Here’s a quick lesson on how to count like a Sumerian. (Note: there are many different historical counting systems. This is one, and simplified at that.)

Sumerians counted in base 60

This practice has survived down to today in the number of seconds in a minute, and minutes in an hour. This all originated with Sumerian mathematics. Why 60? We’re not entirely sure, but many have pointed out that 60 makes it very easy to express common fractions including:

1/2 hour -> 30 minutes
1/3 hour -> 20 minutes
1/4 hour -> 15 minutes
1/5 hour -> 12 minutes
1/6 hour -> 10 minutes
1/10 hour -> 6 minutes
1/12 hour -> 5 minutes
1/15 hour -> 4 minutes
1/20 hour -> 3 minutes
1/30 hour -> 2 minutes

So there you go.

Sumerians didn’t have a decimal point

What does this number mean? -> 1.

In cuneiform numbering it could mean 1, or 60, or even 60×60=3600. Or it could mean 1/60.

So, if you wanted to express half of something, you’d write 30, exactly as you’d express half an hour as 30 minutes. They used context to tell whether 30 meant half of something, or 30 of something, or maybe even (30×60=) 1800 of something.

Five and-a-half might be written as 5 (space) 30.

Sumerians didn’t have the concept of zero

Sometimes they’d leave a blank gap to indicate zero, but mostly not. Again this turned out to be less of a problem, in context than one might expect. The only really confusing situation was when you wanted to express, say, 240-and-a-half of something.

They couldn’t write 4 0 30, so instead they’d write 4 (larger space) 30, or simply 4 30, much as above. But it was really rare to run into numbers like this. A shepherd counting his large flock wouldn’t worry about counting halves 🙂

Writing numbers in cuneiform

To write cuneiform a scribe would obtain a reed, the kind commonly growing alongside rivers or canals, and cut it off at a angle, resulting in a precision tool that could make neat triangular impressions in soft clay. Numbers 1-9 would be written by vertical tick marks. Here’s “5”:

c05The arrangement in up to 3 rows of 3 make it easy to count 1-9 in a glance.

There’s a little bit of base ten involved as well, so that tens would be represented by a heavier, sideways impression. Here’s 25:
c25For larger groups of ten, scribes would typically stack up the tens in a easily-to-glance manner.

For completeness, I need to say that the exact scheme for writing numbers varied, sometimes quite a lot, over the thousands of years that Sumerians and Babylonians did their thing. There was also some room for variation at the hand of a particular scribe. But now you’ve got the basics.

What you see above are images, but there are also Unicode code points for these (and many other) cuneiform signs. Your milage may vary depending on fonts installed. Mac OS X, for example, provides a system font that supports cuneiform, but it looks terrible. This sentence includes the inline characters for 25 so you can see for yourself . [Update: having a problem getting WordPress to accept these characters.]

For the images I’m using the font Akkadian from George Doros, which includes the following notice:

In lieu of a licence; fonts and documents in this site are free for any use;

Like this, there’s much more in Broken Tablet. Check out the series page for details.

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