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Re: Number system

From:Ray Brown <ray.brown@...>
Date: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.
>> 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: >
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 Traditional Welsh decimal mixed 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 :) Max (and others) might find this page interesting also: Ray =============================================== =============================================== Anything is possible in the fabulous Celtic twilight, which is not so much a twilight of the gods as of the reason." [JRRT, "English and Welsh" ]