Wednesday seminar:

Mathematical thinking is often about finding patterns.

My favorite environment for thinking about patterns is watching a crowd move. The ideal condition is to watch from above and from a distance such that you do not focus on individuals. We are looking for patterns, so we do not care about individuality. Mathematicians do not care that much that they think about "particles" instead of people. In my case: nice orange particles as in the videos.

Watching a crowd, you can see typical things. A group of people is waiting for something and people slightly wander around. We can call it a chaotic movement without a particular direction. Often people go in a specific direction, like all these people heading to a shop entrance. You can also look for a typical distance between people. Most people come close enough but not too close to each other for a chat.