The study of modern “primitive” cultures offers another window into human mathematical development. By “primitive,” I mean cultures that lack a written language or the use of modern tools and technology. Many “primitive” societies have well-developed arts and a deep sense of ethics and morals, and they live within sophisticated societies with complex rules and expectations.
In these cultures, counting is often done silently by bending down fingers or pointing to specific parts of the body. A Papuan tribe of New Guinea can count from 1 to 22 by pointing to various fingers as well as to their elbows, shoulders, mouth and nose.
Most primitive cultures use object-specific counting, depending on what’s prevalent in their environment. For example, the Aztecs would count one stone, two stone, three stone and so on. Five fish would be “five stone fish.” Counting by a native tribe in Java begins with one grain. The Nicie tribe of the South Pacific counts by fruit.
English number words were probably object-specific as well, but their meanings have long been lost. The word “five” probably has something to do with “hand.” Eleven and 12 meant something akin to “one over” and “two over” – over a full count of 10 fingers.
The math Americans use today is a decimal, or base 10, system. We inherited it from the ancient Greeks. However, other cultures show a great deal of variety. Some ancient Chinese, as well as a tribe in South Africa, used a base 2 system. Base 3 is rare, but not unheard of among Native American tribes.
The ancient Babylonians used a sexagesimal, or base 60, system. Many vestiges of that system remain today. That’s why we have 60 minutes in an hour and 360 degrees in a circle.