originally published by Gary Wallace on February 10, 2009 and titled:
Why Are There 60 Minutes In An Hour?
We are all familiar with dividing our days into 24 hours and our hours into 60 minutes. But why do we use these particular units for measuring time?
To understand the units of time we need to investigate the number systems of ancient civilizations. How did the Sumerians count to 12 on one hand and to 60 on two? What advances did the Babylonians make and how did they use this number system for measurement? And what refinements did the Egyptians make to time measurement to give us the system we still use today?
Sumerian Counting
It is easy to see the origins of a decimal (base 10) number system. Our hands have 10 digits to count on, so a decimal system follows naturally. With the addition of the toes on our feet a vigesimal (base 20) number system, like that of the Maya, also makes sense. But understanding a sexagesimal (base 60) number system, as used by the Sumerians, takes a little more thought. A quick glance at a hand shows us four fingers and a thumb that can be used for counting. But the human hand is a complex machine consisting of 27 bones, as shown in the diagram below. 
Some of these features are evident externally, especially in the fingers. By using the thumb as a pointer, and marking off the distal phalanx, middle phalanx and proximal phalanx of each finger, we can count up to 12 on one hand, as shown below.
Furthermore, by using the other hand to mark five multiples of 12 we can extend the count up to 60. For instance, 32 (= 2 x 12 + 8 ) would appear as follows.
Babylonian Mathematics
The Sumerian number system was passed on to the Babylonians. Sexagesimal was a useful system as 60 has a large number of factors. Each collection of 60 objects could be divided into whole groups of 2, 3, 4, 5, 6, 10, 12, 15, 20 or 30. The Babylonians used just two symbols for their mathematical notation.
There was a 
for 1 and a 
for 10. All the numbers from 1 to 59 were written as combinations of these marks. For instance, 32 appeared as 
A significant advance from earlier notation was the use by the Babylonians of a positional system. In our decimal notation we represent 10 as a column containing a 1 followed by a column containing a 0. In a similar way the Babylonians represented numbers over 59 in multiple columns. For instance, 64 was 1 x 60 + 4 or
Although there was no symbol for a zero it was shown as a larger gap between the columns.
Measurement and Time
The number 60 and its factors were used in the measurement of many things, several of which are still in use today. In length there are 12 inches to a foot. In angular measurement there are 6 x 60 = 360 degrees in a circle. In pre-decimalised currency in the UK there were 12 pence in a shilling.
But let us bring our attention back to time and the division of a day. The Babylonians divided each hour of the day into 60 minutes. Each minute they divided into 60 seconds. These are not, however, the minutes and seconds we would recognise today.
Each day was divided into a daylight portion and a night portion. These portions were then divided into 12 hours each. As the length of day and night varied throughout the year, so the length of the Babylonian hours, minutes and seconds varied too.
Egyptian Refinements
The Egyptians refined the measurement of time to remove these variations. They ignored the distinction between daylight hours and night hours but kept the total of 24. The whole day was then divided into 24 equal periods creating the hour that we still use today.
Despite occasional suggestions that we should adopt decimal time, this ancient system of measurement has survived for thousands of years. And so, the reason there are 60 minutes in an hour is due to the mathematics of the Sumerians, Babylonians and Egyptians and the structure of the human hand.
MICH 26 – OSU 45
CIN 13 – KENT 25
1938
CIN 98 – UGA 63
