Early Human Counting Tools

Period: Approximately 44,000 BCE ~

The exploitation of counting was a very gradual process in human history, and much of the details of this development is unknown. However, three major tools that helped early humans count seem to be sticks and bones used for marking notches, stones and other small objects, and fingers and toes. It makes sense that these tools would be of the first used, as they are readily available in essentially any natural setting.

Some of the earliest evidence of humans counting involve notched sticks and bones, used by people living tens of thousands of years ago. These pieces of evidence show that early humans did in fact use simple notations to symbolize quantity.

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The purpose for these notches are still not fully understood, but some artifacts may have been used to keep track of animals hunted or patterns of the moon for religious purposes, both potentially relevant activities for people at that time. It has also been suggested that perhaps stones were originally used to keep track of quantities, but were too ephemeral for preserving information. Therefore, by cutting grooves in a stick or bone, a record could be kept in a more effective fashion.
 
Whatever the case, it is almost certain that early used of numbers by humans were somehow linked to purposes of survival.

Border Cave Notched Bones

One of the earliest evidence found of human counting is a set of notched bones found at Border Cave in South Africa, dating to approximately 44,000 BCE.  

These notched bones show the ability of very early humans to represent the concept of number in symbolic form, a very fine primary distinction between humans and the rest of the animal kingdom in terms of mental capacities. 

This recent finding surprised many archealogists, as the total set of artifacts that were found showed that the people who used them were hunting with poison arrows and adorned themselves with ostrich eggs and marine shells, showing a far earlier evidence of modern-type behavior than was previously thought to have existed.

Notched bones found at Border Cave.

Other artifacts found at the Border Cave site: 1-7: bone awls and points, 8-21: beads of ostrich eggs, 22-23: Nassarius kraussianus beads, 24: lump of organic material bound with vegetal fibers, 25: digging stick, 26: poison applicator. Scale bars = 1 cm.

Ishango Bone

One of the most famous artifacts of early counting discovered is the Ishango bone, dated between 8,000 to 30,000 years old, but typically thought to be closer to the earlier dating. 

This bone displays a peculiar set of notches with interesting numerical properties that may show the ability of the creator of it to have recognized, among other things, the doubling and halving of numbers.  

On part of the bone, 3 notches are doubled to 6, 4 notches doubled to 8, and then 10 notches are halved to two sets of 5.

There are other sections that show only odd numbers, and one column shows only prime numbers between 10 and 20 (11, 13, 17, 19).  However, the notion of prime numbers was certainly not conceived of yet at this point in time.  

Another interesting observation is that the columns all add up to either 48 or 60, both multiples of 12.  

What type of thinking may have been behind this organization is unknown.  However, some theories suggest that the bone was used as a type of lunar calendar or for a woman who may have kept track of menstruation cycles.

This bone was discovered by the Belgian geologist and explorer Jean de Heinzelin de Braucourt in 1960 by Lake Edwards in what is today the Democratic Republic of the Congo.  

Image simultaneously showing the different sides of the Ishango bone.

Numbers displaying the strokes found along the bone.

References for this page

Boyer, C. B., Merzbach, U. C. (3rd Ed.) (2011). A history of mathematics. New Jersey: John Wiley & Sons, Inc.

Mankiewicz, R. (2000). The story of mathematics. New Jersey: Princeton University Press.

Pickover, C. A. (2009). The math book: from pythagoras to the 57th dimension. New York/London: Sterling.

Sci-News.com (2012). Artifacts point to modern culture 44,000 years ago. Retrieved from http://www.sci-news.com/othersciences/anthropology/article00496.html

Author: Jonathan Sack (2012)