Numbers

Summary

Introduction

People began to count long before they began to write. In the late 1930s, an archaeologist sifting dirt in what is now the Czech Republic stumbled upon the most ancient math- ematical object found so far: a 30,000-year-old wolf bone with 57 notches in it. These were arranged in groups of five, much as in today's tally-method, suggesting that people may have counted on their fingers then. The relic offers no clue as to what was being counted. Was it days? food supplies? Some 25,000 years later, when trading had grown more widespread, such missing information became important, and filling it in was often done by including pictograms akin to simplified analogues of ancient cave paintings. For example, a clay token might have a stick figure animal inscribed on it to symbolize one sheep. In a sense, writing arose from business math. The original Sumerian writing system evolved from such clay tokens, and its pictograms slowly became more abstract through time. Egyptian hieroglyphs, too, are similar testimony to such evolution. Drawing upon word-sounds (spoken language developed long before writing), hieroglyphs were linked pictograms whose pronunciation could approximate a spoken word. The word itself might be abstract so that, charades-style, we could today draw a pictogram of a reed to stand for the verb “read.”

Most people assume man has always counted in base ten. Not so. The earliest bases were 2, 3, 4, and especially 5, which became very widespread.