Two Ways to Count to Thirty
Does language have an effect on counting ball-tosses?
It came up as I was walking Annie the dog. I try to throw her ball thirty times on each walk — she is young and needs the exercise. And I was thinking about how language does or does not shape our thought. It is a question people have been arguing about since Sapir and Whorf.
TL;DR Your thought is influenced by what you must notice to use the language properly. It is the case of required distinctions in the language. And as Benjamin Whorf pointed out that usually means grammar.
Are the gender systems of those cultures with gendered languages caused by or causal of the languages they speak? Zarinah Agnew lyrically explains how a change in names for connections might change relationships.
My guess is that it is not vocabulary — words you can say — that shapes our thought. It is grammar, because grammar regulates what you must say.
Indo-European requires us to pay attention to number, because we need to know it to use singular and plural.
Indo-European languages oblige us to pay attention to time so we can use tense. You can’t speak English if you don’t understand “I was about to have said that.” This complex mix of past and future makes distinctions about temporal order that we are required to understand to use the language.
A skilled German translator converted my novel Sister Clare’s Lover into its German version Schwester Claras Geliebter. We spent a week trying to figure out when she should use Sie (formal “you”) and when to change to using du (informal “you”). It would indicate a change in intimacy and power. In English we do not make that distinction, and it was not built into the English original. In German you must choose between them. It is a grammatically required distinction.
But which came first, the distinctions the languages require or the cultures in which they grew up? I go back to my patient dog and her ball.
A test case: Counting to 30 two ways
How could we find languages that are not embedded firmly in cultures?
How about (just to try the idea out) the miniature languages used when we count? If we change the way we count, will we change what we notice?
When I am out with Annie the dog, I am counting to thirty as I throw her blue and orange ball with the throw-stick. How many ways can you count to thirty, and what effect does each of those miniature “languages” have on thought?
Counting by tens — the way we usually do
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
11, 12, 13, 14, 15, 16, 17, 18, 19, 20
21, 22,23, 24, 25, 26, 27, 28, 29, 30
Just for the novelty of it — counting by sixes
(in this case, a six is indicated by the word “ki” for no good reason. It is like the “-ty” in twenty, thirty, forty…)
1, 2, 3, 4, 5, ki (ki is six)
1ki1, 1ki2, 1ki3, 1ki4, 1ki5, 2ki (two ki is 12)
2ki1, 2ki2, 2ki3, 2ki4, 2ki5, 3ki (three ki is 18)
3ki1, 3ki2, 3ki3, 3ki4, 3ki5, 4ik (four ki is 24)
4ki1, 4ki2, 4ki3, 4ki4, 4ki5, 5ki (and five ki is 30!)
Effects of two ways of counting
In the tens case, multiples of ten are emphasized (10,20,30).
The counter must keep track of the tens to use the system. There is some emphasis on half-tens (5,15,25) in order to be able to say “We’re halfway to” some landmark, and some slighter emphasis on the second-to-last in each ten (9, 19, 29) so one can say “We’re almost there!”
In counting by sixes, however, one must keep track of multiples of six.
They each have a name, and other numbers in the line take their name from the previous six. So our “7” is in six-base “one-ki-one” = one six plus one. The user’s attention is strongly drawn to numbers that are NOT emphasized in a tens system: 6,12,18,24. The two systems both notice 30, as does Annie when her ball-game stops.
As in the tens system, there is some attention to half-way-there numbers, but they are “half-sixes.” Three is one, being halfway from zero to “ki” or six. Nine is halfway between one-ki (6) and two-ki (12). In the six system, nineis called “one ki three”. Fifteen is 2ki3 (= 12 +3), 21 is 3ki3 (18+3), and 27 is 4ki3 (24+3). When was the last time you thought about 21 or 27? But in a six-based system, your attention is drawn to them not infrequently.
And I just noticed that a dozen is “two ki.” It is the sort of thought that would arise only in this six system.
Hmm, I’d say the results of this one little test say “Yes.”
In order to use either the six-based system that we made up for this story, or the ten-based system we are accustomed to, we must think in terms of the base number and its multiples. So may I submit:
This miniature language of counting by sixes does change what one thinks about and pays attention to. The rigid grammar of a counting system does direct our attention, and thus our thought.
Thank you Annie!
