Number systems

[TriceraTiger]

Is a hexadecimal counting system attested in any natural language? I'd figure that they'd use the joints on the fingers to count. How common are octal and duodecimal? Is the former really only attested in Pamean, and is the latter only attested in some languages in central Nigeria and then Chepang in Nepal?

[gach]

You seem to be pretty much on the spot with bases 8 and 12. Hammarström has a paper dealing with the rarer numeral bases and spends a few pages on these starting from p. 20. I'm not aware of any language having a numeral system working in base 16.

Occasionally you'll see some very exotic numeral bases being suggested for a number of languages. An example is the Wikipedia article of Oksapmin claiming that the language has a base 27 counting system. That is just wrong, what the language has is a body part counting system with 27 places in total which doesn't count as a true numeral base.

[jal]

An example is the Wikipedia article of Oksapmin claiming that the language has a base 27 counting system.

Not any more :)


JAL

[gach]

Not any more

Very nice to know that there are people here who aren't as pathologically lazy in these things as I am

[CatDoom]

The northern Yukian languages (Yuki and Coast Yuki) in California also used a base-8 counting system. Perhaps more unusually, the Chumash languages had a base-4 counting system, though the surviving records of the Ventureño counting system show that there was a fair amount of irregularity. Notably, however, there's a unique word for 16, which is also used in forming the terms for 17 (which appears to be something like "16 and 1") and 32, which is constructed as "two 16's". So, while it's far from a regular hexadecimal system, 16 is used as a sub-base.

EDIT: Hmmm... according to the Hammarström article, Yuki numerals are more properly Base 4-8, somewhat similar to the Chumash ones; Pamean is apparently the only known language that goes *directly* to eight, without deriving 5-7 from previous numerals.

[gach]

Hammarström mentions base-4 systems in the Skou languages. My favourite is the system found in Skou itself. This is a system of various sub bases going up to 24, though none of these have multiplicative behaviour. This means that the system simply stops at 24 and the language resorts to loaning above that. The full system is:

Code: Select all

1    áling                         "1"
2    hìngtung                      "2"
3    héngtong                      "3"
4    nongpong                      "4"
5    nápang                        "5"
6    nápánghì                      "5+n"
7    nápang héngtong               "5+3"
8    náhìpa                        "8"
9    náhìpa pa áling               "8+1"
10   náhìpa pa hìngtung            "8+2"
11   náhìpa pa héngtong            "8+3"
12   hangpà                        "12"
13   hangpà pa áling               "12+1"
14   hangpà pa hìngtung            "12+2"
15   hangpà pa héngtong            "12+3"
16   hangpà pa nongpong            "12+4"
17   hangpà pa nápang              "12+5"
18   hangpà pa nápang pa áling     "12+5+1"
19   hangpà pa nápang pa héngtong  "12+5+3"
20   hangpà pa náhìpa              "12+8"
21   hangpà pa náhìpa pa áling     "12+8+1"
22   hangpà pa náhìpa pa hìngtung  "12+8+2"
23   hangpà pa náhìpa pa héngtong  "12+8+3"
24   mabírí                        "24"

You can identify here apparent sub bases 5, 8, 12 and 24. Notice how the system gets broken at 5. Instead of a sub base at 4 you only start adding smaller units to 5, 6 is irregular and formed with an affix unknown from the rest of the language, and against the rules of addition 7 is formed as "5+3".

The reason behind this seems to be that the Skou numeral 5 is cognate to the numeral 4 in its relatives. These languages have in general more regular base-4 systems, so it seems that Skou just coined a new word for 4, pushed the old sub base at 4 to 5 and pretended that it still had a working base-4-8-12-24 system.

[KathTheDragon]

'hì' looks like a reduced form of 2.

[gach]

That's most likely where it comes from. Though the loss of nasalisation in the only remaining syllable looks a bit random since the language is otherwise very liberal in which syllables can be nasal.

[Pole, the]

There's also the Sora language (of „the Linguists” fame) with a base 20 and subbase 12.

[KathTheDragon]

Having looked at that a bit further, 8 is possibly analysable as 'ná-hì-pa', where 'hì' is 2 as above, and is infixed into 'nápa' 4. Thus, 2 4's = 8.

[2+3 clusivity]

My favourite is the system found in Skou itself. * * *

Code: Select all

* * *
3    héngtong                      "3"
* * *
5    nápang                        "5"
6    nápánghì                      "5+n"
7    nápang héngtong               "5+3"
* * *

. . . and against the rules of addition 7 is formed as "5+3".

The reason behind this seems to be that the Skou numeral 5 is cognate to the numeral 4 in its relatives. These languages have in general more regular base-4 systems, so it seems that Skou just coined a new word for 4, pushed the old sub base at 4 to 5 and pretended that it still had a working base-4-8-12-24 system.

Wow. That is unusual.