7/14/09  Digital Time

Infrequently Answered Question #35: Why are there 24 hours in a day and 60 minutes in an hour? Why not a metric clock with 10 hours of 100 minutes or something?

A: These numbers come from the ancient Sumerians who counted in units of 12 with their fingers instead of ten. Which might have you wondering if Sumerians where six-fingered, 12-toed freaks or something. Not at all. They just saw the hand differently for counting.

Instead of seeing each finger (and the thumb) as one each, the Sumerians saw four fingers made of three bones each. By counting these segments you go up to twelve on one hand instead of ten on two. That's four fingers of three segments each, or 4x3=12 for the mathematically challenged.

In this method you don't count the thumb, you use it to indicate the segment you've counted to. To show seven the other way you extend seven digits on two hands as below left. In the Sumerian method to count seven you touch your thumb to the seventh segment on the tip of the ring finger as below right.

This leaves the other hand free for bigger numbers. In this case each of the four fingers represents a full four fingers of the other hand, or 12. This makes the index finger 12, the middle 24, the ring finger 36, and the pinky 48.

This way the highest number you get with Sumerian hand counting is 60. That's 48 on one hand plus the 12 on the other. That's why there's 60 minutes in an hour and 60 seconds per minute. The 24 hour day is 12 hours of daylight and 12 hours of night. All come from the Sumerian way of counting to twelve and sixty with the fingers.

A base twelve system is quite useful because it divides to whole numbers easily. Twelve hours divides in half (6), thirds (4), and quarters (3) evenly. Even better, 60 minutes divides in half (30), thirds (20), quarters (15), fifths (12), and sixths (10) evenly. Try that with 100 and you get 50, 33.3333..., 25, 20, and 16.666... respectively.

Base twelve shows up in other places: 12 months, 12 in a dozen, 12 inches in a foot. The size of an inch is related, too. The average adult man's index finger is around three inches long with each segment being about one inch. Though, none of this explains why clocks have hands without any fingers at all. Unless it's a Mickey Mouse watch. But then, Mickey only has three fingers and a thumb.

Another thing which might relate to this base 12 counting, the English words we use to count to twelve and then beyond. Notice we don't say oneteen, twoteen, thirteen, fourteen... nor maybe firsteen, seconteen, thirteen, fourteen.... We have unique words eleven, twelve and then start adding the teen suffix after that. So 1-12 are unique and beyond we start in with suffixes and prefixes, -teen, twenty-, thirty-, etc.