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:  

1 ka ta pa ya2 kha tha pha ra3 ga da ba la4 gha ddha bha va5 nga nna ma sa6 cha tha sha7 chha thha sa8 ja da ha9 jha dha la0 nja na 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 order 1    7    1    2    2     1      0

Thus, the day in the Kali era on which  the work was completed

1712210

Between Medam and Medam 365 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.