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Number Systems in Samskrit

Ramamurthy N ,

."Like the crest of the peacock, like the gem on the head ofa snake, so is mathematics at the head of all knowledge."

Vedanga Jyothisha - Lagadha, Verse 35

Mathematics is universally regarded as the

science of all sciences and the priestess of

definiteness and clarity. Everything that

the greatest minds of all times haveaccomplished towards the comprehension

of forms by means of concepts is gathered

into one great science, Mathematics. J.F.

Herbert

Indian Mathematicians gave the world the

numerals now in universal use. The

crowning glory of Indian Mathematics was

the invention of zero and the introduction

of decimal notation without which

mathematics as a scientific discipline

could not have made this much headway.

A mathematical equation had a meaning

because it expressed a thought of God, S.

Ramanujam, the man who knew infinity.

In keeping with the ingrained tradition of

mathematics in India, the genius who was

one of the greatest mathematicians of our

time and the mystic for whom blazed new

mathematical trails in Cambridge

University in the second decade of the

twentieth century, even though he did not

himself possess a University degree.

Representation of Numbers in

Samskrit

In ancient times, throughout India, almost

all the scientific books were written

using three types of number systems viz.,

Katapayaadi-Sankhya, Bhoota-SankhyaandAryabhateeya-Sankhya

Katapayaadi Method:

Katapayaadi MOmrS, (beginning withka, ta, pa & ya), is one of the generalmethods of representing numerals in

Samskrit. This method was described by

the Rishi Vararuchi. The numberscorresponding to each of the Samskrit

consonants are given in the table below.

Vedic knowledge is in the form of slokasor poems in Sanskrit verse. A number was

encoded using consonant groups of theSanskrit alphabet, and vowels were

provided as additional latitude to the

author in poetic composition. The coding

key is given as Kaadi nav, taadi nav,

paadi panchak, yaadashtak ta kshashunyam - translated as below

letter k and the following eightletters

letter t and the following eightletters

letter p and the following fourletters

letter y and the following sevenletters, and

letter ksha or zero.This method operates as below:

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Numbers corresponding to eachletter of any word is taken from the

table

Write them from left to rightserially

Transpose them from right to left Consider for further calculations.

Mka

Zkha

aga

bgha

Xa

cca

Ncha

eja

fjha

ga

Oa

Pha

Qa

Rha

ha

ita

jtha

Sda

kdha

lna

mpa

Tpha

oba

pbha

qma

rya

Ura

sla

uva

za wa xsa Wha ka

Melakarta Raagaas:

An interesting feature of the MelakartaRaagas of Carnaticmusic is described toexplain the above method of numerals in

Samskrit. The table in Annexure 1 lists

down all the 72 Melakarta Raagas, in thatorder. Read the numbers corresponding to

first two letters of the Raaga from the

above table and then transpose the same.

We can get the number of the Raaga.

For example:

a. Raaga Maayaamaalavagoula

qrqsuasqrqsuasqrqsuasqrqsuas The first two lettersare qqqq (M) and rrrr (Ya). Thenumbers corresponding to these

letters in the above table are 5 and

1 = 51. By transposing 51 we get

15, which is the number for

Maayaamaalavagaula Raaga.

b. Raaga Naaganandini lallkllallkllallkllallkl The first two letters arellll NandaaaaGa. The numbers correspondingto these letters in the above table

are 0 and 3 = 03. By transposing

03 we get 30, which is the number

for Naaganandini Raaga.

Note: In Samskrit the half letters are not

taken into consideration for any of the

counting/ calculations.

Lalit Sahasranma

1. Lalit Sahasranmais a hymn has182 and half verses. One Thousand names

of Lalit have been embedded in theseverses. The greatness of Samskrit language

is mentioned in the name itself

(Samskritam done in a perfect way).

Each word has lots of meanings. In the

same manner splitting of each word

differently will provide different

meanings. This makes different people

split the words differently and interpret

differently. Though it can be taken that

this does not affect heavily, this hymn

exactly has 1000 names not even a single

more or less. Hence if splitting of words is

not done properly and the names read

individually, then count of 1000 may

change. That is the reason, to split the

verses properly, Salkshara Stras were

first formulated. Because this is notavailable now Paribhsh Maalam,with 40 verses, was written by

Bhaaskararaayaa, who first wrote

bhaashyam to Lalit Sahasranma. It is aself-contained research paper on LalitSahasranma. It is perfect allegory. Atthe outset the surface meaning of these

verses is as praising and bowing ree

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Devee. But the deep meaning is that, itexplains the structure of all the thousand

names how many names contain how

many letters, the next-next names start

with which letter, the starting letter of

every hundredth name, etc. It is a delight

to read these 40 verses.

These Paribhsh stotras use a blend ofKatapayaadi-Sankhya as well as Bhoota-Sankhya to denote the numbers throughSamskrit words. It is a delight to read these

verses and appreciate the inherent

meanings.

Bhoota-Sankhya and Aryabhateeya-Sankhya have been described in someother articles.

Ramamurthy N, a banker cum ITprofessional, pursues research onhidden scientific treasures in

Samskrit.