randomness via stillness

Randomness conjures up images of chaos and dynamism. But from a structural point of view the picture is quite opposite.

As human beings trapped in time, we can only sample the reality in time. However, the parameters of a random distribution may change across time. Hence, the resulting samples may exhibit a non-random distribution even if the underlying dynamics is random. In other words, for randomness to reveal itself it must be of static nature! The parameters should stay more or less constant.