30 Days Hath November: The Ancient Magic (and Modern Math) of 60

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30 Days Hath November: The Ancient Magic (and Modern Math) of 60
By Heath Shive

“Thirty days hath September/April, June, and November/All the rest have thirty-one/Except February.”

As a poem, this stinks.  As a way to remember numbers, it’s helpful.

Math doesn’t have to be profound, poetic, or even comprehensible.  Math only needs to be helpful. 

As science author Brian Clegg writes in his book Are Numbers Real?: “Math, in the end, provides nothing more or less than a set of rules that are used to get from a starting point to an outcome.”

And if we have problems with numbers today, imagine what it was like for humanity in the Bronze Age?!

How did the ancients get along with numbers?

They used the magic of the number 60!  And we still do today, sometimes.

To the math!

The Magic of 60

The modern metric system is brilliantly based on the number 10.  And yet in Bronze Age Babylon, the base number used was 60.  Why?  The number 10 makes sense (10 fingers, 10 toes, etc), right? 

But 10 is awful for fractions.  In the year 2000 B.C., you do not need fractions.  Fractions are so abstract, and the real world uses whole numbers.  Ancient merchants didn’t sell 1/3 of a camel or 2/7 of a jug of wine. 

And yet they still needed to be able to divide things up.    

So they used 60.  The number 10 is divisible only by 1, 2, 5, and 10.  But the number 60 can be divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.  So 60 is just so much more useful!

And ancient Babylon did use it.  Twelve months to a year.  Each month has 30 days.  A total of 360 days. 

Hey, you say, there are 364.25 days in a year!

That’s right!  That is why ancient calendars threw in extra days with intercalation (or epagomenal days in Ancient Egypt).

Where Is the 60?

We see 60-base numbers pop up in strange ways: ancient pantheons had 12 gods, 12 signs to a zodiac, 12 tribes in Ancient Israel, 12 apostles, 12 months a year, 30 days a month, 4 seasons, 24 hours in a day, 60 minutes an hour, etc.

But you say: Hey, I see more 12 than 60!

That’s right. You would almost believe that the number system was based on 12.  But no.  The number 12 is just the most common (and most accessible for the illiterate) factor of 60!

The ancient world used 60 in other ways, especially with money.  The talent was a large denomination of money used by Babylonians, Sumerians, and Hebrews.  Originally, a talent was divided into 60 minas, and each mina was divided into 60 shekels.  Jesus was betrayed by Judas for “30 pieces of silver,” or 30 shekels. 

And of course, November still has 30 days.
   
Conclusion

No one ever invented geometry, algebra, or calculus for fun.  Math in all its forms and numeric glory must - in the end - serve a purpose.

And after a while, 60 wasn’t useful anymore and was left behind.  Ten is the new base number for our society. 

But back when there was no such thing as a calculator, abacus, slide rule, algebra, or geometry – not even a public school system to teach fundamentals – the number 60 was the world’s math teacher.

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Source:
Clegg, Brian.  Are Numbers Real? The Uncanny Relationship of Mathematics and the Physical World.  St. Martin’s Press, 2016. 
 
  
         
 

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