In Chapter 10 of “Flutes of Fire: Essays on
California Indian Languages”, Leanne Hinton discusses the different counting
methods present in various American Indian languages and how they came to be. I’m
an engineering student, so numbers are very near and dear to my heart, and this
chapter in particular really blew my mind. My immediate thought was to find the
counting systems of the world that are most unlike the English system. In this
blog, I’m going to try and explain some of those systems and hopefully help you
learn something new!
Number Terminology and Binary
Before I start getting
into some different counting systems, there is some terminology that is worth
mentioning. Going forward in this blog, I will be referring to number systems with
the word “Base” followed by a number. The “Base” refers to the number of unique
digits that are used to represent the numbers within a specific number system.
As an example, English (and many other languages around the world) use a “Base-10”
system. We have ten, single digit numbers – 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Another system you may be familiar with is called “Base-2” or binary, which is
a system most commonly used in computers. Below this paragraph, I have included
a table that will show you how to count in binary. Notice that after you count to
1 in binary, you have now run out of single digits! This means that you represent
the next number larger, in this case 2, with a 10. Similarly, in Base-10, once
you count to 9, you have run out of single digits, and the next number you
represent with a two-digit number, or 10.
With that, I think we are
ready to begin with our first language!
Up First Is… French?
If you know nothing about
French, you may be slightly surprised to see this language on this list. After
all, English and French share a wide range of words, and a number of the
grammar rules are shared between the languages. On top of that, French, Spanish,
and Italian are among the “Romance Languages”, a group of languages that evolved
from Latin, and only French has a system that deviates from the “Base-10 norm,”
so to speak.
French is primarily Base-10
with a light sprinkling of Base-20 in the larger numbers, along with some extra
special quirks that seem to be thrown in to trip up new learners of the
language. There is a single word to represent every number from 0 to 16, and
then at 17 there is a sudden shift to using two words hyphenated together. From
0 to 69, French uses a Base-10 system that has a sudden switch to a Base-20
system at 70. Included in a table below are some direct translations that show
this change in Bases.
Multiple Methods in Mountain Arapesh
In Papua New Guinea,
there is a language called Bukiyip (or Mountain Arapesh) with around 16,000
speakers that has a very interesting system of counting, primarily due to the
fact that it actually has two systems in place, each with its own base! One
system uses Base-3, while the other system uses Base-4. How does this work you
ask? Well, the counting system used depends entirely on what exactly you are counting!
The table below, taken from page 191 of K. David Harrison’s “When Languages Die”,
gives a list of objects and things that are counted in each system.
On top of the fact that,
according to this list, there are two systems in place for counting yams, Bukiyip
also has a word that is present in both systems. The Bukiyip word “anauwip”
translates to “hand” in English, and when used in the Base-3 system, “anauwip”
means 6, corresponding to the “five fingers plus the thumb joint” (Harrison:
191). When used in the Base-4 system, “anauwip” instead means 24, “because it
implies multiplying each of the six points on the hand [by four]” (Harrison:
191).
This Last One is in Base-27
When doing my research
for this blog, I found a bunch of different numbering systems that I found interesting
and slightly strange by the English counting system standards. I saw Base-6, Base-12,
as well as a few systems that only have words for a small selection of numbers
(1, 2, 5, and 20 for example) and build the rest of their numbers from there. However,
there was one system that made me quietly gasp and whisper “Oh my god” all
alone in my room. And that honor belongs to none other than the Base-27 number system
from the Oksapmin people of New Guinea.
The Oksapmin people use a
counting system that is based on body parts. The words used for the first 27
numbers are also the words for the body part used in counting. The counting
begins with the thumb of one hand, cycles along the fingers, travels up the
neck, across the face, and then travels back to the other side of the body
where it ends with the little finger, before starting to loop back in the same
direction. To help visualize this, I have included a photo describing how to “count
the 27 body parts” and linked a video below of an Oksapmin woman counting
across her entire body (Saxe).
I hope you enjoyed this blog
entry! If you enjoyed reading about these languages and number systems, I highly recommend a quick
google search to learn about more. The world has some really interesting
languages and systems in place and I merely scratched the surface with these!
Link
Oksapmin Woman Counting
Oksapmin Woman Counting
References
Harrison, K. David.
2007. When Languages Die: The Extinction
of the World’s Languages and the Erosion of Human Knowledge. Oxford University Press.
Hinton, Leanne.
1996. Flutes of Fire: Essays on California Indian Languages.
Berkeley: Heyday Books.
Saxe, G. B. 1982. The development of measurement operations
among the Oksapmin of Papua New Guinea. Child
Development. 53. 1242-1248.
No comments:
Post a Comment