Have you heard the one about life before clocks? There’s a joke that never fails to crack me up: “Did you know that, before the clock was invented, people had to actively roam around and ask others for the time?” It’s a simple yet amusing observation on how essential information used to be obtained in the past.
“Did you know that, before the clock was invented, people had to actively roam around and ask people the time?”
While the joke is light-hearted, it touches upon a concept that mathematicians find intriguing. It’s about how information about a single entity can influence the behavior of an entire group. This idea has profound implications and can be further explored.
Consider self-organized systems like bird flocking or fish schooling. These systems consist of individual entities, or particles, which interact and move in synchrony. Each particle adjusts its position based on two factors:
- The best position known to the specific particle: Essentially, what each bird or fish deems as optimal for themselves.
- The global best position determined by all particles communicating with each other: This reflects the collective decision-making within the group, akin to following a leader bird in a flock.