really exist at all?

And if it does, could we
one day even overcome it?

This is the story of how we
discovered how chance works,

learnt to tame it,

and even to work out
the odds for the future.

How we tried, but so often
failed, to conquer it,

and may finally be learning to love it.

(lively instrumental music)

Chance plays its part in all our lives,

though mine perhaps more than most.

I'm a mathematician at
Cambridge University

and trying to make sense
of chance is my job.

I study how we can use
the mathematics of chance

to calculate probabilities,

numbers that can give us a handle

on what might happen in the future.

(splashing)

(applauding)

(gasping)

Did you know that, on average,

each person in Britain has a
one-in-a-million daily chance

of some kind of violent
or accidental death?

To put it in perspective, one in a million

is roughly the chance of
flipping heads 20 times.

Imagine it like this.

Flip a coin, 20 heads, you're dead.

Heads.

Heads.

Oh, dear.

Heads.

Tails.

Oh, phew.

It's easy to say that it's 50/50

for a coin to come up heads,

but we can even put a
probability on things

that seem utterly chaotic
and unpredictable.

San Francisco.

In October 1989, a huge,
magnitude 7 earthquake

struck totally without warning.

Many people died.

Today, San Francisco

is its usual laid-back and beautiful self.

But the people here know another disaster

could hit at any moment.

- I know that my family members,

we all have the earthquake kits

and we try to have things ready,

but, other than that,
we're not very fazed by it,

I don't think.

Not until the big one comes.

- I believe in being prepared

but I also believe that it is fate.

- I've been here for over 20 years

and it kind of puts you in a place

where you live a bit more in the moment,

where you know as much as you prepare,

something could hit at any time.

- [David] For millennia, we've
met the uncertainties of life

with just a fateful
shrug of the shoulders.

But mathematics can help us quantify fate,

even if we can't banish it.

- What we now know from
our studies is that

the likelihood of a major
earthquake hitting the Bay area

is something like 63%
over the next 30 years.

But, associated with this 63% number,

which sounds very precise,

there's actually a huge
range of uncertainty.

It could be mid-40%

or it could be 80%.

- [David] Probabilities are often as much

a matter of judgment as arithmetic.

But they can still really
help people decide what to do.

- After the 1989 earthquake,

there were a lot of aftershocks

and a woman called me and she said,

"I'm so nervous to be here."

"I think I want to drive to Los Angeles

"to visit my daughter."

And I said, "I don't
think that's a good idea,"

and she said, "Why?"

I said, "Well, the likelihood
that you'll be injured

"in an automobile accident is much higher

"than the likelihood that an
aftershock will harm you."

- There's no escaping chance.

But if we can understand how it works,

then perhaps we can even
turn it to our advantage.

This was what the first
mathematicians to investigate it

hoped to do.

To, as it were, tame chance.

The scholars of the ancient world,

the Egyptians, Babylonians,
Greeks and others,

laid down the foundations for geometry,

algebra, number theory, and so much more.

But extraordinarily, they
never even got started

on the maths of chance.

It wasn't until the Renaissance

that a few pioneering thinkers

first got to grips with probability.

But unlike the ancients,

they weren't loftily pursuing
knowledge for its own sake.

They were trying to crack
the secrets of gambling.

The first was Gerolamo Cardano,

from the Italian city of Milan.

Cardano was a doctor.

But he was also an
obsessive life-long gambler.

This was written in the 1570s,

the earliest known work on probability.

In it, Cardano set out

a seasoned gambler's tips and insights,

including how to cheat,
and in one chapter,

laid out the most fundamental
principle of probability.

Cardano realized a probability
was also a fraction.

So with the roll of a dice,

the probability for each
side coming up was one sixth.

And it gets more
interesting with two dice.

With two dice, and 36
possible combinations,

there's only one way to throw a two.

But you're much more
likely to get a seven.

Cardano's insight works
with games like dice

because we can assume
that each of the faces

is equally likely.

Provided, as Cardano puts it in his book,

"the dice are honest."

This may seem simple to us now

but it was the very first step

in working out how to tame chance.

(playful instrumental music)

Las Vegas, a place Cardano
would have surely loved.

The people who run this city

have the measure of chance so well,

they've built an entire
glittering industry out of it.

It's vital, even so, that
anyone here can get lucky.

You could even bet one
dollar and win a million.

Mike Shackleford is a
professional gambler.

His living depends on his
command of casino maths.

- I analyze every casino game out there

and my goal is to find out the probability

of every possible event in every game.

Almost always, the odds are going to be

in the casino's favor.

For example, in roulette,

the house advantage is
5.26% under American rules.

That means that for every
dollar the player bets,

on average he can expect
to lose 5.26 cents.

- [David] Not only do the casinos

understand the probabilities perfectly,

they also know that most
of the punters don't.

And these games can really
mess with our minds.

- You'll see a series of
outcomes from a slot machine

and believe that there's a
pattern to what you've just seen

but that's really just the human brain

playing a trick on you

because what's happened in the
past has no predictive value

for what is going to happen next.

Yes, the machine may have
had this series of payouts

in the past.

It may have been hot or cold.

But that has no bearing or no influence

on what is going to
happen on that next game.

So you could hit the jackpot symbol

two games in a row.

- We just hit the biggest
jackpot we've ever hit here.

8,600 dollars.

We just went to this machine
about half an hour ago,

so we got lucky.

- [David] Jackpots
don't worry the casinos.

They know the slots are programmed

to deliver high house
edges in the long run.

Smart players, like
Mike, rarely touch them.

- A professional gambler plays games

where the odds are in their favor.

Probably the most well known
is card-counting in Blackjack.

- [David] In Blackjack,
every time a card is dealt,

the odds change for all
the cards that are left.

Mike tracks the cards that are dealt,

to work out how those odds are changing.

- So if the player notices that
in the first 25% of the shoe

a lot of small cards came
out, more than expected,

he knows that the remaining cards

are going to have a surplus of big cards.

So he will adjust his bet size

and he will change how he plays

and by doing that, he can
get the odds in his favor.

- On a good day, Mike can get
a 1% advantage over the house.

It doesn't sound much

but it could mean a lot of money.

The casinos, of course,
don't like card counters

and Mike's been banned from
almost every joint in town.

In the world of games,

if you know the rules, you can
figure out the probabilities.

But what about the chances
of life and death itself?

(laughing evilly)

(bell tolling)
(eerie music)

To be able to put
probabilities on our own lives

needed another great mathematical leap.

And this time, the rewards
would be even bigger.

For most of history, it was almost a given

that we had not the slightest inkling

of when our time on earth was up.

Death visited when he wanted

and the results were never pretty.

Thank goodness for the
consolation of eternal life

in the hereafter.

The sculptors who carved
this terrifying monument

were capturing the brutal
truth of our mortality

as a warning to everyone
here, quaking in the pews.

But around the time this was
carved, about 300 years ago,

scientists began trying to work out

the mathematical chances,
for each individual,

that Death would soon
be paying them a call.

The revelation was that you
could study one group of people,

the residents of this
parish, for instance,

and see how old they were when they died.

From this, you could
estimate the chances of death

at each age for everybody else too.

This was a radical idea.

Count the dead

and Death would become
less of a divine punishment

and more of a predictable force of nature.

The man who really cracked

how to apply the maths
of chance to human lives

was Edmund Halley, the famous astronomer.

Edmund Halley had no interest
in what went on in there.

What fascinated him was
what had happened out here.

Most people now remember
him for his famous comet,

but I salute him as one of
history's greatest nerds.

Halley realized that he could calculate

the probabilities of life and death.

All he needed was some good data.

83,

52,

27.

In faraway Breslau, now a city in Poland,

locals were spooked by
an ancient superstition

that being aged 49 or 63
was particularly risky.

To prove the superstition wrong,

a Breslau clergyman collected details

of all the town's deaths

and circulated these to the
leading scientists of the day.

Halley got hold of the data

and realized the results
would have an impact

far beyond Breslau.

- Halley constructed a table

that was made up of,
essentially, two columns.

The first column was age
and the second column

was how many people
were alive at that age.

The first column started
at birth with 1,000 people,

and as the ages increased,

what we saw is that the number
of people alive decreased

and this wasn't uniformly.

- [David] Halley found nothing
special about 49 or 63.

But his data showed
that the older you got,

the greater the chance of you dying.

It seems obvious to us now.

But before Halley,

people thought the chances
much the same for everyone,

young and old alike.

And Halley's table had an
immediate practical benefit.

- Halley's tables were
also ground-breaking

because not only did he publish

the probability of death at a certain age,

he took that one step further

and applied that to the price of a pension

or the price of life assurance.

He included formulae as to
how you could actually come up

with a price for a pension.

- People in the 17th century
wanted to buy pensions

and life insurance,
just like they do today.

But before Halley,
anybody who provided them

was in danger of going bankrupt.

So Halley's breakthrough
would form the foundation

for the entire pensions and
life insurance industry.

And death would never seem

as capricious and mysterious again.

And what of Edmund Halley?

He lived all the way to
86, off his own table.

Costly if you were his pension provider.

Today, the insurance and
pensions industry is huge,

and has collected so much data

they can correlate your
life and death chances

to your gender, your address,

your job and your lifestyle.

And knowledge of the
odds could help us all.

So what do we know about
what affects our chances,

for better or for worse?

Imagine this 100 meters is
100 years of possible life.

How many of those years are
we actually going to see?

How far along this track
are we going to get?

When I was born, the average British male

expected a much shorter
life than if born today.

I was born in the 1950s and back then,

my expected lifespan was just 67 years.

But thanks to medical advances

and changes to the way we live and work,

our chances are
continually getting better.

The average lifespan

is actually rising by three months a year.

If I were born today, I
could expect to live to 78.

Even better, the longer you live,

the longer you can expect to live,

because you've been lucky
enough not to die young.

So at my age now,

I can expect to live not
to 67, or 78, but 82.

But what's not so cheerful

is the effect of all
those things I might do

throughout my life

that could stop me getting
this far, or even further.

Research tells us that for every day

you're five kilos overweight, like I am,

you can expect to lose
half an hour off your life.

Aah.

Sad to say, if you're a man
sinking three pints a day

then that's also half an hour.

But what about exercise?

Won't that make things better?

Yes, it will.

But there's a catch.

A regular run of half an hour

and you can expect to live longer.

Half an hour longer.

So I hope you actually like running.

'Cause that's how you just
spent your extra half hour.

Surprise, surprise, the worst
news is for all you smokers.

Two cigarettes costs half an hour.

But the average smoker's
on nearly 20 a day.

And it all adds up.

Doing something that
costs half an hour a day.

Well, that's more than
a week off each year

and, in the long run, that's
a whole year off your life.

For that 20-a-day smoker,

that's a staggering 10 years
you should expect to lose.

All these figures tell us a lot.

But as for chance itself,

that's certainly not disappeared.

When I say I can expect to live to 82,

I'm not actually making a prediction.

It may be shorter or, with
luck, it may be longer.

82 is the average.

Imagine 100 possible future
mes, each equally likely.

I'm 58 now and as the years roll by,

in more and more of these
possible futures, I die,

until by the age of 82

about half of my future
selves will be dead

and about half still alive.

Which is going to be me?

That's just chance.

Beyond 82, more and more drop dead.

And there's a very small chance

I could live to be very old indeed.

If I were a smoker, it's just
possible I'd beat the odds.

But overall, my chances
wouldn't look nearly so good.

Of course, many people would
say going on about risks

is being a big killjoy.

The writer Kingsley Amis famously said,

"No pleasure is worth giving up

"for the sake of two more years

"in a geriatric home
at Weston-super-Mare."

But I believe understanding the risks

might actually help us to
have more fun, not less.

- Okay, just put one arm
through there for me,

the other through there and turn around.

Thank you.

What we'll do is we'll
start strapping you in.

- Many of my favorite
experiences would be impossible

without taking some risk,

but I'm about to do something
I've never done before

which really does involve risk.

The best way to compare risky activities

is to use the micromort,

a cheery little unit which represents

a one-in-a-million chance of death.

Skydiving is actually
safer than you might think.

There's only about a
seven-in-a-million chance of dying.

That's seven micromorts.

That's about the same risk
as 40 miles on a motorbike.

But there's still a risk.

And you may think I should
be old enough to know better.

But I think it could be rational

to take more risks when you get older.

An average 18-year-old
has a chance of dying

in the next 12 months
of about 500 micromorts.

But at my age, the equivalent
is 7,000 micromorts.

7,000 micromorts doesn't
sound great, does it?

But my extra risk of skydiving

is only seven micromorts more.

That's not much difference.

So the risk is actually pretty low.

But the funny thing is,

now I'm actually in the plane
and there's no backing out,

it suddenly seems a lot worse.

Will my parachute fail?

I don't know.

Will we be blown into a tree?

I don't know.

Will I be sick with
fright over my jumpsuit?

The probability of that
is getting close to 100%.

It's the moment of truth.

Here we go.

Yes, I'm a Professor of Risk

and I've made a sound decision
rooted in the numbers,

but as I fall, I can't help thinking

there's a chance I'll
die very soon indeed.

- I could buy myself a
pair of silver hairbrushes.

Oh, hello.

I'm having a go at these premium bonds.

They're wonderful things, you can't lose.

Look, there are staggering
prizes each month,

you can get your money
back any time you like,

and, what's more, all your
tickets go back into each draw

whether you've been lucky before or not.

I might win a thousand quid.

I love a bit of a flutter.

Not a word to Bessie about that.

- [David] In 1956, Britain introduced

a brand new kind of savings
scheme, Premium Bonds,

that instead of paying you interest

gave you the chance to win big prizes.

At its heart was something
created by mathematicians,

a world of pure chance, randomness.

This is a world where every element

is disconnected from every other,

that operates beyond our
influence or control.

The Premium Bonds monthly prize draw

needed complete randomness

to make sure it was scrupulously fair.

- There was quite a lot of
human interest in randomness

for the first time,

where people began to think about,

"what are the chances of my winning?"

But what it required was
a source of random numbers

and a special purpose
computer was built for this

and it was one of the very
first special purpose computers.

- We're going to an electronic machine,

if you understand what that is,

but thank goodness its complicated
name is ERNIE for short.

- [David] ERNIE stood for

Electronic Random Number
Indicating Equipment.

Truly random numbers are hard to produce,

and ERNIE got them by
sampling the electrical noise

from a series of vacuum tubes.

It was state-of-the-art engineering.

- Randomness really, in a certain extent,

means unpredictable, but also,
for the purposes of ERNIE,

it needed to be unpredictable and unbiased

and my job as a young mathematician

was to show that it really was unbiased

to any particular Premium Bond number.

This was quite a skilled and lengthy task

to say those weasel words
that mathematicians use,

"We have no reason to suppose
that ERNIE is not random."

- For me, as a mathematician,

complete randomness is fascinating.

It's full of curiosities.

And unexpectedly, it turns
out to have its own rules,

patterns and structure.

This is officially the most
boring book in the world, ever.

It's called One Million Random Digits

and that's literally what it is.

Page after page of random numbers.

Say what you like about this book, though,

at least the plot is unpredictable.

Printed in 1955, these
numbers were produced

by an early computer rather like ERNIE.

And people have used them since

for everything from
randomized clinical trials

to encrypting communications.

I might not read this book cover to cover,

but I promise you there are
some really interesting parts.

I mean, look at this, 00000.

And here's another great bit, 12345.

It seems really strange to see these.

I mean, how can these be random?

But, of course, they're as random

as the numbers next to them.

Not only can you expect to
find patterns like these,

you can even calculate how
often you expect to find them.

A perfect sequence of five numbers.

There should be 50 of these in the book.

And the same number five times in a row,

there should be about 100 of these.

You can even expect,

somewhere in these one
million random numbers,

the same number to occur
seven times in a row.

And I've found it, 6666666.

What makes randomness so useful

is that it is completely unpredictable,

but in a predictable way.

So predictable that it has its own shape.

A lottery is a great example.

Each National Lottery
draw is, well, random.

There seems no pattern at all.

But there are also
seemingly strange results.

Today, after something approaching

2,000 National Lottery
draws over 20 years,

there are huge differences

in how often different
numbers have come up.

Number 38 has been picked 241 times,

while number 20 has come up just 171.

It might look like something's wrong,

but taking all the results together,

the totals match the shape of
randomness remarkably well.

And even the outlying results

are just where the shape
shows they should be.

Here we go.

Let's pick some numbers.

It's not a great bet, I admit.

There's only a one-in-14-million chance

of me winning the jackpot.

In fact, I'm very unlikely
to win anything at all.

There's only a one-in-56 chance

of me getting the smallest
prize of 10 pounds.

Overall, the lottery only pays back

45% of the money it takes in.

Far, far worse than any casino game.

If you must play,

though you can't change
your chances of winning,

you can improve your chances
of not sharing the jackpot.

Many people pick birthdays
or other significant dates,

so avoid the numbers up to 31.

You may even want to steer clear

of that supposedly lucky number, 38.

In the end, it doesn't matter
what numbers you choose,

every combination, say 1, 2, 3, 4, 5, 6,

is as likely as any other.

That's because it's completely random.

But randomness can confuse us.

For example, use the shuffle
feature on the original iPod

to play its tracks in random
order and before too long

you're very likely to land
on the same album again.

People found it so off-putting

that the shuffle on later-generation iPods

was supposedly tweaked.

Apple famously explained,

"We're making it less random
so it feels more random."

Patterns and connections like this

are what we call coincidences.

And no matter how much
we should expect them,

they nonetheless still
make our heads spin.

I love coincidences so much

I decided to try to collect them.

Luckily, it's an interest
the nation shares.

Let's talk about coincidences now,

at 7:24, why do they happen?

- Professor David
Spiegelhalter, good morning.

- Good morning.
- You are an expert

in risk and chance, is what I'm reading,

at Cambridge University,

but why is it you're interested
in chance and coincidence?

- Well, it's part of my job.

I'm Professor of the Public
Understanding of Risk,

so everything to do with chance,

uncertainty and coincidences
is what I'm interested in.

And we've set up this website

where we're collecting coincidence stories

which people are sending in,

and the sort of things where people,

when they happen to them, they say,

"Ooh, what are the chances of that?"

And we're trying to work out

what the chances of that really are.

It's like a family having three children

all with the same birthday,
born in different years,

but all three children
being born on the same,

having the same birthday.

You'd think, "Wow, what's
the chances of that?"

Well, we can work those out.

And it turns out, because
there's a million families

in this country with three children,

we'd expect there's about
eight families like that.

Now, we've found three of them.

- People read great significance,
though, into these things.

Are they misguided in doing that?

- Well, it's Friday 13th,

exactly the day that
shows people do believe

in luck and fortune and things like that.

But I suppose I'm being a
bit scientific about them,

so some of them we try to
take apart and do the maths,

but other ones are just amazing.

There's a lovely example last
year where a French family,

their house was hit by a meteorite.

Well, that's pretty surprising itself,

but their name was Comette.

Isn't that just beautiful?

- [Host] "What are the chances

"of never experiencing a coincidence?"

says Steve in Cheshire.

- Oh, very low indeed.

That would be really, really bizarre.

- Good one, Steve.

- 7:29.

What are the chances of any
decent weather over the weekend?

- [Man] Pretty good, actually, Rachel.

We've got some clear skies
out there at the moment,

but because of those clear skies

temperatures are hovering
at or just below freezing.

- The radio show was a huge success.

The stories flooded in.

Over 3,000 of them.

We got lots of coincidences
with numbers, names and words.

And loads of calendar ones,

including one more of those
rare triple birthdays.

Some of these stories are really amazing.

Lots of them are about
running into friends

and acquaintances in the
most unlikely places.

And I love this one.

Mick Preston was on a cycling
holiday in the Pyrenees

and during one stop-over,

he wrote his friend, Alan, a postcard.

But, incredibly, on the way to
post it, he bumped into Alan,

who just by chance was on
holiday in the same place,

so Mick gave him the postcard in person.

As Mick himself said, that
was a waste of a good stamp.

What's striking is that

although these and other coincidences

happened a long time ago,
people were so jolted by them

they still remember them years later.

I think our brains are hard-wired

to look for cause and effect,

to try to come up with
reasons why things happen.

So when things happen for
no apparent reason at all,

we find it really spooky.

We just don't seem to easily accept

that we might not be able
to understand or control

what happens in our lives.

Random events that have no
explanation beyond chance

saturate our lives,

but some people think

they can eliminate the
random, control everything,

and that chance has nothing
to do with them at all.

Ed Smith was once said
to be the golden boy

of English cricket.

For years he held an idea about chance,

or, as he called it, luck, that he shared

with many of his fellow
sporting professionals.

- When I turned full-time
professional in 1999,

we had all these meetings

about how we were going
to approach the season

and someone put his hand up and said,

"I don't think we should
say, bad luck, to each other.

"That's an excuse.

"It's not bad luck.

"If someone gets out, it's their fault."

I think as sportsmen
we're conditioned to think

that you are in total control.

I mean, if you walk out to
bat in professional cricket

and you say, "Well, maybe I'll
be lucky and maybe I won't,

"and maybe someone will bowl
a good ball and I'll be out,

"and I can't do anything about it,"

then you're stacking the
deck against yourself

before you even begin.

- [David] Ed played for England

and became captain of Middlesex.

Everything went well for him,

until one day during a county
cricket match at Lord's.

- So, we're in the middle of
this match, it's going well,

we're pretty much cantering to victory.

We're on a bit of a streak
of five, six wins in a row,

everything's going well

and I'm doing the most
routine thing in cricket,

I'm running a two.

It happens all the time, you know,

it's not particularly
demanding, athletically,

to run 20 yards and then come back again.

And I ran the first one and
then you just rub the bat in,

and I just, sort of, collapsed.

And I'm lying in this,

and have this shooting pain in my ankle,

and it was only quite a few weeks later

that there was an X-ray,

and it turned out that
I'd broken my ankle,

and I wasn't going to play any time soon.

I missed the rest of that season

and then I retired, effectively,

at the end of that season

and didn't play
professional cricket again.

- [David] In a single moment,
Ed's entire career vanished.

He had been touched by chance.

No one and nothing was to blame.

- I think I found it hard to accept.

You know, my own willpower,
my determination to control,

to shape my own life, was so great

but the reality is that
I wasn't in control.

The fact that I had a broken
ankle was just a fact.

It was a circumstance
that had happened to me.

So, it was like a clash between, er,

my own desire to control everything

and the fact of luck,
and, you know, luck won.

- The moral of Ed's story is clear.

Don't beat yourself up
about every failure.

But the opposite is also true.

Don't be too chuffed with
yourself about every success.

Remember this?

I know you can't get rid of luck,

but right now I wish you could.

The parachute hasn't failed at least.

I don't seem to be being
blown into a forest.

And I haven't even been sick.

That was so cool.

Can we do it again?

You know, the really interesting thing

is that whilst I was
confident I would land safely,

I couldn't be absolutely certain.

The question is, why not?

Why does chance exist?

The story of science, for
centuries, has been a triumph,

unlocking the mathematical
laws behind everything,

from the atom to the universe.

So why is there still room for the random?

For unpredictability?

Why, instead, can't everything
in nature be determined?

In which case, we could get
rid of chance altogether

and I would be out of a job.

In the 1680s Isaac Newton
revolutionized science

with a set of universal laws.

He calculated the orbits
of moons and planets,

even predicted the timings of eclipses

and, of course, explained the
fall of an earthbound apple.

(gasps)

Newton's friend, Edmund Halley,

predicted the returns of comets,

and other scientists eagerly
worked to discover new laws

and make more predictions.

The Enlightenment, it came to be called.

In 1779, the French scientist
Pierre-Simon Laplace

had a bold vision.

If some vast intellect

could not only comprehend
all the laws of nature,

but could also measure everything,

even down to the tiniest atom,

then he might predict
the future precisely.

And uncertainty would simply disappear.

- [Man] Hmm.

- In theory, with the right mathematics,

everything in the physical universe

could be measured and predicted,

just like the movement of
the stars and the planets.

So, for example, if I threw a dice

I could predict exactly how it would land.

This theory is what we call
scientific determinism.

In theory, if we gather the
data and do the calculations,

we should be able to get
rid of chance altogether,

but, in practice, prediction
has proved frustratingly hard.

It's as if there is something
about our physical world

that makes prediction all but impossible.

Despite the promise of the laws of Newton

and all the scientists who followed him,

we remain in the dark.

But why?

In the 20th century,

scientists, like meteorologist Ed Lorenz,

discovered that even tiny
influences could have immense

and unpredictable consequences.

As Lorenz put it, "The flap of
a butterfly's wings in Brazil

"could cause a tornado in Texas."

The theory of determinism

had to acknowledge complexity and chaos.

The laws of physics weren't wrong,

but the real world was
just too complicated

to ever fully comprehend.

Also in the 20th century,

physicists, like Werner Heisenberg,

delving ever deeper into
the nature of matter,

realized there was an absolute limit

to what they could ever know.

In his work on quantum mechanics,

Heisenberg set out the
uncertainty principle.

Essential parts of the subatomic world

could at best only ever be
described as a probability.

The dreams scientists once
had of conquering chance

have been shattered.

Quantum mechanics has
shown us a subatomic world

that is fundamentally uncertain.

Beyond the subatomic, we are
still governed by mechanical

and therefore deterministic laws,

but, paradoxically, the
mathematics of chaos and complexity

means that things are still
ultimately unpredictable.

So what is chance?

Is it real?

Is it something out there in
the fabric of the universe?

Or is chance in here?

Just an excuse?

What Laplace called, "Merely
the measure of our ignorance?"

Or is it a bit of both?

After centuries of discovery,
we are still not much closer

to knowing what chance really is.

One thing is certain.

Chance is here to stay.

What's more, it has
actually been put to work.

Faced with complex and
unpredictable problems,

scientists have found
ways to use chance itself

to convert blind uncertainty
into computable probability.

In the early years of the Cold War,

nuclear physicists at Los Alamos

were working to design a new atomic bomb.

They wanted to predict when
an atomic chain reaction

might go critical,

but the physics was so complex

that at each step in the chain

they were uncertain about
what would happen next.

So they turned to the
mathematics of chance.

For each step, they chose
an outcome at random

and then calculated

what the resulting
chain reaction would do.

Then they randomly chose
a new set of outcomes

and calculated a new result.

They did this repeatedly

until they had hundreds of different,

but equally likely, possible results.

And combining them all gave
the Los Alamos scientists

an extremely accurate probability

for what the chain
reaction would do for real.

They called it the Monte Carlo method,

like rolling a dice over and over again.

And the bomb worked.

Today, that very same Monte Carlo method,

creating arrays of possible futures

to compute probabilities,

is being used to try to solve problems

in many different fields.

And what's most exciting
for me and my fellow Brits

is that this might help to answer

that all-important question:

When I go out, do I take an umbrella?

In the 1920s, the economist
John Maynard Keynes

wrote a famous book about chance.

And for the ultimate metaphor
of impenetrable uncertainty

he chose the British weather.

He wrote, "Is our expectation of rain,

"when we start out for a walk,
always more likely than not,

"or less likely than
not, or as likely as not?

"I am prepared to argue
that on some occasions

"none of these alternatives hold,

"and that it will be an arbitrary matter

"to decide for or against the umbrella."

But we want certainty.

And so we demand it from
our weather forecasters.

And then after wet weekends
and washed-out holidays

we blame the poor old
forecasters for getting it wrong.

- Hello to you.

Well, it was a disappointing
day today in many places

and I'm optimistic it's
going to be a better day

for most of us tomorrow.

- [David] Britain's most
famously wrong weather forecast

was on 15th of October, 1987.

- Good afternoon to you.

Earlier on today, apparently
a woman rang the BBC

and said she heard

that there was a hurricane was on the way.

Well, if you're watching,
don't worry, there isn't.

- [David] But there was.

That night England was
lashed by the strongest winds

for almost 300 years.

- [Reporter] Southern England
suffered the full fury

of the freak hurricane force winds,

in their wake, a trail of devastation,

the worst damage to property
since the Second World War.

Nowhere escaped unscathed.

- [David] Today the most
advanced meteorologists

don't try making predictions
like Michael Fish did.

In Reading at the

European Centre for
Medium-Range Weather Forecasts,

they use a form of Monte Carlo method

to make forecasts using
probabilities instead.

To show why they do this,

they've revisited the same weather data

Michael Fish had in 1987.

- What this shows us is that October '87

was an exceptionally unpredictable

and exceptionally chaotic situation

and so it was always
going to be impossible

to make a precise, deterministic forecast.

- [David] Weather forecasts go wrong

because even small errors at the beginning

can grow into huge differences
after just a few days.

And that's as true for everyday weather

as it is for hurricanes.

To tackle the problem, Tim
Palmer and his colleagues

routinely compute 50 different forecasts,

each with slightly varying starting points

to reflect the uncertainty.

Before returning to the hurricane,

Tim shows us an everyday example.

- So we're looking at
today's weather forecast

pretty much right at the
beginning of the forecast period.

These are all basically giving
the same type of weather.

So a weather forecaster

would look at these pressure maps and say,

okay, there's a northwesterly airstream

coming down over the UK,

it's giving us slightly cool temperatures,

but fundamentally it's exactly the same

no matter which of these 50
forecasts you're looking at.

- [David] Taking the same set of forecasts

to three days in the future,
it's a different story.

- Now there are discernible differences.

For example, member 14
has a stronger wind,

there are tighter
gradients in the pressure

than, say, member 15 and
that's telling us that

although the general direction of the wind

we can be certain about, it's
coming from the northwest,

the strength of the wind we
cannot be so certain about.

So we have to make a prediction
in probabilistic terms.

- [David] To work out the probabilities,

Tim counts how many of
the three-day forecasts

show a particular kind of weather.

- It turns out that in
about 30% of the forecasts

there are gale force winds
over much of England.

Similarly rainfall we find
across much of England about 30%.

What this doesn't mean

is that it's raining for 30% of the day.

What it means is that over
the 50 possible futures,

in 30% of them it is raining.

- [David] So what can Tim see

using the new method with
the 1987 hurricane data?

- There's around a 20 to 30% probability

over parts of southern England
of hurricane force winds.

Now, the probability normally
of hurricane force winds

in southern England is negligibly small,

so even though there's a
divergence of solutions,

there's real information here.

- [David] Adapting the Monte Carlo method

and embracing chance
gives much better results.

But in Britain the
forecasts most of us see

don't give us this kind
of information yet.

- We should now be trying to get

this type of information out
on the daily weather forecast.

And indeed I think it will enhance

the credibility of
meteorologists themselves

to be able to say

not only is weather forecasting
an uncertain science,

but we can actually
quantify the uncertainty

in a very precise way.

- If you were a cynic,

you might think that weather forecasters

who give you probabilities
and not predictions

are just hedging their bets,

ducking out of doing the one
thing they're supposed to

so they can never be accused
of being wrong again.

But I don't agree.

Better a reliable probability
than a wrong prediction.

And knowing the probabilities

we can all make our own decisions.

(thunder rumbling)

Like to bring that umbrella.

Remember that San Francisco probability?

A 40 to 80% chance of an earthquake?

In 1906, the city's worst-ever earthquake

killed 3,000 people

and destroyed almost 30,000 buildings.

Even if a similar
catastrophe in the future

can't be predicted, it
certainly can't be ignored.

So today's scientists are
applying new mathematical methods

to the problem.

They're computing probabilities

literally building by building,

so bold decisions can be
taken about what to do.

In Berkeley, across the
bay from San Francisco,

one major fault runs
right across the pitch

of the California Memorial Stadium,

home of the Golden Bears Football Team.

They're rebuilding the stadium

at a cost of over $200 million.

- The fault starts just to the
west of the south scoreboard,

and you can see in the bowl

there are those double
stair-step curves at two points.

That's where our joints are
for that piece of the stadium.

- Right.
- And it allows

this part of the building
to move independently

in an earthquake from the
two sides of the stadium

on either side of it.

- Right.
- And the base

of the entire part of that
building is on layers of sand

and high density polyethylene plastic.

- That's amazing.
- Which allows

that part of the building

to move a little easier
than it would otherwise,

so when the ground moves
six feet horizontal

and two feet vertical,

it can just go along for the ride

and the rest of the stadium is protected.

- [David] The stadium is just
one part of a massive building

and strengthening program
all round San Francisco Bay.

A colossal $30 billion has
been committed in total.

Will it be enough?

They can only hope so.

- Even if we knew exactly what
earthquake is going to occur,

we may not know exactly how
strong the shaking will be

and how it will vary across the city

because of different soil types.

So you set a standard,

you agree the buildings
will be built to that

and then you hope that that's good enough.

You can't actually engineer chance

out of the system altogether.

- [David] At least in San Francisco

they've a good idea of what to expect,

even if they can't know exactly.

But there's one last sting in the tail.

Chance can sometimes
come up with something

you never even thought of.

- As we know, there are known knowns,

there are things we know we know.

We also know there are known unknowns.

That is to say we know there
are some things we do not know.

But there are also unknown unknowns,

the ones we don't know we don't know.

And if one looks throughout
the history of our country

and other free countries,

it is the latter category

that tend to be the difficult ones.

- Donald Rumsfeld may
have just been trying

to excuse an unfolding disaster in Iraq.

But unknown unknowns are a
real and profound challenge

for us all.

And don't we just know it.

The Bank of England is
the rock-solid institution

to which we all turn in
these turbulent times.

Surely I can find some certainty here?

I'm meeting Spencer Dale.

The Bank of England is the
main financial institution

in the country.

People look to it to tell them

what's going on in the economy,

but can you predict
what's going to happen?

- Unfortunately not.

Forecasting the economy is a
very difficult thing to do,

in part because the economy
is very large and complex

and it's made even more difficult

because it depends on
people and their decisions

and that makes trying to model behavior

and how the economy is
going to change over time

even more difficult.

- [David] Every quarter,
the Bank makes a forecast

for the nation in the form
of what it calls a fan chart.

And it deliberately builds in uncertainty.

The chart shows that Britain's
future economic growth

might have a 5% chance

of lying in each one of the shaded bands.

This was the Bank's chart from 2007,

just before the big crash.

- At the time we made this forecast,

we thought in three years' time

the annual growth of the
economy may be anywhere

between 5% or close to zero.

- [David] But the Bank is
even less certain than that.

It also leaves room for
the unknown unknowns.

- This only shows 90% of probability.

So it's shows you 90 times out of 100

we think the economy will
go somewhere in this range.

- So there's a one-in-10 chance
it could just do anything?

- There's a one-in-10 chance

it will fall outside of this fan chart.

We don't try and put precise probabilities

on those very extreme outcomes.

- Right, okay.

With these charts, the Bank
is making one thing clear.

We must expect the unexpected.

And soon after the Bank made
this chart, chance struck.

- It was a genuinely surprising event,

the economy to behave in a way

which we hadn't seen for
almost an entire generation.

The environment which we operate
in is inherently uncertain,

the future is uncertain

and the impact of our decisions
are often very uncertain.

- Some people might want to
hammer the Bank of England

for not knowing what's around the corner.

But you can't blame them
for the nature of chance.

And though the Bank can't give
us the information we want,

I think they show the way
to the wisdom we need.

There's just no use in looking
for absolute certainty.

We can never rely on predictions.

We can tame chance,
but only up to a point.

Putting numbers on
chance is a powerful way

to get a handle on the future.

But these numbers can only ever be as good

as the information we have to hand.

Though we try to measure
reality with precision,

sometimes they're little
more than guesses.

What all this means is that uncertainty

is an essential part of being alive.

And whether our uncertainty

ultimately comes from out there or in here

won't, in the end, matter,

because either way surprises
will most certainly happen.

For instance, in this year
of the Diamond Jubilee,

I found a chicken nugget

in the shape of Her Majesty the Queen.

What's the chances of that?

(playful instrumental music)

(bell dinging)