A brief history of numbers and counting, Part 1: Mathematics advanced with civilization

By Steven Law

For the Deseret News

Published: Sunday, Aug. 5 2012 11:00 a.m. MDT

The origins of numbers are cloaked in mystery.


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The origins of numbers are cloaked in mystery. But, I think it’s safe to say that as civilization advanced numbers advanced with it; and it is equally safe to say that civilization could not have advanced without it.

Common intuition, and recently discovered evidence, indicates that numbers and counting began with the number one. (Even though in the beginning, they likely didn’t have a name for it.) The first solid evidence of the existence of the number one, and that someone was using it to count, appears about 20,000 years ago. It was just a unified series of unified lines cut into a bone. It’s called the Ishango Bone.

The Ishango Bone (it’s a fibula of a baboon) was found in the Congo region of Africa in 1960. The lines cut into the bone are too uniform to be accidental. Archaeologists believe the lines were tally marks to keep track of something, but what that was isn’t clear.

But numbers, and counting, didn’t truly come into being until the rise of cities. Indeed numbers and counting weren’t really needed until then. Numbers, and counting, began about 4,000 BC in Sumeria, one of the earliest civilizations. With so many people, livestock, crops and artisan goods located in the same place, cities needed a way to organize and keep track of it all, as it was used up, added to or traded.

Their method of counting began as a series of tokens. Each token a man held represented something tangible, say five chickens. If a man had five chickens he was given five tokens. When he traded or killed one of his chickens, one of his tokens was removed. This was a big step in the history of numbers and counting because with that step subtraction — and thus the invention of arithmetic — was invented.

In the beginning Sumerians kept a group of clay cones inside clay pouches. The pouches were then sealed up and secured. Then the number of cones that were inside the clay pouch was stamped on the outside of the pouch, one stamp for each cone inside. Someone soon hit upon the idea that cones weren’t needed at all. Instead of having a pouch filled with five cones with five marks written on the outside of the pouch, why not just write those five marks on a clay tablet and do away with the cones altogether? This is exactly what happened.

This development of keeping track on clay tablets had ramifications beyond arithmetic, for with it, the idea of writing was also born.

But, if you’re keeping track of your wealth with marks made on a clay tablet what’s to stop you from making your own clay tablet and stamping in 50 marks, and trading those 50 marks on a clay tablet for grain?

To prevent this from happening, the Sumerians needed an official method of keeping track, and an official group of people who kept track. A select few were allowed to enter this group. They essentially became the world’s first accountants. So a farmer may have made his own clay tablet with 50 marks on it and claimed that this proved that he was the owner of 50 chickens, but if that tablet didn’t have an official seal from the accountants it was worthless.

It was the Egyptians who transformed the number one from a unit of counting things to a unit of measuring things. In Egypt, around 3,000 BC, the number one became used as a unit of measurement to measure length. If you’re going to build pyramids, temples, canals and obelisks you’re going to need a standard unit of measurement — and an accurate method of applying it to real objects. What they invented was the cubit, which they considered to be a sacred measurement. A cubit is the length of a man’s forearm, from elbow to fingertips, plus the width of his palm. Considered sacred as they were, they had officially ordained sticks which they kept in the temples. If copy cubits were needed they were made from one of the original cubits kept in the temple. Thanks to this very official, very guarded and very precise unit of measurement the Egyptians were able to create colossal buildings and monuments with wondrous accuracy.

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