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Mental Model: Critical Mass

The term “critical mass” seems to have first appeared in nuclear physics. In this discipline, “critical mass” is the minimum amount of a given fissile material necessary to achieve a self-sustaining fission chain reaction.

The term, however, is now used as a much broader construct. In astrophysics, for example, critical mass is a concept used to designate any mass that when exceeded causes something to happen.

The concept of critical mass exists outside of physics and can easily be thought of as a tipping point. A Tipping Point, according to noted author Malcolm Gladwell in The Tipping Point: How Little Things Can Make a Big Difference, “is the moment of critical mass, the threshold, the boiling point.”

The term Tipping points comes from epidemiology. It’s the name given to that moment in an epidemic when a virus reaches critical mass. (It’s the moment on the graph when the line starts to shoot straight upwards.)

In The Tipping Point Gladwell writes:

The best way to understand the Tipping Point is to imagine a hypothetical outbreak of the flu. Suppose, for example, that one summer 1,000 tourists come to Manhattan from Canada carrying an untreatable strain of twenty-four-hour virus. This strain of flu has a 2 percent infection rate, which is to say that one out of every 50 people who come into close contact with someone carrying it catches the bug himself. Let’s say that 50 is also exactly the number of people the average Manhattanite — in the course of riding the subways and mingling with colleagues at work — comes into contact with every day. What we have, then, is a disease in equilibrium. Those 1,000 Canadian tourists pass on the virus to 1,000 new people on the day they arrive. And the next day those 1,000 newly infected people pass on the virus to another 1,000 people, just as the original 1,000 tourists who started the epidemic are returning to health. With those getting sick and those getting well so perfectly in balance, the flu chugs along at a steady but unspectacular clip through the rest of summer and fall.

But then comes the Christmas season. The subways and buses get more crowded with tourists and shoppers, and instead of running into an even 50 people a day, the average Manhattanite now has close contact with, say, 55 people a day. All of a sudden, the equilibrium is disrupted. The 1,000 flu carriers now run into 55,000 people a day and at a 2 percent infection rate, that translates into 1,100 cases the following day. Those 1,100, in turn, are now passing on their virus to 55,000 people as well, so that by day three there are 1,210 Manhattanites with the flu and by day four 1,331 and by the end of the week there are nearly 2,000, and so on up, in an exponential spiral until Manhattan has a full-blown flu epidemic on its hands by Christmas Day. That moment when the average flu carrier went from running into 50 people a day to running into 55 was the Tipping Point. It was the point at which an ordinary and stable phenomenon — a low-level flu outbreak — turned into a public health crisis. If you were to draw a graph of the progress of the Canadian flu epidemic, the Tipping Point would be the point on the graph where it suddenly turned upward.

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Thresholds are important to the concept of Critical Mass as not everything or everyone attains critical mass and immediately begins an exponential ascent — given that, when people are involved in the process, they have different thresholds (and the behavior of others is not always the most important variable influencing the decisions process). Social problems can be contagious and spread primarily through peer influence. Unlike the epidemic mentioned above, people sometimes have a “choice” to make in influencing a critical mass.

Perhaps an example from Mark Granovetter (“Threshold Models of Collective Behavior“) will help illustrate.

Consider a riot, different individuals require different levels of safety before entering a riot and also vary in the benefits they derive from rioting. The crucial concept for describing such variation among individuals is that of “threshold.” A person’s threshold for joining a riot is defined as the proportion of the group he would have to see join before he would do so. A “radical” will have a low threshold: the benefits of rioting are high to him, the cost of the arrest, low. Some would be sufficiently radical to have a threshold of 0%–people who will riot even when no one else does. These are the “instigators.” Conservatives will have high thresholds: the benefits of rioting are small or negative to them and the consequences of arrest high since they are likely to be “respectable citizens” rather than “known rabble-rousers.”

Thus, we can conclude that a threshold, at least when humans make decisions, is the point where the perceived benefits of doing the thing in question exceed the perceived costs and thus it is situation-specific.

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In The Tipping Point Gladwell writes:

Because epidemics behave in a very unusual and counterintuitive way. Think, for a moment, about an epidemic of measles in a kindergarten class. One child brings in the virus. It spreads to every other child in the class in a matter of days. And then, within a week or so, it completely dies out and none of the children will ever get measles again. That’s typical behavior for epidemics: they can blow up and then die out really quickly, and even the smallest change — like one child with a virus — can get them started. My argument is that it is also the way that change often happens in the rest of the world. Things can happen all at once, and little changes can make a huge difference. That’s a little bit counterintuitive. As human beings, we always expect everyday change to happen slowly and steadily, and for there to be some relationship between cause and effect. And when there isn’t — when crime drops dramatically in New York for no apparent reason, or when a movie made on a shoestring budget ends up making hundreds of millions of dollars — we’re surprised. I’m saying, don’t be surprised. This is the way social epidemics work.

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Examples: A lot of social behavior can be considered from the perspective of “critical mass” or “tipping point”: strikes, riots, adopting new technology, conformity, rumors, voting, visible and invisible consumer purchases, education, leaving a party, migration decisions, etc.

The Fax Machine

In The Tipping Point, Gladwell explains:

“Sharp introduced the first low-priced fax machine in 1984, and sold about 80,000 of those machines in the United States in that first year. For the next three years, businesses slowly and steadily bought more and more faxes, until, in 1987, enough people had faxes that it made sense for everyone to get a fax. Nineteen eighty-seven was the fax machine Tipping Point. A million machines were sold that year, and by 1989 two million new machines had gone into operation. Cellular phones have followed the same trajectory. Through the 1990s, they got smaller and cheaper, and service got better until 1998, when the technology hit a Tipping Point and suddenly everyone had to have a cell phone. “

Birth Control (diffusion of innovations — from Threshold Models of Collective Behavior):

Women in Korean villages may be wary of adopting birth control devices and wait to do so until some proportion of their fellow villagers do (social proof). Different women will have different thresholds, depending upon their education, age, husband’s opinions, position in a hierarchy of informal leadership, or personal tastes.

Critical Mass is part of the Farnam Street latticework of mental models.