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The air of machine precision casts doubt on what our eyes—or the eyes of referees—can process. As viewers, they argue, our instinct is to assume that all forms of assistance are equally effective, or that they do what they claim in the first place. But what we see on television is usually just a representation, or a calculated guess, based on thermal imaging, sound, or the work of cameras tracking an object’s velocity through air.

Few things are harder to study than human language. The brains of living humans can only be studied indirectly, and language, unlike vision, has no analogue in the animal world. Vision scientists can study sight in monkeys using techniques like single-neuron recording. But monkeys don’t talk. However, in an article published today in Nature, a group of researchers, including myself, detail a discovery in birdsong that may help lead to a revised understanding of an important aspect of human language development. Almost five years ago, I sent a piece of fan mail to Ofer Tchernichovski, who had just published an article showing that, in just three or four generations, songbirds raised in isolation often developed songs typical of their species. He invited me to visit his lab, a cramped space stuffed with several hundred birds residing in souped-up climate-controlled refrigerators. Dina Lipkind, at the time Tchernichovski’s post-doctoral student, explained a method she had developed for teaching zebra finches two songs. (Ordinarily, a zebra finch learns only one song in its lifetime.) She had discovered that by switching the song of a tutor bird at precisely the right moment, a juvenile bird could learn a second, new song after it had mastered the first one. Thinking about bilingualism and some puzzles I had encountered in my own lab, I suggested that Lipkind’s method could be useful in casting light on the question of how a creature—any creature—learns to put linguistic elements together.

Yawning is one of the first things we learn to do. “Learn” may not even be quite the right word. Johanna de Vries, a professor of obstetrics at Vrije University Amsterdam, has discovered that the human fetus yawns during its first trimester in the womb. And, unless we succumb to neurodegenerative disease, yawning is something we keep doing throughout our lives. “You don’t decide to yawn,” Robert Provine, a neuroscientist and the author of “Curious Behavior: Yawning, Laughing, Hiccupping, and Beyond,” told me. “You just do it. You’re playing out a biological program.” We yawn unconsciously and we yawn spontaneously. We can’t yawn on command—and we sometimes can’t stop ourselves from letting out a big yawn, even at the most inopportune times. (Case in point: Sasha Obama’s infamous yawn during her father’s 2013 Inaugural Address.) But what, precisely, are we accomplishing with all this yawning?

Is big data really all it’s cracked up to be? There is no doubt that big data is a valuable tool that has already had a critical impact in certain areas. For instance, almost every successful artificial intelligence computer program in the last 20 years, from Google’s search engine to the I.B.M. “Jeopardy!” champion Watson, has involved the substantial crunching of large bodies of data. But precisely because of its newfound popularity and growing use, we need to be levelheaded about what big data can — and can’t — do.The first thing to note is that although big data is very good at detecting correlations, especially subtle correlations that an analysis of smaller data sets might miss, it never tells us which correlations are meaningful.

Many modern language researchers agree with that premise. Not only does speaking multiple languages help us to communicate but bilingualism (or multilingualism) may actually confer distinct advantages to the developing brain. Because a bilingual child switches between languages, the theory goes, she develops enhanced executive control, or the ability to effectively manage what are called higher cognitive processes, such as problem-solving, memory, and thought. She becomes better able to inhibit some responses, promote others, and generally emerges with a more flexible and agile mind. It’s a phenomenon that researchers call the bilingual advantage.

Lately, Johnson draws for pleasure, but for three decades she had a happily hectic career as an illustrator, sometimes presenting clients with dozens of sketches a day. Her playful watercolors once adorned packages of Lotus software; for a program called Magellan, she created a ship whose masts were tethered to billowing diskettes. She made a popular postcard of two red parachutes tied together, forming a heart; several other cards were sold for years at MOMA’s gift shop. Johnson produced half a dozen covers for this magazine, including one, from 1985, that presented a sunny vision of an artist’s life: a loft cluttered with pastel canvases, each of them depicting a fragment of the skyline that is framed by a picture window. It’s as if the paintings were jigsaw pieces, and the city a puzzle being solved. Now Johnson is obsessed with making puzzles. Many times a day, she uses her grids as foundations for elaborate arrangements of letters on a page—word searches by way of Mondrian. For all the dedication that goes into her puzzles, however, they are confounding creations: very few are complete. She is assembling one of the world’s largest bodies of unfinished art.

From Amie I first heard about Yitang Zhang, a solitary, part-time calculus teacher at the University of New Hampshire who received several prizes, including a MacArthur award in September, for solving a problem that had been open for more than a hundred and fifty years. The problem that Zhang chose, in 2010, is from number theory, a branch of pure mathematics. Pure mathematics, as opposed to applied mathematics, is done with no practical purposes in mind. It is as close to art and philosophy as it is to engineering. “My result is useless for industry,” Zhang said. The British mathematician G. H. Hardy wrote in 1940 that mathematics is, of “all the arts and sciences, the most austere and the most remote.” Bertrand Russell called it a refuge from “the dreary exile of the actual world.” Hardy believed emphatically in the precise aesthetics of math. A mathematical proof, such as Zhang produced, “should resemble a simple and clear-cut constellation,” he wrote, “not a scattered cluster in the Milky Way.” Edward Frenkel, a math professor at the University of California, Berkeley, says Zhang’s proof has “a renaissance beauty,” meaning that though it is deeply complex, its outlines are easily apprehended. The pursuit of beauty in pure mathematics is a tenet. Last year, neuroscientists in Great Britain discovered that the same part of the brain that is activated by art and music was activated in the brains of mathematicians when they looked at math they regarded as beautiful.

Salzman first became interested in wine when he was a graduate student at Stanford University studying neuroscience (Ph.D.) and psychiatry (M.D.). “I was corrupted by some people who were very serious about wine,” he told me. Together, they would host wine tastings and travel to vineyards. Over time, as his interest in wine grew, he began to think about the connections between his tastings and the work he was doing on the ways in which emotion colors the way our brains process information. “We study how cognitive and emotional processes can affect perception,” he said. “And in the case of something like wine, you have the perfect example: even before you open a bottle to experience the wine itself, you already have an arbitrary visual stimulus—the bottle and the label—that comes with non-arbitrary emotional associations, good and bad.” And those emotional associations will, in turn, affect what we taste.

In one recent study, the Caltech neuroscientist Hilke Plassman found that people’s expectations of a wine’s price affected their enjoyment on a neural level: not only did they report greater subjective enjoyment but they showed increased activity in an area of the brain that has frequently been associated with the experience of pleasantness. The same goes for the color and shape of a wine’s label: some labels make us think that a wine is more valuable (and, hence, more tasty), while others don’t. Even your ability to pronounce a winery’s name can influence your appreciation of its product—the more difficult the name is to pronounce, the more you’ll like the wine.

For experts, though, the story is different. In 1990, Gregg Solomon, a Harvard psychologist who wrote “Great Expectorations: The Psychology of Expert Wine Talk,” found that amateurs can’t really distinguish different wines at all, but he also found that experts can indeed rank wines for sweetness, balance, and tannin at rates that far exceeded chance. Part of the reason isn’t just in the added experience. It’s in the ability to phrase and label that experience more precisely, a more developed sensory vocabulary that helps you to identify and remember what you experience. Indeed, when novices are trained, their discrimination ability improves.

In the nineteen-eighties, Allan Rechtschaffen and Bernard Bergmann, both, like Kleitman, sleep researchers at the University of Chicago, performed what is now considered to be one of the classic experiments in the field. It showed that rats, when totally deprived of sleep, would, after two or three weeks, drop dead. But Rechtschaffen and Bergmann could never figure out the precise cause of the rats’ deaths, and so, they wrote in a follow-up paper in 2002, even “that dramatic symptom did not tell us much about why sleep was necessary.” Rechtschaffen has observed that “if sleep doesn’t serve an absolutely vital function, it is the greatest mistake evolution ever made.”

Too often in our debates about freedom of speech, we assume that it already exists and that it is campus activists, particularly over questions of race, who threaten it. But what Princeton’s students have shown is that, before they came along, there was in fact precious little speech about figures like Wilson, and what speech there was, was mostly bland PR for tourists and prospective students. Even more important, Princeton’s students have shown us that it is precisely the kinds of actions they have taken — which are uncivil, frequently illegal and always unruly — that produce speech.

While my general approach to history is one of modulation — past imperfect, always — I’m leery of those who would say, against the students, don’t erase the past. I’m leery of these critics’ timing: if there’s any erasing going on here, it’s in the daily practices of Princeton. In those campus tours, those campus addresses, the general celebration of the man. Why haven’t we heard criticism of how the past is being erased by Princeton’s celebration of Wilson?I’m also leery of these critics’ assumptions that removing a name from a building is about erasing the past. As if once the name is gone, all conversation stops, all memory disappears.