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Who decides what constitutes “proof”? Can “proof” come only from experiments? If so, we’re in trouble, because we can never do an experiment in humans for any exposure that is suspected to be harmful.

The problem is that as new data come along, what was once proven can become unproven again by new expert panels who now consider this new evidence and come to a different conclusion. This leads to the perhaps uncomfortable definition of “proof” as “a consensus of experts.”

The point of emphasis is that there is no hard formula on how to consider the evidence; it is a group decision by a panel of experts (the scientific jury) in which sometimes the epidemiological evidence is so strong that it doesn’t matter whether mice get cancer or not. And sometimes the epidemiology is insufficient to render a verdict on causation and so the toxicology becomes important in making the decision.

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.

The reason typos get through isn’t because we’re stupid or careless, it’s because what we’re doing is actually very smart, explains psychologist Tom Stafford, who studies typos of the University of Sheffield in the UK. “

As with all high level tasks, your brain generalizes simple, component parts (like turning letters into words and words into sentences) so it can focus on more complex tasks (like combining sentences into complex ideas). “We don’t catch every detail, we’re not like computers or NSA databases,” said Stafford. “Rather, we take in sensory information and combine it with what we expect, and we extract meaning.”

Unfortunately, that kind of instinctual feedback doesn’t exist in the editing process. When you’re proof reading, you are trying to trick your brain into pretending that it’s reading the thing for the first time. Stafford suggests that if you want to catch your own errors, you should try to make your work as unfamiliar as possible. Change the font or background color, or print it out and edit by hand. “Once you’ve learned something in a particular way, it’s hard to see the details without changing the visual form,” he said.

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.

A 19th-century French impressionist artist who perished almost a century ago is the world’s leading aesthetic terrorist; you just don’t know it.Fortunately, the Renoir Sucks at Painting (RSAP) movement is here to change that.

t the core of RSAP’s serious political critiques are Eurocentric aesthetics and beauty standards and the domination of art museums by white men. “If the problems with Eurocentricity were personified in a man, Renoir would be the disgusting” embodiment, Geller insisted.Geller did not mince words: “Renoir is the most pulsating, puss-ridden boil which is the most blatant essence of the problem,” he added.“The fact that this utter charlatan can get by the watchmen defending the high altar of art is the proof positive that the system is broken, and that, for far too long, these decisions have been made by people who have access to fancy art educations and pursue them with an eye toward dictating taste,” Geller explained.

Lifetime readers know that reading literature can be transformative, but they can’t prove it. If they tried, they would have to buck the metric prejudice, the American notion that assertions unsupported with statistics are virtually meaningless. What they know about literature and its effects is literally and spiritually immeasurable. They would have to buck common marketplace wisdom, too: in an economy demanding “skill sets”—defined narrowly as technical and business skills—that deep-reading stuff won’t get you anywhere.

Zimbardo’s standard narrative of the Stanford prison experiment offers the prisoners’ emotional responses as proof of how powerfully affected they were by the guards’ mistreatment. The shock of real imprisonment provides a simpler and far less groundbreaking explanation. It may also have had legal implications, should prisoners have thought to pursue them. Korpi told me that the greatest regret of his life was failing to sue Zimbardo.