#base six

An interesting blog post about counting systems on the Morph blog. Excerpt: 

In order to feed his family for the year, and prove himself a worthy man, a man living in southern New Guinea is expected to grow 1296 yams (dioscorea sp.) each season. In Ngkolmpu, a language spoken by around 200 people who live in this region in a single village 15kms within the Indonesian side of the border between West Papua and Papua New Guinea, there is a single word for this number ntamnao.

To speakers of English, this seems like an arbitrarily specific number; yet to Ngkolmpu speakers it’s perfectly natural. Ngkolmpu, along with most of its related languages, has what is known as a senary numeral system also known as a base-six system. In English, we use a decimal system which is based on recursions of ten units while senary systems are based around recursions of six. In Ngkolmpu, the words for one to six are naempr, yempoka, yuow, eser, tampui and traowow. Seven is naempr traowo naempr or ‘one six and one;’ thirteen is yempoka traowo naempr or ‘two six and one.’ You should be starting to see the pattern now. But what happens when you get to six groups of six, i.e. 62 or 36? Well there is a specific word for that ptae.  In fact, in Ngkolmpu there are words for 62, 63, 64 and 65. That’s all the way up to 7776! Related language Komnzo even has a word wi which is used for 66 or 46,656! [...]

The significance of counting yams in these cultures has been hypothesised as the motivation for the development this counting system; something we don’t really see anywhere else in the world. The next question is why base six and not some other number? Well, the main yams consumed in this region are teardrop shaped with a round end and a narrow end. These when placed into small piles naturally fall into neat piles of 6.