Personal Space

2/17/17

If a person decides to sit next to you, on average do they sit so that their legs are touching yours? No, of course not, that would be rather odd. We need our space.

Apparently, so do all animals that I observe. Check out, for example, this picture I took of birds on an overhead wire

Notice that some birds are very close together, while some are farther away. Let's say we can measure the space between them all, which we probably can since that doesn't seem that difficult to do, especially from a photograph.

If there are N birds on a wire, there are N-1 measurements. Let the average of these measurements be X_a. How does X_a change as N increases? What is the distribution of X_a? Do X_a change given the species of bird (or any other animal)? Or are the X_a pretty constant relative to the size of the animal?

How is this related to the concepts of intimate, personal, social, and public space? Do the animals sitting on the ends or those with large distances between their neighbors exhibit antisocial behavior? Note that someone has to be on the end. How about vertical distance? Do the birds on the higher wires have a higher status than the ones below?

Well, there is nothing new under the sun. Apparently some of this was discussed in 2009 by the Czech mathematical physicist Petr Seba. See his "Parking and the visual perception of space" paper for some interesting details!