If you cannot form composite numbers like fifteen then we call this Systemless Counting.
Again by trade counting systems can be evolved from systemless counting.
Pure 2 count which develops from pairing forms numbers like this:
Diffusion spread out the system? (as opposed to independent invention).
Seidenberg assumes that in ancient times 2 count was in use in much larger area then it is now and that it did spread by diffusion.
6 = | 2 + 2 + 2 |
8 = | 2 + 2 + 2 + 2 |
Seems likely that in a lot of places original pure 2 count was replaced by neo - 2 - count. How did this happen?
Could be through tally-sticks. Since counting was in pairs their carried numerals would probably look like this:
111 | 1111 | 1111 |
111 | 111 | 1111 |
6 | 7 | 8 |
Suppose this method of carving was used by a 2 counting population and that this method of noting numbers was taken over by neighbours who had numbers words for 1, 2, 3 and 4.
They might read the sign for 6 as 3 + 3, the sign for 7 as 4 + 3. In this way the passage from pure 2 count to neo 2 count might be explained.
eg.
1 | ||
2 | ||
3 | ||
4 | ||
5 = 4 + 1 | ) | |
6 = 4 + 2 | ) | |
7 = 4 + 3 | ) | Combination of both |
8 = 4 x 2 | ) | found in Huku tribe |
9 = 4 x 2 + 1 | ) | in South America |
10 = 4 x 2 + 2 | ) | |
11 = 4 x 2 + 3 | ) | |
12 | ||
13 = 12 + 1 | ||
14 = 12 + 2 |
5 - 20 count extends 5 count principle to numbers up to 19.
eg.
Aztecs counted 1, 2, 3, 4, 5, 5 + 1, 5 + 2, 5 + 3, 5 + 4, 10,
10 + 2, 10 + 3 ... 20, 20 + 1, 1 x 20 + 10 ... 2 x 20 + 10.
We can represent these systems using staircases:
Can have normal 10 system but then we come to 60 it is a new unit (gesh)
In English we use ' 3 score' - 60.
Danish language count in 20's
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