## Gerbert's Abacus

Gerbert devised a new kind of abacus which one could use to calculate with the Hindu numerals, a flat board with columns drawn on it, corresponding to ones, tens, hundreds, and so forth.  (Some scholars believe he may have been the first person to use the Latin term abacus.)  He had a shield-maker construct small pieces of animal horn with the numerals on them; called apices, the pieces could then be placed on the board to represent numbers.  A zero was not necessary; the absence of a marker in the tens’ place, for instance, meant that there were no tens.  An eleventh-century manuscript found in Limoges illustrates the representation of numbers on such an abacus.  (Note that the numerals had changed slightly in the next hundred years.)

Gerbert compiled a list of rules for computing with his abacus, Regula de Abaco Computi, in which he painstakingly explained how to multiply and divide, as well as add and subtract, in the new system.  A companion work, Liber Abaci, by his student Bernelin, is often included in the collected works of Gerbert; it predates the book of the same name by Fibonacci by two hundred years.

hedgemaker said...

Thanks; this is so helpful. I was not able to visualize the abacus as described -- arced columns...?
This is perfect.

hedgemaker said...

Thanks; this is so helpful. I was not able to visualize the abacus as described -- arced columns...?
This is perfect.

thonyc said...

Sylvester's abacus is actually retrograde. A simple abacus is a perfect decimal place value number system realization. Adding number symbols to the jettons makes it less flexible and less powerful as a computing device.

Pat B said...

Thony,
What part of papal infallibility do you not understand? :-}

Introducing the Arabic numbers may have been part of the plan. He was a pretty good mathematician, I've heard. Why do you think he did it?

thonyc said...

Pat: The answer to your question is that it's not clear what Gerbert intended with his abacus. Apart from anything else he appears not to have really known how the decimal place value system works as he apparently had no knowledge of zero and its function.