An allowance is an ancient calculating “device,” although, as you will learn a couple of paragraphs hence, to call it a device might mislead some readers for a couple of reasons. This is not one of those reasons: Allowances predated abacuses, in fact, it is generally believed that the abacus was simply a more convenient adaptation of an allowance.
The first known use of allowances occurred in Mesopotamia, circa 2900 BC. They are not known to be used today, but, then again, who the hell knows? A lot of terribly weird people do a lot of terribly weird things.
The first reason the word “device” might mislead you is that allowances were much larger than what you might think of as a a device. An allowance has to be set up in a large field or yard. It consists of a few (the number can vary) adjacent oblong animal pens, usually with wooden fences for walls. Back when the allowance was first invented, those walls were generally constructed of rough-hewn logs, but they later became somewhat more engineered.
The width of each of the pens was just large enough to hold a lamb. The length of each pen was twice as large as necessary to contain 10 not-too-restless lambs.
The second reason the word “device” might mislead you is that, rather than purely mechanical, allowances included living components. In fact, it was the living components that performed the useful work. Specifically, allowances made use of animals, namely, as you might have guessed from the dimensions of allowances, lambs.
To use an allowance, ten lambs were herded into one end of each of the adjacent pens. The lambs were pushed one at a time from one end of the pen to another as means of counting, exactly like the beads in the abacuses except, unlike abacus beads, lambs sometimes resisted being moved and often crapped on the ground.
The cleverness of allowances came from the designations of the adjacent pens. The first pen was designated as the units row, representing the numbers 0 through nine.
The next pen was the 10s row, representing 0, 10, 20, 30 … 90.
The third pen was the 100s row, representing 0, 100, 200, 300 … 900.
And so on for as many pens as there were in the allowance.
It was possible to use an allowance to perform a wide variety of arithmetic calculations by appropriately prodding lambs within their pens.
Nobody is sure why the ancients derived the abacus from the allowance, but a few theories have arisen, including the following:
- As people came to find arithmetic more and more useful in commerce, the cost of feeding the lambs used in increasing number of allowances was climbing too high due to supply and demand imbalances in the lamb-feed market.
- People grew tired of dealing with lamb poop.
- As much as they appreciated all that arithmetic could do for them, they appreciated eating lamb more.
- Too many people were getting hernias carting around “portable” allowances.
- The god(s) were getting angrier and required more sacrificial lambs, not leaving enough lambs for use in allowances.
- Some of the above.
- All of the above.