When we think of other cultures with alternative number bases, that is, counting systems other than the decimal system of one to ten that we've arbitrarily become accustomed to in the modern world, many will recall the examples of Sumerian's base-60 system (sexagesimal) or the Mayan base-20 system (vigesimal). A professor of anthropology at Humboldt State University, Victor Golla, describes some other interesting systems on page 220 of California Indian Languages (2011) under the heading 4.10.3 Quaternary and Octonary Systems:
"A small residue of counting schemes that cannot be classed as quinary, decimal, or vigesimal are found in Northern Yukian, Salinan, and Chumash (Appendix D: 3, 9, 6, and 7). In all three language groups the count is by fours, either straighforwardly quaternary (based on four, in Salinan and Chumash) or octonary (based on eight, in Northern Yukian). Counting by fours apparently had its origin in an old practice, attested ethnographically among the Yuki (Kroeber 1925:878-879), of counting sticks held between the fingers rather than counting the fingers themselves."
I know several programmer friends who swear that the world would be a better place with octonary counting system, since it's much easier to divide in an octonary system than in decimal.
ReplyDeleteInteresting that they use sticks to count. I wonder what the motivation behind that is.
Have you ever seen Chinese finger counting? They count up to 9 on one hand. And then they cross their fingers for 10 (to emulate the Hanzi I assume). It always annoyed me though. You have a nice efficient system of counting up to 9 on one hand, they had the chance to count up to 20 with two hands, but the '10' screws it up because it needs to hands. Oh well.
"I know several programmer friends who swear that the world would be a better place with octonary counting system, since it's much easier to divide in an octonary system than in decimal."
ReplyDeleteI wouldn't say that but it is easier to divide by 2 in binary at least because it only requires right-shifting the bits. So 1010 (decimal 10) divided by 2 is 101 (decimal 5). Multiplication by 2 requires left-shifting.
"Interesting that they use sticks to count. I wonder what the motivation behind that is."
It was used in China too. Mahjong players may use sticks for counting points.
Oh and I can't say for certain about the Yuki stick system but I'd assume it would be an advantage over regular finger counting by giving an expanded means to represent numbers than with fingers alone. I'm only guessing on this. I'll have to learn more on this.
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