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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.’’

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.

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.’’

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.’’

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.’’

Contemporary science has refined the old “fight or flight” concept — the idea that those are the two hard-wired options when in mortal danger — to the updated “freeze, flee, fight.”

Why do we freeze? It’s part of a predatory defense system that is wired to keep the organism alive. Not only do we do it, but so do other mammals and other vertebrates. Even invertebrates — like flies — freeze. If you are freezing, you are less likely to be detected if the predator is far away, and if the predator is close by, you can postpone the attack (movement by the prey is a trigger for attack)

The freezing reaction is accompanied by a hormonal surge that helps mobilize your energy and focus your attention. While the hormonal and other physiological responses that accompany freezing are there for good reason, in highly stressful situations the secretions can be excessive and create impediments to making informed choices.

Sometimes freezing is brief and sometimes it persists. This can reflect the particular situation you are in, but also your individual predisposition. Some people naturally have the ability to think through a stressful situation, or to even be motivated by it, and will more readily run, hide or fight as required.

we have created a version of this predicament using rats. The animals have been trained, through trial and error, to “know” how to escape in a certain dangerous situation. But when they are actually placed in the dangerous situation, some rats simply cannot execute the response — they stay frozen. If, however, we artificially shut down a key subregion of the amygdala in these rats, they are able to overcome the built-in impulse to freeze and use their “knowledge” about what to do.

shown that if people cognitively reappraise a situation, it can dampen their amygdala activity. This dampening may open the way for conceptually based actions, like “run, hide, fight,” to replace freezing and other hard-wired impulses.

How to encourage this kind of cognitive reappraisal? Perhaps we could harness the power of social media to conduct a kind of collective cultural training in which we learn to reappraise the freezing that occurs in dangerous situations. In most of us, freezing will occur no matter what. It’s just a matter of how long it will last.

You can’t have a blood family of 300 million, nor even a large enough one to do things like build an agrarian society

In order to have large cities built on agrarianism it was necessary not only to innovate technology, but to transform our very consciousness as it related to how we defined what a person was, both ourselves and others

Instead of needing to have real, flowing blood with common DNA from birth, it was merely necessary to be among the same abstract family organized under a king of some kind — a kind of stand in for the father or patriarch. We developed law and law enforcement as abstract disembodied voices of the father. This allowed total strangers without any family ties to interact in the same society in a constructive and organized way. Thus: civilization as we know it

Those ancient polities have developed finally into the Nation, a kind of tribe so fully abstracted that you can be of any blood and language and religion and still function within it.

So, too, are all other forms of human separation — and the opposition and conflicts they spawn — illusory in nature. We moved beyond blood, but then it was language or religion or fealty that made it impossible to work together, and we warred over that

we’re told these borders mean everything, that they are real and urgent and demand constant sacrifice to maintain.

why is that border there? Why borders?

We’re stuck in a mode of thinking that’s no longer sensible. There isn’t a reason for borders. There never really was, but now more than ever we have no utility for them, no need for them

What humanity has to do is wake up to the reality of post-tribalism. This means seeing through all these invented borders to the truth that we are all people, we are all fundamentally the same, and we can all learn to live with one another.

It was the idea of necessary conflict based on blood that preceded the fights that appeared to justify the belief in that blood-based conflict.

Nations have saturated the entire globe. There are no more frontiers. It’s all Nations butting up against one another.

We are all people of a similar nature and we do have the option to relate to one another as people for the sake of saving our shared homes and futures. We all hunger and thirst and become lonely, we all laugh and weep in the same language. Stripped of confounding symbols we are undivided.

There are a lot of people upset about the illusion of borders. They want a different reality, one in which there are Good Tribes (their tribe) and Bad Tribes (all the other ones).

but the world is already so mixed together they can’t draw those borders anymore. Hence: fascism.

There are no firm foundations for defining this tribe, however, so he’s left to cobble together some kind of ad hoc notion of in- and out-group. Like a magpie he collects ways of dividing people as appeals to his caprice: race, sex, Nation, etc., but there’s no greater sense to it, so it’s all arbitrary, all a mess.

No amount of magical thinking from conservatives can change the reality of globalism, however; what one Nation does to pollute will affect us all, and that is according to the laws of physics. No political movement can change those physics. We have to adapt or perish.

a key part of it is a simple lack of imagination. He just doesn’t realize there’s an option to not have borders, because his entire consciousness is married to the idea of of-me and not-of-me, Us and Them, and if there is no Them there can’t be an Us, and therefore life stops making sense

What has to be true if there are no tribes? We have no need to discriminate among who we may love. Loving and caring for all people as if they were blood family is the path forward

There needs to be a new story for us to share. It’s not enough to stop believing in the old way of borders, we have to actively seek out a new way of thinking and speaking and living that reflects the world as it is and as it can be.

there are others who have more tangible investments in borders: Those who have grown fat off the conflicts driven by these invented borders don’t want us to see how pointless it all is. These billionaires and presidents and kings want us to keep fighting against one another over the borders they so lazily define because it gives them a means of power and control.

We have to be ready for their opposition, however. They’ll do what they can to force us to act as if their borders are real. We don’t need to listen, though we do need to be ready to sacrifice.

Without a globally-coordinated response we can’t resolve a globally-driven problem such as climate change. If we can grant the humanity of all people we can start to imagine ways of relating to one another that aren’t opposed and antagonistic, but which are cooperative and aimed at harmony.

This transformation of consciousness must happen in our own hearts and minds before it can happen in concert.

the Nation has already been shown to be unnecessary because of social globalism. Pick a major city on earth and you’ll find every kind of person living together in peace! Not perfect peace, but not constant and unavoidable war, and that is what counts.

We can’t keep pretending as if borders matter when we can so clearly see that they don’t, but we can’t just have no story at all, there must be a way of contextualizing a future without borders. I don’t know what that story is, exactly, but I believe it is something like love writ large. Once we’re ready to start telling it we can start living it.

We seem driven (so to speak) to transform cars, conveyances that show us the world, into machines that also see the world for

There is evidence that one’s cognitive map can deteriorate. A widely reported study published in 2006 demonstrated that the brains of London taxi drivers have larger than average amounts of gray matter in the area responsible for complex spatial relations. Brain scans of retired taxi drivers suggested that the volume of gray matter in those areas also decreases when that part of the brain is no longer being used as frequently. “I think it’s possible that if you went to someone doing a lot of active navigation, but just relying on GPS,” Hugo Spiers, one of the authors of the taxi study, hypothesized to me, “you’d actually get a reduction in that area.”

A consequence is a possible diminution of our “cognitive map,” a term introduced in 1948 by the psychologist Edward Tolman of the University of California, Berkeley. In a groundbreaking paper, Dr. Tolman analyzed several laboratory experiments involving rats and mazes. He argued that rats had the ability to develop not only cognitive “strip maps” — simple conceptions of the spatial relationship between two points — but also more comprehensive cognitive maps that encompassed the entire maze.

Could society’s embrace of GPS be eroding our cognitive maps? For Julia Frankenstein, a psychologist at the University of Freiburg’s Center for Cognitive Science, the danger of GPS is that “we are not forced to remember or process the information — as it is permanently ‘at hand,’ we need not think or decide for ourselves.” She has written that we “see the way from A to Z, but we don’t see the landmarks along the way.” In this sense, “developing a cognitive map from this reduced information is a bit like trying to get an entire musical piece from a few notes.” GPS abets a strip-map level of orientation with the world.

We seem driven (so to speak) to transform cars, conveyances that show us the world, into machines that also see the world for us.

For Dr. Tolman, the cognitive map was a fluid metaphor with myriad applications. He identified with his rats. Like them, a scientist runs the maze, turning strip maps into comprehensive maps — increasingly accurate models of the “great God-given maze which is our human world,” as he put it. The countless examples of “displaced aggression” he saw in that maze — “the poor Southern whites, who take it out on the Negros,” “we psychologists who criticize all other departments,” “Americans who criticize the Russians and the Russians who criticize us” — were all, to some degree, examples of strip-map comprehension, a blinkered view that failed to comprehend the big picture. “What in the name of Heaven and Psychology can we do about it?” he wrote. “My only answer is to preach again the virtues of reason — of, that is, broad cognitive maps.”

The things you do with your life are mostly chosen: your job, spouse and hobbies.

At our foundation, we were a society with strong covenantal attachments — to family, community, creed and faith. Then on top of them we built democracy and capitalism that celebrated liberty and individual rights.

The deep covenantal institutions gave people the capacity to use their freedom well. The liberal institutions gave them that freedom.

This delicate balance — liberal institutions built atop illiberal ones — is now giving way. The big social movements of the past half century were about maximizing freedom of choice. Right-wingers wanted to maximize economic choice and left-wingers lifestyle choice. Anything that smacked of restraint came to seem like a bad thing to be eliminated.

We’ll call this worldview — which is all freedom and no covenant — naked liberalism

The problem with naked liberalism is that it relies on individuals it cannot create.

Naked liberals of right and left assume that if you give people freedom they will use it to care for their neighbors, to have civil conversations, to form opinions after examining the evidence. But if you weaken family, faith, community and any sense of national obligation, where is that social, emotional and moral formation supposed to come from? How will the virtuous habits form?

Naked liberalism has made our society an unsteady tree. The branches of individual rights are sprawling, but the roots of common obligation are withering away.

Freedom without covenant becomes selfishness. And that’s what we see at the top of society, in our politics and the financial crisis

In my experience, most people under 40 get this. They sense the social and moral void at the core and that change has to come at the communal, emotional and moral level.

And that’s what we see at the bottom of society — frayed communities, broken families, opiate addiction.

Freedom without a unifying national narrative becomes distrust, polarization and permanent political war.

covenantal attachments they become fragile. Moreover, if you rob people of their good covenantal attachments, they will grab bad ones.

First, they will identify themselves according to race. They will become the racial essentialists you see on left and right

Then they resort to tribalism. This is what Donald Trump provides. As Mark S. Weiner writes on the Niskanen Center’s blog, Trump is constantly making friend/enemy distinctions, exploiting liberalism’s thin conception of community and creating toxic communities based on in-group/out-group rivalry.

Trump offers people cultural solutions to their alienation problem. As history clearly demonstrates, people will prefer fascism to isolation, authoritarianism to moral anarchy.

If we are going to have a decent society we’re going to have to save liberalism from itself. We’re going to have to restore and re-enchant the covenantal relationships that are the foundation for the whole deal. The crucial battleground is cultural and prepolitical.

Freedom without connection becomes alienation.

Many public intellectuals were trained in the social sciences and take the choosing individual as their mental starting point. They have trouble thinking about our shared social and moral formative institutions and how such institutions could be reconstituted.

Congressional Republicans think a successful tax bill will thwart populism. Mainstream Democrats think the alienation problem will go away if we redistribute the crumbs a bit more widely.

History is full of examples of nations that built new national narratives, revived family life, restored community bonds and shared moral culture: Britain in the early 19th century, Germany after World War II, America in the Progressive Era. The first step in launching our own revival is understanding that the problem is down in the roots.

She took pride in the basic things, like cleaning engine parts. And she only hinted at the truth: When one fan told her in October, “It’s great to be young,” Soya replied, “Youth does not mean a certain period of life, but how to hold your heart.”

She seemed, well, happy, and FaceApp had made her that way. Creating the lifelike impostor had taken only a few taps: He changed the “Gender” setting to “Female,” the “Age” setting to “Teen,” and the “Impression” setting — a mix of makeup filters — to a glamorous look the app calls “Hollywood.”

Users in the Internet’s early days rarely had any presumptions of authenticity, said Melanie C. Green, a University of Buffalo professor who studies technology and social trust. Most people assumed everyone else was playing a character clearly distinguished from their real life.

Nakajima grew his shimmering hair below his shoulders and raided his local convenience store for beauty supplies he thought would make the FaceApp images more convincing: blushes, eyeliners, concealers, shampoos.

“When I compare how I feel when I started to tweet as a woman and now, I do feel that I’m gradually gravitating toward this persona … this fantasy world that I created,” Nakajima said. “When I see photos of what I tweeted, I feel like, ‘Oh. That’s me.’ ”

The sensation Nakajima was feeling is so common that there’s a term for it: the Proteus effect, named for the shape-shifting Greek god. Stanford University researchers first coined it in 2007 to describe how people inhabiting the body of a digital avatar began to act the part

People made to appear taller in virtual-reality simulations acted more assertively, even after the experience ended. Prettier characters began to flirt.

What is it about online disguises? Why are they so good at bending people’s sense of self-perception?

they tap into this “very human impulse to play with identity and pretend to be someone you’re not.”

Soya pouted and scowled on rare occasions when Nakajima himself felt frustrated. But her baseline expression was an extra-wide smile, activated with a single tap.

“This identity play was considered one of the huge advantages of being online,” Green said. “You could switch your gender and try on all of these different personas. It was a playground for people to explore.”

But wasn’t this all just a big con? Nakajima had tricked people with a “cool girl” stereotype to boost his Twitter numbers. He hadn’t elevated the role of women in motorcycling; if anything, he’d supplanted them. And the character he’d created was paper thin: Soya had no internal complexity outside of what Nakajima had projected, just that eternally superimposed smile.

The Web’s big shift from text to visuals — the rise of photo-sharing apps, live streams and video calls — seemed at first to make that unspoken rule of real identities concrete. It seemed too difficult to fake one’s appearance when everyone’s face was on constant display.

Now, researchers argue, advances in image-editing artificial intelligence have done for the modern Internet what online pseudonyms did for the world’s first chat rooms. Facial filters have allowed anyone to mold themselves into the character they want to play.

researchers fear these augmented reality tools could end up distorting the beauty standards and expectations of actual reality.

Some political and tech theorists worry this new world of synthetic media threatens to detonate our concept of truth, eroding our shared experiences and infusing every online relationship with suspicion and self-doubt.

Deceptive political memes, conspiracy theories, anti-vaccine hoaxes and other scams have torn the fabric of our democracy, culture and public health.

But she also thinks about her kids, who assume “that everything online is fabricated,” and wonders whether the rules of online identity require a bit more nuance — and whether that generational shift is already underway.

“Bots pretending to be people, automated representations of humanity — that, they perceive as exploitative,” she said. “But if it’s just someone engaging in identity experimentation, they’re like: ‘Yeah, that’s what we’re all doing.'

To their generation, “authenticity is not about: ‘Does your profile picture match your real face?’ Authenticity is: ‘Is your voice your voice?’

“Their feeling is: ‘The ideas are mine. The voice is mine. The content is mine. I’m just looking for you to receive it without all the assumptions and baggage that comes with it.’ That’s the essence of a person’s identity. That’s who they really are.”

It wasn’t until the rise of giant social networks like Facebook — which used real identities to, among other things, supercharge targeted advertising — that this big game of pretend gained an air of duplicity. Spaces for playful performance shrank, and the biggest Internet watering holes began demanding proof of authenticity as a way to block out malicious intent.

Perhaps he should have accepted his irrelevance and faded into the digital sunset, sharing his life for few to see. But some of Soya’s followers have said they never felt deceived: It was Nakajima — his enthusiasm, his attitude about life — they’d been charmed by all along. “His personality,” as one Twitter follower said, “shined through.”

In Nakajima’s mind, he’d used the tools of a superficial medium to craft genuine connections. He had not felt real until he had become noticed for being fake.

Nakajima said he doesn’t know how long he’ll keep Soya alive. But he said he’s grateful for the way she helped him feel: carefree, adventurous, seen.

When we consider how we engage with the news, some shortcuts we may want to pay close attention to, and reflect carefully on, are cognitive biases.

In fact, without these heuristics, it would be impossible for us to process all the information we receive daily. However, the use of these shortcuts can lead to “blind spots,” or unintentional ways we respond to information that can have negative consequences for how we engage with, digest, and share the information we encounter

These shortcuts, also called heuristics, streamline our problem-solving process and help us make relatively quick decisions.

Confirmation bias is the tendency to seek out and value information that confirms our pre-existing beliefs while discarding information that proves our ideas wrong.

Cognitive biases are best described as glitches in how we process information

Echo chamber effect refers to a situation in which we are primarily exposed to information, people, events, and ideas that already align with our point of view.

Anchoring bias, also known as “anchoring,” refers to people’s tendency to consider the first piece of information they receive about a topic as the most reliable

The framing effect is what happens when we make decisions based on how information is presented or discussed, rather than its actual substance.

Fluency heuristic occurs when a piece of information is deemed more valuable because it is easier to process or recall

Everyone operates under one or more cognitive biases. So, when searching for and reading the news (or other information), it is important to be aware of how these biases might shape how we make sense of this information.

In conclusion, we may not be able to control the content of the news — whether it is fake, reliable, or somewhere in between — but we can learn to be aware of how we respond to it and adjust our evaluations of the news accordingly.

upervised learning depends on annotated data: images, audio or text that is painstakingly labeled by hordes of workers. They circle people or outline bicycles on pictures of street traffic. The labeled data is fed to computer algorithms, teaching the algorithms what to look for. After ingesting millions of labeled images, the algorithms become expert at recognizing what they have been taught to see.

There is also reinforcement learning, with very limited supervision that does not rely on training data. Reinforcement learning in computer science,

is modeled after reward-driven learning in the brain: Think of a rat learning to push a lever to receive a pellet of food. The strategy has been developed to teach computer systems to take actions.

My money is on self-supervised learning,” he said, referring to computer systems that ingest huge amounts of unlabeled data and make sense of it all without supervision or reward. He is working on models that learn by observation, accumulating enough background knowledge that some sort of common sense can emerge.

redict outcomes and choose a course of action. “Everybody agrees we need predictive learning, but we disagree about how to get there,”

A more inclusive term for the future of A.I., he said, is “predictive learning,” meaning systems that not only recognize patterns but also p

A huge fraction of what we do in our day-to-day jobs is constantly refining our mental models of the world and then using those mental models to solve problems,” he said. “That encapsulates an awful lot of what we’d like A.I. to do.”Image

Currently, robots can operate only in well-defined environments with little variation.

“Our working assumption is that if we build sufficiently general algorithms, then all we really have to do, once that’s done, is to put them in robots that are out there in the real world doing real things,”

these filters will isolate people in information bubbles only partly of their own choosing, and the inaccurate beliefs they form as a result may be difficult to correct."

the proliferation of search engines, news aggregators and feed-ranking algorithms is more likely to perpetuate ignorance than knowledge.

It would seem that excessive social media use may intensify not only feelings of loneliness, but also ideological isolation.

"What the human being is best at doing is interpreting all new information so that their prior conclusions remain intact."

Recent studies show that although most people consume information that matches their opinions, being exposed to conflicting views tends to reduce prejudice and enhance creative thinking.

the desire to prove ourselves right and maintain our current beliefs trumps any attempt to be creative or more open-minded.

"our objects of inquiry are not 'truth' or 'meaning' but rather configurations of consciousness. These are figures or patterns of knowledge, cognitive and practical attitudes, which emerge within a definite historical and cultural context."

the internet is best understood as a cultural lens through which we construct – or distort – reality.

we can only deal with this overwhelming range of choices by ignoring most of them.

trolling is so effective for enticing readers' comments, but so ineffective for changing their viewpoints.

Will accumulating facts help you understand the world?

we have developed a dependency on technology, which has eclipsed our reliance on logic, critical thinking and common sense: if you can find the answer online, why bother thinking?

it is conceivable that individuals' capacity to evaluate and produce original knowledge will matter more than the actual acquisition of knowledge.

Good judgment and decision-making will be more in demand than sheer expertise or domain-specific knowledge.

Some of the most common types of illusory percepts are those that affect the impression of size, length or distance.

As visual processing needs to be both rapid and generally accurate, the brain constantly uses shortcuts and makes assumptions about the world that can, in some cases, be misleading.

These illusions are the result of visual processes shaped by evolution. Using that process may have been once beneficial (or still is), but it also allows our brains to be tricked.

if animals are tricked by the same illusions, then perhaps revealing why a different evolutionary path leads to the same visual process might help us understand why evolution favours this development.

Great bowerbirds could be the ultimate illusory artists. For example, their males construct forced perspective illusions to make them more attractive to mates.

When a male has two smaller clawed males on either side of him he is more attractive to a female (because he looks relatively larger) than if he was surrounded by two larger clawed males.

This effect is known as the Ebbinghaus illusion (see image), and suggests that males may easily manipulate their perceived attractiveness by surrounding themselves with less attractive rivals.

Deceptions of the senses are the truths of perception.

Visual illusions (and those in the non-visual senses) are a crucial tool for determining what perceptual assumptions animals make about the world around them.

One of the first things I ask myself when I read a headline or find a claim about a product is if the phrase is emotionally neutral. Some headlines generate outrage or fear, indicating that there is a clear bias. When we read something that exploits are emotions, we must be careful.

misinformation tends to play on our emotions a lot better than factual reporting or news.

When I’m trying to figure out whether a claim is factual, there are a few questions I always ask myself.Does the headline, article, or information evoke fear, anger, or other strong negative emotions?Where did you hear about the information? Does it cite any direct evidence?What is the expert consensus on this information?

Step 2. Evidence Synthesis and EvaluationSometimes I’m still feeling uncertain if there’s any truth to a claim. Even after taking into account the emotions it evokes, I need to find the evidence of a claim and evaluate its quality

Often, the information that I want to check is either political or scientific. There are different questions I ask myself, depending on the nature of these claims.

Political claims

Looking at multiple different outlets, each with its own unique biases, helps us get a picture of the issue.

I use multiple websites specializing in fact-checking. They provide primary sources of evidence for different types of claims. Here is a list of websites where I do my fact-checking:

SnopesPolitifactFactCheckMedia Bias/Fact Check (a bias assessor for fact-checking websites)Simply type in some keywords from the claim to find out if it’s verified with primary sources, misleading, false, or unproven.

Science claims

Often we tout science as the process by which we uncover absolute truths about the universe. Once many scientists agree on something, it gets disseminated in the news. Confusion arises once this science changes or evolves, as is what happened throughout the coronavirus pandemic. In addition to fear and misinformation, we have to address a fundamental misunderstanding of the way science works when practicing critical thinking.

It is confusing to hear about certain drugs found to cure the coronavirus one moment, followed by many other scientists and researchers saying that they don’t. How do we collect and assess these scientific claims when there are discrepancies?

A big part of these scientific findings is difficult to access for the public

Sometimes the distinction between scientific coverage and scientific articles isn’t clear. When this difference is clear, we might still find findings in different academic journals that disagree with each other. Sometimes, research that isn’t peer-reviewed receives plenty of coverage in the media

Correlation and causation: Sometimes a claim might present two factors that appear correlated. Consider recent misinformation about 5G Towers and the spread of coronavirus. While there might appear to be associations, it doesn’t necessarily mean that there is a causative relationship

When you’re still unsure, follow the consensus of the experts within the field. Scientists pointed out flaws within this pre-print article leading to its retraction. The pre-print was removed from the server because it did not hold up to proper scientific standards or scrutiny.

The next examples I want to bring up refer to retracted articles from peer-reviewed journals. Since science is a self-correcting process, rather than a decree of absolutes, mistakes and fraud are corrected.

Briefly, I will show you exactly how to tell if the resource you are reading is an actual, peer-reviewed scientific article.

How does science go from experiments to the news?

researchers outline exactly how they conducted their experiments so other researchers can replicate them, build upon them, or provide quality assurance for them. This scientific report does not go straight to the nearest science journalist. Websites and news outlets like Scientific American or The Atlantic do not publish scientific articles.

Here is a quick checklist that will help you figure out if you’re viewing a scientific paper.

Once it’s written up, researchers send this manuscript to a journal. Other experts in the field then provide comments, feedback, and critiques. These peer reviewers ask researchers for clarification or even more experiments to strengthen their results. Peer review often takes months or sometimes years.

Some peer-reviewed scientific journals are Science and Nature; other scientific articles are searchable through the PubMed database. If you’re curious about a topic, search for scientific papers.

Peer-review is crucial! If you’re assessing the quality of evidence for claims, peer-reviewed research is a strong indicator

Finally, there are platforms for scientists to review research even after publication in a peer-reviewed journal. Although most scientists conduct experiments and interpret their data objectively, they may still make errors. Many scientists use Twitter and PubPeer to perform a post-publication review

Step 3. Are You Practicing Objectivity?

To finish off, I want to discuss common cognitive errors that we tend to make. Finally, there are some framing questions to ask at the end of our research to help us with assessing any information that we find.

Dunning-Kruger effect: Why do we rely on experts? In 1999, David Dunning and Justin Kruger published “Unskilled and unaware of it: how difficulties in recognizing one’s own incompetence lead to inflated self-assessments.” They found that the less a person understands about a topic, the more confident of their abilities or knowledge they will be

How does this relate to critical thinking? If you’re reading a claim sourced or written by somebody who lacks expertise in a field, they are underestimating its complexity. Whenever possible, look for an authoritative source when synthesizing and evaluating evidence for a claim.

Survivorship bias: Ever heard someone argue that we don’t need vaccines or seatbelts? After all, they grew up without either of them and are still alive and healthy!These arguments are appealing at first, but they don’t account for any cases of failures. They are attributing a misplaced sense of optimism and safety by ignoring the deaths that occurred resultant from a lack of vaccinations and seatbelts

To practice critical thinking with these kinds of claims, we must ask the following questions:Does this claim emerge from a peer-reviewed scientific article? Has this paper been retracted?Does this article appear in a reputable journal?What is the expert consensus on this article?

Now with all the evidence we’ve gathered, we ask ourselves some final questions. There are plenty more questions you will come up with yourself, case-by-case.Who is making the original claim?Who supports these claims? What are their qualifications?What is the evidence used for these claims?Where is this evidence published?How was the evidence gathered?Why is it important?

“even if some data is supporting a claim, does it make sense?” Some claims are deceptively true but fall apart when accounting for this bias.

It makes sense then, that losing a friend, or being rejected by a group might register to a person as a very dangerous thing. Emotional pain might result if a person discovers that they weren’t invited to a dinner party with friends.

One thing we do know is that people who have a lot of friends have high pain thresholds

Look for cutting edge neuroscience coming out in the next few years that helps us understand how to raise the social pain threshold. We could, very soon, have some practical answers for people with debilitating social anxiety, depression, and loneliness.

Saying he had no regrets, he added: "I believe in all circumstances I behaved reasonably and legally. The legal rules do not inevitably cover all circumstances - including those I found myself in." Also on Monday, Johnson expressed "regret" for the "confusion, anger and pain" experienced by the British people as a result of the controversy; when pressed on whether he believes Cummings' decision has compromised the government's coronavirus message, Johnson doubled down on his support for Cummings, asserting, "I do not believe that anybody at Number 10 has done anything to undermine our message."

"The regulations made clear, I believe, that risks to the health of a small child were an exceptional situation."

To talk of the British sense of fair play is almost a cliché. But there is certainly a particular sensitivity among Britons to suggestions of hypocrisy which have thus far thwarted Cummings' attempts to brush off criticism of his excursion, and which contrast with, say, the relative lack of fuss in the US over the revelation that Ivanka Trump, President Donald Trump's daughter, traveled from Washington DC to New Jersey to celebrate Passover last month.

A controversial figure who relishes his role as an outsider, he also has a common touch when it comes to distilling a message with a brilliance complemented by Johnson's own flair for capturing the national mood. So while it was Johnson, then-Mayor of London, who in 2016 sensed an appetite for leaving the EU which his more senior colleagues missed, it was Cummings, head of the Vote Leave Campaign, who boiled it down to the simple and devastatingly effective slogan of "Take Back Control."

For a man known for his gregarious nature, the British Prime Minister has few close political friends; his inexperienced cabinet was appointed as much for their loyalty and support for his key policy of leading the UK out of the European Union as any long-term affinity with Johnson.

At the start of the lockdown, Dr. Catherine Calderwood, Scotland's Chief Medical Officer, fell on her sword after admitting two overnight visits at her seaside holiday cottage, having fronted the campaign urging Scots to stay home. Though Calderwood apologized for her actions and initially said she planned to stay on in her post, she later released a statement that she had quit and acknowledging that the "justifiable focus" on her actions could pose a distraction to the response to the pandemic.

As senior adviser since summer 2019 when Johnson became Prime Minister, the notoriously prickly Cummings has rubbed many Downing Street denizens the wrong way. But when coronavirus hit, it was he who crafted the message, "Stay Home, Protect the NHS, Save Lives," which has come to define Britain's battle against the virus and the protective shield the country threw around its beloved health service.

The hitherto wildly popular Johnson's favorability ratings have begun to slip while a recent poll by YouGov found 49% disapproved of the Prime Minister's path out of lockdown compared to 36% who supported it.

The former Chief Constable of Durham Police, Mike Barton, has warned that Cummings' behavior, and the Prime Minister's defense of it, will make attempts to enforce the lockdown impossible, potentially endangering the slow but steady progress the UK has made in reducing the spread of the virus.

The consequences could be even more serious if a mass loss of faith in both the Johnson government and his lockdown results in the public breaking the rules just at the moment the Prime Minister is urging them to stand firm.

what does living well mean in practice? To Setiya, it lies in embracing one of the many possible “good-enough lives” instead of aching for a perfect one

Setiya’s approach blends empathy with common sense. True, a person who is blind or lacks full movement may not be able to enjoy certain pleasures — at least, in the typical way. And suffering injury can be traumatic. But none of us can fit everything worth doing into one lifetime. Our possibilities and our choices are always limited, and we can live fully within those limits.

he invites the reader to join him as he looks at life’s challenges — loneliness, injustice, grief — and in turning them over to examine every angle. Sometimes these twists make it difficult to grasp his ultimate point; in his discussion of the potential extinction of human beings, for instance, Setiya argues movingly that it is hard to find meaning in our actions without the promise of future societies who will enjoy the result

The golden thread running through “Life Is Hard” is Setiya’s belief in the value of well-directed attention. Pain, as much as we wish to avoid it, forces us to remember that we are indelibly connected to our bodies.

Listening carefully, whether to good friends or to strangers on a bus, can help us feel less lonely. “Close reading” other people, trying as hard as possible to see them in their full humanity, is a small step toward a more just world. By cultivating our sensitivity to ourselves and to others, we escape another destructive modern myth: that we are separate from other people, and that we can live well without caring for them.

Mindfulness is also Setiya’s answer to the threat of personal failure. If we can teach ourselves to notice all the splendid, varied incidents of our lives, he claims, we are much less likely to brand ourselves with a single label, winner or loser.

He encourages readers to abandon simple narratives about success over the course of a lifetime. I suspect this is why Setiya so often finds his conclusions in poetry, not in philosophy: The experience of suffering leads to messy, counterintuitive truths.

“Life Is Hard” is a humane consolation for challenging times. Reading it is like speaking with a thoughtful friend who never tells you to cheer up, but, by offering gentle companionship and a change of perspective, makes you feel better anyway.

People believe that memory should be effortless, but their expectations for how much they should remember are totally out of whack with how much they’re capable of remembering.1

What is the most common misconception about memory?

Another misconception is that memory is supposed to be an archive of the past. We expect that we should be able to replay the past like a movie in our heads.

we don’t replay the past as it happened; we do it through a lens of interpretation and imagination.

How much are we capable of remembering, from both an episodic2 2 Episodic memory is the term for the memory of life experiences. and a semantic3 3 Semantic memory is the term for the memory of facts and knowledge about the world. standpoint?

I would argue that we’re all everyday-memory experts, because we have this exceptional semantic memory, which is the scaffold for episodic memory.

If what we’re remembering, or the emotional tenor of what we’re remembering, is dictated by how we’re thinking in a present moment, what can we really say about the truth of a memory?

But if memories are malleable, what are the implications for how we understand our “true” selves?

your question gets to a major purpose of memory, which is to give us an illusion of stability in a world that is always changing. Because if we look for memories, we’ll reshape them into our beliefs of what’s happening right now. We’ll be biased in terms of how we sample the past. We have these illusions of stability, but we are always changing

And depending on what memories we draw upon, those life narratives can change.

we have this illusion that much of the world is cause and effect. But the reason, in my opinion, that we have that illusion is that our brain is constantly trying to find the patterns

One thing that makes the human brain so sophisticated is that we have a longer timeline in which we can integrate information than many other species. That gives us the ability to say: “Hey, I’m walking up and giving money to the cashier at the cafe. The barista is going to hand me a cup of coffee in about a minute or two.”

There is this illusion that we know exactly what’s going to happen, but the fact is we don’t. Memory can overdo it: Somebody lied to us once, so they are a liar; somebody shoplifted once, they are a thief.

If people have a vivid memory of something that sticks out, that will overshadow all their knowledge about the way things work. So there’s kind of an illus

I know it sounds squirmy to say, “Well, I can’t answer the question of how much we remember,” but I don’t want readers to walk away thinking memory is all made up.

I think of memory more like a painting than a photograph. There’s often photorealistic aspects of a painting, but there’s also interpretation. As a painter evolves, they could revisit the same subject over and over and paint differently based on who they are now. We’re capable of remembering things in extraordinary detail, but we infuse meaning into what we remember. We’re designed to extract meaning from the past, and that meaning should have truth in it. But it also has knowledge and imagination and, sometimes, wisdom.

memory, often, is educated guesses by the brain about what’s important. So what’s important? Things that are scary, things that get your desire going, things that are surprising. Maybe you were attracted to this person, and your eyes dilated, your pulse went up. Maybe you were working on something in this high state of excitement, and your dopamine was up.

It could be any of those things, but they’re all important in some way, because if you’re a brain, you want to take what’s surprising, you want to take what’s motivationally important for survival, what’s new.

On the more intentional side, are there things that we might be able to do in the moment to make events last in our memories? In some sense, it’s about being mindful. If we want to form a new memory, focus on aspects of the experience you want to take with you.

If you’re with your kid, you’re at a park, focus on the parts of it that are great, not the parts that are kind of annoying. Then you want to focus on the sights, the sounds, the smells, because those will give you rich detail later on

Another part of it, too, is that we kill ourselves by inducing distractions in our world. We have alerts on our phones. We check email habitually.

When we go on trips, I take candid shots. These are the things that bring you back to moments. If you capture the feelings and the sights and the sounds that bring you to the moment, as opposed to the facts of what happened, that is a huge part of getting the best of memory.

this goes back to the question of whether the factual truth of a memory matters to how we interpret it. I think it matters to have some truth, but then again, many of the truths we cling to depend on our own perspective.

There’s a great experiment on this. These researchers had people read this story about a house.8 8 The study was “Recall of Previously Unrecallable Information Following a Shift in Perspective,” by Richard C. Anderson and James W. Pichert. One group of subjects is told, I want you to read this story from the perspective of a prospective home buyer. When they remember it, they remember all the features of the house that are described in the thing. Another group is told, I want you to remember this from the perspective of a burglar. Those people tend to remember the valuables in the house and things that you would want to take. But what was interesting was then they switched the groups around. All of a sudden, people could pull up a number of details that they didn’t pull up before. It was always there, but they just didn’t approach it from that mind-set. So we do have a lot of information that we can get if we change our perspective, and this ability to change our perspective is exceptionally important for being accurate. It’s exceptionally important for being able to grow and modify our beliefs

One common strategy for thinking about this is to suggest that what we used to call the whole universe is just a small part of everything there is, and that we live in a kind of bubble universe, a small region of something much larger

Newton realized there had to be some force holding the moon in its orbit around the earth, to keep it from wandering off, and he knew also there was a force that was pulling the apple down to the earth. And so what suddenly struck him was that those could be one and the same thing, the same force

That was a physical discovery, a physical discovery of momentous importance, as important as anything you could ever imagine because it knit together the terrestrial realm and the celestial realm into one common physical picture. It was also a philosophical discovery in the sense that philosophy is interested in the fundamental natures of things.

The problem is that quantum mechanics was developed as a mathematical tool. Physicists understood how to use it as a tool for making predictions, but without an agreement or understanding about what it was telling us about the physical world. And that's very clear when you look at any of the foundational discussions. This is what Einstein was upset about; this is what Schrodinger was upset about. Quantum mechanics was merely a calculational technique that was not well understood as a physical theory. Bohr and Heisenberg tried to argue that asking for a clear physical theory was something you shouldn't do anymore. That it was something outmoded. And they were wrong, Bohr and Heisenberg were wrong about that. But the effect of it was to shut down perfectly legitimate physics questions within the physics community for about half a century. And now we're coming out of that

The basic philosophical question, going back to Plato, is "What is x?" What is virtue? What is justice? What is matter? What is time? You can ask that about dark energy - what is it? And it's a perfectly good question.

right now there are just way too many freely adjustable parameters in physics. Everybody agrees about that. There seem to be many things we call constants of nature that you could imagine setting at different values, and most physicists think there shouldn't be that many, that many of them are related to one another. Physicists think that at the end of the day there should be one complete equation to describe all physics, because any two physical systems interact and physics has to tell them what to do. And physicists generally like to have only a few constants, or parameters of nature. This is what Einstein meant when he famously said he wanted to understand what kind of choices God had --using his metaphor-- how free his choices were in creating the universe, which is just asking how many freely adjustable parameters there are. Physicists tend to prefer theories that reduce that number

You have others saying that time is just an illusion, that there isn't really a direction of time, and so forth. I myself think that all of the reasons that lead people to say things like that have very little merit, and that people have just been misled, largely by mistaking the mathematics they use to describe reality for reality itself. If you think that mathematical objects are not in time, and mathematical objects don't change -- which is perfectly true -- and then you're always using mathematical objects to describe the world, you could easily fall into the idea that the world itself doesn't change, because your representations of it don't.

physicists for almost a hundred years have been dissuaded from trying to think about fundamental questions. I think most physicists would quite rightly say "I don't have the tools to answer a question like 'what is time?' - I have the tools to solve a differential equation." The asking of fundamental physical questions is just not part of the training of a physicist anymore.

The question remains as to how often, after life evolves, you'll have intelligent life capable of making technology. What people haven't seemed to notice is that on earth, of all the billions of species that have evolved, only one has developed intelligence to the level of producing technology. Which means that kind of intelligence is really not very useful. It's not actually, in the general case, of much evolutionary value. We tend to think, because we love to think of ourselves, human beings, as the top of the evolutionary ladder, that the intelligence we have, that makes us human beings, is the thing that all of evolution is striving toward. But what we know is that that's not true. Obviously it doesn't matter that much if you're a beetle, that you be really smart. If it were, evolution would have produced much more intelligent beetles. We have no empirical data to suggest that there's a high probability that evolution on another planet would lead to technological intelligence.

(4) The academic views of a professor are independent of his or her real-world political views; academic disputes don’t track partisan disputes or vice versa; you can’t reason from an academic’s disciplinary views to the positions he or she would take in the public sphere; they are independent variables.

The answer given in the first lecture — “What is Language?” — is that we are creatures with language, and that language as a uniquely human biological capacity appeared suddenly and quite late in the evolutionary story, perhaps 75,000 years ago.

Chomsky gave three lectures under the general title “What Kind of Creatures are We?”

Language, then, does not arise from the social/cultural environment, although the environment provides the stuff or input it works on. That input is “impoverished”; it can’t account for the creativity of language performance, which has its source not in the empirical world, but in an innate ability that is more powerful than the stimuli it utilizes and plays with. It follows that if you want to understand language, you shouldn’t look to linguistic behavior but to the internal mechanism — the Universal Grammar — of which particular linguistic behaviors are a non-exhaustive expression. (The capacity exceeds the empirical resources it might deploy.)

In his second lecture (“What Can We Understand?”), Chomsky took up the question of what humans are capable of understanding and his answer, generally, was that we can understand what we can understand, and that means that we can’t understand what is beyond our innate mental capacities

This does not mean, he said, that what we can’t understand is not real: “What is mysterious to me is not an argument that it does not exist.” It’s just that while language is powerful and creative, its power and creativity have limits; and since language is thought rather than an addition to or clothing of thought, the limits of language are the limits of what we can fruitfully think about

This is as good as it gets. There is “no evolution in our capacity for language.”

These assertions are offered as a counter to what Chomsky sees as the over-optimistic Enlightenment belief — common to many empiricist philosophies — that ours is a “limitless explanatory power” and that “we can do anything.”

In the third lecture (“What is the Common Good?”) Chomsky turned from the philosophy of mind and language to political philosophy and the question of what constitutes a truly democratic society

He likened dogmatic intellectual structures that interfere with free inquiry to coercive political structures that stifle the individual’s creative independence and fail to encourage humanity’s “richest diversity

He asserted that any institution marked by domination and hierarchy must rise to the challenge of justifying itself, and if it cannot meet the challenge, it should be dismantled.

He contrasted two accounts of democracy: one — associated by him with James Madison — distrusts the “unwashed” populace and puts its faith in representative government where those doing the representing (and the voting and the distributing of goods) constitute a moneyed and propertied elite

the other — associated by him with Adam Smith (in one of his moods), J. S. Mill, the 1960s and a tradition of anarchist writing — seeks to expand the franchise and multiply choices in the realms of thought, politics and economics. The impulse of this second, libertarian, strain of democracy, is “to free society from economic or theological guardianship,” and by “theological” Chomsky meant not formal religion as such but any assumed and frozen ideology that blocked inquiry and limited participation. There can’t, in short, be “too much democracy.”

It was thought of the highest order performed by a thinker, now 85 years old, who by and large eschewed rhetorical flourishes (he has called his own speaking style “boring” and says he likes it that way) and just did it, where ‘it” was the patient exploration of deep issues that had been explored before him by a succession of predecessors, fully acknowledged, in a conversation that is forever being continued and forever being replenished.

Yes, I said to myself, this is what we — those of us who bought a ticket on this particular train — do; we think about problems and puzzles and try to advance the understanding of them; and we do that kind of thinking because its pleasures are, in a strong sense, athletic and provide for us, at least on occasion, the experience of fully realizing whatever capabilities we might have. And we do it in order to have that experience, and to share it with colleagues and students of like mind, and not to make a moral or political point.

The term “master class” is a bit overused, but I feel no hesitation in using it here. It was a master class taught by a master, and if someone were to ask me what exactly is it that academics do, I would point to these lectures and say, simply, here it is, the thing itself.