6.894, Sum: Non-decimal counting systems
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LINGUIST List: Vol-6-894. Tue Jun 27 1995. ISSN: 1068-4875. Lines: 647
Subject: 6.894, Sum: Non-decimal counting systems
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1)
Date: Sat, 03 Jun 1995 21:20:53 EDT
From: BENTLEAJ at guvax.acc.georgetown.edu
---------------------------------Messages------------------------------------
1)
Date: Sat, 03 Jun 1995 21:20:53 EDT
From: BENTLEAJ at guvax.acc.georgetown.edu
Summary of Responses Concerning Non-Decimal Counting Systems
************************************
From: IN%"BILLINGS at PUCC.BITNET" "Loren A. Billings"
Orthogonol to your query, Chinese seems not to group its large numbers in
groups of three zeroes (i.e., as English does (thousand, million, billion/
milliard, etc.), but rather groups them with a new word for each fourth
new digit (i.e., word for ten-thousand, then no new word until 10000 x
10000 and so on). This is pretty unclear, but write me back if you have
questions. I can't write right now for long. --Loren (billings at princeton.edu
Subject: query: decimal system in languages of the world
Subject: Languages, base 5
Sender: Bosse Dominique <bossed at ERE.UMontreal.CA>
The Kru languages of East Africa (South East Liberia and South West Ivory
Coast) have a number system based on 5. Six, seven, eight, nine are five
with a modification. Ten is different.
When I was working on the reconstruction of proto-kru for my M.A. thesis,
I did not pay much attention to that aspect of the languages. And there are
hardly any extensive sources for any one of these languages. I used
informants and some semi-published data which are very difficult to come
by. I am listing the most likely sources of information on numerals.
Luckau, S. (1975) "A Tonal Analysis of Grebo and Jabo". Ph.D.
diss., Stanford Univ.
Marchese, Lynnell (1979) "Atlas linguistique kru: essai de typologie".
Universite d'Abidjan.
Kokora, P.C. (1979) Esquisse phonologique du koyo. "Cahiers ivoiriens
de la recherche linguistique." Univ. d'Abidjan.
Sorry for not being able to offer more precise information. For the
reconstruction of Proto-Kru, I have made use of the numerals two, three
and ten only, as they were the only ones that met my regularity criteria
across comparative series.
Regards,
Dominique (fem.) Bosse
Departement de didactique
Universite de Montreal
Montreal (Quebec)
********************************
From: IN%"mjd612 at anu.edu.au"
Subj: counting systems
I know of a number of languages with much funnier counting systems than what=
you described. For instance, Kalam (Papuan) uses a base 27 system with=
each unit related to a body part. Such systems are quite common in the=
highlands of PNG. They start at a finger, count across, up the wrist,=
forearm, shoulder, etc, have a mid point at the neck or chest, and then=
count down the other side. The base of such systems varies from language=
to language according to how many counting positions are used. I've seen=
an article on this (by Laycock I think) in Wurm's handbook of Papuan=
languages. He made a distinction between number systems and tally systems,=
but according to Andy Pawley's description of Kalam, this does not seem to=
be motivated. They can, for instance, quite happily count above 27 (with=
slight wierdness since they lack a zero), although he did say that numerals=
over 80 or 90 were pretty rare.
My personal favourite is Chukchi (Paleosiberian area, Chukotko-Kamchatkan=
family) which has a rather complex base twenty system which can generate=
numerals up to, but not exceeding 419. The numeral for twenty is cognate=
with the word 'person', five with 'hand/foot', so I think you can see where=
they got it from. I've got the handout to a seminar that I gave on this-=
if you are interested I will send it to you (data from Skorik 1961=
_Grammatika chukotskogo jazyka_).
I am going to Chukotka on fieldwork in just over a week's time, so if you=
want any clarification of these (rather haphazard) references you should=
get back to me soon,
Yours,
Michael.________________________________________________________Michael Dunn
Linguistics, The Babel Building
Australian National University
ACT 0200
Australia home: 06-249 1249 fax: 06-279 8
214
*********************************
From: IN%"mgs at unixg.ubc.ca" "Martin Silverman"
Subj: inquiry on numerals
The following are "standards" with which you may already be familiar.
The newer references really don't supersede the older ones, which are
wonderful as long as one can ignore their evolutionary assumptions.
Martin Silverman, Anthropology, UBC
Menninger, Karl
1969 Number Words and Number Symbols: A Cultural History of
Numbers. Translated by Paul Broneer from the revised German
edition (1958). Cambridge, Mass.: M.I.T. Press
Zaslavsky, Claudia
1973 Africa Counts: Number and Pattern in African Culture.
Boston: Prindle, Weber & Schmidt.
Greenberg, Joseph H.
1978. Generalizations about numeral systems. In Universals of Human
Language, ed. by Joseph H. Greenberg, Charles A.
Ferguson and Edith A. Moravcsik, vol. 3, pp. 250-295. Stanford,
Stanford Univ. Press.
Hurford, James R.
1975 The Linguistic Theory of Numerals. Cambridge: Cambridge
University Press.
Hurford, James R., 1987
1987 Language and Number: The Emergence of a Cognitive System.
Oxford: Bla ckwell.
Closs, Michael P.
1986 Native American Number Systems. In Native American
Mathematics, edited by Michael P. Closs, pp. 3-43. Austin:
University of Texas Press.
From: IN%"John_Bowden at muwayf.unimelb.edu.au" "John Bowden"
Subj: Counting systems
REGARDING Counting systems
Hi there,
As far as I'm aware the major reference on counting systems is:
Hurford, James R. 1987. 'Language and number: the emergence of a cognitive
system'. Oxford: Basil Blackwell.
There are certainly a number of languages out there with counting systems
much more seemingly 'bizarre' than what you're expecting. There are a number
of New Guinea languages with (sort of) base 23, 25, 27, etc. I can't
remember specific references at the moment, but I think Hurford should
mention them. There are also a number of languages in other parts of the
world where counting only goes as far as '1, 2, many' (or maybe
'1,2,3,many'). There are a number of Australian langauges of this type.
There's a collection of SIL workpapers with a number of papers on Australian
counting systems: Hargrave, S. ed. 'Work Papers of Summer Institute of
Linguistics, Australian Aborigines Branch', Series B: Vol. 8. Language and
Culture. SIL-AAB: Darwin'
I'm currently writing a grammar of an eastern Indonesian langauge called
Taba, which is a bit like Hawaiian: 'more or less' base ten, with a few
quirks. Taba is a numeral classifier language, where the classifiers are
prefixed to numeral roots; higher numbers like 'ten', 'hundred' etc. belong ???
formally with the classifiers rather than with the numeral roots. I haven't
finished writing up the quantification stuff yet, but if you're interested
I'd be happy to send you a copy once it's done.
Hope that's of some help.
Best wishes,
John Bowden
********************************************
From: IN%"spackman at dfki.uni-sb.de"
Subj: query: decimal system in languages of the world
As I kid I was taught that base 60 was a relatively common choice
(perhaps subdivided somewhat, as the romans subdivided 10s by 5s). It is
justified by all the same mathematical arguments as base 12, of course,
and is perhaps better for calendrical computations. In terms of
practical use, working with large bases having many factors is no more
weird than a syllabic writing system: some things you want to express
become very difficult indeed, but there are compensating conveniences
for a lot of common cases (in base 60 the quick and dirty methods we
have for dividing/checking divisibility by 2, 5 and 10 also apply to 3,
4, 6, 12, 15, 20, 30 and 60! Unless you're a computer scientist, that's
hard to beat).
But tell me, why should a language that doesn't use base 10 be
restricted in mathematics? All in all, 10 is an unhappy compromise base.
It is neither a prime power nor a number with many factors, the two
things that most simplify computation. Its neighbours - these are
sometimes important because of the casting-out-9's trick (which has
nothing to do with 9; in hexadecimal you get casting out 15's) - are 9
and 11; of these only 9 is useful (because it is 3 squared - that's why
you can check if a decimal number is divisible by 3 rapidly). I
*suppose* you could argue that this covers 2, 3 and 5 in some sense -
giving you something with nearly the same coverage as base 30 (but then
this is true of hexadecimal as well) - but really, when you learned
decimal arithmetic at school, was it its simplicity that impressed you
the most? :-)
Really, I know of no reason to favour decimal at all - other than, just
maybe, the weight of tradition in my culture. (Even then, you note that
America, while ridiculing the british for a monetary system that I can
barely remember, *still* tries to launch rockets in some random
combination of bases 10, 12 and 16. What the hell *is* a foot-poundal,
anyway? ;-) Honestly, if asked to pick a nice biggish round number, I'll
go for 256 over 100 any day - and I believe my forebears would have
chosen 144.
Regards
stephen
----------------------------------------------------------------------
stephen p spackman +49 681 302 5288(o) 5282(sec) stephen at acm.org
dfki +1.24 / stuhlsatzenhausweg 3 / D-66123 saarbruecken / germany
----------------------------------------------------------------------
http://cl-www.dfki.uni-sb.de/~spackman finger:spackman at dfki.uni-sb.de
***************************************
From: IN%"Ken.Beesley at Xerox.fr" "Ken Beesley"
Subj: number systems
I'm not by any means an expert in this myself, but I do know you are
working in a well-plowed field.
There's a book by Jim Hurford (Prof. of Linguistics in Edinburgh,
Scotland) on the subject. I vaguely recall that Welsh dialects
differ, with some obvious evidence of base 5, base 10 and base
15 systems (the standard Welsh invented by the BBC for broadcasts
had to devise their own base 10 system). A shepherd somewhere
in south American was spotted counting sheep on his fingers in
base two. I vaguely recall other base 5 systems (Ainu?), and
other exotic systems from Africa. You should be able to find
quite a literature.
There's nothing natural or superior about a base 10 system. The
fact that humans have 10 fingers probably predisposes them to
base 10 systems, but math is basically the same no matter how
you express your numerals. French has certain vestiges of base
twenty numerals, forcing you to say "four-twenty-fifteen" to say
(and write) 95, but France has produced some of the best mathematicians
in the world. Computer scientists deal often in base 8 and base
16 because they translate so easily into base two, the system that
is natural for computer memories and circuits.
Kenneth R. Beesley ken.beesley at xerox.fr
Rank Xerox Research Centre
6, chemin de Maupertuis
38240 MEYLAN, France
***********************************8
From: IN%"larryt at cogs.susx.ac.uk" "Larry Trask"
Subj: Numerals
There are several published sources which will provide the kind of
information you're looking for. The only one I have handy is one
that may not be easy to come by in the USA, since it's a coursebook
published by the Open University (the UK's distance-learning
university). This is
Open University (1975), _Counting I: Primitive and More Developed
Counting Systems_, Milton Keynes: The Open University Press,
Unit AM 289 N1, ISBN 0 335 050166
This book, which is written in a somewhat patronizing manner,
recognizes the following counting systems (or rather non-systems for
the simpler ones):
one-two-many: Bergdama (South Africa), Australian languages
1-2-3-many OR 1-2-3-4-5-many: Kalahari Bushmen
pair counting (1, 2, 2-1, 2-2, 2-2-1, 2-2-2; rarely beyond six
in this manner): Bakairi (Brazil), Gumulgal (Australia),
"Bushman"
neo-2-counting (1, 2, 3, 4, 2+3, 2x3, 1+(2x3), 2x4, etc.): Guarani,
Paiute, "Eskimo", Yukaghir, ...
4-count: Afudu, Huku (both Africa)
5-10 OR 5-20 count: Nahuatl, Mayan, Ainu
10-60 count: Sumerian
In fact, the book lists and maps some dozens of languages with pair
counting or neo-2-counting. The book is only 46 pages long, so I can
send you a photocopy if you can't find it and want to see it; it
provides examples from a fair number of languages.
Ken Hale has suggested that many Australian languages do not strictly
have any numerals at all, but only singular, dual, and plural
determiners (the dual is generally well-developed in Australia).
There are five coursebooks altogether in this series; I also have the
second (on the decimal system, tallies and knobs) and the third (on
written numbers).
A classic older book on the subject, often quoted in the OU
coursebook, is
Karl Menninger (1969), _Number Words and Number Symbols_, MIT Press
There is also much more recent book, but I have this at home and can't
remember the author's name or the book's title; I recall that it
concentrates on written numbers.
Hope this is of use to you.
Larry Trask
COGS
University of Sussex
Brighton BN1 9QH
England
larryt at cogs.susx.ac.uk
**********************************
From: IN%"loebner at sapir.ling.uni-duesseldorf.de" "loebner"
Subj: numeral systems
Here are some references:
For a comprehensive survey and further references see:
James R. Hurford: The linguistic theory of numerals, CUP, 1987
A classical book is:
Karl Menninger: Number words and number symbols, MIT Press, 1969
For native American systems see:
Michael P. Closs: Native American Mathematics, U of Texas Press, 1986
For an elaborated system on the base 20:
Jadran Mimica: Intimations of Infinity, Oxford: Berg, 1988
A radically differrent system with no base at all is described and
discussed by G.B.Saxe in:
Geoffrey B. Saxe: Culture and the development of numerical cognition:
studies among the Oksapmin of Papua New Guinea. in: C.J. Brainerd (ed.):
Children's logical and mathematical cognition, New York: Springer, 1982
Sebastian Loebner
Seminar fuer Allgemeine Sprachwissenschaft
Heinrich-Heine-Universitaet
Universitaetsstr. 1
D-40225 Duesseldorf
Germany
Tel. +49/0 211 3113399
*********************************************
From: IN%"104LYN at muse.arts.wits.ac.za" "M. Lynne Murphy"
Subj: number systems
beng, a southern mande lg of cote d'ivoire, looks like it was
historically base 5. the numbers 6-9 seem to be "5+x":
1 do
2 plaN (N = engma)
3 NaN
4 sieN
5 sON (O = open o)
6 sOdo (5-1)
7 sOpla (5-2)
8 sOwa (5-3--with assimilation of the N's?)
9 sisi (5-4--with some vowel harmony?)
10 ebu
11 bu asiN do
12 bu asiN plaN
etc...
clearly it is now a base 10 system. the asiN ('plus') is used when
concatenating digits, but not when putting together 5 + 1, etc.
the highest digit for which there is a name is 1000.
reference:
gottlieb, alma and m. lynne murphy. in press. _a beng-english
dictionary_. IULC publications.
best,
lynne m.
---------------------------------------------------------------------
Dr. M. Lynne Murphy 104lyn at muse.arts.wits.ac.za
Department of Linguistics phone: 27(11)716-2340
University of the Witwatersrand fax: 27(11)716-8030
Johannesburg 2050
SOUTH AFRICA
From: IN%"dirkj at mpi.nl" "Dirk Janssen"
Subj: counting systems
Hi, although I liked your question to the linguist list (and I'm very
interested in which counting systems actually do exist in the world), I
have to comment on what you say about counting systems and mathematics:
> [..] And it seems to me that such [non decimal]
> languages would be unlikely to be terribly advanced in terms of
> mathematics or even counting beyond 40 to 1 or 200.
This is utterly untrue, the counting systems has NOTHING to do with
mathematics. All mathematics, knowledge of proportions, economics, etc
known to us could equally well be expressed in any other counting system.
Especially so if the other counting system is 'arabic', ie. positions
encode powers of the base-number.
Although it's not a very convincing argument, consider that your computer
is using a binary system and is very well capable of counting beyond 200
as well as performing complex math.
dirk
***reply: I was aware that the decimal system is not a naturally superior syste
m;
I simply meant that any language with much exposure to our highly decim
al-
based culture of today would have long since comformed to that system;
I believe the information in these posts bears that out; in spite of th
e binary,
octal, and hexidecimal used in computing (which are by no means at all
widespread among your average educated folk,) it seems to be true that
decimal-based systems are the only ones (i'm speaking of contemporary
languages here) that are very highly advanced mathematically
************************************************************
From: IN%"Paul.Foulkes at newcastle.ac.uk" "Paul Foulkes"
Subj: RE: 6.753, Qs: Decimals
Hi
the only one I can think of, but I expect you know this already, is
Old French. There are remnants of a duodecimal counting system in
modern French (dix-sept, quatre-vingts etc).
Not sure of refs, but they shouldn't be difficult to find.
Paul
***************************************
From: IN%"nostler at chibcha.demon.co.uk" "Nicholas Ostler"
Subj: decimal system in languages of the world
See Roy Andrew Miller: The Japanese Language (U. Chicago Press, 1967) p. 337-8
for the original Japanese numeral system, which marked multiplication by 2
with a vowel-ablaut! (e.g. Fito 1 Futa 2; mi 3 mu 6; yo 4 ya 8; itu 5 to
10)
Weird, huh?
Nicholas Ostler
Linguacubun Ltd
17 Oakley Road
London N1 3LL
+44-171-704-1481 nostler at chibcha.demon.co.uk
**************************************
From: IN%"rws at research.att.com"
Subj: decimal systems
The old Yoruba system seems to be base 20, according to Hurford, but
you probably already know this.
In any event, I would be interested in the replies that you get, so
I'll look forward to your summary.
Richard Sproat
Linguistics Research Department
AT&T Bell Laboratories | tel (908) 582-5296
600 Mountain Avenue, Room 2d-451 | fax (908) 582-7308
Murray Hill, NJ 07974, USA | rws at research.att.com
***********************************
From: IN%"smburt at heartland.bradley.edu"
Subj: non-decimal counting systems
I passed your query on to my husband, Lawrence Stout, a mathema
tician. You should look in Ruric e. Wheeler *Modern Mathematics*
(eighth edition) (Brooks/Cole Publishing), a text for math ed.
for elelmentary teachers.
According to this text, the Babylonians had a base-60 system, and
Mayans, base-20--and both were advanced in counting and
calculations. What this says about the corresponding languages,
I don;t know--but you can look into that.
Good luck!
Susan Meredith Burt
***********************************
From: IN%"m200754 at er.uqam.ca" "MICHEL PLATT"
Subj: non 10 base systems
I read your query. Many languages on the Indian subcontinent use non-10.
But unfortunately I cannot think of any names. One uses 15, 3 for each
finger (count the number of spaces between the knuckles). French borrowed
from Celtic giving oddities such as quatre-vingts (4 twenties) for 80.
People in Belgium and Switzerland don't use this (they use septante,
huitante, nonante for 70-80-90) as they were less affected by early Celts
(who were on the Western edge of France). I can give you more insights on
French (as I speak it) if you wish but I think somebody else might be
better versed in the theory behind it than I. I am a phonologist.
As for the Indian sub-continent languages, cannot give you names. I have
seen it being done by Canadians of recent Indian origin. The basic thing
is that whatever systems you will find, they will no doubt be based on
body-part.
Michel Platt, m200754 at er.uqam.ca
Universite du Quebec (Montreal)
***********************************
From: IN%"sharder at ling.hum.aau.dk" "=?UNKNOWN?Q?S=F8ren?= Harder"
Subj: non-decimal counting
Dear Sir,
Danish and French both have an, at least underlying, system
of twenty. French: quatrevingt = 4x20 = 80, Danish: tres (60), firs
(80) and halvfems (90) are three + X, four + X, half + five + X, where
X is some remnant of an earlier morpheme, sometimes represented in
oldfashioned modern Danish as '-sindstyve' ('times twenty').
Both Danish and English has a counting system that is unsystematic
till 12 and systematic from 13 up.
I believe Greenlandic has a system of 12 as well, having loaned
numbers from 13 up from Danish.
Hope this helps,
Soren Harder
***********************************
From: IN%"kelly at bard.edu" "Robert Kelly"
Subj: non-decimal
Consider the Mayan languages and their vigesimal counting systems (Base
20) though graphically evidently based on a quinary model. I don't have
references at hand, but Barbara Tedlock, Time and the Ancient Maya would
be a starting place, or the relevant chapters in any survey (Sylvanus
Morley, for instance).
And in Otto Neugebauer, The Exact Sciences in Antiquity, you'll find much
on Babylonian "heximals"
==================================================
Robert Kelly
Division of Literature and Languages, Bard College
Annandale-on-Hudson NY 12504
Voice Mail: 914-758-7600 Box 7205
***************************************
From: IN%"westaley at OREGON.UOREGON.EDU"
Subj: Numerical systems of the world
You had a recent query on counting systems that are non base 10. I can give
you some instances from Papua New Guinea.
Olo, Torricelli Phylum --Sandaun Province Papua New Guinea
The counting system is an additive system. I will give you the masculine
numerals.
niliye one
winges two
winges niliye three
winges winges four
eti plen five
"hand side"
eti plen niliye six
eti plen winges seven
eti plen winges niliye eight
eti plen winges winges nine
eti plen eti plen ten.
You can add feet so to get to 20 you have eti plen, eti plen, uro plen uro plen
.
The data is mine and is as yet unpublished, but if you wanted to cite
something it is in Staley, William E., 1994, Dictionary of the Olo Language
Papua New Guinea. ms. University of Oregon.
Another system from Papua New Guinea that works in a similar fashion is
Nankina. The data is in:
Spaulding, Craig and Pat Spaulding, 1994 Phonology and Grammar of Nankina,
Summer Institute of Linguistics, Ukarumpa Papua New Guinea.
There is no genetic link between Olo and Nankina.
You could also look at another PNG language that has data on this type of
system:
Toland, Norma R. and Donald F. Toland, 1991, Reference Grammar of the
Karo/Rawa Language. Summer Institute of Linguistics, Ukarumpa Papua New
Guinea.
This later work has a few things not found in the others. There are even
more exotic systems in PNG. I have heard of some in which all the joints
from one hand up the arm over the head and down the other arm are used to
form the system. To find something like this, you might try searching on,
Enga, Chuave, Bena Bena, Fore, Gadsup. Or authors like Graham Scott, or
Andy Pawley. You could also look at Foley, William, 1991, The Yimas
Language of New Guinea, Stanford University Press, Stanford. This will
probably be more accessable to you.
hope this helps
Bill Staley
***********************************
From: IN%"Anthony.Diller at anu.edu.au"
Subj: Khmer numbers
Good day from Australia. On your Linguist List inquiry on non-decimal
systems, Khmer (Cambodian) uses a base-5 system for the numbers from one to
nine. That is, to say "six" one says "five-one" (pram-muey) and so on up to
"nine" = "five-four" (pram-buen). After ten they become more decimal, with
separate words for ten (dop) and twenty (mphey), although the units after
these are still base-5, so "sixteen" is 10 + 5 + 1 (dop-pram-muey). The
words for "thirty" "forty" etc. are borrowed from Thai, which in turn the
Thais borrowed much earlier from Chinese. Thai, by the way, is strictly
decimal - in fact, more decimal than English, having a distinct word for
each power of ten from one up to one million (nu'ng, sip, ro'i, phan, mu'n,
saen, laan, tone marks to be added.) For references on Khmer, see Judith
Jacob's Introduction to Cambodian or Franklin Huffman's Cambodian series
(Huffman used to be at Georgetown, so maybe you know all of this already.)
The following may be a bit off the track for your inquiry, but it is
interesting that Old Khmer texts use the base-5 system for quantities
stated in words but use decimal digits for quantities written in numerals,
ultimately from Sanskrit. It is interesting too that Southeast Asia (rather
than India) preserves the earliest surviving material representation of
zero used in the familiar place-holding decimal function - several examples
from the decade 680-690 AD. Hope this helps. Best wishes. Tony Diller,
Faculty of Asian Studies, Australian National University, Canberra.
**************************************
From: IN%"stampe at uhunix.uhcc.Hawaii.Edu" "David Stampe"
The Sora language (Orissa, India; Austroasiatic/Munda/South Munda/
Koraput group) has a duodecimal/vigesimal numeral system: One counts
to 12 and adds units to reach 1*20, then one counts units times 20 to
399 [[12 + 7] * 20] [12 + 7]: m+jgAl-gulji koRi m+jgAl-gulji. This
number epitimizes the syntax, which is regular. Or one counts thus to
99, and thereafter by units times 100 (using an old borrowed 100 word)
to 999, and then by units ti)ds 1000 (using an invented 1000 word).
The morphemes are 1 AbOy, 2 bagu, 3 yagi, 4 unji, 5 mOnlOy, 6 tudru, 7
gulji, 8 tamji, 9 tinji, 10 gAlji, 11 gAlmuj, 12 m+jgAl, 20 koRi, 100
sOa, 1000 mARiN (where A = schwa, O = open O, + = barred-i, j =
alveopalatal affricate, R = 2dtroflex flap, N = alveopal. nasal). The
unit AbOy is pronounced bOy when suffixed to another number. A unit
prefixed to koRi 20 is shortened: AbOy > bO, bagu > ba, yagi > ya.
There are no relational morphemes (`and') in Sora numbers.
An alternative counting system used for days of work given/owed during
planting or harvest is based on hands and feet: 1, ..., 4, 1-hand,
1-hand 1, ..., 1-hand 4, 2-hand, ..., 1-foot, ..., 1-foot 4. The hand
and foot forms are m+-si (1-hand), bar-si (2-hand), m+-je9 (1-foot,
where 9 = engma). For 20 the form is bO-da9gu, which also means
1-stick, but perhaps the actual original meaning has been lost.
Sora was an unwritten language until this century, so the history of
the duodecimal system can only be reconstructed. Austroasiatic
languages generally share a decimal system, and other Munda languages
count by tens. The Sora unit numbers are native (-gu, -gi, -ji are
probably old dual or plural markers); the innovated numbers 11 and 12
contain the 10 form gAl.
The koRi morpheme (20) is found in many Dravidian, Indo-Aryan, and
Munda languages in eastern India; its origin is often attributed to
Munda, but is really unknown. The sOa morpheme (100) is Indo-Aryan.
I think the mARiN morpheme (1000) is native to Sora, but I don't
recall just now whether I found it in a nonnumeric meaning.
In a paper on cardinal number systems in languages in general in the
1976 Chicago Linguistic Society volume, I speculated that duodecimal
counting (also reflected in dozen, gross, an old English use nf 100 to
mean 120, etc.) reflects counting the 3 knuckles of the 4 fingers with
the thumb* Although I have never seen a Sora use this one-handed
counting method, it is fairly commonplace in weekly markets in India.
The same paper discusses also counting systems based on 2( 4, 5, 8,
10, 20, and perhaps 60. Sora is the only system I know based on 12.
My source for Sora is my own fieldwork, and a Sora dictionary in
preparation by Patricia Donegan and myself. On the Munda numerals in
general there is a monograph by Norman H. Zide, _Studies in the Munda
numerals_, Mysore: Central Institute of Indian Languages, 1978.
David Stampe <stampe at uhunix.uhcc.hawaii.edu>, <stampe at uhunix.bitnet>
Dept. of Linguistics, Univ. of Hawaii/Manoa, Honolulu HI 96822
*************************************************
From: IN%"Bob_Reed at sil.org"
The Mayas and Aztecs of Mexico use a base 20 system, and they were capable
of advanced math capable of producing an accurate calendar.
***end of summary***
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