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by CityVista
1 week, 6 days ago

Why We Count Seconds and Minutes in Units of 60

Why We Count Seconds and Minutes in Units of 60
By Wendell W. Solomons

I put the question this way in an email. I was addressing the Royal Observatory in Edinburgh about Assyrian-period money in precious metals, which was often weighed at the point of exchange:

"In Assyrian times shekels and minas bore a relationship of 1:60. Interest per month was also calculated as the percentage 1/60th. Would you have an idea how the figure of 60 came to be derived?"

On Sunday, Sep 5th, 1999, I received a reply from the Institute for Astronomy in Edinburgh:

"Briefly, the reason that the Assyrians and related civilisations (Babylonians etc.) used factors of 60 for the relative value of coins, interest rates etc. was that they represented numbers using a sexagesimal, or rather semi-sexagesimal system, so it was only natural to use factors of sixty. Our present practice of dividing angles (degrees) and time (hours) into sixty minutes and further subdividing the minutes into sixty seconds has the same origin.'

"Of course, why they developed a sexagesimal number system is another matter..." (email sent by Clive Davenhall)

That is what I was trying to find out.

I proceeded onwards this way.

Division into small units was the task of the ancients. Folding a piece of beaten copper or silver into halves could, with some degree of perfection, make smaller linear measures and weights.

In linear measure, by the Middle Ages people could go down to 1/8th inch. In marking linear rules with a sharp scriber, 1/16th of an inch was about the ultimate.

Folding beaten copper in halves would also crudely divide circles. Yet, folding circular copper sheet to create exact halves is not easy. If used by astronomers for reckoning large distances in the study of the paths of heavenly bodies, folded circles would create vagaries. The study of heavenly bodies was essential for creating a calendar for sowing the seed. Without a reliable calendar, a village could starve.

Drawing circles could be done by using dividers. These were created from rods of fixed size. The rod of length "M" used to draw a circle could next be used to make a mark on the perimeter of the circle. It was found to cut off length "M" six times. This created six geometrically analogous wedges of this circle. In short, six was a sweet number for the circle.

So the ancients used these 'sextiles.' The sextiles gave a higher degree of accuracy in studying heavenly bodies. That provided for the creation and use of more reliable calendars in agriculture.

The development of 60s (that is, sexagesimal counting) came from the sextiles. We can see that happen in land surveying.

When labourers were used for drawing radials on land, hybridisation could happen. Labourers in the field would combine the decimal system of folk culture - in use through counting on one's fingers - with the astronomy scholar's sextile.

That combination created the 10 x 6 or sexagesimal system. From surveying landed property, the system was transferred to map-making for navigation.

The division into the customary 12 hours also seems to have come from the sextiles.

If six sextiles represented daylight hours, important with the sundial, the division of each sextile into two would help the monastery and the castle. By this means the long summer day could be divided into 12 hours with the sundial. From the sundial, the hour could be broadcast to a village community by the ringing of a bell in a steeple or tower. The sun beamed the same way in a large province and so the sundial was helpful in co-ordination and also in calibrating accurate waterclocks and hourglasses for those months when the skies were clouded and darkened.

As an afternote to this story, let us see why the days of the week are counted in sevens.

The ancients were able to observe seven heavenly bodies. The days of the week came to be named after these heavenly bodies in many civilizations.

In England, Saturday is the day of the planet Saturn. In most of India, it is the same planet's day, (in Sanskrit, that of Senasura.) Monday is the Moon's day and so it is in India, (that of Chandra.) The flag of Bhutan shows seven globes in that tradition and a Buddhist shrine also reflects the same concept with seven successive roofs. The idea of Seventh Heaven may also be sought here.

The Semitic languages (such as Arabic or Hebrew) and the Slav languages (such as Russian or Ukrainian) set aside the system of naming days after the planets. Monday in most Semitic languages is now simply the first day as it is in many Slav languages. To discover why people adopted this change, we need do no more than consider the revolution caused in West Asia by the Code of Moses.

© 1999 by Wendell W. Solomons
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