Archive for the ‘Periodicity’ Category

Measuring Time

July 22, 2007

Time is defined by reference to astronomical phenomena. Astronomical recurrences mark out equal intervals of time:

– a year is defined as one trip of the earth around the sun

– a day is defined as one rotation of the earth

Relegation of the determination of the measure of time to the astronomer arises from the consistency[1] of the recurrences with which they deal. If such consistency had been noted among the recurrences characteristic of the human body, we would have looked to the doctors of medicine to determine the measure of time[2].

[1] Example of a “consistent” recurrence: the number of days it takes for the earth to orbit the sun is 365.25 days, year after year … the recurrences are consistent. For all ordinary purposes of life on earth, the various astronomical recurrences may be looked on as absolutely consistent.

[2] The heart beat is periodic, but not consistent; it beats quickly when we are active, slower when we are resting; such inconsistent recurrences would not be useful for measuring time.

— Alfred North Whitehead, An Introduction to Mathematics

Question: how is “hour” measured? Is there an astronomical recurrence that indicates an hour? An hour is one twenty-fourth of a day, of course, but how did the ancients realize that one twenty-fourth of a day has elapsed?

Imagine a World without Periodicity

July 15, 2007

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?