Counting systems
Various methods of counting existed before written numbers became a thing. Fingers, number gestures, counting across the body existed before various forms of tally marks.
ScienceABC and By Nigel Cross - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=81756631
For example, it is theorized, based on the extensive use of numbers divisible by 12 in their mathematics, that ancient Babylonians, and possibly Sumerians, counted to 12 on a single hand by using the thumb to count the finger bones (3 per finger), giving them 60 if using the other hand only as digits, or 144 if counting each bone. Other counting systems, such as the Pre-Columbian Mayan and many other in the Americas, are base-20 systems, using fingers and toes. There are others in the Americas that used a base-8 system by counting the spaces between their fingers. In areas around Papua New Guinea, body counting results in a base-27 system.
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After the development of finger counting, or perhaps in tandem with it, tally systems were developed, maybe to keep track of larger numbers or to communicate across language barriers and different counting styles. Prehistoric hand stencils in what might be counting positions from one through five have been found in the Cosquer Cave in France. There are artifacts that date to at least 40,000 years ago that seem to have counting notches on them, maybe recording the lunar cycle or other types of record keeping.
By © Marie-Lan Nguyen / Wikimedia Commons, Public Domain, https://commons.wikimedia.org/w/index.php?curid=8452539The earliest definitive accounting system that we know of are the clay tokens found in Tell Abu Hureyra, a site in the Upper Euphrates valley of Syria dating to the 10th millennium BCE. These tokens had animals and symbols that indicated whether the token was for a unit (single animal) or a group of ten, and a third type for sixty, and others for higher numbers that indicated counting was done in base-60. Number tokens were then placed into clay envelopes, hallow balls to hold the number tokens, to help prevent them from being tampered with, after the accounting was done. At some point, these tokens were impressed on the outside of the envelope before the container was sealed.
Around the middle of the fourth millennium, this system started to be streamlined, leading to the development of number systems. The Sumerians also had complex arithmetic based these impressions or maybe a form of an abacus or counting board before they developed numbers. These numbers likely developed as a way to streamline the process of accounting as more commodities were counted. In the beginning of development, there were over a dozen systems in use around Uruk with nearly as many counting systems, depending on what was being counted, which are common around the world today, allowing us to broadly figure out how the Sumerian system worked.
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Approximately 2700 BCE, the wedge-shaped stylus began to be used, shifting how cuneiform was written. While the system allowed for the writing of fractions, there wasn't a system, like our decimal point, in place that we're aware of that definitively separated full numbers from fractional numbers. By 2100 BCE, a system was in place to define the value of numbers. It was a base-60 system that we now call Assyro-Babylonian Common.
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The remainders of this base-60 system remains in our modern world in the number of minutes in an hour, the number of seconds in a minute, and degrees in a circle. The base-12 counting system remains in our dozen and gross remaining numbers that have specific names and significance.
