कटपयादि Katapayadi and reintroduction to Vararuchi

One of my friends shared a reference to Sanskrit verse quoted in a book by foreign author. This purportedly had  value of π up to 31 decimal points. I had not come across this example earlier. This piqued my interest and I did some more digging. 

The method of assigning numeric values (0-9) to alphabets comes from Katapyadi system this acted as mnemonic devise to memorize and remember . This कटपयादि system was widely used across diverse fields such as mathematics, music theory, astronomy etc. It also goes to show that scholars were well versed with several discipline linguistics, mathematics and even poetry to name a few. 

It is believed that the कटपयादि system (name corresponds to first letter of first row in the matrix) was developed by Vararuchi (वररुचि). Vararuchi  has authored several books in Sanskrit and Prakrit व्याकरण grammar and is also part of innumerable myths and legends in oral traditions. It is said he could repeat any verse after hearing it once, was and one of नवरत्न nine jewels of Vikramaditya's court. He is believed to have spend later years in Kerala. 

His name is also invoked while learning Sanskrit Grammar among 3 sages (मुनित्रयं) other being Panini and Patanjali. With the exploration of कटपयादि system Vararuchi's genius was revealed and he suddenly became more than just a name mentioned in the verse below:  

Mechanism of this system-

1. All stand-alone vowels (like अ, आ, इ etc.) represent zero.
2. The consonant group have numerals assigned as per the following table.-

3. In a conjunct consonant, the last of the consonants alone will count (Like in क्या, it is formed by क्+य+अ. The only consonant standing with a vowel is य. So the corresponding numeral for क्या will be 1).
4. A consonant without a vowel is to be ignored (Like द् is associated with 0).

Sankara Varman once wrote a verse in the 4th chapter of his book Sadratnamala-

भद्राम्बुधिसिद्धजन्मगणितश्रद्धा स्म यद् भूपगी:

Splitting the consonants in the relevant phrase gives,

Reversing the digits to modern-day usage of descending order of decimal places, we get 314159265358979324 which is the value of π to 17 decimal places, except the last digit, which might be rounded off to 4.

Jagadguru Shankaracharya Swami Bharati Krishna Tirtha wrote a sloka (?? Missing reference), which is literally in seance the praise for Lord Krishna-

गोपीभाग्य मधुव्रात:

शृङ्गिशोदधि सन्धिग।

खलजीवितखाताव

गलहाला रसंधर॥

("O Lord anointed with the yoghurts of the milkmaids' worship, O savior of the fallen, O master of Shiva, please protect me")

If you want to decode this verse in terms of the Katapayadi system, you can get, 31415926535897932384626433832792. It means this verse encrypts the exact value of π up to 31 decimal places. Please note the decode is not classical reverse order. 

Let us now talk about कटपयादि संख्या method how ancient Indians encoded the value of one more famous irrational number 'e' (2.7182818....) into the following verse-

रथ यह राजा का है।

After deciphering this verse into number we get 27182818, which is the exact value of e upto 7 decimal points.

In my childhood days I used to read Hardy Boys, Famous Five. Nancy Drew et el. and created a secret language by replacing standard alphabet with other one. The stand words and sentences would appear to be gibberish. It could be deciphered by any one having the key or enough time and inclination to break the code. 

There is much utility of Katapayadi system unfortunately this is known to very few people. To compose verses in कटपयादि system require extreme mastery over language. The key is easily available if we know certain verse or sentence is in katapyadi we can easily decipher it.  For example, remembering historical dates could be made very simple using this method. Or someone's name equivalent could be an open secret among friends. These digits could be easily used in conversation even in their presence.  

रतीश पंड्या would translate to below numerals

265    11

As per classic way this is inverted 

रतीश = 562  (Sum of all numerals = 13 = root 4 - It will be good to check the numerology aspects too)

पंड्या = 11

Reference:

Katapayadi - an ancient Indian art of encoding

© Ratish