Thirteen million people visit the Notre Dame Cathedral in Paris every year, entering through massive wooden doors at the base of towers as solidly planted as mountains. They stand in front of walls filigreed with stained glass and gaze at a ceiling supported by delicate ribs of stone.

If its beauty and magnificence is instantly apparent, so much about Notre Dame is not. To begin with, we don't know who built this cathedral—or how. (Discover the 800-year history of Notre Dame Cathedral.)

The bishop of Paris, Maurice de Sully, commissioned the massive church complex around 1160. Yet the names of those who first constructed this masterpiece are lost to history. They left no records—only centuries of speculation—behind.

"So much ink has been spilled over that building," says art historian Andrew Tallon. "So much of it is completely wrong."

A former composer, would-be monk, and self-described gearhead—or, as he puts it, "tacklehead"—Tallon intends to make that history right. With the help of 21st-century laser scanners, he is teasing out clues hidden in the ancient stones of Notre Dame and other medieval structures—and revolutionizing our understanding of how these spectacular buildings were made.

One Billion Points of Data

Tallon, who died Nov. 18, 2018, at 49, wasn't the first to realize that laser scanners could be used to deconstruct Gothic architecture. But he was the first to use the scans to get inside medieval builders' heads.

"Every building moves," he says. "It heaves itself out of shape when foundations move, when the sun heats up on one side." How the building moves reveals its original design and the choices that the master builder had to make when construction didn't go as planned. Tracking this thought process requires precise measurements. (See vintage pictures of the cathedral from Nat Geo's archive.)

For a long time, the tools used to measure medieval buildings were nearly as old as the buildings themselves: plumb bobs, string, rulers, and pencils. Using them was tedious, time- consuming, and error-prone.

"You can't hang from a vault and measure it by hand," says Michael Davis, an art historian at Mount Holyoke College who once spent nine weeks surveying two churches with these primitive tools.

Laser scans, with their exquisite precision, don't miss a thing. Mounted on a tripod, the laser beam sweeps around the choir of a cathedral, for example, and measures the distance between the scanner and every point it hits. Each measurement is represented by a colored dot, which cumulatively create a three-dimensional image of the cathedral. "If you've done your job properly," says Tallon, the scan is "accurate to within five millimeters [.5 centimeter]."

Two researchers at Columbia University—Peter Allen, a computer scientist, and Stephen Murray, an art historian—attempted one of the first laser scans of a Gothic building in 2001 at the cathedral in Beauvais, north of Paris, which Murray had once measured by hand with steel tape and wooden calipers.

Unfortunately, the scanner "actually went up in a puff of smoke. It really did emit smoke," says Murray. "And at that point people didn't know how to render [the data] into a three-dimensional model that was manageable."

Tallon figured out how to knit the laser scans together to make them manageable and beautiful. Each time he makes a scan, he also takes a spherical panoramic photograph from the same spot that captures the same three-dimensional space. He maps that photograph onto the laser-generated dots of the scan; each dot becomes the color of the pixel in that location in the photograph.

As a result, the stunningly realistic panoramic photographs are amazingly accurate. At Notre Dame, he took scans from more than 50 locations in and around the cathedral—collecting more than one billion points of data.

Tallon, says Murray, his Ph.D. adviser at Columbia, is "able to combine that astonishing grasp of technology with the big humanistic vision that one hopes that art historians have."

'I Want to Go Up There'

Tall and lean with short-cropped hair and narrow eyeglasses, Tallon leans forward when he talks, sketching architectural features with his hands. He pops up and down from his chair, eager to show a visitor the exact spot on a projected image that demonstrates his point.

His high-tech approach to Gothic architecture seemed preordained. As a kid growing up in Milwaukee, "I loved gadgets," he says. He took apart reel-to-reel tape decks and played around with synthesizers.

He was also obsessed with Notre Dame. "I had this little guidebook and I annotated it like a nutcase," he says, describing the year he was in fourth grade and living in Paris while his mother worked on her dissertation in theater history. "I longed to know the usual questions. Who made that thing? How did they make it? Could I ever go up in one of those passages?"

The answer to that last question was yes, but it would take a long time to get there. "I have a career I don't really tell my French colleagues about," he admits, "because they'll think I'm not serious."

As an undergraduate at Princeton, he majored in music but also took every class taught by Robert Mark, an engineer who studied the structure of Gothic buildings.

After graduation, his peripatetic journey began. First he went to France, where he studied medieval acoustics. Next stop was New York City, where he started a music composition studio. Then he paused in a Northern California monastery to explore the life of a monk. (The monks told him he wasn't cut out for it.)

Music led him back to Gothic cathedrals. Murray, the Columbia University art historian, was putting together a multimedia project on Amiens Cathedral and needed someone to create "sounds that a cathedral might make." Mark told him there was only one person he should contact—Andrew Tallon.

The project was a labor of love. "I finally realized that what I really wanted to do was to be able to mix all these things together—love for medieval buildings, for art, for technology, for knowledge," Tallon says.

Murray introduced him to laser scanning. More than a decade later, Tallon, now a tenured professor at Vassar College in the art department, has scanned some 45 historic buildings. "That very same thrill that I longed for as a kid looking up at those passageways in Notre Dame—'I want to go up there'—well, here I am up there, and it's thrilling," he says.

Detective Work

Some of the thrill comes from the dizzying heights Tallon must ascend to do his job. At the Laon Cathedral in northern France, "I wanted to see the building right below the great eastern rose window," he says, but his tripod filled the narrow ledge, which was more than 80 feet (25 meters) off the ground. "I had to step out into the void to go around it." When his wife, Marie, saw the resulting image, showing the precipitous drop, she threatened to smash his camera.

"You can't really just fly over with a helicopter, scan the building, and call it a day," says John Ochsendorf, an MIT engineer who is using Tallon's scans to create a small-scale model of Bourges Cathedral with a 3-D printer. "You really need to get up into all the difficult places you can access: the top of the roof, the top of the vaults, inside the stairwells, all the hidden spaces people don't normally see."

To Tallon, the father of four boys under the age of eight, the discoveries make the scrambling around worthwhile. "If I had texts at every point, I could look in the texts and try to get back into the heads of the builders," he says. "I don't have it, so it's detective work for me."

The laser scans have led to surprising new information about Notre Dame's builders. For one thing, they sometimes took shortcuts. Even though medieval builders strove to create perfect dwelling places for the spirit of God, Tallon's scans reveal that the western end of the cathedral is "a total mess ... a train wreck." The interior columns don't line up and neither do some of the aisles. Rather than removing the remains of existing structures from the site, the workers appear to have built around them. (Read Nat Geo's 1968 ode to the cathedral.)

That cost cutting could have been catastrophic. Based on stylistic changes, scholars have long suspected that work on the western facade stopped for a while before the towers could be built. When Tallon scanned it, he discovered why. The Gallery of Kings—the line of statues above the three massive doorways—was almost a foot (.3 meters) out of plumb. Tallon concluded that the western facade, built on unstable soil, began leaning forward and to the north. Construction had to be halted until the builders could be confident that the ground had compressed enough to resume. After an anxious decade or so, it had.

The builders were more sensible when it came to constructing flying buttresses, which some scholars have argued were added after the cathedral was built. After measuring the walls, Tallon determined that the flyers, as he calls them, were part of the cathedral's original design. The vaults in the ceiling should push walls outward but "the upper part of the building has not moved one smidgen in 800 years." The reason? "The flying buttresses were there from the get-go," pushing the walls inward and creating a stable balance of forces.

Built on Faith

Last spring, Tallon scanned the National Cathedral in Washington, D.C., which was begun in 1907, long after the Middle Ages had ended. He was looking for evidence of the influence of William Goodyear, a renowned American art historian who believed that the allure of Gothic cathedrals can be traced to imperfections that builders purposefully introduced.

The architects charged with completing the National Cathedral had consulted Goodyear, and Tallon wondered whether he'd find some intentional flaws in the neo-Gothic building.

He did. Though most of the structure is perfectly plumb, the great columns at the center of the cathedral were built ever-so-slightly outwards, and the choir doesn't align exactly with the nave. To Goodyear, imperfection "was the secret sauce," says Tallon, "that medieval folks sprinkled on their buildings to make them beautiful."

Tallon believes the true "secret sauce" was faith. "There was a biblical, a moral imperative to build a perfect building," he says, "because the stones of the building were directly identified with the stones of the Church"—the people who make up the body of the church.

"I like to think that this laser scanning work and even some of the conventional scholarship I do is informed by that important world of spirituality," says Tallon. "It's such a beautiful idea."