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Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself? Jeff Dekofsky traces some famous arguments in this ancient and hotly debated question.

Bos­trom writes, “Artificial intelligence already outperforms human intelligence in many domains.” The examples range from chess to Scrabble. One program from 1981, called Eurisko, was designed to teach itself a naval role-playing game. After playing ten thousand matches, it arrived at a morally grotesque strategy: to field thousands of small, immobile ships, the vast majority of which were intended as cannon fodder. In a national tournament, Eurisko demolished its human opponents, who insisted that the game’s rules be changed. The following year, Eurisko won again—by forcing its damaged ships to sink themselves.

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.

Female impersonators, midgets, hermaphrodites, tattooed (all over) men, an albino sword swallower, a human pincushion, a Jewish giant: “Characters in a Fairy Tale for Grown Ups” is the way Diane Arbus once described her subjects—“people who appear like metaphors somewhere further out than we do,” she also said, “invented by belief.”

Language, Darwin believed, was not a conscious invention but a phenomenon “slowly and unconsciously developed by many steps.” But what makes a language a language? In this short animation from TED Ed, linguist John McWhorter, author of the indispensable The Power of Babel: A Natural History of Language (public library), explores the fascinating world of fantasy constructed languages — known as conlangs — from Game of Thrones’ Dothraki to Avatar’s Na’vi to Star Trek’s Klingon to Lord of the Rings’ Elvish. Though fictional, these conlangs reveal a great deal about the fundamentals of real human communication and help us understand the essential components of a successful language — extensive vocabulary, consistent grammar rules but peppered with exceptions, and just the right amount of room for messiness and evolution.

In July of 2008, Dylan Breves, then a seventeen-year-old student from New York City, made a mundane edit to a Wikipedia entry on the coati. The coati, a member of the raccoon family, is “also known as … a Brazilian aardvark,” Breves wrote. He did not cite a source for this nickname, and with good reason: he had invented it. He and his brother had spotted several coatis while on a trip to the Iguaçu Falls, in Brazil, where they had mistaken them for actual aardvarks.

There is one clear difference, though: Iyer has not invented them. The definitions she illustrates – 60 so far, from 30 different languages – match The Meaning of Liff for absurdity, but all of them are real. There is komorebi, Japanese for ‘the sort of scattered dappled light effect that happens when sunlight shines in through trees’; or rire dans sa barbe, a French expression meaning ‘to laugh in your beard quietly while thinking about something that happened in the past’.

Entertaining the idea of a peculiar long number such as pi puts me in mind of its cousins twice removed, prime numbers, which have so many strange properties. Prime numbers are those numbers, such as 3, 5, 7, 11, and so on, that can be cleanly divided only by one and themselves. Primes and pi suggest a benign infinity, a pleasing order—pi because of its endlessness and its relation to the circle, and primes because no matter how far you travel on the number line you will always encounter a prime, as Euclid proved in 300 B.C. Recently, Yitang Zhang solved a problem involving prime numbers called bounded gaps that had been open for more than a hundred years. Zhang proved that no matter how far you go on the number line, even to the range where the numbers would fill many books, there will, on an infinite number of occasions, be two prime numbers within seventy million places of each other. (Other mathematicians have reduced this gap to two hundred and forty six.) Before, it had not been known whether any such range applied to prime numbers, which seem to behave, especially as they get larger, as if they appear at random.

We soon realized we were dealing with differing concepts of time. In our culture, time has substance. It is not to be wasted. It is a container to be filled. We maintain calendars and make schedules to manage separate blocks of time. We measure accomplishment by how well the allotted segments are used. We take appointments seriously, and see promptness as a virtue. Our language is full of adages urging us to use time wisely, "to fill the unforgiving minute with 60 seconds worth of distance run." Our approach to time, which developed after the invention of the mechanical clock, is probably one of the reasons why Europe, a stagnant and peripheral backwater in the year 1000, became the predominant culture by 1500. Our own industrial and scientific preeminence and material wealth is also rooted in efficient use of time. But we have paid a price. We think that with schedules we can control the future, but often find instead that we have become the prisoners of schedules. We are compulsive about filling blocks of time with useful activity and hurry like the Mad Hatter from appointment to appointment. We are frustrated when a task takes longer than the time we had planned. We interrupt work we have almost finished and stop activities we're enjoying because we're "running behind schedule." From this can come stress and alienation. Seeing reality as a series of segmented time compartments can blind us to the wholeness of life.

"Metaphorical thinking—our instinct not just for describing but for comprehending one thing in terms of another—shapes our view of the world, and is essential to how we communicate, learn, discover and invent. ... Our understanding of metaphor is in the midst of a metamorphosis. For centuries, metaphor has been seen as a kind of cognitive frill, a pleasant but essentially useless embellishment to 'normal' thought. Now, the frill is gone. New research in the social and cognitive sciences makes it increasingly plain that metaphorical thinking influences our attitudes, beliefs, and actions in surprising, hidden, and often oddball ways." Geary further unpacks metaphor's influence in his foreword: "Metaphor conditions our interpretations of the stock market and, through advertising, it surreptitiously infiltrates our purchasing decisions. In the mouths of politicians, metaphor subtly nudges public opinion; in the minds of businesspeople, it spurs creativity and innovation. In science, metaphor is the preferred nomenclature for new theories and new discoveries; in psychology, it is the natural language of human relationships and emotions."

The upshot of the boom in metaphor studies, Geary makes clear, is the overturning of that presumption toward literalism: Nowadays, it's believers in a literalism that goes all the way down (so to speak) who are on the defensive in intellectual life, and explorers of metaphor who are on the ascendant. As a result, Geary hardly feels a need to address literalism, devoting most of his book to how metaphor connects to etymology, money, mind, politics, pleasure, science, children, the brain, the body, and such literary forms as the proverb and aphorism.

The invention of religion is a big bang in human history. Gods and spirits helped explain the unexplainable, and religious belief gave meaning and purpose to people struggling to survive. But what if everything we thought we knew about religion was wrong? What if belief in the supernatural is window dressing on what really matters—elaborate rituals that foster group cohesion, creating personal bonds that people are willing to die for. Anthropologist Harvey Whitehouse thinks too much talk about religion is based on loose conjecture and simplistic explanations. Whitehouse directs the Institute of Cognitive and Evolutionary Anthropology at Oxford University. For years he’s been collaborating with scholars around the world to build a massive body of data that grounds the study of religion in science. Whitehouse draws on an array of disciplines—archeology, ethnography, history, evolutionary psychology, cognitive science—to construct a profile of religious practices.

I suppose people do try to fill in the gaps in their knowledge by invoking supernatural explanations. But many other situations prompt supernatural explanations. Perhaps the most common one is thinking there’s a ritual that can help us when we’re doing something with a high risk of failure. Lots of people go to football matches wearing their lucky pants or lucky shirt. And you get players doing all sorts of rituals when there’s a high-risk situation like taking a penalty kick.

We tend to take a few bits and pieces of the most familiar religions and see them as emblematic of what’s ancient and pan-human. But those things that are ancient and pan-human are actually ubiquitous and not really part of world religions. Again, it really depends on what we mean by “religion.” I think the best way to answer that question is to try and figure out which cognitive capacities came first.

The Danish Medical Association said it had considered suggesting a legal ban on the procedure for children under the age of 18, because it believed circumcision should be “an informed, personal choice” that young men make for themselves.ADVERTISINGinRead invented by Teads When parents have their sons circumcised, it robs boys of the ability to make decisions about their own bodies, and choose their cultural and religious beliefs for themselves, the organisation said.