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It seems we may all be vulnerable to moral illusions the ethical equivalent of the bending lines that trick the eye on cereal boxes and in psychology textbooks. Illusions are a favorite tool of perception scientists for exposing the workings of the five senses, and of philosophers for shaking people out of the naïve belief that our minds give us a transparent window onto the world (since if our eyes can be fooled by an illusion, why should we trust them at other times?). Today, a new field is using illusions to unmask a sixth sense, the moral sense.

The first hallmark of moralization is that the rules it invokes are felt to be universal. Prohibitions of rape and murder, for example, are felt not to be matters of local custom but to be universally and objectively warranted. One can easily say, “I don’t like brussels sprouts, but I don’t care if you eat them,” but no one would say, “I don’t like killing, but I don’t care if you murder someone.”The other hallmark is that people feel that those who commit immoral acts deserve to be punished.

Until recently, it was understood that some people didn’t enjoy smoking or avoided it because it was hazardous to their health. But with the discovery of the harmful effects of secondhand smoke, smoking is now treated as immoral. Smokers are ostracized; images of people smoking are censored; and entities touched by smoke are felt to be contaminated (so hotels have not only nonsmoking rooms but nonsmoking floors). The desire for retribution has been visited on tobacco companies, who have been slapped with staggering “punitive damages.” At the same time, many behaviors have been amoralized, switched from moral failings to lifestyle choices.

“Two things fill the mind with ever new and increasing admiration and awe, the oftener and more steadily we reflect on them,” wrote Immanuel Kant, “the starry heavens above and the moral law within.” These days, the moral law within is being viewed with increasing awe, if not always admiration. The human moral sense turns out to be an organ of considerable complexity, with quirks that reflect its evolutionary history and its neurobiological foundations. These quirks are bound to have implications for the human predicament. Morality is not just any old topic in psychology but close to our conception of the meaning of life. Moral goodness is what gives each of us the sense that we are worthy human beings. We seek it in our friends and mates, nurture it in our children, advance it in our politics and justify it with our religions. A disrespect for morality is blamed for everyday sins and history’s worst atrocities. To carry this weight, the concept of morality would have to be bigger than any of us and outside all of us. So dissecting moral intuitions is no small matter. If morality is a mere trick of the brain, some may fear, our very grounds for being moral could be eroded. Yet as we shall see, the science of the moral sense can instead be seen as a way to strengthen those grounds, by clarifying what morality is and how it should steer our actions.

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 ‘‘-phobic’’ suffix has emerged as the activist’s most trusted term of art for pinning prejudice on an opponent. There’s ‘‘xenophobic,’’ ‘‘homophobic,’’ ‘‘Islamophobic,’’ ‘‘transphobic,’’ ‘‘fatphobic’’ and ‘‘whorephobic’’: Any blowhard who spews bigotry against a marginalized group — or any journalist who pens an article perceived as insufficiently sensitive — risks being called out for an irrational anxiety over one Other or another. When did this particular diagnosis become such a powerful weapon in the identity wars?

It’s an intuitive claim, but also a profound one. It asserts that the benefits of bilingualism extend well beyond the realm of language, and into skills that we use in every aspect of our lives. This view is now widespread, heralded by a large community of scientists, promoted in books and magazines, and pushed by advocacy organizations.

Five years ago, Google — one of the most public proselytizers of how studying workers can transform productivity — became focused on building the perfect team. In the last decade, the tech giant has spent untold millions of dollars measuring nearly every aspect of its employees’ lives. Google’s People Operations department has scrutinized everything from how frequently particular people eat together (the most productive employees tend to build larger networks by rotating dining companions) to which traits the best managers share (unsurprisingly, good communication and avoiding micromanaging is critical; more shocking, this was news to many Google managers).The company’s top executives long believed that building the best teams meant combining the best people. They embraced other bits of conventional wisdom as well, like ‘‘It’s better to put introverts together,’’ said Abeer Dubey, a manager in Google’s People Analytics division, or ‘‘Teams are more effective when everyone is friends away from work.’’ But, Dubey went on, ‘‘it turned out no one had really studied which of those were true.’’In 2012, the company embarked on an initiative — code-named Project Aristotle — to study hundreds of Google’s teams and figure out why some stumbled while others soared.

‘“What if?” is a waste of time’ went the headline to the Cambridge historian Richard Evans’ piece in The Guardian last year. Surveying the many instances of public counterfactual discourse in the anniversary commemorations of the First World War, Evans wrote: ‘This kind of fantasising is now all the rage, and threatens to overwhelm our perceptions of what really happened in the past, pushing aside our attempts to explain it in favour of a futile and misguided attempt to decide whether the decisions taken in August 1914 were right or wrong.’

But hold on a minute.

If well-done counterfactuals can help us think them through, shouldn’t we allow what-ifs some space at the history table?

MORAL quandaries often pit concerns about principles against concerns about practical consequences. Should we ban assault rifles and large sodas, restricting people’s liberties for the sake of physical health and safety? Should we allow drone killings or torture, if violating one person’s rights could save a thousand lives? We like to believe that the principled side of the equation is rooted in deep, reasoned conviction. But a growing wealth of research shows that those values often prove to be finicky, inconsistent intuitions, swayed by ethically irrelevant factors. What you say now you might disagree with in five minutes. And such wavering has implications for both public policy and our personal lives.

For a recent paper to be published in the Journal of Experimental Social Psychology, subjects were made to think either abstractly or concretely — say, by writing about the distant or near future. Those who were primed to think abstractly were more accepting of a hypothetical surgery that would kill a man so that one of his glands could be used to save thousands of others from a deadly disease. In other words, a very simple manipulation of mind-set that did not change the specifics of the case led to very different responses. Class can also play a role. Another paper, in the March issue of the Journal of Personality and Social Psychology, shows that upper-income people tend to have less empathy than those from lower-income strata, and so are more willing to sacrifice individuals for the greater good. Upper-income subjects took more money from another subject to multiply it and give to others, and found it more acceptable to push a fat man in front of a trolley to save five others on the track — both outcome-oriented responses.

Even the way a scenario is worded can influence our judgments, as lawyers and politicians well know. In one study, subjects read a number of variations of the classic trolley dilemma: should you turn a runaway trolley away from five people and onto a track with only one? When flipping the switch was described as saving the people on the first track, subjects tended to support it. When it was described as killing someone on the second, they did not. Same situation, different answers.

The researchers culled tens of thousands of photos from an online-dating site, then used an off-the-shelf computer model to extract users’ facial characteristics—both transient ones, like eye makeup and hair color, and more fixed ones, like jaw shape. Then they fed the data into their own model, which classified users by their apparent sexuality. When shown two photos, one of a gay man and one of a straight man, Kosinski and Wang’s model could distinguish between them eighty-one per cent of the time; for women, its accuracy dropped slightly, to seventy-one per cent.

“Adjectives in English absolutely have to be in this order: opinion-size-age-shape-colour-origin-material-purpose Noun. So you can have a lovely little old rectangular green French silver whittling knife. But if you mess with that word order in the slightest you’ll sound like a maniac. It’s an odd thing that every English speaker uses that list, but almost none of us could write it out.”