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Bush wanted to remake the world. President Trump, by contrast, just wants to make it up as he goes along

Through all their debates over who is to blame for imperiling truth (whether Trump, postmodernism, social media or Fox News), as well as the consequences (invariably dire) and the solutions (usually vague), a few conclusions materialize, should you choose to believe them.

There is a pattern and logic behind the dishonesty of Trump and his surrogates; however, it’s less multidimensional chess than the simple subordination of reality to political and personal ambition

Trump’s untruth sells best precisely when feelings and instincts overpower facts, when America becomes a safe space for fabrication.

Rand Corp. scholars Jennifer Kavanagh and Michael D. Rich point to the Gilded Age, the Roaring Twenties and the rise of television in the mid-20th century as recent periods of what they call “Truth Decay” — marked by growing disagreement over facts and interpretation of data; a blurring of lines between opinion, fact and personal experience; and diminishing trust in once-respected sources of information.

In eras of truth decay, “competing narratives emerge, tribalism within the U.S. electorate increases, and political paralysis and dysfunction grow,”

Once you add the silos of social media as well as deeply polarized politics and deteriorating civic education, it becomes “nearly impossible to have the types of meaningful policy debates that form the foundation of democracy.”

To interpret our era’s debasement of language, Kakutani reflects perceptively on the World War II-era works of Victor Klemperer, who showed how the Nazis used “words as ‘tiny doses of arsenic’ to poison and subvert the German culture,” and of Stefan Zweig, whose memoir “The World of Yesterday” highlights how ordinary Germans failed to grasp the sudden erosion of their freedoms.

Kakutani calls out lefty academics who for decades preached postmodernism and social constructivism, which argued that truth is not universal but a reflection of relative power, structural forces and personal vantage points.

postmodernists rejected Enlightenment ideals as “vestiges of old patriarchal and imperialist thinking,” Kakutani writes, paving the way for today’s violence against fact in politics and science.

“dumbed-down corollaries” of postmodernist thought have been hijacked by Trump’s defenders, who use them to explain away his lies, inconsistencies and broken promises.

intelligent-design proponents and later climate deniers drew from postmodernism to undermine public perceptions of evolution and climate change. “Even if right-wing politicians and other science deniers were not reading Derrida and Foucault, the germ of the idea made its way to them: science does not have a monopoly on the truth,

McIntyre quotes at length from mea culpas by postmodernist and social constructivist writers agonizing over what their theories have wrought, shocked that conservatives would use them for nefarious purposes

pro-Trump troll and conspiracy theorist Mike Cernovich , who helped popularize the “Pizzagate” lie, has forthrightly cited his unlikely influences. “Look, I read postmodernist theory in college,” Cernovich told the New Yorker in 2016. “If everything is a narrative, then we need alternatives to the dominant narrative. I don’t seem like a guy who reads [Jacques] Lacan, do I?

When truth becomes malleable and contestable regardless of evidence, a mere tussle of manufactured narratives, it becomes less about conveying facts than about picking sides, particularly in politics.

In “On Truth,” Cambridge University philosopher Simon Blackburn writes that truth is attainable, if at all, “only at the vanishing end points of enquiry,” adding that, “instead of ‘facts first’ we may do better if we think of ‘enquiry first,’ with the notion of fact modestly waiting to be invited to the feast afterward.

He is concerned, but not overwhelmingly so, about the survival of truth under Trump. “Outside the fevered world of politics, truth has a secure enough foothold,” Blackburn writes. “Perjury is still a serious crime, and we still hope that our pilots and surgeons know their way about.

Kavanaugh and Rich offer similar consolation: “Facts and data have become more important in most other fields, with political and civil discourse being striking exceptions. Thus, it is hard to argue that the world is truly ‘post-fact.’ ”

McIntyre argues persuasively that our methods of ascertaining truth — not just the facts themselves — are under attack, too, and that this assault is especially dangerous.

Ideologues don’t just disregard facts they disagree with, he explains, but willingly embrace any information, however dubious, that fits their agenda. “This is not the abandonment of facts, but a corruption of the process by which facts are credibly gathered and reliably used to shape one’s beliefs about reality. Indeed, the rejection of this undermines the idea that some things are true irrespective of how we feel about them.”

“It is hardly a depressing new phenomenon that people’s beliefs are capable of being moved by their hopes, grievances and fears,” Blackburn writes. “In order to move people, objective facts must become personal beliefs.” But it can’t work — or shouldn’t work — in reverse.

More than fearing a post-truth world, Blackburn is concerned by a “post-shame environment,” in which politicians easily brush off their open disregard for truth.

it is human nature to rationalize away the dissonance. “Why get upset by his lies, when all politicians lie?” Kakutani asks, distilling the mind-set. “Why get upset by his venality, when the law of the jungle rules?”

So any opposition is deemed a witch hunt, or fake news, rigged or just so unfair. Trump is not killing the truth. But he is vandalizing it, constantly and indiscriminately, diminishing its prestige and appeal, coaxing us to look away from it.

the collateral damage includes the American experiment.

“One of the most important ways to fight back against post-truth is to fight it within ourselves,” he writes, whatever our particular politics may be. “It is easy to identify a truth that someone else does not want to see. But how many of us are prepared to do this with our own beliefs? To doubt something that we want to believe, even though a little piece of us whispers that we do not have all the facts?”

This does not mean they will succeed in fixing every problem their tech creates — and in some cases their fixes may well raise other problems, like questions about their power over freedom of expression. But at least they can try to address the wide variety of externalities posed by tech, which may have been impossible for an internet more fragmented by smaller firms.

Rob Atkinson, president of the Information Technology and Innovation Foundation, a think tank, and co-author of “Big Is Beautiful,” a coming book that extols the social and economic virtues of big companies.

“As long as their innovation rents are recycled into research and development that leads to new products, then what’s to complain about?”

At the same time, they are all locked in intense battles for new markets and technologies. And not only do they keep creating new tech, but they are coming at it in diverse ways — with different business models, different philosophies and different sets of ethics.

it was perhaps inevitable that we would see the rise of a handful of large companies take control of much of the modern tech business.

But it wasn’t inevitable that these companies would be based in and controlled from the United States. And it’s not obvious that will remain the case — the top tech companies of tomorrow might easily be Chinese, or Indian or Russian or European. But for now, that means we are dealing with companies that feel constrained by American laws and values.

Some of you said you had formed new habits that you think might stick, including meditating online and gathering weekly with pals over Zoom.

Some readers said they were grateful for virtual stand-ins but could not wait to get back to the library and hugging their family members.

This year, reading together has strengthened our bond at a distance. He calls me all of the time, asking me to please read him another story.

During lockdown, we discovered we could use an app called JamKazam to play music together over the internet in real time.

reading e-books on my iPad

To be honest, I miss holding a physical book in my hand, turning a page and the satisfying feeling of closing the book when you’ve finished.

My new tech habit is meditation class by Zoom. I have never before been able to successfully meditate

But being at home, in my most comfortable chair in front of the fireplace with a cup of coffee has worked for me. Meditation has been a great tool to help me cope with the stress and anxiety of this terrible, no-good year.

I started drawing cartoons that highlight how our lives have changed during the pandemic

I’ve been able to maintain my social ties with my musician friends and make some new musical friends as well. Last, but not least, I am encouraged to keep practicing.

My new habit is ordering groceries online and no contact pickup

My “shoppers” have done an outstanding job! It’s a true improvement that should remain in place

I am 86 years old and haven’t hugged anyone in my family for one year. But I’ve learned to use Zoom and to order my groceries online, both of which helped me keep myself fed, independent and sane

I’ve attended services at my synagogue without having to put on my snow boots. I’ve gone to art galleries and operas without having to dress up or worry about where to park.

My psychologist is now doing telehealth visits, and I love it. It’s my hope that this becomes a permanent option in the future.

Not only for me, but for the multitudes of people who need mental health care and aren’t in a position to access it in person.

I teach ballet to older women. When we had to stop dancing together in person, I was motivated to find a way to deliver a class in some form. With an iPhone, my teenager’s tripod and the tech advice of my three adult children and my son-in-law, I was able to quickly learn to record a ballet class, edit it on my laptop, make a YouTube channel, upload the video and share it.

I purchased Duolingo and brushed up on French and picked up Arabic and German.

I go to an annual girls’ weekend trip on Lake Gaston with five other women. That had to be canceled last year. We’ve instituted a weekly Zoom call on Tuesday nights after we put the kids to bed to catch up with each other and talk and laugh, and sometimes cry.

It’s brought us even closer together than the usual once per year weekend could

Patterns that didn’t change one generation to the next, Dr. Conway called still lifes — such as the four-celled block, the six-celled beehive or the eight-celled pond. Patterns that took a long time to stabilize, he called methuselahs.

The second thing Life shows us is something that Darwin hit upon when he was looking at Life, the organic version. Complexity arises from simplicity!

I first encountered Life at the Exploratorium in San Francisco in 1978. I was hooked immediately by the thing that has always hooked me — watching complexity arise out of simplicity.

Life shows you two things. The first is sensitivity to initial conditions. A tiny change in the rules can produce a huge difference in the output, ranging from complete destruction (no dots) through stasis (a frozen pattern) to patterns that keep changing as they unfold.

Life shows us complex virtual “organisms” arising out of the interaction of a few simple rules — so goodbye “Intelligent Design.”

I’ve wondered for decades what one could learn from all that Life hacking. I recently realized it’s a great place to try to develop “meta-engineering” — to see if there are general principles that govern the advance of engineering and help us predict the overall future trajectory of technology.

Melanie Mitchell— Professor of complexity, Santa Fe Institute

Given that Conway’s proof that the Game of Life can be made to simulate a Universal Computer — that is, it could be “programmed” to carry out any computation that a traditional computer can do — the extremely simple rules can give rise to the most complex and most unpredictable behavior possible. This means that there are certain properties of the Game of Life that can never be predicted, even in principle!

I use the Game of Life to make vivid for my students the ideas of determinism, higher-order patterns and information. One of its great features is that nothing is hidden; there are no black boxes in Life, so you know from the outset that anything that you can get to happen in the Life world is completely unmysterious and explicable in terms of a very large number of simple steps by small items.

In Thomas Pynchon’s novel “Gravity’s Rainbow,” a character says, “But you had taken on a greater and more harmful illusion. The illusion of control. That A could do B. But that was false. Completely. No one can do. Things only happen.”This is compelling but wrong, and Life is a great way of showing this.

In Life, we might say, things only happen at the pixel level; nothing controls anything, nothing does anything. But that doesn’t mean that there is no such thing as action, as control; it means that these are higher-level phenomena composed (entirely, with no magic) from things that only happen.

Stephen Wolfram— Scientist and C.E.O., Wolfram Research

Brian Eno— Musician, London

Bert Chan— Artificial-life researcher and creator of the continuous cellular automaton “Lenia,” Hong Kong

it did have a big impact on beginner programmers, like me in the 90s, giving them a sense of wonder and a kind of confidence that some easy-to-code math models can produce complex and beautiful results. It’s like a starter kit for future software engineers and hackers, together with Mandelbrot Set, Lorenz Attractor, et cetera.

if we think about our everyday life, about corporations and governments, the cultural and technical infrastructures humans built for thousands of years, they are not unlike the incredible machines that are engineered in Life.

In normal times, they are stable and we can keep building stuff one component upon another, but in harder times like this pandemic or a new Cold War, we need something that is more resilient and can prepare for the unpreparable. That would need changes in our “rules of life,” which we take for granted.

Rudy Rucker— Mathematician and author of “Ware Tetralogy,” Los Gatos, Calif.

That’s what chaos is about. The Game of Life, or a kinky dynamical system like a pair of pendulums, or a candle flame, or an ocean wave, or the growth of a plant — they aren’t readily predictable. But they are not random. They do obey laws, and there are certain kinds of patterns — chaotic attractors — that they tend to produce. But again, unpredictable is not random. An important and subtle distinction which changed my whole view of the world.

William Poundstone— Author of “The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge,” Los Angeles, Calif.

The Game of Life’s pulsing, pyrotechnic constellations are classic examples of emergent phenomena, introduced decades before that adjective became a buzzword.

Fifty years later, the misfortunes of 2020 are the stuff of memes. The biggest challenges facing us today are emergent: viruses leaping from species to species; the abrupt onset of wildfires and tropical storms as a consequence of a small rise in temperature; economies in which billions of free transactions lead to staggering concentrations of wealth; an internet that becomes more fraught with hazard each year

Looming behind it all is our collective vision of an artificial intelligence-fueled future that is certain to come with surprises, not all of them pleasant.

The name Conway chose — the Game of Life — frames his invention as a metaphor. But I’m not sure that even he anticipated how relevant Life would become, and that in 50 years we’d all be playing an emergent game of life and death.

There might be desks, cushions, or benches arranged in rows or circles—however the teachers want them, as not every classroom will follow a template. Each classroom will be set up based on what is necessary to meet learning objectives. But schools will prioritize configuring classes to inspire learning first and foremost, and, where appropriate, reflect the diversity of environments that students are exposed to outside a school setting.

Students will have beautiful spaces that make them feel good to be at school—with art, living plants, music where appropriate, comfortable seating, and fast internet access.

Windows that open are a nice feature, as are clean bathrooms and individual desks that can be rearranged

Smaller schools and smaller rooms seem to work better than larger schools and larger rooms.  

My experience as a high-school principal taught me to never spend too much time worrying about the “small stuff.”

High-school classrooms will be designed by students themselves, providing breakout space for group work and more private areas for individual work and studying. High-school classrooms will reflect the transition that students are facing, allowing for independence but also providing a nurturing environment for curiosity.

There will be areas where students can post ideas to help make the learning environment more engaging and fun. The classroom will also be tailored to the topic, but all will have interactive stations where hands-on learning can be experienced by all students.

In the future, we won’t have “classrooms.” The enemy of the future of the classroom has arguably been that phrase: “the future of the classroom.” It locks us into a model of believing students will be sorted by age and sit in a room together with one teacher in the front.

Form will follow function, and if one of the key principles of public education is to instill an appreciation for democracy, then classrooms will be arranged so that students are equals with one another

(not some in the front, others in the back), and so that students are active participants in learning, not passive recipients of teachers’ knowledge.

Whereas the traditional lecture hall connotes hierarchy, placing desks in a circle suggests students should be learning to debate and become decision makers. Within the circle, desks will also be clustered in small groups of four to encourage collaboration among students.

There will be a large open space that will serve as a community gathering spot. The classroom will have big windows to let a lot of natural light shine through. The room will be colorful without being obnoxious—colors will be blues, greens, whites, and yellows.

It’s also important to look at the appropriate role of technology in the classroom. Technology can be a powerful tool, but it must be implemented with the intention of enhancing educator-facilitated learning, not replacing i

Over the next decade, officials managing the main U.S. repositories of climate-related information expect their archives’ total volume to grow from about 83 petabytes today to more than 650 petabytes.

One petabyte of digital memory can hold thousands of feature-length movies, with 650 enough to hold the contents of the Library of Congress 30 times over.

All that information, though, is more than conventional data storage can handle and more than any human mind can readily assimilate,

To accommodate it all, the federal workers tasked with managing the data are moving it into the cloud, which offers almost unlimited memory storage while eliminating the need for scientists to maintain their own on-site archive

archive managers are devising new analytical techniques and adapting a standard format for the data no matter who collected it and who wants to study it.

In essence, they are reinventing climate science from the ground up.

“We are in the midst of a technology evolution,

As of last September, government agencies and private companies had about 900 Earth-orbiting satellites gathering data about our planet, according to the Union of Concerned Scientists. That is almost three times as many as were aloft in 2008. More are being readied for launch.

ASA’s $1 billion Surface Water and Ocean Topography mission will measure Earth’s lakes, rivers and oceans in the first detailed global survey of the planet’s surface water.

That is a drop in the data bucket compared with the space agency’s $1.5 billion Nisar radar imaging satellite, which is scheduled for launch in January 2023. Its sensors will detect movements of the planet’s land, ice sheets and sea ice as small as 0.4 inches, transmitting 80 terabytes of data every day.

With current data handling systems and typical internet connections, it would take a climate researcher about a year to download just four days’ worth of Nisar dat

NASA and NOAA are working with Amazon Web Services, Google Cloud and Microsoft Corp. to move their climate databases into the cloud.

Earlier this year, the United Nations Intergovernmental Panel on Climate Change for the first time used data on past climate behavior to gauge the reliability of climate models for policy makers.

It isn’t clear how the American public-school system will survive the COVID years. Teachers, whose relative pay and status have been in decline for decades, are fleeing the field. In 2021, buckling under the stresses of the pandemic, nearly 1 million people quit jobs in public education, a 40 percent increase over the previous year.

These kids, and the investments that come with them, may never return—the beginning of a cycle of attrition that could continue long after the pandemic ends and leave public schools even more underfunded and dilapidated than before. “It’s an open question whether the public-school system will recover,” Steiner said. “That is a real concern for democratic education.”

The high-profile failings of public schools during the pandemic have become a political problem for Democrats, because of their association with unions, prolonged closures, and the pedagogy of social justice, which can become a form of indoctrination.

The party that stands for strong government services in the name of egalitarian principles supported the closing of schools far longer than either the science or the welfare of children justified, and it has been woefully slow to acknowledge how much this damaged the life chances of some of America’s most disadvantaged students.

Public education is too important to be left to politicians and ideologues. Public schools still serve about 90 percent of children across red and blue America.

Since the common-school movement in the early 19th century, the public school has had an exalted purpose in this country. It’s our core civic institution—not just because, ideally, it brings children of all backgrounds together in a classroom, but because it prepares them for the demands and privileges of democratic citizenship. Or at least, it needs to.

What is school for? This is the kind of foundational question that arises when a crisis shakes the public’s faith in an essential institution. “The original thinkers about public education were concerned almost to a point of paranoia about creating self-governing citizens,”

“Horace Mann went to his grave having never once uttered the phrase college- and career-ready. We’ve become more accustomed to thinking about the private ends of education. We’ve completely lost the habit of thinking about education as citizen-making.”

School can’t just be an economic sorting system. One reason we have a stake in the education of other people’s children is that they will grow up to be citizens.

Public education is meant not to mirror the unexamined values of a particular family or community, but to expose children to ways that other people, some of them long dead, think.

If the answer were simply to push more and more kids into college, the United States would be entering its democratic prime

So the question isn’t just how much education, but what kind. Is it quaint, or utopian, to talk about teaching our children to be capable of governing themselves?

The COVID era, with Donald Trump out of office but still in power and with battles over mask mandates and critical race theory convulsing Twitter and school-board meetings, shows how badly Americans are able to think about our collective problems—let alone read, listen, empathize, debate, reconsider, and persuade in the search for solutions.

democratic citizenship can, at least in part, be learned.

The history warriors build their metaphysics of national good or evil on a foundation of ignorance. In a 2019 survey, only 40 percent of Americans were able to pass the test that all applicants for U.S. citizenship must take, which asks questions like “Who did the United States fight in World War II?” and “We elect a President for how many years?” The only state in which a majority passed was Vermont.

he orthodoxies currently fighting for our children’s souls turn the teaching of U.S. history into a static and morally simple quest for some American essence. They proceed from celebration or indictment toward a final judgment—innocent or guilty—and bury either oppression or progress in a subordinate clause. The most depressing thing about this gloomy pedagogy of ideologies in service to fragile psyches is how much knowledge it takes away from students who already have so little

A central goal for history, social-studies, and civics instruction should be to give students something more solid than spoon-fed maxims—to help them engage with the past on its own terms, not use it as a weapon in the latest front of the culture wars.

Releasing them to do “research” in the vast ocean of the internet without maps and compasses, as often happens, guarantees that they will drown before they arrive anywhere.

The truth requires a grounding in historical facts, but facts are quickly forgotten without meaning and context

The goal isn’t just to teach students the origins of the Civil War, but to give them the ability to read closely, think critically, evaluate sources, corroborate accounts, and back up their claims with evidence from original documents.

This kind of instruction, which requires teachers to distinguish between exposure and indoctrination, isn’t easy; it asks them to be more sophisticated professionals than their shabby conditions and pay (median salary: $62,000, less than accountants and transit police) suggest we are willing to support.

To do that, we’ll need to help kids restore at least part of their crushed attention spans.

staring at a screen for hours is a heavy depressant, especially for teenagers.

we’ll look back on the amount of time we let our children spend online with the same horror that we now feel about earlier generations of adults who hooked their kids on smoking.

“It’s not a choice between tech or no tech,” Bill Tally, a researcher with the Education Development Center, told me. “The question is what tech infrastructure best enables the things we care about,” such as deep engagement with instructional materials, teachers, and other students.

The pandemic should have forced us to reassess what really matters in public school; instead, it’s a crisis that we’ve just about wasted.

Like learning to read as historians, learning to sift through the tidal flood of memes for useful, reliable information can emancipate children who have been heedlessly hooked on screens by the adults in their lives

Finally, let’s give children a chance to read books—good books. It’s a strange feature of all the recent pedagogical innovations that they’ve resulted in the gradual disappearance of literature from many classrooms.

The best way to interest young people in literature is to have them read good literature, and not just books that focus with grim piety on the contemporary social and psychological problems of teenagers.

We sell them insultingly short in thinking that they won’t read unless the subject is themselves. Mirrors are ultimately isolating; young readers also need windows, even if the view is unfamiliar, even if it’s disturbing

connection through language to universal human experience and thought is the reward of great literature, a source of empathy and wisdom.

The culture wars, with their atmosphere of resentment, fear, and petty faultfinding, are hostile to the writing and reading of literature.

W. E. B. Du Bois wrote: “Nations reel and stagger on their way; they make hideous mistakes; they commit frightful wrongs; they do great and beautiful things. And shall we not best guide humanity by telling the truth about all this, so far as the truth is ascertainable?”

The classroom has become a half-abandoned battlefield, where grown-ups who claim to be protecting students from the virus, from books, from ideologies and counter-ideologies end up using children to protect themselves and their own entrenched camps.

American democracy can’t afford another generation of adults who don’t know how to talk and listen and think. We owe our COVID-scarred children the means to free themselves from the failures of the past and the present.

Students are leaving as well. Since 2020, nearly 1.5 million children have been removed from public schools to attend private or charter schools or be homeschooled.

“COVID has encouraged poor parents to question the quality of public education. We are seeing diminished numbers of children in our public schools, particularly our urban public schools.” In New York, more than 80,000 children have disappeared from city schools; in Los Angeles, more than 26,000; in Chicago, more than 24,000.

Beitman defines a coincidence as “two events coming together with apparently no causal explanation.” They can be life-changing, like his experience with his father, or comforting, such as when a loved one’s favorite song comes on the radio just when you are missing them most.

Although Beitman has long been fascinated by coincidences, it wasn’t until the end of his academic career that he was able to study them in earnest. (Before then, his research primarily focused on the relationship between chest pain and panic disorder.)

He started by developing the Weird Coincidence Survey in 2006 to assess what types of coincidences are most commonly observed, what personality types are most correlated with noticing them and how most people explain them. About 3,000 people have completed the survey so far.

he has drawn a few conclusions. The most commonly reported coincidences are associated withmass media: A person thinks of an idea and then hears or sees it on TV, the radio or the internet. Thinking of someone and then having that person call unexpectedly is next on the list, followed by being in the right place at the right time to advance one’s work, career or education.

People who describe themselves as spiritual or religious report noticing more meaningful coincidences than those who do not, and people are more likely to experience coincidences when they are in a heightened emotional state — perhaps under stress or grieving.

The most popular explanation among survey respondents for mysterious coincidences: God or fate. The second explanation: randomness. The third is that our minds are connected to one another. The fourth is that our minds are connected to the environment.

“Some say God, some say universe, some say random and I say ‘Yes,’ ” he said. “People want things to be black and white, yes or no, but I say there is mystery.”

He’s particularly interested in what he’s dubbed “simulpathity”: feeling a loved one’s pain at a distance, as he believes he did with his father. Science can’t currently explain how it might occur, but in his books he offers some nontraditional ideas, such as the existence of “the psychosphere,” a kind of mental atmosphere through which information and energy can travel between two people who are emotionally close though physically distant.

In his new book published in September, “Meaningful Coincidences: How and Why Synchronicity and Serendipity Happen,” he shares the story of a young man who intended to end his life by the shore of an isolated lake. While he sat crying in his car, another car pulled up and his brother got out. When the young man asked for an explanation, the brother said he didn’t know why he got in the car, where he was going, or what he would do when he got there. He just knew he needed to get in the car and drive.

David Hand, a British statistician and author of the 2014 book “The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day,” sits at the opposite end of the spectrum from Beitman. He says most coincidences are fairly easy to explain, and he specializes in demystifying even the strangest ones.

“When you look closely at a coincidence, you can often discover the chance of it happening is not as small as you think,” he said. “It’s perhaps not a 1-in-a-billion chance, but in fact a 1-in-a-hundred chance, and yeah, you would expect that would happen quite often.”

the law of truly large numbers. “You take something that has a very small chance of happening and you give it lots and lots and lots of opportunities to happen,” he said. “Then the overall probability becomes big.”

But just because Hand has a mathematical perspective doesn’t mean he finds coincidences boring. “It’s like looking at a rainbow,” he said. “Just because I understand the physics behind it doesn’t make it any the less wonderful.

Paying attention to coincidences, Osman and Johansen say, is an essential part of how humans make sense of the world. We rely constantly on our understanding of cause and effect to survive.

“Coincidences are often associated with something mystical or supernatural, but if you look under the hood, noticing coincidences is what humans do all the time,”

Zeltzer has spent 50 years studying the writings of Carl Jung, the 20th century Swiss psychologist who introduced the modern Western world to the idea of synchronicity. Jung defined synchronicity as “the coincidence in time of two or more causally unrelated events which have the same meaning.”

One of Jung’s most iconic synchronistic stories concerned a patient who he felt had become so stuck in her rationality that it interfered with her ability to understand her psychology and emotional life.

One day, the patient was recounting a dream in which she’d received a golden scarab. Just then, Jung heard a gentle tapping at the window. He opened the window and a scarab-like beetle flew into the room. Jung plucked the insect out of the air and presented it to his patient. “Here is your scarab,” he said.The experience proved therapeutic because it demonstrated to Jung’s patient that the world is not always rational, leading her to break her own identification with rationality and thus become more open to her emotional life, Zeltzer explained

Like Jung, Zeltzer believes meaningful coincidences can encourage people to acknowledge the irrational and mysterious. “We have a fantasy that there is always an answer, and that we should know everything,”

Honestly, I’m not sure what to believe, but I’m not sure it matters. Like Beitman, my attitude is “Yes.”

In 1972, using duct tape and spare parts in the basement on the campus of the University of California, Berkeley, Dr. Clauser and a graduate student, Stuart Freedman, who died in 2012, endeavored to perform Bell’s experiment to measure quantum entanglement. In a series of experiments, he fired thousands of light particles, or photons, in opposite directions to measure a property known as polarization, which could have only two values — up or down. The result for each detector was always a series of seemingly random ups and downs. But when the two detectors’ results were compared, the ups and downs matched in ways that neither “classical physics” nor Einstein’s laws could explain. Something weird was afoot in the universe. Entanglement seemed to be real.

in 2002, Dr. Clauser admitted that he himself had expected quantum mechanics to be wrong and Einstein to be right. “Obviously, we got the ‘wrong’ result. I had no choice but to report what we saw, you know, ‘Here’s the result.’ But it contradicts what I believed in my gut has to be true.” He added, “I hoped we would overthrow quantum mechanics. Everyone else thought, ‘John, you’re totally nuts.’”

the correlations only showed up after the measurements of the individual particles, when the physicists compared their results after the fact. Entanglement seemed real, but it could not be used to communicate information faster than the speed of light.

In 1982, Dr. Aspect and his team at the University of Paris tried to outfox Dr. Clauser’s loophole by switching the direction along which the photons’ polarizations were measured every 10 nanoseconds, while the photons were already in the air and too fast for them to communicate with each other. He too, was expecting Einstein to be right.

Quantum predictions held true, but there were still more possible loopholes in the Bell experiment that Dr. Clauser had identified

For example, the polarization directions in Dr. Aspect’s experiment had been changed in a regular and thus theoretically predictable fashion that could be sensed by the photons or detectors.

Anton Zeilinger

added even more randomness to the Bell experiment, using random number generators to change the direction of the polarization measurements while the entangled particles were in flight.

Once again, quantum mechanics beat Einstein by an overwhelming margin, closing the “locality” loophole.

as scientists have done more experiments with entangled particles, entanglement is accepted as one of main features of quantum mechanics and is being put to work in cryptology, quantum computing and an upcoming “quantum internet

One of its first successes in cryptology is messages sent using entangled pairs, which can send cryptographic keys in a secure manner — any eavesdropping will destroy the entanglement, alerting the receiver that something is wrong.

, with quantum mechanics, just because we can use it, doesn’t mean our ape brains understand it. The pioneering quantum physicist Niels Bohr once said that anyone who didn’t think quantum mechanics was outrageous hadn’t understood what was being said.

In his interview with A.I.P., Dr. Clauser said, “I confess even to this day that I still don’t understand quantum mechanics, and I’m not even sure I really know how to use it all that well. And a lot of this has to do with the fact that I still don’t understand it.”