The Irrefutable Evidence of the Indo-European Numbers

 

The Irrefutable Evidence of the Indo-European Numbers

Shrikant G. Talageri

 

My recent article "The Finality of the Mitanni Evidence", and the response it got (in the sense of new people who are not generally aware of my writings and of the OIT evidence), made me aware that sometimes some very crucial evidence can get lost in the mass of other evidence and remain obscure or little understood, and needs to be highlighted in specific articles. The evidence of the Indo-European numbers is one such very crucial and unchallengeable evidence, which forms part of my very long article "India's Unique Place in the World of Numbers and Numerals", and has again been dealt with in other long summaries of the OIT evidence, where it may be getting submerged as merely one more piece of evidence, and therefore escapes specific scrutiny from readers. So, in this article, I will deal only with the finality of the evidence of the Indo-European Numbers.

As I pointed out in my earlier long article on numbers and numerals, the majority of number systems in the world are decimal systems (with a base of ten) or vigesimal systems (with a base of twenty). There are also rarer and more confusing number systems: the sexagesimal system (with a base of sixty) in the ancient Mesopotamian languages and in the Masai language of Africa, and the incredible quindecimal system  (with a base of fifteen) found in the Huli language of Papua new Guinea. But we need not concern ourselves with these latter two systems here.

An examination of the Indo-European numbers in the different languages shows us that Indo-European numbers are based on a decimal system, with the additional influence of some neighboring languages with vigesimal systems during the evolution of the Indo-European numbers. This shows that the Indo-European Homeland has to be placed in an area where there were neighboring languages with vigesimal systems.

We will examine the absolute evidence in three parts:

I. The Vigesimal Influence.

II. The Four Stages of Evolution of Decimals.

III. The Geographical Location of the Four Stages.

 

I. The Vigesimal Influence

As we saw, the Indo-European Homeland has to be placed in an area where there were neighboring languages with vigesimal systems. But this by itself is not directly helpful because we find non-Indo-European languages with vigesimal systems as neighbors all over the historical Indo-European world: in western Europe (e.g. Basque), in the Caucasus area (e.g. Georgian) as well as throughout India (Burushaski in the Gilgit area in the northwest, Turi in Jharkhand, Mundari in Jharkhand-Orissa, Savara in Andhra-Orissa, Shompeng in the Nicobar Islands, Lepcha in Sikkim, Garo in Assam).

For ready reference, the numbers 1-100 in each of these languages with vigesimal systems:

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).

 

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"].

 

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).

 

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 (4x20+19).

 

Mundari (Austric-KolMunda):

1-10: miyada, bariyā, apiyā, upanā, mōrēyā, turiyā, ēyā, ēraliyā, ariyā, gēlēyā

11-19: gēla +1-9.  

20, 40, 60, 80, 100: mida-hisi, bara-hisi, api-hisi, upana-hisi, mōda sai

Other numbers: vigesimal + 1-19. Thus:

21: mida-hisi miyada (20+1), 99: upana-hisi gēla-ariyā  (80+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+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 (20x1, 20x2, 20x3, 20x4, 100x1)

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

21: khā-kāt sa kāt-thāp (20x1+sa+1+thāp), 99: khā-falī sa kakyōt-thāp (20x4+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

 

At first glance, it appears as if the Indo-European languages could have received the vigesimal influence from any of these languages: either from Basque in western Europe, or from Caucasian (to the south of the steppes) or from one of the languages in India. However, the probabilities lie heavily in favor of India, as we will see:

 

I-A. WESTERN EUROPE:

The chances of the Indo-European family as a whole having been influenced by Basque in respect of the vigesimal effect on its decimal system are zero:

1. No theory places the origins of the IE family in western or southwestern Europe (the area of Basque), and there is no evidence of any influence of Basque on the IE languages as a whole or on the IE numbers as a whole.

2. On the other hand, the evidence shows that the Basque vigesimal numbers did influence certain IE languages at a later stage, and this influence was restricted to the area of France.

Basque is now restricted to a small area on the borders of France and Spain, but is accepted as having been spoken all over the southwestern areas of Europe before the arrival of the IE languages. The only languages which have been influenced by the Basque vigesimal system are the Celtic languages (e.g. Irish, Welsh) which actually replaced the original decimal system with a vigesimal system:

 

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].

 

The Celtic languages are known as having been spoken in France before migrating to the British isles: e.g. the Celtic Gauls in Roman France (made famous in Asterix comics) and the Celtic Breton language still spoken in (and restricted to) France today.

The French language developed in the area after the departure of the Celts (and probably the further weakening of Basque influence), and while it has a decimal system, a special vigesimal influence is seen in its words for the numbers 70, 80 and 90:

 

French (IndoEuropean-Italic):

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", "4x20" and "4x20+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, (4x20+11, 4x20+12) etc. (81-89 are the normal quatre-vingt-un, quatre-vingt-deux, etc.).

 

No other Indo-European language (other than Celtic languages and French) exhibit this kind of vigesimal influence with names indicating multiples of 20. (although we have the English literary style of imitating Celtic forms with phrases containing "score" for 20: "four-scores-and-ten" for 90, or Lincoln in his Gettysburg address using "four-score-and-seven" for 87).

 

I-B. CAUCASUS AREA:

Again, there is no evidence at all that the Caucasian languages (like Georgian) influenced the Indo-European languages with their vigesimal system. No Indo-European language in the vicinity of the Caucasian language area exhibits

a) either the heavily vigesimal-influenced system that we see in the IE languages associated with France,

b) or any vestiges of a pre-vigesimal-influenced decimal system.

So it is extremely unlikely that the vigesimal effect in the Indo-European languages could be due to the influence of the Caucasian languages.

 

I C. INDIA:

On the other hand, centred in and around India we have strong vestiges of languages with pre-vigesimal-influenced decimal systems exhibiting the different stages of evolution of decimal numbers, but we will see this in the next section.

Here, we will first only see why the probabilities for this influence on Indo-European numbers by  vigesimal systems lie more heavily in favor of India rather than any of the other areas:

1. To begin with, the non-Indo-European languages in India with vigesimal systems are found all over the north (from Gilgit in the northwest to Jharkhand and Orissa in the eastern parts) and in Sikkim and Assam in the east, and also as far south as Andhra and the Nicobar islands off the eastern coast. And they cover three different non-Indo-European language families: Burushaski, Austric and Sino-Tibetan.

2. Further, as in the case of the decimal system, we see the different stages of development of the vigesimal system (especially in the Austric languages) more clearly in India than anywhere else in the world, and possibly even a transition from a vigesimal system to the first stage of the decimal one!

Thus, the vigesimal system, like the decimal, originated from a (finger-counting) system of five. As we saw, the most primeval form of this system of five developing into a vigesimal system is found in the Turi language:

 

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 (4x20+19).

[That the Austric number system was originally based on a system of five is confirmed by comparison with the Austric Khmer numbers in Cambodia: the Khmer numbers 1-10 are: muǝy, pii, bǝy, buǝn, pram, pram-muǝy, pram-pii, pram-bǝy, pram-buǝn, dap]

 

A complete vigesimal system with number words up to ten is found in the related neighboring Mundari language:

Mundari (Austric-KolMunda):

1-10: miyada, bariyā, apiyā, upanā, mōrēyā, turiyā, ēyā, ēraliyā, ariyā, gēlēyā

11-19: gēla +1-9.  

20, 40, 60, 80, 100: mida-hisi, bara-hisi, api-hisi, upana-hisi, mōda sai

Other numbers: vigesimal + 1-19. Thus:

21: mida-hisi miyada (20+1), 99: upana-hisi gēla-ariyā  (80+19).

 

And then, incredibly, we find the first stage of the decimal system in another related neighboring language, Santali:

Santali (Austric-KolMunda):

1-10: mit', bar, pɛ, 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]

 

Of course, while all this shows that the probabilities for this vigesimal influence lie more heavily in favor of India rather than any of the other areas, it is not in itself clinching evidence. The clinching evidence comes when we examine the four stages of development of the decimal numbers.

 

II. The Four Stages of Evolution of Decimals

A decimal system is a number system with a base of ten. As man started counting, he first used the five fingers of one hand, and then the ten fingers of two hands. In some cultures, he also used his ten fingers and ten toes; but in most cultures, he used only his ten fingers and therefore invented or created ten number words from one to ten. As his way of living became more complex, he found it necessary to deal with even bigger numbers. And these new numbers, in the earlier stages, were expressed in terms of the number words he already knew and used.

Thus, the speakers of the Onge language of the Andaman islands, whose very simple lifestyle did not require the use of large numbers, only had  number words from one to three or from one to four (depending on how you look at it): 1-3: yuwaiya, inaga, irejidda. The word ilake served for four, but also for any number above four! The Onge language did not develop, or require to develop, words beyond that.

The speakers of another language whose speakers had a similarly simple lifestyle, the Kamilaroi language of the Australian natives, likewise only had number words from one to three: mal, bular, guliba. They then expressed larger numbers with combinations of these words: 4-6 being bular-bular, bular-guliba, and guliba-guliba. 7-9 would then presumably be bular-bular-guliba, bular-guliba-guliba, and guliba-guliba-guliba. The limited scope for further development and use of such number words is obvious.

But most cultures did create number words from one to ten. And used a similar process (like that of the Kamilaroi above) to express bigger numbers from the existing ten number words. But after 99, it became necessary to create a new word for 100. And, as culture and socio-economic activities became more and more complex, it became necessary to create a new word for every multiple of ten (since the base in a decimal system is ten). Thus we get the first stage of the decimal system, best exemplified by the Chinese numbers:

STAGE ONE DECIMAL SYSTEM.

Stage One  of the decimal system has only ten number words before 100, and  is best exemplified by the Chinese numbers:

Chinese:

1-10: yī, èr, sān, sì, wǔ, liù, qī, bā, jiǔ, shí

100: băi (hundred) or yī băi (one hundred)

[Likewise, 1000: yī qiān, 10000: yī wàn, etc.]

The numbers in between are formed by combining these number words:

11-19: shí yī, shí èr, shí sān, shí sì, shí wǔ, shí liù, shí qī, shí bā, shí jiǔ

20, 30, etc.: èr shí, sān shí, etc.

21, 22, etc.: èr shí yī, èr shí èr, etc.

 

STAGE TWO DECIMAL SYSTEM.

Stage two of the decimal system entailed the creation of new number words for the multiples of 10 (i.e. 20, 30, 40, 50, 60, 70, 80, 90), and is best exemplified by the Turkish numbers:

Turkish:

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

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

The numbers in between are formed by combining these number words:

11-19: on bir, on iki, on üҫ, on dört, on beş, on altï, on yedi, on sekiz, on dokuz

21, 22, etc.: yirmi bir, yirmi iki, etc.

 

STAGE THREE DECIMAL SYSTEM.

In stage three of the decimal system, we see the vigesimal effect, which seems to give a special importance to the numbers 1-20 over the subsequent numbers. So languages whose decimal systems are affected by the vigesimal effect create special ways to express or form the numbers 11-19 in a way different from the ways in which subsequent groups (21-29, 31-39, 41-49, etc.) are formed. The best example to give here is English:

English:

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

21, 22, etc.:twenty-one,  twenty-two, etc.

 

STAGE FOUR DECIMAL SYSTEM.

In stage four of the decimal system, the numbers 1-100 became even more complicated. While in all the earlier three stages, the in-between numbers 21-99 were formed simply by juxtaposing (with or without some regular connecting word or phrase) the tens numbers (20, 30, 40, etc.) and the units numbers (1, 2, 3, etc.), in stage four the tens numbers and units numbers were fused together in irregular ways, so that it became necessary to individually learn by heart all the numbers 1-100. The best example to give here is Hindi:

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).

 

III. The Geographical Location of the Four Stages

How does all the data about the numbers 1-100 in the different Indo-European languages irrefutably show that the Indo-European Homeland was located in India?

STAGE ONE:

To begin with the Stage One Decimal System is not found recorded in any Indo-European language. However, the reconstructed Proto-Indo-European language is not recorded anywhere either, and neither has it been possible to reconstruct all the number words from 1-100 in PIE. The first (of twelve branches) to migrate from any postulated Indo-European Homeland is Anatolian/Hittite, and in the case of this branch also, no records have been found of the way in which the languages of this branch formed the tens numbers 20-100 or the numbers 11-19.

 

STAGE TWO:

However, the second (of twelve branches) to migrate from any postulated Indo-European Homeland is Tocharian, and although we do not have records of all the number words, we have enough data in the records to show that Tocharian was in Stage Two of the Decimal System: it has a distinct word for 20, while 11 is formed by juxtaposing the words for 10 and 1.

Tocharian B:

1-10: se, wi, trai, śtwer, piś, ska, sukt, okt, ñu, śak

11-19: ten + unit. Thus 11: śak-se.

20: ikäm.         

[Being an extinct language found only in documents, nothing is known about the exact form of the other numbers]

 

Apart from Tocharian, Sanskrit (though the sandhi system makes it difficult to realize this) and Spoken Sinhalese are the only two Indo-European languages in Stage Two of the Decimal System:

Sanskrit:

1-9: eka, dvi, tri, catur, pañca, ṣaṭ, sapta, aṣṭa, nava

tens 10-90: daśa, viṁśati, triṁśat, catvāriṁśat, pañcāśat, ṣaṣṭi, saptati, aśīti, navati, śatam

Other numbers: unit-form+tens.

[The tens do not undergo any change in combination, with the sole exception of the word for 16, where -daśa becomes -ḍaśa in combination with ṣaḍ-.  And, by the regular Sanskrit phonetic rules of sandhi or word-combination, in the unit-form+tens combinations for 80-, a-+-a becomes ā, and i-+-a becomes ya, so 81: ekāśīti, 82: dvyaśīti, etc].   

Units forms:

1 eka:  ekā- (11), eka- (21,31,41,51,61,71,81,91).

2 dvi:  dvā- (11,22,32), dvi- (42,52,62,72,82,92).

3 tri:  trayo- (13,23,33), tri- (43,53,63,73,83,93).

4 catur:  catur- (14,24,84,94), catus- (34), catuś- (44) catuḥ- (54,64,74).

5 pañca:  pañca- (15,25,35,45,55,65,75,85,95).

6 ṣaṭ:  ṣo- (16), ṣaḍ- (26,86), ṣaṭ- (36,46,56,66,76), ṣaṇ- (96).

7 sapta:  sapta- (17,27,37,47,57,67,77,87,97).

8 aṣṭa:  aṣṭā- (18,28,38,48,58,68,78,88,98).

9 nava:  ūna- (19,29,39,49,59,69,79,89), nava- (99).

[In Sanskrit, 11, 12, etc. (ekā-daśan, dvā-daśan, etc.) are exactly similar formations to 21, 22, etc. (eka-viṁśati, dvā-viṁśati, etc.), although grammatically the Sanskrit numbers 1-19 are supposed to be adjectives, while the numbers above that are supposed to be nouns. The Sanskrit numbers, therefore, clearly represent a frozen form of the earliest Indo-European purely decimal number-system before the vigesimal-effect of Stage Three took place.]

 

Spoken Sinhalese:

1-9: eka, deka, tuna, hatara, pasa, haya, hata, aṭa, navaya, dahaya

Tens 10-100: dahaya, vissa, tisa, hatalisa, panasa, hɛṭa, hɛttɛɛva, asūva, anūva, siyaya

The tens 10-100 stems: daha-, visi-, tis-, hatalis-, panas-, hɛṭa-, hɛttɛɛ-, asū-, anū-, siya-

[The word-order for all the numbers is tens+unit. Even the numbers 11-19 are similarly formed in the form of tens-stem+unit, as daha-eka, daha-deka, etc.]

Thus  21: visi-eka,  99: anū-navaya, etc.

From this we can assume that Proto-Indo-European and Anatolian/Hittite (and the contemporary unrecorded older forms of the other ten branches) may also have been at least in Stage Two of the Decimal System (if not in Stage One).

 

STAGE THREE:

But the common shared IE stage is Stage Three:

a) The recorded forms of all the other (i.e. other than Indo-Aryan, and of course other than Hittite and Tocharian) nine branches have decimal systems in Stage Three (with, as already pointed out, the Celtic branches converting to a vigesimal system under Basque influence. However, the Celtic Irish language also preserves the older Stage Three decimal system along with a separate new vigesimal system).

b) Even the only Indo-Aryan language outside North India (Literary Sinhalese in Sri Lanka) preserves Stage Three of the decimal system.

c) Amazingly, the Dravidian languages of South India also preserve Stage Three of the decimal system.

 

One modern example from each of the nine IE branches (plus ancient Latin, Ancient Greek, Literary Sinhalese, and Telugu as a Dravidian example):

Persian (IndoEuropean-Iranian):

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

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

tens 20-100: bīst, sī, 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, dṓdeka, treîs-kaì-déka, téssares-kaì-déka, pentekaídeka, hekkaídeka, heptakaídeka, oktokaídeka, enneakaídeka

tens 20-100: eíkosi, triákonta, tessarákonta, pentḗkonta, heksḗkonta, hebdomḗkonta, ogdoḗkonta, enenḗkonta, 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: enenḗkonta kaì ennéa, or ennéa kaì enenḗkonta

[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 1x20, 2x20].

 

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

 

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.

 

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: vienti-uno, etc. Others: tens+y+unit. Thus:

31: treinta y uno,  99: noventa y nueve

 

Irish (IndoEuropean-Celtic):

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

11-19: aon-dēag (1+10), etc.

Tens 20-100: deikh, fikhe, trīokha, daikhead, kaoga, seaska, seakhtō, okhtō, nōkha, kēad.

Other numbers: 21-29: aon is fikhe,, etc.

 

Literary Sinhalese:

1-9: eka, deka, tuna, hatara, pasa, haya, hata, aṭa, navaya, dahaya

1-9 unit stems: ek-, de-, tun-, hatara-, pas-, ha-, hat-, aṭa-, nava-

11-19: ekoḷaha, doḷaha, teḷaha, tudaha, pahaḷoha, soḷaha, hataḷoha, aṭaḷoha, ekun-vissa

tens 10-100: dahaya, vissa, tisa, hatalisa, panasa, hɛṭa, hɛttɛɛva, asūva, anūva, siyaya

Other numbers: unit-stem+tens. Thus the word-order for all the numbers is unit+tens.

[And, like Sanskrit and Latin (and the other modern Indo-Aryan languages which retain this feature), the number -9 is expressed by a minus-principle, where ekun- is used with the following tens-form (except, as in Sanskrit and most other modern Indo-Aryan languages, for 99)].

Thus: 21: ek-vissa,  89: ekun-anūva. Only 99 is nava-anūva.

 

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

 

STAGE FOUR:

Languages in the Stage Four Decimal System are found only in North India: i.e. only the modern Indo-Aryan languages of North India, among all the languages of the world, have the Stage Four Decimal System.

Why did this complicated system − where every single one of the numbers 1-100 has to be individually learnt, since the tens words and units words are irregularly fused together and there is no regular system of joining the tens words and the units words − develop in North India?

It developed because the concept of numbers developed to the extreme in ancient India. The Yajurveda, for example, in the course of a hymn (Yaj. 17.2), casually lists the following words for numbers from ten (10¹ or 10) to one trillion (10¹² or 1,000,000,000,000): 10¹: daśa, 10²: śata, 10³: sahasra, 10⁴: ayuta, 10⁵: niyuta, 10⁶: prayuta, 10⁷: arbuda, 10⁸: nyarbuda, 10⁹: samudra, 10¹⁰: madhya, 10¹¹: anta, 10¹²: parārdha.

The Lalitavistara, a Buddhist text, actually describes an even more elaborate system (where some of the above words from the Yajurveda are now replaced by other words, and all the names are given in multiples of hundred. Here in fact some of the above words, like ayuta and niyuta, are given higher values):

10³: sahasra, 10⁵: lakṣa, 10⁷: koṭi, 10⁹: ayuta, 10¹¹: niyuta, 10¹³: kaṅkara, 10¹⁵: vivara, 10¹⁷: akṣobhya, 10¹⁹: vivāha, 10²¹: utsāṅga, 10²³: bahula, 10²⁵: nāgabala, 10²⁷: tiṭilambha, 10²⁹: vyavasthānaprajñāpti, 10³¹: hetuhila, 10³³: karaphū, 10³⁵: hetvindriya, 10³⁷: samāptalambha, 10³⁹: gaṇanāgati, 10⁴¹: niravadya, 10⁴³: mudrābala, 10⁴⁵: sarvabala, 10⁴⁷: visaṁjñāgati, 10⁴⁹: sarvasaṁjña, 10⁵¹: vibhūtaṅgamā, 10⁵³. tallakṣaṇa.

The text does not stop there: it points out that this is just the first of a series of nine counting systems that can be expanded geometrically, and then goes on to mention the names of the culmination points of each of the nine systems (starting with the number 10⁵³ above, as tallakṣaṇa, dhvajāgravatī, dhvajāgraniśāmaṇī, vāhanaprajñapti, iṅgā, kuruṭu, kuruṭāvi, sarvanikṣepa and agrasārā), culminating in a large number, 10⁴²¹, or one followed by 421 zeroes! This text, and many other Sanskrit texts, go even further in indulging in flights of fantasy involving even higher numbers. The point is not whether such incredibly high numbers could possibly serve any practical purpose: obviously they could not! The point is that the ancient Indian theoretical concept of numbers had a vision which was limitless.

Modern western numbers, for example, are named in sets of three zeros: thus thousand has three zeros, the next number million has six zeros, the next number billion has nine zeros, and so on. But these ancient Indian numbers were named in sets of two zeros: sahasra has three zeros, lakṣa has five zeros, koṭi has seven zeros, and so on. Therefore the qualifying number for each of the number words could only be 1-99, since when the qualifying number became 100 it would lead to the next number word: ninety-nine lakhs, but not hundred lakhs: that would be one crore. So the qualifying numbers (1-99) were fused together to prevent confusion, resulting in the Stage Four Decimal System.

 

How does all this prove that India was the Original PIE Homeland?

The Stage One Decimal System is not recorded in any IE language (though we can idly speculate that the Proto-Indo-European or Anatolian/Hittite languages may have had this system). But all the other three stages are recorded in and around India:

1. Stage Two is recorded only in India (Sanskrit), to the north of India (Tocharian) and to the south of India (Spoken Sinhalese).

2. Stage Three is recorded in all the other nine IE branches outside India. And also in the only Indo-Aryan language known to have migrated to its historical habitat (Sri Lanka) from North India. And also in the non-IE Dravidian languages of South India. This shows that there was a period of time when all the IE as well as Dravidian languages of India had the Stage Three Decimal System, and it was during this period that the other nine IE branches as well as the Indo-Aryan Sinhalese language migrated out of North India.

3. The Stage Four Decimal System developed all over North India after the migration of the other nine IE branches and Sinhalese, and so we do not have direct records of the Stage Three IE Decimal System in India. But its earlier presence in North India is testified by its continuance in the Dravidian languages as well as in Literary Sinhalese (which was based on some unrecorded Buddhist Prakrit from North India).

 

India is the only place in the world where we have all the three recorded stages of the IE decimal system, the Second, Third and Fourth stages (further west, in West Asia, in the Steppes and in Europe, we have only the Third stage), and the evidence shows that all the migrations took place from the Homeland when the common IE decimal system was in the Third Stage. This is irrefutable evidence for the Indian Homeland.

 

APPENDIX added 18-3-2024:

The above evidence is so absolute that it cannot be answered. And the best proof of this is when someone clownishly tries to answer it by a classic piece of meaningless whataboutery. What exactly he means, and how he thinks it answers anything is a mystery. The one certain thing is that it unwittingly shows that he totally foxed by the evidence: