Egyptian Addition

The mathematical notation and the techniques we use to compute with it are so concise and removed from the physical world that it is easy for mathematics students to lose awareness of its meaning when using it, so I think it is a useful thing for helping students understand the meaning of arithmetic to learn some more primitive methods for doing it. The ancient Egyptian system is particularly good for this because of its simplicity and concreteness. (See also How to Add and Subtract with a Counting Board  for another interesting method.) This article is about how to add using Egyptian symbols. It is not entirely historically accurate, because I will be using hieroglyphic symbols, when all the documentary evidence says that they would have used a more shorthand system, the hieratic symbols when they would have been doing additions, but one might imagine that in some pre historical time they might have thought of how to do the operation in the way that I will be describing it below, and also we need to make it simpler, because we haven't been trained for years and years in a scribe school.

First of all, before I talk about how to do addition I need to talk a little about what addition would have meant when it was first done. The earliest addition was probably physical addition. You have a flock of sheep and a pile of pebbles to keep track of them with. Your brother dies and you get his sheep and to keep track of how many sheep you have now, you physically add his pile of pebbles to yours. Later when number notation was invented adding wasn't much changed, except that special symbols were introduced for larger numbers so that you didn't need to use so many marks.

If you were a young scribe apprentice in ancient Egypt you would learn that each line represents 1 thing and when you get up to enough lines so that there is one for each finger on your two hands, then you replace them with a symbol like this.

Then for as many of these as you have fingers you write and this continues for a number of symbols that stand for our modern day powers of ten. Then you might be taught addition, so here's an example.

Add

to To perform this operation the first thing you would do would be pretty much like what you might have done with the pebbles. Just physically add the symbols from the first group to the second group by copying all of the symbols from the one to the other to get Now you just have to neaten it up by using the above chart. Replace the ten s shown circled with a . Then replace the ten s shown circled with a . And finally replace the ten s shown circled with a  to get for the final answer.