When you enter the room in the Louvre that contains the Mona Lisa you find people crowded around the bullet-proof case that contains the Mona Lisa and largely ignoring the other paintings in the room, which include other masterpieces by Leonardo da Vinci. Four-fifths of the people who visit the Louvre do so to visit the Mona Lisa, and its insurance value is £700m, way ahead of any other painting. Why is it the most famous painting in the world? And why are Facebook, Harry Potter novels, Shakespeare, and Katy Perry so popular?

Common sense says that Mona Lisa is the most famous painting in the world because it’s the best, but there are many paintings that to the eye of both the naive and expert viewer are equally good. Indeed, the painting which was completed in 1519, was largely unknown until 1911 when it was stolen from the Louvre. It was stolen by an Italian patriot who believed the painting should hang in Italy, and when recovered after two years the painting was shown all over Italy before being returned to Paris. The massive media coverage helped make the picture famous.

One part of the explanation of why particular paintings, books, or anything become famous is “circular reasoning,” explains the sociologist Duncan J Watts in Everything is Obvious (Once You Know the Answer): How Common Sense Fails: “X succeeded because X has the attributes of X.” Watts uses the example of a review of Harry Potter books: “A Cinderella plot set in a novel type of boarding school peopled by jolly pupils has a lot going for it. Add in some easy stereotypes illustrating meanness, gluttony, envy, or black-hearted evil to raise the tension, round off with a sound, unchallenging moral statement about the value of courage, friendship, and the power of love, and there already are some of the important ingredients necessary for a match-winning formula.” “In other words,” writes Watts, Harry Potter succeeded because it had exactly the attributes of Harry Potter, and not something else.”

But how did the Mona Lisa and Harry Potter become famous in the first place? Watts starts to explain this through Mark Granovetter’s “riot model.” Consider 100 students furious about an increase in student fees. All are likely to experience a tension between thinking it important to protest in a civilised manner and being furious enough to want to smash something or hit somebody. Some of the students, perhaps anarchists, might be keen to riot, while others will very much want to remain calm. All will have a different threshold. If we imagine that the threshold of one of the students is zero and that other students have thresholds of 1, 2, 3, 4, etc up to 99, then the zero student will riot, prompting the student with a threshold of one to riot, so prompting the student with a threshold of two to riot, so on until all the students are rioting.

But imagine another university where the threshold of the students is 0,1, 2, 4, 5, 6, up to 99 in unit intervals: students with the thresholds of 0,1, and 2 will riot, but that will be all—because the next threshold of 4 is never reached. Observers will search for a common sense explanation of why one group of students has rioted and not the other group: perhaps one group was more angry or desperate, the university mismanaged relations with the students, or the police were too rough. In fact the difference would be explained by only two students having different thresholds: one a 3 and the other a 4.

The riot model illustrates the effects of accumulation, and Watts uses it to introduce the idea “cumulative advantage,” meaning that “once, say a song or a book [or painting] becomes more popular than another, it will tend to become more popular still.” Watts and his colleagues illustrated this with an experiment.

They enlisted through the web 14 000 people and asked them to listen to, rate, and if they wanted to download songs. One group saw simply the songs while another group saw how many times other participants had downloaded the songs. Those who saw how often the songs were downloaded were then divided into eight groups in which the songs were presented in different random orders: all of the groups started with songs with zero downloads. As the theories of “cumulative advantage” and “social advantage” predict in the group that could see the number of downloads the more songs were downloaded the higher they were rated—that is popular songs were popular and unpopular ones unpopular. Furthermore, in the eight groups different songs were rated most popular: introducing social influence increased inequality and unpredictability. As Watts concludes, “unpredictability was inherent in the dynamics of the market itself.”

Now we can understand why the Mona Lisa is the most famous painting in the world. It is a fine painting but many others are equally fine and even finer. At some point, when it was stolen and received media coverage, it became known and “cumulative advantage” meant that it became ever more popular. Luckily, there was no “missing link” as in the case of the missing 3 in the riot theory, and once it was famous “circular reasoning” explained why it was famous.

In other words, chance determines what becomes famous. I saw this as editor of The BMJ in that I found it almost impossible to predict before publication which papers would attract a lot of attention. I find the same now with the many blogs I write—some attract hundreds of Facebook likes (some sort of measure of popularity) while others attract only none. It brings us back to Kipling’s observation on triumph and disaster: “treat those two imposters just the same.”

Richard Smith was the editor of The BMJ until 2004.