The General Expression

In order to understand the structure of the niseka which constitutes the karma paramanus with state, from the first instant to x the last one then the above matrices can be generalized. Let B denotes a set of karma paramanus B is denoted by the yz bounded fluent of karmic matter, x is for the karma configurations is supervarifoms and z is geometric regression, all are changing from 1,2, -…….,. Let variform V contained in the B

then B = V1+ V2 +V3+…………

Where V1 is the variform possessing the least amount of energy. If c is the least amount of recoil energy or

energy possessed by ICS.

Then the bounded karmic fluent (bandh dravya rasi) of the first super variform of the first geometric regression of

the first configuration is given from the values in the matrix as follows :

1     c+1     c+2      2c-1

B =   V   +   V   +…………..+   V

11     v-d     v-2d     v-(c-1)d

The bounded karmic fluent of the second super variform of the first geometric regression of the first configuration

can be written as


1     2c+2     2c+1           3c-1
B =     V    +    V   +…………..+    V

21     v-wd    v-(w+2)d    v-(2w-1)d

Similarly the expressions for bounded karmic fluent can be formed by taking different values of the

configurations, super variforms and geometric regressions. Then all these conclusions can be generalized as


x ycsxz-1 ycsz-1+1 2ycsz-1

B = V + V +………………..+V

yz v/ 2z-1 –(y-1)cs/(z-1) v/2z-1 [(y-1)csz-1/2z-1]d/2z-1 v/2z-1[{ycsz-1/2z-1}-1]d/2z-1

Thus the total neo matrix can be considered as space neo matrix instead the planer one. This three dimensional

matrix can be shown by the diagram I .For simplicity, single structure of one configuration is taken into account,

leaving apart the time lag (abadha kala) then the pre described neo quanta can be placed according to the

subsidence or decay form matrix as shown below where Bxy is taken into consideration and z is taken constant.

The above triangular matrix of subsidence of karma, at any instant represents the total amount of energy, with

input and output at every next instant. The manipulation of such triangular matrices would be helpful in exploring

the karmic mechanics. Let the triangular matrix should be discussed in detail as follows:

A .Right Triangular Matrix

The state of karma can be represented in the right triangular matrix given in Gommatsâra karmakan da, i.e.sthiti

racanâ yantra known as lifetime matrix. This matrix contains certain group of instants, which are studied

together as shown in table (V). The elements of matrix are nisekas, which contain particular number of karma

paramânus. Each niseka is associated with different types of configurations (Prakrits) but similar lifetime (sthiti)

and similar energy level (anubhâga). Here is state matrix has the same input and same output. The right column has

the 48 nisekas from bottom at 512 karma paramânus to top at 9 karma paramânus. This contains six geometric

regressions as shown in the table (VI). The first geometric regression (Gunahâni) as it is in arithmetical

progression, the first element is 512 karma paramanus and the last element is 288 as last term with 32 as its

common difference, its number of terms is 8. The next one lying above it has its first term as 256, which is half of

512, last terms as 144 which is half of 288, 16 as common difference and the number of terms is same as 8. The

set of these six regressions was designated as various geometric regressions. Thus the total numbers

of nisekas accommodating the various types of Karma Paramânus were 6 X 8 = 48.

The bottom most nisekas contain 512 Karma Paramânus has the least life time and the upper most nisekas 9

Karma Paramânus has largest life time i.e. it will be exhausted in 48 instants. The whole set of 48 columns and

48 rows is thus triangular matrix. Thus in the whole matrix grand total of Karma paramânus is 71304 and 6300

Karma paramânus will be considered in an instant. The number of karma paramânus goes on decaying when

there is no input at zero instant omitting time lag. So, the number reduces in particular fashion.

The input is due to operators, namely volition (yoga) and decation (Kasâya) actions. Here volition means the

disturbance in bios due to mind, vocal and body structures. And decation is protector or affection. Disposition of

attachment is also called decation. Therefore, for bounded bios the lifetime matrix remains constant because

there is constant input of Karma paramânus though there is constant output. The lifetime of Karmic bond for a

particle is different for different configurations of Karma and varies from minimum value of number of Karma

paramânus to the maximum value depending upon the variation in volition and decation. Acharya Nemichandra

Sidhanta Chakravorti described the state of Karma matrix using three methods given in the Gommatsara text

book having there different summation technology: i) Successively increasing summation (Sankalana), (ii)

Successively decreasing summation (Adhika) and (iii) Diagonal. Each technique requires the Knowledge of

summation of arithmetic progression (A.P) and geometric progression (G.P) and mixed progression. These

methods are only numerical and just examples for certain phenomena i.e., the state.

The structure of state may be different, the inputs and outputs may be different so generalization was essential

which can be obtained by modern techniques to solve the problem of optimization of karmas so that bios can get

the best of output and develops potentials hidden in it. So in the present work all the three methods have been

studied and then generalized by modern method of summation, which were not known at that time.


The text “The Labdhisåra of Nemicandra Siddhåntacakravartî” is regarded as a final companion text, to be taught

in continuation of the Gomma²asåra [Jivakå¿ða and Karmakå¿ða] text, and before all these, mathematical

foundations are required to be laid down through a study of the Trilokasåra. All these texts were composed as

summaries, predominant in mathematical manoeuvre, by Nemicandra Siddhånta Cakravartî in the late tenth

century A.D. and early eleventh century A.D. This systemic programming in summary form of aphorisms, from

the ¬a²kha¿ðågama texts of Pu¼padanta and Bhýtabali preceptors (C. 2nd century A.D.), as well as from the

Kasåya Påhuða Sutta of Gu¿adhara preceptor (c. 1st century A.D.) seems to be intended for the purpose of lay

man studies, for memorizing the essence of the ¬a²kha¿ðågama and as well as the Kasåyapåhuða Sutta which

belong to the Digambara Jaina1 sect and are regarded as authentic by this community. The scheme of

Nemicandra Siddhånta Cakravartî appears to be as follows, in the compilation of the summary and essential

texts :



(C. 5th Century A.D.) [TILOYASÅRA]



BHÝTABALI (C. 2nd century A.D.) KARMA KůÐA]



(c. 1st century A.D.) K¬APA¯ÅSÅRA

It also appears that Nemicandra Siddhånta Cakravartî took help of the various commentaries of the above original

texts, specially the Dhavalå (DVL) commentary of Vîrasenåcårya (c. 9th century, A.D.). The Mahåbandha (MBD)

part of the ¬a²kha¿ðågama (SKG), was completed by Bhýtabali åcårya in great details and is known as the

Mahå Dhavalå (MDL). Further the Kasåyapåhuða Sutta (KPS)was first commented inform of Cýr¿isýtras by

Yativâ¼abhåcårya and later commented upon by Vîrasenåcårya, left incomplete by him owing to his death, and

completed by his disciple Jinasenåcårya, in the form known as the Jaya-Dhavalå (JDL).

The second press publication2 of the manuscript form of the Labdhisåra (LDS)as well as its commentaries,

known as the Jîvatattva Pradîpikå (JTP) by Ke¹avavar¿î3 in Sanskrit, and the Samyak jñånacandrikå by

¢oðaramala4 in Ðhu´ðhårî (a dialect of Hindi in Rajsthan), appears to be round above 1919 by the Gandhi Hari

Bhai Devakarana Jaina Granthamala of Bharatiya Jaina Siddhanta Prakashini Samstha, Calcutta. This contained

the Artha Sa´dâ¼²i chapters on the Gomma²asåra and the LDS (ASG and ASL), an original contribution of

¢oðaramala to the exposition of the manoeuvre of the mathematical symbolism, used in the earlier commentary

of the text. The K¼apa¿åsåra, how of the mathematical symbolism, used in the earlier commentary of the text.

The K¼apa¿åsåra, however had the commentary by ¢oðaramala alone, who is said to have taken help of the

partial text (commentary) by Mådhavacandra Traividya.5 This work on the Labdhisåra of Nemicandra Siddhånta

Cakravartî is intended to furnish the basis for a chapter on Indian mathematical systems theory in a larger history

of ancient mathematical science.

It will be too premature to attempt to arrive at general historical conclusions, however, this introduction provides

with necessary background of the Indian mathematical system theory whose ancient form in India was called the

“Karma Theory” or “Action Theory”Functional Theory”.

It has been aimed to reach completeness so far as the text and its relevant texts are concerned in the

Digambara Jaina School of Mathematics, because the “Karma theory has been dealt with Sa´dâ¼²i in this

school through mathematical symbolism, called the Artha, A½ka and Åkåra Sa´dâ¼²is which iare usually in

algebraic, arithmetic and geometric forms. We find the words “Artha Sa´dâ¼²i” (gauge-symbolism)6 “, A½ka

Sa´dâ¼²i(numerical-symbolism) and “Åkåra rýpa Sa´dâ¼²i” (geometric- form of symbolism) in the introduction to

the “Artha- Sa´dâ¼²i” chapters by ¢oðaramala . The first two terms appear in earlier commentaries of the

Gomma²asåra. The Karma theory needed a symbolic manipulation which appears to be in full swing in the

detailed commentaries of the GJK, GKK and LDS. Those on GJK and GKK were compiled by Ke¹avavar¿î in

Kannada in the 14th century A.D., probably. These are said to have been based on the Vîramårta¿ðî

commentary of the GJK, GKK compiled in Kannada by Cåmu¿ðaråya, the commander-in-chief and prime

minister of the kingdom of the Western Ga½gas during the reigns at least of Mårasi´ha II (961-974 A.D.) and

Råcamalla IV (975-984 A.D.) He was contemporary of Nemicandra Siddhånta Cakravartî and his great devotee,

and builder of fifty seven feet high superb Båhubali colosus at Shravanabelgola. Although we find a few traces of

this symbolism in the Tiloyapa¿¿attî and the Dhavalå commentary,

Apart from the mathematical & symbolic manoeuvre of the karma theory in the Digambara Jaina School,

specially in the commentaries of the GJK, GKK and LDS, there appears to be a profound attempt to develop a

new methodology of Scientific inquiry for investigation of inner “mechanisms” of life and the development of

complex objects of reality, through a systems-approach as will appear later in the systems-analysis of the

Functional (Karma) theory.

Notes: 1. For a brief introduction to the life and works of some preceptors of this school, cf. Jain, L.C. and Dr..

  1. K. Trivvedi, Philopher Karma Scientists, Jabalpur, 2004.
  2. The work was edited by Gajadhara Lala Jaina Sri Lala Jaina. The first publication was on abridged

commentary in Hindi, in 1916. Cf. LDS.

  1. c. 1359 A.D.
  2. c. 1761 A.D., at Jaipur.
  3. c. 1203 A.D. cf. LDS, p. 39. Cf. also LDS (o), p. t. foreword.
  4. Artha is defined by ¢oðaramala as the measure, etc. of arbitrarily chosen fluent (dravya), quarter (k¼etra),



The Labdhisåra is a celebrated text in the metaphysico-ontological literature of the Digambara Jaina School. For

about a thousand years, this text alongwith its companion texts, the Gomma²asåra Jîvakå¿ða and the

Gommatasara Karmakå¿ða, as well as the K¼apa¿åsåra, succeeded in holding the field of study of the

functional-theory (karma-theory). These texts were regarded as the most popular and handy work for memorizing

the intricate and deep theory through Prakrit verses, which contained mathematico-philosophical material.1

It appears that the study of these, meant for the laymen,2 had in a way eclipsed the study of their source

material, the ¬a²kha¿ðågama and its Dhavalå commentary, the Mahåbandha or the Mahådhavalå, and the

Kasåyapåhuða and its Jayadhavalå commentary in Prakrit language, conventionally meant for voluminous study

by the ascetics.3 The voluminous source material of the summary texts has been translated into Hindi during the

last fifty years, and this has paved the way for study of mathematical and scientific contents and material

embedded in these volumes.4 The foundation mathematical material is found in the Tiloyapa¿¿attî of

Yativâ¼abhåcårya. This is elaborated in the Dhavalå.5 The Labdhisåra, including the K¼apa¿åsåra, as already

seen, is to be studied after a thorough knowledge of the Trilokasåra and the Gomma†asāra, the former being a

text of the Kar¿ånuyoga group and the latter being the text of the Dravyånuyoga group; all these texts having

been written by the same author, Nemicandra Siddhånta Cakravartî (later half of the 10th and first half of the 11th

century, A.D.). Hence it is desirable to introduce the author and his earlier texts for an

easy access to the description of the Labdhisåra and its mathematical contents.

There is a political history in the background of the writing of texts, specifically the Gomma†asāra, for

Cåmu¿ðaråya, his devoter, also known as Gomma†arāya*, who was the prime minister and commander-in-chief

of king Råyamalla of the Ga½ga dynasty. The Ga½gas of the west, were among the ancient royal dynasties of

India. They were devoted followers of Jainism. The first king of the Ga½ga dynasty was ©ivamåra who was

helped by a Jaina preceptor, Si´hanandi, who belonged to Nandiga¿a. The Repertoire d’epigraphic Jaina6 (A.A.

Guerinot), inscriptions nos. 213, 214 mention that ©ivamåra Kongunivarå was the disciple of Si´hanandi. The

inscription7 in Pår¹va nåtha Basti on Candragiri Hill, Shravana Belgola, Mysore, no. 54, also confirms this. From

the Manual of the Salem district, it is found that the race of the Ga½gas prospered through the sage