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Last Word is Â鶹´«Ã½â€™s long-running series in which readers give scientific answers to each other’s questions, ranging from the minutiae of everyday life to absurd astronomical hypotheticals. To answer a question or ask a new one, email lastword@newscientist.com
Why are there 60 seconds in a minute and 60 minutes in an hour? Who decided on this and when?
Ron Dippold
San Diego, California, US
First, keep in mind that in the 400,000-odd years that Homo sapiens has been around, most people had no use for exact time. Dawn, sunrise, sunset and night were very important, but no cave person cared if it was 3.29 pm. A mere 4000 or so years ago, the Egyptians divided night and day into 12 hours each because it was important for astronomy and religion, and we still use that.
Why 12? Probably due to the Sumerian duodecimal (base 12) counting system. We count to 10 on our fingers, but there is a more compact way to count using just one hand. With your dominant hand, tap the tip of your thumb to the outer bone of your index finger. That’s 1. Now move your thumb to the next bone along. That’s 2, and the last bone is 3. With three bones per finger and four fingers, you can count to 12 on just one hand.
The Egyptians had a decimal (base 10) system, but used duodecimal for some things like hours. If you have 10-hour nights and want to schedule guard watch, you can do two people for 5 hours each or five people for 2 hours each. With 12, you can do two people for 6 hours each, three people for 4 hours, four people for 3 hours or six people for 2 hours.
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Ancient Egyptian hours were variable. If the day were shorter because it was winter, the hours of the day were shorter too
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For the same reason, the Babylonians loved the number 60. It is so much more divisible than 100 is. What can you trivially divide a batch of 100 things into? Ignoring 1 and 100, there are seven options: 2, 4, 5, 10, 20, 25 and 50 things. On the other hand, how about a batch of 60 things? A lavish 10 options: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30! That matters a lot for commerce, taxes and maths. If you want a simple 8 per cent-ish tax, just take five jars out of every 60. The Babylonians also liked 360 because it is 6 × 60 and around the number of days in a year.
Back to timekeeping: ancient Egyptian hours were variable. If the day were shorter because it was winter, the hours of the day were shorter and those of the night were longer! They varied from 53 to 67 (modern) minutes long. It was the Greek philosopher Hipparchus, 2200 years ago, who proposed combining day and night into 24 fixed-length hours.
He also used the Babylonian system to divide what was known of Earth up into 360 degrees of latitude and longitude. Three-hundred years later, the Greco-Roman Claudius Ptolemy subdivided these into 60 “partes minutae primae” and then each of those into 60 “partes minutae secundae”. This is where “minute” and “second” come from.
These were still mostly for geometry, not timekeeping. It wasn’t until the invention of the pendulum clock 400 years ago that clocks were precise enough to warrant more precise markings. At that point, they just borrowed the existing minutes (and later seconds) from geometry.
Chris Daniel
Glan Conwy, UK
Modern time measurement has its roots in the Sumerian civilisation, which flourished from 4500 BC to about 2000 BC in Mesopotamia in what is now Iraq.
The Sumerians must have recognised the versatility of the number 60, as it can be divided in more ways than any other number less than itself, having 12 factors (divisors) and being the smallest number that is divisible by the first six digits from 1 to 6.
Among their many innovations, the Sumerians pioneered cuneiform, or wedge-shaped writing on clay tablets, representing numbers up to 60 in a base 10 sequence of increasing stylus strokes.
These numbers were written with place value: the placement of the symbols denoted their value. Combined with the utility of 60, this made advanced calculations possible, involving multiples and fractions, connected to trade, construction and astronomical observations. The Sumerians also had a deep understanding of geometry – there is evidence that they understood the properties of right-angled triangles 2000 years before Pythagoras.
The “perfect” number 60 had a mystical association with the Sumerian supreme god Anu, who was depicted by the symbol for 60. The number 12 was also auspicious, being the number of major deities in the Sumerian pantheon, the number of lunar cycles in a year and the number of zodiacal signs in the sky. Like 60, it has several useful divisors.
Hillary Shaw
Newport, Shropshire, UK
Sixty is 5 × 12, and these numbers are significant anatomically and astronomically. The year is approximately 60 × 6 days long and there are just over 12 lunar months in a year. We have five fingers, and some early counting methods used base 12. Sixty also has more factors than 10, 12 or 24.
Seven is the worst, being a prime number, but we are stuck with seven-day weeks, probably from the biblical Book of Genesis’s account of the world’s creation. We are also stuck with base 10. Given that, we could rationally decimalise time, with 100,000 seconds in a day (coincidentally the same rate as the average human heartbeat), 100 such short-seconds in a minute, 100 such minutes in a long-hour and 10 long-hours in a day.
We could go on to have 12 months of 30 days and a leap holiday of five or six days. Each month could have three weeks of 10 days each, including a three-day weekend, which would leave us with 30 per cent of the week as leisure time, not the 28 per cent (two of seven) we have now. Every year would have the exact same calendar, apart from leap years, which would get that six-day holiday.
But then people born on, say, Monday would never get their birthday on a weekend. A seven-day work week could be tiring, and religions of one holy day a week would find this hard to adjust to.
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