In his Muqaddimah, the fourteenth-century Arab historian Ibn Khaldun describes talismans that make use of “the loving numbers” 220 and 284 to create the perfect union between friends or lovers. Two effigies are created, and the larger number is placed on the effigy of “the person whose friendship is sought.” The result of this “magical operation,” he explains, is a connection between the two such that “one is hardly able to break away from the other.”

A 2013 study involving American college students found that participants were more likely to deem a face more attractive if it was presented amid a group of faces than if it was displayed alone. This “cheerleader effect,” scientists ventured, was “due to the averaging out of unattractive idiosyncrasies.” Two years later a similar study conducted with Japanese participants failed to replicate the results of the initial study.

Friendship cannot exist “between the well-fed, prosperous / and the lean and down-and-out in the world,” states the Panchatantra, a collection of Indian animal fables from around the third century bc. In one story, when a crow tries to befriend a mole after witnessing his impressive skill in escaping from hunters’ traps, the mole exclaims, “You are the eater; I am the food. What kind of friendship can exist between us?”

Looking at the records of 35,000 Union Army veterans who had served between 1861 and 1865, a 2010 study found that soldiers whose military units lacked a sense of camaraderie were six times more likely to have had heart attacks or strokes by their late fifties or early sixties than counterparts from units with strong esprit de corps. “Somehow being armed with close social bonds in the extremely stressful situation of battlefield combat,” said one of the researchers, “has a protective effect that continues long after the fighting has ended.”

While walking around New York City, a young Meyer Lansky was stopped by a group of Italian teenagers demanding protection money. Their leader, later known to the public as Lucky Luciano, had been recruited into the Lower East Side’s Five Points Gang at a young age and would go on to develop a national crime syndicate. “Go fuck yourself,” Lansky responded. A lifelong friendship between the two gangsters grew out of this encounter. “They would just look at each other,” recalled Bugsy Siegel. “A few minutes later, one would say what the other was thinking.”