Original subtitles

(slow dramatic music)

(mid-tempo vibrant music)

This is the story of climate change.

(tense ominous music)

But told in a way you've never heard before.

Because we're not climate scientists,

we're three mathematicians.

And we're gonna use the clarity of numbers

to cut through the complexity and controversy

that surrounds climate change.

Understanding what's happening

to the Earth's climate is perhaps

the biggest scientific endeavor

the human race has ever taken on.

From the masses of data,

we've chosen just three numbers

that hold the key to understanding climate change.

0.85 degrees.

95%.

And one trillion tons.

Just by looking at these crucial numbers

we're gonna try and get to the heart

of the climate change controversy.

They are three numbers that represent what we know

about the past, present and future of Earth's climate.

And it's not just the numbers themselves

that are important, the stories behind them,

how they are calculated,

are equally intriguing and revealing.

[Flight Controller] Ignition sequence start.

We'll see how the methods using everything

from the Moon landings.

[Flight Controller] What a ride B, what a ride.

To early 20th century cotton mills,

and motor racing have fed into the numbers we've chosen.

These three numbers tell an extraordinary

story about our climate, and take us to the limits

of what it is possible for science to know.

(mid-tempo calm music)

(mid-tempo hypnotic music)

Every minute of every day all over the planet

scientists are collecting data on the climate.

(explosion booms)

Around 10,000 weather stations monitor conditions

at the Earth's surface.

Some 1,200 buoys and 4,000 ships

record the temperature of the oceans.

And more than a dozen satellites

continuously observe the Earth's oceans and atmosphere.

All science starts with collecting data,

and when it comes to our climate we've got masses of it,

but what story about our planet is all that data telling us?

(slow tranquil music)

Thousands of scientists

are trying to answer that question,

their results are summarized in a series of huge reports

by the Intergovernmental Panel on Climate Change.

The three numbers we've chosen

all come from the IPCC's reports.

Molly.

I'm Doctor Hannah Fry,

and I use numbers to reveal patterns in data.

I'm looking at one number that answers a critical question,

is climate change really happening?

Our first number is 0.85%.

Now this number represents what we know

about our climate in the recent past

because it's the number of degrees Celsius

that scientists say our Earth has warmed since the 1880s.

But how can they be so precise?

Now we're talking about less than one degree here.

So how is it possible to be sure

that the Earth's temperature is changing

by such a tiny amount.

After all, our climate is complex and extremely varied.

(thunder crackles)

(rain splashes)

Temperatures change from season to season,

place to place and even minute by minute.

(wind howls)

As if it wasn't hard enough to try

and find an average temperature of the Earth for now,

we also need to go back in time

and compare it to the average temperature of the Earth

in the past when we didn't have the luxury

of modern measurement techniques.

(slow relaxed music)

Working out how the planet's temperature has changed

over more than a century is a huge challenge.

(Molly barks)

It's a bit like trying to work out the route

I'm taking across this park,

if you only had the route Molly is taking to go on.

You have to identify the trend, my path,

from all those changing temperatures, Molly's path,

and it all starts with the quality of the data.

Now that's not such a problem for the recent past,

but what about further back in time?

(airplane whirs)

(slow dreary music)

Up until the middle of the 19th century,

the temperature record as measured

by instruments is patchy and unreliable.

And there is some controversy

about how you reconstruct temperatures before this time.

But the record improves from the 1880s

due to the efforts of one man.

Now the key man in this story, the man with a plan,

is a guy called Matthew Fontaine Maury.

Now Maury was a lieutenant in the US Navy,

and from even when he was a small boy was obsessed

with mathematics and data and analysis.

But in 1839, Maury had a coaching accident

where he broke his thigh bone and dislocated his kneecap.

And while he was recovering he spent his time

studying captains' log books.

And the data that he found there set the path

for his next 14 years' worth of work,

so much so that on the 23rd of August in 1853,

he called together a meeting of 12 countries

surrounding the North Atlantic, all to talk about one thing.

(slow gentle music)

He wanted to improve the way

that data about the oceans was collected.

Captains record all sorts of information in their log books,

things like wind speed and direction,

or the speed and temperature of the sea currents.

Now this wasn't just interesting to Maury

from a scientific perspective,

but also because it was something

he could sell to commercial ship owners.

Maury had realized that he collected all the information

that sea captains were measuring in order to navigate.

He could see patterns emerging.

He started to produce maps of ocean currents

like the Gulf Stream.

This meant that ships could use these currents

to increase their speed.

Average passage times on some routes

were reduced by a 1/3, and it saved companies millions.

But there was a problem,

different sailors took the same measurements

in different ways.

That was particularly true

for one of the measurements climate scientists

are interested in, sea surface temperature.

Now the way to measure sea surface temperature

is actually surprisingly simple,

all you do is chuck a bucket over the side of the ship

and get the temperature from it.

(water splashes)

But the problem is that the result that you get

actually depends quite a lot

on the type of bucket that you use.

So let me just take the temperature of this now

and in the meantime I'm gonna throw this guy over.

In the early 19th century, some sailors used wooden buckets,

others used buckets made of canvas.

This meant that the measurements were not consistent.

The wooden bucket's coming out as a surprisingly warm,

uh, 15.1 and if we make a comparison,

the canvas bucket, unlike the wooden bucket,

isn't insulated so things like,

the air temperature are gonna make a much bigger difference

so the temperature has dropped below 15.1 degrees.

It may not sound like a lot but even tiny discrepancies

undermine the accuracy of the data.

Now Maury knew this, and so at his conference in 1853,

he came up with a standardized way

for everyone across the world

to measure sea surface temperature.

(water splashes)

Now just in case you think

things have changed massively since the 1850s,

here is the bucket that resides here on this ship,

and that's used to measure sea surface temperatures.

It's rubber, it's supplied by the Met Office,

and has it's own thermometer sitting inside.

The rubber means it's well insulated

like Maury's wooden buckets.

And just as in his day,

once this ship has taken its measurements,

the data is sent to the Met Office via its standard form,

only now that form's electronic.

(slow piano music)

It wasn't just sea surface temperatures

that Maury was interested in.

He soon turned his attention to standardizing

land based measurements too.

That's why our 0.85 degrees Celsius figure

is measured from 1880,

it's the date from which the temperature data

is generally well standardized.

But despite Maury's efforts,

the data was still far from perfect,

not everyone stuck to the rules.

For example, over time canvas buckets

made a comeback because they were lighter,

so there were still errors,

some of which were pretty obvious.

So here is the sea surface temperature data

between 1880 and 1980.

And the first thing that you really notice

about this graph, is this huge spike that happens

where it looks like the sea surface temperature's raised

by 0.85 degrees Celsius.

Or at least it looks that way

until you realize that spike happened in 1941

when during the Second World War,

understandably, sailors didn't much want to go up on deck

with a torch and a bucket

to record sea surface temperature levels.

So instead, during that time,

they used the water that was coming in

through the engine room, which is hence why

the data is a lot higher.

Now after the Second World War,

people gradually started returning to using

uninsulated canvas buckets,

but unfortunately, we don't who was using them or when.

And so in all of this big massive data,

how do we get accurate temperature readings

for land and sea from the past?

(slow reserved music)

(machines whir and click)

We have millions of measurements

from the past that need checking.

Sometimes there are obvious jumps

or notes in the records about the change of method.

But sometimes there are more insidious changes,

and ones that could cause us to think

the Earth's warming when it isn't.

Take the classic case of measurements from Las Vegas.

In 1942, the local weather station

was positioned on the air field, a nice rural location,

but then, Las Vegas grew.

(upbeat energetic music)

The city scene surrounded the airfield,

and the temperature measured

at the weather station started to rise.

But this was only because urban areas

are usually warmer than the countryside.

It was a local effect, not global warming.

Now people spotted this and said,

hang on, could global warming just be an artifact?

What if the average is being raised

just by urbanization near weather stations?

Well, mathematicians have been working on techniques

to solve these kinds of problems for awhile.

And it turns out,

the answer is related to a mathematical technique

that was used to help solve

one of history's greatest challenges.

At Cape Kennedy, it's a wonderful day

for a wonderful event, the first manned flight to the Moon.

In a mission fraught with difficulties,

one of the biggest was how to navigate

1/4 of a million miles through space

to the surface of the Moon.

In the 1950s, as the earliest computer systems

were being developed, automatic navigation

became a really important research problem.

Now this was used in things like missile guidance systems,

and rockets, and submarines,

things where it's really important

to have a really precise understanding

of exactly where you are in space at any point in time.

(upbeat lively music)

It's a feat of navigation all the more astonishing

when you consider how difficult

finding our way around can be even down here on the ground.

Working out exactly where you are on the Earth

at any point in time is actually a surprisingly

difficult problem, especially if you want really,

really precise information.

It's tricky because tracking your position,

just like measuring temperatures over time,

is prone to error.

Not the easiest thing ever.

Take dead reckoning,

timing how long you've traveled in a particular direction

from your last known position.

About three miles an hour.

Lovely, three miles an hour, hang on one second.

(Hannah laughs)

It's easy to drift off course as inaccuracies build up.

Hang on.

Even more high tech methods can get it wrong.

Actually the GPS is putting us over there

at the moment which is less than ideal.

So when it comes to navigating

the problem is which measurement

of your position do you trust?

In the 1950s, a young Hungarian-born mathematician,

Rudolf Kalman, devised an elegant algorithm

to solve this problem.

(slow riveting music)

Kalman's method uses a matrix algebra,

and takes into account all of the errors

to give you the best possible estimate

of your position at any point in time.

So how does Kalman's method work?

In 1969, NASA gave it its ultimate test

in the mission to land men on the Moon.

[Flight Controller] Ignition sequence start.

[Flight Controller] Check.

[Flight Controller] Five, four.

Navigating in space poses particular challenges.

[Flight Controller] We have a lift off.

Lift off on Apollo 11.

The spacecraft was being tracked

by four radar stations on Earth.

[Flight Controller] What a ride B, what a ride.

Onboard instruments

were also estimating its position,

but each of these measurements could be wrong.

So how could NASA be sure of Apollo 11's position?

[Flight Controller] Control go.

This is where Kalman's algorithm came in.

Moment by moment it compared

each position measurement with the others,

looking for differences

that fell outside the expected margin.

We're a go same time, we're a go.

If the algorithm had found

significant disagreement the mission

would have been aborted,

but it didn't,

and the rest is history.

[Flight Controller] 3 1/2 down, nine forward.

Tranquility Base here, the Eagle has landed.

So this process is now known as Kalman filtering

and has been used in everything

from cleaning up grainy video

to looking for trends in economics.

And a lot of the underlying principles

are exactly the same as you see in the processes

used for climate science.

So knowing when to trust your data

and picking out when the errors are big enough

to flag up a deeper underlying issue,

but the process in climate science

is instead known as, homogenization.

Homogenization has allowed climate scientists today

to clean up data gathered in the past.

Unreliable measurements can be corrected or discarded.

So what homogenization process is doing effectively

is taking all of the data from all of the weather stations

and comparing it on a day by day basis.

Now in doing that if a particular data set

starts to look a bit unusual

it will really stand out from the others.

It's kind of like the mathematical

objective way of looking at a graph,

and picking out a data point

that just doesn't fit well with the others.

You can see what happens

when scientists homogenize a data set

by looking at how they corrected the unusual jump

in sea surface temperature in the early 1940s.

So once you've applied this homogenization process,

here is what the sea surface

temperature data will look like.

So we have the original data here in yellow

and the cleaned up version also available in blue.

Now the first thing that you notice

is that the big jump that we had in 1940

has dramatically reduced.

There is still a bit of a jump

because there was an El Nino that year

which meant that the sea surface did actually warm.

But the jump that was down

to the difference in measurements,

the error in the way that people were measuring,

has been taken away completely from the graph.

All the big scientific groups

that work with climate data

use homogenization methods like this

to try and clean up the records of past temperature.

And it's absolutely vital

that you account for some of these errors in measurement

that have occurred in historical data,

otherwise you've got no hope

of finding any kind of underlying patterns in your data.

But inevitably as soon as you start

applying these mathematical recipes to clean things up

other people will start accusing you

of building in biases into your data.

Perhaps the best defense against bias

is scientists' own skepticism.

Many different groups work on climate data

using slightly different homogenization methods

and all are subjected to searching scrutiny by their peers.

(slow playful music)

But even after homogenizing the historical data,

climate scientists face a further problem,

gaps in the temperature record.

Even today we do not have temperature

measurements for the whole planet.

If you look at where we have temperature data for,

if you split the Earth into a grid,

it becomes very obvious that there are some areas

where we have much more information on than others.

The black squares show where we have

hardly any weather data at all.

So if you take the Arctic, for example,

it's very obvious there are almost

no sample points in the Arctic.

The gaps in places like Africa and the Poles

can affect how we calculate

the average temperature of the whole planet.

Now if you take an average across the whole of the Earth

and don't take into account the fact

that you have a lot less data for the Arctic,

you're gonna end up with a really biased average,

and something that doesn't really

represent the Earth properly.

Now there is actually a mathematical solution

to this problem that climate scientists

are beginning to use,

but it's one that wasn't even devised by a mathematician.

(gripping rock music)

The attempt to fill in gaps in the temperature data

begins in the gold fields of South Africa in the 1950s,

where a mining engineer was grappling with a problem.

Danie Krige was in charge of the leases

of the country's very valuable gold fields

and was inundated by companies desperate to mine them.

But until each plot of land had been mined,

he had no way of knowing how valuable each area would be.

What he needed was a systematic way

of working out how much each lease was worth,

and so turned to spatial statistics.

To understand the challenge Krige faced,

I've come to gold mining country, to Dolaucothi in Wales.

All Krige had to go on were a few scattered core samples

that had been taken across the gold fields

as miners tried to find more gold.

(riveting rock music)

Just as mining engineer, Dr. Hazel Prichard

has done herself at this very site.

And this is Dolaucothi drill core

which we drilled just here.

Oh, okay.

Because it's always a good idea to be quite close

to where gold is known.

So we wanted to extend the knowledge of where the gold was,

and so we drew it just here.

So how much gold actually is there in these bits here.

Well, in the white quartz there's probably

something like two parts per million.

Okay, is that a lot, two parts per million?

That's quite a lot.

An investor would get quite excited about that.

Okay, and how does this compare then

to their mines in South Africa?

The thing about South Africa is there's lots of it.

It's a huge area.

This is just a kilometer, or maybe two.

In South Africa, it goes for 100 kilometers,

so it's a much bigger system.

So what would the core samples look like

if we had one from South Africa with us?

Well, I have a piece here,

and this is an amazing sample

lent to us from Witwatersrand and--

That's the mine where Danie Krige was--

Yes, exactly, and so this is a quartz,

and here's the sulfites.

And you can even see the bits of gold.

And you can see the gold,

that's really unusual to see gold,

but here you see there's lots of small particles of gold.

And you know it's gold 'cause it's gold in color.

And so from these samples then

can you get a good understanding of all of the gold

around us in the gold field?

Yes, in a way, these tell us exactly

where the gold is just here.

We know there's gold over there,

and if we drill over there, there's more gold.

But what we don't know is where the gold goes between.

'Cause we know absolutely in the drill core,

but we don't know what's under the surface

between two holes.

(mid-tempo mellow music)

So with a few scattered core samples,

Danie Krige had to find a way of working out

how much gold there was in each plot of land

just like climate scientists have to work out

the temperature in places

where they don't have measurements.

So what I'm gonna do here

is show you how Danie Krige's method worked

using these as my core samples.

(slow calm music)

Imagine each of these poles represents a core sample

and the number of lights indicates

the amount of gold found in it.

So our first core sample is giving us

a reading of 16 parts per million

all the way up there into the red.

Now 16 parts per million is a very high grade sample,

and gives us enough evidence to dig a few more core samples.

The core sampling is often done in little clusters.

If you get a very high reading on one sample,

you want to find out if that's a freak occurrence,

or whether there really is a lot of gold nearby.

So I'm gonna do the same, 28, 29, 30.

Okay, 30 paces away, time for our second core sample,

giving us a reading of eight.

It's not quite as good as the 16 we had over there,

but it's still pretty good,

and enough evidence to carry on digging.

And this core sample is giving us a reading

of only six parts per million.

Danie Krige's samples were often around a kilometer apart.

Climate scientists have weather stations

that might be hundreds or even thousands

of kilometers apart, especially in regions like the Arctic.

The problem in each case is the same,

how to fill in the gaps in the data.

So one more core sample to do,

and then I can show you the map.

So our last reading is only giving us two parts per million,

so we're still on the gold field,

but we're at a much lower grade of gold than we were before.

But the real question that Danie Krige wanted to ask was

how can you tell what happens in between the core samples?

How can you tell how much gold is in the middle?

His answer was to use maths to take into account

both the amount of gold in each sample

and the distances between them.

So Krige's method would take the first

exciting strike of gold and look at how far away

the neighboring samples are,

as well as how high the levels of gold found in them are.

This helps estimate how much the gold levels

drop off around each strike.

The process is then repeated over the whole field.

It may not sound like it,

but the maths is relatively simple.

Now it's so powerful that this method

has been used all across the world

in everything from looking at gold mines, to forestry,

and even temperature data, and it's even been named

after the great man himself, now known as krigeing.

krigeing is now being used to throw new light

on the biggest recent climate change controversy,

what's happened to the temperature of the planet

since the turn of the century?

The issue is how you account for gaps

in the record of global temperature.

If you take the UK Met Office's Hadley Center, for example,

and their data on the changing global temperatures

in the recent past, they leave blanks in regions

where they don't have any information.

But if you look at the temperature set

you can see that it demonstrates an effect

that's become known as the pause

which is the temperature of the Earth doesn't appear

to have risen since the year 2000.

This pause in the Earth's rising temperature

is controversial.

Some climate change skeptics say

it shows that global warming is not real,

but most climate scientists say they would expect pauses

every now and again within a warming trend.

But whether there even is a pause depends on how you

account for the gaps in the temperature record.

When this data set was Kriged

by an independent scientist in 2014,

so that they could take into account the little data

that you have in The Arctic,

he found that the graph changed.

krigeing put more weight

on the few temperature points we have from The Arctic,

and there the temperatures are rising fast.

The impact of krigeing on the original incomplete data

is to turn the pause into a small temperature rise.

Now you might think that this

doesn't necessarily represent reality either,

but it does demonstrate an important point,

what you do with your data has an impact

on how you make your conclusions.

It's not to say that krigeing the Arctic figures

has really shown that there isn't a pause,

it remains an area of debate,

but techniques like this offer scientists the only way

they have to overcome the inevitable limitations

of incomplete data.

(slow unsettling music)

It doesn't matter how much effort scientists go to,

temperature data will never be perfect

and the trouble is mathematical manipulation of the raw data

can look like fiddling the figures.

But the techniques that climate scientists have used

are well understood, they're open to scrutiny

and they all lead in the same direction.

Three major research groups have contributed

to the IPCC's reconstruction of past temperature.

They've each used slightly different methods

to clean up the historical data and account for gaps

in the temperature record.

And here are their results.

So in the top left hand side, you have the results

from The Global Historical Climatology Network.

Top right, you have the results

from The Goddard Institute of Space Studies.

And in the bottom left, you have the results

from The Met Office's Hadley Centre.

Now just these three graphs show pretty similar results,

they all seem to be showing a very similar shape,

especially when you take into account the fact

that all of the groups were using different techniques.

The overall shapes of these graphs

all seem to show a rise since 1880,

but there's also a lot of zigging and zagging.

So it's fair to ask,

is the apparent rise that these graphs show actually real?

What's needed is a way to tell whether the temperature today

really is significantly higher than it was back in 1880.

(slow chiming music)

And there's a mathematical test

devised for that kind of problem.

Devised in a rather unusual place.

As the 20th century approached,

the guys here at the Guinness factory in Dublin

began to take much more of a scientific view of brewing.

One of their recent recruits was a guy

called William Sealy Gosset, a recent Oxford graduate.

And a man who was once described as having the energy

and focus of a St. Bernard in a snowstorm.

But even as Gosset arrived here at Guinness,

he didn't realize,

and none of the people here realized either,

that he was about to invent a statistical method

that would revolutionize experimental science.

(lighthearted piano music)

Gosset had been hired especially to apply

his scientific mind to some specific brewing problems.

It was time when industries like this

were really looking to improve

their products and their profits by using science.

Now one of the real problems that Gosset encountered

was how to assess the quality of different batches

of hops or barley or malt.

Now unlike before, it was no longer good enough

to just smell them and see how they were.

The newly recruited scientist were getting stuck in

measuring things like the resin content of the hops,

or the yields of the different varieties of barley.

And they kept their notes meticulously

in printed and bound volumes.

Now these lab reports are a real joy to read

'cause I think they give you a real sense

of what things were like at the time.

So in particular, in the front of one of them, it reads,

this report is a valuable edition to our knowledge.

It's also worth noting that these lab reports

are incredibly detailed and just exceptionally well written.

It's like reading an academic report

rather than just, you know, the jottings down

of an average brewery assistant.

You know, these guys really knew what they were doing.

The whole point of getting scientifically

trained people like Gosset into the brewery

was to get them to do this kind of careful analysis

of what makes the perfect pint.

Which varieties of barley are best?

How to ensure they're buying top quality hops and malt.

But of course, every time that you measure

hops or barley or malt,

it's gonna cost you time and money,

so what Gosset was really looking for

was a way to test between small samples

and see if they're significantly different from each other

or equivalently to be able to tell whether one batch

will be better or worse than another.

It's the same kind of problem as that faced

by climate scientists today.

How can we objectively say whether the temperature

in one place now is really warmer than it was in the 1880s.

And Gosset eventually came up with the first solution,

a new mathematical technique.

Now Gosset's most famous finding

became known as the t-test,

that's the letter T not the drink unfortunately.

Now the t-test is a way to tell whether

two samples of data differ significantly from one another.

Whether they have the same underlying pattern

that's creating both of them.

And it's actually an incredibly simple equation,

but with a very profound result.

One that has massive implications in experimental science.

Now Gosset, during his time here at Guinness,

published all of these findings

in a series of academic papers

which I've been allowed to see today.

And what's quite nice is that in flicking through them,

you've been able to really see his character

coming out in his papers.

And there's one particular comment

which I found where he says,

in a similar tedious way, I find the following.

Which I think is particularly nice

and really echoes probably how most academics feel

about their work at some time or another.

(delicate piano music)

The t-test was only one of many

important statistical advanced that Gosset made.

His tests started to allow any scientist collecting data

to be able to make sense of what they were looking at,

to understand what the numbers really meant.

Okay, if Gosset's work was so important and so profound,

why is it that nobody's really heard of him?

And the reason why is one of Gosset's predecessors

here at Guinness was also allowed to publish academic work

during their time in the experimental laboratories.

Unfortunately, he gave away some of the more

commercially sensitive data about Guinness at the time.

So to try and avoid that,

and to protect his commercial identity,

Gosset instead, published under a pseudonym.

And chose the actually quite modest pseudonym of Student

which is why his work become known as the Student's t-test.

Today, we all still enjoy the fruits of Gosset's labor.

Statistically, his technique is used all the time

by scientist wanting to analyze their data.

(lively electronic music)

Now, I haven't actually done the t-test myself

for awhile now, but if you take two types of data,

what Gosset's formula will do

is give you a way to tell if those two data sets

are significantly different from one another.

The t-test is one of many that climate scientists use

in order to tell whether the temperature

in each particular location on the globe

has changed significantly through time.

Now the climate scientists,

when they're looking at how temperature

has changed over the century,

have to do something a little bit more complicated

because the temperature data

isn't completely independent of each other,

and also it sort of changes a bit more slowly over time.

But the basic principle is exactly

the same as Gosset's t-test formula.

Using these sorts of mathematical techniques

climate scientists have been able to show

that within all the variation of temperature

over the last 135 years,

there has indeed been significant warming.

So all that remains now is to put a figure on that rise.

How did the IPCC come up with the 0.85 degrees?

This bit is surprisingly simple.

(slow gentle music)

Now rather than all of the zigging and zagging,

the groups put a line through each of their graphs,

and from there it's very easy to just read off

how much the temperature has risen.

These three lines show the trend

in the average temperature since 1880 for each data set.

But the IPCC then took the average

of each of these three lines

and come up with the value of 0.85 degrees Celsius,

the most accurate measure that we have

for how much the Earth's temperature

has risen by since 1880.

That doesn't mean it's perfect,

the limitations, mean the exact figure

is always going to be uncertain.

But the 0.85 degrees figure

is based on tried and tested scientific techniques.

Scientists have done their best to try and compensate

for imperfections in the historical temperature record.

They've applied mathematical methods

to patchy, unreliable and erroneous data.

Now 0.85 degrees is itself just a symbolic figure.

I could have averaged the data in several different ways

and ended up with a slightly different figure

every single time, but that's not really the point.

Looking at how this number is produced

you can see that it doesn't matter

how you collect your data, how you measure your data,

or how you treat it, one point still stands overall,

the Earth's temperature has been rising

in the last 130 years.

(slow tense music)

Different groups using different techniques,

each scrutinizing the others,

have all arrived at pretty much the same conclusion.

That's why it's now relatively uncontroversial

to say that the Earth's temperature has risen

by just under a degree since the 1880s.

There's far less agreement though

on the answers to the big questions all this raises,

why did the Earth's temperature rise?

And can we stop it?

Once again, the clarity of numbers can help.

And in the next program,

we're gonna look at a very different number.

One which answers one of the most difficult

and controversial questions

in the whole climate change debate.

Mathematician, Professor Norman Fenton

is going to look at the figure of 95%.

The climate change number I'm looking at

is all about cause and effect.

The scientists have made a big statement,

they say they're 95% sure of the main cause

of the Earth's recent warming.

And that cause, they say, is us.

But how can they know with such a degree of certainty?

It's a story that will take us

from the glacial landscapes of the north

to the world's biggest meteorological supercomputer.

(frenetic electronic music)

And then, we will come to our final figure

with statistician Professor David Spiegelhalter.

The number I'm looking at is one trillion.

This rather unimaginably big number

may be crucial to the future of our planet.

It's the best estimate that climate scientists have made

of the number of tons of carbon that we could burn

before we run the risk of causing

what's been called dangerous climate change.

(car roars)

Its story will take us from motor racing

to the cotton mills of Lancashire.

It takes us to the limit of what science and maths can do.

And it's crucial that we understand it,

and the uncertainties around it

in order for us all to make informed decisions

about our future.

(slow stirring music)