*How do we translate between group behavior and individual behavior?*

Calculus is the study of change. More specifically, it is a method for understanding rates of change. If you know an object’s velocity and want to calculate its acceleration, then you need calculus because acceleration is the rate at which speed changes. And if you’re interested in change, there are two big things you want to know.

First, if you already know the speed, you want to figure out the acceleration. This allows you to understand the object’s cumulative behavior over time by singling out its behavior at any given moment. In calculus, this is called differentiation. The second thing you want to know is how to determine the speed if you already know the acceleration. You understand the individual moments by assessing them cumulatively. This is the reverse of differentiation, called integration. What the fundamental theorem of calculus states is that differentiation and integration are two sides of the same coin.

The reason that the theorem is fundamental is that it relates the two different strategies for quantifying change. It allows you to reserve direction—from individual moments to their cumulative activity, and then back again. The ability to shift between the two strategies provides the basis for the rest of calculus, and the fundamental theorem tells you how to do it.

There is a similar problem in the study of human behavior. There are, broadly speaking, two different strategies for how we try to understand humans. The first is psychological. This strategy focuses on the individual, how to explain what is going on in her head and account for her behavior. The second strategy is sociological, which looks not at individuals but at the behavior of groups.

What is clear is that individuals and social groups are two sides of the same coin. Groups are made up of individuals. And individuals are organized into groups. What is not clear is how to translate between the two strategies. If we know the speed and want to calculate the acceleration, we can appeal to the fundamental theorem of calculus. But if we know an individual’s behavior, how do we calculate the resulting group behavior? We need a fundamental theorem of human behavior.

There is a theory by sociologist Mark Granovetter which gives us a basis for performing this behavioral calculus. It is known under the broad heading of threshold models of behavior.

The classic example of this idea is the beginning of a riot. A riot begins when the first person throws a brick through a window. This person has a threshold of zero. They will throw the brick through the window even when no one else is doing it. The riot continues when the second person throws a brick through a window. This person has a threshold of two. They will throw the brick if there is one other person doing it. Then it continues with three and four and so on. If the riot continues long enough, you eventually get to a state where everyone’s threshold is crossed. The collective behavior is the riot, and the individual behavior is the threshold. If this idea seems familiar, it is because threshold models are the theoretical basis for Malcolm Gladwell’s book *The Tipping Point*.

Threshold models give us a fundamental theorem of behavior because they tell us how to reconcile the collective with the individual. Sociologists study things like riots, events where lots of people have agreed to participate and the consequences of that group activity. Psychologists study things like decisions, when and how someone gets involved in the riot in the first place. Much of what psychologists study—social groups, personality, emotions, cognition, happiness—is an elaboration of when people decide to go with the flow and when they go against the grain. In other words, their threshold.

The power of threshold models is that they relate the psychological and sociological modes of explanation. This is not something that’s easy to do. Usually we just stick to one strategy or the other. It’s easier to talk about groups or individuals separately rather than trying to consider both at the same time. Threshold models give you a language for doing so.

But as anyone who has taken a calculus class knows, just because you learn the fundamental theorem doesn’t mean that the rest of the material falls easily into place. Likewise, threshold models don’t explain all of behavior. What they give us is something more fundamental—a fulcrum on which we can swing between the behavior of collectives and individuals. Going further and plumbing the depths of that collective and individual behavior, then, is what sociology and psychology are all about.

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Originally posted on __Psychology Today__.