South -Asian Journal of Multidisciplinary Studies (SAJMS) ISSN:2349-7858:SJIF:2.246:Volume 3 Issue 2
A TYPOLOGY OF RARE FEATURES IN NUMERALS
Sandhya Shankar, Research Scholar, JNU
INTRODUCTION
Numerals hold a special place in human cognition. Be it counting exactly or estimating or
grouping, numbers have always been significant. This paper deals with certain features of
numerals which are not common in many languages.
We begin by first distinguishing the often interchangeable terms ‘numbers’ and ‘numerals’.
Numbers convey the quantity or the order (i.e. how much or which one) while they are
represented using numerals. So the quantity of fingers on my one hand, five, would be the
number while the representation as ‘5’ would be the numeral. Numeral thus would be just as
abstract as any ‘word’ in a language.
A BRIEF HISTORY OF NUMERALS
It is speculated that when human species began to speak, it may have been able to name only the
numbers 1, 2 and perhaps 3. “Oneness, twoness and threeness are perceptual qualities our brain
computes effortlessly, without counting” (Dehaene, 1997). He states that the etimology of the
first three numerals also bears testimony to their antiquity, wherein he provides an example that,
“the word for ‘2’ and ‘second’ often convey the meaning of ‘another’, as in verbs to second or
the adjective secondary. Another interesting etimological example that he states is, ‘the IndoEuropean root of the word ‘three’ suggests that it might have once been the largest numeral,
synonymous with ‘a lot’ and ‘beyond all others’- as in the French tres (very) or the Italian troppo
(too much).
In fact up to this day there are some tribes which only have number names for quantities 1 and 2
or maybe 3 (some don’t even have that much but debate is still on for that). But this limit on the
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numerals need not limit their ability to cognitively conceptualize quantity (and thereby numbers).
The restriction in numerals is an external matter and not related to the genes of homo sapiens.
‘The transition toward more advanced numeration systems seems to have involved the counting
of body parts. Historically then, digits and other parts of the body have supported a body based
language of numbers, which is still in use in some isolated communities. In more advanced
numeration systems, pointing is not needed anymore: naming a body part suffices to evoke the
corresponding numeral (e.g. in many societies in New Guinea, the word six is literally “wrist”)’
(Dehaene, 1997). He further adds that number syntax probably emerged spontaneously from an
extension of body-based numeration.
As for the written account of numbers there is no clear record of when did it start, Dehaene
writes in his book that the invention of written number notations probably unfolded in parallel
with the development of oral numeration.
The oldest written record available is from the Aurignacian period, when several bones were
found having numbers represented as notches. The principle of one to one correspondence, in
keeping track of number of objects is quite old and has been reinvented over and again. The
Sumerians filled spheres of clay with as many marbles as the objects they counted, the Incas
recorded numbers by tying knots on strings. In fact the very word ‘calculation’ itself comes from
the Latin word calculus which means ‘pebble’ (Dehaene, 1997). It shows that numeration
systems have evolved through the brain and for the brain; through the brain, because the history
of number notations is clearly limited by the inventiveness of the human brain and its ability to
fathom new principles of numeration and for the brain because numerical investigations have
been transmitted from generation to generation only when they closely matched the limits of
human perception and memory, and therefore increased humankind’s computational potential.
AIM OF THE PAPER
The aim of this paper is to look at the rare features found in the numeral systems of the
languages of the world. The paper is divided into four parts. Each part looks at a parameter that
distinguishes these numerical systems. The parameters are as follows:
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



Different bases: 

How do they count? (different methods used to count) 

What do they count? (restrictions on using the numerals) 

How are numbers formed? (i.e. their internal structure) 
METHOD OF DATA COLLECTION
The data given in this paper is secondary data, collected from various books, references to which
are given at the end. As the name of the paper suggests only those features have been taken into
account which are relatively rare in the languages of the world. By rare it is meant that either the
feature is found in few languages or say specific to a geographical region only. That is, for
example, in case of number bases decimal is not dealt with since it’s the most common base
system.
SOME DEFINITIONS
Numeral:I follow the definition of numerals as given by Harald Hammarstrom, as
“spokennormed expressions that are used to denote the exact number of objects for an open class
of objects in an open class of social situations with the whole speech community in question.”
(Hammarstrom, 2009)
So words which denote an approximate quantity like ‘few’ or ‘many’ would not be treated as
numerals.
Base: The base of a natural numeral system is defined asThe number ‘n’ is a base if the next higher base (or set of normed expressions) is a multiple of
‘n’ and a proper majority of the expressions for numbers between ‘n’ and the next higher base
are formed by (a single) addition or subtraction of n or a multiple of ‘n’ with expressions for
numbers smaller than ‘n’. (Hammarstrom, 2009)
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For example, if ‘n’ is ten, then the set of bases should be multiples of ten, like twenty (2*10),
thirty (3*10), forty (4*10) etc. and the expressions till the next higher base must be based on the
previous base, e.g. ‘twenty one’ (20+1), ‘twenty two’ (20+2), ‘twenty three’ (20+3) etc.
In simple terms it could be said that a base functions like the building block of a number system,
with other numerals formed from it.
Now numeral systems don’t always consist of a single base system. More often in numeral
systems with a higher base, like say 60, the lower numbers are formed using some other base,
called the ‘auxiliary base’. For example, the language Sumerian which had 60 as base used 6 and
10 as auxiliary bases. (Mazaudon, 2007)
RARE BASES
The most common base found in the languages of the world is decimal base, i.e. base 10. In this
paper we shall look at some of the other bases found in different languages:

No numbers at all: There are some languages which don’t seem to have any numbers
atall. The linguist Everett claims that there is no grammatical number in Piraha (1983,
1986). To the debate that there might be reference for the first three numbers, Everett
says that 

“There are three words in Piraha which are easy to confuse with numerals
becausetheycan be translated as numerals in some of their uses h i ‘small si e or amount’,
ho 
‘somewhat larger si e or amount’, b giso ‘cause to come together’ (i.e.many).
tioba´hai
ho´ i hii
child
small predicate
”small child/child is small/one child”
tı´
’ı´tı´i’isi
hoı´ hii
I
fish
larger predicate
“I want [a few/larger/several] fish.”
tı´
’ı´tı´i’isi
ba´agiso
’oogabagaı´
want
’oogabagaı´
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I
fish
many/group want
“I want [a group of/many] fish.”
There are also no ordinals in Piraha. Some functions of ordinals are expressed via body
parts. Example:
Ti
’apaı´ ka´obı´I
’ahaigı´
hi
tı´ohio´’ı´o/gaaba
ka´obı´i
I
head fall
samegeneration he
towards me/there stay fall
“I was born first then my sibling was born.” (lit.“I head fall sibling to me/there at fall.”)
They have no word for individual fingers (e.g. ring finger etc.). They don’t have a word
for ‘last’. They have no gestures to indicate tallying. (Everett, 2005)
Another language Xilixana, belonging to the Yanomama language family, spoken
in Brazil (along the Mucujai river), also does not have any numerals to represent
exact quantities, not even ‘one’. For example (Hammarstrom, 2009)
‘moli’ : Means ‘one or a few’.
Kup/ yalukup Means ‘two or a few’.
pək : Can refer to any number more than two or a few.
That is the representations are in exact and cannot be strictly treated as numerals.

No bases: Some languages have a very limited set of numbers. For example,
Nadeblanguage, part of the Nadahup language family spoken in and around the
Amazonian Vaupes region, has only three lexical terms for numbers (i.e. for one, two and
three) and even these are not primarily used to represent a single numerical value. 

Another language, Daw (spoken just outside the Vaupes region) combines two primary
numeral strategies: Lexical terms for one, two and three and a system based on the term 

‘brother’ for expressing even and odd values from 4-10. That is numerals 1-3 are in
common use for representing quantities (e.g. one month) but the native system of four
and above is used only by the oldest speakers (Epps, 2006). Unlike the lexical terms for
1-3, the tally values for 4-10 is minimally linguistic in that it has only two terms “even”
(Lit. ‘Has a brother’) and “odd” (lit. ‘Has no brother’), which supplement a gesture
system relying on fingers. For example they indicate ‘four’ by holding the fingers of one 
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hand separated into two groups while for ‘five’ they add the thumb and for each value the
corresponding term ‘has a brother’ or ‘has no brother’ is uttered.
The language Jarawara, (Arawan language family) spoken in Brazil, also shows some
overlap between forms for the number words 2, 3, ‘few’ and ‘many’ (Hammarstrom,
2009)
In his paper Harald Hammarstrom says that the languages which have very few
languages, say no numeral above 1, it may still be possible to communicate a higher
exact quantity by using gestures, or one to one pairings; however the normed quantities
are still ‘few’, ‘many’ when they occur in discourse. It cannot be possible to say
something like ‘few+1’ or ‘few+few’ or ‘1+1’ to designate an exact number. (pp 20)
Kayardild (Australia) has number words only up to four. To describe larger groups they
might use words like ‘ngankirra’ which means ‘mob aggregation’ and ‘mumurra’ which
means ‘big mob of people’. (Harrison, 2007)


Base 2: Aiome speakers (751 speakers, New Guinea) employ only base 2
countingsystem. (Harrison, 2007). Example: 
Aiome numbers
Meaning
Nogom
‘one’
Omngar
‘two’
omngar nogom
‘two and one’
omngar omngar
‘two and two’
omngar omngar nogom
‘two and two and one’
omngar omngar omngar
‘two and two and two’
Base 3: It has been recorded that some languages have a base 3 number system.
TheAmbulas of Weingei (PNG) count in 3. For example the number names are as
follows: 
Nawurak
‘one’
Vetik
‘two’
Kupuk
‘three’
Kupukiva
‘four’
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kupuk etik
‘five’
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Taabak
‘six’
Another example of base 3 language which reaches up to 9 is Bine (PNG). However it is
said that this is a very restricted system and thus the base 3 system is also considered
dubious in this case.

Base 4: Some extinct Chumash languages show base 4 systems reaching up to
32.Ventureno, a Chumash language, now extinct had base 4 system often extending to
base 8 and 16. Interestingly, in this language, explicit reference to base could be omitted
from speech because it was understood from the context which base was being referred
to, for example: for additive expressions of 5, 6, 7, the base 4 could be omitted. Fifteen
was simply one less and it was understood that the base must be 16. Four could also be
omitted in multiplicative sequences, like twenty eight which would be “three comes
again” (4* (4+3)). 

Base 4 can also be found in Yuki (California), who use the gaps between fingers to count
and Kewa (PNG), who don’t include the thumb in denoting ‘one hand’. 

Nyali (Bantu variety, Africa) also shows base 4 system. For example: eight is (4*2), nine
is (4*2) +1, thirteen is 12+1, etc. (Hammarstom, 2009:26) 


Base 5: Yakkha (East Nepal) follows a base 5 system where the word for five
meanshand: 
1
Kolok
1
2
Hitci
2
3
Sumci
3
4
sumcibi usongbi kolok
3 and 1
5
Muktapi
Hand
6
muktapi usongbi kolok
Hand and 1
7
muktapi usongbi hitci
Hand and 2
8
muktapi usongbi sumci
Hand and 3
9
mukcurukbi kolok hongbi
Hand-s 1 less
10
muktapi hita
hand 2
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20
lang-curuk-muk-curuk
foot-s hand-s (20)
(Mazaudon, 2007)
Many Californian languages follow base 5 system mainly in combination with higher
base, since otherwise it becomes cumbersome to keep track. Nahualt (Uto-Aztecan,
Central Mexico); Yolngu (Northern Australia), Hayu (Tibeto burman, Nepal), Eti
languages (Austronesian, Vanuatu) are some languages which have base 5 numeral
system. (Dixon and Kroeber, 1907)

Base 6: Ndom language (1,200 speakers, PNG) uses base 6. The word for 6, ‘mer’ isused
in forming higher numbers, both through addition and multiplication. Example: 
1
2
3
4
5
6
Sas
Thef
Ithin
Thonith
Meregh
Mer
7
8
9
10
11
12
mer abo sas (6+1)
mer abo thef (6+2)
mer abo ithin (6+3)
mer abo thonith (6+4)
mer abo meregh (6+5)
mer an thef (6*2)
Base 6 is also attested in languages of Kolopom Island in south west Indonesian Papua
(Hammarstrom, 2009)


Base 8: Northern Pame (Mexico) is the sole case of a base 8 language which does
nothave a base 4 sub sytem. (Hammarstrom, 2007) 
Example: 
1
Santé
9
kara tenhiuŋ santa (8+1)
2
nuji
10
kara tenhiuŋ nuji(8+2)
3
rnu?
11
nda kara tenhiuŋ rnu? (8+3)
4
giriui
12
kara tenhinŋ giriu (8+4)
5
gitʃai
13
kara tenhinŋ gitʃai (8+5)
6
teria
14
kara tenhinŋ teria (8+6)
7
teriuhiŋ
15
kara tenhinŋ teriuhiŋ (8+7)
8
tenhiuŋ
16
kanuje tenhiuŋ (2*8)
17
kanuje tenhiuŋ santé (2*8+1)
20
kanuje tenhiuŋ giriui (2*8+4)
24
Karnu? Tenhiuŋ (3*8)
25
Karnu? tenhiuŋ santa (3*8+1)
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 Base 12: Chepang (South West Nepal) also has a base 12 system. Though it is also
getting influenced by the Nepali numeral system, its base 12 system can still be seen:
1 yat
13 yat hale yat (1*12+1)
3 sum
15 yat hale sum (1*12+3)
5 poŋa
60 poŋa hale (5*12)
12 yat hale (1*12)
29 nis hale poŋa (2*12+5)
(Mazaudon, 2007)
Dhivehi (Indo Aryan, Maldavies) has a base 12 base (but now extinct)
Base 12 system is also found in many languages of the Plateau area of Northern Nigeria.
(Hammarstrom, 2009)
 Base 15: There is only one accounted data for a base 15 system, which is Huli
language(PNG). It is basically a body tally system with a cycle of 29, where the midpoint
is 15. Under influence from neighboring Tok Pisin base system turned into a base 15.
(Hammarstrom, 2009)
 Base 20: Diola-Fogny, a language of Senegal also follows base 20 system; example: the
number ‘51’ would be written as ‘two twenties and eleven’ (Comrie, 2011)
bukan ku-gaba
di
uɲɛn
di
b-əkɔn
twenty cls-two
and
ten
and
cls-one
Mayan (Mexico), Welsh (England), Pomo of California, Chukchi (ChukotkaKomchatkam, Eastern Siberia) also have a vigesimal system.

Base 60: Ekari numerals (Trans New Guinea, Papua-Indonesia) follow a base 60 system.
For example, the number 71 would be represented as (Comrie, 2011)
èna ma gàati dàimita mutò one and
ten and sixty
Sumerian numerals (Mesopotamia, but now extinct) also followed base 12 system.

Hybrid bases: 
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205 2
1) 5 and 20 and 80: Supyire (346,000 speakers, Mali) uses base 5 and base 20. Till the
number 20, it uses base 5, while 20 above it becomes a vigesimal system till 80. For
example 1000 would be ‘(400*2) + (80*2) + (20*2)’ (Harrison, 2007)
The number 399 would be ’80 x 4 + 20 x 3 + 10 + 5 + 4’ (Comrie, 2011)
sicyɛɛré ˈná
four
and
eighty
béé-tàànrè
twenty-three
ná
and
kɛ
ten
ˈná
and
báárì-cyɛɛ rè
five-four
Similarly Loboda (PNG) also has base 5 and 20 but they don’t use it much.
2) 3 and 4: Bukiyip language (PNG) uses both base 3 and 4 depending on the object to
be counted. Interestingly the word for hand, ‘anauwip’ appears in both counting
system. In base 3 system, it stands for 6. Since they count all the fingers and the
thumb joint also as one hand. In base 4 system, it stands for 24, since they multiply all
the 6 points on the hand by the base. Thus the same word stands for different numbers
in different bases.
3) 2 and 5: Wampar (5,150 speakers, PNG) is a language which uses base 2 and base 5.
Example: (Harrison, 2007)
1
orots
2
serok
3
serok orots
2+1
4
srok a serok
2+2
5
bangid ongan 5 once
10 bangid serok 5 x 2
4) 10 and 20: Basque (language isolate, Spain) uses base 20 to form numerals till 99 and
after that it uses decimal base. Example: the number 256 would be (Comrie, WALS)
berr-eun
two-hundred
eta
and
berr-ogei-ta-hama-sei
two-twenty-and-ten-six
5) Body part and numerals: the Iqwaye people (2,500 speakers, PNG) have number
words for only ‘one’ and ‘two’. For all higher numbers they use combine one or two
with body parts (which are grouped into basic units of 5). For example five is ‘two
hands’, ten is ‘two hands’, eleven is ‘(two hands then) down to the leg one’, fifteen is
‘half of the legs’ while twenty is ‘one man’. Five hundred gets expressed as
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I am one person: 1
Now count all digits of my legs and hands: 20
Now count the digits on the other guy’s hand 5
i.e. 1* (20+5)
Now count all digits on the legs and hands of that many people: 20*25 = 500
The Lengua people of Paraguay (6,705 speakers) also use a mixed system of
numerals for one, two and three along with use of hands and feet in units of five. An
interesting fact is that they use the concept of symmetry to denote number four as
‘two sides alike’ (Harrison, 2007 179)

No Arithmetic Bases: There are some languages which do not have any arithmetic
bases,like the extended body part system which uses the names of various body parts to
represent numerals as well. Example: Kobon (PNG) with a full cycle at 23. They start
counting from the little finger, Similarly Bororo and Kaluli (both PNG) languages also
use the extended body part system instead of numerals. (Detailed discussion in the
section on ‘how to count’) 
DIFFERENT METHODS FOR COUNTING
The most common method is the use of ‘number words’ but as mentioned earlier this method
is relatively new. Initially different methods were used and some of which are found to this
date.

Notched up bones: Archaeological evidence dating back to 13,000 to 17,000 years
foundin Le Placard, France, shows a notched up eagle bone indicating that numerals were
marked like that, which were corresponding to the lunar cycles. 


Sticks and Stones: The Kpelle people of Liberia (487,000 speakers) count with piles
ofpebbles. The Pomo of California (less than 60 speakers) count with sticks. The word
for 1 is k’áli and for stick is ‘xày’. Being a base 20 numeral system, the word for 20 is
‘one stick’, that for say 61 is ‘three sticks and one’, 400 is ‘one big stick’ while 500 is
‘one big stick and 5 small ones’. 
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
Fingers, Toes and Body parts: bororo (complex phrases), fingers gap types,
extendedbody parts. The Borôro language (850 speakers) uses complex phrases referring
to fingers as numbers. 

Example number 9 would be ‘the one to the left side of my middle finger’, ten would be
‘my fingers all together in front’ and thirteen would be ‘now the one on my foot that is in
the middle again’, which of course assumes that the fingers have been already counted.
(Harrison, 2007) 

Body part counting is also as abstract as the number names we use (except of course if it
is only denoting the corresponding five fingers). Interesting examples of abstraction in
body part numerals can be found in some languages. The Yuki language (California)
counts the spaces between the fingers (base 4); the Vanimo and Kewa (PNG) also base 4
consider a hand as 4 fingers and thumb is counted separately, i.e. 12 would be ‘three
hands’ while five would be ‘one hand and a thumb’. 

Apart from fingers and toes, some languages also use extended body parts as numerals.
For example, in Kaluli (2,500 speakers, PNG) no separate word for numerals exist,
instead it’s the body part name that represents it. Kaluli counting starts with the pinkie
finger of the left hand and by the time it reaches the right hand pinkie finger it has
completed a full cycle (corresponding to thirty five). Similarly the Kobon (6,000
speakers, PNG) also use extended body part system. In fact Kobon completes a full cycle
reaching twenty three, an odd number! Also after the midpoint (which is the ‘hollow at
the base of the throat’) they attach the word ‘bong’ to the body parts meaning ‘the other
side’; i.e. say ‘shoulder bong’ or ‘thumb bong’ etc. (Harrison, 2007) 
WHAT TO COUNT?
Commonly we can use numerals to count almost anything. But this is not the situation in all
parts of the world. Calculations seem to arise to meet the need. Even people living in similar
environments might develop different scenarios for counting.

Loboda people of Papua New Guinea region (less than 8,000 speakers) apparently
countnothing but money. (The barter system is getting replaced by the currency system
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in 
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almost all parts of the world. There is an emerging need to count money and many
tribes are accommodating that).
 The Yupno tribe again from PNG counts ‘string bags, grass skirts, pigs, traditional string
money and modern paper money’, but do not count ‘days, people, sweet potatoes, or betel
nuts’. Now the reason for this is not specified other than the speculation that it might be
because of some kind of taboo or simply because they don’t consider it necessary. One of
the reasons might be that they count those things which they trade with others.

Another interesting tribe from PNG, the Bukiyip, has base 3 and base 4 numeral system
used to count different objects. For example: things counted in base 4 include coconuts,
small yams, bundles of firewood, days, eggs, birds, lizards, fish, breadfruit, bows and
arrows while those which are counted in base 3 include betel nuts, big yams, single sticks
of firewood, months, bananas, shields. Now the reason for grouping these things is not
known but it doesn’t seem to be absolutely random. (Harrsion, 2007) 
HOW ARE NUMERALS FORMED?

Overcounting: Vogul, a language spoken in Western Siberia (3,184 speakers), uses
thetechnique of overcounting in forming its numerals. They look ahead to the next tenunit and express how many steps in units of one are required to reach it. For example:
twenty three is expressed as ‘two towards thirty’. 

Old Turkic (a ninth century language, now extinct) also used overcounting as a strategy
to form numbers, for example twenty seven was expressed as ‘seven thirty’. (Harrison,
2007) 

The word for 20 in Mayan is ‘kal’, the numbers 40, 60, 80 etc are based on that (i.e.
‘cakal’, ‘oxcal’, ‘cankal’ respectively). Till 40 also the numerals are for compounds of 
20. But numerals after 40 take the form of overcounting. E.g. the numeral 41, instead of
being ‘twice twenty and one’ is expressed as ‘huntuyoxkal’ , which means the first of the
third score (i.e. the first number approaching 60). (Hurford, 1975)
In Dzonkha (national language of Bhutan) actually has two numeral systems, the decimal
is the one borrowed from Tibetan while the one they had was the vigesimal (the decimal
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South -Asian Journal of Multidisciplinary Studies (SAJMS) ISSN:2349-7858:SJIF:2.246:Volume 3 Issue 2210
system being a comparatively recent addition) where the numeral /khe/ (twenty) means
‘bundle’. An interesting phenomena to be seen in the vigesimal system is that the number
30 is not mentioned as ‘one score plus ten’ but instead as ‘half in the second twenty
group’. 30 is
Khe
pɟhe-da
ˈɲiː
20
½ da
2
(where ‘pɟhe’ means half and ‘da’ is the connector)
This is an example of overcounting involving fractions! It means that half of twenty
approaching the second score (i.e. 40), resulting in 30.
Similarly 55 is expressed as:
Khe
ko-da sum
20
¾-da 3
i.e. quarter of 20 approaching the third score (60) resulting in 55.
Ao Naga (Nagaland) also use overcounting, example:
rokvr maben trok (60 not-reached 6) i.e. ‘fifty-six’

Subtraction: The Ainu (language isolate, Japan) numeral system makes use
ofsubtraction. There are single words for the numbers 1-5, and the numerals 6-9 are
formed by subtraction, for example: 





1 is ‘schnepf’, 2 is ‘tup’ while 10 is ‘wambi’
8 is ‘tubischambi’ (2 – 10) 
9 is ‘schnebischambi’ (1 – 10) 
Another interesting feature is that the odd decades (30, 50, 70, 90, etc) are formed by
subtracting 10 from the immediate higher even decade, i.e. 30 would be ‘40-10’ 
30 is ‘wambi i-docho ’ (lit. 10 from (2 * 20)) 
While the expression for 31 is ‘schnepu igaschima wambi idochoz) (1 plus 10 from 2*20)
(Hurford, 1975). 


Feature of subtraction is also found closer home in Indo Aryan languages (Hindi,
Sanskrit) but it is limited to the immediate number before the ten unit base. 
Example 19 is ‘unnis’ (1 from 20 (bis)); 29 is ‘unnatis’ (1 from 30 (tis)) 


Number Name Discrepancies: Normally the numeral formation is semantically
coherentin its name, i.e. twenty three means (20+3) and not say (*50+ 7). But there are
certain languages where the numerals are not semantically coherent. 
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South -Asian Journal of Multidisciplinary Studies (SAJMS) ISSN:2349-7858:SJIF:2.246:Volume 3 Issue
211 2
In Hawaiian, the word for 9 is ‘iwa’ and for two is ‘lua’ but the numeral ‘iwakalua’
denotes 20!
In Bantu (Central Africa), the word for 5 is ‘tan’ and the word for 3 is ‘datu’ while
the numeral ‘tandatu’ denotes 6 instead of the assumed 8.
In Wintuns (Northern California), the word for 10 is ‘cema’ and the word for 2 is
‘palel’ while the numeral ‘cema-palel’ denotes 11 instead of the assumed 12. A
hypothesis suggests that the word for 11 got displaced to position 9, perhaps under the
principle of subtractive principle, and then the words fell back one step!(Hurford, 1975)
But somehow the question of how these discrepancies came about is not yet clear.
NUMBER SENSE AND NUMERALS
The limit on numerals does not mean there is limit on the number sense. Harrison
mentions in his book that as per anthropologist Hans Becher, the Yanoama people even
though don’t have numbers higher than three, can detect small differences in quantities.
Example “if twenty arrows are standing together and one increases or reduces the bundle
by only one during the owner’s absence, he will notice it at once upon his return”,
showing that they have a keen ‘number sense’ even though they don’t have a numeral
system above three.
The Damara of South Africa (56,000 speakers) also don’t have numerals above three yet
they seldom lose oxen. And the way they discover that they have lost one is not by
counting but by the missing face they remember! (Harrison, 2007)
CHANGING TIMES, SHIFTING NUMERALS
The world’s number systems are facing a danger with changing times. Many languages are
shifting their number systems into the predominantly decimal base or else into the dominant
language spoken in the region. For example the Yuki Indian are now shifting to base 10 from
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base 4, many Chumash languages under the Spanish influence also shifted to base 10; Ainu (a
language isolate) is shifting to Japanese number system; the Thulung people (Nepal) is shifting
to the national language, Nepali number system and numerals; Huli (base 15) is also shifting to
base 10, in a need to deal with English money (Harrison, 2007:198). As a result many
uncommon systems are quickly vanishing along with the incredible mathematical insights they
hold. Number systems provide an insight into the human cognition and along with their socio
cultural background, losing them would be losing our history and a way towards our future.
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REFERENCES
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Avelino, Heriberto.2005.The Typology of Pame number systems ans the limits of
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Butterworth, Brian & Gelman, Rochel.2006. number and Language: How they are
related? Trends in Congnitive Sciences, Vol.9, No. 1 
Comrie, Bernard. 2011. Numeral bases. In: Dryer, Matthew S. & Haspelmath, Martin
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