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You might expect 10 ÷ 5 is the same as 10/5 is the same as 10 over a 5 with a vinculum between them, but each has its own eccentricities. We’ve already noted that ÷ can mean “divide the number on the left by the number on the right” or “divide the expression on the left by the expression on the right.” But it gets really tricky when people assume that a slash replaces a vinculum. Does ab/cd = (ab)÷(cd) or ((ab)÷c)÷d? Does a/b/c mean (a)÷(b)÷(c) or a÷(b/c) or (a/b)÷c? (Answer: Use some parentheses!)

The bottom line is that “order of operations” conventions are not universal truths in the same way that the sum of 2 and 2 is always 4. Conventions evolve throughout history in response to cultural and technological shifts.

There are a number of problems with teaching science as a collection of facts. First, facts change. Before oxygen was discovered, the theoretical existence of phlogiston made sense. For a brief, heady moment in 1989, it looked like cold fusion (paywall) was going to change the world. In the field of medical science, “facts” are even more wobbly. For example, it has been estimated that fewer than 10% of published high profile cancer studies are reproducible (the word “reproducible” here is a euphemism for “not total poppycock”).

when a scientific study ends by stating that there’s uncertainty about whether a correlation proves a cause, it doesn’t mean that correlations are meaningless in every circumstance. Everyone knows that creating false correlations between two unrelated elements is easy. But it can be that a correlation is so powerful and reliable that it may actually point to that rare thing in the social sciences, a demonstrable causal relation. As a wise man once said, “Correlation is not causation, but it sure is a hint.” When you can separate out a truly robust correlation between two elements in our social life, it’s a big deal. What makes a correlation causal? Well, it should be robust, showing up all over the place, across many states and nations; it should exclude some other correlation that might be causing the same thing; and, ideally, there ought to be some kind of proposed mechanism that would explain why one element affects the other. There’s a strong correlation between vaccines and less childhood disease, for instance, and a simple biological mechanism of induced immunity to explain it. The correlation between gun possession and gun violence—or, alternately, between gun control and stopping gun violence—is one of the most robust that you can find.

The human mind is incredibly averse to uncertainty and ambiguity; from an early age, we respond to uncertainty or lack of clarity by spontaneously generating plausible explanations. What’s more, we hold on to these invented explanations as having intrinsic value of their own. Once we have them, we don’t like to let them go.

Heightened need for cognitive closure can bias our choices, change our preferences, and influence our mood. In our rush for definition, we tend to produce fewer hypotheses and search less thoroughly for information. We become more likely to form judgments based on early cues (something known as impressional primacy), and as a result become more prone to anchoring and correspondence biases (using first impressions as anchors for our decisions and not accounting enough for situational variables). And, perversely, we may not even realize how much we are biasing our own judgments.

In 2010, Kruglanski and colleagues looked specifically at the need for cognitive closure as part of the response to terrorism.

There are various ways a corporate name can seem apposite. In the case of existing words, connotations are crucial: a Corvette is a light, speedy attack ship; Tesla was an inventor of genius. Made-up names often rely instead on resonances with other words: Lexus evokes luxurious; Viagra conjures virility and vitality. Bad names bring the wrong associations to consumers’ minds. In the nineteen-eighties, United Airlines tried to turn itself into a diversified travel company called Allegis. The move was a fiasco. No less an authority than Donald Trump (whose faith in brand-name power is total) said that the name sounded “like the next world-class disease.”

No, I’m not skeptical about the idea of universal human rights. I’m skeptical about what I call positive rights.

So I say that you can make a good case for universal human rights of a negative kind, but that you cannot make the comparable case for universal human rights of a positive kind.

As a professor in Berkeley I have certain rights, and certain obligations. But the idea of universal rights—that you have certain rights just in virtue of being a human being—is a fantastic idea. And I think, Why not extend the idea of universal rights to conscious animals? Just in virtue of being a conscious animal, you have certain rights. The fact that animals cannot undertake obligations does not imply that they cannot have rights against us who do have obligations. Babies have rights even before they are able to undertake obligations. Now I have to make a confession. I try not to think about animal rights because I fear I’d have to become a vegetarian if I worked it out consistently. But I think there is a very good case to be made for saying that if you grant the validity of universal human rights, then it looks like it would be some kind of special pleading if you said there’s no such thing as universal animal rights. I think there are animal rights.

The Nonhuman Rights Project is the only organization working toward actual LEGAL rights for members of species other than our own. Our mission is to change the common law status of at least some nonhuman animals from mere “things,” which lack the capacity to possess any legal right, to “persons,” who possess such fundamental rights as bodily integrity and bodily liberty, and those other legal rights to which evolving standards of morality, scientific discovery, and human experience entitle them. Our first cases were filed in 2013.

hortly before the dreadful crash of Germanwings Flight 9525, I happened to be reading part of “The Second Machine Age,” a book by two academics at M.I.T., Erik Brynjolfsson and Andrew McAfee, about the coming automation of many professions previously thought of as impervious to technological change, such as those of drivers, doctors, market researchers, and soldiers. With the advances being made in robotics, data analysis, and artificial intelligence, Brynjolfsson and McAfee argue, we are on the cusp of a third industrial revolution.

An elderly Chinese woman is only able to speak English after suffering a stroke, it's been reported. Liu Jaiyu, a 94-year-old former English teacher, has found herself no longer able to speak Chinese after parts of her brain relating to native language were damaged by a cerebral infarction, the local Hunan TV reports. Television pictures show her in bed, answering simple questions in English, which means the nursing staff are having to brush up on their language skills. "She greets me in the morning using English, after she's eaten her meals in the afternoon she uses English," one nurse tells the TV. "My memory of the language isn't too good, sometimes I don't understand what she's saying!" A doctor at the hospital says that Ms Liu is suffering from paralysis of all her limbs, as well as an "obstacle" to her language functions. "It seems the part of her brain responsible for her mother tongue has been damaged, however the part that uses English has been preserved," Li Yanfang says. There have been rare cases where patients develop a different accent after a stroke, migraine or head trauma. But Ms Liu's case appears different because she has apparently turned to an already-learned language. Experts say that the complex Chinese language requires the use of both parts of the brain, while English only uses one side.

Clinical research can never prove that an intervention has an effect size of zero. Rather, clinical research assumes the null hypothesis, that the treatment does not work, and the burden of proof lies with demonstrating adequate evidence to reject the null hypothesis. So, when being technical, researchers will conclude that a negative study “fails to reject the null hypothesis.” Further, negative studies do not demonstrate an effect size of zero, but rather that any possible effect is likely to be smaller than the power of existing research to detect. The greater the number and power of such studies, however, the closer this remaining possible effect size gets to zero. At some point the remaining possible effect becomes clinically insignificant. In other words, clinical research may not be able to detect the difference between zero effect and a tiny effect, but at some point it becomes irrelevant. What David and I have convincingly argued, in my opinion, is that after decades of research and more than 3000 trials, acupuncture researchers have failed to reject the null hypothesis, and any remaining possible specific effect from acupuncture is so tiny as to be clinically insignificant.

It is clear from meta-analyses that results of acupuncture trials are variable and inconsistent, even for single conditions. After thousands of trials of acupuncture and hundreds of systematic reviews,18 arguments continue unabated. In 2011,Pain published an editorial31 that summed up the present situation well. “Is there really any need for more studies? Ernst et al.18 point out that the positive studies conclude that acupuncture relieves pain in some conditions but not in other very similar conditions. What would you think if a new pain pill was shown to relieve musculoskeletal pain in the arms but not in the legs? The most parsimonious explanation is that the positive studies are false positives. In his seminal article on why most published research findings are false, Ioannidis32 points out that when a popular but ineffective treatment is studied, false positive results are common for multiple reasons, including bias and low prior probability.” Since it has proved impossible to find consistent evidence after more than 3000 trials, it is time to give up. It seems very unlikely that the money that it would cost to do another 3000 trials would be well-spent.

One of the problems is that no narrative feature is going to be able to convey the absolute truth. Characters inevitably get conflated and information omitted.“I think if you have two hours to tell a story, you have to contract things, you have to make your point in ways that a documentary would make them differently,” says David Oyelowo, the British actor who portrays Martin Luther King Jr.

From Amie I first heard about Yitang Zhang, a solitary, part-time calculus teacher at the University of New Hampshire who received several prizes, including a MacArthur award in September, for solving a problem that had been open for more than a hundred and fifty years. The problem that Zhang chose, in 2010, is from number theory, a branch of pure mathematics. Pure mathematics, as opposed to applied mathematics, is done with no practical purposes in mind. It is as close to art and philosophy as it is to engineering. “My result is useless for industry,” Zhang said. The British mathematician G. H. Hardy wrote in 1940 that mathematics is, of “all the arts and sciences, the most austere and the most remote.” Bertrand Russell called it a refuge from “the dreary exile of the actual world.” Hardy believed emphatically in the precise aesthetics of math. A mathematical proof, such as Zhang produced, “should resemble a simple and clear-cut constellation,” he wrote, “not a scattered cluster in the Milky Way.” Edward Frenkel, a math professor at the University of California, Berkeley, says Zhang’s proof has “a renaissance beauty,” meaning that though it is deeply complex, its outlines are easily apprehended. The pursuit of beauty in pure mathematics is a tenet. Last year, neuroscientists in Great Britain discovered that the same part of the brain that is activated by art and music was activated in the brains of mathematicians when they looked at math they regarded as beautiful.

Last month marked six years since the start of the Syrian war, which has forced millions of people to flee their homes in one of the largest humanitarian crises in modern history. Perhaps the artist who has most visibly used his work to draw attention to the conflict is Ai Weiwei, whose political activism has earned him a reputation as China’s foremost creative dissident. Ai has made works focused on the refugee crisis for years, but lately his projects have taken on a greater sense of urgency. His newest exhibit, Law of the Journey, was recently unveiled at the National Gallery in Prague and features a massive inflatable lifeboat with 258 faceless, rubber figures on board—evoking the treacherous journey some refugees make to Europe.

Last month marked six years since the start of the Syrian war, which has forced millions of people to flee their homes in one of the largest humanitarian crises in modern history. Perhaps the artist who has most visibly used his work to draw attention to the conflict is Ai Weiwei, whose political activism has earned him a reputation as China’s foremost creative dissident. Ai has made works focused on the refugee crisis for years, but lately his projects have taken on a greater sense of urgency. His newest exhibit, Law of the Journey, was recently unveiled at the National Gallery in Prague and features a massive inflatable lifeboat with 258 faceless, rubber figures on board—evoking the treacherous journey some refugees make to Europe. Earlier this week, the Public Art Fund announced Ai would build more than 100 fence-themed installations in New York across multiple boroughs, asking the city’s inhabitants to reflect on the ideas of barriers, nationhood, and security.

Polls show a gradual improvement in perceptions of Stalin, who led the Soviet Union from the late 1920s until his death in 1953. A survey released on March 1 by the Levada Center, a research organization based in Moscow, found that 40 percent of Russians thought the Stalin era brought “more good than bad,” up from 27 percent in 2012. In an annual Levada survey published in January 2015, a majority of Russians (52 percent) said Stalin “probably” or “definitely” played a positive role in the country.