Meet Kushim. It is very rare that we get an insight into an individual from ancient history, let alone one from ancient Sumer. This is one of the truly distant civilizations, and just as dynastic Egypt was getting its act together Kushim was counting beans in the Sumerian city of Uruk sometime between 3,400 and 3,000 BC.
More accurately, he was counting barley. We know four things about Kushim, which is in itself is incredible as almost nothing survives of anyone below the ruling class in this era. People, in the broad sense, are almost always treated as an amorphous mass from the standpoint of history.
The first thing we know about Kushim is his name. The second is his title, with which he signed all his documents: he was “Administrator” Kushim.
The third fact about Kushim is what he was administrator of: he appears to have been in charge of a grain silo or storehouse, where he handled barley shipments and had a supervisor named Nisa who would countersign his documents.
And the fourth fact we know about Kushim is that he added one of his shipments up incorrectly.
The Mistake
The ancient Sumerians used clay tablets to track the shipments. Thery had discovered that people are dreadful at remembering what was agreed in any given transaction and that independent records were required to confirm the volumes of barley that were received.
The imprints on the tablets are therefore among the first attempts to develop language, not for poetry but for accounting. These tablets, centuries earlier than cuneiform, were purely practical items to avoid mercantile disputes.
18 of Kushim’s tablets survive, all relating to shipments of barley to his warehouse and all signed “Administrator Kushim”. The tablets contain dates, which tell us that the Sumerians tracked the seasons with 12 months, as we do, but apparently with a long “leap” month every three years to account for the lunar shift, similar to our leap days every four years.
The tablets also recorded the amounts of barley received, using a fiddly accounting system. One bowl, the smallest unit on the tablets, is equal to a little under five liters. One sideways bowl with a dot, the largest unit, is equal to 9,000 bowls, or 43,200 liters.
These tablets were exacting, and accounted for even the largest barley transaction down to the last bowl. The totals would be tallied and then the total amount would be written on the reverse of the tablet.
And here we find what may be the first example of an accounting error in history. One such tablet contains the symbols for several transactions where barley was received at the storehouse. The total of these transactions, signed by Administrator Kushim and countersigned by Nisa, is 3,910 bowls.
However, on the other side the total stated is 3,895 bowls, some 15 bowls short. It would appear that, looking at the list of transactions, a small group of symbols was missed in tallying the amount, an error which was then carried to the back of the tablet.
Or possibly Kushim and Nisa were skimming barley off the top. At this point in history the barley was used for making beer, and the 18 tablets contain no fewer than eight separate recipes for beer making. Maybe Kushim and Nisa needed a little refresher after a hard day’s accounting, and beer made with 15 bowls of barley was just the thing.
So, possibly an error, possibly fraud, but this is not the actual mistake. That comes when we look at Kushim’s cheat sheet, with its list of equivalent measurements for different symbols. Here fractions are introduced, and as many young children at school will tell you, when fractions are introduced things go off the rails.
The table indicates symbols for smaller volumes as a fraction of symbols for larger volumes. But the first equivalent listed states that a sideways bowl (equivalent to 5 bowls) when divided in half, still equals a sideways bowl.
Who knows how many errors were driven by reference to this table which have not survived. What we are lucky enough to witness however is the first accounting error, and indeed the first math error, in recorded history.
Top Image: Sumerian clay tablet from the Louvre. The circular and crescent impressions are volumes of barley, and the glyphs in the top left read “Administrator Kushim” Source: Louvre Museum / CC BY-SA 3.0.
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By Joseph Green
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