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Why are there 60 seconds in a minute and 60 minutes in an hour? Who decided on this and when? (continued)

Peter Simons
via email

Several correspondents recently pointed out how the division of hours into 60 minutes and minutes into 60 seconds (and a full turn into 360 degrees) is almost certainly based on the Sumerians’ very sensible use of base-12 numbering. One correspondent mentioned how one can count to 12 using the finger joints of one hand. Another one I worked out for myself – though others have done so too – is how to count to 31 on one hand and 1023 on two. Using Leibniz’s binary system, let your right pinky be worth 1, the next finger to the left worth 2, the next worth 4 and so on, to your left pinky worth 512. I find it easiest to count with my hands resting on a surface. A finger off the surface counts 0, and down on the surface counts 1. Then a bit of musicianly raising and lowering of fingers allows you to count to a maximum of 10 fingers down, or 1023. Allowing a third state for each finger – half-bent – gives the possibility of counting to 59,048. My fingers sadly don’t seem to want to bend that way, but for those who want to do their tax returns on their fingers, practise that bending!

Peter Bursztyn
Barrie, Ontario, Canada

For the most part, animals are either diurnal (active in daylight) or nocturnal (night owls). Humans are diurnal and, at night, our visual acuity drops sharply and colour vision is lost.

For many millennia, our ancestors sought shelter from carnivores, such as big cats, which had excellent night vision. Many millennia later, after our predecessors learned to control fire, we might have set fires at the entrance, which predators fear and avoid. Against that background, our ancestors would have started looking for shelter well before dark, using the sun’s height in the sky as a crude clock. Timekeeping precision would have been limited to “meet you at the large rock tomorrow morning”.

Ancient Egypt is credited with inventing the solar clock, or sundial. The oldest known solar clock dates back 3500 years. However, the way the pyramids were built (around 4500 years ago) precisely aligned with the north-south meridian. Egyptians would have achieved that by planting a vertical pole in the soil and observing its shadow.

The shortest shadow would point to astronomical north, with the noon shadow line itself indicating the north-south meridian. Clearly, the shadow of such a pole could indicate time, but how was it calibrated?

The story of how it was done begins 2700 years ago in Babylon where mathematician-astronomers divided “the heavens” into 12 sectors. Each sector was named after a prominent constellation. Ancient Greece adopted this scheme, translating the Babylonian names into those we recognise today: Gemini, Leo, Pisces, Aquarius, Virgo, Cancer, etc. Where we count to base 10 today, the Babylonians used base 60. While base 10 has only two divisors yielding whole numbers (2 and 5), base 60 has many (2, 3, 4, 5, 6, 10, 12, 15, 20 and 30). Babylonians subdivided each of their 12 sky sectors into 30 smaller units, yielding 360 subdivisions. The Greeks adopted this into their geometry, so a circle has 360 subdivisions (degrees). Two millennia on, we continue to use this same scheme!

Since the sun traverses the 12 sectors daily, an obvious sun clock calibration would divide the day time into 12 parts. We call them “hours”. Nighttime was similarly divided. In the 1600s, the pendulum clock’s precision made it sensible to add a minute hand to every clock. Since this hand made a full rotation every hour, the ancient Babylonian scheme of dividing a circle into 360 small units (degrees) was pressed into service. Each degree became a minute, and 1440 such minutes make up a day.

Inés AntÓn Méndez
Madrid, Spain

The sexagesimal (base 60) system was developed by the Babylonians millennia ago. It was them who decided to divide each hour into 60 minutes, and each minute into 60 seconds.

This may seem an odd choice from our point of view, but the system itself has quite a few advantages. To start with, 60 has more divisors than 10. Also, counting can be done just as easily and far more efficiently with the help of our fingers.

It is to the Egyptians, however, that we owe the division of the day into 24 hours. They assigned 12 hours to the night and 12 hours to the day.

So, here we are in our own era with a decimal system for most measures (that is, if you live in places where the metric system won and the King´s Foot and other such odd units went out of fashion) and an anachronistic sexagesimal system to parse time and, not coincidentally, the circle.

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