Mathematicoscientific Ideas In The Jaina Karma Theory

By Prof. L C Jain

The Jaina Karma Theory is very little known in its mathematical aspect outside the circle of the learned votaries
in the Digambara Jaina Community. Even the mathematical symbols are left out while studying the
Gomma†asāra and the Labdhisåra texts which are the summary texts compiled by Nemicandra
Siddhåntacakarvartî in the 10th-11th century. The present paper summarizes the fundamental ideas of the Karma
Theory on which the foundations were laid, specifically in the Digambara Jaina School.


The Gomma†asāra Karma Kå¿ða starts with the following verse introducing the nature or configuration of karma:
payaði sîla sahåo jîva½gå¿a´ a¿åi sa´ba´dho/
ka¿ayovale mala´ vå tå¿itthatta´ saya´siddha´// GKK-I/2//
Just as fire moves up, wind moves horizontally and water moves down, similarly whatsoever happens absolutely is called the nature or celibate or nature. The purpose here is with the nature of the bios and the karma. The nature of the bios is to transform in form of love, etc., and the nature of the Karma is to generate or create love, etc. However, without the fault of interdependence, the relation between the bios and Karma has been said to be about aeterno. Moreover the bios is non-material and the Karma is material, still their relation exists as such, a the mineral god is found as a combination of pure gold and stone. Thus the existence of such a relation is self evident.

The bios, through its yogic action at the rise of the bodily genetic coding Karma, assimilates eight types of karmas, known as knowledge screening, etc., at every instant, in all its points. This amount has been shown to be infinitesimal part of the set of the accomplished beings and infinite times the set of the non-accomplishable bios, and called as an instant-effective-bond (samaya prabaddha). This amount is a variable lying between the minimal and the maximal. Similarly there are the measurable amounts of the existent, rising and decaying karmas according to various circumstances.

In general qualitatively Karma is one alone. According to the classification based on the fluent(dravya) and phase(bhåva), Karma is of two types. The fluent Karma is a mass of matter and the energy lying in it to give fruition is called the phase Karma. Otherwise also due to formality of cause and effect, the ignorance, etc., generated due to energy of fruition are also called the phase Karmas. The basic eight types of Karmas are further subdided into 48 types and could be again further subdivided into innumerate universes types. Some of them are blocking and others are non-blocking. In Samayasåra one may find a similar detail of the relation as jîva pari¿åma hedu´ kammatta´ puggalå pari¿amanti´/
puggala kamma ¿imitta´ taheva jîvo vi pari¿amaî//SS-403//
¿avi kuvvai kamma´gu¿e jîvo kamma´taheva jîva gu¿e/
a¿¿o¿¿a ¿imitte¿a du pari¿ama´ jå¿a do¿ha´pi//SS-404//
Due to the stimulus phase of a bios, the matter gets transformed into Karma. The bios also gets transformed does not transform the attributes(gu¿as) of the Karmas, nor does the Karmas transform the attributes of the bios. The relation of the stimulus and the responder exists in the bonding and the bonder phase. But the unbounded matter and the bios have no relation of the stimulus and the responder. Thus both the fluents, in the state of the stimulus and the responder have the similar state. Wheresoever both these fluents have not equal state, there is said to be characteristic of a neutral external stimulus (medium) as in case of the aether fluent. Such a relation is called the stimulus and the field(upådåna) relation.
This has again been emphasized in the Samasåra
Ja´ ku¿ai bhåvamådå kattå so hodi tassa bnåvassa/
Kammatta´ pari¿amade tamhi saya´ puggala´ davva´//SS-417//
Whatsoever the phase(bhåva), the bios acts upon, it becomes the actor of that phase, and on becoming an actor, the matter-fluent gets transformed automatically. There are many types of variforms(varga¿ås), well described are of the twenty-three types out of which is the Karmå¿a varga¿å which is capable of being transformed into the state of akarma as a fluent(dravya). “davvavagga¿å duvihå—kammavagga¿å–¿o kammavagga¿å”//DVL, vol. 14, 5/6/71/52/5//. The Karma fluent pervades the whole universe in the form of a fine
dust. Those Karma matter particles get into flow towards the bios , assimilated when he is involved in the yogic activity through the operations of the mind, speech and corpus. They are rather arrested or bonded due to emotional (mohic or ka¼åyika phases of the bios These bound particles have been called as various Karmas, creating deformation in the very dispositional activities and behaviour of the soul keeping him bond ordependence. The charmed bios feels pleasure or pain while absorbed in them. Thence arose the search for getting independence from transmigration through getting rid of a single foreign agency, the Karma, which was then made a mathematical object, rather a complete system in itself. The modern set up of the system theory is a development of the twentieth century.

Thus the purpose of diverting the attention from very many things and images as friendly or otherwise, led them to have a unified theory which could explain every even of the life of a bios as an individual or in a group of species, search began to probe into the mathematical manoeuvre of separating the two systems which had non-linear interactions, actions and reactions between the bios and the Karma. They turned their attention towards a scientific view of cause and effect, leaving the teleological speculation far behind.

It was thus observed that the configurations and the particles bonds were due to yogic activity or volitions and the life-time as well as energy intensity bonds were due to emotions or mohic activity. The configurations of Karma worked as hubs of a Karmic wheel round which the number of mass particles, their life-time and intensity of energy bonds corresponded in varying measures. Thus the school needed a measuring process for their values between their maxima and minima. They might have taken resource to the following process

  1. Formation of constants, variables, parameters and correspondence relations between them.
  2. Formation of measuring units for quantitative measures of fluents, phases, yoga, emotion, time, and space.
  3. Formation of maxima and minima of various sets(rå¹is) where the units worked as members.
  4. Formation of correspondence relations between phases of the bios and Karmas in individual as well as collective cases.
  5. Formation of conditions, constraints and restraints, serving as limitations in the natural world of events in absolute flat space and absolute time, for correspondence relations between actions, reactions and interactions of the bios and Karmas.

Now we pass on to see that the Jaina school tried to systemize the actions, etc., or the henomenological events expected to happen in the life of a bios through their measure system which included the proper infinities, comparability of the sets which were finite or transfinite through divergent sequences locating them in terms and their stations as follows:

  1. Present set of state(sattva) or states corresponding to its heredity consideration. This might have evolved the idea of a remnant structural system, constantly hanging and tending to to have inputs through yogic and mohic activities every instant which was regarded as indivisible as a space point or an ultimate particle of matter (paramå¿u). This system was alsopouring out the decayed cells (ni¼ekas) in course of time or through certain yogic or mohic retarded or accelerated activities. This can be seen very well by their manipulation through a life-time structure matrix of a very simple type as shown in the figure.
  2. Defining the constituents of the present state, the structure of the state, transformation in the state due to input of yogic and mohic activities and output of activities t various rates, through constants, variables and parameters of Karma fluent as well as phases. These gave equations of motion of the system or a systems.
  3. Overall effects of changing the growth or decay in the rate of Karmas due to their rise, decay, destruction, etc., on the bios activities or on faculty of its negentropic structures and functions, even beyond the range of the Karmas.
  4. Observational data collected in states of retarded yoga and emotions and setting up correspondence relations as equation of motion of the unified system for observing the change in the state as well as in the output. This also included the study of yogic and mohic controllability of the unified system.
  5. The ultimate results guessed as approximate states of the bios on completely detaching it from the Karma system. This, according to their finding, meant the paragon state of a bios attained after annihilating the total Karma system for setting the soul wholly free from all foreign agencies, and fully endowed with the natural eternal existence with endless knowledge, vision, power and bliss.