At a time when prophecies of doomsday are predicted to fall on December 21, speculation of apocalypse is spread and people are discussing about the end of the world. This time this centers on Mayan Calendar.
The Mayan calendar of Long Count started in 3114 BC. According to scholars, August 11 of 3114 BC was the first date of Mayan Calendar. In this Calendar, a cyclic period ends after 5,126 years. The date of the end of Mayan Calendar according to their own day count falls on Dec. 21, 2012.The Mayans call a period of 400 years as Baktun. We are at the end of 13th Baktun now. Why is there an end at 13th Baktun?
Comparing the other calendars of Mayan origin, it is seen that their classification of time or period is based on human anatomy, life cycle, number system and celestial observations or astronomy.
The Mayan Numerical system is not a 10-based decimal system but a 20-based vigesimal system. That is why Baktun year period is 20 years x20=400 years. However their solar year is based on days. 18 days x 20 = 360 days which is very close to our present 365 days count for a year.
Another Mayan Calendar called tzolk’in is based on a period of 260 days denoting the average period of pregnancy. This was used to count days and not the years. Here they followed 20 names for days whereas the successive number cycle ends at 13 and starts again at 1 after 13. These thirteen numbers of the trecena cycle produce 260 unique days. This is how we arrive at 20 days X 13 =260 days. We should note that there are 260 days between zenithal passages in astronomical observation.
Can we imagine something will happen because we are caught in the period of multiplication of their Long period of 400 years and short period of 13 days? I mean 400 x 13 = 5200. We have to also consider that Sivapuranam of Thiruvasagam states that the evolution is classified as 13 different groups in which the present human species occupies 8th position. Further according to the current western beliefs, 13 is not a good number.
Mayans used another ‘ Haab’ solar calendar. This is (18 months x 20days) + 5 days. The twenty days have names. But the isolated 5 days would have no names and are evil days like Indian Raagu kaalam etc. They were so inauspicious that they dared not even name it?
One more Calendar called Round is based on 18980 days or 52 years, the average life expectancy of Mayan population. Moreover this is also mathematically 260 x 365= 18960.
It appears some of the smaller discrepancies or inaccuracies in Mayan calendar are due to mismatches between 20- based number system and astronomy. What is the significance of 20 as followed by Mayans in counting or numerical system?
It is very simple. Early man used fingers to count. The total number of fingers in the hands and legs is 20. Therefore a numerical system with base 20 evolved from human body. Romans initially had written only up to 20. While some group of people adopted 20, Tamils counted only fingers in the hands and thus they used ten based numerical system right from their classical period dating back to pre-Christian era. The English word ‘digit’ is the anatomical term for fingers and toes.
There are many more systems like 2-based tribal number system, 60-based Mesopotamian Sexagesimal system. Mesopotamians obtained this system from Sumerians (3000 BCE).The Europeans initially had a 60-based system. 60 is also a prominent number since our time in seconds and minutes are in 60s. The Tamil calendar is having a cycle of 60 years with sixty names for the years. The time taken by the biggest planet to complete its one orbit around the sun is also about 60 years.
But when population migrated and got mixed up, they finally arrived at a common numerical system of scripting the numbers due to scientific developments. An analysis of number names can indicate which languages used 20-based number systems as in Mayan calendar in the formative stages of the languages to arrive at 10-based numerical systems later.
Let us see the number names in English and the classical languages – Sanskrit and Tamil:
1. One – ekam – onru
2. Two – dve – irandu
3. Three – treeni – moonru
4. Four – chatvaari – naangu
5. Five – pancha – ainthu
6. Six – shat – aaru
7. Seven – sapta – ezhu
8. Eight – ashta – ettu
9. Nine – nava – onbathu
10. Ten – dasha- paththu
11. Elelven – ekaa dasha –pathin onru
12. Twelve – dvaa dasha – pani randu
13. Thirteen – trayo dasha – pathin moonru
14. Fourteen – chatur dasha- pathin naangu
15. Fifteen- pancha dasha- pathin ainthu
16. Sixteen – sho dash- pathin aaru
17. Seventeen – saptadasha- pathin ezhu
18. Eighteen – ashtaadasha- pathin ettu
19. Nineteen- navaviṁśati or ekonatriṁśat- pathth onbathu
20. Twenty – vimsati – iru- pathu
21. Twenty one – eka vimshatihi- Irupathth onru
29. Twenty nine – navadaśan or ekonaviṁśati- Twenty nine
30.Thirty – trimsati – muppathu
40. Fourty – catvarimsati- naar pathu
50. Fifty – pancasati – aim pathu
90. Ninety- navati satam
99. Nintynine -navanavati or ekonaśata
100. Hundred – sata – nooru
900.Nine Hundred- navaśata – thollaayiram
1000.Thousand –sahasra – aayiram
From the above we can see a change in the method of naming at 12 &20 in English and at 10 in Sanskrit and Tamil. In Hindi, the daughter of Sanskrit, numbers up to 20 have unique number names.
Although Sanskrit and Tamil have a common shift at 10, the logical way the people belonging to these language groups calculated the numbers are just opposite to each other.
Sanskrit speakers calculated 11 as 1+10. The Tamil speakers calculated 11 as 10+1. In this kind of calculation, English follows Sanskrit from 12 to 19 and follows Tamil from 20 onwards.
The French have unique number names up to 16 and then go for 10+7=17 style. Their number names for 20 is vingt. They have separate number names for 10,20,30,40,50 and 60. But strangely for seventy, they go to a style 60+10 in naming. For them 80 is quatre vinget and 81 is quatre vinget un ( 4 x 20 ) +1. And 90 is quatre vinget dix ( (4 x 20) + 10. This is the confirmation of 20 as base for the entire Europe initially.
If we consider the fact the Romans originally had number notations only up to 20 we can realize that whatever the later evolution may be, Europeans had 20-based counting in their early mathematics.
When men had to count beyond 20, they had to use pebbles. What is the origin of English word Calculation? It is derived from a Latin word ‘calculus’ meaning a small stone used for counting. This word closely resembles the Tamil word Koozhankal which means a well-finished round stone, a pebble. The root word kal (stone) in Tamil has also got its significance. Early men after scribbling graffiti marks started writing on rocks. Therefore in the early stages of learning the scripts were written on rocks. From this only, the word kalvi in Tamil meaning Education evolved. In Greek language, the word mathematica means things that are learned. For them learning is nothing but Mathematics. In Tamil too, the 2000-year old Thirukkural in one of its couplets says that numbers and other scripts for sounds are like two eyes for the living beings. In learning, Mathematics was given first priority compared to literature.
Again counting with pebbles for numbers above 20 was a habit initiated in India which evolved in to abacus later.
Those who read the history of decimal system accept that the present universal decimal system originated from India, spread to Arabia and then to Europe. The spread was possible due to commerce and trade between these regions.
Tamil scholar Mu. Varadarajan ( 1912- 1974) popularly known as Mu.Va, claimed that the present 10-based numerical system followed all over the world evolved from Tami. He showed evidences from the stone inscriptions on the evolution of signs for the numbers.
Like in Greek, Roman, Tamils too adopted the alphabets used in their own writing system to indicate the numerical symbols. It is explained by Tamil Scholars that the present forms of 1,2,3,4,5,6,7,8,9 are hidden in the Tamil number notations and has also graphically explained the same. (see the pictures on evolution of Tamil numerals).
The earliest Tamil literature for grammar Tholkappiam dated to many centuries before Christian era consists of three parts each having 9 chapters. In this work, only 10-based numbers are used. The Classical Tamil masterpiece in Literature, Thirukkural, a work translated in most number of languages next to Bible also contains 3 parts, 133 chapters with 10 couplets in each chapter. More over, all the other anthologies of Tamil classical poetry like aha Naanooru ( Internal 400), Puranaanooru (External 400), Pathinenekeezhk kanaukku ( poetry with less than 18 lines) are named based on 10 numerical system only.
Tamil number names for 10s follow a style of naming 2×10= 20. 3x 10 =30 etc up to eighty. For ninety the number name thonnooru (meaning 10 short of hundred) in Tamil indicates arrival of hundred (nooru). Similarly 900 is thollaayiram meaning 1000-100 = 900. Even the number 9 is named as onpathu i.e 10-1=9. ( meaning, one is deducted from 10). In some form of Tamil poetry, the last but one line is reduced by one word when compared to the words in the last line. This logic about 9 is found in Sanskrit also. This may be due to the special nature of number nine in multiplication.
The Sanskrit number names for 10s are compound words consisting the number name for hundred sata. This has to be explained by Sanskrit experts. Sata is 100 in Sanskrit. All the number names for 10s from 20 onwards contain the word ‘sati’ a derivative from sata.
The significance of Tamil decimal numerical system can be felt when compared to other systems which existed in pre- Christian era. By that time in Tamil, numerical names had been formed with decimal order and positional value.
Since Sanskrit belongs to Indo-European language group, it should have initially followed a 20-based number system as followed in early European languages and later adopted the decimal system from the land of their settlement, i.e India from Tamil. The present number signs and the decimal system in Sanskrit evolved later than such evolution in Tamil.
The history of mathematics written by scholars in the last century indicates prejudice against Tamil and Pride for Sanskrit since it was the language of the elite.
The Periods of eminent Sanskrit Mathematicians are
Arya Bhatta – 499 AD
Prama Guptha – 7th Century AD
Mahavir – 9th century AD
Bhaskara – 12th century AD
The 11th poem of Paripaadal one of the Sangam Literature of Tamil classical period consists of an astronomical description of celestial positions of planets and happenings of eclipses which is confirmed to have occurred in 161 BC. In this work, many poems mention numerals with positional values and decimal orders including infinity.
The arbitrary claims made in the last century that the decimal system evolved from Sanskrit stands exposed now and it is time to accept that Decimal system is the contribution of Tamil to the world. This is not to belittle the contribution of those great Sanskrit mathematicians. This is only an exploration of truth about the origin of 10-based and 20-based number system.
As a conclusion of this article, we can see that the important languages including English, French, Sanskrit, Hindi and other Indo-European languages had followed a base of 20 initially (like Mayans) in their formative or classical periods and have later adopted the decimal system. Therefore it is time to change the misnomers like ‘Arabic Numerals”, ‘ Indo Arabic Numerals” or ‘ Hindu Arabic Numerals”. The real name is “ Tamil numerals”.