Sunday, June 12, 2016

The Abacus

Medieval people used Roman numerals.  The Arabs had used what we call Arabic numerals (big surprise), 1, 2, 3 etc., having probably gotten them ultimately from India.  Arabic numerals first became known in the West around the year 1000, and were pushed by the Italian scholar Fibonacci around the year 1200, but they were really not used widely until the late Middle Ages.

It is very difficult to do arithmetic with Roman numerals.  Try adding the following, and you'll see what I mean:

XLIV
+IX

The answer of course is LIII.  But you knew that.

Because arithmetic was (and is) very useful for a lot of things, medieval people used the abacus.  The most basic version is a series of wires with beads, set in a frame.  The bottom wire is for the "ones place," the next for the "tens place," and so.  (You learned about "tens place" in school, right?)  So the number LIII (53) would be represented by three beads pushed along on the bottom wire and five on the next wire.  The use of the abacus goes back at least to the ancient Greeks and probably Egypt and Babylon.


In the twelfth century in England, the royal treasury used what was essentially a checker board for the same purpose, putting stones on the squares rather than moving beads on a wire.  England's treasury is still known as the Exchequer.

Medieval people thus conceptualized numbers as we do, even if they wrote them as Roman numerals.  This is not at all strange.  Think about the following:

seventeen
+ eleven

We switch them into numbers in our heads to get the answer and don't even think about it.  Medieval people did the same thing.

Medieval arithmetic was complicated by not having a zero.  They of course knew about "nothingness." The number "ten" on an abacus was a 1 in the "tens place" and nothing in the "ones place."  But when counting backwards, minus-one was next to one, without a zero in between.  Thus, when AD-BC dating was invented in the fifth century AD, the year 1 BC came immediately before the year 1 AD.  Zero came from the Arabs and was first really explained as a number by Fibonacci.

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