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# Re: Number system

From: Ray Brown Tuesday, April 26, 2005, 17:50
```On Monday, April 25, 2005, at 06:23 , Tim May wrote:

> Ray Brown wrote at 2005-04-25 18:04:33 (+0100)
>> If Max wants to look for a real vigesimal natlang number system, he
>> must look outside of Europe. On his own continent he will find the
>> Maya. They used a proper vegesimal system like the one he
>> outlined.[snip]

>> I regret I do not know the Mayan names for the numbers. But this is
>> surely the sort of system that Max has in mind.
>>
>
> You can see a description of the Tzotzil number system here:
> http://www.sf.airnet.ne.jp/~ts/language/number/tzotzil.html
Thanks - very interesting.

But it is not _completely_ vigesimal, as the page claims, tho it is far
more nearly vigesimal that anything found among European languages. In
particular, the counting in scores which, as in Basque, starts at 20,
unlike Basque, continues until 399. There is no word for 100, which is
merely _vo'-vinik_ (5 x 20), as there is in both Basque and the Insular
Celtic languages; the higher numbers are: _j-bok'_ 400 (20^2) and _j-pik_
8000 (20^3) which is exactly what we would expect from a proper vigesimal
system.

The only place where Trotzil is not fully vigesimal is from 11 to 19;
these are formed from numbers for 2 to 10, i.e. are decimal. Tho
interestingly, 11 and 12 (as in the Germanic langs) do not follow he same
pattern as 13 to 19; while 11 is "ninetwo" and 12 is "tentwo" where the
morphemes are modified when compounded, those from 13 to 19 are two
separate words "three ten", "four ten" etc.

It suggests to me the following stages in development:
1. An early system counting 1 to 10 (finger) and probably just vague words
like 'several[', 'many' etc.
2. An extension to counting 12s.
3. Later extension of system and coining an original word for 20 (j-tob).
4 the developing a fully fledged vigesimal system of counting for all
numbers > 20.

So, to summarize my recent mails:
11-19      20-99        Greater than 99
Modern Welsh  decimal    decimal       decimal
Breton  decimal    mixed         decimal
Basque  decimal    vigesimal     decimal
Trotzil  decimal    vigesimal     vigesimal

Of these, Trotzil most closely resembles Max's "vbazi". Are there any
natlangs that are actually 100% vigesimal, i.e. have distinct & unique
morphemes for all the numbers from 1 to 19 inclusive?

> (Of course, these won't be the same words used by the Classic Maya,
> but they probably are cognates, and I imagine the system was
> grammatically similar.)
I imagine so also. I did not mention this above, I think it is worth
referring to it. I found the system of counting the scores from 21 up to
399 quite interesting. We are so used from the languages of the old world
of adding the unit number to the number of 10s (or 20s) - tho there are
some exception. Latin, e.g. normally expressed the 8 and 9 by subtracting
from the next 10 along, e.g.
18 duodeuigenti
19 undeuiginti
20 uigenti
...
28 duodetriginta
29 undetriginta
39 triginta
etc.

But between multiples of 20, Trotzil uses neither the addition principle
nor subtraction; it uses the form _x of y_ where _x_ is the _remainder_
and _y_ is the next highest multiple of 20!
Thus, for example, 26 is: vakib xcha'-vinik "six of forty". Presumably
'shorthand' for:
"number six in the score which terminates with 40" 9i.e. the score from 21
to 40.

Now there's an idea for an artlang    :)