The Egyptian Numerals
1.2.5?
The Egyptian Numerals
Introduction
As we learned earlier Mesopotamia was very much the birth of civilization, and many firsts occurred there. Historians have established that there was regular contact between Mesopotamia and Egypt even before the third millennium B.C.E. There is little doubt that the learning and knowledge of the Sumerians and Babylonians had a profound influence on the Egyptians, however they took the ideas of writing and numeration and went in a completely different direction, reflecting their own culture.
The Egyptian writing system which employs what we call today hieroglyphs, was on one hand very different than the pictograms of the sumerian's and far more literal. At the same time, it was also far more lose. For example, the Egyptians could write their hieroglyphs from left to right, right to left, top to bottom, or bottom to top. The egyptians also employed very different tools for writing. Whereas the Sumerians wrote using a stylus on a clay tablet, the egyptians carved their writing into stone with a hammer and chisel, or painted them on shards of stone or earthenware. Because they tended to write things in stone, much of their writing in tombs has been preserved over the millennia. For our purposes, however the most important difference is that the Egyptians employed a very different numeration system, in many ways a step back.
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EGYPTIAN NUMBER GLYPHS
The Egyptians had a remarkably straight forward way of notating numbers that is easy for the modern person to understand. They had special "glyphs" (symbols) assigned exclusively for the purpose of numbers.
The Egyptians used a total of 7 glyphs for their notation ...
A Number was simply written out by writing a string of such symbols in succession.
The first glyph , a simple line , represented a single tally mark ...
The second glyph , a bow , represented "ten" tally marks ...
The third glyph , a curly staff , represented ten bows ...
The fourth glyph , a lotus plant , represented ten curly staffs ...
The fifth glyph , a bent finger , represented ten lotus plants ...
The sixth glyph , a falcon , represented ten bent fingers ...
and the seventh glyph , a man with arms raised in astonishment , represented ten falcons or a great multitude ...
In other words, the symbols represented the denominations of ones, tens, hundreds, thousands, ten thousands , hundred thousands , and millions.
In order to represent any number, one would simply write out the symbols whose sum was the appropriate number. The symbols were usually written in descending order starting with the largest from left to right. It was also intended that the least number of glyphs be used in a representation, so one would never actually write out 10 of any single type of glyph, because it could always be replaced by one copy of the next higher glyph.
For convenience, allow me to establish the following ascii form. Let "|" represent a tally mark, "n" represent a bow, "@" represent a curly staff, "<" represent a lotus, "i" represent a bent finger, "&" represent a falcon, and "V" represent a man with arms raised up in astonishment.
So for example, if an Egyptian scribe wanted to write out 523,406 he would have to write out ...
&&&&& ii <<< @@@@ ||||| |
While this system is certainly a big improvement over a simple "tally system", it does have some major draw backs. When denominations have a large number of units, the scribe has to individually write out each unit. This makes some numbers very long to write. For example 999,999 would require 54 symbols:
VVVVV VVVV &&&&& &&&& iiiii iiii <<<<< <<<< @@@@@ @@@@ nnnnn nnnn ||||| ||||
Also this system is limited in the numbers it can express in practice. There is no "ten million" symbol, so in order to write out ten million, you would have to write out ten of the seventh glyph ( Man with arms raised in astonishment) . A large enough number would require more copies of the seventh glyph than a scribe could reasonably write out
VVVVVVVVVV ... ... VVVVVVVVVV (with V Vs) = million million
From the Egyptians standpoint however this was not an important draw back, because numbers in the millions were rare. So rare in fact that the seventh glyph was sometimes used to represent a very large unknown quantity; in other words, "many".
Later civilizations would go along similar lines as the Egyptians in their numeration systems. The popular Roman numerals provide a few interesting innovations on the basic scheme laid out by the Egyptians.