I'm fascinated by the Inuit-Yupik-Unangan languages in Alaska, Canada and Greenland. There are many of these languages: they ring much of the Arctic Ocean. I just learned that they use a base 20 system for numbers, with a 'sub-base' of 5. That is, quantities are counted in scores (twenties) with intermediate numerals for 5, 10, and 15. This makes a lot of sense if you look at your fingers and toes.

But the Inuit didn't have a written form of their number system - until the early 1990s, when high school students in the town of Kaktovik, Alaska invented one! There were just 9 students at this small school, and they all joined in.

They used 5 principles:

• Visual simplicity: The symbols should be easy to remember.

• Iconicity: There should be a clear relationship between the symbols and their meanings.

• Efficiency: It should be easy to write the symbols without lifting the pencil from the paper.

• Distinctiveness: There should be no confusion between this system and Arabic numerals.

• Aesthetics: They should be pleasing to look at.

They decided that the symbol for zero should look like crossed arms, meaning that nothing was being counted.

This was the start of quite a tale!

(1/n)

The students built base-20 abacuses. These were initially intended to help convert decimal numbers to base 20 and vice versa, but soon the students started using them to do arithmetic in base 20.

The upper section of their abacus has 3 beads in each column for the values of the sub-base of 5, while the lower section has 4 beads in each column for the remaining units.

(2/n)

@johncarlosbaez. French people will love it
@Catweazle @johncarlosbaez Bretons especially: 40, 60, 80 and sometimes 100, 120 and 140 are counted as multiples of 20.
@graham_knapp @Catweazle - do Bretons use base 20 more than French? In French 80 is "quatre-vingts".
@johncarlosbaez @Catweazle yes in French it is just 80 but in Breton it is
40: daou-ugent (2-20)
60: tri-ugent (3-20)
80: pevar-ugent (4-20)
then 90: dek ha pevar-ugent(10 & 4-20)
50 is hanter kant, a half hundred !
@johncarlosbaez @Catweazle I once made the mistake of deciding to code all these #Breton counting rules in Python https://github.com/dancergraham/num2words #bzh
GitHub - dancergraham/num2words: Modules to convert numbers to words. 42 --> forty-two

Modules to convert numbers to words. 42 --> forty-two - dancergraham/num2words

GitHub