The Specialisterne school uses Legos, too. Frank Paulsen, a red-haired man with a thin beard who is the school’s principal, told me about a session he once led in which he handed out small Lego boxes to a group of young men and asked them to build something that showed their lives. When the bricks had been snapped together, Paulsen asked each boy to say a few words. One boy didn’t want to talk, saying his construction was “nothing.” When Paulsen gathered his belongings to leave, however, the boy, his teacher by his side, seemed to want to stay. Paulsen tried to draw him out but failed. So Paulsen excused himself and stood up.
The boy grabbed Paulsen’s arm. “Actually,” he said, “I think I built my own life.”
Paulsen eased back into his seat.
“This is me,” the boy said, pointing to a skeleton penned in by a square structure with high walls. A gray chain hung from the back wall, and a drooping black net formed the roof. To the side, outside the wall, two figures—a man with a red baseball cap and a woman raising a clear goblet to her lips—stood by a translucent blue sphere filled with little gold coins. That, the boy continued, represented “normal life.” In front of the skeleton were low walls between a pair of tan pillars, and a woman with a brown ponytail looked in, brandishing a yellow hairbrush. “That is my mom, and she is the only one who is allowed in the walls.”
The boy’s teacher was listening, astonished: In the years she’d known him, she told Paulsen later, she had never heard him discuss his inner life. Paulsen talked to the boy, now animated, for a quarter of an hour about the walls, and Paulsen suggested that perhaps the barriers could be removed. “I can’t take down the walls,” the boy concluded, “because there is so much danger outside of them.”
In June, Sonne announced the opening of a U.S. headquarters in Wilmington, Delaware. The state’s governor, Jack Markell, was there, as was a representative from CAI, the company that is Specialisterne’s first real partner in the United States. The company says it plans to begin recruiting and training autistic software testers in Delaware next month, and if all goes well, it will expand the program to other states. Specialisterne is also talking with Microsoft about setting up a pilot program in Fargo, North Dakota, where it has a large software-development operation.
Tyler Cowen, an economist at George Mason University (and a regular contributor to the New York Times), published a much-discussed paper last year that addressed the ways that autistic workers are being drawn into the modern economy. The autistic worker, Cowen wrote, has an unusually wide variation in his or her skills, with higher highs and lower lows. Yet today, he argued, it is increasingly a worker’s greatest skill, not his average skill level, that matters. As capitalism has grown more adept at disaggregating tasks, workers can focus on what they do best, and managers are challenged to make room for brilliant, if difficult, outliers. This march toward greater specialization, combined with the pressing need for expertise in science, technology, engineering, and mathematics, so-called STEM workers, suggests that the prospects for autistic workers will be on the rise in the coming decades. If the market can forgive people’s weaknesses, then they will rise to the level of their natural gifts.
“Specialization is partly about making good use of the skills of people who have one type of skill in abundance but not necessarily others,” says Daron Acemoglu, an economist at MIT and coauthor of Why Nations Fail. In other words, there is good money to be made doing the work that others do not have the skills for or are simply not interested in.
As Sonne tries to build up his business in the United States, though, he faces practical challenges. For one thing, in Denmark, the government helps cover some of the additional expense of managing autistic workers, and it pays Specialisterne so it can give its employees full-time salaries even though they work only part-time. Specialisterne pays its consultants in Denmark between $22 and $39 an hour, a rate negotiated with unions, and in Delaware it plans to start with salaries between $20 and $30 an hour. And while two Delaware charitable foundations have pledged $800,000 to Specialisterne, Sonne estimates that it will take $1.36 million, and three years, for the business to become self-sustaining.
Another challenge involves expectations. A new stereotype of autistic people as brainiacs endowed with quirky superminds is just as misguided as the old assumption that autistic people are mentally disabled, Sonne says. Autistic people, like everyone else, have diverse abilities and interests, and Specialisterne can’t employ all of them. Most people Specialisterne evaluates in Denmark don’t have the right qualities to be a consultant—they are too troubled, too reluctant to work in an office, or simply lack the particular skills Specialisterne requires. The company hires only about one in six of the men and women it assesses.
April Schnell, who is organizing a Specialisterne effort in the Midwest and has an autistic son, told me that she traveled to Copenhagen for a conference organized by the company for their volunteers from around the world. One day she and the others were given the Mindstorms challenges used to assess candidates. As she struggled to solve one of the more difficult ones, she realized that her son, Tim, who is fifteen, would find the work uninteresting and probably too difficult: Specialisterne is not likely to be the answer for him. “I was just very aware, there is a gap here,” she said. “My heart was a little sad.”
One Friday evening, Sonne drove me to his house southwest of Copenhagen, navigating through whipping rain and the last clots of rush-hour traffic. Lars was waiting at the door to welcome us. Now sixteen, Lars evokes a Tolkien elf—thin and blond with exceptionally pale skin. He was outgoing from the start, eager to give me a tour of the house, yet he only glanced at my face.
Lars has the sweet demeanor of a much younger boy. Several times he affectionately rubbed his father’s head, the hair a short thin fur, calling the bald spot “Mr. Moon.” He gushed about trains, and at dinner Annette gently told him that we might not want to hear too much more about international conventions on track signals. I played Lars in a round of speed chess in the living room. There was never much doubt about the outcome, but at one point he issued an earnest warning: “Take care to not weaken your king’s position unnecessarily.” It was too late. After we put the pieces away, I complimented him on his final moves—an elegant and lethal attack with rooks, a bishop, and a knight—and he did a balletic twirl, arms out. I joked with his family about how crushed I felt in defeat, and Lars walked over and put a consoling hand on my shoulder. Perhaps, I suggested to Lars, I would be allowed a rematch? “No,” he said simply.
When I asked Lars what he thought about his father’s company, he said he has played with the Mindstorms robots but does not see himself working there. “I want to be a train driver,” Lars announced. “It is the country’s most beautiful job. You get to control a lot of horsepower. Who wouldn’t want to do that?”
At the outset, it was Thorkil’s aim to persuade Danish tech companies to hire his autistic employees. Now he wants all kinds of companies, all over the world, to learn from what Specialisterne is doing. He figures that if he is successful, then maybe a national railway will consider hiring a candidate as seemingly unlikely as his son, as long as he has the right skills.
Certainly he has seen how transformative getting the right job can be for the autistic workers themselves. Before coming to Specialisterne, Iversen, who works at TDC, had not had a job for twelve years and spent the days sleeping and nights surfing the Internet. Niels Kjaer once worked as a physicist, receiving his diagnosis only after becoming clinically depressed when he didn’t get an academic job. When he came to Specialisterne, where he works on improving technology that grades eggs as they pass by on a conveyor belt, he was on sick leave from a job driving a cab.
Christian Andersen, who works at Lundbeck, the pharmaceutical company, was bullied and beaten for years as a schoolboy. He received his diagnosis at age fifteen only because, fearing he might be suicidal, he checked himself into a hospital. After high school—inspired by a Hemingwayesque teacher who regaled
his students with tales of outdoor exploits—Andersen tried a vocational school for landscaping. But he was overwhelmed by the requirement that he learn to drive. He tried another tech school but failed, became depressed, and had a breakdown in 2005. Andersen was living at home without prospects, playing video games. He couldn’t even land a job at a grocery store. Later that year, his parents encouraged him to apply to Specialisterne.
I joined Andersen one morning on his commute to Lundbeck’s headquarters across town. Riding on a yellow city bus, we talked about video games. He still loves Halo; Diablo 3 he finds frustrating. “You turn a corner and then—splat!—you are dead.” As we drew closer to the office, our conversation drifted to his job. He spoke with surprising insight about the psychological importance of work. “I have grown very much as a person,” Andersen told me. “I have become more confident and self-assured.” The job allowed him to move out of his parents’ house and into an apartment. After a while, Andersen informed me, he “started using body language.” It’s not something anyone taught him. He just watched people, he said, and “monkey see, monkey do.”
When he started at Lundbeck, he was constantly anxious because he dreaded making an error. Now the stress grips him far less often and is readily dispelled with a phone call to a coach at Specialisterne. He admits to being proud, having come so far. He was touched to be invited recently to join his department for some after-work bowling. But he doesn’t spend a lot of time thinking about these aspects of his employment anymore. “Of course it feels good,” Andersen said, “but there is such a thing as ‘here we go again.’” It’s only a job, after all.
NATALIE ANGIER
The Life of Pi, and Other Infinities
FROM The New York Times
ON THIS DAY (December 31) that fetishizes finitude, that reminds us how rapidly our own earthly time share is shrinking, allow me to offer the modest comfort of infinities.
Yes, infinities, plural. The popular notion of infinity may be of a monolithic totality, the ultimate, unbounded big tent that goes on forever and subsumes everything in its path—time, the cosmos, your complete collection of old Playbills. Yet in the ever-evolving view of scientists, philosophers, and other scholars, there really is no single, implacable entity called infinity.
Instead, there are infinities, multiplicities of the limit-free that come in a vast variety of shapes, sizes, purposes, and charms. Some are tailored for mathematics, some for cosmology, others for theology; some are of such recent vintage their fontanels still feel soft. There are flat infinities, hunchback infinities, bubbling infinities, hyperboloid infinities. There are infinitely large sets of one kind of number, and even bigger, infinitely large sets of another kind of number.
There are the infinities of the everyday, as exemplified by the figure of pi, with its endless postdecimal tail of nonrepeating digits, and how about if we just round it off to 3.14159 and then serve pie on March 14 at 1:59 P.M.? Another stalwart of infinity shows up in the mathematics that gave us modernity: calculus.
“All the key concepts of calculus build on infinite processes of one form or another that take limits out to infinity,” said Steven Strogatz, author of the recent book The Joy of x: A Guided Tour of Math, from One to Infinity and a professor of applied mathematics at Cornell. In calculus, he added, “infinity is your friend.”
Yet worthy friends can come in prickly packages, and mathematicians have learned to handle infinity with care.
“Mathematicians find the concept of infinity so useful, but it can be quite subtle and quite dangerous,” said Ian Stewart, a mathematics researcher at the University of Warwick in England and the author of Visions of Infinity, the latest of many books. “If you treat infinity like a normal number, you can come up with all sorts of nonsense, like saying infinity plus one is equal to infinity, and now we subtract infinity from each side and suddenly naught equals one. You can’t be freewheeling in your use of infinity.”
Then again, a very different sort of infinity may well be freewheeling you. Based on recent studies of the cosmic-microwave afterglow of the Big Bang, with which our known universe began 13.7 billion years ago, many cosmologists now believe that this observable universe is just a tiny, if relentlessly expanding, patch of spacetime embedded in a greater universal fabric that is, in a profound sense, infinite. It may be an infinitely large monoverse, or it may be an infinite bubble bath of infinitely budding and inflating multiverses, but infinite it is, and the implications of that infinity are appropriately huge.
“If you take a finite physical system and a finite set of states, and you have an infinite universe in which to sample them, to randomly explore all the possibilities, you will get duplicates,” said Anthony Aguirre, an associate professor of physics who studies theoretical cosmology at the University of California, Santa Cruz.
Not just rough copies, either. “If the universe is big enough, you can go all the way,” Aguirre said. “If I ask, will there be a planet like Earth with a person in Santa Cruz sitting at this colored desk, with every atom, every wave function exactly the same, if the universe is infinite the answer has to be yes.”
In short, your doppelgängers may be out there and many variants, too, some with much better hair who can play Bach like Glenn Gould. A far less savory thought: there could be a configuration, Aguirre said, “where the Nazis won the war.”
Given infinity’s potential for troublemaking, it’s small wonder the ancient Greeks abhorred the very notion of it.
“They viewed it with suspicion and hostility,” said A. W. Moore, a professor of philosophy at Oxford University and the author of The Infinite (1990). The Greeks wildly favored tidy rational numbers that, by definition, can be defined as a ratio, or fraction—the way 0.75 equals ¾ and you’re done with it—over patternless infinitums like the square root of 2.
On Pythagoras’s Table of Opposites, “the finite” was listed along with masculinity and other good things in life, while “the infinite” topped the column of bad traits like femininity. “They saw it as a cosmic fight,” Moore said, “with the finite constantly having to subjugate the infinite.”
Aristotle helped put an end to the rampant infiniphobia by drawing a distinction between what he called “actual” infinity, something that would exist all at once at a given moment—which he declared an impossibility—and “potential” infinity, which would unfold over time and which he deemed perfectly intelligible. As a result, Moore said, “Aristotle believed in finite space and infinite time,” and his ideas held sway for the next 2,000 years.
Newton and Leibniz began monkeying with notions of infinity when they invented calculus, which solves tricky problems of planetary motions and accelerating bodies by essentially breaking down curved orbits and changing velocities into infinite series of tiny straight lines and tiny uniform motions. “It turns out to be an incredibly powerful tool if you think of the world as being infinitely divisible,” Strogatz said.
In the late nineteenth century, the great German mathematician Georg Cantor took on infinity not as a means to an end but as a subject worthy of rigorous study in itself. He demonstrated that there are many kinds of infinite sets, and some infinities are bigger than others. Hard as it may be to swallow, the set of all the possible decimal numbers between 1 and 2, being unlistable, turns out to be a bigger infinity than the set of all whole numbers from 1 to forever, which in principle can be listed.
In fact, many of Cantor’s contemporaries didn’t swallow, dismissing him as “a scientific charlatan,” “laughable,” and “wrong.” Cantor died depressed and impoverished, but today his set theory is a flourishing branch of mathematics relevant to the study of large, chaotic systems like the weather, the economy, and human stupidity.
With his majestic theory of relativity, Einstein knitted together time and space, quashing old Aristotelian distinctions between actual and potential infinity and ushering in the contemporary era of infinity-seeking. Another advance came in the 1980s, when Alan Guth introduced the
idea of cosmic inflation, a kind of vacuum energy that vastly expanded the size of the universe soon after its fiery birth.
New theories suggest that such inflation may not have been a one-shot event but rather part of a runaway process called eternal inflation, an infinite ballooning and bubbling outward of this and possibly other universes.
Relativity and inflation theory, said Aguirre, “allow us to conceptualize things that would have seemed impossible before.”
Time can be twisted, he said, “so from one point of view the universe is a finite thing that is growing into something infinite if you wait forever, but from another point of view it’s always infinite.”
Or maybe the universe is like Jorge Luis Borges’s fastidiously imagined Library of Babel, composed of interminable numbers of hexagonal galleries with polished surfaces that “feign and promise infinity.”
Or like the multiverse as envisioned in Tibetan Buddhism, “a vast system of 10^59 universes, that together are called a Buddha Field,” said Jonathan C. Gold, who studies Buddhist philosophy at Princeton.