Definition: an event is periodic if there are successive events so analogous to each other that they may be termed recurrences of the same event.
Imagine a world in which there are no periodic events.
There would be no concept of a day or a month or a year.
The whole conception of experience as a guide to conduct would be absent.
There would be no heartbeat, no breathe.
There would be no seasons, no tides, no phases of the moon.
We may be able to identify sequences of events, e.g. A occurred before B which occurred before C, but we would not be able to measure the time between events because time is intimately dependent on periodicity.
Periodicity is fundamental to our conception of life.
We cannot imagine a course of nature in which, as events progresses, we should be unable to say: “This has happened before.”
— The above is extracted from a book by Alfred Whitehead North
P.S. There is a book called Flatlander, which describes a world in which there is no third dimension. It would be fascinating, I think, to write a book which describes a world in which there is no periodicity. What would be the title of such a book?