India’s Unique Place in the World of Numbers and Numerals – III

The Indo-Aryan languages of North India are the most complex decimal system of all, where there is such complete fusion and inflection between the tens and unit numbers that it becomes necessary to learn individually the exact form of every number from 1-100.

[This is the third part of an exciting new series by Shrikant Talageri on India’s unique place in the world of numbers and numerals and its implications for the Out-of-India Theory of Indo-European Origins. In this part he discusses number systems with different bases and the delves into Indo-Aryan numbers.]

C. INDO-ARYAN NUMBERS

One aspect of Indian numbers which is not generally recognized is that the numbers in the Indo-Aryan languages of North India have one feature (though not exactly a positive feature) which makes them unique among all the languages of the world: they are probably the only languages in the world where anyone learning the language (any North Indian Indo-Aryan language) necessarily finds that he has to individually learn or memorize every single number from one to hundred.

To understand this fully, one must first understand the methods by which the different world languages form their numbers 1-100. We will examine the subject under the following heads:

C-I. Sexagesimal systems (with a base of 60).

C-II. Quindecimal systems (with a base of 15).

C-III. Vigesimal systems (with a base of 20).

C-IV. Decimal systems (with a base of 10) with words for 1-10 and 100.

C-V. Decimal systems (with a base of 10) with words for units 1-9 and tens 10-100.

C-VI. Decimal systems (with a base of 10) with words for numbers 1-19 and tens 20-100.

C-VII. Decimal systems (with a base of 10) with words for numbers 1-100.

C-VIII. Historical Implications of the Indo-Aryan number system.

C-I. SEXAGESIMAL SYSTEMS (WITH A BASE OF 60):

The sexagesimal system (with a base of 60, although with a subset of 10) is very rare, and we will look at it before moving on to the two main systems. I can personally think of only one language today with such a system (probably also found in some related neighboring languages), though the ancient Mesopotamians (Sumerians/Akkadians/Assyrians, etc., who were the only ones to use a sexagesimal numeral system) may have had sexagesimals in the spoken number system as well. This rare language is the Masai language, belonging to the NiloSaharan/Sudanic language family, and spoken in southern Kenya and northern Tanzania in east Africa. The numbers are as follows:

1-9: nabu, ari, üni, ungwun, miet, elle, nabishäna, issiet, nawdu

10, 20, 30, 40, 50, 60: tomon, tigitum, ossom, arrtam, orrnom, ïp

70, 80, 90, 100, 110: ïptomon, ïptigitum, ïpossom, ïparrtam, ïporrnom

Other numbers in between 10-60 are formed by the tens word followed by the following secondary forms of 1-9: obbo, are, ogüni, ungwun, oimiet, oīille, nabishäna, oissiet, nawdo

sexagesimals 60, 120, 180, 240, etc: ïp, ari-ïp, ünip, ungwunp, etc. (60, 2×60, 3×60, 4×60, etc.)

Other numbers above 60: sexagesimal (60, 120, etc) followed by 1-59. Thus:

11 is tomon-obbo (10+1), 99 is ïp ossom-nawdo (60+30+9), 179 is ari-ïp orrnom-nawdo (60×2+50+9).

C-II. QUINDECIMAL SYSTEMS (WITH A BASE OF 15):

Unlikely though it seems, there is even a language with a quindecimal system, i.e. with a base of 15 (and it does not even have a subset of 10)! This is the Huli language of Papua New Guinea, belonging to the Papuan language family. The possible origin of such a system (as also the above sexagesimal system) is hard to pinpoint: perhaps it is based on the number of days in a lunar fortnight.

The numbers are as follows:

1-14: mbira, kira, tebira, maria, duria, waragaria, karia, halira, dira, pira, bearia, hombearia, haleria, deria

15, 30, 45, 60, 75, 90, 105 (and so on): ngui-ra, ngui-ki, ngui-tebo, ngui-ma, ngui-dau, ngui-waraga, ngui-ka (and so on, i.e. 15×1, 15×2, 15×3, etc.).

16-29: nguira-ni-mbira….nguira-ni-deria (i.e. 15+1 to 15+14)

Other numbers between the quindecimals are counting according to the serial position: e.g. the numbers 31-44 belong to the “third series of 15” culminating in 45, the numbers 46-59 belong to the “fourth series of 15” culminating in 60, etc. The names of the series (covering the numbers upto 100) are as follows:

third series 31-45: ngui-tebone-gonaga (45: ngui-tebo)

fourth series 46-60: ngui-mane-gonaga (60: ngui-ma)

fifth series 61-75: ngui-dauni-gonaga (75: ngui-dau)

sixth series 76-90: ngui-waragane-gonaga (90: ngui-waraga)

seventh series 91-105: ngui-kane-gonaga (105: ngui-ka)

Other numbers (between the quindecimals) 31 onwards: previous quindecimal + new series (to which the following unit belongs) + unit number. Thus 31: ngui-ki ngui-tebone-gonaga mbira. (i.e. 30+third-series+1)

99: ngui-waraga ngui-kane-gonaga dira (i.e. 90+seventh-series+9).

The Huli numbers are complicated because of two things:

  1. The odd (to everyone else in the world, except the speakers of Huli) base of 15.
  2. The illogical addition of the series name (based actually on the name of the following quindecimal) between the previous quindecimal and the unit: thus, 31 could well have simply been ngui-ki mbira (30+1) and 99 could have been ngui-waraga dira (90+9).

However, the first complication is part of this rare system, and the second one can be eliminated as shown above, and (even if it isn’t eliminated, still) we get a very regular quindecimal system.

C-III. VIGESIMAL SYSTEMS (WITH A BASE OF 20):

Vigesimal number systems are those which are based on 20, although they usually have a subset of 10. To learn the numbers, one necessarily has to memorize the numbers 1-19, the vigesmals/tens numbers from 20-100, and the regular procedure for forming the other in-between numbers.

The two characteristics of these languages are:

  1. The vigesimal numbers 40, 60, 80, and sometimes 100, are based on the word for 20.
  2. The other numbers are formed by adding the numbers 1-19 to the vigesimals.

In a few languages, the numbers 1-19 are based on an internal subset not of ten but of five. The most perfect example of this is the Turi language from the Austric (Austro-Asiatic) family, spoken in the adjoining parts of Jharkhand-W. Bengal-Orissa in India, which shows this subset of five very clearly, with the words for 5, 10 and 15 literally meaning “one hand”, “two hands” and “three hands” respectively. Another example is the Nahuatl/Aztec language of Mexico:

Turi (Austric-KolMunda):

1-5: miad, baria, pea, punia, miadti

6-10: miadti-miad, miadti-baria, miadti-pea, miadti-punia, baranti

11-15: baranti-miad, baranti-baria, baranti-pea, baranti-punia, peati

16-19: peati-miad, peati-baria, peati-pea, peati-punia

20, 40, 60, 80, 100: lekacaba, bar-lekacaba, pea-lekacaba, punia-lekacaba, miadti-lekacaba

Other numbers: vigesimal numbers 20, 40, 60 or 80 followed by 1-19. Thus:

21: lekacaba miad (20+1), 99: punia-lekacaba peati-punia (4×20+19).

[Khmer (Cambodian), which also belongs to the Austric family, also originally had this subset of five, but the language now uses numbers borrowed from the unrelated Thai language for numbers beyond 10. The Khmer numbers 1-10 are:

muǝy, pii, bǝy, buǝn, pram, pram-muǝy, pram-pii, pram-bǝy, pram-buǝn, dap].

Nahuatl/Aztec (Amerindian):

1-5: ce, ome, yey, naui, macuilli

6-10: chica-ce, chic-ome, chicu-ey, chic-naui, matlactli

11-15: matlactli-on-ce, matlactli-on-ome, matlactli-on-yey, matlactli-on-naui, caxtulli

16-19: caxtulli-on-ce, caxtulli-on-ome, caxtulli-on-yey, caxtulli-on-naui

20, 40, 60, 80, 100: cem-poualli, ome-poualli, yey-poualli, naui-poualli, macuil-poualli

Other numbers: vigesimal numbers followed by (the word) on and the numbers 1-19. Thus:

21: cem-poualli on ce (20+on+1), and 99: naui-poualli on caxtulli-on-naui (80+on+19).

[on-ce can be shortened to oce].

The majority of vigesimal systems, however, have a sub-set of 10. These number systems are found in every continent (except perhaps Australia). Some examples from the Caucasian, Basque, Burushaski, Ainu, Niger-Congo, Austric/Austro-Asiatic, Sino-Tibetan and the Ameridian-superfamily language-families:

Georgian (Caucasian):

1-10: erti, ori, sami, otxi, xuti, ekwsi, šwidi, rwa, ҫxra, ati

11-19: tertmeti, tormeti, ҫameti, totxmeti, txutmeti, tekwsmeti, cwidmeti, twrameti, ҫxrameti

20, 40, 60, 80, 100: oҫi, ormoҫi, samoҫi, otxmoҫi, asi

Other numbers: vigesimal + 1-19 with the ending oҫi of the first word becoming oҫda. Thus:

21: oҫda erti (20+1), 99: otxmoҫda ҫxrameti (80+19).

[Note: x is pronounced “kh”].

Euskara/Basque (Basque):

1-10: bat, biga, hirur, laur, bortz, sei, zazpi, zortzi, bederatzi, hamar

11-19: hameka, hamabi, hamahirur, hamalaur, hamabortz, hamasei, hamazazpi, hamazortzi, hemeretzi

20, 40, 60, 80, 100: hogei, berrogei, hiruetanogei, lauetanogei, ehun

Other numbers: vigesimal + ta + 1-19. Thus:

21: hogei ta bat (20+ta+1), 99: lauetanogei ta hemeretzi (80+ta+19).

Burushaski (Burushaski):

1-10: hǝn, ālto, ůsko, wālto, tsůndo, mıšīndo, tǝlo, āltǝmbo, hůnčo, tōrůmo

11-19 tůrma + 1-9.

20, 40, 60, 80, 100: āltǝr, ālto-āltǝr, īski-āltǝr, wālti-āltǝr, thā

Other numbers: vigesimal + 1-19 (but before the words tōrůmo and tůrma preceded by the word ga). Thus:

21: āltǝr hǝn (20+1), 90: wālti-āltǝr ga tōrůmo, (80+ga+10), 99: wālti-āltǝr ga tůrma hůnčo (80+ga+19).

Ainu (Ainu):

1-10: shine, tu, re, ine, ashikne, iwan, arwan, tupesan, shinepesan, wan

20, 40, 60, 80, 100: hotne, tu-hotne, re-hotne, ine-hotne, ashikne-hotne

30, 50, 70, 90: wane-tu-hotne, wane-re-hotne, wane-ine-hotne, wane-ashikne-hotne

(literally, 30 is “ten-less-than-forty”, etc).

Other numbers (including 11-19): unit + ishama + tens. Thus:

11: shine ishama wan (1+ ishama+10), 21: shine ishama hotne (1+ishama+20), 99: shinepesan ishama wane-ashikne-hotne (9+ishama+90).

Mende (NigerCongo):

1-10: yira, fere, sawa, nani, lolu, woita, wofela, wayakpa, tau, pu

11-19: pu-mahũ-yira (10-mahũ-1) etc.

20, 40, 60, 80, 100: nu-yira-gboyongo, nu-fere-gboyongo, nu-sawa-gboyongo, nu-nani-gboyongo, nu-lolu-gboyongo

Other numbers: vigesimal + 1-19. Thus:

21: nu-yira-gboyongo mahũ yira (20-mahũ-1), 99: nu-nani-gboyongo mahũ pu-mahũ-tau (80-mahũ-19).

Savara/Saora (Austric-KolMunda):

1-10: bo, bagu, yagi, uñji, molloi, tuḍru, gulji, tamji, tiñji, galji

11: galmui, 12: miggal, 13-19: miggal-aboi (13: 12+1), etc.

20, 40, 60, 80, 100: bo-koḍi, bagu-koḍi, yagi-koḍi, uñji-koḍi, molloi-koḍi

Other numbers: vigesimal + 1-19. Thus:

21: bo-koḍi bo (20+1), 99: uñji-koḍi miggal-gulji (80+12+7).

[A special word is aboi instead of bo for 1 in the number 13]

Shompeng (Austric-Nicobarese):

1-10: heng, au, luge, fuat, taing, lagau, aing, towe, lungi, teya

11-19: heng-mahaukoa-teya (1+mahaukoa+10), etc.

20, 40, 60, 80, 100: heng-inai, au-inai, luge-inai, fuat-inai, taing-inai

Other numbers: vigesimal + 1-19. Thus:

21: heng-inai heng (20+1), 99: fuat-inai lungi-mahaukoa-teya (80+mahaukoa+19).

Lepcha/Rōng/Sikkimese (SinoTibetan-Tibetic):

1-10: kāt, ñat, sām, falī, fango, tarak, kakyak, kaku, kakyōt, katī

11-19: katī kāt-thāp (10+1+thāp), etc.

20, 40, 60, 80, 100: khā-kāt, khā-ñat, khā-sām, khā-falī, gyo-kāt (20×1, 20×2, 20×3, 20×4, 100×1)

Other numbers: vigesimal + sa + 1-19. Thus:

21: khā-kāt sa kāt-thāp (20×1+sa+1+thāp), 99: khā-falī sa kakyōt-thāp (20×4+sa+9+thāp).

[Note: The word thāp is dropped after katī, 10. Thus 30 is khā-kāt sa katī].

Garo (SinoTibetan-Tibetic):

1-9: sa, gini, gittam, bri, boṅga, dok, sini, cet, sku

10, 20, 30: ci, korgrik, koraci

Other numbers 11-39: tens+unit. Thus 11, 21, 31, etc.: ci-sa, korgrik-sa, koraci-sa, etc.

40, 60, 80, 100: korcaṅ-gini, korcaṅ-gittam, korcaṅ-bri, ritca-sa

Other numbers 41-99: vigesimal + 1-19. Thus:

41: korcaṅ-gini sa, 99: korcaṅ-bri ci-sku

Welsh (IndoEuropean-Celtic):

1-10: un, dau, tri, pedwar, pump, chwech, saith, wyth, naw, deg

11-15 un-ar-ddeg, deuddeg, tri-ar-ddeg, pedwar-ar-ddeg, pymtheg

16-19 un-ar-bymtheg, dau-ar-bymtheg, tri-ar-bymtheg, pedwar-ar-bymtheg

20, 40, 60, 80, 100: hugain, deugain, triugain, pedwarugain, cant

The numbers from 21-99 are regularly formed by the numbers 1-19 + ar + vigesimal (here the units come first. Note, in Old English also, the units came first, as in the nursery rhyme “four-and-twenty blackbirds“). Thus:

21: un ar hugain (1+ar+20) and 99: pedwar-ar-bymtheg ar pedwarugain (19+ar+80).

Irish (IndoEuropean-Celtic):

1-10: aon, dō, trī, keathair, kūig, sē, seakht, okht, naoi, deikh

11-19: aon-dēag (1+10), etc.

20, 40, 60, 80, 100: fikhe, dā-fhikhid, trī-fhikhid, kheithre-fhikhid, kēad

Other numbers: the numbers 1-19 + is + vigesimal (here also the units come first). Thus:

21: aon is fikhe, 99: naoi-deag is kheithre-fhikhid (19+is+80).

[But the language also alternatively retains the original Indo-European tens numbers:

10, 20, 30, etc: deikh, fikhe, trīokha, daikhead, kaoga, seaska, seakhtō, okhtō, nōkha, kēad].

French (IndoEuropean-Italic) [but only partially]:

1-10: un, deux, trois, quatre, cinq, six, sept, huit, neuf, dix

11-19: onze, douze, treize, quatorze, quinze, seize, dix-sept, dix-huit, dix-neuf

20-100: vingt, trente, quarante, cinquante, soixante, soixante-dix, quatre-vingts, quatre-vingt-dix, cent

The numbers from 21-99 are generally formed as follows, e.g. 20: vingt, 1: un, 21: vingt et un

The et (“and”) only comes before un, otherwise 22 vingt-deux, etc.

But note the words for 70, 80 and 90 mean “60+10”, “4×20” and “4×20+10” respectively. So the numbers 71-79 are soixante et onze, soixante-douze, (60+11, 60+12) etc., and the numbers 91-99 are quatre-vingt-onze, quatre-vingt-douze, (4×20+11, 4×20+12) etc. (81-89 are the normal quatre-vingt-un, quatre-vingt-deux, etc.).

It is very likely that this sub-system of 20, found in the Indo-European family only in French and in the Celtic languages may be due to the influence of Basque.

Yucatec/Mayan (Amerindian):

1-10: hun, ca, ox, can, ho, uac, uc, uaxac, bolon, lahun

11-19: buluc, lahca, ox-lahun, can-lahun, ho-lahun, uac-lahun, uuc-lahun, uaxac-lahun, bolon-lahun

20, 40, 60, 80, 100: kal/hun-kal, ca-kal, ox-kal, can-kal, ho-kal

30, 50, 70, 90: lahu-ca-kal, lahu-ox-kal, lahu-cankal, lahu-hokal (10 less than 40, etc.).

Other numbers:

21-39 (except 30): 1-19 + tu kal. Thus: 21 is hun tu kal (1+tu+20).

Other numbers (after 40, except the actual non-vigesimal tens numbers 50, 70, 90, etc., where the word tu is dropped): 1-19 + tu and the following vigesimal. Thus:

41 is hun tu ox-kal (1 below 60), 99 is bolon-lahun tu ho-kal (19 below 100).

[Some additional, but not necessary, euphonic variations in speech are:

  1. a) 15, ho-lahun, is sometimes contracted to ho-lhun
  2. b) a y is sometimes inserted between a word ending in u and a following ox or ho. Thus: lahu-oxkal and lahu-hokal (50 and 90) become lahu-y-oxkal and lahu-y-hokal, and similarly hun tu ox-kal, 41, becomes hun tu y-ox-kal]
  3. c) l of lahun is dropped before tu. Thus bolon-lahun tu kal, 39, becomes bolon-lahu tu kal]

[Note: This is important since the Mayans were the only people to invent a vigesimal numeral system. Hence also, perhaps, the system of forming the other numbers (21-99) is slightly less regular or more complicated (but still explicable by certain rules]

[Note: the x is pronounced “sh” and the c as well as k as “k”].

Yupik (EskimoAleut):

1-10: atauciq, malruk, pingayun, cetaman, talliman, arving-legen, malrung-legen, pingayun-legen, qulngunritaraan, qula.

11-19: qula-atauciq, qula-malruk, qula-pingayun, akimiarunrita’ar, akimiaq, akimiaq-ataucik, akimiaq-malruk, akimiaq-pingayun, yuinaunrita’ar

vigesimals 20, 40, 60, 80, 100: yuinaq, yuinaak-malruk, yuinaat-pingayun, yuinaat-cetaman, yuinaat-talliman

Other numbers: vigesimal + 1-19. Thus:

21: yuinaq atauciq, 99: yuinaat-cetaman yuinaunrita’ar

C-IV. DECIMAL SYSTEMS (WITH A BASE OF 10) WITH WORDS FOR 1-10 AND 100

Decimal number systems are those which are based on 10. The simplest types of decimal systems are those where, to learn the numbers, one necessarily has to memorize the numbers 1-10, and the number 100, and the regular procedure for forming the other in-between numbers.

Typical examples of these numbers are found in the major languages of the Sino-Tibetan family [The sign after each word shows the tone: low, rising, falling, etc.]:

Chinese Mandarin (SinoTibetan-Sinitic):

1-10: yi_ , erh, sān, szә↘, wu↗, liu, ch’i_ , pā_ , chiu↗, shih_

tens 20-90: erh↘ shih_ , etc. 100: bai↗

Other numbers: tens+unit. Thus 11: shih_ yi_ , 21: erh↘ shih_ yi_ , 99: chiu↗ shih_ chiu↗

Thai/Siamese (SinoTibetan-Sinitic):

1-10: hnïng_ , sɔng↗, sām↗, sī_ , hā↘, hok_ , chet_ , bpɛt_ , kɔ↘, sip_

tens 20-90: sɔng↗ sip_ , etc. 100: hnïng_ rɔy↘

Other numbers: tens+unit.

Thus 11: sip_ hnïng_, 21: sɔng↗ sip_ hnïng_, 99: kɔ↘ sip_ kɔ↘

Tibetan (SinoTibetan-Tibetic):

1-10: gchig, gnyis, gsum, bzhi, lnga, drug, bdun, brgyad, dgu, bchu

tens 20-90: gnyis bchu, etc. 100: brgya

Other numbers: tens+unit. Thus 11: bchu bchig, 21: gnyis bchu gchig, 99: dgu bchu dgu

[Note: the initial letter in lnga is small L, not capital i]

Burmese (SinoTibetan-Tibetic):

1-10: tit, hnit, sũ, le, ngā, cowk, khuhnit, shit, kɔ, ta-cheh

tens 20-90: hnit-cheh, etc. 100: ta-yā

Other numbers: tens+hnin+unit.

Thus 11: ta-cheh hnin tit, 21: hnit-cheh hnin tit, 99: kɔ-cheh hnin kɔ

Abor-Miri (SinoTibetan-Tibetic):

1-10: ā, ānyī, āūm, āpī, ānga, ākheng, kīnit, pinyī, kanāng, ēing

tens 20-90: ēing-ānyī, etc. 100: ling

Other numbers: tens+lāng+unit. Thus 11: ēing lāng ā, 21: ēing-ānyī lāng ā, 99: ēing- kanāng lāng kanāng

[Note: the suffix -ko is attached at the end of every composite number. Thus: 1: ā-ko, 10: ēing-ko, 11: ēing lāng ā-ko, 20: ēing-ānyī-ko , 21: ēing-ānyī lāng ā-ko, 99: ēing-kanāng lāng kanāng-ko]

Some languages of the Austric family:

Santali (Austric-KolMunda):

1-10: mit’, bar, , pon, mɔrɛ, turūi, ēāe, irәl, arɛ, gɛl

tens 20-90: bar-gɛl, etc. 100: mit-sae

Other numbers: tens+khān+unit.

Thus: 11: gɛl khān mit’, 21: bar-gɛl khān mit’, 99: arɛ-gɛl khān arɛ

[Alternately, the other numbers can be formed without inserting the word khān]

Vietnamese (Austric-MonKhmer):

1-10: mot↘_ , hai, ba, bôn↗, nǎm, sau↗, bay↘↗, tam↗, chin↗, muoi↘

tens 20-90: hai muoi↘, etc. 100: mot↘_ trǎm

Other numbers: tens+unit.

Thus 11: muoi↘ mot↘_ , 21: hai muoi↘ mot↘_ , 99: chin↗ muoi↘ chin↗

Khasi (Austric-MonKhmer):

1-10: ši, ār, lāi, sāw, sàn, hinrīw, hinniew, p’rā, k’ündāi, ši-p’ew

tens 20-90: ār-p’ew, etc. 100: ši-spå

Other numbers: tens+unit: Thus 21: ār-p’ew ši, 99: k’ündāi-p’ew k’ündāi

Some languages of the Austronesian family:

Hawaiian (Austronesian):

1-10: akahi, alua, akolu, aha, alima, aono, ahiku, awalu, aiwa, umi

20: iwak-alua, 30-90: kan-akolu, etc. 100: haneli

Other numbers: tens+kumam+unit.

Thus: 11: umi kumam-akahi 21: iwak-alua kumamakahi, 99: kan-aiwa kumam-aiwa

Some languages from African families:

Hausa (SemitoHamitic-Hamitic):

1-10: daia, biu, uku, fudu, biar, shidda, bakoi, takos, tara, goma

tens 20-90: gomia-biu, etc. 100: dari

Other numbers: 11-17, etc.: tens+sha+unit. Thus 11: goma sha daia, 21: gomia-biu sha daia

18-19: following tens+gaira+biu/daia (i.e. following tens-minus-2/1). Thus:

18: gomiabiu gaira biu (20-minus-2), 99: dari gaira daia (100-minus-1).

Wolof (NigerCongo):

1-10: ben, nīar, nīat, nīanit, jiūrum, jiūrumrumben, jiūrum-nīar, jiūrum-nīat, jiūrum-nīanit, fūk

tens 20-90: nīar-fūk, etc. 100: tēmēr

Other numbers: tens+a+unit. Thus 11: fūk a ben, 21: nīar-fūk a ben, 99: jiūrum-nīanit-fūk a jiūrum-nīanit

Fulani (NigerCongo):

1-10: goo, zizi, tati, nayi, joyi, jeegom, jeezizi, jetati, jenayi, sappo

20: noogas, tens 30-90: capanze-tati, etc. 100: temedere

Other numbers: tens+e+unit.

Thus 11: sappo e goo, 21: noogas e goo, 99: capanze-jenayi e jenayi

Namagua-Hottentot (Khoisan):

1-10: ckui, ckam, qnona, haka, kore, qnani, , xkhaisi, goisi, disi

tens 20-100: ckam-disi, etc. [even 100: disi-disi]

Other numbers: tens+unit+ckha.

Thus: 11: disi ckui-ckha, 21: ckam-disi ckui-ckha, 99: goisi-disi goisi-ckha

[the four letters c, v, q, and x represent four different types of clicking sounds. Clicking sounds as part of the language are unique in the whole world to the Khoisan languages, though some non-Khoisan neighboring languages like Zulu have also borrowed this feature from them]

Some languages from the Amerindian super-family of languages from America:

Quechua/Inca (Amerindian):

1-10: huk, iskay, kimsa, tawa, pisqa, suqta, qanchis, pusaq, iskun, chunka

tens 20-90: iskaychunka, etc. 100: pachak

Other numbers: tens+unit+yuq/niyuq [-yuq after vowel, –niyuq after consonant. final y in 2 is consonant]. Thus:

11: chunkahukniyuq, 13: chunka kimsayuq, 99: iskunchunka iskunniyuq

Guarani (Amerindian):

1-10: peteĩ, mokoĩ, mbohapy, irundy, po, poteĩ, pokoĩ, poapy, porundy, pa

tens 20-90: mokoĩ-pa, etc. 100: sa

Other numbers: tens+unit. Thus 11: pa peteĩ, 21: mokoĩ-pa peteĩ, 99: porundy-pa porundy

Tarahumara (Amerindian):

1-10: bire, oka, beka, nawo, mari, usani, kichao, osanawo, kimakoi, makoi

tens 20-90: oka-makoi, etc. 100: makoi-makoi

Other numbers: tens+wamina+unit. Thus:

11: makoi wamina bire, 21: oka-makoi wamina bire, 99: kimakoi-makoi wamina kimakoi

Tonkawa (Amerindian):

1-10: wē’isbax, gedai, med’is, sigid, gasgwa, sikwālau, sigidyē’es, sikwē’isxw’ēl’a, sikbax

tens 20-90: sikbax-‘āla-gedai, etc. 100: sendo-wē’isbax (borrowed from Spanish)

Other numbers: tens+‘en+unit+‘en. Thus 11: sikbax-‘en wē’isbax-‘en,

21: sikbax-‘āla-gedai-‘en wē’isbax-‘en, 99: sikbax-‘āla-sikwē’isxw’ēl’a-‘en sikwē’isxw’ēl’a-‘en

Zuñi (Amerindian):

1-10: t’opa, kwili, ha’i, awiten, apte, t’opaleqä, kwilileqä, ha’eleqä, tenaleqä, astemła

tens 20-90: kwili-qän-astemła, etc. 100: asi-astemlä

Other numbers: tens+unit+yäłto. Thus 11: astemła t’opa-yäłto, 21: kwili-qän-astemła t’opa- yäłto, 99: tenaleqä-qän-astemła tenaleqä-yäłto

C-V. DECIMAL SYSTEMS (WITH A BASE OF 10) WITH WORDS FOR UNITS 1-9 AND TENS 10-100:

These are the decimal systems where, to learn the numbers, one necessarily has to memorize the numbers 1-10, and the tens numbers 20-100, and the regular procedure for forming the other in-between numbers.

Typical examples of these numbers are found in the major languages of the Uralo-Altaic family:

Mongolian (UraloAltaic-Altaic):

1-10: nigen, khoyar, gorban, dörben, tabun, jirgugan, dologan, naiman, yisun, arban,

Tens 20-100: khorin, gochin, döchin, tabin, jiran, dalan, nayan, yeren, jagon

Other numbers: tens+unit, e.g. 11 is arban nigen (10+1), etc.

Turkish (UraloAltaic-Altaic):

1-10: bir, iki, üҫ, dört, beş, altï, yedi, sekiz, dokuz, on

Tens 20-100: yirmi, otuz, kïrk, elli, altmïş, yetmiş, seksen, doksan, yüz

Other numbers: tens+unit, e.g. 11 is on bir (10+1), etc.

Manchu (UraloAltaic-Altaic):

1-10: emu, juwe, ilan, duin, sunja, ninggun, nadan, jakūn, uyun, juwan

Tens 20-100: orin, gusin, dehi, susai, ninju, nadanju, jakūnju, uyunju, tanggū

Other numbers: tens+unit, e.g. 11 is juwan emu (10+1), etc.

[The only special form is 15, tofohun].

Korean (UraloAltaic-KoreoJapanese):

1-10: hana, tul, set, net, tasәt, yәsәt, ilgop, yәdәlp, ahop, yәl

tens 20-100: sïmïl, sәlïn, mahïn, sühïn, yecun, ilhïn, yәdïn, ahïn, pɛk

Other numbers: tens+unit. Thus 11: yәl hana, 21: sïmïl hana, 99: ahïn ahop

[usually a –ïi is inserted after the final word. Thus 1: hanaïi, 20: sïmïlïi, 21: sïmïl hanaïi, etc.]

Japanese (UraloAltaic-KoreoJapanese):

1-10: hitotsu, futatsu, mittsu, yottsu, itsutsu, muttsu, nanatasu, yattsu, kokonotsu,

tens 20-100: hatachi, miso, yoso, iso, muso, nanaso, yaso, kokonoso, momo [Note: miso, yoso, etc. can alternately be misoji, yosoji, etc]

Other numbers: tens+amari+unit

Thus 11: amari hitotsu, 21: hatachi amari hitotsu, 99: kokonoso amari kokonotsu

[Modern Japanese, however, uses numbers basically borrowed from Chinese]

Hungarian (UraloAltaic-Uralic):

1-10: egy, kettő, három, négy, öt, hat, hét, nyolcz, kilencz, tíz

tens 20-100: húsz, harmincz, negyven, ötven, hatvan, hetven, nyolczvan, kilenczven, száz

Other numbers: tens+unit [But here, in line with the –n endings, 10: tizen, 20: huszon]. Thus:

11: tizen-egy, 99: kilenczven-kilencz

Also, sometimes in some other languages in Asia and Africa:

Tengima Naga (SinoTibetan-Tibetic):

1-10: po, kenna, sê, , pangu, suru, thenā, thethā, tekwü, kerr

tens 20-100: kerr, mekwü, serr, lhidā, lhisuru, lhithenā, lhithethā, lhitekwü, krā

Other numbers: 11-13, etc. previous tens+o+1-3 [Here, 1 has the special form pokrō],

14-19, etc. following tens+pemo+7-9.

e.g. 11 is kerr o pokrō (10+o+1), 21 is mekwü o pokrō, (20+o+1), 99 is krā pemo tekwü (100+pemo+9)

Amharic/Ethiopian (SemitoHamitic-Semitic):

1-10: and, hulat, sost, arāt, am’st, sad’st, sabāt, sam’nt, zaṭañ, ašr

tens 20-100: hāyā, šalāsā, arbā, amsā, salsā, sabā , samānyā, zaṭanā, mato

Other numbers: tens+unit, e.g. 11: ašrā and, 21: hāyā and, 99: zaṭanā zaṭañ

[The only special form is the first tens number in combining with units: ašr becomes aš].

Swahili (NigerCongo):

1-9: mosi, pili, tatu, ‘nne, tano, sita, saba, nane, kenda

Tens 10-100: kumi, makumi-mawili, makumi-matatu, makumi-ma’nne, makumi-matano, makumi-sita, makumi-saba, makumi-manane, makumi-kenda, mia

(The word for 100 is borrowed from Arabic)

Other numbers: tens+na+unit 1-9 [Here, 1 and 2 have special forms: moja, mbili], e.g. 11 is kumi na moja (10+na+1).

Languages of this category are found in the Amerindian superfamily of America as well. One example:

Sahaptin (Amerindian):

1-10: naxc, nipt, mәtad, pinipt, paxad, ptәxninc, tusxas, paxatumad, t’smәst, putәmd

tens 20-100: nibtid, mәtabtid, pinibtid, paxabtid, ptәxninseibtid, tusxaseibtid, paxatumadeibtid, tsmaseibtid, naxcputabdid

Other numbers: tens+unit or tens+wiya+unit. Thus:

11: putәmd wiya naxc, 21: nibtid wiya naxc, 99: tsmaseibtid wiya t’smәst

C-VI. DECIMAL SYSTEMS (WITH A BASE OF 10) WITH WORDS FOR NUMBERS 1-19 and TENS 20-100:

These are the decimal systems where, to learn the numbers, one necessarily has to memorize the numbers 1-10 and the tens numbers 20-100 and the regular procedure for forming the other numbers in-between 21-99, but (due perhaps to the influence of some vigesimal number systems in the vicinity) also the separate numbers or the regular procedure for forming the numbers 11-19.

Many languages form the numbers differently for 11-19 than for the other later numbers 21-29, 31-39, etc., but by a regular procedure rather than with different words. Thus we have the following languages from the Uralo-Altaic family:

Finnish (Uralo-Altaic-Finno-Ugrian):

1-10: yksi, kaksi, kolme, neljä, viisi, kuusi, seitsemän, kahdeksan, yhdeksän, kymmenen

11-19: yksi-toista, etc.

tens 20-90: kaksi-kymmentä, etc. 100: sata

Other numbers: tens+unit. Thus 21: kaksi-kymmentä yksi, 99: yhdeksän-kymmentä yhdeksän

Estonian (Uralo-Altaic-Finno-Ugrian):

1-10: üks, kaks, kolm, neli, viis, kuus, seitse, kaheksa, üheksa, kümme

11-19: üks-teist, etc.

tens 20-100: kaks-kümmend, etc. 100: sada

Other numbers: tens+unit. Thus 21: kaks-kümmend üks, üheksa-kümmend üheksa

Some languages of the Austronesian family:

Malay (Austronesian):

1-10: satu, dua, tiga, empat, lima, enam, tujuh, lapan, sembilan, se-puluh

11-19: se-belas, dua-belas, etc.

tens 20-90: dua-puluh, etc., 100: se-ratus

Other numbers: tens+unit. Thus: 21: dua-puluh satu, 99: sembilan-pulu sembilan

Tagalog (Austronesian):

1-10: isá, dalawá, tatló, apat, limá, anim, pitó, waló, siyam, sang-pouó

11-19: labing-isá, etc.

tens 20-100: dalawá-ngpouó, tatló-ngpouó, apat-napouó, limá-ngpouó, anim-napouó, pitó-ngpouó, waló-ngpouó, siyam-napouó [ie. –ngpouó after vowel, –napouó after consonant]

100: sangdáan

Other numbers: tens+‘t+unit. Thus 21: dalawá-ngpouó-‘t isá, 99: siyam-napouó-‘t siyam

Then we have the languages where the numbers 11-19 are formed with distinct words or by a process of fusion and inflection, but the later in-between numbers (21-29, 31-39, etc.) are formed in a very regular way.

Some languages of Africa:

Kanuri (NiloSaharan/Sudanic):

1-10: tilo, ndi, yasgә, degә, ugu, arasgә, tulur, wusgә, lәgar, megu

tens 20-90: pindi, piyasgә, pidegә, piugu, pirasgә, pitulur, pitusgu, pilәgar

11-19: lәgari, nduri, yasgәn, deri, uri, arasgәn, tulurri, wusgәn, lәgarri

Other numbers: tens+unit, or tens+tata+unit [units ending in vowels add a –n, and units ending in consonants add a –nyin in the compound words].

Thus: 21: pindi tata tilon, 99: pilәgar tata lәgarnyin

Some languages from the Amerindian language super-family of America:

Cherokee (Amerindian-):

1-10: sowo, tali, tsoi, nvgi, hisgi, sudali, galiquogi, tsunela, sonela, sgohi

11-19: sadu, talidu, tsogadu, nigadu, hisgadu, daladu, galiquadu, neladu, soneladu

tens 20-100: tali-sgohi, tsoi-gohi, nvg-sgohi, hisgi-sgohi, sudali-sgohi, galiqua-sgohi, tsunela-sgohi, sonela-sgohi, sgohitsiqua

Other numbers: tens (minus –hi)+unit. Thus 21: tali-sgo sowo, 99: sonela-sgo sonela

Navaho (Amerindian):

1-10: dałai, nak’i, txā, , ashdla, hastxá, tsosts’ed, tsebi, naast’ai, naezná

11-19: ładzáda, nak’idzada, txádzáda, didzáda, ashdlaáda, xastxaáda, tsosts’edzáda, tsebidzáda, naas’aidzáda

tens 20-100: nadīn, txadīn, dísdīn, ashdládīn, hastą́dīn, tsosts’idīn, tseebídīn, náhást’édīn, naennádīn

Other numbers: tens+ła+unit. Thus 21: nadīn ła dałai, 99: náhást’édīn ła naezná

Some of the Semitic languages (which also have dual forms in 1-19 because of grammatical gender):

Arabic (SemitoHamitic-Semitic):

1-10 masc.: ḥidun, isnāni, salasatun, ‘arba’atun, khamsatun, sittatun, sab’atun, samāniyatun, tis’atun, ‘asharatun

1-10 fem.: ḥidatun, isnatāni, salasun, ‘arba’un, khamsun, sittun, sab’un, samānin, tis’un, ‘ashrun

11-12 masc.: ‘aada-‘ashar, isnā-‘ashar. 11-12 fem.: ‘iḥdai-‘ashrat, isnatā-‘ashrat

13-19 masc.: salasata-‘ashar, etc. (-tun becomes -ta).

13-19 fem.: salasa-‘ashar, etc. (-un becomes -a). [Note: 18 is samāniya‘ashar]

Tens 20-100: i’shrūna, salasūna, ‘arba’ūna, khamsūna, sittūna, sab’ūna, samānūna, tis’ūna

Other numbers 21-99: unit (m/f) followed by (the word) wa and the tens. Thus:

21(masc.): ḥidun-wa-i’shrūna, 99 (masc.): tis’atun-wa-tis’ūna.

Hebrew (SemitoHamitic-Semitic):

1-10 masc.: ɛḥɔd, shnayim, shloshɔh, arbɔ’ɔh, amishɔh, shishɔh, shiv’ɔh, shmōnɔh, tish’ɔh, ‘ɛsɔrɔh

1-10 fem.: aḥad, shtayim, shlosh, arba, ḥɔmesh, shesh, shɛva’, shmōnɛh, tesha’, ‘ɛsɛr

11-12 masc.: ‘aḥad-‘ɔsɔr, shnem-‘ɔsɔr. 11-12 fem.: ‘aḥad-‘ɛsreh, shtem-‘ɛsreh.

13-19 masc: shloshɔh-‘ɔsɔr, etc. (3+ɔsɔr). 13-19 fem.: shlosh‘ɛsreh, etc. (3+‘ɛsreh).

Tens 20-100: ‘ɛsrīm, shloshīm, arbɔ’īm, amishīm, shishīm, shiv’īm, shmōnīm, tish’īm, meɔh

Other numbers 21-99: unit (m/f) followed by (the word) w and the tens. Thus:

21(masc.): ɛḥɔd-w-‘ɛsrīm, 99 (masc.): tish’ɔh-w-tish’īm

Maltese (SemitoHamitic-Semitic):

1-10: wieħed, tnejn, tlieta, erbgħa, ħamsa, sitta, sebgħa, tmienja, disgħa, għaxra

11-19: ħdax, tnax, tlettax, erbatax, ħmistax, sittax, sbattax, tmintax, dsatax

tens 20-100: għoxrin, tletin, erbgħin, ħamsin, sittin, sebgħin, tmenin, disgħin

Other numbers: unit+u+tens. Thus 21: wieħed u għoxrin, 99: disgħa u disgħin

But the Dravidian family of languages of India as a whole falls in this category, with clear fusion or inflection in 11-19.

Tamil (Dravidian):

1-10: onṛu, iraṇḍu, mūnṛu, nāngu, aindu, āṛu, ēlu, eṭṭu, onbadu, pattu

11-19: padinonṛu, panniraṇḍu, padimūnṛu, padināngu, padinaindu, padināṛu, padinēlu, padineṭṭu, pattonbadu

tens 20-100: irubadu, muppadu, nāṛbadu, aimbadu, aṛubadu, elubadu, eṇbadu, toṇṇūṛu, nūṛu

Other numbers: tens+unit [The final –du and –ṛu of the tens become –tt and –ṭṛ before vowels and –ttu and –ṭṛu before consonants]. Thus:

21: irubatt-onṛu, 23: irubattu-mūnṛu, 93: toṇṇūṭṛu-mūnṛu, 99: toṇṇūṭṛ-onbadu

[In Dravidian languages, initial e, ē, o, ō are pronounced ye, , wo, . In Tamil, a final u is pronounce ï]

Malayalam (Dravidian):

1-10: onn, raṇṭ, mūnn, nāl, añc, āṛ, ēl, eṭṭ, onpat, patt

11-19: patinonn, panṛaṇṭ, patimmūnn, patināl, patinañc, patināṛ, patinēl, patineṭṭ, pattonpat

tens 20-100: irupat, muppat, nālpat, anpat, aṛupat, elupat, eṇpat, toṇṇūṛ, nūṛ

Other numbers: tens+unit [The final –at of the tens becomes –att before vowels and –atti before consonants. The final ūṛ of 90 becomes ūṭṛi alternately pronounced ūṭi, before the units]. Thus 21: irupatt-onn, 23: irupatti-mūnn, 99: toṇṇūṭṛi-onpat

Kannada (Dravidian):

1-10: ondu, erḍu, mūru, nalku, aidu, āru, ēḷu, eṇṭu, ombattu, hattu

11-19: hannondu, hannerḍu, hadimūru, hadinālku, hadinaidu, hadināru, hadinēḷu, hadineṇṭu, hattombattu

tens 20-100: ippattu, mūvattu, nālvattu, aivattu, ārvattu, eppattu, embattu, tombattu, nūru

Other numbers: tens+unit. [The final –ttu of the tens become –tt before vowels].

Thus 21: ippatt-ondu, 99: tombatt-ombattu

Telugu (Dravidian):

1-10: okaṭi, reṇḍu, mūḍu, nālugu, ayidu, āru, ēḍu, enimidi, tommidi, padi

11-19: padakoṇḍu, panneṇḍu, padamūḍu, padanālugu, padihēni, padahāru, padihēḍu, paddenimidi, pandommidi

tens 20-100: iruvai, muppai, nalubhai, yābhai, aravai, ḍebbhai, enabhai, tombhai, vandala

Other numbers: tens+unit. Thus 21: iruvai okaṭi, 99: tombhai tommidi

And so do the languages from all the other branches of Indo-European languages outside India:

Persian (IndoEuropean-Iranian):

1-10: yak, , si, cahār, pañj, shish, haft, hasht, nuh, dah

11-19: yāzdah, davāzdah, sīzdah, chahārdah, pānzdah, shānzdah, hīvdah, hījdah, nūzdah

tens 20-100: bīst, , chihil, pañjāh, shast, haftād, hashtād, navad, sad

Other numbers: tens+u+unit. Thus 21: bīst u yak, 99: navad u nuh

Armenian (IndoEuropean-ThracoPhrygian):

1-10: mēk, erkou, erekh, chors, hing, veçh, eòthә, outhә, inә, tas

11-19: tasnmēk, tasnerkou, tasnerekh, tasnchors, tasnhing, tasnveçh, tasneòthә, tasnouthә, tasninә

tens 20-100: khsan, eresoun, kharrasoun, yisoun, vathsoun, eòthanasoun, outhsoun, innsoun, hariur

Other numbers: tens+unit. Thus: 21: khsan mēk, 99: innsoun inә

Ancient Greek (IndoEuropean-Hellenic):

1-10: heîs/mía/hen (m/f/n), dúo, treîs, téssares, pénte, héks, heptá, oktṓ, ennéa, déka

11-19: héndeka, ddeka, treîs-kaì-déka, téssares-kaì-déka, pentekaídeka, hekkaídeka, heptakaídeka, oktokaídeka, enneakaídeka

tens 20-100: eíkosi, triákonta, tessarákonta, pentkonta, hekskonta, hebdomkonta, ogdokonta, enenkonta, hekatón

Other numbers: tens+kaì+unit or unit+kaì+tens. Either form can be used. Thus:

21: eíkosi kaì heîs or heîs kaì eíkosi, 99: enenkonta kaì ennéa, or ennéa kaì enenkonta

[Note: Greek vowels have a tonal accent, which is marked. A special form for neuter 4: téssara]

Modern Greek (IndoEuropean-Hellenic):

1-10: henas, duo, treis, tessereis, pente, eksi, hephta, okhtō, ennia, deka

11-12: hendeka, dōdeka, 13-19: deka-treis, etc.

tens 20-100: eikosi, trianta, saranta, penēnta, heksēnta, hebdomēnta, ogdonta, enenēnta, hekato

Other numbers: tens+unit. Thus: 21: eikosi-henas, 99: enenēnta-ennia

[Modern Greek has no tonal accent, hence accent not marked here].

Albanian (IndoEuropean-Illyrian):

1-10: një, dy, tre, katër, pesë, gjashtë, shtatë, tetë, nënd, dhjëte

1-18: një-mbë-dhjëte, etc. 19: nëntë-mbë-dhjëte

tens 20-100: njëzet, tridhjet, dyzet, pesë-dhjet, gjashtë-dhjet, shtatë-dhjet, tetë-dhjet, nënd-dhjet, një-qind

Other numbers: tens+e+unit. Thus 21: njëzet e një, 99: nënd-dhjet e nënd

[Note: 20 and 40 seem to be formed on a principle of 1×20, 2×20].

Polish (IndoEuropean-Slavic):

1-10: jeden, dwa, trzy, cztery, pięć, sześć, siedem, osiem, dziewięć, dziesięć

11-19: jeden-naście, dwa-naście, trzy-naście, czter-naście, pięt-naście, szes-naście, siedem-naście, osiem-naście, dziewięt-naście

tens 20-100: dwa-dzieścia, trzy-dzieści, cztery-dzieści, pięć-dzieśiąt, sześć-dzieśiąt, siedem-dzieśiąt, osiem-dzieśiąt, dziewięć-dzieśiąt, sto

Other numbers: tens+unit. Thus 21: dwa-dzieścia jeden, 99: dziewięćdzieśiąt dziewięć

Russian (IndoEuropean-Slavic):

1-10: odin, dva, tri, cyetyrye, pyat’, shyest’, syem’, vosyem’, dyevyat’, dyesyat’

11-19: odi-nadçat’, dvye-nadçat’, tri-nadçat’, cyetyr-nadçat’, pyat-nadçat’, shyest-nadçat’, syem-nadçat’, vosyem-nadçat’, dyevyatnadçat’

tens 20-100: dvadçat’, tridçat’, sorok, pyat’-dyesyat, shyest’-dyesyat, syem’-dyesyat, vosyem’-dyesyat, dyevyanosto, sto

Other numbers: tens+unit: Thus 21: dvadçat’ odin, 99: dyevyanosto dyevyat’

Lithuanian (IndoEuropean-Baltic):

1-10: vienas, du, trys, keturi, penki, šeši, septyni, aštuoni, devyni, dešimtis

11-19: vienuolika, dvylika, trylika, keturiolika, penkiolika, šešiolika, septyniolika, aštuoniolika, devyniolika

tens 20-100: dvidešimt, trisdešimt, keturiasdešimt, penkiasdešimt, šešiasdešimt, septyniasdešimt, aštuoniasdešimt, devyniasdešimt, šimtas

Other numbers: tens+unit. Thus 21: dvidešimt vienas, 99: devyniasdešimt devyni

Latvian (IndoEuropean-Baltic):

1-10: viens, divi, tris, četri, pieci, seši, septiņi, astoņi, deviņi, desmits

11-19: vienspadsmit, divspadsmit, trispadsmit, četrpadsmit, piecpadsmit, sešpadsmit, septiņpadsmit, astoņpadsmit, deviņpadsmit

tens 20-100: divdesmit, trisdesmit, četrdesmit, piecdesmit, sešdesmit, septiņdesmit, astoņdesmit, deviņdesmit, simts

Other numbers: tens+unit. Thus 21: divdesmit viens, 99: deviņdesmit deviņi

Danish (IndoEuropean-Germanic):

1-10: en/et, to, tre, fire, fem, seks, syv, otte, ni, ti

11-19: elleve, tolv, tretten, fjorten, femten, seksten, sytten, atten, nitten

tens 20-100: tyve, tredive, fyrre, halvtreds, tres, halvfjerds, firs, halvfems, hundrede

Other numbers: unit+og+tens. Thus: 21: en-og-tyve, 99: ni-og-halvfems.

Norwegian (IndoEuropean-Germanic):

1-10: en/et, to, tre, fire, fem, seks, sju, åtte, ni, ti

11-19: elleve, tolv, tretten, fjorten, femten, seksten, sytten, atten, nitten

tens 20-100: tjue, tretti, førti, femti, seksti, sytti, åtti, nitti, hundre

Other numbers: unit+og+tens. Thus: 21: en-og-tjue, 99: ni-og-nitti.

Swedish (Indo-European-Germanic):

1-10: en/ett, två, tre, fyra, fem, sex, sju, åtta, nio, tio

11-19: tio, elva, tolv, tretton, fjorton, femton, sexton, sjutton, aderton, nitton

tens 20-100: tjugo, trettio, fyrtio, femtio, sextio, sjuttio, åttio, nittio, hundra

Other numbers: tens+unit. Thus 21: tjugo-en, 99: nittio-nio

Icelandic (IndoEuropean-Germanic):

1-10: einn, tveir, ƥrīr, fjórir, fimm, sex, sjö, átta, níu, tíu

11-19: ellefu, tólf, ƥrettán, fjórtán, fimmtán, sextán, seytján, átján, nítjan

tens 20-100: tuttugu, ƥrjátíu, fjörutíu, fimmtíu, sextíu, sjötíu, áttatíu, níutíu, hundrađ

Other numbers: tens+og+unit. Thus 21: tuttugu og einn, 99: níutíu og níu

German (IndoEuropean-Germanic):

1-10: eins, zwei, drei, vier, fünf, sechs, sieben, acht, neun, zehn

11-19: elf, zwölf, dreizehn, vierzehn, fünfzehn, sechzehn, siebzehn, achtzehn, neunzehn

tens 20-100: zwanzig, dreissig, vierzig, fünfzig, sechzig, siebzig, achtzig, neunzig, hundert

Other numbers: unit+und+tens (as one word, but eins becomes ein). Thus:

21: einundzwanzig, 99: neunundneunzig

Dutch (IndoEuropean-Germanic):

1-10: een, twee, drie, vier, vijf, zes, zeven, acht, negen, tien

11-19: elf, twaalf, dertien, veertien, vijftien, zestien, zeventien, achttien, negentien

tens 20-100: twintig, dertig, veertig, vijftig, zestig, zeventig, tachtig, negentig, honderd

Other numbers: unit+en+tens. Thus 21: een en twintig, 99: negen en negentig

Old English (IndoEuropean-Germanic):

1-10: ān, twēgen, ƥrīe, fēower, fīf, siex, seofon, eahta, nigon, tīen

11-19: endleofan, twelf, ƥrēotīene, fēowertīene, fīftīene, siextīene, seofontīene, eahtatīene, nigontīene

tens 20-100: twentig, ƥrītig, fēowertig, fīftig, siextig, hundseofontig, hundeahtatig, hundnigontig, hundtēontig

Other numbers: unit+and+tens. Thus 21: ān and twentig, 99: nigon and hundnigontig

[ƥ is pronounced “th”]

English (IndoEuropean-Germanic):

1-10: one, two, three, four, five, six, seven, eight, nine, ten

11-19: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen

tens 20-100: twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, hundred

Other numbers: tens+unit. Thus: 21: twenty-one, 99: ninety-nine

Latin (IndoEuropean-Italic):

1-10: unus, duo, tres, quattuor, quinque, sex, septem, octo, novem, decem

11-19: undecim, duodecim, tredecim, quattuordecim, quindecim, sedecim, septemdecim, duode-viginti, unde-viginti

tens 20-100: viginti, triginta, quadraginta, quinquaginta, sexaginta, septuaginta, octoginta, ninaginta, centum

Other numbers: tens+unit (1-7) or unit (1-7)+et+tens. Either form can be used.

Tens (including 100)+unit (8-9): duode/unde+following-tens (i.e. 2-less-then, 1-less-then the following tens). Thus:

21: viginti-unus or unus et viginti, 99: undecentum

Spanish (IndoEuropean-Italic):

1-10: uno/una, dos, tres, cuatro, cinco, séis, siete, ocho, nueve, diez

11-19: once, doce, trece, catorce, quince, dieciséis, diecisiete, dieciocho, diecinueve

tens 20-100: veinte, treinta, cuarenta, cincuenta, sesenta, setenta, ochenta, noventa, ciento

Other numbers: 21-29: vientiuno, etc. Others: tens+y+unit. Thus:

31: treinta y uno, 99: noventa y nueve

Portuguese (IndoEuropean-Italic):

1-10: um/uma, dois, três, quatro, cinco, seis, sete, oito, nove, dez

11-19: onze, doze, treze, catorze, quinze, dezasseis, dezassete, dezoito, dezanove

tens 20-100: vinte, trinta, quarenta, sessenta, setenta, oitenta, noventa, cento

Other numbers: tens+e+unit. Thus 21: vinte e um, 99: noventa e nove

Romanian (IndoEuropean-Italic):

1-10: unu, doi, trei, patru, cinci, şase, şapte, opt, nouă, zece

11-19: unsprezece, doisprezece, treisprezece, paisprezece, cincisprezece, şaisprezece, şaptesprezece, optsprezece, nouăsprezece

tens 20-100: douăzeci, treizeci, paizeci, cincizeci, şaizeci, şaptezeci, optzeci, nouăzeci, o sută

Other numbers: tens+şi+unit. Thus 21: douăzeci şi unu, 99: nouăzeci şi nouă

Italian (IndoEuropean-Italic):

1-10: uno, due, tré, quattro, cinque, sei, sette, otto, nove, dieci

11-19: undici, dodici, tredici, quattordici, quindici, sedici, diciassette, diciotto, diciannove

tens 20-100: venti, trenta, quaranta, cinquanta, sessanta, settanta, ottanta, novanta, cento

Other numbers: tens+unit [last vowel of tens dropped before vowels in uno, otto]. Thus:

21: vent-uno, 99: novanta-nove

C-VII. DECIMAL SYSTEMS (WITH A BASE OF 10) WITH WORDS FOR NUMBERS 1-100:

Finally, we come to the most complex decimal system of all, where there is such complete fusion and inflection between the tens and unit numbers that it becomes necessary to learn individually the exact form of every number from 1-100, above the usual necessity of learning the unit words 1-9 and tens words 10-100.

Basically, one has to first learn the numbers from 1-10, 11-19 and the tens 20-100. The other numbers 21-99 are naturally formed by a combination of the tens and unit words.

But these words are fused together in such a way that it becomes necessary to individually learn every number from 1-100. [In addition, the words 19, 29, 39, etc. are formed on the principle “one less than the following tens” (usually except 89 and 99)].

The only languages in the world which have a number system of this kind are the Indo-Aryan languages of North India. We will take the example of just three of these languages: Hindi, Marathi and Gujarati. Compare the difference in the forms in both the languages:

Hindi:

1-9: ek, do, tīn, cār, pāñc, chah, sāt, āṭh, nau

11-19: gyārah, bārah, terah, caudah, pandrah, solah, satārah, aṭhārah, unnīs

tens 10-100: das, bīs, tīs, cālīs, pacās, sāṭh, sattar, assī, nabbe, sau

The other numbers are formed by unit-form+tens-form, e.g. 21: ek+bīs = ikk-īs.

The different changes taking place in the tens forms as well as the units form in the numbers 21-99 must be noted:

Tens forms:

20 bīs: –īs (21, 22, 23, 25, 27, 28), –bīs (24, 26).

30 tīs: –tīs (29, 31, 32, 33, 34, 35, 36, 37, 38).

40 cālīs: –tālīs (39, 41, 43, 45, 47, 48), –yālīs (42, 46), –vālīs (44).

50 pacās: –cās (49), –van (51, 52, 54, 57, 58), –pan (53, 55, 56).

60 sāṭh: –saṭh (59, 61, 62, 63, 64, 65, 66, 67, 68).

70 sattar: –hattar (69, 71, 72, 73, 74, 75, 76, 77, 78).

80 assī: –āsī (79, 81, 82, 83, 84, 85, 86, 87, 88, 89).

90 nabbe: –nave (91, 92, 93, 94, 95, 96, 97, 98, 99).

Unit forms:

1 ek: ikk- (21), ikat- (31), ik- (41, 61, 71), iky- (81), ikyā- (51, 91).

2 do: bā- (22, 52, 62, 92), bat- (32), ba- (42, 72), bay- (82).

3 tīn: te- (23), ten- (33, 43), tir- (53, 63, 83), ti- (73), tirā- (93).

4 cār: cau- (24, 54, 74), ca- (44), caun- (34, 64), caur- (84), caurā- (94).

5 pāñc: pacc- (25), paĩ (35, 45, 65), pac- (55, 75, 85), pañcā- (95).

6 che: chab- (26), chat- (36), chi- (46, 76), chap- (56), chiyā- (66, 96), chiy- (86).

7 sāt: sattā- (27, 57, 97), saĩ (37, 47), saḍ- (67), sat- (77), satt- (87).

8 āṭh: aṭṭhā- (28, 58, 98), aḍ- (38, 48, 68), aṭh- (78, 88).

9 nau: un- (29, 39, 59, 69, 79), unan- (49), nav- (89), ninyā- (99).

Marathi:

1-9: ek, don, tīn, cār, pāç, sahā, sāt, āṭh, naū

11-19: akrā, bārā, terā, çaudā, pandhrā, soḷā, satrā, aṭhrā, ekoṇīs

tens 10-100: dahā, vīs, tīs, cāḷīs, pannās, sāṭh, sattar, aĩśī, navvad, śambhar

The other numbers are formed by unit-form+tens-form, e.g. 21: ek+vīs = ek-vīs.

The different changes taking place in the tens forms as well as the units form in the numbers 21-99 must be noted:

Tens forms:

20 vīs: –vīs (21, 22, 23, 24, 25, 26, 27, 28).

30 tīs: –tīs (29, 31, 32, 33, 34, 35, 36, 37, 38).

40 cāḷīs: –cāḷīs (39, 41, 42, 43, 44, 45, 46, 47, 48).

50 pannās: –pannās (49), –vanna (51, 52, 55, 57, 58), –panna (53, 54, 56).

60 sāṭh: – sāṭh (59), –saṣṭa (61, 62, 63, 64, 65, 66, 67, 68).

70 sattar: –sattar (69), –hattar (71, 72, 73, 74, 75, 76, 77, 78).

80 aĩśī: –aĩśī (79, 81, 82, 83, 84, 85, 86, 87, 88).

90 navvad: –navvad (89), –ṇṇav (91, 92, 93, 94, 95, 96, 97, 98, 99).

Unit forms:

1 ek: ek- (21, 31, 61), ekke- (41), ekkyā- (81, 91), ekkā- (51, 71).

2 don: bā- (22, 52, 62, 72), bat- (32), be- (42), byā- (82, 92).

3 tīn: te- (23), teha- (33), tre- (43, 53, 63), tryā- (73, 83, 93).

4 cār: co- (24), çau- (34, 54, 64), çavve- (44), çauryā- (74, 84, 94).

5 pāç: pañc- (25), pas- (35), pañce- (45), pañçā- (55), pā- (65), pañcyā (75, 85, 95) .

6 sahā: sav- (26), chat- (36), sehe- (46), chap- (56), sahā- (66), śahā- (76, 86, 96).

7 sāt: sattā- (27, 57), sada- (37), satte- (47), sadu- (67), sattyā- (77, 87, 97).

8 āṭh: aṭṭhā- (28, 58), aḍ- (38), aṭṭhe- (48), aḍu- (68), aṭṭhyā- (78, 88, 98).

9 naū: ekoṇ- (29, 39, 49, 59, 69, 79, 89), navvyā- (99).

Gujarati:

1-9: ek, be, traṇ, cār, pāñc, cha, sāt, āṭh, nav

11-19: agyār, bār, ter, caud, pandar, soḷ, sattar, aḍhār, ogṇis

tens 10-100: das, vīs, trīs, cālīs, pacās, sāīṭh, sitter, , nevũ, so

The other numbers are formed by unit-form+tens-form, e.g. 21: ek+vīs = ek-vīs.

The different changes taking place in the tens forms as well as the units form in the numbers 21-99 must be noted:

Tens forms:

20 vīs: –īs (25), –vīs (21, 22, 23, 24, 26, 27, 28).

30 trīs: –trīs (29, 31, 32, 33, 34, 35, 36, 37, 38).

40 cālīs: –tālīs (41, 42, 43, 45, 46, 47, 48), –cālīs (39), –ālīs (44).

50 pacās: –pacās (49), –van (51, 52, 55, 57, 58), –pan (53, 54, 56).

60 sāīṭh: –sāṭh (59), saṭh (61, 62, 63, 64, 65, 66, 67, 68).

70 sitter: sitter (69), –oter (71, 72, 73, 74, 75, 76, 77, 78).

80: (79), –āsī (81, 82, 83, 84, 85, 86, 87, 88, 89).

90 nevũ: –ṇu (91, 92, 93, 94, 95, 97, 98, 99), –nnu (96).

Unit forms:

1 ek: ek- (21, 41, 61, 71), eka- (31), ekā- (51, 91), eky- (81).

2 be: bā- (22, 52, 62, 92), ba- (32), be- (42), b- (72), by– (82).

3 traṇ: te- (23, 33), tre- (43, 53, 63), ty- (83), t- (73), trā- (93).

4 cār: co- (24, 34, 54, 64), cum- (44, 74), cory- (84), corā- (94).

5 pāñc: pacc- (25), ã (35, 65), pis– (45), pañc- (75, 85), pañcā- (55, 95).

6 cha: cha- (26, 36.96), che- (46), chap- (56), chā- (66), chay- (86), ch– (76).

7 sāt: sattā- (27, 57, 97), saḍa- (37), suḍ– (47), saḍ- (67), sity- (77, 87).

8 āṭh: aṭṭhā- (28, 58, 98), aḍ- (48, 68), aḍa– (38), iṭhy- (78, 88).

9 nav: ogaṇ- (29, 39, 49, 59), agṇo- (69), ogṇā- (79), nevy- (89), navvā– (99).

The same irregularity or inflectional complexity can be seen in the formation of the numbers between 21 and 99 in all the Indo-Aryan languages of North India (right up to Kashmiri in the extreme north, and going so far westwards as to influence the Pashto language in the northwest which, although it belongs to the Iranian branch, has also been influenced by the Indo-Aryan cerebral sounds), but is found nowhere else outside the sphere of North India . Note that the irregularity of the fusion of the forms in one Indo-Aryan language do not correspond to those in another Indo-Aryan language. Thus, ek (1) has one form (ek-) in Marathi in 21, 31 and 61, but Hindi has three different forms ikk- (in 21), ikat- (in 31) and ik- (in 61), and Gujarati has two forms ek– (in 21, 61) and eka– (in 31). Or pāñc (5) has one form (paĩ) in Hindi in 35, 45 and 65, and Gujarati has two forms ã– (in 35, 65) and pis– (in 45), but Marathi pāç (5) has three different forms pas- (in 35), pañce- (in 45) and pā- (in 65).

We have shown the numbers 21-99 in these three Indo-Aryan languages in classified table form, but obviously it is simpler to learn each individual number by rote than with the help of these classification tables.

This is in sharp contrast with all the other languages in the world other than the Indo-Aryan languages of North India. In all the other languages, it is necessary to learn by heart at the most the numbers from 1-10, or from 1-19, and the tens forms (20, 30, 40, 50, 60, 70, 80, 90). All the numbers between 21 and 99 are formed from these numbers by some sort of regular process which does not require all these individual numbers to be learnt by heart. This is the case with all other languages, including all the other non-Indo-European Indian languages (Dravidian, Austric, Sino-Tibetan, Burushaski. The Andamanese languages, as already pointed out, do not have numbers beyond 3 or 5) as well as all the non-Indian Indo-European languages (spoken outside India), including even the Indo-Aryan Sinhalese language spoken to the south of India.

This feature of the Indo-Aryan numbers has very definite practical disadvantages:

  1. The first and most obvious disadvantage is that it makes it more difficult for the learner to learn the exact forms of the numbers 1-100 in an Indo-Aryan language than in any other language, even if the learner is himself a speaker of another Indo-Aryan language (though in that case, of course, he is likely to recognize the numbers when spoken by someone else more easily than the learner who is a speaker of a non-Indo-Aryan language).
  1. The second disadvantage is that, like all the other many languages (including, for example, Old English and German) which have a similar word-order for the numbers 21-99, the word-order of the tens and unit words is irrational and unordered since the unit word comes before the tens word. Thus, the number 45, 396 (four, five, three, nine, six) in English, for example, would be “forty-five thousand, three hundred and ninety-six” (in the order four, five, three, nine, six), which is rational and ordered, but in Hindi would be “paintālīs hazār tīn-sau chiyā-nave” (in the order five, four, three, six, nine).

This is somewhat like the irrational and unordered American style of writing the date as compared to the British style: 4th January 2018 is written 1/4/2018 in the American style and 4/1/2018 in the British style. Logically, the month should come between the day and the year, and the only reason the irrational and unordered American style is gaining ground in modern usage is because of the political and economic clout of the U.S.A and its monopoly over computer technology.

The unordered nature of the Indo-Aryan numbers 21-99, compounded with the irregular and inflected forms, adds to the difficulty of the numbers. On a personal note, I myself regularly fumble for the right words (although I know them well) when suddenly called upon to say, for example, 67, when I automatically say sainsaṭh (or even chiya-…) instead of saḍsaṭh, and then pause and correct myself.

But the nature of the Indo-Aryan numbers is very important from the cultural and historical view-point. As the Muslim saying goes, “mulla ki dor masjid tak“: I find in the nature of the Indo-Aryan number system one more clear piece of evidence for the OIT (the Out-of-India Theory of Indo-European origins).

To be continued …

The article originally appeared here and has been republished with permission.

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Shrikant Talageri is a scholar and acclaimed author of The Rigveda: A Historical Analysis, the seminal work on the Aryan Invasion debate. His latest work is “Rigveda And Avesta The Final Evidence.”