Fortunately, as an undergrad, I did have a chemistry professor who embodied Flynn’s ideal. On every exam, amid typical chemistry questions, was something like this: “How many piano tuners are there in New York City?” Students had to estimate, just by reasoning, and try to get the right order of magnitude. The professor later explained that these were “Fermi problems,” because Enrico Fermi—who created the first nuclear reactor beneath the University of Chicago football field—constantly made back-of-the-envelope estimates to help him approach problems.* The ultimate lesson of the question was that detailed prior knowledge was less important than a way of thinking.
On the first exam, I went with gut instinct (“I have no clue, maybe ten thousand?”)—way too high. By the end of the class, I had a new tool in my conceptual Swiss Army knife, a way of using what little I did know to make a guess at what I didn’t. I knew the population of New York City; most single people in studio apartments probably don’t have pianos that get tuned, and most of my friends’ parents had one to three children, so how many households are in New York? What portion might have pianos? How often are pianos tuned? How long might it take to tune a piano? How many homes can one tuner reach in a day? How many days a year does a tuner work? None of the individual estimates has to be particularly accurate in order to get a reasonable overall answer. Remote Uzbek villagers would not perform well on Fermi problems, but neither did I before taking that class. It was easy to learn, though. Having grown up in the twentieth century, I was already wearing the spectacles, I just needed help capitalizing on them. I remember nothing about stoichiometry, but I use Fermi thinking regularly, breaking down a problem so I can leverage what little I know to start investigating what I don’t, a “similarities” problem of sorts.
Fortunately, several studies have found that a little training in broad thinking strategies, like Fermi-izing, can go a long way, and can be applied across domains. Unsurprisingly, Fermi problems were a topic in the “Calling Bullshit” course. It used a deceptive cable news report as a case study to demonstrate “how Fermi estimation can cut through bullshit like a hot knife through butter.” It gives anyone consuming numbers, from news articles to advertisements, the ability quickly to sniff out deceptive stats. That’s a pretty handy hot butter knife. I would have been a much better researcher in any domain, including Arctic plant physiology, had I learned broadly applicable reasoning tools rather than the finer details of Arctic plant physiology.
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• • •
Like chess masters and firefighters, premodern villagers relied on things being the same tomorrow as they were yesterday. They were extremely well prepared for what they had experienced before, and extremely poorly equipped for everything else. Their very thinking was highly specialized in a manner that the modern world has been telling us is increasingly obsolete. They were perfectly capable of learning from experience, but failed at learning without experience. And that is what a rapidly changing, wicked world demands—conceptual reasoning skills that can connect new ideas and work across contexts. Faced with any problem they had not directly experienced before, the remote villagers were completely lost. That is not an option for us. The more constrained and repetitive a challenge, the more likely it will be automated, while great rewards will accrue to those who can take conceptual knowledge from one problem or domain and apply it in an entirely new one.
The ability to apply knowledge broadly comes from broad training. A particular skilled group of performers in another place and time turned broad training into an art form. Their story is older, and yet a much better parable than chess prodigies for the modern age.
CHAPTER 3
When Less of the Same Is More
ANYWHERE A TRAVELER to seventeenth-century Venice turned an ear, they could hear music exploding from its traditional bounds. Even the name of the musical era, “Baroque,” is taken from a jewelers’ term to describe a pearl that was extravagantly large and unusually shaped.
Instrumental music—music that did not depend on words—underwent a complete revolution. Some of the instruments were brand-new, like the piano; others were enhanced—violins made by Antonio Stradivari would sell centuries later for millions of dollars. The modern system of major and minor keys was created. Virtuosos, the original musical celebrities, were anointed. Composers seized on their skill and wrote elaborate solos to push the boundaries of the best players’ abilities. The concerto was born—in which a virtuoso soloist plays back and forth against an orchestra—and Venetian composer Antonio Vivaldi (known as il Prete Rosso, the Red Priest, for his flame-red hair) became the form’s undisputed champion. The Four Seasons is as close to a pop hit as three-hundred-year-old music gets. (A mashup with a song from Disney’s Frozen has ninety million YouTube plays.)
Vivaldi’s creativity was facilitated by a particular group of musicians who could learn new music quickly on a staggering array of instruments. They drew emperors, kings, princes, cardinals, and countesses from across Europe to be regaled by the most innovative music of the time. They were the all-female cast known as the figlie del coro, literally, “daughters of the choir.” Leisure activities like horseback riding and field sports were scarce in the floating city, so music bore the full weight of entertainment for its citizens. The sounds of violins, flutes, horns, and voices spilled into the night from every bobbing barge and gondola. And in a time and place seething with music, the figlie dominated for a century.
“Only in Venice,” a prominent visitor wrote, “can one see these musical prodigies.” They were both ground zero of a musical revolution and an oddity. Elsewhere, their instruments were reserved for men. “They sing like angels, play the violin, the flute, the organ, the oboe, the cello, and the bassoon,” an astonished French politician remarked. “In short, no instrument is large enough to frighten them.” Others were less diplomatic. Aristocratic British writer Hester Thrale complained, “The sight of girls handling the double bass, and blowing into the bassoon did not much please me.” After all, “suitable feminine instruments” were more along the lines of the harpsichord or musical glasses.
The figlie left the king of Sweden in awe. Literary rogue Casanova marveled at the standing-room-only crowds. A dour French concert reviewer singled out a particular violinist: “She is the first of her sex to challenge the success of our great artists.” Even listeners not obviously disposed to support the arts were moved. Francesco Coli described “angelic Sirens,” who exceeded “even the most ethereal of birds” and “threw open for listeners the doors of Paradise.” Especially surprising praise, perhaps, considering that Coli was the official book censor for the Venetian Inquisition.
The best figlie became Europe-wide celebrities, like Anna Maria della Pietà. A German baron flatly declared her “the premier violinist in Europe.” The president of the parliament of Burgundy said she was “unsurpassed” even in Paris. An expense report that Vivaldi recorded in 1712 shows that he spent twenty ducats on a violin for sixteen-year-old Anna Maria, an engagement-ring-like sum for Vivaldi, who made that much in four months. Among the hundreds of concertos Vivaldi wrote for the figlie del coro are twenty-eight that survived in the “Anna Maria notebook.” Bound in leather and dyed Venetian scarlet, it bears Anna Maria’s name in gold leaf calligraphy. The concertos, written specifically to showcase her prowess, are filled with high-speed passages that require different notes to be played on multiple strings at the same time. In 1716, Anna Maria and the figlie were ordered by the Senate to intensify their musical work in an effort to bring God’s favor to the Venetian armies as they battled the Ottoman Empire on the island of Corfu. (In that siege, the Venetian violin, and a well-timed storm, proved mightier than the Turkish cannon.)