Re: Number system

On Sunday, April 24, 2005, at 08:55 , Ray Brown wrote:

> On Sunday, April 24, 2005, at 06:38 , Gregory Gadow wrote:
[re vigesimal number systems]

>> Traces of it can be found in English (a score of something) and
>> French (vignt=20; quatre-vignt=80)
>
> I would say also that only traces of it are found in the Brittonic
> varieties of Insular Celtic; it's just that there's slightly more trace of
> it than in standard French. I believe the same is true for the Gaelic
> langs. But we have people on this list far more familiar with those
> languages than I am, so I'll leave it to them   :)
Further to my mail, another language is also often claimed to use a
vigesimal system, namely Basque. But on inspection it will be found also
to be a decimal system with some 'vigesimality'. Like the Insular Celtic
languages, it does _not_ have separate morphemes for 11 to 19; 11 is a
derivative of 10, and the others are clearly compouns of 10 + 2 to 9
respectively, cf:
1 bat        11 hamaika
2 bi         12 hamabi
3 hiru       13 hamahiru
4 lau        14 hamalau
5 bost       15 hamabost
6 sei        16 hamasei
7 zazpi      17 hamazazpi
8 zortzi     18 hemezortzi
9 bederatzi  19 hemeretzi
10 hamar     20 hogei

Also, like the Insular Celtic langs, it has a word for 100, _ehun_, and
1000 _mila_. OK - _mila_, like Welsh & Breton _mil_, it is derived from
Latin; but _ehun_ is not (nor are Welsh _cant_ or Breton _kant_ derived
from Latin - they are inherited from PIE).

The only vigesimal part is that the numbers from 20 to 99 inclusive are
counted in scores; also, unlike either the 'traditional' Welsh system or
Breton, Basque is consistent in this, thus:
21 hogeitabat (-ta- = 'and'), 22 hogeitabi, 23 hogeitahiru etc
31 hogeitahamaika, 32 hogeitahamabi, 33 hogeitahamahiru etc

40 berrogei; 50 berrogeitahamar; 60 hirurogei; 70 hirurogeitahamar; 80
laurogei; 90 laurogeitahamar.

So, like the Insular Celtic langs, it uses a mix of decimal & vigesimal
for the tens-and-units combos. But then it uses _ehun_ (10^2) and _mil_
(10^3) - i.e. basically decimal.

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. Also, unlike the
pre-Arabic European number notations, the ancient Maya did have a symbol
for zero and used place notation.

Unlike us, they wrote their numbers in columns, not left ro right,
starting with the highest values at the top and the lowest at the bottom.
For convenience, I'll turn them through 90 degrees and write them as we do
and use the our western Arabic symbols and letters in the style of
hexadecimal, except that we must extend it   :)
0 1 2 3 4 5 6 7 8 9 A B C D E F G H J K   (omitted I to avoid confusion
with 1!)
Mayan        Value
   10   =  (1 x 20) + 0 = 20
   2F   =  (2 x 20) + 15 = 55
   C9   =  (12 x 20) + 9 = 249
  20K   =  (2 x 400) + (0 x 20) + 19 = 819
9033   = (9 x 8000) + (0 x 400) + (3 x 20) + 3 = 72 063

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.

Ray
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Anything is possible in the fabulous Celtic twilight,
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as of the reason."      [JRRT, "English and Welsh" ]

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