L.C. Jain

The author of the text, Nemichandra Siddhantacakravarti (981 A.D.) compiled the Trilokasara , the Gommatasara the Labdhisara and the Ksapanasara late in the tenth cen¬tury and in the beginning of the eleventh century A.D. Some more details about the title works of Nemicandra can be seen in the monograph {Philosopher Mathe-maticians-Yativrasabhacarya Virasenacarya and Nemi-candracarya)of the same author (D.J. Institute of Cosmographic Research Hastinapur—Meerut INDIA 250 404).

These were the summary texts from the detailed texts on the Karma theory, the Tiloyapannatti, , the Kasaya Pahuda the Chakkhandagama as well as their detailed commentaries in thousands of verses. These texts have an unbroken tradi¬tion of about 1800 years in the Digambara Jain School of Mathematics, of the South India.

The Trilokasara belongs to the Karanamyoga group and the latter three are regarded as belonging to the Karanamyoga or Dravyamyoga group of studies in this school. The first is related to the cosmology and cosmogony, founding a base for the theory of Karma which resembles the modern set up of the Cybernetical Systems Theory.

Consequently, the latter three texts depict the preliminary and advanced mathematical theory of Karma, symbolic in its layout in their commentaries com¬piled round about the 14th, 16th and the 18th centuries respectively. They are quite different in the terminology and layout from the views taken on the nature of Karma in the other Indian philosophical thought the Nyaya Vaisesika the Buddhist .

The Mimamsaka, J- C. Sikdar has specifically tried to correlate these terms and their significance in his doctoral thesis on the ‘Doctrine of Matter in Jainism’, (University of Jabalpur, 1967) . A preliminary article was published by L.C. Jain on ‘System Theory in Jaina School of Mathematics’, (IJHS, 14.1, 31-65), 1979. This gave an elementary description of the material (dravya joir).

Karma and phase (bhava Karma play their role in the interaction between the phases of a bios and those of the material Karma. The study starts with the Gommatasara texts described in its Jivakanda and Karmakanda , Actually the problem is the optimization of the Karmas so that a’bios could get the best of output and deve¬lop its potentials hidden in itself, due to its own clouded vision, knowledge and disposition.

Thus, the strategy is towards attainment of the serenity (samyaktva against the’various types of bond conditions described in the Gommata¬sara, rising to the target through fourteen control-stations (gunasthan nWfssTH’).

These conditions are worthy of mention, in relation to Karma Thus, bond (bandha), state (sartvarise (udaya premature-rise (udirana pfjlpi|i|i., up-traction Qutkarsana down-traction (apakarsana transition (samkraman ,subsidence (upasama , reservation (nidhatti fasrfrr), preservation (nikacana ftqrspr), are the ten operations karanas .

There happens to be relation between the soul and the new matter trans¬formed into form of Karma, this bond relation is depicted mathematically. This is of four kinds Configuration-bond , (particle-bandha) , particle-bond(pradesa bandha ), life -time bond and enegy bond (anubhaga bandha) .

The transformation of matter (pudgala in form of functional variforms (,karmana varganas ), fit to become in form of Karma, into original or suboriginal forms of configurations is the configuration bond, viz., knowledge- screening, etc. The measured number of the transformed material ultimate- particles (into the configuration forms, is the particle-bond.

This measure lies between the cardinals of two sets: the set of non-accomplish- able bios and the set of the accomplished souls. Such is the measure of the instant-effective-bond (samaya prabaddha ). This lies between the minimal and the maximal depending on the decrease or increase in the measure of of volition (yoga).

The instant-effective-bond, taken as input (asrava ) at an instant (samaya) gets transformed into the configurations in accordance with certain rules of distribution. Whatever ultimate-particles are bound in form of a configuration the measure of their life-time for which they remain in bond with the bios for that period is called life-time-bond.

After a certain well-defined time-lag period, §abadha kala 3TRTSTT q>Fr), there is rise of the bound ultimate-particles, in nisusus (nisekas faqqr) corresponding to every passing instant, there being no nisus-structure in case of the time-lag. period. . This process goes on from the first instant upto the last instant of the life-time bond excluding the time-lag period. This gives a form of a triangular matrix to the instant-effective-bonds bound from the infinite past to the present.

The nisus at the lowest and of the input column has a life-time of one instant after which it rises and decays. Similarly, the upper and upper nisuses have life-time of two, three, four and so on of instants. Hence, they rise one by one after having descended the various columns, rise and decay after fruition of energy, from the last row of the matrix.

The life-time of the last nisus is the measure of the whole life-time-bond of the corresponding input column. Such is the rule for all the seven original Karmas, the age Karma being excluded out of the eight. The time-lag period is not accounted for the age Karma, because its time-lag period lapses during the previous birth.

The mathematical structure of the matrix of the nisusus is defined through the measure of the number of particles bound at an instant, their life-time geo- metric-regression gunahnai , various geometric-regressions, mutual pro¬duct-set (anyohyabhyasta rasi , nisus-divisor (nisekahara two geometricoregression-set (niseka hara).

The Karma particles carry energy which is powerful enough to screen the knowledge, and so on of the bios, less or more, specifically during the period of the rise of Karma. Such binding of energy is called the energy-bond. There happens to be various types of energy among the ultimate-particles bound as an instant, .corresponding to a configuration.

The structure of energy of Karma is mathematically detailed as below: The indivisible part of energy is called an indivisible-corresponding-section (avibhagi praticcheda ) . The ultimate-particle of matter (pudgala associated with an assembly of indivisible-corresponding-section is called a variate (yarga ). The class of variates having the same number of indivisible-corresponding-sections is called a variform (vargana ) .

The ultimate particle associated with minimal energy is called minimal-variate (Jaghanya varga). An assembly of such minimal-variates is minimal-variform {jaghanya-vargana). Assembly of variates each of which has one more indivisi¬ble corresponding-section than that of the minimal-variate is called second-vari¬form (dvitiya vargana). In this sequence, variforms in assembly forms of variates, goes on increasing in an arithmetical progression with common difference one.

This goes to form a minimal-supervariform (jagahnya spardhaka). The assembly of variates associated with twice the number of indivisible-corresponding- sections than that of the minimal variate is the first-variform of the second super- variform. Similarly, the Variates of the first-variform of the third, fourth, etc., supervariforms have associated with them, three, four times, etc.

indivisible-Vol: 3 (1), Jan-91 corresponding-sections than those of the assembly of the variates of first-variform of minimal-super-variform. Here the measure of all ultimate-particles is the fluent (dravya). The measure of variforms having infinite measure is called life-time. For finding the structure,;formula for the calculation corresponds to the geometric regressions.

The number of super variforms found in a geometric-regression is called a geo- metric-regression-supervariform counting-rod. In the Karma matrix the first, second, etc. supervariforms are called the lower ones, while the latter ones are called the upper ones. Corresponding to these the measure of the Ultimate particles goes on decreasing, whereas the measures of the energy goes on increas¬ing from lower to the upper ones. So far is the description of the Karma bond.

Further, the Karinas bound at several instants, at an arbitrary instant, have an existence associated with the bios, and this is called state (sattva). This is of four kinds configuration-state, life-time-state, energy-state, particle-state. Mathe¬matically this is represented through a triangular matrix. Similarly, when the Karmas tend to impart the fruits at the proper period, they are said to rise. This is also of four types: configuration-rise, particle-rise, life-time-rise and energy- rise.

The rise is also to be explained through the triangular matrix. Similar details are given about the Karma which rise prematurely. The nisusus lying in a trail (avali snqfir) and are fit to rise from its first instant to its last one are called the rise trail. Those which lie out of this are called rise-trail external which are mixed in the nisusus of the rise-trail lower to it. Such are the prematurely rising.

Increasing of the life-time or energy is called uptraction (utkarsana). In the Karma matrix this is effected by tracting the lower ultimate-particles upwards. Similarly, when it is required to down-tract (apakarsana) the opposite process is adopted. When a secondary configuration gets changed into another, the phenomenon is called transition (sankramana).

Corresponding to the transition there are five types of divisors, called: perturbation (udvelana statutory (yidhata , low-tended (adhah pravrtta srw: geometric-transition (guna san¬kramana) and all-transition (sarva sankramana). When the ultimate-particles corresponding to an arbitrary transition-configuration are divided by the corres¬ponding divisor, the one part is the corresponding transition.

The ultimate-particles out of the rise-trail and unfit for being obtained at the rise-trail are called the stibsidence-fluent (upasanta dravya. The operation of subsidence is found in all the configurations. This is to be differen¬tiated from the subsidence phase {upasanta bhava ). The ultimate-particles of an arbitrary configuration may be such that aeriher .

They could transit nor fit for being brought into the rise trail, they are afled reservation-operation-fluent (nidhatti karana dravya). In addition to the afcove condition when they could neither be uptracted nor down-tracted, they are called preservation-fluent (nikacana dravya). In this way the ten operations are described in the Gommatasara. In the Labdhisara (essence of attainment), this theory is put to application for attaining the path of optimization.

which is said to be achieved through im- pedence and annihilation of Karmas as a consequence of reduction in bond and state of Karmas. Here this phenomenon is related with the attainment of vision and disposition. Thus the annihilation of four types of bond is described in the following sequence. Owing to attainment of vision-disposition, first of all there happens to be no binding of extremely ungracious configurations.

Then that of ungracious and then of gracious configurations. Here the reduction of configuration-bond gradually is called configuration bond reduction (parkti bandhapasarana . Further the particle-bond is in accordance with the yogas, hence on reduction in the vibratory activity of yogas, there is reduction in particle-bond. When there is complete annihilation of (the variability) in the yogas, there is com¬plete absence of the particle-bond.

The life-time-bond is a function of affections- Hence the life-time-bond decreases as illusion, affection decreases. Sequential reduction of life-time-bond is called life-time-bond-regression. Through such manner of reduction in sequ¬ence, at the instant of its termination, there happens to be minimal-life-time-bond. Afterwards there is annihilation of life-time-bond.

This sequence happens to be with regard to all types of configurations (prakrtis) except the age configuration. Hence the life-time-bond; of three types of age (exclusive of that of hell), is large owing to elevation ( visuddhi fcgrfe). Similarly, the life-time-bond of all other gracious and non-giacious configuration is greater owing to depression, but smaller owing to elevation.

Now the energy-bond of ungracious configurations is greater owing to depression, and it is smaller owing to elevation. Thus, the energy-bond increases or decreases in sequence with infinite common ratio. However, in spite of greater amount of energy-bond of gracious configuration the bios is not effected badly as to live in the world is according to life-time-bond.

The soul is effected badly owing to destructive karmas, hence they are ungracious. Hence, owing to attain¬ment of vision-character, there is excess of energy-bond of gracious configura¬tions. When there is annihilation or absence of affections, there is complete absence of energy-bond. From the above, the law of impedance (samvara follows.

The ultimate-particles of nisusus of state disintegrate one by one, instant by instant after rising. Further, owing to the same field, the ultimate-particles of upper nisusus transform to become lower nisusus. Thus instant by instant, there is disintegration of instant-effective-bond in excess, that is there is disintegration of many instant-effective-bonds.

As there is bonding of instant-effective-bond, one- by-one, and up hence there is ample disintegration and small amount of bond¬ing. Sometimes there is no bonding and there is only disintegration. In this way after destruction of all Karma ultimate-particles, there happens to be com¬plete annihilation of particle-state (pradesa sattva.

Oidinaiily, the life-time-state reduces one by one, instant by instant. But owing to the field of the vision-character attainment this reduction of life-time- state happens to be according to the law of the life-time-split (sthiti-kandaka f^rfcTand as per the law of the downtract (apakrstazprfnse) .First we relate the law of the split. There is a great amount of life-time-state.

There is a set of many nisusus fit to rise instant after instant. In it several of the upper nisusus are destroyed in the frustule-sequence, reducing the life-time-state. After such a destruction a trail amount of nisusus above it are excluded, and injection is made of the nisusus into all other nisusus. The injection is made upto the inter-muhurta period, and ultimate-particles are obtained into the lower nisusus.

All the remaining ultimate- particle remaining at the last instant, while obtaining them into the lower nisusus of the state matrix, there is annihilation of the nisusus fit for being annihilated. Then whatever is the amount of nisusus destroyed, that much of time-measure of life-time-state gets reduced there.

When the set of all ultimate-particles corresponding to all the nisusus of an arbitrarily chosen configuration is divided by the down-traction-divisor, then one part thereof set of ultimate-particles is called down-tracted-fluent. Out of that down-tracted-fluent some ultimate-particles are mixed into rise-trail, some are mixed into geometric-regression length, and the remaining are mixed into the upper-life-time.

There, from present instant to the instants of a trail-measure, correspond the nisusus called as the rise-trail. Into those nisusus the fluent fit for being given into the rise-trail, is mixed into, nisus after nisus, in the sequence of being reduced by common difference, one by one. The nisusus corresponding to the instants of conformally possible intermuhurta lying above the trail measure of nisusus, are named as geometric-saries-length.

Into those nisusus the fluent fit to be given into the geometric-progression-length, is mixed, nisus after nisus, in the sequence of innumerate multiple. The nisusus corresponding to remaining all life-time lying above those, are called the upper-life-time. Into those no fluent in mixed into the trail amount of nisusus at the last, its name is over-installation-trail.

Excluding this, into other nisusus, the fluent fit for being given into upper- fife-time, is mixed in the sequence of reducing common difference per nisus I through the structure of various-geometric-regressions. Thus, mixing up of fluent is in the arithmetical and geometric sequences ‘ respectively. There happens to be initial rise-progeometric-progression-length.

In this phenomenon, some fluent of the down-tracted fluent is mixed in geometri¬cal sequence with innumerate common ratio into the nisusus corresponding to the initial instant upto the geometric-progression length. The remaining are mixed into the upper life-time, hence the rise-trail is included in the geometric-progre¬ssion length, hence the denomination.

This happens to be decayed-remainder somewhere and stable else-where. Many nisusus at the end of this geometric- progression-length are called geometric-progression-top somewhere, which may contain somewhere only one nisus at the end. Here the law of the geometric- progression-disintegration is to be known. The fluent given to the rise-trail here is called premature-rise.

Somewhere the over-installation-trail is denominated as the minimal premature-rise under the law of the down-traction. According to the law of split (kandaka the reduction of the life-time-state is from the origin, on annihilation of some nisusus lying above.

According to the law of subsequent tract (anukrsti 3R§>ffe), the life-time of only some ultimate-particles of the nisusus lying above is reduced and there is no annihilation of nisusus from the origin. When there remains a trail in the life-time-state, its name is fragment-trail (ucchista avali suffer), in which there is.

In the description of Karma-configurations, their ultimate-particles are named as fluent (dravya). The ultimate-particles in form of bond are called bond-fluent. Those in form of state, are called state-fluent. The ultimate-particles of nisusus | of life-time-split are called split-fluent. Similarly, there is frustule-fluent for first second, etc., frustules.

The process of annihilation of nisusus of the middle, leaving ‘ the upper and lower portions is called interval-operation (antara-karma), the corresponding fluent known as interval-operation-fluent. The name of the ultimate-particles made unfit for rise is subsidence-fluent (upasama-dravya g-ou) . The nisusus in form of state into which new ultimate-particles are mixed, is arbitrarily chosen, and the latter is called giv able-fluent.

When the new ultimate- particles are mixed into those of state, they are classed as observable-fluent The name of portion (is split (kandaka.Boundary of a piece is called portion. The boundary or limit in the reduction of life-time is called life-time-split. Similarly the limit of the reduction of energy is called energy-split. There are portions at which there is endless-binding at four places related with life-time, and there is down-lraction of fluent which is mixed at three portions.

The measure of an object from one end to the other is called length (ayama apuTR-) . It may also be in case of measure of time. That is how the measure of life-time in terms of instants is life-time-length. Similarly there is life-time-split-length measuring the nisusus of the life-time-length. The amount of nisusus of made nonexistent correspooding to interval operation is called interval-length.

The name of the measure of the nisusus of a geometric- progression is geometric-progression-length. The name of multiple (guna) is multiplier (,gunakara.Whenever fluent is given into nisusus in row of multipliers its names is geometric-progression (guna-sreni JFT-srfcr). When there is transition of ultimate-particles from a configuration to other arbitrarily chosen configuration with a multiplier, instant by instant, there is geometric-transition (guna sankramana).

Whenever, this is in a reducing sequence it is called geometric-regression (guna hani ipq . The nisusus lying above the arbitrarily chosen nisusus are called upper-life- time. The name of the lower nisusus with an arbitrarily chosen measure is called first-life-time. Similar is the second-life-time, which denote the nisusus all life-time lying in upper portion.

The process of distinguishing by division into different parts the corresponding to an activity in form an assembly, is called a frustule (phali tfiifcr) . That Which corresponds to first instant is first-frustule, and so on. Whenever a certain amount of fluent is subsided at the first instant of subsidence-period, it is called first-frustule of subsidence.

When ultimate- particles of certein nisusus are mixed into another set of nisusus, the process is called mixing, giving or injecting (niksepana fipjfaor) . The class of nisusus into which mixing is not to be effected are known to be in the form of over-installation. When the fluent of nisusus of second-life-time is mixed into the nisusus of the first-life-time, the process is called gulp (agala arpnsr). The reverse process is called anti-gulp (pratyagala srpTPTT^r) .

Whatever is the time taken for annihilation of a split, it is called split-casting-period. The fall time of the fall of first, socond, etc., frustules are recorded transition-trial (sankramanavali), and that during which there is found subsidence of Karma, the trail is subsidence-trail. The name of interevning is (mahi is inter (antah 3Rf:)} hence the as first instant, second instant and so on. The set of instants in the period of a trail (avali), or the nisusus corresponding to that much period is simple called a trail.

The measure upto a trail from the present instant is called a trail of their nisusus are also called a trail or a rise-trail (udayavali). Above the rise-trail is the second-trail or anti-trail (pratyavali). From the bond-instant upto a trail there cannot be the process of premature-rise (udirana), etc., this is bond-trial, (bandhavali) or invariant-trial (acalavali) or time-lag-trail (abadhavali).

While injecting fluent, the trail measure of nisusus into which injection is not to be effected is called over-installation-trail (atisthapanavali 3TffcgrTRrefcr). Whatever trail measure of life-time remains on reduction of life-time-state, that is named as a fragment-trail (ucchistaval . The trail during which there is transition, that is transiiion-trail (sankramanavali), and that during .

which there is found subsidence of Karma the trail is subsidence-trail (upasamanavali). The name of intervening is (mahi) is inter (antah), hence the measure which is slightly smaller than the quoted measure it is called inter. For example, the intermuhurta is smaller than a muhurta by an instant and greater than a trail.

That natural number which is greater than three and smaller than nine is called separation (prthaktva qareR). This word has other significant meanings also. The denomination of an arithmetical regression is cow-tail (gopuccha . !’3 decrease or increase in case of injection of fluent, like the back of a camel is denominated as camel-back .

The law of distribution of fluent ifegiven through cause-operation formula. Either the life-time-structure or the energy-structure, are is to be calculated through the nature and measure of the following, fluent, life-time, geometric-regression, two-geometric-regression-set, various-geometric-regression- set, mutual-product-set.!

From these the measure of fluent corresponding to life-time. Measure of fluent corresponding t® both is associated. The rules are given for calculation of the measure of fluent in different nisusus or terms of a geometric-regression as well as those of an arithmetical regression in the state matrix. For example, when the fluent is divided by slightly greater than one and half geometric-regression-set, the first nisus is obtained.

When this is divided by two-geometric-regression-set, one gets the common-difference • When the nisus of the first geometric-regression is halved one gets the nisus of the second geometric-regression. On dividing the total fluent by the mutual-product-set, the last geometric-regression is obtained. Similarly, the rules regarding the energy-structures are given. There is also the use of the middle-sum (madhyama a dhana).

The laws are given for the process of mixing of the fluent into the geometric regression-length. These are abit complicated and may be seen in the text. Here the concepts of projection t mixed-lump (misra pinda fuw iw), tubular vessel , proportion , projector , and counting rod are . The rules are also given for finding out the fluent of the nisusus in the state matrix.

The total fluent of the state matrix is also calculated. Its total energy may also be calculated. All this requires the knowledge of instant- effective-bond, summing rules for the arithmetical and geometrical seque¬nces through the naive methods adopted by the commentators of the Gommatasam and the Labdhisara.

This set of calculations is for a dynamical system which is changing every instant, owing to the change in the phases of the bios and the matter (pud-gala or yin-yang) due to mutual instructions. The aim is to separt separate the system so that both may become independent to each other. The rules for finding the measure of variforms in energy-state are also given. All these require complicated handling of various sequences.

In short a mathematical model simulates the real process of separating the mutually interacting system to make them independent of each, other, once for all his article is proposed to serve as a prelude for a study of the INSA Labdhisara Project (1984-1987) in four volumes, due for publication soon.

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