## Archive for the ‘Consistent Recurrences’ 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?