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An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. This is known as the einstein problem.

black and white squares also can make weird nonperiodic patterns, in addition to the familiar, periodic checkerboard pattern. “It’s really pretty trivial to be able to make weird and interesting patterns,” he said. The magic of the two Penrose tiles is that they make only nonperiodic patterns — that’s all they can do.“But then the Holy Grail was, could you do with one — one tile?” Dr. Goodman-Strauss said.

now a new paper — by Mr. Smith and three co-authors with mathematical and computational expertise — proves Mr. Smith’s discovery true. The researchers called their einstein “the hat,

“The most significant aspect for me is that the tiling does not clearly fall into any of the familiar classes of structures that we understand.”

“I’m always messing about and experimenting with shapes,” said Mr. Smith, 64, who worked as a printing technician, among other jobs, and retired early. Although he enjoyed math in high school, he didn’t excel at it, he said. But he has long been “obsessively intrigued” by the einstein problem.

Sir Roger found the proofs “very complicated.” Nonetheless, he was “extremely intrigued” by the einstein, he said: “It’s a really good shape, strikingly simple.”

The simplicity came honestly. Mr. Smith’s investigations were mostly by hand; one of his co-authors described him as an “imaginative tinkerer.”

When in November he found a tile that seemed to fill the plane without a repeating pattern, he emailed Craig Kaplan, a co-author and a computer scientist at the University of Waterloo.

“It was clear that something unusual was happening with this shape,” Dr. Kaplan said. Taking a computational approach that built on previous research, his algorithm generated larger and larger swaths of hat tiles. “There didn’t seem to be any limit to how large a blob of tiles the software could construct,”

The first step, Dr. Kaplan said, was to “define a set of four ‘metatiles,’ simple shapes that stand in for small groupings of one, two, or four hats.” The metatiles assemble into four larger shapes that behave similarly. This assembly, from metatiles to supertiles to supersupertiles, ad infinitum, covered “larger and larger mathematical ‘floors’ with copies of the hat,” Dr. Kaplan said. “We then show that this sort of hierarchical assembly is essentially the only way to tile the plane with hats, which turns out to be enough to show that it can never tile periodically.”

some might wonder whether this is a two-tile, not one-tile, set of aperiodic monotiles.

Dr. Goodman-Strauss had raised this subtlety on a tiling listserv: “Is there one hat or two?” The consensus was that a monotile counts as such even using its reflection. That leaves an open question, Dr. Berger said: Is there an einstein that will do the job without reflection?

“the hat” was not a new geometric invention. It is a polykite — it consists of eight kites. (Take a hexagon and draw three lines, connecting the center of each side to the center of its opposite side; the six shapes that result are kites.)

“It’s likely that others have contemplated this hat shape in the past, just not in a context where they proceeded to investigate its tiling properties,” Dr. Kaplan said. “I like to think that it was hiding in plain sight.”

Incredibly, Mr. Smith later found a second einstein. He called it “the turtle” — a polykite made of not eight kites but 10. It was “uncanny,” Dr. Kaplan said. He recalled feeling panicked; he was already “neck deep in the hat.”

Dr. Myers, who had done similar computations, promptly discovered a profound connection between the hat and the turtle. And he discerned that, in fact, there was an entire family of related einsteins — a continuous, uncountable infinity of shapes that morph one to the next.

this einstein family motivated the second proof, which offers a new tool for proving aperiodicity. The math seemed “too good to be true,” Dr. Myers said in an email. “I wasn’t expecting such a different approach to proving aperiodicity — but everything seemed to hold together as I wrote up the details.”

Mr. Smith was amazed to see the research paper come together. “I was no help, to be honest.” He appreciated the illustrations, he said: “I’m more of a pictures person.”

For Francis Bacon and the other early Scientific Revolutionaries, this was a fair price to pay for doing divine work – God, after all, was thought to be himself transcendent and perhaps even alienated from nature. But without this theistic assumption, it becomes difficult to justify the unfettered pursuit of science, once both the costs and benefits are each given their due. Of course, we could simply say that science is what turns humans into gods. For all its hubris, this response would at least possess the virtues of candor and consistency. As it stands, scientists shy away from any such strong self-understandings, preferring to hide behind more passive accounts of their activities – e.g. they ‘describe’ rather than generate phenomena, they ‘explain’ rather than justify nature, etc. Lost in this secular translation of an originally sacred mission is the scientist’s sense of personal responsibility qua scientist.

Rather than thinking of science as a “force for good”, we should think of it as an inherent human activity, like com

merce.

This means that, even under the best circumstances, scientists can’t directly test what the results of a given gun policy are. The best you can do is to compare what was happening in a state before and after a policy was enacted, or to compare two different states, one that has the policy and one that doesn’t. And that’s a pretty inexact way of working.

Add in enough assumptions, and you can eventually come up with an estimate. But is the estimate correct? Is it even close to reality? That’s a hard question to answer, because the assumptions you made—the correlations you drew between cause and effect, what you know and what you assume to be true because of that—might be totally wrong.

It’s hard to tease apart the effect of one specific change, compared to the effects of other things that could be happening at the same time.

This process of taking the observational data we do have and then running it through a filter of assumptions plays out in the real world in the form of statistical modeling. When the NAS report says that nobody yet knows whether more guns lead to more crime, or less crime, what they mean is that the models and the assumptions built into those models are all still proving to be pretty weak.

From either side of the debate, he said, scientists continue to produce wildly different conclusions using the same data. On either side, small shifts in the assumptions lead the models to produce different results. Both factions continue to choose sets of assumptions that aren’t terribly logical. It’s as if you decided that anybody with blue shoes probably had a belly-button piercing. There’s not really a good reason for making that correlation. And if you change the assumption—actually, belly-button piercings are more common in people who wear green shoes—you end up with completely different results.

The Intergovernmental Panel on Climate Change (IPCC) produces these big reports periodically, which analyze lots of individual papers. In essence, they’re looking at lots of trees and trying to paint you a picture of the forest. IPCC reports are available for free online, you can go and read them yourself. When you do, you’ll notice something interesting about the way that the reports present results. The IPCC never says, “Because we burned fossil fuels and emitted carbon dioxide into the atmosphere then the Earth will warm by x degrees.” Instead, those reports present a range of possible outcomes … for everything. Depending on the different models used, different scenarios presented, and the different assumptions made, the temperature of the Earth might increase by anywhere between 1.5 and 4.5 degrees Celsius.

What you’re left with is an environment where it’s really easy to prove that your colleague’s results are probably wrong, and it’s easy for him to prove that yours are probably wrong. But it’s not easy for either of you to make a compelling case for why you’re right.

Statistical modeling isn’t unique to gun research. It just happens to be particularly messy in this field. Scientists who study other topics have done a better job of using stronger assumptions and of building models that can’t be upended by changing one small, seemingly randomly chosen detail. It’s not that, in these other fields, there’s only one model being used, or even that all the different models produce the exact same results. But the models are stronger and, more importantly, the scientists do a better job of presenting the differences between models and drawing meaning from them.

“Climate change is one of the rare scientific literatures that has actually faced up to this,” Charles Manski said. What he means is that, when scientists model climate change, they don’t expect to produce exact, to-the-decimal-point answers.

“It’s been a complete waste of time, because we can’t validate one model versus another,” Pepper said. Most likely, he thinks that all of them are wrong. For instance, all the models he’s seen assume that a law will affect every state in the same way, and every person within that state in the same way. “But if you think about it, that’s just nonsensical,” he said.

On the one hand, that leaves politicians in a bit of a lurch. The response you might mount to counteract a 1.5 degree increase in global average temperature is pretty different from the response you’d have to 4.5 degrees. On the other hand, the range does tell us something valuable: the temperature is increasing.

The problem with this is that it flies in the face of what most of us expect science to do for public policy. Politics is inherently biased, right? The solutions that people come up with are driven by their ideologies. Science is supposed to cut that Gordian Knot. It’s supposed to lay the evidence down on the table and impartially determine who is right and who is wrong.

Manski and Pepper say that this is where we need to rethink what we expect science to do. Science, they say, isn’t here to stop all political debate in its tracks. In a situation like this, it simply can’t provide a detailed enough answer to do that—not unless you’re comfortable with detailed answers that are easily called into question and disproven by somebody else with a detailed answer.

Instead, science can reliably produce a range of possible outcomes, but it’s still up to the politicians (and, by extension, up to us) to hash out compromises between wildly differing values on controversial subjects. When it comes to complex social issues like gun ownership and gun violence, science doesn’t mean you get to blow off your political opponents and stake a claim on truth. Chances are, the closest we can get to the truth is a range that encompasses the beliefs of many different groups.

Similarly, the stereotype that women are weaker drivers may negatively affect their performance behind the wheel.

Because of this disconnect between perception and reality, visual illusions demonstrate the ways in which the brain can fail to re-create the physical world.

While she says her parents are not overbearing, she relishes their praise for performing well. “Hearing my parents talk about me in a positive way, or hearing other parents talk about their kids doing well in academics or extracurriculars, that’s where I got some of the expectations for myself,” she said. “It was like self-fulfillment: I’d feel fulfilled and happy when other people were happy with what I’m doing, or expectations they have are met.”

Getting a B can cause some students to fall apart, she said. “What you and I would call disappointments in life, to them feel like big failures.”

a shift in how some young adults cope with challenges. “A small setback used to mean disappointment, or having that feeling of needing to try harder next time,” he said. Now? “For some students, a mistake has incredible meaning.”

When students remark during a counseling session that everyone else on campus looks happy, he tells them: “I walk around and think, ‘That one’s gone to the hospital. That person has an eating disorder. That student just went on antidepressants.’ As a therapist, I know that nobody is as happy or as grown-up as they seem on the outside.”

In the era of social media, such comparisons take place on a screen with carefully curated depictions that don’t provide the full picture. Mobile devices escalate the comparisons from occasional to nearly constant.

The existential question “Why am I here?” is usually followed by the equally confounding “How am I doing?” In 1954, the social psychologist Leon Festinger put forward the social comparison theory, which posits that we try to determine our worth based on how we stack up against others.

Madison Holleran’s suicide provided what might be the ultimate contrast between a shiny Instagram feed and interior darkness. Ms. Holleran posted images that show her smiling, dappled in sunshine or kicking back at a party. But according to her older sister, Ashley, Madison judged her social life as inferior to what she saw in the online posts of her high school friends

These cultural dynamics of perfectionism and overindulgence have now combined to create adolescents who are ultra-focused on success but don’t know how to fail.

Julie Lythcott-Haims watched the collision of these two social forces up close. In meetings with students, she would ask what she considered simple questions and they would become paralyzed, unable to express their desires and often discovering midconversation that they were on a path that they didn’t even like.

“They could say what they’d accomplished, but they couldn’t necessarily say who they were,”

She was also troubled by the growing number of parents who not only stayed in near-constant cellphone contact with their offspring but also showed up to help them enroll in classes, contacted professors and met with advisers (illustrating the progression from helicopter to lawn mower parents, who go beyond hovering to clear obstacles out of their child’s way). But what she found most disconcerting was that students, instead of being embarrassed, felt grateful. Penn researchers studying friendship have found that students’ best friends aren’t classmates or romantic partners, but parents.

Eventually she came to view her students’ lack of self-awareness, inability to make choices and difficulty coping with setbacks as a form of “existential impotence,” a direct result of a well-meaning but misguided approach to parenting that focuses too heavily on external measures of character.

“The Drama of the Gifted Child: The Search for the True Self.” In the book, published in 1979 and translated into 30 languages, Ms. Miller documents how some especially intelligent and sensitive children can become so attuned to parents’ expectations that they do whatever it takes to fulfill those expectations — at the expense of their own feelings and needs. This can lead to emotional emptiness and isolation

“In what is described as depression and experienced as emptiness, futility, fear of impoverishment, and loneliness,” she wrote, “can usually be recognized as the tragic loss of the self in childhood.”

Economies dominated by hedge financing—that is, those with strong cashflows and low debt levels—are the most stable. When speculative and, especially, Ponzi financing come to the fore, financial systems are more vulnerable. If asset values start to fall, either because of monetary tightening or some external shock, the most overstretched firms will be forced to sell their positions. This further undermines asset values, causing pain for even more firms. They could avoid this trouble by restricting themselves to hedge financing. But over time, particularly when the economy is in fine fettle, the temptation to take on debt is irresistible. When growth looks assured, why not borrow more? Banks add to the dynamic, lowering their credit standards the longer booms last. If defaults are minimal, why not lend more? Minsky’s conclusion was unsettling. Economic stability breeds instability. Periods of prosperity give way to financial fragility.

Minsky’s insight might sound obvious. Of course, debt and finance matter. But for decades the study of economics paid little heed to the former and relegated the latter to a sub-discipline, not an essential element in broader theories.

Minsky was a maverick. He challenged both the Keynesian backbone of macroeconomics and a prevailing belief in efficient markets.

t Messrs Hicks and Hansen largely left the financial sector out of the picture, even though Keynes was keenly aware of the importance of markets. To Minsky, this was an “unfair and naive representation of Keynes’s subtle and sophisticated views”. Minsky’s financial-instability hypothesis helped fill in the holes.

His challenge to the prophets of efficient markets was even more acute. Eugene Fama and Robert Lucas, among others, persuaded most of academia and policymaking circles that markets tended towards equilibrium as people digested all available information. The structure of the financial system was treated as almost irrelevant

In recent years, behavioural economists have attacked one plank of efficient-market theory: people, far from being rational actors who maximise their gains, are often clueless about what they want and make the wrong decisions.

But years earlier Minsky had attacked another: deep-seated forces in financial systems propel them towards trouble, he argued, with stability only ever a fleeting illusion.

Investors were faster than professors to latch onto his views. More than anyone else it was Paul McCulley of PIMCO, a fund-management group, who popularised his ideas. He coined the term “Minsky moment” to describe a situation when debt levels reach breaking-point and asset prices across the board start plunging. Mr McCulley initially used the term in explaining the Russian financial crisis of 1998. Since the global turmoil of 2008, it has become ubiquitous. For investment analysts and fund managers, a “Minsky moment” is now virtually synonymous with a financial crisis.

it would be a stretch to expect the financial-instability hypothesis to become a new foundation for economic theory. Minsky’s legacy has more to do with focusing on the right things than correctly structuring quantifiable models. It is enough to observe that debt and financial instability, his main preoccupations, have become some of the principal topics of inquiry for economists today

As Mr Krugman has quipped: “We are all Minskyites now.”

Just as the loss of a species decreases the richness of an ecosystem, the addition of new animals could achieve the opposite effect.

National Geographic Society hosted a larger conference to debate the scientific and ethical questions raised by the prospect of “de-extinction.

“De-extinction went from concept to potential reality right before our eyes,

“This may be the biggest attraction and possibly the biggest benefit of de-extinction. It would surely be very cool to see a living woolly mammoth.”

less scientific, if more persuasive, argument was advanced by the ethicist Hank Greely and the law professor Jacob Sherkow, both of Stanford. De-extinction should be pursued, they argued in a paper published in Science, because it would be really

They will replace chunks of band-tailed-pigeon DNA with synthesized chunks of passenger-pigeon DNA, until the cell’s genome matches their working passenger-pigeon genome.

Scientists predict that changes made by human beings to the composition of the atmosphere could kill off a quarter of the planet’s mammal species, a fifth of its reptiles and a sixth of its birds by 2050

This cloning method, called somatic cell nuclear transfer, can be used only on species for which we have cellular material.

There is a shortcut. The genome of a closely related species will have a high proportion of identical DNA, so it can serve as a blueprint, or “scaffold.”

By comparing the fragments of passenger-pigeon DNA with the genomes of similar species, researchers can assemble an approximation of an actual passenger-pigeon genome.

“We’ve framed it in terms of conservation,”

the genome will have to be inscribed into a living cell.

As with any translation, there may be errors of grammar, clumsy phrases and perhaps a few missing passages, but the book will be legible. It should, at least, tell a good story.

MAGE (Multiplex Automated Genome Engineering). MAGE is nicknamed the “evolution machine” because it can introduce the equivalent of millions of years of genetic mutations within minutes

Developmental and behavioral biologists would take over, just in time to answer some difficult questions. Chicks imitate their parents’ behavior. How do you raise a passenger pigeon without parents of its own species? And how do you train band-tailed pigeons to nurture the strange spawn that emerge from their eggs; chicks that, to them, might seem monstrous: an avian Rosemary’s Baby?

For endangered species with tiny populations, scientists would introduce genetic diversity to offset inbreeding.

They will try to alter the birds’ diets, migration habits and environment. The behavior of each subsequent generation will more closely resemble that of their genetic cousins.

“There’s always this fear that somehow, if we do it, we’re going to accidentally make something horrible, because only nature can really do it right. But nature is totally random. Nature makes monsters. Nature makes threats. Many of the things that are most threatening to us are a product of nature. Revive & Restore is not going to tip the balance in any way.”

For species threatened by contagion, an effort would be made to fortify their DNA with genes that make them disease-resistant

This optimistic, soft-focus fantasy of de-extinction, while thrilling to Ben Novak, is disturbing to many conservation biologists, who consider it a threat to their entire discipline and even to the environmental movement.

The first question posed by conservationists addresses the logic of bringing back an animal whose native habitat has disappeared. Why go through all the trouble just to have the animal go extinct all over again?

There is also anxiety about disease

“If you recreate a species genetically and release it, and that genotype is based on a bird from a 100-year-old environment, you probably will increase risk.”

The scientific term for this type of genetic intervention is “facilitated adaptation.”

De-extinction also poses a rhetorical threat to conservation biologists. The specter of extinction has been the conservation movement’s most powerful argument. What if extinction begins to be seen as a temporary inconvenience?

De-extinction suggests that we can technofix our way out of environmental issues generally, and that’s very, very bad.

How will we decide which species to resurrect?

Philip Seddon recently published a 10-point checklist to determine the suitability of any species for revival, taking into account causes of its extinction, possible threats it might face upon resurrection and man’s ability to destroy the species “in the event of unacceptable ecological or socioeconomic impacts.”

But the most visceral argument against de-extinction is animal cruelty.

“Is it fair to do this to these animals?” Shapiro asked. “Is ‘because we feel guilty’ a good-enough reason?” Stewart Brand made a utilitarian counterargument: “We’re going to go through some suffering, because you try a lot of times, and you get ones that don’t take. On the other hand, if you can bring bucardos back, then how many would get to live that would not have gotten to live?”

In “How to Permit Your Mammoth,” published in The Stanford Environmental Law Journal, Norman F. Carlin asks whether revived species should be protected by the Endangered Species Act or regulated as a genetically modified organism.

He concludes that revived species, “as products of human ingenuity,” should be eligible for patenting.

The term “de-extinction” is misleading. Passenger pigeons will not rise from the grave

Our understanding of the passenger pigeon’s behavior derives entirely from historical accounts.

There is no authoritative definition of “species.” The most widely accepted definition describes a group of organisms that can procreate with one another and produce fertile offspring, but there are many exceptions.

Theseus’ ship, therefore, “became a standing example among the philosophers . . . one side holding that the ship remained the same, and the other contending that it was not the same.”

What is coming will go well beyond the resurrection of extinct species. For millenniums, we have customized our environment, our vegetables and our animals, through breeding, fertilization and pollination. Synthetic biology offers far more sophisticated tools. The creation of novel organisms, like new animals, plants and bacteria, will transform human medicine, agriculture, energy production and much else.

Not surprisingly, the perception of financial security is a big deal for online Juliets. In one study, Ariely and his colleagues calculated that a man who's 5'9" must outearn a 5'10" suitor by at least $35,000 a year just to be seen as equally attractive.

Noether’s theorem shows that a symmetry of time — like the fact that whether you throw a ball in the air tomorrow or make the same toss next week will have no effect on the ball’s trajectory — is directly related to the conservation of energy, our old homily that energy can be neither created nor destroyed but merely changes form.

Increasingly, I’ve found myself retreating to smaller groups, where the stakes are lower and people are more honest and less determined to prove a point, freer to joke and experiment, more trusting in one other and open to real conversation.

Twitter is starting to feel calcified, slowed down by the weight of its own users, cumbersome, less exciting than exhausting. It may be why less public forms of communication — messaging applications like Snapchat, GroupMe, Instagram Direct and even old-fashioned e-mail threads and Google groups — are playing a bigger and bigger role in the most meaningful interactions during my day online.

even if the company were to snap to attention and give its community something other than Twitter lists and block or unfollow buttons to help users tailor their feeds, it most likely wouldn’t be enough. We, the users, the producers, the consumers — all our manic energy, yearning to be noticed, recognized for an important contribution to the conversation — are the problem. It is fueled by our own increasing need for attention, validation, through likes, favorites, responses, interactions. It is a feedback loop that can’t be closed, at least not for now.

But there's another reason as well: Every time computers break some new barrier, we decide—or maybe just finally get it through our thick skulls—that we set the bar too low.

the best estimates of the human brain suggest that our own processing power is about equivalent to 10 petaflops. ("Peta" comes after giga and tera.) That's a lot of flops, but last year an IBM Blue Gene/Q supercomputer at Lawrence Livermore National Laboratory was clocked at 16.3 petaflops.

in Lake Michigan terms, we finally have a few inches of water in the lake bed, and we can see it rising. All those milestones along the way—playing chess, translating web pages, winning at Jeopardy!, driving a car—aren't just stunts. They're precisely the kinds of things you'd expect as we struggle along with platforms that aren't quite powerful enough—yet. True artificial intelligence will very likely be here within a couple of decades. Making it small, cheap, and ubiquitous might take a decade more.

In other words, by about 2040 our robot paradise awaits.

“Educational investment will not be attractive to those without unique skills,” she said. Graduates, she noted, need to earn a return on their investment in training: “But instead they will lose jobs, replaced by information simulation. They will stay uneducated.” In such a scenario, high-salary jobs would remain for those equipped with problem-solving skills, she predicted. But many common tasks now done by college graduates might vanish.

Over the next 10 to 20 years, “10 percent to 20 percent pushed out of work by A.I. will be a catastrophe,” she says. “I can’t begin to think what 50 percent would mean — way beyond a catastrophe and such numbers can’t be ruled out if A.I. performs well in the future.”

A recent study published by the Program on the Impacts of Future Technology, at Oxford University’s Oxford Martin School, predicted that nearly half of all jobs in the United States could be replaced by computers over the next two decades.

Smart machines will give companies “the opportunity to automate many tasks, redesign jobs, and do things never before possible even with the best human work forces,” according to a report this year by the business consulting firm McKinsey.

Advances in speech recognition, translation and pattern recognition threaten employment in the service sectors — call centers, marketing and sales — precisely the sectors that provide most jobs in developed economies.

Gartner’s 2013 chief executive survey, published in April, found that 60 percent of executives surveyed dismissed as “‘futurist fantasy” the possibility that smart machines could displace many white-collar employees within 15 years.

Kenneth Brant, research director at Gartner, told a conference in October: “Job destruction will happen at a faster pace, with machine-driven job elimination overwhelming the market’s ability to create valuable new ones.”

Optimists say this could lead to the ultimate elimination of work — an “Athens without the slaves” — and a possible boom for less vocational-style education. Mr. Brant’s hope is that such disruption might lead to a system where individuals are paid a citizen stipend and be free for education and self-realization. “This optimistic scenario I call Homo Ludens, or ‘Man, the Player,’ because maybe we will not be the smartest thing on the planet after all,” he said. “Maybe our destiny is to create the smartest thing on the planet and use it to follow a course of self-actualization.”

The results were similarly disturbing when students were tested to determine understanding of basic concepts. More instruction wasn't helping students advance from novice to expert. In fact, the data indicated the opposite: students had more novice-like beliefs after they completed a course than they had when they started.

But in addition, experts have a mental organizational structure that facilitates the retrieval and effective application of their knowledge.

experts have an ability to monitor their own thinking ("metacognition"), at least in their discipline of expertise. They are able to ask themselves, "Do I understand this? How can I check my understanding?"

But that is not what cognitive science tells us. It tells us instead that students need to develop these different ways of thinking by means of extended, focused mental effort.

new ways of thinking are always built on the prior thinking of the individual, so if the educational process is to be successful, it is essential to take that prior thinking into account.

. Everything that constitutes "understanding" science and "thinking scientifically" resides in the long-term memory, which is developed via the construction and assembly of component proteins.

What is elementary, worldly wisdom? Well, the first rule is that you can't really know anything if you just remember isolated facts and try and bang 'em back. If the facts don't hang together on a latticework of theory, you don't have them in a usable form.

"So it makes perfect sense," Wieman writes, "that they are not learning to think like experts, even though they are passing science courses by memorizing facts and problem-solving recipes."

Anything one can do to reduce cognitive load improves learning.

A second way teachers can improve instruction is by recognizing the importance of student beliefs about science

My third example of how teaching and learning can be improved is by implementing the principle that effective teaching consists of engaging students, monitoring their thinking, and providing feedback.

I assign students to groups the first day of class (typically three to four students in adjacent seats) and design each lecture around a series of seven to 10 clicker questions that cover the key learning goals for that day.

The process of critiquing each other's ideas in order to arrive at a consensus also enormously improves both their ability to carry on scientific discourse and to test their own understanding. [Change]

Puett puts a fresh spin on the questions that Chinese scholars grappled with centuries ago. He requires his students to closely read original texts (in translation) such as Confucius’s Analects, the Mencius, and the Daodejing and then actively put the teachings into practice in their daily lives. His lectures use Chinese thought in the context of contemporary American life to help 18- and 19-year-olds who are struggling to find their place in the world figure out how to be good human beings; how to create a good society; how to have a flourishing life. 

Puett began offering his course to introduce his students not just to a completely different cultural worldview but also to a different set of tools. He told me he is seeing more students who are “feeling pushed onto a very specific path towards very concrete career goals”

Puett tells his students that being calculating and rationally deciding on plans is precisely the wrong way to make any sort of important life decision. The Chinese philosophers they are reading would say that this strategy makes it harder to remain open to other possibilities that don’t fit into that plan.

Students who do this “are not paying enough attention to the daily things that actually invigorate and inspire them, out of which could come a really fulfilling, exciting life,” he explains. If what excites a student is not the same as what he has decided is best for him, he becomes trapped on a misguided path, slated to begin an unfulfilling career.

He teaches them that:   The smallest actions have the most profound ramifications. 

From a Chinese philosophical point of view, these small daily experiences provide us endless opportunities to understand ourselves. When we notice and understand what makes us tick, react, feel joyful or angry, we develop a better sense of who we are that helps us when approaching new situations. Mencius, a late Confucian thinker (4th century B.C.E.), taught that if you cultivate your better nature in these small ways, you can become an extraordinary person with an incredible influence

Decisions are made from the heart. Americans tend to believe that humans are rational creatures who make decisions logically, using our brains. But in Chinese, the word for “mind” and “heart” are the same.

If the body leads, the mind will follow. Behaving kindly (even when you are not feeling kindly), or smiling at someone (even if you aren’t feeling particularly friendly at the moment) can cause actual differences in how you end up feeling and behaving, even ultimately changing the outcome of a situation.

In the same way that one deliberately practices the piano in order to eventually play it effortlessly, through our everyday activities we train ourselves to become more open to experiences and phenomena so that eventually the right responses and decisions come spontaneously, without angst, from the heart-mind.

Whenever we make decisions, from the prosaic to the profound (what to make for dinner; which courses to take next semester; what career path to follow; whom to marry), we will make better ones when we intuit how to integrate heart and mind and let our rational and emotional sides blend into one. 

Aristotle said, “We are what we repeatedly do,” a view shared by thinkers such as Confucius, who taught that the importance of rituals lies in how they inculcate a certain sensibility in a person.

“The Chinese philosophers we read taught that the way to really change lives for the better is from a very mundane level, changing the way people experience and respond to the world, so what I try to do is to hit them at that level. I’m not trying to give my students really big advice about what to do with their lives. I just want to give them a sense of what they can do daily to transform how they live.”

Their assignments are small ones: to first observe how they feel when they smile at a stranger, hold open a door for someone, engage in a hobby. He asks them to take note of what happens next: how every action, gesture, or word dramatically affects how others respond to them. Then Puett asks them to pursue more of the activities that they notice arouse positive, excited feelings.

Once they’ve understood themselves better and discovered what they love to do they can then work to become adept at those activities through ample practice and self-cultivation. Self-cultivation is related to another classical Chinese concept: that effort is what counts the most, more than talent or aptitude. We aren’t limited to our innate talents; we all have enormous potential to expand our abilities if we cultivate them

To be interconnected, focus on mundane, everyday practices, and understand that great things begin with the very smallest of acts are radical ideas for young people living in a society that pressures them to think big and achieve individual excellence.

One of Puett’s former students, Adam Mitchell, was a math and science whiz who went to Harvard intending to major in economics. At Harvard specifically and in society in general, he told me, “we’re expected to think of our future in this rational way: to add up the pros and cons and then make a decision. That leads you down the road of ‘Stick with what you’re good at’”—a road with little risk but little reward.

after his introduction to Chinese philosophy during his sophomore year, he realized this wasn’t the only way to think about the future. Instead, he tried courses he was drawn to but wasn’t naturally adroit at because he had learned how much value lies in working hard to become better at what you love. He became more aware of the way he was affected by those around him, and how they were affected by his own actions in turn. Mitchell threw himself into foreign language learning, feels his relationships have deepened, and is today working towards a master’s degree in regional studies.

“I can happily say that Professor Puett lived up to his promise, that the course did in fact change my life.”

But it's another example of this mountain of studies that suggest that the social context in the social world changes our behavior even when we're not aware of it.

The study, in other words, isn’t about how much see level rise happens this century, but whether this century’s emissions bank enough carbon for total ice melt down—or some less drastic version. “Our analysis really looks at a 2000 year envelope,” says Strauss.

Under the ice, Greenland and Antarctica are uncharted territories. In order to calculate the rate at which those massive ice sheets slough off, Levermann says he would need to know more about the texture of the underlying rock.