It happened last Sunday at football stadiums around the country. Suddenly, 50,000 individuals became a single unit, almost a single mind, focused intently on what was happening on the field—that particular touchdown grab or dive into the end zone. Somehow, virtually simultaneously, each of those 50,000 people tuned into what the other 49,999 were looking at.

Becoming part of a crowd can be exhilarating or terrifying: The same mechanisms that make people fans can just as easily make them fanatics. And throughout human history...