Betel nuts, bananas, and shields are counted in base-4. Coconuts, days, and fish are counted in base-3. In Bukiyip, another Papua New Guinea language also known as Mountain Arapesh, there are two counting systems, and which one you use depends on what you are counting. However 80 in Huli is ngui dau, ngui waragane-gonaga duria ((15x5)+the 5th member of the 6th 15). Where the English word for 225 is quite long, the Huli word is ngui ngui, or 15 15. Numbers which are multiples of 15 are simple words. The Papua New Guinea language Huli uses a base-15, or pentadecimal system. The number 25 is tondor abo mer abo sas (18+6+1), and 90 is nif thef abo tondor ((36x2)+18). It has basic words for 6, 18, and 36 (mer, tondor, nif) and other numbers are built with reference to those. Ndom, another language of Papua New Guinea, has a base-6, or senary number system. So 14 is (5x2)+2+2, or tir hosfi hosfihosf, and 59 is (20x2)+(5x(2+1))+(2+2) or yima hosfi tir hosfirpati hosfihosf. In Alamblak, a language of Papua New Guinea, there are only words for 1, 2, 5, and 20, and all other numbers are built out of those. Alamblak, numbers built from 1, 2, 5, and 20 So 16 is un ar bymtheg (one on 15), 36 is un ar bymtheg ar hugain (one on 15 on 20), and so on. Once you advance by 15 (pymtheg) you add units to that number. Though modern Welsh uses base-10 numbers, the traditional system was base-20, with the added twist of using 15 as a reference point.
Traditional Welsh, base-20 with a pivot at 15
So, combining base-20 and subtraction means 77 is m?tadil?g?rin, or (20x4)-3.
Yoruba, a Niger-Congo language spoken in West Africa, also has a base-20 system, but it is complicated by the fact that for each 10 numbers you advance, you add for the digits 1-4 and subtract for the digits 5-9. Twenty-one is jun scha'vinik (first digit of the second man), 42 is chib yoxvinik (second digit of the third man), and 70 is lajuneb chanvinik (tenth digit of the fourth man).
#DIFFERENT NUMBERS IN DIFFERENT LANGUAGES FULL#
Why might a base-20 system come about? Fingers and toes! For numbers above 20, you refer to the digits of the next full man (vinik). Tzotzil, a Mayan language spoken in Mexico, has a vigesimal, or base-20, counting system. 'One' is tip^na (thumb), 6 is dopa (wrist), 12 is nata (ear), 16 is tan-nata (ear on the other side), all the way to 27, or tan-h^th^ta (pinky on the other side). The words for numbers are the words for the 27 body parts they use for counting, starting at the thumb of one hand, going up to the nose, then down the other side of the body to the pinky of the other hand, as shown in the drawing. The Oksapmin people of New Guinea have a base-27 counting system. Does that blow your mind a little too much? Well there are all sorts of weird things that languages can do with number words. But a dozenal system would require us to change our number words so that, for example, what we know as 20 would mean 24 (2x12), 30 would mean 36, and so on. 1, 2, 5 and 10), such a system would neaten up our mathematical lives in various ways. Because 12 is cleanly divisible by more factors than 10 is (1, 2, 3, 4, 6 and 12 vs. The Dozenal Society advocates for ditching the base-10 system we use for counting in favor of a base-12 system. Today is a big day for lovers of the number 12, and no one loves 12s more than the members of the Dozenal Society.