Let’s say you want something to happen. And it’s not something small. It’s something that requires people to change their behavior in a big way.

I’m not taking about wanting a bunch of people to watch a funny video or get chicken pox (aka simple contagion). I’m talking about big social changes, like wanting a bunch of people to think it’s best for professionally employed women to wear flats instead of high heels (aka complex contagion).

As I explained in my April post How to Go Viral and Spread Social Change, Damon Centola, an expert in social science, wrote a fascinating book called Change: How to Make Big Things Happen. Centola figured out that not all social change is the same: complex contagion is much harder to make happen than simple contagion.

He discovered something further through his research. Complex contagion has a magic tipping point number. The word “magic” here is mine, not his—but I use it because the phenomenon seems miraculous. There is an actual percentage of people that can cause a tipping point among a population, and this percentage is consistent across different populations.

At first, almost no one in a neighborhood has solar panels. Then, seemingly overnight, almost everyone does.

At first, no Arab Spring uprisings. Then, Arab Spring uprisings.

As Centola writes, “Social change often appears abrupt.”

So, what percentage of a population needs to make a behavioral change in order to spark real change across the entire population? Can you guess?

It’s a simple number to guess—not like 37 or 86.

Okay. Do you have your guess?

Ready for the answer?

The answer is one-quarter of a population. If you go to a social club every Saturday and 100 people tend to show up to the event, 25 of them will have to start wearing hats with purple and green feathers before the fad will catch on amongst almost all attendees.

If I can convince one-quarter of professionally employed Americans to accept it as desirable that professionally employed women wear flats, suddenly real societal change will occur.

Of course, I can’t personally convince that many people.

But this magic number, 25 percent, works on a smaller scale, too. Let’s say you are an extreme introvert and the only people you ever see are your brother, sister, hairdresser, doctor, boss, neighbor, friend, and lawnmower. And you never go online or watch TV. Let’s say suddenly your brother and your hairdresser start wearing hats with purple and green feathers. That’s 25 percent of your social network, and you are likely to strongly consider getting one of those hats for yourself.

Isn’t that interesting?