German mathematician Gottfried Wilhelm Leibniz is accredited with determining binary arithmetic in the early 1700s. Unfortunately for his legacy, it appears that the Polynesians beat him by about 300 years. This announcement comes from Andrea Bender and Sieghard Beller of the University of Auckland, and their results were published in the Proceedings of the National Academy of Sciences.
While conventional mathematics uses a base 10 numbering system, binary uses base 2. In base 10, numbers increase like this: 100 (1), 101 (10), 102 (100), etc. Base 2 proceeds like this: 20 (1), 21 (2), 22 (4), etc. With a base 2 system, all numbers can be represented by either a 1 or a 0. This is the same binary number system that drives digital devices today, as a computer can easily send (1) or not send (0) electrical signals based on the desired task.
The discovery of the binary system being used as far back as 1450 CE is particularly surprising, given its location. The island of Mangareva in Polynesia was not a technological hub by any standards and the fact that they were able to develop such a simple yet intricate mathematical system speaks both to the of math as well as a cultural complexity that was not expected from this group.
This old way of common numbering has been all but lost. Because the islands were controlled by the French for such a long period of time, the Arabic number system with which we are most familiar has taken its place. The researchers also discovered that mathematicians on the island combined the two number systems into a novel binary system, in which 10 was multiplied by increasing powers of two and . This also allowed them to cut down on the number of digits involved in traditional binary systems. For example, 130 is represented in binary as 10100010110000010, but with the Mangarevan system, it is shortened to VTK. V (varu) stands for 80, T (tataua) is 40, and K (takau) is 10.
Though the blended system wasn’t perfect, it had several advantages because of its simplicity. Because it was wholly unexpected to find such a sophisticated mathematical system on these small, undeveloped island hundreds of years before some of the most intelligent Europeans were able to figure it out, there may be much more to discover about blending human culture and mathematical comprehension.