Why the Dozen?

Fact: 12, 24, 60, these are the big numbers of your everyday life.  These are surely different from the nickel, dime, quarter, and dollar.  Just why is that?

You may have questioned why do we, users of a base 10 system of numbers, seem so dedicated to the dozen (12), the 24 hour clock ( = 2 x 12), the minute (= 60 seconds), and the hour (= 60 minutes).  The answer lies in divisibility.

Clearly, a dozen (12) is divisible by 2, 3, 4, and 6.  This means you can ask for a quarter dozen, third of a dozen, half a dozen, etc.  The math is simple.  If the basic multiple were ten (10 = 2 x 5) we could only do a half or a fifth.  That would be it.

For the day (24 hours), we can divide it by 2, 3, 4, 6, 8, and 12.  This allows a half day, a third of a day (typical shift), a sixth of a day (= 4 hours which is the morning shift), and more.

For an hour (60 minutes) we can divide by 2, 3, 4, 6, 12, 20, 30.  This allows a half hour, a quarter hour, a third of an hour, and more.  The divisibility makes the calculation convenient and easy.  Imagine an hour of 100 minutes.  Then we could divide it into only half, fourth, fifth, tenth, twentieth, and a couple of others. There is less flexibility.

The ancient Babylonians used a base 60 system of enumeration for good reason.  Why? It's all in the divisibility.  Also, it made dealing with fractions a whole lot easier.   BTW, handling fractions were a problem for all the ancient civilizations.   Naturally, the multiplication tables were horrific.  But they had tricks to make calculations easy (well, easier than memorizing all products x times y for x and y in the range from 1 to 59).  Isn't it interesting that in the schools, the multiplication tables taught are for all products x times y for x and y in the range from 1 to 12.  There is that number, 12, once again. 

The year of 365 1/4 days, we can do nothing about.  It is what it is. But note, we have conveniently divided the year into 12 months.  Sure, the numbers of days differ a bit, but calculations are easy in this context.  On the other hand, imagine a year with ten months.  Divisibility is only possible into halves and fifths.  This is the same as if the basic multiple unit consisted of ten items, just like the discussion about the dozen.

Fingers and toes.  These are the basis of our monetary and measurement systems.  This means tens and twenties.  It is an apparent explanation of one system in contradistinction to the more facile base 12, 24, and 60 systems of everyday counting.  Go figure.