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If replication is what separates the rigor of science from the squishiness of pseudoscience, where do we put all these rigorously validated findings that can no longer be proved? Which results should we believe?

Schooler demonstrated that subjects shown a face and asked to describe it were much less likely to recognize the face when shown it later than those who had simply looked at it. Schooler called the phenomenon “verbal overshadowing.”

The most likely explanation for the decline is an obvious one: regression to the mean. As the experiment is repeated, that is, an early statistical fluke gets cancelled out. The extrasensory powers of Schooler’s subjects didn’t decline—they were simply an illusion that vanished over time.

yet Schooler has noticed that many of the data sets that end up declining seem statistically solid—that is, they contain enough data that any regression to the mean shouldn’t be dramatic. “These are the results that pass all the tests,” he says. “The odds of them being random are typically quite remote, like one in a million. This means that the decline effect should almost never happen. But it happens all the time!

this is why Schooler believes that the decline effect deserves more attention: its ubiquity seems to violate the laws of statistics

In 2001, Michael Jennions, a biologist at the Australian National University, set out to analyze “temporal trends” across a wide range of subjects in ecology and evolutionary biology. He looked at hundreds of papers and forty-four meta-analyses (that is, statistical syntheses of related studies), and discovered a consistent decline effect over time, as many of the theories seemed to fade into irrelevance.

Jennions admits that his findings are troubling, but expresses a reluctance to talk about them

publicly. “This is a very sensitive issue for scientists,” he says. “You know, we’re supposed to be dealing with hard facts, the stuff that’s supposed to stand the test of time. But when you see these trends you become a little more skeptical of things.”

While publication bias almost certainly plays a role in the decline effect, it remains an incomplete explanation. For one thing, it fails to account for the initial prevalence of positive results among studies that never even get submitted to journals. It also fails to explain the experience of people like Schooler, who have been unable to replicate their initial data despite their best efforts.

Jennions, similarly, argues that the decline effect is largely a product of publication bias, or the tendency of scientists and scientific journals to prefer positive data over null results, which is what happens when no effect is found. The bias was first identified by the statistician Theodore Sterling, in 1959, after he noticed that ninety-seven per cent of all published psychological studies with statistically significant data found the effect they were looking for

Sterling saw that if ninety-seven per cent of psychology studies were proving their hypotheses, either psychologists were extraordinarily lucky or they published only the outcomes of successful experiments.

One of his most cited papers has a deliberately provocative title: “Why Most Published Research Findings Are False.”

suspects that an equally significant issue is the selective reporting of results—the data that scientists choose to document in the first place. Palmer’s most convincing evidence relies on a statistical tool known as a funnel graph. When a large number of studies have been done on a single subject, the data should follow a pattern: studies with a large sample size should all cluster around a common value—the true result—whereas those with a smaller sample size should exhibit a random scattering, since they’re subject to greater sampling error. This pattern gives the graph its name, since the distribution resembles a funnel.

after Palmer plotted every study of fluctuating asymmetry, he noticed that the distribution of results with smaller sample sizes wasn’t random at all but instead skewed heavily toward positive results. Palmer has since documented a similar problem in several other contested subject areas. “Once I realized that selective reporting is everywhere in science, I got quite depressed,” Palmer told me. “As a researcher, you’re always aware that there might be some nonrandom patterns, but I had no idea how widespread it is.”

Palmer summarized the impact of selective reporting on his field: “We cannot escape the troubling conclusion that some—perhaps many—cherished generalities are at best exaggerated in their biological significance and at worst a collective illusion nurtured by strong a-priori beliefs often repeated.”

Palmer emphasizes that selective reporting is not the same as scientific fraud. Rather, the problem seems to be one of subtle omissions and unconscious misperceptions, as researchers struggle to make sense of their results. Stephen Jay Gould referred to this as the “sho

horning” process.

“A lot of scientific measurement is really hard,” Simmons told me. “If you’re talking about fluctuating asymmetry, then it’s a matter of minuscule differences between the right and left sides of an animal. It’s millimetres of a tail feather. And so maybe a researcher knows that he’s measuring a good male”—an animal that has successfully mated—“and he knows that it’s supposed to be symmetrical. Well, that act of measurement is going to be vulnerable to all sorts of perception biases. That’s not a cynical statement. That’s just the way human beings work.”

For Simmons, the steep rise and slow fall of fluctuating asymmetry is a clear example of a scientific paradigm, one of those intellectual fads that both guide and constrain research: after a new paradigm is proposed, the peer-review process is tilted toward positive results. But then, after a few years, the academic incentives shift—the paradigm has become entrenched—so that the most notable results are now those that disprove the theory.

John Ioannidis, an epidemiologist at Stanford University, argues that such distortions are a serious issue in biomedical research. “These exaggerations are why the decline has become so common,” he says. “It’d be really great if the initial studies gave us an accurate summary of things. But they don’t. And so what happens is we waste a lot of money treating millions of patients and doing lots of follow-up studies on other themes based on results that are misleading.”

In 2005, Ioannidis published an article in the Journal of the American Medical Association that looked at the forty-nine most cited clinical-research studies in three major medical journals.

the data Ioannidis found were disturbing: of the thirty-four claims that had been subject to replication, forty-one per cent had either been directly contradicted or had their effect sizes significantly downgraded.

the most troubling fact emerged when he looked at the test of replication: out of four hundred and thirty-two claims, only a single one was consistently replicable. “This doesn’t mean that none of these claims will turn out to be true,” he says. “But, given that most of them were done badly, I wouldn’t hold my breath.”

According to Ioannidis, the main problem is that too many researchers engage in what he calls “significance chasing,” or finding ways to interpret the data so that it passes the statistical test of significance—the ninety-five-per-cent boundary invented by Ronald Fisher.

One of the classic examples of selective reporting concerns the testing of acupuncture in different countries. While acupuncture is widely accepted as a medical treatment in various Asian countries, its use is much more contested in the West. These cultural differences have profoundly influenced the results of clinical trials.

The problem of selective reporting is rooted in a fundamental cognitive flaw, which is that we like proving ourselves right and hate being wrong.

“It feels good to validate a hypothesis,” Ioannidis said. “It feels even better when you’ve got a financial interest in the idea or your career depends upon it. And that’s why, even after a claim has been systematically disproven”—he cites, for instance, the early work on hormone replacement therapy, or claims involving various vitamins—“you still see some stubborn researchers citing the first few studies

That’s why Schooler argues that scientists need to become more rigorous about data collection before they publish. “We’re wasting too much time chasing after bad studies and underpowered experiments,”

The current “obsession” with replicability distracts from the real problem, which is faulty design.

“Every researcher should have to spell out, in advance, how many subjects they’re going to use, and what exactly they’re testing, and what constitutes a sufficient level of proof. We have the tools to be much more transparent about our experiments.”

Schooler recommends the establishment of an open-source database, in which researchers are required to outline their planned investigations and document all their results. “I think this would provide a huge increase in access to scientific work and give us a much better way to judge the quality of an experiment,”

scientific research will always be shadowed by a force that can’t be curbed, only contained: sheer randomness. Although little research has been done on the experimental dangers of chance and happenstance, the research that exists isn’t encouraging.

The disturbing implication of the Crabbe study is that a lot of extraordinary scientific data are nothing but noise. The hyperactivity of those coked-up Edmonton mice wasn’t an interesting new fact—it was a meaningless outlier, a by-product of invisible variables we don’t understand.

The problem, of course, is that such dramatic findings are also the most likely to get published in prestigious journals, since the data are both statistically significant and entirely unexpected

This suggests that the decline effect is actually a decline of illusion. While Karl Popper imagined falsification occurring with a single, definitive experiment—Galileo refuted Aristotelian mechanics in an afternoon—the process turns out to be much messier than that.

Many scientific theories continue to be considered true even after failing numerous experimental tests.

Even the law of gravity hasn’t always been perfect at predicting real-world phenomena. (In one test, physicists measuring gravity by means of deep boreholes in the Nevada desert found a two-and-a-half-per-cent discrepancy between the theoretical predictions and the actual data.)

Such anomalies demonstrate the slipperiness of empiricism. Although many scientific ideas generate conflicting results and suffer from falling effect sizes, they continue to get cited in the textbooks and drive standard medical practice. Why? Because these ideas seem true. Because they make sense. Because we can’t bear to let them go. And this is why the decline effect is so troubling. Not because it reveals the human fallibility of science, in which data are tweaked and beliefs shape perceptions. (Such shortcomings aren’t surprising, at least for scientists.) And not because it reveals that many of our most exciting theories are fleeting fads and will soon be rejected. (That idea has been around since Thomas Kuhn.)

The decline effect is troubling because it reminds us how difficult it is to prove anything. We like to pretend that our experiments define the truth for us. But that’s often not the case. Just because an idea is true doesn’t mean it can be proved. And just because an idea can be proved doesn’t mean it’s true. When the experiments are done, we still have to choose what to believe. ♦

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This methodology involves one party proving it has information it claims is true and a second party that wants to verify that the first party's information is indeed true. With a zero-knowledge proof system, the proving party does not transmit any secretive information that could substantiate whether what it claims is true.

– SearchSecurity

A zero-knowledge proof requires no real knowledge or secret information to prove the claim.

Zero-knowledge proofs are used in modern cybersecurity in situations where one system claims to possess sensitive data yet does not want to transmit that data to prove it to another system.

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.

“The studies were biased,” he says. “Sometimes they were overtly biased. Sometimes it was difficult to see the bias, but it was there.” Researchers headed into their studies wanting certain results—and, lo and behold, they were getting them. We think of the scientific process as being objective, rigorous, and even ruthless in separating out what is true from what we merely wish to be true, but in fact it’s easy to manipulate results, even unintentionally or unconsciously. “At every step in the process, there is room to distort results, a way to make a stronger claim or to select what is going to be concluded,” says Ioannidis. “There is an intellectual conflict of interest that pressures researchers to find whatever it is that is most likely to get them funded.”

Ioannidis laid out a detailed mathematical proof that, assuming modest levels of researcher bias, typically imperfect research techniques, and the well-known tendency to focus on exciting rather than highly plausible theories, researchers will come up with wrong findings most of the time.

if you’re attracted to ideas that have a good chance of being wrong, and if you’re motivated to prove them right, and if you have a little wiggle room in how you assemble the evidence, you’ll probably succeed in proving wrong theories right. His model predicted, in different fields of medical research, rates of wrongness roughly corresponding to the observed rates at which findings were later convincingly refuted: 80 percent of non-randomized studies (by far the most common type) turn out to be wrong, as do 25 percent of supposedly gold-standard randomized trials, and as much as 10 percent of the platinum-standard large randomized trials.

He zoomed in on 49 of the most highly regarded research findings in medicine over the previous 13 years, as judged by the science community’s two standard measures: the papers had appeared in the journals most widely cited in research articles, and the 49 articles themselves were the most widely cited articles in these journals

Ioannidis was putting his contentions to the test not against run-of-the-mill research, or even merely well-accepted research, but against the absolute tip of the research pyramid. Of the 49 articles, 45 claimed to have uncovered effective interventions. Thirty-four of these claims had been retested, and 14 of these, or 41 percent, had been convincingly shown to be wrong or significantly exaggerated. If between a third and a half of the most acclaimed research in medicine was proving untrustworthy, the scope and impact of the problem were undeniable.

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.”

Since the 1960s, advances in resuscitation had helped to revive thousands of people who might otherwise have died. About 10% or 20% of those people brought with them stories of near-death experiences in which they felt their souls or selves departing from their bodies

According to several international surveys and studies, one in 10 people claims to have had a near-death experience involving cardiac arrest, or a similar experience in circumstances where they may have come close to death. That’s roughly 800 million souls worldwide who may have dipped a toe in the afterlife.

In the 1970s, a small network of cardiologists, psychiatrists, medical sociologists and social psychologists in North America and Europe began investigating whether near-death experiences proved that dying is not the end of being, and that consciousness can exist independently of the brain. The field of near-death studies was born.

in 1975, an American medical student named Raymond Moody published a book called Life After Life.

Meanwhile, new technologies and techniques were helping doctors revive more and more people who, in earlier periods of history, would have almost certainly been permanently deceased.

“We are now at the point where we have both the tools and the means to scientifically answer the age-old question: What happens when we die?” wrote Sam Parnia, an accomplished resuscitation specialist and one of the world’s leading experts on near-death experiences, in 2006. Parnia himself was devising an international study to test whether patients could have conscious awareness even after they were found clinically dead.

Borjigin, together with several colleagues, took the first close look at the record of electrical activity in the brain of Patient One after she was taken off life support. What they discovered – in results reported for the first time last year – was almost entirely unexpected, and has the potential to rewrite our understanding of death.

“I believe what we found is only the tip of a vast iceberg,” Borjigin told me. “What’s still beneath the surface is a full account of how dying actually takes place. Because there’s something happening in there, in the brain, that makes no sense.”

Over the next 30 years, researchers collected thousands of case reports of people who had had near-death experiences

Moody was their most important spokesman; he eventually claimed to have had multiple past lives and built a “psychomanteum” in rural Alabama where people could attempt to summon the spirits of the dead by gazing into a dimly lit mirror.

near-death studies was already splitting into several schools of belief, whose tensions continue to this day. One influential camp was made up of spiritualists, some of them evangelical Christians, who were convinced that near-death experiences were genuine sojourns in the land of the dead and divine

It is no longer unheard of for people to be revived even six hours after being declared clinically dead. In 2011, Japanese doctors reported the case of a young woman who was found in a forest one morning after an overdose stopped her heart the previous night; using advanced technology to circulate blood and oxygen through her body, the doctors were able to revive her more than six hours later, and she was able to walk out of the hospital after three weeks of care

The second, and largest, faction of near-death researchers were the parapsychologists, those interested in phenomena that seemed to undermine the scientific orthodoxy that the mind could not exist independently of the brain. These researchers, who were by and large trained scientists following well established research methods, tended to believe that near-death experiences offered evidence that consciousness could persist after the death of the individua

Their aim was to find ways to test their theories of consciousness empirically, and to turn near-death studies into a legitimate scientific endeavour.

Finally, there emerged the smallest contingent of near-death researchers, who could be labelled the physicalists. These were scientists, many of whom studied the brain, who were committed to a strictly biological account of near-death experiences. Like dreams, the physicalists argued, near-death experiences might reveal psychological truths, but they did so through hallucinatory fictions that emerged from the workings of the body and the brain.

Between 1975, when Moody published Life After Life, and 1984, only 17 articles in the PubMed database of scientific publications mentioned near-death experiences. In the following decade, there were 62. In the most recent 10-year span, there were 221.

Today, there is a widespread sense throughout the community of near-death researchers that we are on the verge of great discoveries

“We really are in a crucial moment where we have to disentangle consciousness from responsiveness, and maybe question every state that we consider unconscious,”

“I think in 50 or 100 years time we will have discovered the entity that is consciousness,” he told me. “It will be taken for granted that it wasn’t produced by the brain, and it doesn’t die when you die.”

it is in large part because of a revolution in our ability to resuscitate people who have suffered cardiac arrest

In his book, Moody distilled the reports of 150 people who had had intense, life-altering experiences in the moments surrounding a cardiac arrest. Although the reports varied, he found that they often shared one or more common features or themes. The narrative arc of the most detailed of those reports – departing the body and travelling through a long tunnel, having an out-of-body experience, encountering spirits and a being of light, one’s whole life flashing before one’s eyes, and returning to the body from some outer limit – became so canonical that the art critic Robert Hughes could refer to it years later as “the familiar kitsch of near-death experience”.

Loss of oxygen to the brain and other organs generally follows within seconds or minutes, although the complete cessation of activity in the heart and brain – which is often called “flatlining” or, in the case of the latter, “brain death” – may not occur for many minutes or even hours.

That began to change in 1960, when the combination of mouth-to-mouth ventilation, chest compressions and external defibrillation known as cardiopulmonary resuscitation, or CPR, was formalised. Shortly thereafter, a massive campaign was launched to educate clinicians and the public on CPR’s basic techniques, and soon people were being revived in previously unthinkable, if still modest, numbers.

scientists learned that, even in its acute final stages, death is not a point, but a process. After cardiac arrest, blood and oxygen stop circulating through the body, cells begin to break down, and normal electrical activity in the brain gets disrupted. But the organs don’t fail irreversibly right away, and the brain doesn’t necessarily cease functioning altogether. There is often still the possibility of a return to life. In some cases, cell death can be stopped or significantly slowed, the heart can be restarted, and brain function can be restored. In other words, the process of death can be reversed.

In a medical setting, “clinical death” is said to occur at the moment the heart stops pumping blood, and the pulse stops. This is widely known as cardiac arrest

In 2019, a British woman named Audrey Schoeman who was caught in a snowstorm spent six hours in cardiac arrest before doctors brought her back to life with no evident brain damage.

That is a key tenet of the parapsychologists’ arguments: if there is consciousness without brain activity, then consciousness must dwell somewhere beyond the brain

Some of the parapsychologists speculate that it is a “non-local” force that pervades the universe, like electromagnetism. This force is received by the brain, but is not generated by it, the way a television receives a broadcast.

In order for this argument to hold, something else has to be true: near-death experiences have to happen during death, after the brain shuts down

To prove this, parapsychologists point to a number of rare but astounding cases known as “veridical” near-death experiences, in which patients seem to report details from the operating room that they might have known only if they had conscious awareness during the time that they were clinically dead.

At the very least, Parnia and his colleagues have written, such phenomena are “inexplicable through current neuroscientific models”. Unfortunately for the parapsychologists, however, none of the reports of post-death awareness holds up to strict scientific scrutiny. “There are many claims of this kind, but in my long decades of research into out-of-body and near-death experiences I never met any convincing evidence that this is true,”

In other cases, there’s not enough evidence to prove that the experiences reported by cardiac arrest survivors happened when their brains were shut down, as opposed to in the period before or after they supposedly “flatlined”. “So far, there is no sufficiently rigorous, convincing empirical evidence that people can observe their surroundings during a near-death experience,”

The parapsychologists tend to push back by arguing that even if each of the cases of veridical near-death experiences leaves room for scientific doubt, surely the accumulation of dozens of these reports must count for something. But that argument can be turned on its head: if there are so many genuine instances of consciousness surviving death, then why should it have so far proven impossible to catch one empirically?

The spiritualists and parapsychologists are right to insist that something deeply weird is happening to people when they die, but they are wrong to assume it is happening in the next life rather than this one. At least, that is the implication of what Jimo Borjigin found when she investigated the case of Patient One.

Given the levels of activity and connectivity in particular regions of her dying brain, Borjigin believes it’s likely that Patient One had a profound near-death experience with many of its major features: out-of-body sensations, visions of light, feelings of joy or serenity, and moral re-evaluations of one’s life. Of course,

“As she died, Patient One’s brain was functioning in a kind of hyperdrive,” Borjigin told me. For about two minutes after her oxygen was cut off, there was an intense synchronisation of her brain waves, a state associated with many cognitive functions, including heightened attention and memory. The synchronisation dampened for about 18 seconds, then intensified again for more than four minutes. It faded for a minute, then came back for a third time.

n those same periods of dying, different parts of Patient One’s brain were suddenly in close communication with each other. The most intense connections started immediately after her oxygen stopped, and lasted for nearly four minutes. There was another burst of connectivity more than five minutes and 20 seconds after she was taken off life support. In particular, areas of her brain associated with processing conscious experience – areas that are active when we move through the waking world, and when we have vivid dreams – were communicating with those involved in memory formation. So were parts of the brain associated with empathy. Even as she slipped irre

something that looked astonishingly like life was taking place over several minutes in Patient One’s brain.

Although a few earlier instances of brain waves had been reported in dying human brains, nothing as detailed and complex as what occurred in Patient One had ever been detected.

In the moments after Patient One was taken off oxygen, there was a surge of activity in her dying brain. Areas that had been nearly silent while she was on life support suddenly thrummed with high-frequency electrical signals called gamma waves. In particular, the parts of the brain that scientists consider a “hot zone” for consciousness became dramatically alive. In one section, the signals remained detectable for more than six minutes. In another, they were 11 to 12 times higher than they had been before Patient One’s ventilator was removed.

“The brain, contrary to everybody’s belief, is actually super active during cardiac arrest,” Borjigin said. Death may be far more alive than we ever thought possible.

“The brain is so resilient, the heart is so resilient, that it takes years of abuse to kill them,” she pointed out. “Why then, without oxygen, can a perfectly healthy person die within 30 minutes, irreversibly?”

Evidence is already emerging that even total brain death may someday be reversible. In 2019, scientists at Yale University harvested the brains of pigs that had been decapitated in a commercial slaughterhouse four hours earlier. Then they perfused the brains for six hours with a special cocktail of drugs and synthetic blood. Astoundingly, some of the cells in the brains began to show metabolic activity again, and some of the synapses even began firing.

ways of working are critical in mathematical work and when they are taught and valued, many more students contribute, leading to higher achievement

mathematics education we suffer from the widespread, distinctly American idea that only some people can be “math people.” This idea has been disproved by scientific research showing the incredible potential of the brain to grow and adapt. But the idea that math is hard, uninteresting, and accessible only to “nerds” persists. 

harsh stereotypical thinking—mathematics is for select racial groups and men. This thinking, as well as the teaching practices that go with it, have provided the perfect conditions for the creation of a math underclass.

online platform explaining research evidence on ability and the brain and on good mathematics teaching, for teachers and parents. The course had a transformative effect. It was taken by 40,000 people, and 95 percent said they would change their teaching or parenting as a result.

does not simply test a mathematical definition, as the first does. It requires that students visualize a triangle, use transformational geometry, consider whether different cases satisfy the mathematical definition, and then justify their thinking.

There is a good reason for this: Justification and reasoning are two of the acts that lie at the heart of mathematics. They are, in many ways, the essence of what mathematics is.  Scientists work to prove or disprove new theories by finding many cases that work or counter-examples that do not. Mathematicians, by contrast prove the validity of their propositions through justification and reasoning.

The young people who are successful in today’s workforce are those who can discuss and reason about productive mathematical pathways, and who can be wrong, but can trace back to errors and work to correct them.

American idea that those who are good at math are those who are fast. Speed is revered in math classes across the U.S., and students as young as five years old are given timed tests—even though these have been shown to create math anxiety in young children. Parents use flash cards and other devices to promote speed, not knowing that they are probably damaging their children’s mathematical development

The fact of being quick or slow isn't really relevant

gives more time for depth and exploration than the curricula it has replaced by removing some of the redundant methods students will never need or use.

I thought that the best places simply did a better job at controlling and minimizing risks—that they did a better job of preventing things from going wrong. But, to my surprise, they didn’t. Their complication rates after surgery were almost the same as others. Instead, what they proved to be really great at was rescuing people when they had a complication, preventing failures from becoming a catastrophe.

this is what distinguished the great from the mediocre. They didn’t fail less. They rescued more.

This may in fact be the real story of human and societal improvement. We talk a lot about “risk management”—a nice hygienic phrase. But in the end, risk is necessary. Things can and will go wrong. Yet some have a better capacity to prepare for the possibility, to limit the damage, and to sometimes even retrieve success from failure.

When things go wrong, there seem to be three main pitfalls to avoid, three ways to fail to rescue. You could choose a wrong plan, an inadequate plan, or no plan at all. Say you’re cooking and you inadvertently set a grease pan on fire. Throwing gasoline on the fire would be a completely wrong plan. Trying to blow the fire out would be inadequate. And ignoring it—“Fire? What fire?”—would be no plan at all.

All policies court failure—our war in Iraq, for instance, or the effort to stimulate our struggling economy. But when you refuse to even acknowledge that things aren’t going as expected, failure can become a humanitarian disaster. The sooner you’re able to see clearly that your best hopes and intentions have gone awry, the better. You have more room to pivot and adjust. You have more of a chance to rescue.

But recognizing that your expectations are proving wrong—accepting that you need a new plan—is commonly the hardest thing to do. We have this problem called confidence. To take a risk, you must have confidence in yourself

Yet you cannot blind yourself to failure, either. Indeed, you must prepare for it. For, strangely enough, only then is success possible.

So you will take risks, and you will have failures. But it’s what happens afterward that is defining. A failure often does not have to be a failure at all. However, you have to be ready for it—will you admit when things go wrong? Will you take steps to set them right?—because the difference between triumph and defeat, you’ll find, isn’t about willingness to take risks. It’s about mastery of rescue.

“Since my debut on television in 1979, I have been an eyewitness to the many changes in technology, society, and how we communicate. I am one who embraces change, and celebrates the higher quality of life we enjoy now thanks to this progress.

I realize the instant communication platforms we enjoy now do have some negatives that are troubling. Just a few examples in recent days…”

“This is a lenticular cloud. They have always been around, and quite frankly aren’t that unusual (although it is an anomaly to see one away from a mountain range). The one thing that is different today is that almost everyone has a camera phone, and almost everyone shares pictures of weather events. You didn’t see these often in earlier decades because technology didn’t allow it. Lenticular clouds are nothing new. But, yes, they are cool to see.”

This age of misinformation can lead to dangerous consequences, and promote an agenda, he warns.

“The Houston flooding is a great example. We are being told this is unprecedented’… Houston is ‘under water… and it is due to manmade global warming. “Yes, the flooding in Houston yesterday was severe, and a serious threat to life and property. A genuine weather disaster that has brought on suffering.

this was not ‘unprecedented.’ Flooding from Tropical Storm Allison in 2001 was more widespread, and flood waters were deeper. There is no comparison.”

“Those on the right, and those on the left hang out in ‘echo chambers,’ listening to those with similar world views refusing to believe anything else could be true

“Everyone knows the climate is changing; it always has, and always will. I do not know of a single ‘climate denier.’ I am still waiting to meet one.

“The debate involves the anthropogenic impact, and this is not why I am writing this piece. Let’s just say the Houston flood this week is weather, and not climate, and leave it at that.”

Spann lays much of the blame on the mainstream media and social media “hype and misinformation.”

“They will be sure to let you know that weather events they are reporting on are unprecedented,’ there are ‘millions and millions in the path,’ it is caused by a ‘monster storm,’ and ‘the worst is yet to come since these events are becoming more ‘frequent.’

“You will never hear about the low tornado count in recent years, the lack of major hurricane landfalls on U.S. coasts over the past 10 years, or the low number of wildfires this year. It doesn’t fit their story.

never let facts get in the way of a good story…. there will ALWAYS be a heat wave, flood, wildfire, tornado, tyhpoon, cold wave, and snow storm somewhere. And, trust me, they will find them, and it will probably lead their newscasts

“At one point, my supervisor was so concerned that he suggested that I wear my belt backward so that a rapist would have more difficulty pulling down my pants.

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

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

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

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

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

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

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

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

angst and sadness promote “information-processing strategies best suited to dealing with more-demanding situations.” This helps explain why test subjects who are melancholy — Forgas induces the mood with a short film about death and cancer — are better at judging the accuracy of rumors and recalling past events; they’re also much less likely to stereotype strangers and make fewer arithmetic mistakes.

shoppers in the “low mood” condition remembered nearly four times as many of the trinkets. The wet weather made them sad, and their sadness made them more aware and attentive.

There are two important lessons of this research. The first is that our fleeting feelings can change the way we think. While sadness makes us more focused and diligent — the spotlight of attention is sharpened — happiness seems to have the opposite effect, so that good moods make us 20 percent more likely to have a moment of insight. The second takeaway is that many of our creative challenges involve tasks that require diligence, persistence and focus. It’s not easy making a collage or writing a poem or solving a hard technical problem, which is why sometimes being a little miserable can improve our creative performance.

Why is mental illness so closely associated with creativity? Andreasen argues that depression is intertwined with a “cognitive style” that makes people more likely to produce successful works of art. In the creative process, Andreasen says, “one of the most important qualities is persistence.”

While Andreasen acknowledges the burden of mental illness — she quotes Robert Lowell on depression not being a “gift of the Muse” and describes his reliance on lithium to escape the pain — she argues that many forms of creativity benefit from the relentless focus it makes possible. “Unfortunately, this type of thinking is often inseparable from the suffering,” she says. “If you’re at the cutting edge, then you’re going to bleed.”

Western Governors is entirely online, for one thing. Technically it doesn't offer courses; instead it provides mentors who help students prepare for a series of high-stakes homework assignments. Those assignments are designed by a team of professional test-makers to prove competence in various subject areas. The idea is that as long as students can leap all of those hurdles, they deserve degrees, whether or not they've ever entered a classroom, watched a lecture video, or participated in any other traditional teaching experience. The model is called "competency-based education."

Ms. Johnson explains that Western Governors essentially splits the role of the traditional professor into two jobs. Instructional duties fall to a group the university calls "course mentors," who help students master material. The graders, or evaluators, step in once the homework is filed, with the mind-set of, "OK, the teaching's done, now our job is to find out how much you know," says Ms. Johnson. They log on to a Web site called TaskStream and pluck the first assignment they see. The institution promises that every assignment will be graded within two days of submission.

Western Governors requires all evaluators to hold at least a master's degree in the subject they're grading.

Evaluators are required to write extensive comments on each task, explaining why the student passed or failed to prove competence in the requisite skill. No letter grades are given—students either pass or fail each task.

Another selling point is the software's fast response rate. It can grade a batch of 1,000 essay tests in minutes. Professors can set the software to return the grade immediately and can give students the option of making revisions and resubmitting their work on the spot.

All evaluators initially receive a month of training, conducted online, about how to follow each task's grading guidelines, which lay out characteristics of a passing score.

Other evaluators want to push talented students to do more than the university's requirements for a task, or to allow a struggling student to pass if he or she is just under the bar. "Some people just can't acclimate to a competency-based environment," says Ms. Johnson. "I tell them, If they don't buy this, they need to not be here.

She and some teaching assistants scored the tests by hand and compared their performance with the computer's.

The graduate students became fatigued and made mistakes after grading several tests in a row, she told me, "but the machine was right-on every time."

He argues that students like the idea that their tests are being evaluated in a consistent way.

The graders must regularly participate in "calibration exercises," in which they grade a simulated assignment to make sure they are all scoring consistently. As the phrase suggests, the process is designed to run like a well-oiled machine.

He said once students get essays back instantly, they start to view essay tests differently. "It's almost like a big math problem. You don't expect to get everything right the first time, but you work through it.

robot grading is the hottest trend in testing circles, says Jacqueline Leighton, a professor of educational psychology at the University of Alberta who edits the journal Educational Measurement: Issues and Practice. Companies building essay-grading robots include the Educational Testing Service, which sells e-rater, and Pearson Education, which makes Intelligent Essay Assessor. "The research is promising, but they're still very much in their infancy," Ms. Leighton says.

It is a dance Republican candidates often do when they hedge their answers about whether evolution should be taught in schools. It is what makes the fight over global warming such a liability for their party, and what led last year to a widely criticized response to the Ebola scare.

There is evidence that vaccinations have become more of a political issue in recent years. Pew Research Center polls show that in 2009, 71 percent of both Republicans and Democrats favored requiring the vaccination of children. Five years later, Democratic support had grown to 76 percent, but Republican support had fallen to 65 percent.

The debate does not break entirely along right-left lines. The movement to forgo vaccinations has been popular in more liberal and affluent communities where some parents are worried that vaccines cause autism or other disorders among children.

Howard Dean, a presidential candidate in 2004 and a former chairman of the Democratic National Committee, said there are three groups of people who object to required vaccines: “One is people who are very much scared about their kids getting autism, which is an idea that has been completely discredited. Two, is entitled people who don’t want to put any poison in their kids and view this as poison, which is ignorance more than anything else. And three, people who are antigovernment in any way.”

The issue has more political potency among conservative voters who are highly skeptical of anything required by the government.

for Republicans like Mr. Paul who appeal to the kind of libertarian conservatives who are influential in states like Iowa and New Hampshire, which hold the first two contests in the battle for the nomination, there is an appeal in framing the issue as one of individual liberty.Asked about immunizations again later on Monday, Mr. Paul was even more insistent, saying it was a question of “freedom.” He grew irritated with a CNBC host who pressed him and snapped: “The state doesn’t own your children. Parents own the children.”