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Confirmation bias shows up most blatantly in our current political divide, where each side seems unable to allow that the other side is right about anything.

The whole idea of cognitive biases and faulty heuristics—the shortcuts and rules of thumb by which we make judgments and predictions—was more or less invented in the 1970s by Amos Tversky and Daniel Kahneman

versky died in 1996. Kahneman won the 2002 Nobel Prize in Economics for the work the two men did together, which he summarized in his 2011 best seller, Thinking, Fast and Slow. Another best seller, last year’s The Undoing Project, by Michael Lewis, tells the story of the sometimes contentious collaboration between Tversky and Kahneman

Another key figure in the field is the University of Chicago economist Richard Thaler. One of the biases he’s most linked with is the endowment effect, which leads us to place an irrationally high value on our possessions.

In an experiment conducted by Thaler, Kahneman, and Jack L. Knetsch, half the participants were given a mug and then asked how much they would sell it for. The average answer was $5.78. The rest of the group said they would spend, on average, $2.21 for the same mug. This flew in the face of classic economic theory, which says that at a given time and among a certain population, an item has a market value that does not depend on whether one owns it or not. Thaler won the 2017 Nobel Prize in Economics.

“The question that is most often asked about cognitive illusions is whether they can be overcome. The message … is not encouraging.”

that’s not so easy in the real world, when we’re dealing with people and situations rather than lines. “Unfortunately, this sensible procedure is least likely to be applied when it is needed most,” Kahneman writes. “We would all like to have a warning bell that rings loudly whenever we are about to make a serious error, but no such bell is available.”

At least with the optical illusion, our slow-thinking, analytic mind—what Kahneman calls System 2—will recognize a Müller-Lyer situation and convince itself not to trust the fast-twitch System 1’s perception

Kahneman and others draw an analogy based on an understanding of the Müller-Lyer illusion, two parallel lines with arrows at each end. One line’s arrows point in; the other line’s arrows point out. Because of the direction of the arrows, the latter line appears shorter than the former, but in fact the two lines are the same length.

Because biases appear to be so hardwired and inalterable, most of the attention paid to countering them hasn’t dealt with the problematic thoughts, judgments, or predictions themselves

Is it really impossible, however, to shed or significantly mitigate one’s biases? Some studies have tentatively answered that question in the affirmative.

what if the person undergoing the de-biasing strategies was highly motivated and self-selected? In other words, what if it was me?

Over an apple pastry and tea with milk, he told me, “Temperament has a lot to do with my position. You won’t find anyone more pessimistic than I am.”

I met with Kahneman

“I see the picture as unequal lines,” he said. “The goal is not to trust what I think I see. To understand that I shouldn’t believe my lying eyes.” That’s doable with the optical illusion, he said, but extremely difficult with real-world cognitive biases.

In this context, his pessimism relates, first, to the impossibility of effecting any changes to System 1—the quick-thinking part of our brain and the one that makes mistaken judgments tantamount to the Müller-Lyer line illusion

he most effective check against them, as Kahneman says, is from the outside: Others can perceive our errors more readily than we can.

“slow-thinking organizations,” as he puts it, can institute policies that include the monitoring of individual decisions and predictions. They can also require procedures such as checklists and “premortems,”

A premortem attempts to counter optimism bias by requiring team members to imagine that a project has gone very, very badly and write a sentence or two describing how that happened. Conducting this exercise, it turns out, helps people think ahead.

“My position is that none of these things have any effect on System 1,” Kahneman said. “You can’t improve intuition.

Perhaps, with very long-term training, lots of talk, and exposure to behavioral economics, what you can do is cue reasoning, so you can engage System 2 to follow rules. Unfortunately, the world doesn’t provide cues. And for most people, in the heat of argument the rules go out the window.

Kahneman describes an even earlier Nisbett article that showed subjects’ disinclination to believe statistical and other general evidence, basing their judgments instead on individual examples and vivid anecdotes. (This bias is known as base-rate neglect.)

over the years, Nisbett had come to emphasize in his research and thinking the possibility of training people to overcome or avoid a number of pitfalls, including base-rate neglect, fundamental attribution error, and the sunk-cost fallacy.

Nisbett’s second-favorite example is that economists, who have absorbed the lessons of the sunk-cost fallacy, routinely walk out of bad movies and leave bad restaurant meals uneaten.

When Nisbett asks the same question of students who have completed the statistics course, about 70 percent give the right answer. He believes this result shows, pace Kahneman, that the law of large numbers can be absorbed into System 2—and maybe into System 1 as well, even when there are minimal cues.

about half give the right answer: the law of large numbers, which holds that outlier results are much more frequent when the sample size (at bats, in this case) is small. Over the course of the season, as the number of at bats increases, regression to the mean is inevitabl

When Nisbett has to give an example of his approach, he usually brings up the baseball-phenom survey. This involved telephoning University of Michigan students on the pretense of conducting a poll about sports, and asking them why there are always several Major League batters with .450 batting averages early in a season, yet no player has ever finished a season with an average that high.

we’ve tested Michigan students over four years, and they show a huge increase in ability to solve problems. Graduate students in psychology also show a huge gain.”

, “I know from my own research on teaching people how to reason statistically that just a few examples in two or three domains are sufficient to improve people’s reasoning for an indefinitely large number of events.”

isbett suggested another factor: “You and Amos specialized in hard problems for which you were drawn to the wrong answer. I began to study easy problems, which you guys would never get wrong but untutored people routinely do … Then you can look at the effects of instruction on such easy problems, which turn out to be huge.”

Nisbett suggested that I take “Mindware: Critical Thinking for the Information Age,” an online Coursera course in which he goes over what he considers the most effective de-biasing skills and concepts. Then, to see how much I had learned, I would take a survey he gives to Michigan undergraduates. So I did.

he course consists of eight lessons by Nisbett—who comes across on-screen as the authoritative but approachable psych professor we all would like to have had—interspersed with some graphics and quizzes. I recommend it. He explains the availability heuristic this way: “People are surprised that suicides outnumber homicides, and drownings outnumber deaths by fire. People always think crime is increasing” even if it’s not.

When I finished the course, Nisbett sent me the survey he and colleagues administer to Michigan undergrads

It contains a few dozen problems meant to measure the subjects’ resistance to cognitive biases

I got it right. Indeed, when I emailed my completed test, Nisbett replied, “My guess is that very few if any UM seniors did as well as you. I’m sure at least some psych students, at least after 2 years in school, did as well. But note that you came fairly close to a perfect score.”

Nevertheless, I did not feel that reading Mindware and taking the Coursera course had necessarily rid me of my biases

For his part, Nisbett insisted that the results were meaningful. “If you’re doing better in a testing context,” he told me, “you’ll jolly well be doing better in the real world.”

The New York–based NeuroLeadership Institute offers organizations and individuals a variety of training sessions, webinars, and conferences that promise, among other things, to use brain science to teach participants to counter bias. This year’s two-day summit will be held in New York next month; for $2,845, you could learn, for example, “why are our brains so bad at thinking about the future, and how do we do it better?”

Philip E. Tetlock, a professor at the University of Pennsylvania’s Wharton School, and his wife and research partner, Barbara Mellers, have for years been studying what they call “superforecasters”: people who manage to sidestep cognitive biases and predict future events with far more accuracy than the pundits

One of the most important ingredients is what Tetlock calls “the outside view.” The inside view is a product of fundamental attribution error, base-rate neglect, and other biases that are constantly cajoling us into resting our judgments and predictions on good or vivid stories instead of on data and statistics

In 2006, seeking to prevent another mistake of that magnitude, the U.S. government created the Intelligence Advanced Research Projects Activity (iarpa), an agency designed to use cutting-edge research and technology to improve intelligence-gathering and analysis. In 2011, iarpa initiated a program, Sirius, to fund the development of “serious” video games that could combat or mitigate what were deemed to be the six most damaging biases: confirmation bias, fundamental attribution error, the bias blind spot (the feeling that one is less biased than the average person), the anchoring effect, the representativeness heuristic, and projection bias (the assumption that everybody else’s thinking is the same as one’s own).

most promising are a handful of video games. Their genesis was in the Iraq War

Together with collaborators who included staff from Creative Technologies, a company specializing in games and other simulations, and Leidos, a defense, intelligence, and health research company that does a lot of government work, Morewedge devised Missing. Some subjects played the game, which takes about three hours to complete, while others watched a video about cognitive bias. All were tested on bias-mitigation skills before the training, immediately afterward, and then finally after eight to 12 weeks had passed.

“The literature on training suggests books and classes are fine entertainment but largely ineffectual. But the game has very large effects. It surprised everyone.”

he said he saw the results as supporting the research and insights of Richard Nisbett. “Nisbett’s work was largely written off by the field, the assumption being that training can’t reduce bias,

even the positive results reminded me of something Daniel Kahneman had told me. “Pencil-and-paper doesn’t convince me,” he said. “A test can be given even a couple of years later. But the test cues the test-taker. It reminds him what it’s all about.”

Morewedge told me that some tentative real-world scenarios along the lines of Missing have shown “promising results,” but that it’s too soon to talk about them.

In the future, I will monitor my thoughts and reactions as best I can

“It’s going to be publicly accessible to the people you date, the people you work for. It’s fast becoming mainstream.”

Audi would begin offering promotions to Facebook users based on their Klout score. Last year, Virgin America used the company to offer highly rated influencers in Toronto free round-trip flights to San Francisco or Los Angeles.

If you have a Facebook, Twitter or LinkedIn account, you are already being judged — or will be soon. Companies with names like Klout, PeerIndex and Twitter Grader are in the process of scoring millions, eventually billions, of people on their level of influence — or in the lingo, rating “influencers.” Yet the companies are not simply looking at the number of followers or friends you’ve amassed. Rather, they are beginning to measure influence in more nuanced ways, and posting their judgments — in the form of a score — online.

focus your digital presence on one or two areas of interest. Don’t be a generalist. Most importantly: be passionate, knowledgeable and trustworthy.

As for influence in the offline world — it doesn’t count.

Klout “lacks sentiment analysis” — so a user who generates a lot of digital chatter might receive a high score even though what’s being said about the user is negative.

we are moving closer to creating “social media caste systems,” where people with high scores get preferential treatment by retailers, prospective employers, even prospective dates.

History: from 18.5 percent to 10.7 percent

But the deeper explanation resides not in something that has happened to it, but in what it has done to itself. English has become less and less coherent as a discipline and, worse, has come near exhaustion as a scholarly pursuit.

The twin focus, then, was on the philological nature of the enterprise and the canon of great works to be studied in their historical evolution.

Studying English taught us how to write and think better, and to make articulate many of the inchoate impulses and confusions of our post-adolescent minds. We began to see, as we had not before, how such books could shape and refine our thinking. We began to understand why generations of people coming before us had kept them in libraries and bookstores and in classes such as ours. There was, we got to know, a tradition, a historical culture, that had been assembled around these books. Shakespeare had indeed made a difference—to people before us, now to us, and forever to the language of English-speaking people.

today there are stunning changes in the student population: there are more and more gifted and enterprising students coming from immigrant backgrounds, students with only slender connections to Western culture and to the assumption that the “great books” of England and the United States should enjoy a fixed centrality in the world. What was once the heart of the matter now seems provincial. Why throw yourself into a study of something not emblematic of the world but representative of a special national interest? As the campus reflects the cultural, racial, and religious complexities of the world around it, reading British and American literature looks more and more marginal. From a global perspective, the books look smaller.

With the cost of a college degree surging upward during the last quarter century—tuition itself increasing far beyond any measure of inflation—and with consequent growth in loan debt after graduation, parents have become anxious about the relative earning power of a humanities degree. Their college-age children doubtless share such anxiety. When college costs were lower, anxiety could be kept at bay. (Berkeley in the early ’60s cost me about $100 a year, about $700 in today’s dollars.)

Economists, chemists, biologists, psychologists, computer scientists, and almost everyone in the medical sciences win sponsored research, grants, and federal dollars. By and large, humanists don’t, and so they find themselves as direct employees of the institution, consuming money in salaries, pensions, and operating needs—not external money but institutional money.

These, then, are some of the external causes of the decline of English: the rise of public education; the relative youth and instability (despite its apparent mature solidity) of English as a discipline; the impact of money; and the pressures upon departments within the modern university to attract financial resources rather than simply use them up.

several of my colleagues around the country have called for a return to the aesthetic wellsprings of literature, the rock-solid fact, often neglected, that it can indeed amuse, delight, and educate. They urge the teaching of English, or French, or Russian literature, and the like, in terms of the intrinsic value of the works themselves, in all their range and multiplicity, as well-crafted and appealing artifacts of human wisdom. Second, we should redefine our own standards for granting tenure, placing more emphasis on the classroom and less on published research, and we should prepare to contest our decisions with administrators whose science-based model is not an appropriate means of evaluation.

“It may be that what has happened to the profession is not the consequence of social or philosophical changes, but simply the consequence of a tank now empty.” His homely metaphor pointed to the absence of genuinely new frontiers of knowledge and understanding for English professors to explore.

In this country and in England, the study of English literature began in the latter part of the 19th century as an exercise in the scientific pursuit of philological research, and those who taught it subscribed to the notion that literature was best understood as a product of language.

no one has come forward in years to assert that the study of English (or comparative literature or similar undertakings in other languages) is coherent, does have self-limiting boundaries, and can be described as this but not that.

to teach English today is to do, intellectually, what one pleases. No sense of duty remains toward works of English or American literature; amateur sociology or anthropology or philosophy or comic books or studies of trauma among soldiers or survivors of the Holocaust will do. You need not even believe that works of literature have intelligible meaning; you can announce that they bear no relationship at all to the world beyond the text.

With everything on the table, and with foundational principles abandoned, everyone is free, in the classroom or in prose, to exercise intellectual laissez-faire in the largest possible way—I won’t interfere with what you do and am happy to see that you will return the favor

Consider the English department at Harvard University. It has now agreed to remove its survey of English literature for undergraduates, replacing it and much else with four new “affinity groups”

there would be no one book, or family of books, that every English major at Harvard would have read by the time he or she graduates. The direction to which Harvard would lead its students in this “clean slate” or “trickle down” experiment is to suspend literary history, thrusting into the hands of undergraduates the job of cobbling together intellectual coherence for themselves

Those who once strove to give order to the curriculum will have learned, from Harvard, that terms like core knowledge and foundational experience only trigger acrimony, turf protection, and faculty mutinies. No one has the stomach anymore to refight the Western culture wars. Let the students find their own way to knowledge.

In English, the average number of years spent earning a doctoral degree is almost 11. After passing that milestone, only half of new Ph.D.’s find teaching jobs, the number of new positions having declined over the last year by more than 20 percent; many of those jobs are part-time or come with no possibility of tenure. News like that, moving through student networks, can be matched against, at least until recently, the reputed earning power of recent graduates of business schools, law schools, and medical schools. The comparison is akin to what young people growing up in Rust Belt cities are forced to see: the work isn’t here anymore; our technology is obsolete.

unlike other members of the university community, they might well have been plying their trade without proper credentials: “Whereas economists or physicists, geologists or climatologists, physicians or lawyers must master a body of knowledge before they can even think of being licensed to practice,” she said, “we literary scholars, it is tacitly assumed, have no definable expertise.”

English departments need not refight the Western culture wars. But they need to fight their own book wars. They must agree on which texts to teach and argue out the choices and the principles of making them if they are to claim the respect due a department of study.

They can teach their students to write well, to use rhetoric. They should place their courses in composition and rhetoric at the forefront of their activities. They should announce that the teaching of composition is a skill their instructors have mastered and that students majoring in English will be certified, upon graduation, as possessing rigorously tested competence in prose expression.

The study of literature will then take on the profile now held, with moderate dignity, by the study of the classics, Greek and Latin.

But we can, we must, do better. At stake are the books themselves and what they can mean to the young. Yes, it is just a literary tradition. That’s all. But without such traditions, civil societies have no compass to guide them.

Essentially, the “generalized friendship paradox” applies to all interpersonal networks, regardless of whether they’re set in real life or online.

Whenever we interact with other people, we glimpse lives far more glamorous than our own.

you know now, if you did not before, that the police departments of your country have been endowed with the authority to destroy your body. It does not matter if the destruction is the result of an unfortunate overreaction. It does not matter if it originates in a misunderstanding. It does not matter if the destruction springs from a foolish policy

But a society that protects some people through a safety net of schools, government-backed home loans, and ancestral wealth but can only protect you with the club of criminal justice has either failed at enforcing its good intentions or has succeeded at something much darker.

It is hard to face this. But all our phrasing—race relations, racial chasm, racial justice, racial profiling, white privilege, even white supremacy—serves to obscure that racism is a visceral experience, that it dislodges brains, blocks airways, rips muscle, extracts organs, cracks bones, breaks teeth

ou must never look away from this. You must always remember that the sociology, the history, the economics, the graphs, the charts, the regressions all land, with great violence, upon the body.

And should one live in such a body? What should be our aim beyond meager survival of constant, generational, ongoing battery and assault? I have asked this question all my life.

The question is unanswerable, which is not to say futile. The greatest reward of this constant interrogation, of confrontation with the brutality of my country, is that it has freed me from ghosts and myths.

I was afraid long before you, and in this I was unoriginal. When I was your age the only people I knew were black, and all of them were powerfully, adamantly, dangerously afraid. It was always right in front of me. The fear was there in the extravagant boys of my West Baltimore neighborhood

The fear lived on in their practiced bop, their slouching denim, their big T- shirts, the calculated angle of their baseball caps, a catalog of behaviors and garments enlisted to inspire the belief that these boys were in firm possession of everything they desired.

To be black in the Baltimore of my youth was to be naked before the elements of the world, before all the guns, fists, knives, crack, rape, and disease. The law did not protect us. And now, in your time, the law has become an excuse for stopping and frisking you, which is to say, for furthering the assault on your body

I remember being amazed that death could so easily rise up from the nothing of a boyish afternoon, billow up like fog. I knew that West Baltimore, where I lived; that the north side of Philadelphia, where my cousins lived; that the South Side of Chicago, where friends of my father lived, comprised a world apart. Somewhere out there beyond the firmament, past the asteroid belt, there were other worlds where children did not regularly fear for their bodies

here will surely always be people with straight hair and blue eyes, as there have been for all history. But some of these straight-haired people with blue eyes have been “black,” and this points to the great difference between their world and ours. We did not choose our fences. They were imposed on us by Virginia planters obsessed with enslaving as many Americans as possible. Now I saw that we had made something down here, in slavery, in Jim Crow, in ghettoes. At The Mecca I saw how we had taken their one-drop rule and flipped it. They made us into a race. We made ourselves into a people.

I came to understand that my country was a galaxy, and this galaxy stretched from the pandemonium of West Baltimore to the happy hunting grounds of Mr. Belvedere. I obsessed over the distance between that other sector of space and my own. I knew that my portion of the American galaxy, where bodies were enslaved by a tenacious gravity, was black and that the other, liberated portion was not. I knew that some inscrutable energy preserved the breach. I felt, but did not yet understand, the relation between that other world and me. And I felt in this a cosmic injustice, a profound cruelty, which infused an abiding, irrepressible desire to unshackle my body and achieve the velocity of escape.

Before I could escape, I had to survive, and this could only mean a clash with the streets, by which I mean not just physical blocks, nor simply the people packed into them, but the array of lethal puzzles and strange perils which seem to rise up from the asphalt itself. The streets transform every ordinary day into a series of trick questions, and every incorrect answer risks a beat-down, a shooting, or a pregnancy. No one survives unscathed

When I was your age, fully one-third of my brain was concerned with who I was walking to school with, our precise number, the manner of our walk, the number of times I smiled, who or what I smiled at, who offered a pound and who did not—all of which is to say that I practiced the culture of the streets, a culture concerned chiefly with securing the body.

Why were only our heroes nonviolent? Back then all I could do was measure these freedom-lovers by what I knew. Which is to say, I measured them against children pulling out in the 7-Eleven parking lot, against parents wielding extension cords, and the threatening intonations of armed black gangs saying, “Yeah, nigger, what’s up now?” I judged them against the country I knew, which had acquired the land through murder and tamed it under slavery, against the country whose armies fanned out across the world to extend their dominion. The world, the real one, was civilization secured and ruled by savage means. How could the schools valorize men and women whose values society actively scorned? How could they send us out into the streets of Baltimore, knowing all that they were, and then speak of nonviolence?

the beauty of the black body was never celebrated in movies, in television, or in the textbooks I’d seen as a child. Everyone of any import, from Jesus to George Washington, was white. This was why your grandparents banned Tarzan and the Lone Ranger and toys with white faces from the house. They were rebelling against the history books that spoke of black people only as sentimental “firsts”—first black four-star general, first black congressman, first black mayor—always presented in the bemused manner of a category of Trivial Pursuit.

erious history was the West, and the West was white. This was all distilled for me in a quote I once read, from the novelist Saul Bellow. I can’t remember where I read it, or when—only that I was already at Howard. “Who is the Tolstoy of the Zulus?,” Bellow quipped

this view of things was connected to the fear that passed through the generations, to the sense of dispossession. We were black, beyond the visible spectrum, beyond civilization. Our history was inferior because we were inferior, which is to say our bodies were inferior. And our inferior bodies could not possibly be accorded the same respect as those that built the West. Would it not be better, then, if our bodies were civilized, improved, and put to some legitimate Christian use?

now I looked back on my need for a trophy case, on the desire to live by the standards of Saul Bellow, and I felt that this need was not an escape but fear again—fear that “they,” the alleged authors and heirs of the universe, were right. And this fear ran so deep that we accepted their standards of civilization and humanity.

“Tolstoy is the Tolstoy of the Zulus,” wrote Wiley. “Unless you find a profit in fencing off universal properties of mankind into exclusive tribal ownership.” And there it was. I had accepted Bellow’s premise. In fact, Bellow was no closer to Tolstoy than I was to Nzinga. And if I were closer it would be because I chose to be, not because of destiny written in DNA. My great error was not that I had accepted someone else’s dream but that I had accepted the fact of dreams, the need for escape, and the invention of racecraft.

still and all I knew that we were something, that we were a tribe—on one hand, invented, and on the other, no less real. The reality was out there on the Yard, on the first warm day of spring when it seemed that every sector, borough, affiliation, county, and corner of the broad diaspora had sent a delegate to the great world party

I could see now that that world was more than a photonegative of that of the people who believe they are white. “White America” is a syndicate arrayed to protect its exclusive power to dominate and control our bodies. Sometimes this power is direct (lynching), and sometimes it is insidious (redlining). But however it appears, the power of domination and exclusion is central to the belief in being white, and without it, “white people” would cease to exist for want of reasons

There is nothing uniquely evil in these destroyers or even in this moment. The destroyers are merely men enforcing the whims of our country, correctly interpreting its heritage and legacy. This legacy aspires to the shackling of black bodies

Think of all the embraces, all the private jokes, customs, greetings, names, dreams, all the shared knowledge and capacity of a black family injected into that vessel of flesh and bone. And think of how that vessel was taken, shattered on the concrete, and all its holy contents, all that had gone into each of them, was sent flowing back to the earth. It is terrible to truly see our particular beauty, Samori, because then you see the scope of the loss. But you must push even further. You must see that this loss is mandated by the history of your country, by the Dream of living white.

I don’t know if you remember how the film we saw at the Petersburg Battlefield ended as though the fall of the Confederacy were the onset of a tragedy, not jubilee. I doubt you remember the man on our tour dressed in the gray wool of the Confederacy, or how every visitor seemed most interested in flanking maneuvers, hardtack, smoothbore rifles, grapeshot, and ironclads, but virtually no one was interested in what all of this engineering, invention, and design had been marshaled to achieve. You were only 10 years old. But even then I knew that I must trouble you, and this meant taking you into rooms where people would insult your intelligence, where thieves would try to enlist you in your own robbery and disguise their burning and looting as Christian charity. But robbery is what this is, what it always was.

American reunion was built on a comfortable narrative that made enslavement into benevolence, white knights of body snatchers, and the mass slaughter of the war into a kind of sport in which one could conclude that both sides conducted their affairs with courage, honor, and élan. This lie of the Civil War is the lie of innocence, is the Dream.

I, like every kid I knew, loved The Dukes of Hazzard. But I would have done well to think more about why two outlaws, driving a car named the General Lee, must necessarily be portrayed as “just some good ole boys, never meanin’ no harm”—a mantra for the Dreamers if there ever was one. But what one “means” is neither important nor relevant. It is not necessary that you believe that the officer who choked Eric Garner set out that day to destroy a body. All you need to understand is that the officer carries with him the power of the American state and the weight of an American legacy, and they necessitate that of the bodies destroyed every year, some wild and disproportionate number of them will be black.

Here is what I would like for you to know: In America, it is traditional to destroy the black body—it is heritage. Enslavement was not merely the antiseptic borrowing of labor—it is not so easy to get a human being to commit their body against its own elemental interest. And so enslavement must be casual wrath and random manglings, the gashing of heads and brains blown out over the river as the body seeks to escape. It must be rape so regular as to be industrial. There is no uplifting way to say this.

It had to be blood. It had to be the thrashing of kitchen hands for the crime of churning butter at a leisurely clip. It had to be some woman “chear’d ... with thirty lashes a Saturday last and as many more a Tuesday again.” It could only be the employment of carriage whips, tongs, iron pokers, handsaws, stones, paperweights, or whatever might be handy to break the black body, the black family, the black community, the black nation. The bodies were pulverized into stock and marked with insurance. And the bodies were an aspiration, lucrative as Indian land, a veranda, a beautiful wife, or a summer home in the mountains. For the men who needed to believe themselves white, the bodies were the key to a social club, and the right to break the bodies was the mark of civilization.

“The two great divisions of society are not the rich and poor, but white and black,” said the great South Carolina senator John C. Calhoun. “And all the former, the poor as well as the rich, belong to the upper class, and are respected and treated as equals.” And there it is—the right to break the black body as the meaning of their sacred equality. And that right has always given them meaning, has always meant that there was someone down in the valley because a mountain is not a mountain if there is nothing below.

There is no them without you, and without the right to break you they must necessarily fall from the mountain, lose their divinity, and tumble out of the Dream. And then they would have to determine how to build their suburbs on something other than human bones, how to angle their jails toward something other than a human stockyard, how to erect a democracy independent of cannibalism. I would like to tell you that such a day approaches when the people who believe themselves to be white renounce this demon religion and begin to think of themselves as human. But I can see no real promise of such a day. We are captured, brother, surrounded by the majoritarian bandits of America. And this has happened here, in our only home, and the terrible truth is that we cannot will ourselves to an escape on our own.

I think now of the old rule that held that should a boy be set upon in someone else’s chancy hood, his friends must stand with him, and they must all take their beating together. I now know that within this edict lay the key to all living. None of us were promised to end the fight on our feet, fists raised to the sky. We could not control our enemies’ number, strength, or weaponry. Sometimes you just caught a bad one. But whether you fought or ran, you did it together, because that is the part that was in our control. What we must never do is willingly hand over our own bodies or the bodies of our friends. That was the wisdom: We knew we did not lay down the direction of the street, but despite that, we could—and must—fashion the way of our walk. And that is the deeper meaning of your name—that the struggle, in and of itself, has meaning.

I have raised you to respect every human being as singular, and you must extend that same respect into the past. Slavery is not an indefinable mass of flesh. It is a particular, specific enslaved woman, whose mind is as active as your own, whose range of feeling is as vast as your own; who prefers the way the light falls in one particular spot in the woods, who enjoys fishing where the water eddies in a nearby stream, who loves her mother in her own complicated way, thinks her sister talks too loud, has a favorite cousin, a favorite season, who excels at dressmaking and knows, inside herself, that she is as intelligent and capable as anyone. “Slavery” is this same woman born in a world that loudly proclaims its love of freedom and inscribes this love in its essential texts, a world in which these same professors hold this woman a slave, hold her mother a slave, her father a slave, her daughter a slave, and when this woman peers back into the generations all she sees is the enslaved. She can hope for more. She can imagine some future for her grandchildren. But when she dies, the world—which is really the only world she can ever know—ends. For this woman, enslavement is not a parable. It is damnation. It is the never-ending night. And the length of that night is most of our history. Never forget that we were enslaved in this country longer than we have been free. Never forget that for 250 years black people were born into chains—whole generations followed by more generations who knew nothing but chains.

You must resist the common urge toward the comforting narrative of divine law, toward fairy tales that imply some irrepressible justice. The enslaved were not bricks in your road, and their lives were not chapters in your redemptive history. They were people turned to fuel for the American machine. Enslavement was not destined to end, and it is wrong to claim our present circumstance—no matter how improved—as the redemption for the lives of people who never asked for the posthumous, untouchable glory of dying for their children. Our triumphs can never redeem this. Perhaps our triumphs are not even the point. Perhaps struggle is all we have

I am not a cynic. I love you, and I love the world, and I love it more with every new inch I discover. But you are a black boy, and you must be responsible for your body in a way that other boys cannot know. Indeed, you must be responsible for the worst actions of other black bodies, which, somehow, will always be assigned to you. And you must be responsible for the bodies of the powerful—the policeman who cracks you with a nightstick will quickly find his excuse in your furtive movements. You have to make your peace with the chaos, but you cannot lie.

“I could have you arrested,” he said. Which is to say: “One of your son’s earliest memories will be watching the men who sodomized Abner Louima and choked Anthony Baez cuff, club, tase, and break you.” I had forgotten the rules, an error as dangerous on the Upper West Side of Manhattan as on the West Side of Baltimore. One must be without error out here. Walk in single file. Work quietly. Pack an extra No. 2 pencil. Make no mistakes.

the price of error is higher for you than it is for your countrymen, and so that America might justify itself, the story of a black body’s destruction must always begin with his or her error, real or imagined—with Eric Garner’s anger, with Trayvon Martin’s mythical words (“You are gonna die tonight”), with Sean Bell’s mistake of running with the wrong crowd, with me standing too close to the small-eyed boy pulling out.

You are called to struggle, not because it assures you victory but because it assures you an honorable and sane life

I am sorry that I cannot save you—but not that sorry. Part of me thinks that your very vulnerability brings you closer to the meaning of life, just as for others, the quest to believe oneself white divides them from it. The fact is that despite their dreams, their lives are also not inviolable. When their own vulnerability becomes real—when the police decide that tactics intended for the ghetto should enjoy wider usage, when their armed society shoots down their children, when nature sends hurricanes against their cities—they are shocked by the rages of logic and the natural world in a way that those of us who were born and bred to understand cause and effect can never be.

I would not have you live like them. You have been cast into a race in which the wind is always at your face and the hounds are always at your heels. And to varying degrees this is true of all life. The difference is that you do not have the privilege of living in ignorance of this essential fact.

I never wanted you to be twice as good as them, so much as I have always wanted you to attack every day of your brief bright life determined to struggle. The people who must believe they are white can never be your measuring stick. I would not have you descend into your own dream. I would have you be a conscious citizen of this terrible and beautiful world.

human beings evolved big brains not to understand the world, but to understand each other.

In a 2014 paper, the Australian psychology professor Arthur E. Poropat cites research showing that both conscientiousness (which he defines as a tendency to be “diligent, dutiful and hardworking”) and openness (characterized by qualities like creativity and curiosity) are more highly correlated with student performance than intelligence is.

Some already have. “Grit” — which the psychology professor Angela Duckworth of the University of Pennsylvania and her co-authors define in a 2007 paper as “perseverance and passion for long-term goals,” and which they see as overlapping in some ways with conscientiousness — has become part of the curriculum at a number of schools.

We know that these noncognitive traits can be taught. We also know that it is necessary for success. You look at anybody who has had long-term sustainable success, and every one of them exhibited at some point this grit, this tenacity to keep going.”

One result of the class, which includes lessons on people, like Malala Yousafzai, who have overcome significant challenges: Students “are now willing to do the hard thing instead of always running to what was easy.” Ms. Benedix also coordinates a districtwide grit initiative — since it began, she says, the number of high schoolers taking advanced-placement classes has increased significantly.

pi’s infinite randomness can also be seen more as richness. What amazes, then, is the possibility that such profusion can come from a rule so simple: circumference divided by diameter. This is characteristic of mathematics, whereby elementary formulas can give rise to surprisingly varied phenomena. For instance, the humble quadratic can be used to model everything from the growth of bacterial populations to the manifestation of chaos. Pi makes us wonder if our universe’s complexity emerges from similarly simple mathematical building blocks.

Pi also opens a window into a more uncharted universe, the one consisting of transcendental numbers, which exclude such common irrationals as square and cube roots. Pi is one of the few transcendentals we ever encounter. One may suspect that such numbers would be quite rare, but actually, the opposite is true. Out of the totality of numbers, almost all are transcendental. Pi reveals how limited human knowledge is, how there exist teeming realms we might never explore.

But pi, on cue, reminds us that it is an abstraction, like all else in mathematics. The perfect flat circle is impossible to realize in practice. An area calculated using pi will never exactly match the same area measured physically. This is to be expected whenever we approximate reality using the idealizations of math.

Dichotomy. Suppose a car is moving from to A to B . Let’s measure the distance between A and B by a scale according to which A is at point 0 and B is at point 1. Then before the car gets to point 1, it has to get half way there, point 1/2; and once it has got there, it has to get to a point half way between 1/2 and 1, 3/4; and so on… In other words, it has to get to every one of the infinite number of points 1/2, 3/4, 7/8

But you can’t do an infinite number of things in a finite time. So the car never get to point B.

At any rate, even after two and a half thousand years of trying to come up with an explanation of what is wrong with the argument in the Liar Paradox, there is still no consensus on the matter.

Interestingly, virtually everything else that Aristotle ever defended has been overthrown — or at least seriously challenged. The principle of noncontradiction is, it would seem, the last bastion!

A common suggestion of what it is for B to follow logically from A is that you can’t have A without having B. Given the principle of noncontradiction, if A is a contradiction, you can’t have it. And if you can’t have A, you certainly can’t have A and B. That is, everything follows from a contradiction.

. In the 17th century, even Galileo writes about why, in a game with three dice, the number 10 should come up more than the number 9. It’s an observation that one would only be able to detect after thousands of rolls, but the reason behind it involves how many combinations of numbers can add up to each different option.

All these changes in dice come about, says Eerkens, “as different astronomers are coming up with new ideas about the world, and mathematicians are starting to understand numbers and probability.” Which came first: Did people begin to intuitively understand what true chance felt like, and adjusted dice accordingly, or did it trickle out from what would eventually become known as the scientific community?

And it does make you wonder: Would you know that fair dice should fall equally on each side, or that in a three-dice game, it’s better to bet on 10 than nine, if someone hadn’t told you?

Our Connections With Others Make Life More Meaningful

Supporting Others Is Linked to a Longer Life

05 of 05 It's Possible to Become More Empathetic

These come, as far as I can tell, in two broad types, corresponding to the two fundamental complaints that people voice about their undergraduate experience

The first complaint is that college did not prepare them for the real world: that the whole exercise—papers, busywork, pointless requirements; siloed disciplines and abstract theory—seemed remote from anything that they actually might want to do with their lives. 

Above all, they are student-centered. Participants are enabled (and expected) to direct their education by constructing bespoke curricula out of the resources the program gives them access to. In a word, these endeavors emphasize “engagement.”

A student will identify a problem (a human need, an injustice, an instance of underrepresentation), then devise and implement a response (a physical system, a community-facing program, an art project). 

Professors were often preoccupied, with little patience for mentorship, the open-ended office-hours exploration. Classes, even in fields like philosophy, felt lifeless, impersonal, like engineering but with words instead of numbers. Worst of all were their fellow undergraduates, those climbers and careerists. “It’s hard to build your soul,” as one of my students once put it to me, “when everyone around you is trying to sell theirs.”

Not everything in the world is a problem, and to see the world as a series of problems is to limit the potential of both world and self. What problem does a song address? What problem will reading Voltaire help you solve, in any predictable way? The “problem” approach—the “engagement” approach, the save-the-world approach—leaves out, finally, what I’d call learning.

that is the second complaint that graduates tend to express: that they finished college without the feeling that they had learned anything, in this essential sense.

That there is a treasure out there—call it the Great Books or just great books, the wisdom of the ages or the best that has been thought and said—that its purpose is to activate the treasure inside them, that they had come to one of these splendid institutions (whose architecture speaks of culture, whose age gives earnest of depth) to be initiated into it, but that they had been denied, deprived. For unclear reasons, cheated.

I had students like this at Columbia and Yale. There were never a lot of them, and to judge from what’s been happening to humanities enrollments, there are fewer and fewer. (From 2013 to 2022, the number of people graduating with bachelors degrees in English fell by 36%. As a share of all degrees, it fell by 42%, to less than 1 in 60.)

They would tell me—these pilgrims, these intellectuals in embryo, these kindled souls—how hard they were finding it to get the kind of education they had come to college for.

what bothers me about this educational approach—the “problem” approach, the “STEAM” (STEM + arts) approach—is what it leaves out. It leaves out the humanities. It leaves out books. It leaves out literature and philosophy, history and art history and the history of religion. It leaves out any mode of inquiry—reflection, speculation, conversation with the past—that cannot be turned to immediate practical ends

The Catherine Project sees itself as being in the business of creating “communities of learning”; its principles include “conversation and hospitality, “simplicity [and] transparency.” Classes (called tutorials, in keeping with the practice at St. John’s) are free (BISR’s cost $335), are capped at four to six students (at BISR, the limit is 23), run for two hours a week for twelve weeks, and skew towards the canon: the Greeks and Romans, Pascal and Kierkegaard, Dante and Cervantes (the project also hosts a large number of reading groups, which address a wider range of texts). If BISR aspires to create a fairer market for academic labor—instructors keep the lion’s share of fees—the Catherine Project functions as a gift economy (though plans are to begin to offer tutors modest honoraria).

As Russell Jacoby has noted, the migration of intellectuals into universities in the decades after World War II, which he documented in The Last Intellectuals, has more recently reversed itself. The rise, or re-rise, of little magazines (Dissent, Commentary, Partisan Review then; n+1, The New Inquiry, The Point, The Drift, et al. now) is part of the same story. 

a fourth factor. If there are students who despair at the condition of the humanities on campus, there are professors who do so as well. Many of her teachers, Hitz told me, have regular ladder appointments: “We draw academics—who attend our groups as well as leading them—because the life of the mind is dying or dead in conventional institutions.” Undergraduate teaching, she added, “is a particularly hard pull,” and the Catherine Project offers faculty the chance to teach people “who actually want to learn.

I’d add, who can. Nine years ago, Stephen Greenblatt wrote: “Even the highly gifted students in my Shakespeare classes at Harvard are less likely to be touched by the subtle magic of his words than I was so many years ago or than my students were in the 1980s in Berkeley. … The problem is that their engagement with language … often seems surprisingly shallow or tepid.” By now, of course, the picture is far worse.

The response to the announcement of our pilot programs confirmed for me the existence of a large, unmet desire for text-based exploration, touching on the deepest questions, outside the confines of higher education

Applicants ranged from graduating college seniors to people in their 70s. They included teachers, artists, scientists, and doctoral students from across the disciplines; a submarine officer, a rabbinical student, an accountant, and a venture capitalist; retirees, parents of small children, and twentysomethings at the crossroads. Forms came in from India, Jordan, Brazil, and nine other foreign countries. The applicants were, as a group, tremendously impressive. If it had been possible, we would have taken many more than fifteen.

When asked why they wanted to participate, a number of them spoke about the pathologies of formal education. “We have a really damaged relationship to learning,” said one. “It should be fun, not scary”—as in, you feel that you’re supposed to know the answer, which as a student, as she noted, makes no sense

“We need opportunities for reading and exploration that lie outside the credentialing system of the modern university,” he went on, because there’s so much in the latter that cuts against “the slow way that kind of learning unfolds.”

“How one might choose to live.” For many of our applicants—and this, of course, is what the program is about, what the humanities are about—learning has, or ought to have, an existential weight.

I detected a desire to be free of forces and agendas: the university’s agenda of “relevance,” the professoriate’s agenda of political mobilization, the market’s agenda of productivity, the internet’s agenda of surveillance and addiction. In short, the whole capitalistic algorithmic ideological hairball of coerced homogeneity

The desire is to not be recruited, to not be instrumentalized, to remain (or become) an individual, to resist regression toward the mean, or meme.

That is why it’s crucial that the Matthew Strother Center has no goal—and this is true of the Catherine Project and other off-campus humanities programs, as well—beyond the pursuit of learning for its own sake.

This is freedom. When education isn’t pointed in particular directions, its possibilities are endless

Irsadi Aksun, a professor of electrical engineering at Koc, said, “There are two different groups of Turkish students who go abroad.” The first, he said, is “very competitive — some have taken Advanced Placement courses in high school. Some have followed the International Baccalaureate.” “This group is quite small,” he went on, adding that most came from a handful of Turkish private schools that offer English instruction in many subjects. Such schools are increasingly popular among wealthy families in Istanbul and Ankara.

But we’d like to get more American students to come here.” In the 2010-11 academic year, the most recent year for which Open Door statistics are available, the United States sent slightly more than 2,000 students to Turkey — a jump of 34 percent from the previous year, and more than double the 2006-7 number. “I can definitely see Turkey as the next frontier in studying abroad,” Mr. Pierce said.

“It used to take me an hour to memorize 20 words. Now I can learn, like, 40 new words in 20 minutes.”

“I don’t know if it makes you smarter. But when you get to each new level on the math and reading tasks, it definitely builds up your self-confidence.”

. “What you care about is not an intelligence test score, but whether your ability to do an important task has really improved. That’s a chain of evidence that would be really great to have. I haven’t seen it.”

Still,a new and growing body of scientific evidence indicates that cognitive training can be effective, including that offered by commercial services.

He looked at 340 middle-school students who spent two hours a week for a semester using LearningRx exercises in their schools’ computer labs and an equal number of students who received no such training. Those who played the online games, Dr. Hill found, not only improved significantly on measures of cognitive abilities compared to their peers, but also on Virginia’s annual Standards of Learning exam.

I’ve had some kids who not only reported that they had very big changes in the classroom, but when we bring them back in the laboratory to do neuropsychological testing, we also see great changes. They show increases that would be highly unlikely to happen just by chance.”

where crosswords and Sudoku are intended to be a diversion, the games here give that same kind of reward, only they’re designed to improve your brain, your memory, your problem-solving skills.”

More than 40 games are offered by Lumosity. One, the N-back, is based on a task developed decades ago by psychologists. Created to test working memory, the N-back challenges users to keep track of a continuously updated list and remember which item appeared “n” times ago.

The largest single faith group is Catholics, who make up about 22 percent of the population. Their numbers have held steady, mostly because an influx of immigrants

more than one-third of those ages 18 to 22 are religiously unaffiliated.

The “Nones,” as they are called, now make up the nation’s second-largest religious grouping

“The significant majority of the religiously unaffiliated tend to be left-leaning, tend to support the Democratic Party, support gay marriage and environmental causes,”

it is not clear that Americans are necessarily moving toward the European model. The Pew report found that even among Americans who claimed no religion, few qualified as purely secular. Two-thirds say they still believe in God, and one-fifth say they pray every day. Only 12 percent of the religiously unaffiliated group said they were atheists and 17 percent agnostic.

it makes no sense to compare the federal budget to a family budget, which is what the Consumer Price Index is based on. One needs to use a broader index, like the gross domestic product deflator, which measures price changes throughout the entire economy.

For large numbers, the percentage of the gross domestic product is both the easiest to find and best to use.

Since the “burden” of the debt basically falls on the entire economy, the debt-to-G.D.P. ratio is generally considered the best measure of that burden. It also facilitates international comparisons without having to worry about exchange-rate adjustments.

international price comparisons can be especially tricky because current market exchange rates may not accurately reflect relative values or standards of living. Economists generally prefer to use something called “purchasing power parity,” but such data is not always easy to come by

There is much more to say on this topic. I recommend an essay on the Measuring Worth website that discusses different measures of value over time and how they materially affect our perceptions. There are also new statistical measures coming online that may provide even better data, like the Billion Prices Project from M.I.T., which gathers price data in real time directly from store price scanners.

This is an area where trial and error is the best strategy. The important thing is to make an effort to provide proper context where it appears necessary and not to simply ignore the problem.

“It depends on what you mean by artificial intelligence.”

Computers are flexible enough to model the strange evolved convolutions of our thought, and yet responsive only to precise instructions. So if the endeavor succeeds, it will be a double victory: we will finally come to know the exact mechanics of our selves—and we’ll have made intelligent machines.

Ever since he was about 14, when he found out that his youngest sister, Molly, couldn’t understand language, because she “had something deeply wrong with her brain” (her neurological condition probably dated from birth, and was never diagnosed), he had been quietly obsessed by the relation of mind to matter.

How could consciousness be physical? How could a few pounds of gray gelatin give rise to our very thoughts and selves?

Consciousness, Hofstadter wanted to say, emerged via just the same kind of “level-crossing feedback loop.”

In 1931, the Austrian-born logician Kurt Gödel had famously shown how a mathematical system could make statements not just about numbers but about the system itself.

But then AI changed, and Hofstadter didn’t change with it, and for that he all but disappeared.

By the early 1980s, the pressure was great enough that AI, which had begun as an endeavor to answer yes to Alan Turing’s famous question, “Can machines think?,” started to mature—or mutate, depending on your point of view—into a subfield of software engineering, driven by applications.

Take Deep Blue, the IBM supercomputer that bested the chess grandmaster Garry Kasparov. Deep Blue won by brute force.

Hofstadter wanted to ask: Why conquer a task if there’s no insight to be had from the victory? “Okay,” he says, “Deep Blue plays very good chess—so what? Does that tell you something about how we play chess? No. Does it tell you about how Kasparov envisions, understands a chessboard?”

AI started working when it ditched humans as a model, because it ditched them. That’s the thrust of the analogy: Airplanes don’t flap their wings; why should computers think?

It’s a compelling point. But it loses some bite when you consider what we want: a Google that knows, in the way a human would know, what you really mean when you search for something

Cognition is recognition,” he likes to say. He describes “seeing as” as the essential cognitive act: you see some lines a

How do you make a search engine that understands if you don’t know how you understand?

s “an A,” you see a hunk of wood as “a table,” you see a meeting as “an emperor-has-no-clothes situation” and a friend’s pouting as “sour grapes”

That’s what it means to understand. But how does understanding work?

analogy is “the fuel and fire of thinking,” the bread and butter of our daily mental lives.

there’s an analogy, a mental leap so stunningly complex that it’s a computational miracle: somehow your brain is able to strip any remark of the irrelevant surface details and extract its gist, its “skeletal essence,” and retrieve, from your own repertoire of ideas and experiences, the story or remark that best relates.

in Hofstadter’s telling, the story goes like this: when everybody else in AI started building products, he and his team, as his friend, the philosopher Daniel Dennett, wrote, “patiently, systematically, brilliantly,” way out of the light of day, chipped away at the real problem. “Very few people are interested in how human intelligence works,”

For more than 30 years, Hofstadter has worked as a professor at Indiana University at Bloomington

The quick unconscious chaos of a mind can be slowed down on the computer, or rewound, paused, even edited

project out of IBM called Candide. The idea behind Candide, a machine-translation system, was to start by admitting that the rules-based approach requires too deep an understanding of how language is produced; how semantics, syntax, and morphology work; and how words commingle in sentences and combine into paragraphs—to say nothing of understanding the ideas for which those words are merely conduits.

, Hofstadter directs the Fluid Analogies Research Group, affectionately known as FARG.

Parts of a program can be selectively isolated to see how it functions without them; parameters can be changed to see how performance improves or degrades. When the computer surprises you—whether by being especially creative or especially dim-witted—you can see exactly why.

When you read Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought, which describes in detail this architecture and the logic and mechanics of the programs that use it, you wonder whether maybe Hofstadter got famous for the wrong book.

ut very few people, even admirers of GEB, know about the book or the programs it describes. And maybe that’s because FARG’s programs are almost ostentatiously impractical. Because they operate in tiny, seemingly childish “microdomains.” Because there is no task they perform better than a human.

“The entire effort of artificial intelligence is essentially a fight against computers’ rigidity.”

“Nobody is a very reliable guide concerning activities in their mind that are, by definition, subconscious,” he once wrote. “This is what makes vast collections of errors so important. In an isolated error, the mechanisms involved yield only slight traces of themselves; however, in a large collection, vast numbers of such slight traces exist, collectively adding up to strong evidence for (and against) particular mechanisms.

So IBM threw that approach out the window. What the developers did instead was brilliant, but so straightforward,

The technique is called “machine learning.” The goal is to make a device that takes an English sentence as input and spits out a French sentence

What you do is feed the machine English sentences whose French translations you already know. (Candide, for example, used 2.2 million pairs of sentences, mostly from the bilingual proceedings of Canadian parliamentary debates.)

By repeating this process with millions of pairs of sentences, you will gradually calibrate your machine, to the point where you’ll be able to enter a sentence whose translation you don’t know and get a reasonable resul

Google Translate team can be made up of people who don’t speak most of the languages their application translates. “It’s a bang-for-your-buck argument,” Estelle says. “You probably want to hire more engineers instead” of native speakers.

But the need to serve 1 billion customers has a way of forcing the company to trade understanding for expediency. You don’t have to push Google Translate very far to see the compromises its developers have made for coverage, and speed, and ease of engineering. Although Google Translate captures, in its way, the products of human intelligence, it isn’t intelligent itself.

“Did we sit down when we built Watson and try to model human cognition?” Dave Ferrucci, who led the Watson team at IBM, pauses for emphasis. “Absolutely not. We just tried to create a machine that could win at Jeopardy.”

For Ferrucci, the definition of intelligence is simple: it’s what a program can do. Deep Blue was intelligent because it could beat Garry Kasparov at chess. Watson was intelligent because it could beat Ken Jennings at Jeopardy.

“There’s a limited number of things you can do as an individual, and I think when you dedicate your life to something, you’ve got to ask yourself the question: To what end? And I think at some point I asked myself that question, and what it came out to was, I’m fascinated by how the human mind works, it would be fantastic to understand cognition, I love to read books on it, I love to get a grip on it”—he called Hofstadter’s work inspiring—“but where am I going to go with it? Really what I want to do is build computer systems that do something.

Peter Norvig, one of Google’s directors of research, echoes Ferrucci almost exactly. “I thought he was tackling a really hard problem,” he told me about Hofstadter’s work. “And I guess I wanted to do an easier problem.”

Of course, the folly of being above the fray is that you’re also not a part of it

As our machines get faster and ingest more data, we allow ourselves to be dumber. Instead of wrestling with our hardest problems in earnest, we can just plug in billions of examples of them.

Hofstadter hasn’t been to an artificial-intelligence conference in 30 years. “There’s no communication between me and these people,” he says of his AI peers. “None. Zero. I don’t want to talk to colleagues that I find very, very intransigent and hard to convince of anything

Everything from plate tectonics to evolution—all those ideas, someone had to fight for them, because people didn’t agree with those ideas.

Academia is not an environment where you just sit in your bath and have ideas and expect everyone to run around getting excited. It’s possible that in 50 years’ time we’ll say, ‘We really should have listened more to Doug Hofstadter.’ But it’s incumbent on every scientist to at least think about what is needed to get people to understand the ideas.”

Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, “When will I use this?”

In schools, as I’ve heard several teachers lament, the opportunity to immerse students in interesting mathematical ideas is usually jettisoned to make more time for testing and arithmetic drills.

Keith Devlin argues in his book “The Math Gene,” human beings are wired for mathematics. At some level, perhaps we all crave it.

So what math ideas can be appreciated without calculation or formulas? One candidate that I’ve found intrigues people is the origin of numbers. Think of it as a magic trick: harnessing emptiness to create the number zero, then demonstrating how from any whole number, one can create its successor.