Amazing TAMIL Mathematics

(This article is available in Tamil as well)

By London Swaminathan

Srinivasa Ramanujan (1887-1920) was one of the greatest mathematicians of India. He was born in a poor Tamil Brahmin family. Tamils are proud of his achievements. Viswanathan Anand is a World Chess champion. He is from Tamil Nadu and Tamils are proud of his success year after year. Tamil Nadu supplies a large number of computer software personnel in the world. All these prove that Tamils are good at anything where maths is used. But the history of Tamil mathematics began at least two thousand years ago.

 

Kapilan, the Brahmin poet who contributed highest number of poems in the Sangam literature was good at maths. He made a passing remark about numbers. He says that Pari’s Parambu hills had 300 towns (Pura Nanuru verse 110). This is the first statistics we get about Sangam period towns. If Pari’s Parambu Hills (a small area) had 300 towns, how many villages and towns Tamil Nadu would have had 2000 years ago! No wonder India, at present, has over 600,000 villages and 4000 towns.

In another poem, Kapilan gives a talk in bullet points like company executives. “Hey, Three Tamil kings, Listen to me. If you want Pari’s Parambu hills, don’t attack him. Do this. He gives three suggestions. In another verse (Puram 201) he talks about 49 generations of Irungovel, another Tamil chieftain like Pari. Kapilan was the poet who gave 99 plants names at one go. He beat all the ancient botanist. Just one poet gives us so many numbers and so much information.

 

The world came to know about nuclear power and atom bomb only around1945. But the concept of atom bomb was sung by Idaikkadar 1500 years ago. When she wanted to praise Tirukkural, the Veda of the Tamils, what she said was this:

It is like cramping seven seas in to a single mustard seed. The meaning of Kural is vast. But poet Tiruvalluvar put seven seas in to one mustard seed was the message given by Idaikkadar. Why should he sing about putting seven seas into one tiny seed? Will the Tamil world understand such a simile without some knowledge of huge power in tiny things?

 

The story did not stop there. Actually Tamils knew more than what Idaikkadar said. Because the earlier Upanishads praise god as smaller than the smallest particle, larger than the largest (Anooar aneeyaam, mahator maheeyaam). They knew that if one tiny seed is split into,  energy equal to seven seas will be generated.

Some readers may think that I am interpreting it in un scientific way. But if you read the following , all their doubts will be cleared. An old Tamil poem says that one mustard seed has 2,62,144 anu (anu=atom). Though their atom is very different from what we read in Today’s Physics book about Atoms, my point is that they knew smallest measurements which others did not at that time in the history

The verse goes as follows:

 

8 Anus= one Ther Tugal ( Chariot dust particle)

8 Ther Tugal= one cotton thread

8 cotton thread = one hair

8 hair = one sand particle

8 sand particles= one mustard seed

8 mustard seeds= one paddy seed

8 paddies = one finger length

12 fingers= I saan

2 saan= 1 muzam

4 muzam= 1 kol

500 kol= 1 kuuppidu

4 kuuppidu= 1 Katham

(Source: Senthamiz Volume 12, page 127)

 

When the first nuclear device was exploded the scientist behind it Oppenheimer quoted a Bhagavd Gita sloka about the Viswarupa darsanam of Lord Krishna (Please read my post A to Z of Bhagavad Gita to get full details.)

Tirumular’s brilliant calculation

Tirumular was one of the 18 Tamil Siddhars ( saints who have attained magical powers). He sings about splitting a cow’s hair in to 10000 million hairs. He takes the readers step by step. He asks one to take one hair from the tail of a cow. Then ask us to split it in to 100. Then in to 1000……….. on and on 100X1000X100 000= 100 000 00 000.(Tirumanthiram 1974).

One may wonder whether there was any practical use for such minute numbers. But these saints have seen such things through their third eye or intuition. When the western world was still struggling with their complicated Roman numerals Indians were far advanced in mathematics. Look at the table below that existed 2500 years ago.

 

World Tamil Conference Souvenir (1968) gives another interesting measurement:

How many grains are there in one measure?

One measure contains (measure is bigger than a litre)

1800 beans or

12,800 black peppers or

14,400 paddies or

14,800 green grams or

38,000 rice grains or

1,15,200 sesame  seeds (gingili seeds).

Tamils must be a patient race to count grains this way!

 

Tamils very often use a word called “IMMI” in their day today conversation. Like English phrase not even one iota, they used to say not even an Immi. This is an interesting word.

 

Sculptor V Ganapathy explains Immi quoting a book called Manasaram. It is as follows:

8 anu=1 ther thugal (Chariot dust particle)

8 ther thugal= 1 immi

8 immi= 1 sesame seed (Ellu)

8 Ellu= 1 paddy

8 paddies= 1 finger length

Mr V Ganapathy also added the book Manasaram says one inch= 190650 anus.

He says that different books give slightly different measurements for the same word in the Silpa Shastra( Science of Sculpting)

Another table giving the lowest Tamil number Munthiri:

I/8 is Araikaal

1/16 = maakaani

1/32= arai veesam

1/64=kaal veesam

1/80=kaani

1/320=munthiri

 

The other numbers very often attributed to Tamil are actually Sanskrit words. Moreover they have no secondary evidence to support those big numbers. They were not used by the Sangam poets. At least immi is used by Tamils till today like Iota ( Iota is a Greek letter).

Some Tamil blogs give incredible lowest and highest numbers without any proof. At a glance anyone can find Sanskrit words in the list! They are not Tamil words.

( Sanskrit has words for biggest numbers. But I couldn’t find words for smallest number like Tamil).

 

Numbers in Sanskrit:

From Wikipedia: A few large numbers used in India by about 5th century BCE (See Georges Ifrah: A Universal History of Numbers, pp 422–423):

  • lakṣá (लक्ष) —105
  • kōṭi (कोटि) —107
  • ayuta (अयुता) —109
  • niyuta (नियुता) —1013
  • pakoti (पकोटि) —1014
  • vivara (विवारा) —1015
  • kshobhya (क्षोभ्या) —1017
  • vivaha (विवाहा) —1019
  • kotippakoti (कोटिपकोटी) —1021
  • bahula (बहूला) —1023
  • nagabala (नागाबाला) —1025
  • nahuta (नाहूटा) —1028
  • titlambha (तीतलम्भा) —1029
  • vyavasthanapajnapati (व्यवस्थानापज्नापति) —1031
  • hetuhila (हेतुहीला) —1033
  • ninnahuta (निन्नाहुता) —1035
  • hetvindriya (हेत्विन्द्रिया) —1037
  • samaptalambha (समाप्तलम्भा) —1039
  • gananagati (गनानागती) —1041
  • akkhobini (अक्खोबिनि) —1042
  • niravadya (निरावाद्य) —1043
  • mudrabala (मुद्राबाला) —1045
  • sarvabala (सर्वबाला) —1047
  • bindu (बिंदु or बिन्दु) —1049
  • sarvajna (सर्वज्ञ) —1051
  • vibhutangama (विभुतन्गमा) —1053
  • abbuda (अब्बुदा) —1056
  • nirabbuda (निर्बुद्धा) —1063
  • ahaha (अहाहा) —1070
  • ababa (अबाबा). —1077
  • atata (अटाटा) —1084
  • soganghika (सोगान्घीका) —1091
  • uppala (उप्पाला) —1098
  • kumuda (कुमुदा) —10105
  • pundarika (पुन्डरीका) —10112
  • paduma (पद्मा) —10119
  • kathana (कथाना) —10126
  • mahakathana (महाकथाना) —10133
  • asaṃkhyeya (असंख्येय) —10140
  • dhvajagranishamani (ध्वजाग्रनिशमनी) —10421
  • bodhisattva (बोधिसत्व or बोधिसत्त) —1037218383881977644441306597687849648128
  • lalitavistarautra (ललितातुलनातारासूत्र) —10200infinities
  • matsya (मत्स्य) —10600infinities
  • kurma (कुरमा) —102000infinities
  • varaha (वरहा) —103600infinities
  • narasimha (नरसिम्हा) —104800infinities
  • vamana (वामन) —105800infinities
  • parashurama (परशुराम) —106000infinities
  • rama (राम) —106800infinities
  • khrishnaraja (कृष्णराज) —10infinities
  • kaiki (काईकी or काइकी) —108000infinities
  • balarama (बलराम) —109800infinities
  • dasavatara (दशावतारा) —1010000infinities
  • bhagavatapurana (भागवतपुराण) —1018000infinities
  • avatamsakasutra (अवताम्सकासुत्रा) —1030000infinities
  • mahadeva (महादेव) —1050000infinities
  • prajapati (प्रजापति) —1060000infinities
  • jyotiba (ज्योतिबा) —1080000infinities

Tamil Numerals

1 =௧ ,2 =௨ ,3=௩ ,4 =௪ ,5=௫ ,6=௬ ,7 =௭ ,8 =௮ ,9=௯ ,10=௰ ,100=௱ ,1000=௲

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3 Comments

  1. 1 – ஒன்று – onRu
    3/4 = 0.75 – முக்கால் – mukkaal
    1/2= 0.5 – அரை – arai
    1/4 = 0.25 – கால் – kaal
    1/5 = 0.2 – நாலுமா – naalumaa
    3/16 = 0.1875 – மும்மாகாணி – mummaakaani
    3/20 = 0.15 – மும்மா – mummaa
    1/8 = 0.125 – அரைக்கால் – araikkaal
    1/10 = 0.1 – இருமா – irumaa
    1/16 = 0.0625 – மாகாணி (வீசம்) – maakaaNi (veesam)
    1/20 = 0.05 – ஒருமா – orumaa
    3/64 = 0.046875 – முக்கால்வீசம் – mukkaal veesam
    3/80 = 0.0375 – முக்காணி – mukkaaNi
    1/32 = 0.03125 – அரைவீசம் – araiveesam
    1/40 = 0.025 – அரைமா – araimaa
    1/64 = 0.015625 – கால் வீசம் – kaal veesam
    1/80 = 0.0125 – காணி – kaaNi
    3/320 = 0.009375 – அரைக்காணி முந்திரி – araikkaaNi munthiri
    1/160 = 0.00625 – அரைக்காணி – araikkaaNi
    1/320 = 0.003125 – முந்திரி – munthiri
    3/1280 = 0.00234375 – கீழ் முக்கால் – keel mukkal
    1/640 = 0.0015625 – கீழரை – keelArai
    1/1280 = 7.8125e-04 – கீழ் கால் – keel kaal
    1/1600 = 0.000625 – கீழ் நாலுமா – keel nalumaa
    3/5120 ≈ 5.85938e-04 – கீழ் மூன்று வீசம் – keel moondru veesam
    3/6400 = 4.6875e-04 – கீழ் மும்மா – keel mummaa
    1/2500 = 0.0004 – கீழ் அரைக்கால் – keel araikkaal
    1/3200 = 3.12500e-04 – கீழ் இருமா – keel irumaa
    1/5120 ≈ 1.95313e-04 – கீழ் வீசம் – keel veesam
    1/6400 = 1.56250e-04 – கீழொருமா – keelorumaa
    1/102400 ≈ 9.76563e-06 – கீழ்முந்திரி – keezh munthiri
    1/2150400 ≈ 4.65030e-07 – இம்மி – immi
    1/23654400 ≈ 4.22754e-08 – மும்மி – mummi
    1/165580800 ≈ 6.03935e-09 – அணு – aNu
    1/1490227200 ≈ 6.71039e-10 – குணம் – kuNam
    1/7451136000 ≈ 1.34208e-10 – பந்தம் – pantham
    1/44706816000 ≈ 2.23680e-11 – பாகம் – paagam
    1/312947712000 ≈ 3.19542e-12 – விந்தம் – vintham
    1/5320111104000 ≈ 1.87966e-13 – நாகவிந்தம் – naagavintham
    1/74481555456000 ≈ 1.34261e-14 – சிந்தை – sinthai
    1/1489631109120000 ≈ 6.71307e-16 – கதிர்முனை – kathirmunai
    1/59585244364800000 ≈ 1.67827e-17 – குரல்வளைப்படி – kuralvaLaippidi
    1/3575114661888000000 ≈ 2.79711e-19 -வெள்ளம் – veLLam
    1/357511466188800000000 ≈ 2.79711e-21 – நுண்மணல் – nuNNmaNal
    1/2323824530227200000000 ≈ 4.30325e-22 – தேர்த்துகள் – thaertthugal

    How is it

  2. Nagarajan

     /  August 26, 2016

    Nice material to contemplate and reasearch. I understand there is an ancient Tamil book known as ‘Kanakkadhikaram’ (கணக்கதிகாரம்) possibly available in Tanjavur Sraswati Mahal library, which explains many of the ancient Tamil History of mathematics. I invite to read my blog on this subject.
    https://lvnaga.wordpress.com/2012/10/24/evolution-of-indoarabic-numerals/

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