The question of Tamil numeral, number, number system and mathematics (1)

The question of Tamil numeral, number, number system and mathematics (1)

The oldest stone inscription featuring a numeral is the Tamil-Brahmi cave inscription from Tondur, near Gingee, in Villupuram district[1]: When I was preparing for a write-up on the Indian mathematician Ramanujan[2], I came across the news-item, “Ancient numbers in the land of Ramanujan” in “The Hindu,” contributed by Iravatham Mahadevan and M.V.Bhaskar. Though, it appeared in December 2011, as it has bearing on the Tamil numerals, it is taken up for discussion. It started with an interesting question, “How were numerals written in ancient times in the Tamil country, the land of Srinivasa Ramanujan, ‘The Man Who Knew Infinity’?”. Then, it went on – “Literary sources in Tamil mention numbers only in words. However, we do have ancient literary references specifically mentioning eN (‘numeral’) as distinguished from ezhuttu (‘letter of the alphabet,’ for example, Tolkappiyam 655.4, Tirukkural 392). But as palm leaf manuscripts decay with time and hardly last for more than 200 years, we have to turn to durable stone or pottery inscriptions to know what the ancient Tamil numerals looked like. We illustrate two of them here, one from each class (Figs. 1 & 2). The oldest stone inscription featuring a numeral is the Tamil-Brahmi cave inscription from Tondur, near Gingee, in Villupuram district, assigned to about the 3rd century C.E. (Fig. 1)[3]. The numeral 3 engraved at the end of a short two-line inscription in the cave is represented by three horizontal parallel lines[4]. The inscription records that the village of Agalur gifted three stone beds in the cave chiselled by Mosi. The gift was made to the Jaina monks resident in the cave. The village still exists with the same name Agalur, near Tondur, both of which still have sizeable Jaina populations. The numeral 3 has the same form as in contemporary Prakrit inscriptions in the Brahmi script in North India”. Thus, the learned writers have not informed the fact that neither the language was Tamil nor the script Tamil-Brahmi.

A number on the Pottery inscription: Then, they had taken the Alagankulam broken pottery bit, “A well-preserved pottery inscription from Alagankulam near Rameswaram has only the numeral incised in fairly large size (Fig. 2). The inscription is dated to the 1st or 2nd century C.E. The number is read 408, from right to left, following the ancient convention of reading the digits from the right (ankaanaam vaamato gatih). The first digit at right looking like the cross is the symbol for 4. It is followed by the symbol for 100 (resembling the Brahmi letter sa) and the last symbol at left is 8, incised in reversed direction. As there is no accompanying text, we do not know the significance of the number. The find is still interesting for the absence of the place-value system. The convention of using symbols for 10, 100, and 1000 in expressing the higher numerals was current in Tamil Nadu until the advent of printing and the adoption of the international form of Indian numerals with place-value system. The pottery inscription is also good evidence for widespread literacy, including numeracy, in the ancient Tamil country”.

What the news-item reveal: Iravatham Mahadevan and  M. V. Bhaskar have very carefully worded, but, they could not be free from their apologetic approach to interpret that the numerals found were Tamil.

1. Literary sources in Tamil mention numbers only in words, not in numerals.
2. They accept that – The numeral 3 has the same form as in contemporary Prakrit inscriptions in the Brahmi script in North India.
3. The oldest stone inscription featuring a numeral is the Tamil-Brahmi cave inscription from Tondur – the script is neither Tamil nor the number is Tamil.
4. Had the Tamil numeral was written, it should have been “௩ (3)” and not “≡”.
5. The Jains used Sanskrit / Prakrut and the Brahmi script.
6. In the same way, coming to the pottery script, the claim that, “The number is read 408, from right to left, following the ancient convention of reading the digits from the right (ankaanaam vaamato gatih)” is incorrect, because, Tamil is written from left to right.
7. अङ्कानां वामतो गतिः Nowhere such rule has been prescribed in the Tamil literature. And it is a wonder that, that they should take the help of “Aryan dictum” to prove the number was Tamil!
8. Moreover, those three numerals are not Tamil, but, Sanskrit and it has to be mentioned as “Indian.”
9. Had the Jains of the ancient Tamizhagam been Tamils or Tamil speaking and knowing, they would have inscribed “௪௦௮” and not in Brahmi – India numerals.
10. They accept that – The find is still interesting for the absence of the place-value system[5]. The convention of using symbols for 10, 100, and 1000 in expressing the higher numerals was current in Tamil Nadu until the advent of printing and the adoption of the international form of Indian numerals with the place-value system.
11. The Indian number system is called a place value system because the value of a digit depends on its position, or place, in a number. The number 408 has a different value than the number 804. Even though they use the same digits, their value is different because of the different placement of the 4 and the 0 and the 8.
12. And the Tamils never knew 0 and used till modern times.

With all these facts, they had cleverly manipulated and it was published in “The Hindu.” And the pro-Tamil enthusiastic bloggers and social media activists have been so happy to spread it with the claims that Tamil only invented decimal number system including zero.

The position of Tamil numerals: Now with the Keeladai dating, the antiquity of Tamil literature goes back to c.580 BCE.  Coming to the Tamil numerals, the following facts are noted and listed:

1. The “Sangam literature,” Ettuttogai and Pattuppattu do not mention any Tamil numeral[6].
2. The post-Tamil Sangam literature Padinenkizhkanakku and Imperum Kappiyangal do not record numerals in the Tamil language.
3. The fragmentary inscriptions [mentioned as Tamil-Brahmi] do not mention any numeral in Tamil till the 9^th-10^th centuries CE.
4. In Uttiramerur inscription of Partiva Varman dated to 10^th cent CE, a lengthy number is mentioned.
5. Then, in the inscription dated to 1204 CE of Kulutunga Cholan, some fractions are seen to be mentioned denoting to ¼, ½ and ⅛.
6. The 13^thCE poetry notes eight and quarter in words as ௮ = 8 and வ = ¼, i.e, the expressions, “Avalalkshnam” and “ettekal” are equated to bring out the meaning[7].
7. Therefore, from the period of “Sangam” to 9^th – 10^th centuries, no numeral in Tamil was used to represent numbers[8].
8. The fact is that the “Tamils” never had any numerals at all to be identified as numbers!
9. The notation of writing Tamil numerals has been as follows: ௦ (0), ௧ (1), ௨ (2), ௩ (3), ௪ (4), ௫ (5), ௬ (6), ௭ (7), ௮ (8), ௯ (9), ௰ (10)
10. They were widely used in the inscriptions from 10t-11^th centuries in the inscriptions.
11. Only “Kanakkathhikaram,” a Tamil mathematical work mentions all together[9]. Its author has been one Kari, Kari Nayanar and the work is dated to 15^thCE, considering the internal evidences[10]. He acknowledges that he composed the work only translating material from the Sanskrit works available during his time[11]. In other words, it can be said that for the science and technological works, Sanskrit works were used and hence, the common Indian numbers were followed for practical purposes.

Ironically, with the fragmentary inscriptions, the “Tamil researchers” have so far tried to prove Indian numerals as their numerals, as if the “Tamils” discovered separately.

Interestingly, the number 0 was never used as a numeral, but, in word. This usage came during the medieval period.

When the schools of mathematics and astronomy were existing in Cheranadu, why not in Tamizhagam?: R Champakalakshmi[12] virtually surveyed the secondary sources, but noted, “The educational system of this period was not organised institutionally, but was taught from kakkayar, āśiriyar, āśār, uvāttiyar) toö teacher (ka student in private collecting a group of students i.e. palli The main subjects taught and passed on by memory and also written down on Palm Leaf manuscripts were Grammar, Poetics and Mathematics and its ancillary Astronomy.” P. P. Divakaran, makes some passing references that Kerala was sanskritised so that the Mathematics and astronomy flourished there as Nila / Kerala school[13]. Al most, all researchers on the history of science and technology or Mathematics and Astronomy of South India or Sangam period have been perplexed about the absence of any “school” existing in Tamizhagam, when, the Kerala school was functioning well attracting many professors and mathematicians. Thus, a question arises as to, “When the schools of mathematics and astronomy were existing in Cheranadu, why not in Tamizhagam?” Who prevented or opposed such a system in the Tamizagam or the existing schools were shifted there.

© K. V. Ramakrishna Rao

14-05-2020

[1] The Hindu, Ancient numbers in the land of Ramanujan, Iravatham Mahadevan, M. V. Bhaskar, CHENNAI:, DECEMBER 29, 2011 01:28 IST’UPDATED: DECEMBER 29, 2011 01:30 IST

[2] K.V. Ramakrishna Rao, Srinivasa Ramanujan (1887-1920): The Mathematical genius of Erode, who got PhD from Cambridge, but, ignored by Tamilnadu!, April.26, 2020. https://kvramakrishnarao.wordpress.com/2020/04/26/srinivasa-ramanujan-1887-1920-the-mathematical-genius-of-erode-who-got-phd-from-cambridge-but-ignored-by-tamilnadu/

[3] Tamil-Brahmi cave inscription from Tondur (3rd century C.E.). Photo Courtesy: Central Institute of Classical Tamil, Chennai | Photo Credit: HANDOUT_E_MAIL.

[4] https://www.thehindu.com/features/friday-review/history-and-culture/ancient-numbers-in-the-land-of-ramanujan/article2755518.ece

[5] A place value system is one in which the position of a digit in a number determines its value. In the standard system, called base ten, each place represents ten times the value of the place to its right.

[6] Sathyabhama Kameswaran, Kanakkathikaram (Part – II), Thanjavur Maharaja Sarboji Saraswati Mahal Library, Publication No.388, Thanjavur, 1998.

[7]  The expressions ‘எட்டேகால் லட்சணமே’  and ‘அவலட்சணமே’ were used by the poets Ottakkuutthar, Pugazhendi and Avvaiyar of 13^th cent.CE.

[8] Tamil lexicons, Nikandus and other works too have been silent about the origin, though, tried to give the list of numbers ets., as usual.

[9] Sathyabhama Kameswaran, Kanakkathikaram (A compiled work), Thanjavur Maharaja Sarboji Saraswati Mahal Library, Publication No.504, Thanjavur, 2007.

[10] M. Arunachalam

[11] “As the firefly before the Sun, I decided to present the mathematical work of the Aryans that is in Sanskrit, in Tamil. Therefore, the experts need not criticize me,” he noted in the introduction. Kanakkathikaam 1, Payiram, poem.16. He repeated the same in the next poem also, no.17.

Kari Nayanar, Kanakkathikaram, Tirunelveli Saiva Siddhanta Nurpathippuk Kazhagam, Chennai, 1958.

[12] R Champakalakshmi, In Search of the Beginnings and Growth of Knowledge Production in Tamil, Indian Journal of History of Science, 51.1 (2016) 118-124; felying upon Subrahmanian, 1966, pp.326–29.

[13] P. P. Divakaran, The Mathematics of India: Concepts, Methods, Connections, Springer and Hindudthan Book Agency, New Delhi, 2018.