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Why is fact-checking so popular? The traditional American view of democracy has a ready answer: The people know that, to be responsible voters, they must know the facts.

There’s a complex myth of democracy packed into that little story. There’s a basic premise: Democracy can work because we humans are rational animals. We are built to be fact-checkers; we all have the capacity to separate true facts from lies. And once we have true facts, we know how to analyze them logically to come to reasonable conclusions. If that weren’t true, democracy would be a foolish experiment, indeed.

But, the myth goes on to say, a capacity is useless unless it is developed through training. That’s why democracy demands universal access to education

Only educated people can be responsible citizens because only the educated have actualized their potential for fact-checking and rational thinking.

When the final book is written on this campaign, one-sided deception will still have played a central role. As it stands, the very notions of fact and truth are employed in American politics as much to distort as to reveal. And until the voting public demands something else, not just from the politicians they oppose but also from the ones they support, there is little reason to suspect that will change.

they must have honesty from their leaders and transparency from their government.

Hence, the need for fact-checkers at every step on the campaign trail. It’s only logical.Except that there’s no evidence all the fact-checking has any measurable impact on the voters’ choices.

ideas hardly mattered any more than facts in the outcome of the first debate. Romney won on style points alone.

The “theater state” is a performance art. Every candidate is judged, above all, on their performance. Good theatrical performers know how to create satisfying illusory images of truth. It’s one of their highest skills. Mitt Romney proved that in the first debate.

The myth of democracy says that citizens must educated enough to know which policies are best for their community. But good citizens must also bring their rationality into the polling booth.

The fact-checkers, too, are seasoned performers skilled in the art of creating satisfying illusory images of truth.

Above all, they create the illusion that American democracy is alive and well because the public is apparently being informed of the facts and the veracity of each candidate is apparently being carefully evaluated and widely reported. Fact-checking, then, is the ritual enactment of our myth of democracy. As long as the myth keeps getting acted out, we can trust that it is alive and well.

Fifty Republican national-security experts signed an open letter declaring Trump a danger to the republic; several staffers quit the Republican National Committee rather than work to elect Trump. Allegiances have been sundered, and professional trajectories thrown into confusion.

Several Republicans I know, finding the campaign intolerable, have rediscovered old hobbies.

Although he was originally drawn to the party for its emphasis on economic freedom and self-reliance, he now believes that a substantial portion of Republicans were never motivated by those ideas. Rather than a conservative party that happens to incorporate cultural grievances, today’s GOP is, in his view, a vehicle for the racial resentment, nationalism, and nostalgia of older white voters.

Trump is the “logical end point” of the GOP’s long history of racialized politics.

(An early conclusion: while we were late to understand how angry white voters were, a perhaps even more serious lapse was in failing to recognize how many disaffected Democrats there were who would stay home rather than support their party’s flawed candidate.)

Stories that would have killed any other politician—truly worrisome revelations about everything from the federal taxes Trump dodged to the charitable donations he lied about, the women he insulted and allegedly assaulted, and the mob ties that have long dogged him—did not stop Trump from thriving in this election year

the Oxford Dictionaries announced that “post-truth” had been chosen as the 2016 word of the year, defining it as a condition “in which objective facts are less influential in shaping public opinion than appeals to emotion and personal belief.”

Meantime, Trump personally blacklisted news organizations like Politico and The Washington Post when they published articles he didn’t like during the campaign, has openly mused about rolling back press freedoms enshrined by the U.S. Supreme Court, and has now named Stephen Bannon, until recently the executive chairman of Breitbart—a right-wing fringe website with a penchant for conspiracy theories and anti-Semitic tropes—to serve as one of his top White House advisers.

none of this has any modern precedent. And what makes it unique has nothing to do with the outcome of the election. This time, the victor was a right-wing demagogue; next time, it may be a left-wing populist who learns the lessons of Trump’s win.

This is no mere academic argument. The election of 2016 showed us that Americans are increasingly choosing to live in a cloud of like-minded spin, surrounded by the partisan political hackery and fake news that poisons their Facebook feeds.

To help us understand it all, there were choices, but not that many: three TV networks that mattered, ABC, CBS, and NBC; two papers for serious journalism, The New York Times and The Washington Post; and two giant-circulation weekly newsmagazines, Time and Newsweek. That, plus whatever was your local daily newspaper, pretty much constituted the news.

Fake news is thriving In the final three months of the presidential campaign, the 20 top-performing fake election news stories generated more engagement on Facebook than the top stories from major news outlets such as The New York Times.

Eventually, I came to think of the major media outlets of that era as something very similar to the big suburban shopping malls we flocked to in the age of shoulder pads and supply-side economics: We could choose among Kmart and Macy’s and Saks Fifth Avenue as our budgets and tastes allowed, but in the end the media were all essentially department stores, selling us sports and stock tables and foreign news alongside our politics, whether we wanted them or not. It may not have been a monopoly, but it was something pretty close.

This was still journalism in the scarcity era, and it affected everything from what stories we wrote to how fast we could produce them. Presidents could launch global thermonuclear war with the Russians in a matter of minutes, but news from the American hinterlands often took weeks to reach their sleepy capital. Even information within that capital was virtually unobtainable without a major investment of time and effort. Want to know how much a campaign was raising and spending from the new special-interest PACs that had proliferated? Prepare to spend a day holed up at the Federal Election Commission’s headquarters down on E Street across from the hulking concrete FBI building, and be sure to bring a bunch of quarters for the copy machine.

I am writing this in the immediate, shocking aftermath of a 2016 presidential election in which the Pew Research Center found that a higher percentage of Americans got their information about the campaign from late-night TV comedy shows than from a national newspaper. Don Graham sold the Post three years ago and though its online audience has been skyrocketing with new investments from Amazon.com founder Jeff Bezos, it will never be what it was in the ‘80s. That same Pew survey reported that a mere 2 percent of Americans today turned to such newspapers as the “most helpful” guides to the presidential campaign.

In 2013, Mark Leibovich wrote a bestselling book called This Town about the party-hopping, lobbyist-enabling nexus between Washington journalists and the political world they cover. A key character was Politico’s Mike Allen, whose morning email newsletter “Playbook” had become a Washington ritual, offering all the news and tidbits a power player might want to read before breakfast—and Politico’s most successful ad franchise to boot. In many ways, even that world of just a few years ago now seems quaint: the notion that anyone could be a single, once-a-day town crier in This Town (or any other) has been utterly exploded by the move to Twitter, Facebook, and all the rest. We are living, as Mark put it to me recently, “in a 24-hour scrolling version of what ‘Playbook’ was.”

Whether it was Walter Cronkite or The New York Times, they preached journalistic “objectivity” and spoke with authority when they pronounced on the day’s developments—but not always with the depth and expertise that real competition or deep specialization might have provided. They were great—but they were generalists.

I remained convinced that reporting would hold its value, especially as our other advantages—like access to information and the expensive means to distribute it—dwindled. It was all well and good to root for your political team, but when it mattered to your business (or the country, for that matter), I reasoned, you wouldn’t want cheerleading but real reporting about real facts. Besides, the new tools might be coming at us with dizzying speed—remember when that radical new video app Meerkat was going to change absolutely everything about how we cover elections?—but we would still need reporters to find a way inside Washington’s closed doors and back rooms, to figure out what was happening when the cameras weren’t rolling.

And if the world was suffering from information overload—well, so much the better for us editors; we would be all the more needed to figure out what to listen to amid the noise.

Trump turned out to be more correct than we editors were: the more relevant point of the Access Hollywood tape was not about the censure Trump would now face but the political reality that he, like Bill Clinton, could survive this—or perhaps any scandal. Yes, we were wrong about the Access Hollywood tape, and so much else.

These days, Politico has a newsroom of 200-odd journalists, a glossy award-winning magazine, dozens of daily email newsletters, and 16 subscription policy verticals. It’s a major player in coverage not only of Capitol Hill but many other key parts of the capital, and some months during this election year we had well over 30 million unique visitors to our website, a far cry from the controlled congressional circulation of 35,000 that I remember Roll Call touting in our long-ago sales materials.

, we journalists were still able to cover the public theater of politics while spending more of our time, resources, and mental energy on really original reporting, on digging up stories you couldn’t read anywhere else. Between Trump’s long and checkered business past, his habit of serial lying, his voluminous and contradictory tweets, and his revision of even his own biography, there was lots to work with. No one can say that Trump was elected without the press telling us all about his checkered past.

politics was NEVER more choose-your-own-adventure than in 2016, when entire news ecosystems for partisans existed wholly outside the reach of those who at least aim for truth

Pew found that nearly 50 percent of self-described conservatives now rely on a single news source, Fox, for political information they trust.

As for the liberals, they trust only that they should never watch Fox, and have MSNBC and Media Matters and the remnants of the big boys to confirm their biases.

And then there are the conspiracy-peddling Breitbarts and the overtly fake-news outlets of this overwhelming new world; untethered from even the pretense of fact-based reporting, their version of the campaign got more traffic on Facebook in the race’s final weeks than all the traditional news outlets combined.

When we assigned a team of reporters at Politico during the primary season to listen to every single word of Trump’s speeches, we found that he offered a lie, half-truth, or outright exaggeration approximately once every five minutes—for an entire week. And it didn’t hinder him in the least from winning the Republican presidential nomination.

when we repeated the exercise this fall, in the midst of the general election campaign, Trump had progressed to fibs of various magnitudes just about once every three minutes!

By the time Trump in September issued his half-hearted disavowal of the Obama “birther” whopper he had done so much to create and perpetuate, one national survey found that only 1 in 4 Republicans was sure that Obama was born in the U.S., and various polls found that somewhere between a quarter and a half of Republicans believed he’s Muslim. So not only did Trump think he was entitled to his own facts, so did his supporters. It didn’t stop them at all from voting for him.

in part, it’s not just because they disagree with the facts as reporters have presented them but because there’s so damn many reporters, and from such a wide array of outlets, that it’s often impossible to evaluate their standards and practices, biases and preconceptions. Even we journalists are increasingly overwhelmed.

So much terrific reporting and writing and digging over the years and … Trump? What happened to consequences? Reporting that matters? Sunlight, they used to tell us, was the best disinfectant for what ails our politics.

2016 suggests a different outcome: We’ve achieved a lot more transparency in today’s Washington—without the accountability that was supposed to come with it.

The 2004 campaign was the year of the “Web log,” or blog, when mainstream reporters and campaigns officially began losing any control they may have had over political new

Marco Rubio’s campaign marched into the election season ready to fight the usual news-cycle-by-news-cycle skirmishes. It was surprised to learn that, lo and behold, “There was no news cycle — everything was one big fire hose,” Alex Conant, a senior Rubio strategist, told me. “News was constantly breaking and at the end of the day hardly anything mattered. Things would happen; 24 hours later, everyone was talking about something else.”

Snapchat represents a change to something else: the longevity of news, how durably it keeps in our brain cells and our servers.

Snapchat is recording the here and the now, playing for today. Tomorrow will bring something new that renders today obsolete. It’s a digital Tibetan sand painting made in the image of the millennial mind.

Snapchat executives say they set up the app this way because this is what their tens of millions of younger users want; it’s how they live.

They can’t possibly have enough bandwidth to process all the incoming information and still dwell on what already was, can they?

Experienced strategists and their candidates, who could always work through their election plans methodically — promoting their candidacies one foot in front of the other, adjusting here and there for the unexpected — suddenly found that they couldn’t operate the way they always did.

The question this year has been whether 2016 will be the “Snapchat election,

Then there was Jeb Bush, expecting to press ahead by presenting what he saw as leading-edge policy proposals that would set off a prolonged back-and-forth. When Mr. Bush rolled out a fairly sweeping plan to upend the college loan system, the poor guy thought this was going to become a big thing.

It drew only modest coverage and was quickly buried by the latest bit from Donald Trump.

In this “hit refresh” political culture, damaging news does not have to stick around for long, either. The next development, good or bad, replaces it almost immediately.

Mr. Miller pointed to a recent episode in which Mr. Trump said a protester at a rally had “ties to ISIS,” after that protester charged the stage. No such ties existed. “He says ‘ISIS is attacking me’; this was debunked in eight minutes by Twitter,” Mr. Miller said. “Cable talked about it for three hours and it went away.”

“Hillary Clinton said that she was under sniper fire in Bosnia” — she wasn’t — “and that has stuck with her for 20 years,”

Mr. Trump has mastered this era of short attention spans in politics by realizing that if you’re the one regularly feeding the stream, you can forever move past your latest trouble, and hasten the mass amnesia.

It was with this in mind that The Washington Post ran an editorial late last week reminding its readers of some of Mr. Trump’s more outlandish statements and policy positions

The Post urged its readers to “remember” more than two dozen items from Mr. Trump’s record, including that he promised “to round up 11 million undocumented immigrants and deport them,” and “lied about President Obama’s birth certificate.”

as the media habits of the young drive everybody else’s, I’m reminded of that old saw about those who forget history. Now, what was I saying?

the lesson in Virginia, as the Washington Post reporter Paul Farhi wrote at the time, was that nothing exceeds the value of shoe-leather reporting, given that politics is an essentially human endeavor and therefore can defy prediction and reason.

Yet when Mr. Trump showed up on the scene, it was as if that had never happened.

It was another thing to declare, as The Huffington Post did, that coverage of his campaign could be relegated to the entertainment section (and to add a disclaimer to articles about him) and still another to give Mr. Trump a “2 percent” chance at the nomination despite strong polls in his favor, as FiveThirtyEight did six months before the first votes were cast.

Predictions that far out can be viewed as being all in good fun. But in Mr. Trump’s case, they also arguably sapped the journalistic will to scour his record as aggressively as those of his supposedly more serious rivals. In other words, predictions can have consequences.

The problems weren’t at all only due to the reliance on data. Don’t forget those moments that were supposed to have augured Mr. Trump’s collapse: the certainty that once the race narrowed to two or three candidates, Mr. Trump would be through, and what at one point became the likelihood of a contested convention.

That’s all the more reason in the coming months to be as sharply focused on the data we don’t have as we are on the data we do have (and maybe watching out for making any big predictions about the fall based on the polling of today). But a good place to start would be to get a good night’s sleep, and then talk to some voters.

But Obama’s early opposition to the Iraq war gave him a political firewall that protected him throughout that primary campaign, while Romney has no such policy safe harbor to safeguard him from an intramural backlash.

Romney and Obama share a lack of natural affinity for this key group of swing voters, but it is Romney who needs to figure out some way of addressing this shortcoming if he wants to make it to the White House. It’s Romney’s misfortune that the voters’ prioritization of economic issues, his own privileged upbringing and his lack of connection with his party’s base on other core issues put him in a much more precarious position than candidate Obama ever reached.

By the time the 2008 general election rolled around, Obama had bolstered his outreach to these voters by recruiting the blue-collar avatar Joe Biden as his running mate. Should Romney win the Republican nomination this year, his advisers will almost certainly be tempted by the working-class credentials that a proletarian like New Jersey Governor Chris Christie or Florida Senator Marco Rubio would bring to the ticket.

Of more immediate concern to Team Romney should be how their candidate can overcome his habit of economic tone-deafness before Rick Santorum steals away enough working-class and culturally conservative voters to throw the Republican primary into complete and utter turmoil.

The curious thing about Romney’s verbal missteps is how limited they are to this very specific area of public policy. He is usually quite articulate when talking about foreign affairs and national security. Despite his complicated history on social and cultural matters like health care and abortion, his explanations are usually both coherent and comprehensible, even to those who oppose his positions. It’s only when he begins talking about economic issues – his biographical strength – that he seems to get clumsy.

The second possibility would be for him to outline a series of proposals specifically targeted at the needs of working-class and poor Americans, not only to control the damage from his gaffes but also to underscore the conservative premise that a right-leaning agenda will create opportunities for those on the lower rungs of the economic ladder. But while that approach might help Romney in a broader philosophical conversation, it’s unlikely to offer him much protection from the attacks and ridicule that his unforced errors will continue to bring him.

The question is why Romney hasn’t embraced a third alternative – admitting the obvious and then explaining why he gets so tongue-tied when the conversation turns to money. Romney’s upbringing and religious faith suggest a sense of obligation to the less fortunate and an unspoken understanding that it isn’t appropriate to call attention to one’s financial success.It wouldn’t be that hard for him to say something like:I was taught not to brag and boast and think I’m better than other people because of the successes I’ve had, so occasionally I’m going to say things that sound awkward. It’s because I’d rather talk about what it takes to get America back to work.

the human tendency to see what we want to see, unconscious bias is inevitable. Without any ill intent, a scientist may be nudged toward interpreting the data so it supports the hypothesis, even if just barely.

He found that a large proportion of the conclusions were undermined or contradicted by later studies.

He and his colleagues could not replicate 47 of 53 landmark papers about cancer

esearchers deeply believed that their findings were true. But that is the problem. The more passionate scientists are about their work, the more susceptible they are to bias

“The slightest shift in their microenvironment can alter the results — something a newcomer might not spot. It is common for even a seasoned scientist to struggle with cell lines and culture conditions, and unknowingly introduce changes that will make it seem that a study cannot be reproduced.

The good news is that timing is relatively controllable, especially in the long run.

If you’re just starting out in your career, it won’t be easy to find a job that gives you a flexible schedule. The best approach is a strategy of moving toward more flexibility over the course of your life.

There isn’t one formula for finding schedule flexibility. Just make sure all of your important decisions are consistent with an end game of a more flexible schedule. Otherwise you are shutting yourself off from the most accessible lever for happiness — timing.

if you knew that pasta is far lower on the glycemic index than a white potato, you would make a far healthier choice that requires no willpower at all. All it took was knowledge.

The most important thing to know about staying fit is this: If it takes willpower, you’re doing it wrong. Anything that requires willpower is unsustainable in the long run.

studies show that using willpower in one area diminishes how much willpower you have in reserve for other areas. You need to get willpower out of the system

My observation is that you can usually replace willpower with knowledge.

the trick for avoiding unhealthy foods is to make sure you always have access to healthy options that you enjoy eating. Your knowledge of this trick, assuming you use it, makes willpower far less necessary.

don’t give up too much income potential just to get a flexible schedule. There’s no point in having a flexible schedule if you can’t afford to do anything.

the fittest people have systems, not goals, unless they are training for something specific. A sensible system is to continuously learn more about the science of diet and the methods for making healthy food taste great. With that system, weight management will feel automatic. Goals aren’t needed.

Did you know that sleepiness causes you to feel hungry?

Did you know that eating peanuts is a great way to suppress appetite?

Did you know that eating mostly protein instead of simple carbs for lunch will help you avoid the afternoon energy slump?

Cheese adds calories, but the fat content will help suppress your appetite, so you probably come out ahead. If you didn’t already know that, you might end up using willpower to avoid cheese at dinner and willpower again later that night to resist snacking. A little knowledge replaces a lot of willpower.

Did you know that exercise has only a small impact on your weight?

after I started noticing how drained and useless I felt after eating simple carbs, french fries became easy to resist.

I also learned that I can remove problem foods from my diet if I target them for extinction one at a time. It was easy to stop eating three large Snickers every day (which I was doing) when I realized I could eat anything else I wanted whenever I wanted

If you’re on a diet, you’re probably trying to avoid certain types of food, but you’re also trying to limit your portions. Instead of waging war on two fronts, try allowing yourself to eat as much as you want of anything that is healthy.

healthier food is almost self-regulating in the sense that you don’t have an insatiable desire to keep eating it the way you might with junk food. With healthy food, you tend to stop when you feel full

One of the biggest obstacles to healthy eating is the impression that healthy food generally tastes like cardboard. So consider making it a lifelong system to learn how to season and prepare healthy foods

Did you know that eating simple carbs can make you hungrier?

’m limiting my portion size. You only need to do that if you are eating the wrong foods. Eating half of your cake still keeps you addicted to cake. And portion control takes a lot of willpower. You’ll find that healthy food satisfies you sooner, so you don’t crave large portions.

No one can exercise enough to overcome a bad diet. Diet is the right button to push for losing weight, so long as you are active. People who eat right and stay active usually have no problems with weight.

I’m about to share with you the simplest and potentially most effective exercise plan in the world. Here it is: Be active every day.

When you’re active, and you don’t overdo it, you’ll find yourself in a good mood afterward. That reward becomes addictive over time.

After a few months of being moderately active every day, you’ll discover that it is harder to sit and do nothing than it is to get up and do something. That’s the frame of mind you want. You want exercise to become a habit with a reward so it evolves into a useful addiction

the intensity of your workout has a surprisingly small impact on your weight unless you’re running half-marathons every week. If your diet is right, moderate exercise is all you need.

When your body is feeling good, and you have some flexibility in your schedule, you’ll find that the petty annoyances that plague your life become nothing but background noise. And that’s a great launch pad for happiness.

As you find yourself getting healthier and happier, the people in your life will view you differently too. Healthy-looking people generally earn more money, get more offers and enjoy a better social life. All of that will help your happiness.

Keep in mind that happiness is a directional phenomenon. We feel happy when things are moving in the right direction no matter where we are at the moment.

The true work of the mathematician is not experienced until the later parts of graduate school, when the student is challenged to create knowledge in the form of a novel proof. It is common to fill page after page with an attempt, the seasons turning, only to arrive precisely where you began, empty-handed — or to realize that a subtle flaw of logic doomed the whole enterprise from its outset. The steady state of mathematical research is to be completely stuck. It is a process that Charles Fefferman of Princeton, himself a onetime math prodigy turned Fields medalist, likens to ‘‘playing chess with the devil.’’ The rules of the devil’s game are special, though: The devil is vastly superior at chess, but, Fefferman explained, you may take back as many moves as you like, and the devil may not. You play a first game, and, of course, ‘‘he crushes you.’’ So you take back moves and try something different, and he crushes you again, ‘‘in much the same way.’’ If you are sufficiently wily, you will eventually discover a move that forces the devil to shift strategy; you still lose, but — aha! — you have your first clue.

Tao has emerged as one of the field’s great bridge-­builders. At the time of his Fields Medal, he had already made discoveries with more than 30 different collaborators. Since then, he has also become a prolific math blogger with a decidedly non-­Gaussian ebullience: He celebrates the work of others, shares favorite tricks, documents his progress and delights at any corrections that follow in the comments. He has organized cooperative online efforts to work on problems. ‘‘Terry is what a great 21st-­century mathematician looks like,’’ Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison, who has collaborated with Tao, told me. He is ‘‘part of a network, always communicating, always connecting what he is doing with what other people are doing.’’

Most mathematicians tend to specialize, but Tao ranges widely, learning from others and then working with them to make discoveries. Markus Keel, a longtime collaborator and close friend, reaches to science fiction to explain Tao’s ability to rapidly digest and employ mathematical ideas: Seeing Tao in action, Keel told me, reminds him of the scene in ‘‘The Matrix’’ when Neo has martial arts downloaded into his brain and then, opening his eyes, declares, ‘‘I know kung fu.’’ The citation for Tao’s Fields Medal, awarded in 2006, is a litany of boundary hopping and notes particularly ‘‘beautiful work’’ on Horn’s conjecture, which Tao completed with a friend he had played foosball with in graduate school. It was a new area of mathematics for Tao, at a great remove from his known stamping grounds. ‘‘This is akin,’’ the citation read, ‘‘to a leading English-­language novelist suddenly producing the definitive Russian novel.’’

For their work, Tao and Green salvaged a crucial bit from an earlier proof done by others, which had been discarded as incorrect, and aimed at a different goal. Other maneuvers came from masterful proofs by Timothy Gowers of England and Endre Szemeredi of Hungary. Their work, in turn, relied on contributions from Erdos, Klaus Roth and Frank Ramsey, an Englishman who died at age 26 in 1930, and on and on, into history. Ask mathematicians about their experience of the craft, and most will talk about an intense feeling of intellectual camaraderie. ‘‘A very central part of any mathematician’s life is this sense of connection to other minds, alive today and going back to Pythagoras,’’ said Steven Strogatz, a professor of mathematics at Cornell University. ‘‘We are having this conversation with each other going over the millennia.’’

As a group, the people drawn to mathematics tend to value certainty and logic and a neatness of outcome, so this game becomes a special kind of torture. And yet this is what any ­would-be mathematician must summon the courage to face down: weeks, months, years on a problem that may or may not even be possible to unlock. You find yourself sitting in a room without doors or windows, and you can shout and carry on all you want, but no one is listening.

An effort to prove that 1 equals 0 is not likely to yield much fruit, it’s true, but the hacker’s mind-set can be extremely useful when doing math. Long ago, mathematicians invented a number that when multiplied by itself equals negative 1, an idea that seemed to break the basic rules of multiplication. It was so far outside what mathematicians were doing at the time that they called it ‘‘imaginary.’’ Yet imaginary numbers proved a powerful invention, and modern physics and engineering could not function without them.

Early encounters with math can be misleading. The subject seems to be about learning rules — how and when to apply ancient tricks to arrive at an answer. Four cookies remain in the cookie jar; the ball moves at 12.5 feet per second. Really, though, to be a mathematician is to experiment. Mathematical research is a fundamentally creative act. Lore has it that when David Hilbert, arguably the most influential mathematician of fin de siècle Europe, heard that a colleague had left to pursue fiction, he quipped: ‘‘He did not have enough imagination for mathematics.’’

Many people think that substantial progress on Navier-­Stokes may be impossible, and years ago, Tao told me, he wrote a blog post concurring with this view. Now he has some small bit of hope. The twin-prime conjecture had the same feel, a sense of breaking through the wall of intimidation that has scared off many aspirants. Outside the world of mathematics, both Navier-­Stokes and the twin-prime conjecture are described as problems. But for Tao and others in the field, they are more like opponents. Tao’s opponent has been known to taunt him, convincing him that he is overlooking the obvious, or to fight back, making quick escapes when none should be possible. Now the opponent appears to have revealed a weakness. But Tao said he has been here before, thinking he has found a way through the defenses, when in fact he was being led into an ambush. ‘‘You learn to get suspicious,’’ Tao said. ‘‘You learn to be on the lookout.’’

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.

Other expats find that their alienation – sometimes called reverse culture shock – can take a more serious turn

Ms. Okona stopped leaving the house and cut herself off from friends. Finally, her father asked her if she wanted to see a therapist. When she did, she was diagnosed with “situational depression,” or a depression caused in her case by her inability to adjust to the transition of her new life.

it’s easy for returning expats to feel isolated. “Nobody gets it. It’s like having somebody dying and there’s no funeral and you’re not supposed to talk about it. You feel guilty talking about it.”

many companies limit the amount of time employees can spend in a particular posting. “They may say you have to go home or go somewhere else. But you might say, I actually like living here,” he says.

Children, who may appear to be excited to return home and reunite with old friends, sometimes hide their identities as Third Culture Kids. Ms. Foley, who had lived for years in France with her family, says that her children were fluent in French. But when one daughter took a French class back in Canada, she spoke French with a strong Anglo accent.

Many repatriated expats find it hard to connect to friends again at home. Ms. Hattaway says that expat life draws people together: “You’re in a circle or tribe with other expats. But back home, you’re only one in a sea of people. Some of them have never left, some don’t have passports. And you look like everyone els

Tina Quick, who lives outside of Boston, says that although she’s been back in the States for 10 years, she still doesn’t have a best friend, someone she could call in an emergency.  She didn’t understand why she never heard from the other soccer parents she met after the season ended

The Rev. Ken MacHarg, who served as a pastor in six countries around the world, says that he tells people that moving overseas will “mess you up for the rest of your life. You’re constantly torn between those places, and you’re a changed person.”

Expats need to know that the toughest assignment of all might be coming home. “Send me home?” asks Ms. Pascoe. “It’s easier to go to Bangkok than to repatriate in Vancouver.”

A survey of 43 countries, published on October 30th, found that people in emerging markets are within a whisker of expressing the same level of satisfaction with their lives as people in rich countries.

While Scrooge found it easy to count his riches, happiness is harder to pin down. People are prone to what philosophers call “adaptive preferences”, meaning that they may fail to report their “true” happiness

If measuring happiness is so difficult, what else could economists look at? Amartya Sen, of Harvard University, argues that “capabilities” are the way to go. The definition of a capability is a bit fuzzy: at its simplest, a capability is something that people have reason to value. The list of potential capabilities is endless: the opportunity to live a long and healthy life, the freedom to take part in political life or to be well nourished.

Capabilities, says Mr Sen, are ends that economists should strive to maximise: income is just one of the many means by which we get there.

That begs the question of which capabilities a society should maximise. Some worry that the capability approach is deeply paternalistic

Ms Nussbaum goes so far as to recommend “ten central capabilities” that are essential for a good life. For economists, who tend to be lovers of freedom, this is controversial stuff.

But the capability approach may be less illiberal than it seems. Insisting that GDP is the true measure of economic progress is itself a value-judgment. What is more, according to Mr Sen and Ms Nussbaum, people must have the freedom to select which capabilities they ultimately pursue.

Measuring capabilities may be even more difficult than measuring GDP or happiness. There are, though, decent proxies. A country with a high life expectancy probably offers its citizens things like good health care and helps to shield them from pollution, which makes it easier for them to live a long, healthy life.

Some measures of economic success use such data. The Human Development Index (HDI), which Mr Sen helped to devise in 1990, considers not only income, but also life expectancy and schooling, as elements of development

the capability approach has spawned so many measures, each more complicated than the last, that GDP starts to look appealing again. What other single number can give a decent approximation of quality of life?

Scientists have done studies where they give people different colored candies and ask if they taste differently

Your brain is constantly filtering it through your sense of taste, touch, smell, and – most importantly – your memories.

The human eye is actually really bad at perceiving color.

Your brain has to fill in the gaps.

"When color is processed by the brain, a lot of information has to be extracted from not very much incoming information," said Mathan. "The color that we perceive doesn't correspond - at all - with the colors that are in the world."

One of her team's preliminary tasks—a sort of archeological literature review—was to pore through the written canons of Theravadin, Tibetan, and Zen Buddhism, as well as texts within Christianity, Judaism, and Sufism. "Not every text makes clear reference to a period of difficulty on the contemplative path," Britton says, "but many did." Related Story What Happens to the Brain During Spiritual Experiences?

the oscillations of spiritual life parallel the experience of learning to walk, very similar to the metaphor Saint John of the Cross uses in terms of a mother weaning a child … first you are held up by a parent and it is exhilarating and wonderful, and then they take their hands away and it is terrifying and the child feels abandoned."

while meditators can better avoid difficult experiences under the guidance of seasoned teachers, there are cases where such experiences are useful signs of progress in contemplative development. Distinguishing between the two, however, remains a challenge.

this widespread assumption—that meditation exists only for stress reduction and labor productivity, "because that's what Americans value"—narrows the scope of the scientific lens. When the time comes to develop hypotheses around the effects of meditation, the only acceptable—and fundable—research questions are the ones that promise to deliver the answers we want to hear.

"Does it promote good relationships? Does it reduce cortisol? Does it help me work harder?" asks Britton, referencing these more lucrative questions. Because studies have shown that meditation does satisfy such interests, the results, she says, are vigorously reported to the public. "But," she cautions, "what about when meditation plays a role in creating an experience that then leads to a breakup, a psychotic break, or an inability to focus at work?"

Given the juggernaut—economic and otherwise—behind the mindfulness movement, there is a lot at stake in exploring a shadow side of meditation. Upton Sinclair once observed how difficult it is to get a man to understand something when his salary depends on his not understanding it.

Among the nearly 40 dark night subjects her team has formally interviewed over the past few years, she says most were "fairly out of commission, fairly impaired for between six months [and] more than 20 years."

The Dark Night Project is young, and still very much in progress. Researchers in the field are just beginning to carefully collect and sort through the narratives of difficult meditation-related experiences. Britton has presented her findings at major Buddhist and scientific conferences, prominent retreat centers, and even to the Dalai Lama at the 24th Mind and Life Dialogue in 2012.

"There are parts of me that just want meditation to be all good. I find myself in denial sometimes, where I just want to forget all that I've learned and go back to being happy about mindfulness and promoting it, but then I get another phone call and meet someone who's in distress, and I see the devastation in their eyes, and I can't deny that this is happening. As much as I want to investigate and promote contemplative practices and contribute to the well-being of humanity through that, I feel a deeper commitment to what's actually true."

means you love nothing more than beer, working out and the feeling that you get when you rhetorically defend a marginalized community from systems of oppression!

But the season also targeted the rise of Donald J. Trump, a phenomenon who has thrived on a resentment of things p.c., just this week crowing that his plan to ban Muslims from the United States was “probably not politically correct.”

used to be so anti-continuity

acknowledging, for instance, that sometimes outrage culture has a basis in actual outrages.

assign a single child to filter every negative comment from their social media, to protect their self-esteem from all manner of “-shaming.”