jyotisha-shala

The main purpose of creating this blog is to provide material and guidance to the students of Vedanga Jyotisha who are appearing for BA as well as MA level examinations of Kavi Kulaguru Kalidas Sanskrit University. I hope this effort will be welcomed by all the students of the Vedanga Jyotish and this effort will be useful to them. Dewavrat Buit dewavrat2000@yahoo.com

Friday, July 07, 2006

BA PART III : PAPER 5.16






Introduction to Varnamala

The 16 svaras provide the basis for béjäkñaras or seed syllables which are prefixed before mantras. They reside in the vi­çuddha cakra in the form of a 16 petalled lotus. By meditating on each petal one is blessed with the powers of speech. Each vowel is like a béja or seed which when attached to a consonant, produces an akñara or syllable. The consonant is the body; so when a seed attaches itself to a body, an akñara comes into existence. For example, consonants ‘r’ and ‘l’ when attached to the vowel ‘a’ produces the béjas ra and la. Ra or ram béja is ruled by Agni tatva and portrays repulsion. La or lam béja is ruled by jala tatva and signifies attraction. Ram as Agni moves the energy of the worshipper upwards, towards God. It is the fire that burns sin and this çakti or energy that must evolve within is best described by Käli, as she is the only one who can devour the sins burning within the deepest recesses of one’s being. Hence she is worshipped with the krém béja, ra or Agni added to the consonant ‘k’ and the vowel ‘i’. La or lam as jala tatva brings God down to the worshipper and is responsible for blossoming divine love or bhakti within the heart, and hence Kåñëa, the Eternal Lover, is worshipped with the klém béja. Here la is added to the same consonant ‘k’, and this enables the devotee to move towards the path of divine love or bhakti märga. Similarly there are multifarious béjas, both singular and compound, which are used in Mantra Çästra especially in the Tantra paramparäs.

The above table shows the sanskrit alphabets arranged in the form of katapayadi vargas.Let us see the basics of the system:


Ancient Sanskrit Numerical Notations

Notation is representation of numbers by symbols. Ancient India had developed different systems of numerical notations. Two systems viz. 1. bhütasaìkhyä system and 2. kaöapayädi system are the most popular among these. Let us try to have a glimpse of the bhütasaìkhyä system .

Bhütasaìkhyä system
Well known and universally accepted objects were associated with numbers and were used in this system.

For example:
Objects Meaning Represents
Äkäça or çünya space or nothing 0
Çaçi or Bhümi moon or earth 1
Locanaà eyes 2
Guna (satva rajas tamas) qualities 3
Veda or Abdhi vedas or Sea 4
Mahäbhütäù great elements 5
Rasa or åtu tastes or seasons 6
Svara åñisvaras or Rishis 7
Vasu or dikpäläname set of gods or quarters 8
Graha or Ratna grahas or gems 9
Avatäraù or Aìgulayaùincarnations or fingers 10

The logic of assigning a specific number to an object is evident. Çünya which is nothing is given the value of ‘0’. The moon is given a value of one because there is only one moon. Locana or eyes are given the value ‘2’ because they are two in number. In the same way for the other objects also.

The Numbers were always read from right to left and not left to right as expressed by this dictum : ankänäà vämato gatiù.



Now let us try to decipher a few of the words .
Examples:
1. - 302
locana- äkäça- gunam
eyes-space-qualities
2 0 3
2. - 265
mahäbhüta-rasa-locanam
great elements-taste-eyes
5 6 2
3. - 2003
guëa- äkäça-gagana-netram
qualities-space-space-eyes
3 0 0 2
4. - 18
vasu-bhümi
name of a set of gods -earth
8 1
5. - 25
bhüta-netram
elements-eyes
5 2


After this let us study the katapayadi vargas


Ancient Sanskrit Numerical Notations
Earlier we learnt about the unique system of representing numerals and numbers through words and phrases which indicate well known objects. That is known as Bhütasamkhya system of representation. This time let us know about the kaöapayädi system. This system is more popular in the south particularly in Kerala. ka-öa-pa-ya-ädi means starting with ka, öa, pa and ya. The counting of numeral starts With ka standing for 1, kha for 2, ga for 3, gha for 4, ìa for 5, ca for 6, cha for 7, ja for 8, jha for 9. Again öa stands for 1 öha for 2 and so on up to dha standing for 9. pa to ma stand for 1 to 5 and ya and øa stand for 1 to 9. ïa and na represent zero.

We have the following verse in the kaöapayädi system enunciating the above:

naïävacaçca çünyäni saìkhya kaöapayädayaù .miçrocä'ntyahalssaìkhyä na ca cintyä halassvaräù . (sadratnamälä

"Zero is denoted by na and ïa, 1 is represented by ka öa pa ya and other successive digits by successive consonants respectively. If a mixed consonant is of two consonants the latter one is to be considered and if a mixed word is of a consonant and a vowel then the vowel is to be ignored.


We have thus the fixed value of each of the letters of the Sanskrit alphabet (See the table on the top)





Thus sill literally water stands for 337. To explain salila sa+ li +la
7 3 3

Note that vowels (A to AaE) have no numerical values. Also the placement of figures is from right to left as found in the Bhütasamkhya system.
Similarly jy (literally victory and the original name of Mahabharata) stands for 18.

Let us see a few more words.

1. The word neta stand for 60
0 6
2. The word geeta stand for 63
3 6
3. The word mahabharata stand for 62485
5 8 4 2 6

It is noteworthy that the last word AayuraraeGysaeOy< color="#993399" size="4">Katapayaadi or Paralpperu

(The Letter-Number System)"Paralpperu" is an ancient method for memorising oft-used numbers, by converting them into words or word-clusters. Vararuchi, the great grammarian is the proponent of this technique, very widely used by Namboothiris. Letters in the "ka" and "ta" groups represent the digits from 1 to 9, while in the "pa" group, the first five letters signify numbers 1 to 5. Similarly, letters from "ya" to "la" also signify numbers 1 to 9. In compound letters, the final letter should be taken into consideration. Letters "na", "nja" and the vowels not attached to any consonant too indicate zero (0). Example: ka, kaa, ki, kku, ska = 1 Numbers are reckoned in the reverse order. For example, the numbers for the word "khagam" are 2 and 3, the resultant number will be 32. Again, take "taralaangam" : 6 2 9 3 The number in the reverse order should be taken, i.e., 3 9 2 6 "kula": 1, 3 -> 31 (u attached to a consonant) "ula" : 0, 3 -> 30 (u unattached to a consonant = 0) These facts can be summarised as follows: 1katapaya 2khathaphara 3gadabala 4ghaddhabhava 5ngannamasa 6chatha sha 7chhathha sa 8jada ha 9jhadha la 0njana zha, ra unattached vowels
Note: Since ka, ta, pa, ya stand for 1, the system got the name "katapayaadi". The system came to be used widely in India and particularly in Kerala. As it is easy to indicate numbers like 28 using words like "hari", "dwaaram" and "dukkham", it is used to incorporate numbers into verses. It is also convenient to remember that by subtracting "taralaangam" from the Kali year, the year in Malayalam Era can be calculated. It is more difficult to remember the numbers 3926 than the word it represents, namely, "taralaangam". How this system can be used for historical periodisation can be illustrated.
The last word in Melpathur Narayana Bhattathiri's "Naaraayaneeyam" is "aayuraarogyasoukhyam". It is said to indicate the day in the Kali Era on which the composition of the poem was completed. This date can be derived in the following manner:

"aayuraarogyasoukhyam"aa yu raa ro gya sou khyam 0 1 2 2 1 7 1 In the reverse order1 7 1 2 2 1 0
Thus, the day in the Kali era on which the work was completed1712210
Between Medam and Medam365 days, 6 hours and 12 minutes or 365 days, 6 1/5 hours or 365 days + (31) / (5 x 24) days = 365 + (31 / 120) days
Divide the Kali day with this number to get the year in the Kali era:
The year in the Kali era in which the work was completed= 1712210 / (365 + (31/120)) = 4687 years, 244 days
Subtract 3926 from this to get the year in the Malayalam era:
Date in Malayalam era= (4867 - 3926) years, 244 days = 761 years, 244 days or the 244th day in the year 762 in Malayalam era (since year 0 to 1 is counted as 1, and not 0) Starting from the Malayalam month Medam through Tulam, one gets (31+31+32+31+31+30+30)= 216 days (& 244 - 216 = 28)
This means that the work was completed on the 28th day of the month Vrischikam in the year 762 of the Malayalam era. It is said that the first day in the Kali era was a Friday. This has been supported by Kelalloor Neelakandha Somayaji in his "Aaryabhatteeya Bhashyam". So, if the remainder is 1 after dividing the number in Kali era by 7, then it was a Friday. Now, the number 1712210 divided by 7 yields a remainder of 3, and hence the day of the week must have been a Sunday. Therefore, it is clear that the "katapayaadi" system has historical value also.

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