Original subtitles

NARRATOR: Gothic cathedrals...

giant walls of glass in a kaleidoscope of colors,

surrounded by a spider web of masonry

and crowned with eerie gargoyles.

These skyscrapers of stone dominate skylines

for nearly 1,000 years.

How, in the Middle Ages,

without the benefit of modern tools and technology,

did engineers construct Gothic cathedrals?

This web is definitely ramped up to meet that.

NARRATOR: Now, experts explore a radical new theory:

A hidden mathematical code

ripped from the pages of the Bible

was used as a blueprint.

WOMAN: People were using the proportions

by which God had created the universe.

NARRATOR: But to unlock the cathedral code,

investigators must strip these medieval megastructures

to their bare bones.

MAN: Very slowly,

let the pressure go.

NARRATOR: They've got to figure out how cathedrals could reach

such spectacular heights

and what pushed some to the brink of collapse.

Now, can these experts solve

one of the greatest medieval mysteries?

How on earth did they build the Gothic cathedral?

Up next on NOVA, "Building the Great Cathedrals."

Major funding for NOVA is provided by the following.

Supporting NOVA and promoting public understanding of science.

And the Corporation for Public Broadcasting,

and by PBS viewers like you.

NARRATOR: Taller than the ancient pyramids in Egypt,

large enough to hold the Statue of Liberty...

A hundred million pounds of stone, seemingly weightless,

yet as heavy as the Empire State Building.

This is a revolution in building.

Gothic cathedrals.

From the moment they appear in Europe

about a thousand years ago,

they spark an intense rivalry between cities.

They consume the labor of entire towns,

sometimes taking a hundred years to build.

With just hand tools and stone, master craftsmen find ways

to defy gravity, pushing to greater and greater heights.

But this race for height sometimes leads to disaster.

One of the tallest cathedrals collapses... twice.

Many others still teeter on the brink of catastrophe.

STEPHEN MURRAY: I mean, it's frightening to see.

This is the least stable bay in the entire building.

NARRATOR: How on earth did medieval builders construct

these skyscrapers of stone?

And what caused some to collapse?

Now, two teams uncover the engineering secrets

locked inside Gothic cathedrals.

One team reassembles a Gothic church in California

to discover how cathedrals went up.

FRANK HELMHOLZ: The first time we see it together, it's really amazing.

NARRATOR: Another team, in France, uses laser scanning to investigate

why some of the tallest cathedrals fell down.

MURRAY: This is an exciting building

because it's come through a whole series of catastrophes.

NARRATOR: What pushed cathedral builders to such dangerous heights?

Experts explore a radical new theory...

Medieval builders used sacred numbers from the Bible

as a blueprint.

JOAN BRANHAM: We can analyze medieval manuscripts

that show the Temple of Solomon.

And guess what it looks like?

It looks like a Gothic church.

NARRATOR: Embedded in stone and stained glass,

is there a hidden mathematical code

that unlocks the secrets of Gothic cathedrals?

At the dawn of cathedral construction

in the late Middle Ages, around the 12th century,

building with stone was dirty, difficult work.

No one knows this better than these modern craftsmen.

Southeast of Paris, France, they are building a medieval castle

using only traditional tools and local materials:

stone, iron and wood.

They're rediscovering the same methods used

to construct Gothic cathedrals.

Their castle, called Guédelon, stretches about half the length

of a football field.

It's part tourist attraction

and part medieval construction lab.

MARYLINE MARTIN: We're building to understand.

It's an experimental archaeological site

and the idea is to get as close as we can

to the reality of medieval construction work.

NARRATOR: The team's challenge today is how to build a wall

on the upper floor of the castle.

The first problem is cutting through solid rock.

Stonecutters find

that if they hammer along natural fault lines,

they can split the rocks open.

Next, masons carve the pieces into building blocks.

But each weighs over 100 pounds and has to be lifted

all the way up top, almost five stories high.

From medieval manuscripts, the crew discovered

that builders in cathedral times

turned an ancient Roman war engine into a hoisting machine.

Workers can lift six times their own weight.

They call this curious contraption the squirrel cage.

Thibaut Desjardins is trying it out for the first time.

It's harder than it looks.

It's tough because there's a lot of resistance.

The wheel slows down regularly, so you have to keep speeding up.

NARRATOR: Step by step, the wheel lifts the stones to the roof.

Meanwhile, another team mixes mortar.

It's a long-lost recipe of burnt limestone and sand.

The mortar smoothes out gaps between stones,

but it's no super glue.

SARAH PRESTON: It's a very slow-drying mortar.

In fact, in the inside of these walls

where there's very little air,

it could take over a thousand years

for the mortar to completely dry.

NARRATOR: Instead of mortar holding the blocks together,

it's something much more basic.

Pressure, the weight of the castle... 60,000 tons...

keeps each stone in place.

But each layer of stone must be level

or the entire wall will topple.

In pre-Gothic times, the only way to build tall

is to construct big, thick walls.

So the result is buildings that are bulky and dark.

Then, all that changes.

On June 11, 1144 A.D.,

a "Who's Who" of medieval France,

including the king and queen,

gather in the outskirts of Paris.

Here, at Saint-Denis, the king's official church,

they witness a revolution in engineering.

Brilliantly colored light

streams through enormous stained glass windows,

washes over impossibly slender walls

and reflects off soaring ceilings.

Abbot Suger, the visionary behind Saint-Denis,

calls his architecture modern.

Critics scoff and name it after barbarians known as the Goths.

The name sticks... Gothic.

But to Suger, his church recalls the glory

of what the Bible calls God's house on earth,

the Temple of Solomon.

BRANHAM: Abbot Suger associates Saint-Denis

with biblical prototypes,

especially the Temple of Solomon.

And these temples often have jewels, glass, gold

set within them.

NARRATOR: To Suger, light was a symbol for God.

By bringing in more light,

he hoped to bring people closer to God.

Villagers living in small dark spaces must have been

awe-inspired by the church's towering walls of light.

BRANHAM: Suger's walls become windows.

Suger actually uses light as a building material.

NARRATOR: Amazingly, Gothic engineers built thin, super-tall walls

made not of stone but mostly of glass.

And somehow these walls of windows

support towering ceilings of stone.

How did medieval builders pull off

such a dramatic transformation?

The answer may lie in this chapel, which falls somewhere

between the thick, bulky walls of Guédelon

and the tall, thin walls of Saint-Denis.

The trouble is, the chapel is in pieces.

In 1931, American newspaper tycoon William Randolph Hearst

bought the church in Europe and shipped it,

block by block, back to California.

But the Great Depression stopped Hearst from ever rebuilding it.

Today, that's Frank Helmholz's job in Vina, California.

He's a master stonemason who's worked on French cathedrals.

HELMHOLZ: Stones from the monastery

were taken apart about 70 years ago, stone by stone, in Spain.

Right in here, we actually have

a lot of the stones still stored.

NARRATOR: It's taken about a decade to sort through all these blocks,

and after 800 years and shipping halfway around the world,

many are damaged.

Start the blade.

NARRATOR: To resurface them, they use this five-foot power saw.

Over the last seven years,

they have rebuilt the chapel's exterior walls.

The team has found that the chapel is constructed

with two different building techniques.

The back of the chapel is the older Romanesque style,

thick and bulky.

The rounded windows don't let in much light

because they have to be small and narrow

to support the weight of the wall.

But the front of the chapel is Gothic.

Similar to cathedrals, the walls are taller and thinner,

with big openings to allow in more light.

And the arches are a different shape... pointed.

Could this pointed arch hold the key

to constructing tall cathedral walls?

To find out, Helmholz and his team build a scale model

of a cathedral arch.

Like the cathedral builders,

the crew constructs a wooden frame

that will hold the arch together

until all the stones are in place.

So this would be SR3.

All right, let's put that one on.

NARRATOR: This model is 1/16 the size of a cathedral arch.

HELMHOLZ: I still feel like we could do a little better here.

NARRATOR: Even though it is smaller, he still has to make sure

that each of the stones is precisely aligned.

All right.

Place it nicely in the center.

HELMHOLZ: It's a little funky up there.

Keep going with two on this side more.

NARRATOR: Here, where the stones start running diagonally,

gravity comes into play,

introducing a pressure known as a stress line.

In a round Roman arch,

the stress line goes mostly sideways,

pushing the columns apart.

If it's too tall or wide,

the arch starts to sag in the middle and collapses.

But the pointed arch redirects the stress line

down to the ground, rather than to the sides,

and that allows engineers to build higher.

HELMHOLZ: The great advantage of the pointed arch is

it guides the thrust of the arch forces more downwards,

rather than outwards.

You have your fingers out?

NARRATOR: So the pointed arch is the first advance

that led to towering cathedrals.

But even this arch has limitations.

Right now, Helmholz has a problem.

The arch is pressing outwards.

You can see it in this movement here.

There is something that wants to go out

because the stones are pushing downwards.

NARRATOR: Even though the pointed arch redirects gravity,

it creates stress at the top of the columns.

It's a problem the crew will have to resolve,

or the stones will hinge open and the entire arch will cave.

HELMHOLZ: And we are the half here,

so we have a quarter-inch.

NARRATOR: The forces on this scale model

are just a fraction of those in a real-world structure.

And 80 miles north of Paris,

these forces may be pushing

a great medieval cathedral

to its breaking point.

In 1220, villagers in the boomtown of Amiens

decided to build a new cathedral

large enough to fit their entire population of 20,000 people.

They are not alone.

The opening of the king's church in Saint-Denis

inspires dozens of towns surrounding Paris...

and then throughout Europe...

to go Gothic, each hoping to construct

the tallest, most luminous building on earth.

Like many cathedrals, Amiens is built in the shape of a cross.

At its very center,

workers built tall walls with pointed arches

to create an enormous central bay 12 stories high.

But Professor Stephen Murray believes the race for height

may have come at a steep price.

This large bay, although beautiful...

it opens up the space; it creates a fabulous dramatic,

almost a theatrical center to the building...

but the large bay has left a structural problem.

NARRATOR: Just like the pointed arch in California,

this arch is showing signs of stress.

Murray climbs to the second level for a closer look.

From this level, we can really see very easily

the extraordinary signs of structural distress

in the building.

The visible evidence is all those cracks and fissures.

I mean, it's frightening to see.

NARRATOR: These cracks could be the first signs of catastrophe,

because to the left of the damaged arch

is an enormous central support column

that holds up the ceiling... thousands of tons of stone.

So these cracks could be a warning

that the very heart of the cathedral

is in danger of collapse.

Murray is anxious to investigate.

He brings in a team of scientists

using the latest laser scanning technology.

MURRAY: What this machine can do is give you the entire superstructure.

We can begin to see the deformations in the building

and begin to understand its structural problems.

NARRATOR: Murray enlists the help of Andrew Tallon,

a medieval architecture specialist,

to scan every nook and cranny of Amiens Cathedral.

TALLON: It sends a little laser beam out from its eye

and it measures thousands of times a second

the distance between itself and whatever it's hitting.

And so as it slowly pans across the wall,

it's shooting this laser out

and taking a whole series of measurements,

which then are represented in three dimensions

as a series of X-Y-Z coordinates.

Now it's switched to the higher window.

And now we are actually acquiring the model.

It's shooting right up over here.

NARRATOR: In only a matter of minutes,

the laser scans the entire central space

of Amiens Cathedral.

TALLON: This is the thrilling moment of the scan,

when we see the building start to appear.

NARRATOR: It's a highly accurate 3D model... a virtual cathedral.

But can it reveal the lurking structural problems

that threaten Amiens?

A building is a naughty thing.

It misbehaves.

The arches want to push outwards.

The building sometimes is guilty of misbehavior

that could produce collapse.

NARRATOR: To understand this misbehavior,

Murray and Tallon run a structural analysis

back at their lab in New York City.

MURRAY: This is a whole new tool

to understand exactly what's going on.

Isn't that a wonderful view?

NARRATOR: They zero in on the central columns

to look for signs of damage.

TALLON: We can measure the distance at different levels of elevation.

So we'll start at the base level.

NARRATOR: They measure the distance between the columns

at three levels.

If the columns are straight, the distances should be the same.

So we'll take a measurement at the lowest point, 11.6 meters,

so that's our basic measurement.

If we go three meters above,

we get 11.5 meters.

So we're dealing with 10 centimeters.

That is considerable.

That's a considerable distance.

NARRATOR: Right away, the model shows the stone columns are not straight.

But it gets worse.

So now let's go up to the very top of the building

and measure the distance just under the high capitals.

So we'll select a point here

and a point just across the way here.

The distance is 11.7.

Wow.

So we're dealing with fully 20 centimeters difference.

NARRATOR: The laser model reveals the columns are moving

in two different directions...

in at the bottom...

and out at the top.

In both cases, the stones in the surrounding arches

are pushing out and exerting pressure on the columns.

This is a recipe for disaster.

NARRATOR: Next door, structural analyst Rory O'Neill wants to find out

just how bad that disaster would be.

O'NEILL: By entering it into a simulation system like this,

we can push things to the point of their hypothetical collapse

and then examine what's going on.

Where are the moments in the building

that the builder would lose sleep over at night?

NARRATOR: O'Neill simulates what would happen over time

if the force of the lower arch pushes too hard on the column.

O'NEILL: What's happening now is

that all of the structure is starting to slide this way.

And I'll pause it for a second

so we can go in and take a closer look.

We see that the bricks are starting to separate

from the arch.

NARRATOR: The cracks in the model look strikingly familiar.

These cracks are a tell.

They're letting us know that, in fact,

the wall has shifted over time.

NARRATOR: The virtual model reveals that the real cracks have formed

because the arch has pushed the column to one side.

O'Neill simulates what happens next.

O'NEILL: It would continue to push out until at one point,

it would just give way

and everything would come crashing down.

NARRATOR: At the root of the problem are the stress lines in the arch.

We can go further on this side.

NARRATOR: It's the same problem Frank Helmholz needs to solve

in California with his pointed arch.

HELMHOLZ: The stress line is pushing outwards.

NARRATOR: If the crew removes the wooden frame now,

the arch will collapse

because the stress line is pushing these two stones out.

Helmholz needs to counter this force,

so he builds a supporting arm to prop it up.

That's the way it goes.

The stress line comes down here and wants to push out.

This arch is designed to counteract that.

NARRATOR: This ingenious solution is called a flying buttress.

To do its job, the buttress must be precisely placed.

If this buttress is attached too high,

then you still have the buckling possibility underneath here.

If it's placed too low,

then up here, this arch can fail right above here.

So it really is important that this is placed

in the right height.

Let's take off these two side pieces.

NARRATOR: It's the moment of truth.

Helmholz is about to find out if his stone arch,

without any mortar, will stand on its own.

His team slowly removes the wooden supports,

called the centering.

HELMHOLZ: And very slowly

let the pressure go.

Great.

That looks good, and I'll do the same, I'll let go.

And there's no movement.

It looks very good.

HELMHOLZ: It's quite exciting, actually, to see it work.

It's always a miracle

when you see an arch finally freed from the centering.

NARRATOR: The flying buttress reaches dramatic proportions

in a full-scale Gothic cathedral.

Rising spectacularly from the ground,

an intricate spider web of masonry.

With the pointed arch,

the flying buttress is the second Gothic innovation

that allowed medieval engineers to capture heavenly light

and to reach celestial heights.

The arch and buttress make up the basic building blocks

of an entire cathedral.

But it's a house of cards,

where the placement of every individual stone

plays a critical role.

To see how critical, Helmholz moves just one stone.

Shall we go?

Here we go.

NARRATOR: Without the buttress to counter it,

the sideways force of the arch pushes the column outwards

and the structure collapses.

It's the same sideways force that caused this collapse

that's making the central columns back at Amiens

bend out of shape, threatening disaster.

Yet to support the arch at the top of the central columns,

outside, Amiens' engineers did build the flying buttress.

So, what's gone wrong?

Is that good? There you sort of see it.

NARRATOR: Back at their lab at Columbia University,

Stephen Murray and Andrew Tallon investigate.

Their 3D model immediately reveals a critical error:

the exterior flying buttress is not in the right place.

TALLON: They've pushed it much, much too high.

In other words, the flying buttress is doing precious little.

NARRATOR: The original builders placed the flying buttress too high

to counteract the force of the ceiling arch pushing outwards.

So, more than two centuries later,

a master mason set out to fix it.

He added another, more solid, buttress

and placed it below the original,

where it provides better support.

That later mason, in a sense, saved the building.

TALLON: This lower flying buttress looks like a flying buttress should;

that is, it's solid.

It's massive, it's structural. Yeah, it's a prop.

NARRATOR: With new buttresses in place,

the medieval builders stabilized the upper wall.

But there was still no side support toward the bottom

where the wall began to crack.

MURRAY: By the late Middle Ages, people were scared to death

to see the enormous cracks opening up in the arcade.

NARRATOR: Medieval builders at Amiens have to find a way

to support the column before it collapses.

In desperation,

engineers go outside the Gothic playbook of stone.

They turn to metal.

Metal had rarely been used as a building material

because blacksmiths didn't have the technology

to make it thick or long enough.

And forging iron was a slow process.

It had to be hammered by hand.

Then, early in the 12th century,

monks reinvent an ancient Greek tool... a hydraulic hammer.

Located next to an iron mine in the village of Fontenay,

southeast of Amiens,

this abbey is one of the oldest metal factories

in all of medieval Europe.

Six hundred years before water-powered machinery

of the Industrial Revolution,

monks used a water wheel to turn a cog

that powers a 400-pound hammer.

Now workers could produce strong iron quickly

and in large enough quantities to be used in building.

But could iron rescue Amiens cathedral?

Builders make an enormous metal chain of linked iron bars.

The chain runs inside the wall

along the entire length of the cathedral

to hold its central columns in place.

MURRAY: The chain was installed red-hot so that it would contract

and pull inwards.

NARRATOR: The medieval iron Band-Aid worked.

Today, the massive metal chain at Amiens

may still be the only thing

that keeps these columns from collapsing.

Iron may have saved Amiens,

but ultimately it's the mastery of engineering

with stone that is the true Gothic breakthrough.

With the pointed arch and the flying buttress,

it was possible to build these light-filled, majestic walls.

But these walls are almost entirely glass.

How are they able to support immense ceilings of stone?

HELMHOLZ: Fire it up.

All right, let's get moving.

NARRATOR: To solve this final engineering mystery,

the California crew rebuilding the 12th-century chapel

is installing one of its last central columns.

Little more.

Okay, stop. That's good.

NARRATOR: They hoist a crowning capital into place.

Five years ago, when we started,

it was hard to imagine we would reach this place.

It's the first time we see it together.

It's really amazing.

NARRATOR: Twelve columns will support the stone ceiling.

And next door,

the crew is building the ceiling in sections.

They carefully lower the final piece...

the boss stone... into place.

It's a dry run to make sure everything fits together

after 800 years.

Great, so that fits, that works.

NARRATOR: The ceiling is called a ribbed vault.

It's made of two intersecting pointed arches.

The ribbed vault channels the weight of the ceiling

to the columns, so the walls don't bear the burden.

HELMHOLZ: Since the forces are concentrated on these ribs,

everything from here all the way across to here

can be opened up for windows.

NARRATOR: The ribbed vault is the third Gothic innovation.

Working with the pointed arch and the flying buttress,

engineers created a skeleton

that bears the weight of the building

and directs it towards the ground.

Gothic craftsmen could now fill these walls

with huge, colorful glass windows.

Today, glassmakers in New York City

are trying to make stained glass the same way

as those medieval craftsmen.

The basic process hasn't changed.

They start with the most elemental chemicals.

So this is where a stained glass window begins.

The basic recipe to make glass is this white powder here.

It's basically pulverized quartz crystal,

various metals and soda ash, which is burnt vegetable matter.

NARRATOR: Glassmaker Danny O'Shea shovels the chemical mixture

into a furnace that is heated to a scorching 2,300 degrees...

hotter than volcanic lava.

To color the glass,

medieval designers had to be craftsmen and chemists,

mixing metals into the molten mass.

MICHAEL DAVIS: They were aware that different metals added

to the glass mixture would give different colors.

Copper can be used to give green;

it can also be used to give red.

Cobalt, blue; selenium is like an orange and a yellow.

Blow, please.

NARRATOR: With color in place, they give the glass its first shape.

DAVIS: Stop.

NARRATOR: O'Shea blows through a steel tube called a blowpipe...

Stop.

NARRATOR: As Michael Davis begins to shape the mass.

DAVIS: As you're turning it, the thing is just getting wider.

It wants to open.

It's kind of a very natural thing for it to do.

NARRATOR: Spinning the glass, he works it into a disc.

Using these techniques, medieval glass builders

construct a kaleidoscope of colors...

from which they create enormous, intricately detailed

stained glass windows like never before.

These walls of glass depict narratives from the Bible

like Adam and Eve...

Noah's Ark...

and the resurrection of Jesus Christ.

In an age when few people can read and write,

stained glass windows become the multimedia stories

of their day... the Bible written in light.

DAVIS: They were a revelation

to the people that would go to a church

and see the colored light.

They were probably just marveling, like, "What is this?

This is incredible."

And I think it was moving.

I mean, we're still moved by them; I'm still moved by them.

NARRATOR: These vast spaces surrounded by towering walls of colored light

lifted medieval minds out of the dirt and darkness of daily life,

creating an otherworldly experience.

Jacqueline Jung is an expert on Gothic cathedrals.

JUNG: What would have impressed an ordinary visitor

the most upon entering this building

is its incredible size and scale.

They would hear the Mass performed,

experience all the sights, the sounds,

the aromas of incense.

People could really experience vicariously heaven on earth.

NARRATOR: The purpose of these immense, sacred spaces was spiritual,

to bring ordinary people closer to God.

Yet cathedrals would have been impossible

without the pointed arch, flying buttress and vaulted ceiling.

But these engineering innovations interact

in complex ways.

And in the quest

for heavenly height,

earthly limitations

brought some cathedrals

crashing to the ground.

While Amiens Cathedral is under construction,

just 35 miles away,

the townspeople of Beauvais want to build

their own stone skyscraper,

bigger and more beautiful than their neighbor.

We're seeing the most beautiful cathedral of Gothic.

This building takes off like a rocket ship.

NARRATOR: But Beauvais's height comes at a cost.

NARRATOR: High above these churchgoers are modern braces

that may be the only thing

keeping the cathedral from collapsing,

an unsettling reminder of a medieval disaster.

MURRAY: On Ascension Day in 1573,

there was a service being celebrated in the church.

Stones began to fall.

There was a solemn procession taking place.

The clergy slowly began to speed up their pace.

They ended up rushing out of the cathedral in a cloud of dust.

NARRATOR: Miraculously, the only injury was a broken arm.

But this wasn't the first time the church collapsed.

During construction in 1284,

part of the ribbed vaulted ceiling...

12 stories high... came crashing down.

The building's columns, or piers,

continue to be plagued by structural problems to this day.

An unstable pier, an overhang...

The pier is buckling to the west.

These are incredibly slender.

This is very, very sick.

This is a recipe for disaster.

NARRATOR: And Beauvais wasn't the only town courting disaster.

Regional rivalry drove many Gothic builders

to ever more dangerous heights.

But why?

Some experts suspect they were motivated

by something beyond earthly bragging rights.

For hidden within the dimensions of the greatest cathedrals

may be a secret mathematical code

that could provide the answer.

At Notre Dame of Paris, perhaps

the best-known Gothic cathedral,

Stefaan van Liefferinge, a physicist turned art historian,

uses a laser scanner to investigate.

He measures the height of the church's two levels.

Each measures 32.8 feet.

But medieval builders used a different unit of measurement.

If you translate it in royal feet,

which is the medieval unit,

then that would be about 30 royal feet for the lower level

and 30 royal feet for the higher level.

NARRATOR: The combined height is 60 royal feet.

These figures... 30 and 60... are strangely familiar

to van Liefferinge.

At one of France's oldest libraries,

the Bibliothèque Mazarine,

he searches a medieval book written by the priest

in charge of building Notre Dame.

VAN LIEFFERINGE: What we have here is a manuscript

from the turn of the 12th century,

which was composed by the chancellor of Notre Dame,

Peter Comestor.

NARRATOR: Called the Historia Scholastica,

the priest wrote this book

during the cathedral's construction.

He fixates on a passage in the Old Testament...

a detailed description of the Temple of Solomon in Jerusalem,

which the Bible refers to as God's house on earth.

Here, van Liefferinge finds an intriguing clue.

NARRATOR: This manuscript reveals that to the builders of Notre Dame,

the dimensions of Solomon's Temple

were profoundly important...

30 cubits to the first level

and 60 cubits to the second level.

These numbers are built into Notre Dame.

So, an interesting correspondence here,

a very intriguing correspondence here.

NARRATOR: Are these numbers purely coincidence,

or did medieval builders intentionally encode

sacred numbers from the Bible into their cathedrals?

Just southwest of Paris,

clues are embedded

in the crown jewel

of Gothic architecture,

Chartres Cathedral.

The stained glass here... most of it 800 years old...

is world famous.

But Chartres has Bible stories etched not only in light,

but also in stone.

These intricate exterior statues

are staples of Gothic cathedrals...

finishing flourishes that took dozens of carvers

decades to complete.

But at Chartres,

alongside statues of Jesus, Mary and the Apostles,

Gothic expert Jacqueline Jung investigates something

completely unexpected...

Greek and Roman scientists

who predate Christianity by hundreds of years.

Among them Aristotle, Euclid

and Pythagoras, the great mathematician.

These ancient pagans were revered by medieval priests

at Chartres.

JUNG: The cathedral of Chartres

was filled with some of the leading thinkers of this time,

who were themselves steeped in classical philosophy,

science and literature,

and were bringing these ideas to Christian theology

in ways that were really quite new.

NARRATOR: While the cathedral was being built,

priests at Chartres studied classical Greek and Roman ideas.

Medieval priests seized on the idea

that the supreme beauty of the universe

is based on perfect proportions and ideal numbers.

They saw God as the Supreme Mathematician...

a divine geometer who used sacred dimensions.

JUNG: People were interested in using numbers as a means

of figuring out the proportions

by which God himself had created the universe.

NARRATOR: Medieval priests found numbers in the Bible

that they believed were God's sacred dimensions.

If they used those numbers in cathedral building,

can experts find them today?

On the hunt for divine dimensions,

Stephen Murray returns to Amiens,

where builders rescued the cathedral with an iron chain.

He starts by measuring the area at the very center of the cross,

where the four central columns form a square.

MURRAY: The geometric code

that gives the shape of this building

involves a great square that sits right here in the middle.

NARRATOR: Each side of the central square

measures almost exactly 50 Roman feet,

the unit of measure used by the builders at Amiens.

Fifty also happens to be an important number from the Bible.

God tells Noah to build an ark that is 50 cubits wide

to save him from the flood.

Noah's ark was 50 cubits.

This is 50 feet.

And this lies at the heart of the building.

NARRATOR: Like at Notre Dame, it looks as if engineers at Amiens

encoded a measurement from the Bible into their cathedral.

Murray and Tallon turn to the laser scan models.

We're using a perspective view as opposed to...

NARRATOR: Using this technology,

for the first time they can measure the height

of the cathedral down to the nearest millimeter.

MURRAY: Let's see if we can choose one of the keystones

and drop a line down to the floor.

We'll get the distance down to the pavement below.

We get 42.55 meters.

NARRATOR: Some quick math converts modern units to medieval units...

A Roman foot is what we think they used.

NARRATOR: and produces another divine figure: 144.

In the New Testament, heaven is called the City of God.

Its height: 144.

MURRAY: This is Book of Revelation,

the vision of Saint John the Divine.

As John measures the city, he finds it's 144 cubits.

NARRATOR: Amazingly, at the dedication ceremony

for the opening of Amiens Cathedral,

the bishop read aloud the very same passage

from the Book of Revelation that describes the divine height,

144.

MURRAY: So we're dealing in the building with clearly a number

that expresses some kind of object and desire.

They wanted 144.

NARRATOR: Their search for divine dimensions continues

at Beauvais, the cathedral that partly collapsed.

So, we're going to take a point here

and down on the floor below.

NARRATOR: They measure the height.

TALLON: Check the measurement and it is... 144.3.

The same number at Beauvais.

They're aiming at this celestial number.

The builders at both Amiens and Beauvais

used the height of God's heavenly city in the Bible

to design the height of their cathedrals.

Along with the discovery of Solomon's Temple

encoded at Notre Dame,

and Noah's Ark at Amiens,

experts have uncovered compelling evidence

that some medieval architects used measurements from the Bible

as a blueprint for building their cathedrals.

Using sacred numbers,

Gothic engineers strived to make cathedrals

a kind of heaven on earth,

a sacred place for transporting medieval minds

from their daily lives of toil

to the lofty heights of eternity.

Even the floor plan of the cathedral

is the ultimate Christian symbol of salvation... the crucifix.

MURRAY: The building is a vehicle; it takes you somewhere else.

A cathedral, in a sense, is a medium, it's a transport.

It takes us to heaven.

NARRATOR: But in striving for godly dimensions,

builders were caught up in a very human race.

At both Amiens and Beauvais,

engineers built cathedrals 144 units high.

But the builders at Beauvais used a clever trick

to reach the top... a different unit of measure;

instead of the Roman foot, the slightly longer royal foot.

Thus, Beauvais reached heavenly dimensions

and built the tallest cathedral on Earth.

But that quest for height

came at the price of structural instability,

and to this day, Beauvais Cathedral remains unfinished.

MURRAY: This is a building that has suffered

all kinds of architectural setbacks

and yet one which remains, still, to my mind,

the most beautiful of all the buildings of French Gothic.

NARRATOR: Fueled by faith and guided by daring engineering,

Gothic architects forever changed how we build big.

Pushing the limits of their technology

and driving to new heights,

cathedral builders created sacred spaces

that still inspire people to this day.