Numeral System in Tamil: Generation

S. Agesthialingom

p. 323-332


Texte intégral

Numerals in any natural language form a separate group of nouns which behave differently in certain respects both in its formation and in its grammatical functions. All the other nouns denote a person, place, thing, time, etc., whereas numerals denote the number of the things, persons etc., in addition to its behaviour as noun.

1The present paper is concerned with the generation of this category of nouns and tries to show that with a small number of generating rules it is possible to generate all the numbers in Tamil, of course with a certain number of morphophonemic rules. Here the integer numbers are alone considered and the fractions and complex numbers like oṉṟē kāl (1 ¼) oṉṟarai (1 ½) are not dealt with. It is to be mentioned here that they can be easily taken care of by certain rules like

Image 10000000000001C00000002C1735D8FAA340880E.jpg

Where NUMcomp stands for complex numbers and NUMF for integer numbers like oṉṟu, iraṇṭu etc., FRA for fractions like kāl (1/4), arai (1/2), mukkāl; (3/4) etc., .

2As is well known, integer numbers are classified into: one-digit numbers, two-digit numbers, three-digit numbers, etc.. In Tamil there are special names for various digits though it is not uniform in all the digits. For example there is no special name for the one-digit numbers, whereas two-digit numbers are denoted by pattu "ten̏, three-digit numbers by nūṟu "hundred̏, four- and five-digits are called āyiram "thousand̏, six- and seven-digits are called ilaṭcam "lakh̏ and eight-digits and above are called kōṭi "crorȅ. This can be shown as follows.

Image 10000000000002E200000109C3298549EA28FE3B.jpg

Since āyiram and its multiples and additions can take care of 1000 to 99999, i.e. both four-digit numbers and five-digit numbers they are clubbed together and are represented by NU4. This is also the case with ilaṭcam. NU5 represents both six-digits and seven-digits.

All these digits or all the numbers can be generated by a rule like the following:

Image 1000000000000248000000B9A2486BA02A544601.jpg

It means that the numbers may be one-digit numbers, or two-digits, or three-digits, …, or eight-digits, or more digit numbers.

  • NU1 stands for oṉṟu "onȅ to oṉpatu "9̏

  • NU2 stands for pattu "ten̏ to toṇṇūṟṟu oṉpatu (99)

  • NU3 stands for nūṟu "hundred̏ to toḷḷāyirattu toṇṇūṟṟu oṉpatu (999)

  • NU4 stands for āyiram "thousand̏ to toṇṇūṟṟu oṉpatu āyirattu toḷḷāyirattu toṇṇūṟṟu oṉpatu (99999)

  • NU5 stands for ilaṭcam "lakh̏ oru ilaṭcam̏ (100000 to 9999999)

  • NU6 stands for kōṭi "crorȅ "oru kōṭi to infinitȅ (10000000 to infinite).

Three kinds of rules

This grammar consists of three kinds of rules namely

  • (1) generation rules (I)

  • (2) allomorphic rules (II)

  • (3) sandhi rules (III).

The first set of rules is responsible for generating all numbers. The second set takes care of allomorphic variations and the third takes care of sandhi changes.

3All these rules put together can generate all the natural numbers in Tamil and they can be used as input data and by various processes it may be possible for us to get the output.

Generation rules

Image 10000000000001C40000010E9B213F8F202B18E2.jpg

NU1 stands for numbers oṉṟu (1) to oṉpatu (9) i.e. one to nine. NU1 is oṉṟu, iraṇṭu or mūṉṟu, etc. All these are represented by NU1

4It is known that all these numbers have allomorphs and they will be taken care of by appropriate morphophonemic rules (II).

5Similarly pattu, nūṟu, āyiram, ilaṭcam, etc. may also have to undergo morphophonemic rules and they will be also treated by morphophonemic rules.

Image 10000000000002420000002CD38B94F63BA1B166.jpg

6Here simple bracket () means optional. i.e. NU1 may be there or may not be there. The second digit number is represented by this rule.

7This rule shows that two digit numbers are the multiples of pattu and also with or without NU1. This can be shown in something like the following.

Image 100000000000024A0000010B645869C7D3DC54E0.jpg

8So this rule can generate

9oṉṟu x pattu>pattu (oṉṟu will be deleted by a rule later 2.13)

10iraṇṭu x pattu>irupatu (2.3; 2.14) etc.,

11Similarly if we add NU1 after pattu we will get

12oṉṟu x pattu + oṉṟu>patiṉoṉṟu (2.11; 13)

13oṉṟu x pattu + iraṇṭu>paṉṉiraṇṭu (2.12; 13) etc.,

Multiplication & Addition

14Here we find two kinds of processes in the generation of numbers in Tamil, namely multiplication and addition. When one to nine are added before pattu they are in the process of multiplication.

15oṉṟu x pattu>pattu "ten" (2.13)

16iraṇṭu x pattu>irupatu "Twenty" (2.3,14)

17But in the case of pattu+oṉṟu, it is in the process of addition.

18pattu + oṉṟu>patiṉoṉṟu (11) (2.11,13)

It is to be noted that it is the same in the case of nūṟu, āyiram, ilaṭcam, etc.,

19When the smaller number comes before a bigger number it is in a multiplication process whereas when the smaller numbers come after the bigger numbers it is in a process of addition. That is why the signs x and + are used in the rule.

In the morphophonemic rules also this is reflected

iraṇṭu x pattu>irupatu (20) (2.3; 14)
irupatu āyiram (multiplication)
irupattu iraṇṭu (addition) (2.3)

Deletion of oṉṟu

When oṉṟu comes before pattu (ten) oṉṟu is deleted (2.13) and the result is pattu only. This may also be the case before nūṟu, āyiram, ilaṭcam and kōṭi where it is optional: it can be said ōrāyiram or āyiram itself (2.1). This will be taken care of by morphophonemic ruleImage 1000000000000461000000BF991338CEA19E00F8.jpg

20By this rule all the three digit numbers from 100 to 999 can be generated.

21NU1 x nūṟu

22nūṟu

23iraṇṭu X nūṟu>irunūṟu (2.3)

24mūṉṟu X nūṟu>muṉṉūṟu (2.3, 3.1) etc.,

25NU1 x nūṟu + NU1

26nūṟṟu oṉṟu (101) (2.15)

27irunūṟṟu iraṇṭu (202) (2.3, 15)

28NU1 x nūṟu + NU2

29nūṟṟup pattu (110)

30nūṟṟup paṉṉiraṇṭu (112)

NU2, as mentioned earlier, represent all the numbers of two digits, that is from 10 to 99. Therefore, when this is added to NU1+nūṟu this would generate all the numbers, in the first case. 101-199, and then 201-299 etc.,

Image 10000000000002AA000000744BB47FB363F08126.jpg

This rule takes care of all the numbers from 1000 to 99999. This rule can be split into two rules, having initial NU1 and NU2 separately. However it is clubbed together.

NU1

NU1 x āyiram

āyiram/ōrāyiram

(1000) (2.2)

oṉpatu āyiram

(9000)

NU1 x āyiram + NU1

āyirattu oṉṟu

(1001) (2.2; 2.16)

oṉpatu āyirattu oṉpatu

(9009) (2.16)

NU1 x āyiram + NU2

āyirattup pattu

(1010) (2.16)

oṉpatu āyirattu toṇṇūṟṟu oṉpatu

(9099) (2.15,16)

NU1 x āyiram + NU3

āyirattu nūṟu

oṉpatu āyirattut toḷḷayirattu toṇṇūṟṟu oṉpatu

(9999) (2.9) (3.7) (2.15; 2.16)

NU2

NU2 x āyiram

pattu x āyiram

(10000)

toṇṇūṟṟu oṉpatu āyiram

(99000) (2.9) (3.7)

NU2 x āyiram + NU1

pattu āyirattu oṉṟu

(10001)

toṇṇūṟṟu oṉpatu āyirattu oṉpatu

(99009) (2.9) (2.16)

NU2 x āyiram + NU2

pattu āyirattu oṉṟu

(10001)

toṇṇūṟṟu oṉpatu āyirattu oṉpatu

(99009) (2.9) (3.7)

NU2 x āyiram + NU3

pattu āyirattu nūṟu

(10100)

toṇṇūṟṟu oṉpatu āyirattut toḷḷāyirattut toṇṇūṟṟu oṉpatu

(99999) (2.9) (3.7)

Image 10000000000002B40000007E4DD64B4FE71C9DCE.jpg

This rule takes care of all the six- and seven-digit numbers, namely (oru) ilaṭcam, 100000 to 9999999.

NU1

NU1 x ilaṭcam

oru ilaṭcam

(100000)

oṉpatu ilaṭcam

(900000)

NU1 x ilaṭcam + NU1

oru ilaṭcattu oṉṟu

(100001) (2.17)

oṉpatu ilaṭcattu oṉpatu

(900009)

NU1 x ilaṭcam +NU2

oru ilaṭcattup pattu

(100010)

oṉpatu ilaṭcattu toṇṇūṟṟu oṉpatu

(900099)

NU1 x ilaṭcam + NU3

oru ilaṭcattu nūṟu

(100100)

oṉpatu ilaṭcattut tonnūṟu oṉpatu āyirattut toḷḷāyirattut toṇṇūṟṟu oṉpatu

(999999)

NU1 x ilaṭcam + NU4

oru ilaṭcattu āyiram

(101000)

oṉpatu ilaṭcattut toll āyirattut toṇṇūṟṟu oṉpatu

(900999)

NU2

NU2 x ilaṭcam

pattu ilaṭcam

(1000000)

toṇṇūṟṟu oṉpatu ilaṭcam

(9900000)

NU2 x ilaṭcam + NU1

pattu ilaṭcattu oṉṟu

(1000001) (2.9)

toṇṇūṟṟu oṉpatu ilaṭcattu oṉpatu

(9900009)

NU2 x ilaṭcam + NU2

pattu ilaṭcattup pattu

(1000010)

toṇṇūṟṟu oṉpatu ilatcattat toṇṇūṟṟu oṉpatu

(9900099)

NU2 x ilaṭcam +NU3

pattu ilaṭcattu nūṟu

(1000100)

toṇṇūṟṟu oṉpatu ilaṭcattu tonnūṟṟu oṉpatu

(9900999)

NU2 x ilaṭcattu + NU4

pattu ilaṭcattu āyiram

(1001000)

toṇṇūṟṟu oṉpatu ilaṭcattu toṇṇūṟṟu oṉpatu āyirattu toḷḷāyirattu toṇṇūṟṟu oṉpatu

(9999999)

Image 100000000000028F000000B85F708B84C6B3B9E9.jpg

This rule takes care of generation of not only 8 digit numbers and also all the possible numbers. orukōṭi, pattuk kōṭi, nūṟu kōṭi, ilaṭcam kōṭi, etc.

31Note that this is a recursive rule which can go on generation kōṭiyēkōṭi pattu kōṭiyē kōṭi etc., by making use of the item NU6. This rule is something like S

Image 10000000000000320000001AECBC6870891BEB5C.jpg(S) ab, which is considered as a recursive rule by Chomsky and other generative grammarians. This rule generates kōṭi to infinite.

NU1 x kōṭi

orukōṭi to oṉpatu kōṭi

NU2 x kōṭi

10000000 to 90000000

NU3 x kōṭi

100, 0000000 to 999, 0000000

Thus we can go on generating higher numbers and we add with these numbers NU1, NU2, NU3, NU4, etc., we can have numbers like 10000001 etc.

2. Allomorphic rules

It has been said that numbers like oṉṟu, iraṇṭu etc have various allomorphs and these variants can be taken care of by the following rules.Image 10000000000004140000010E4B38EABA40EA20CA.jpg

2.2 oṉṟu x āyiram => (ōr-) āyiram

32ōr-āyiram/āyiram

Image 1000000000000256000000FA77BB569A308CF05E.jpg

33This rule accounts for

34irupattu, muppattu, nāṟpattu, aimpattu, aṟupattu, eḻupattu, eṇpattu.
irunūṟu, muṉṉūṟu, nāṉūṟu, ainūṟu, aṟunūṟu, eḻunūṟu, eṇṇūṟu
.

Image 100000000000020C00000082C9C207734FAD339B.jpg

35iraṇṭāyiram / īrāyiram
eṭṭāyiram / eṇṇāyiram

362.5 opt
mūṉṟu x āyiram =>mū-āyiram
mūṉṟāyiram
/ mūvāyiram

372.6 opt
nāṉku>nālu

38It is to be noted that often nāṉku and nālu are used without any distinction, one for the other.

39nāṉku kōṭi / nālu kōṭi

402.7 opt
aintu x āyiram =>ai-āyiram
aintāyiram
/ aiyāyiram

2.8ēḻu x āyiram =>ēḻ-āyiram

Image 10000000000002430000005E73BC726C149AEF2C.jpg

41toṇṇūṟu
toḷḷāyiram

422.10 opt.

43pattu + āyiram>patiṉ - āyiram

44pattāyiram, patiṉāyiram

Image 1000000000000376000000F45ADD62F7FE7E59A0.jpg

It is noted here that when the combinations of oṉṟu x pattu + oṉṟu etc., are generated, we have to get patiṉoṉṟu etc.; pattu has an allomorph patiṉ in this context. That is being taken care of by this rule.

2.12 oṉṟuxpattu+iraṇṭu =>oṉṟu+paṉ+iraṇṭu

Image 100000000000028E00000080E68C4EFDF37528F2.jpg

45pattu, patiṉoṉṟu, paṉṉiraṇṭu.

Image 10000000000002D9000000E8A55081286E0DC156.jpg

Note that when irupattu etc are having changes, pattu>patu when they are followed by no other integer numbers or when they are in multiplication relation.

46iru x pattu x āyiram>irupatu āyiram
irupatu
twenty

472.15 nūṟu + =>nūṟṟu
nūṟu
+ irupatu>nūṟṟu irupatu

482.16 āyiram + =>āyirattu
āyirattu nūṟu

492.17 ilaṭcam + =>ilaṭcattu
ilaṭcattu nāṉku

502.18 kōṭi + =>kōṭiyē
orukōṭiyē nāṉku

III Sandhi rules

513.1 mu - C >mu CC
muppatu, muppattu, munnūṟu

523.2 ai-V >aiyV
aiyāyiram

533.3 ṇ-n>ṇṇ
eṇ-nūṟu
>eṇṇūṟu
eṇ-nūṟṟu
>eṇṇūṟṟu

543.4 m-n>nn
aim-nūṟu
>ainnūṟu

553.5 l-Stop >-Stop
nāl-patu>nāṟpatu

563.6 l-n>
nāl-nūṟu
>nāṉūṟu

573.7 ḷ-n>ṇṇ
toḷ-nūṟu
>toṇṇūṟu

583.8 +n>
patiṉ-nāṉku
>patiṉāṉku

593.9 # (C) VC-V > # (C) VCCV
toḷ-āyiram>toḷḷāyiram
paṉ-iraṇṭu
>paṉṉiraṇṭu

Image 100000000000016900000081182EECA8124DC728.jpg

60aintu + āyiram>aintāyiram
mūṉṟu
+ āyiram>mūnrāyiram
eṭṭu
+ āyiram>eṭṭāyiram
āṟu
+ āyiram>āṟāyiram

Grammar

61It is defined by generative grammarians that "a grammar is a finite set of rules which generates an infinite number of grammatical sentences and no ungrammatical ones̏.

62With the foregoing finite number of rules it is possible to generate thousands of numbers.

63An Electronic grammar is to be thought of in this line. It should be possible to produce large numbers of grammatical sentences and the joint work of linguists and software engineers should make it possible to produce such a grammar.

Bibliographie

Des DOI sont automatiquement ajoutés aux références bibliographiques par Bilbo, l’outil d’annotation bibliographique d’OpenEdition. Ces références bibliographiques peuvent être téléchargées dans les formats APA, Chicago et MLA.

Bibliography

S. Agesthialingom, 1967. A Generative Grammar of Tamil, Annamalai University, A. Nagar.

10.1515/9783112316009 :

Chomsky, Noam A. 1957. Syntactic Structures, The Hague.

10.21236/AD0616323 :

Chomsky, 1965. Aspects of Theory of Syntax, MIT Press, Cambridge.

Davis Garden, B. 1969. Computer Processing McGraw Hill, Inc. Sydney, Rep. 1986.

10.1017/CBO9780511611797 :

Grishman, R. 1986. Computational Linguistics, An Introduction, Cambridge.

Pon. Kothandaraman. A Grammar of Contemporary Literary Tamil. IITS, Chennai.


Le texte seul est utilisable sous licence Licence OpenEdition Books. Les autres éléments (illustrations, fichiers annexes importés) sont « Tous droits réservés », sauf mention contraire.