It can easily be shown that a "random" distribution of points does not appear random to us. Conversely, if asked to scatter points "at random", people will usually avoid putting points close together compared with what happens in a random distribution.

[Technically: I take "random" to mean that the position of each point is independent from the position of the previous point; this can be done assuming a uniform probability per unit volume, but not necessarily. When people manufacture a "random" distribution they usually do somethin akin to what physicists call a "hard-sphere gas", that is, there is a minimum distance below which a new point won't be added, but otherwise the distribution is "random"]

Can the last politician to go out the revolving door please turn the lights off?