Open-ended problem: Do groups of people follow predictable patterns?

My sister and I were walking our kids back from a trip to Science World, when we passed a park sparsely filled with people. My sister looked at the people sitting in the park, and wondered aloud, “I wonder if you can use mathematics to figure out how far apart people will sit on a lawn?” I looked carefully at the park too, and noticed that everyone seemed to be carefully at an maximal distance apart from anyone else on the field. I am particularly excited about my sister’s question, because she has always described herself as “not a math person.”

I decided to generalize her question, to “do groups of people follow predictable patterns?” This would allow for exploration in a wide variety of ways, for example:

  • Do people tend to follow the same paths when crossing open-space, like a field or in the meeting room of a train station?
  • How random is the motion of people as they sit waiting in a theatre?
  • Can you track use of phrases of language through groups of people?
  • What similarities exist, if any, between the networks of relationships each person has?
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