Last year, nearly twenty million pairs of Birkenstocks were sold. The Furkenstocks fashion moment was unsought, Reichert told me, and something of a distraction. “We are not calculating what the next fashion trend is,” he said. “To be honest, it will be better to be not so much in fashion right now.” It had been hard to keep up with demand for certain styles, like the Arizona in white leather with a white sole. It was preferable to satisfy gently rising demand. Reichert said, “We are O.K. with having our critical mass out there, and working with them, and not having millions on top just rush in and rush out one day, because for the company it is heavy to handle this.”

The brand’s resurgence was no mere trend, he argued: a larger cultural shift was under way. Women were recognizing that most footwear was unhealthy. (What is the point of having a Fitbit on your wrist if your shoes make it punishing to walk?) Reichert said, “You cannot walk all day like this”—he shifted his weight onto his toes, then minced forward for a few steps, as if he were wearing heels. “Talk to your friends, and ask them to show you their feet. You will see a lot of crooked feet, and you will say, ‘This is torture.’ ” The popularity of Birkenstocks, he argued, indicated a desire for a return to a more natural state, at least where footwear was concerned. “People say, ‘People will be completely ugly that way’—you don’t do any pedicure at all, you are not washing your hair, you are not taking showers because it is bad for nature, you are not using soap,” he said. “I am not talking about this! I am saying, Accept that the human being is built like this.”

Consumers, Reichert noted, have become increasingly concerned about the provenance of what they wear, and about the environmental and social impact of their clothing choices. Birkenstock is proud that its sandals are still made in Germany, rather than in China, and the company honors a promise to repair worn-out sandals, no matter how decrepit. “Ask your mother and she will say this is normal—yes, you buy shoes at the shoe store, and you bring the shoes back and they repair them,” he said. “In former days, a pair of shoes was an expensive thing. Now you can buy a pair of trousers for under ten euros at Primark”—a low-cost European chain—“but this will be a brief trend, and then it will be gone. Because even the youngest kids will understand that, in Bangladesh, someone had to suffer for their ten-euro trousers, and it is not a fair deal at all.”

Reichert assumed his leadership role at Birkenstock in 2013, with the task of restructuring a company that had become unwieldy in its organization and unreliable in its production. As Karl Birkenstock withdrew from company operations, in the aughts, management and ownership of the company passed to his three sons: Christian, Stephan, and Alex Birkenstock. It was not a successful arrangement. There were dozens of subsidiaries and lines, each headed by a different brother, and often competing against one another. “It was like a huge nightmare—everybody with his teams,” Reichert says. Two years ago, Stephan left the business. (“I was the heavyweight boxer, and I convinced him to leave,” Reichert told me, convincingly.) Ownership is now divided between Christian and Alex, but they are no longer actively involved. “The mistake was done by Karl Birkenstock,” Reichert told me. “A very European mistake. You should choose one. Like in the monarchy. You can’t say, ‘I was king, I have three sons, so I divide the kingdom in three pieces.’ ”

Reichert has sought to explore new markets. He expects to start offering Birkenstock leather bags, and wants to expand into other products that emphasize comfort, including mattresses and desk chairs. These plans may not all pay off—it’s hard to imagine Birkenstock displacing Vitra in the corporate boardroom—but Reichert is undaunted. “It is a sleeping giant,” he said of the company. “If you try to awake a sleeping giant, you should do it slowly and very smoothly, because if he moves too fast he will destroy a lot of things. So we are kissing, touching, very slowly trying to wake him up.”

Reichert has been introducing other Birkenstocks for cold weather. For years, the company has made a mule called the Boston, which in Germany is typically worn as an indoor shoe. Last fall, a shearling-lined Boston, in slate-blue suède, appeared in stores. I own a pair, and they are the best argument I know of for working from home. No matter how odd a new Birkenstock may appear at first, Reichert told me, wearing is believing. “This is the magic about the product—you don’t have to talk about it, you simply show the product, give it to the people to try on,” Reichert said. “You try to survive your first visual influence. It is love on the second sight.”

One of Birkenstock’s main factories is outside Görlitz, which is sixty miles east of Dresden, in Saxony. Görlitz was spared the aerial bombing that gutted Dresden’s architectural heart during the Second World War, and it is sometimes called the most beautiful town in Germany. Gorgeously painted medieval, Baroque, and rococo buildings cluster on hilly cobblestone streets that lead to picturesque market squares. A magnificent Art Nouveau department store, now shuttered but scheduled to reopen as a shopping center, doubled as the interior of the Grand Budapest Hotel in the Wes Anderson film.

Birkenstock employs some nine hundred people in Görlitz. When I visited the factory, it smelled as pungent as a bakery, redolent with the scent of cooking latex and cork. In the area where soles are made, liquid ethylene-vinyl acetate—a flexible, lightweight polymer known as E.V.A.—was being poured into footprint-shaped molds on a carrousel. Nearby were dozens of bales of jute, two layers of which are required for each foot bed. Across the factory were several enormous tanks filled with liquid latex. In a hangar-size room, sacks containing ground-up cork, imported from Portugal, were massed in rows. One sack was open, and I reached in for a handful of cork. It was startlingly light to the touch, and felt as if I were running my fingers through beach sand on a planet with a lesser gravitational pull than Earth’s.

To form the signature Birkenstock foot bed, the latex and the cork are blended in a proprietary formula, creating a brownish granulated paste that, in its prebaked state, bears an unfortunate visual resemblance to cat vomit. In the vulcanization area, which was pleasantly warm, I watched as measured quantities of this paste were spewed mechanically into dozens of stainless-steel, foot-shaped molds. A young man in shorts and a T-shirt worked swiftly along the line: he pressed a layer of jute onto each pile of cork-and-latex mixture, then topped it with a thin suède liner, like a dried tobacco leaf, before shunting it into an oven.

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Upstairs, the production line continued: young women trimmed the excess jute and leather from the vulcanized product of the oven, brown ribbons of material piling around their feet, like the waste left over by a fishmonger. Other women, sitting under bright dressmakers’ lights, marked small pieces of leather with tailors’ chalk, indicating the point where the foot bed would be attached. A team of five was operating a machine that produced black Milano sandals—an Arizona with a heel strap—in size 37. One readied the pieces of leather, now equipped with buckles, to be glued to the foot bed; another supplied the soles. Hilmar Knoll, the factory’s production manager, who conducted me around the factory, did a rapid calculation: among cutters, packers, machine operators, and control checkers, each Birkenstock sandal is touched by the hands of nineteen people in its manufacture.

Birkenstocks aren’t cheap—in Germany, the basic Arizona costs forty-nine euros. (A pair costs a hundred dollars here.) Recently, the company launched an effort to reach customers who need a less expensive shoe, by producing sandals made from ethylene-vinyl acetate. At the factory, liquid E.V.A., in black, white, red, and blue, was being poured into molds cast from Birkenstock’s core styles: the Arizona, the Madrid, the Gizeh. These models, which retail for about twenty-five euros, are intended to penetrate markets where Birkenstock has had little impact, such as South America and parts of Southeast Asia. This summer, the shoes will also be available in some U.S. locations. Finally, there are Birkenstocks that can be worn in the playground sprinkler.