On Contribution Of Jainology To Indian Karm Structures

Author(s): L C Jain, C K Jain
Publisher: Z_Jain_Vidya_evam_Prakrit_014026_HR.pdf
Catalog link: https://jainqq.org/explore/250444/1

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On Contribution of Jainology to Indian Karma Structures Prof. L. C. Jain & C. K. Jain 1. Introduction to the Contents From the Satkhanda gama (c. 2nd ceutury A. D) and the Kasayapahuda sutta (c. 1st century A.D.) Prakrit texts, Nemicandra (c. IIth century A. D.) compiled in abstract form the texts known as Gommatasara and Labd hisara respectively. The author has contributed three research papers regarding the contents of these volumes. The commentaries on the works of Nemicandra were prepared respectively by Kesavarna (c. 14th century A. D.) Nemicandras (c. 16th century A. D.). Madhavacandra Traividya (c. 1203 A. D.) as well as Todaramalas (c. 1761 A. D.), Abhayacandra Saidhanti (c, 13th century) is also known to have compiled a commentary. The approach to the topics is set theoretic? and methodology 1. (a) satkhanda gama with Dhavala commentary, vols. 1-16, Amaraoti and Vidisha, of H. L. Jain, 1939-1959. (b) Mahabandha, volumes 1-7, Bharatiya Jnianapitha, Kashi, 1947 1958. (c) Kasaya Pahuda, Jai Dhavala commentary, Jaina Sangha, Mathura (series). Cf also curni sutras of Yativisabha, Calcutta, 1955. (d) Gommatasara and Labd hisara of Nemicandra, "siddhanta cakravarti' alongwith Manda bodha Prabod hini, Jivat attra Pradipika and Samyak nana Candrika commentaries, edited by G. L. Jain & S. L. Jain, Calcutta, C. 1919, (including Artha Samdrsti chapters contributed by Todaramala). 2. Cf. 2 (d) 3. Cf ibid. Cf ibid. ibid. 6. Cf. ibid. 7. Jain, L. C., Set Theory in Jaina School of Mathematics I. J. H.S. vol. 8 nos. 182, 1973, pp. 1.27 parisaMvAda-4

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On Contribution of Jainology to Indian Karma Structures 207 symbolic. In the earlier portions of the texts, post universal Lokottara measures pramana are set up in relation to the bios detailed with respect to individual control station guna sthanas. The next part of Gommatasara (Karma-kanda) details about the theory of karmic bonds, rise and state in structural forms. 10 The material in Labdhisara deals with the dynamics of the karma system in an elaborate mathematical approach.11 The equation of motion of the complex system dealing with the nisusus (nisekas) expressible as tatrads of (i) Configurations (prakrtis) (ii) mass numbers (pradesas), (iii) energy-levels (anubhaga amsas) and (iv) life-time intervals (sthiti) pose the most trying problems of bio-science pheno mena. 12 8 2. Structures in Karmic Masses 18 One may recall the treatment of an instant-effective-bond (Samayaprabaddha) in a previous research paper. In order to understand the structure of a nisus, with life-time zero to prescribed instants, one has to give a general expression to the instant-effective-bond in terms of the configuration, the syeer-vector-group and the geometric regression. Let Ca BS denote the set of karma particles of Cath configuration Ss Gp (a= 1, 2,...), of SSsth super-vector-group ( 1,2, ...) of karma particles 8. (a) Jain, L. C., On the Jaina School of Mathematics, C. L. Smriti Granth, Calcutta, 1967, 265-292 (Eng. Sec.) (b) Jain L. C., Jaina, Matheinatical Contribution of Todaramala of Jaipur, The Jaina Antiquary, Vol. 30, no 1, 1977, pp 10-22. (c) Jain, L. C., of Perspectives of System-Theoretic Technique in Jaina School of Mathematics, between 1400-1800 A. D., Jain Journal, Calcutta, Vol. 13, no 2, Oct. 1978, pp. 49-66. 9. (a) Jain, L. C., Mathematical Foundations of Karma : Quantum System Theory, I, Anusandhan Patrika, Jaina Visva Bharati, Ladnun, 1073, pp 1-19. (b) Jain, L. C., System Theory in Jaina School of Mathematics, I. J. H. S., vol. 14 no. 1, 1979, pp 31-65 Cf. ibid. Cf. 8 (c) and 9, op cit. Cf. ibid. Cf. 9 (a), op. cit., and Cf also 7, op. cit. 10. 11. 12. 13. parisaMvAda-4

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Roc jaina vidyA evaM prAkRta : antarazAstrIya adhyayana contained in Gyth geometric regression (r=1,2,....) of the instant-effective bond (Samaya prabaddha) which varies in its contents of karma particles according to variations in Yoga or volution and kasaya or affection. Thus not only B varies, but its subparts in Ca Sg and Gy also have varied values, every instant. Let the vector groups contained in (var gana) be denoted by w where I denotes indivisible-corresponding-sections (avibhagi praticchedas) of affine or antiaffine energy-levels (anubhaga ania) of impartation controls in each of subscupt V of vectors (var gas) contained in a particular vector group. Here I will represent the least value of I, *Sa will denote the total number of super-vector-groups (spard hakas) ained in a geometric regression (gunahani) corresponding to Cash configuration of karma, and d will denote the common difference through which the vectors go on decreasing at every next step, in the next nisus having an instant less of life time for a particular configuration.14 Thus, Ca B = WPISZ (B - 1)i s'-'+ wssi*s* - 2+1 *S$ 6, 1- 7-19 OY-1 V (B-1)i*s -1 - hr w2ssi*s* +...+ V - Bi*sy.1 a 2-1 2001 - 27-1 -1). ....(2.1) This gives a general expression which may be further detailed as follows : Thus the bond fluent of first super vector group of the first geometric regression of first configuration (so labelled) is BE +ws+1 V-dtws+2 V-20 + Ws+3 V-3d+...+ W28-1 .(2.2) V-(S-11 The bond fluent of second super-vector-group of the first geometric of first configuration is : RIW2 w2s+ 1 w2s + 2 w3s-1 'v-(s +1 v-(s+2) 14. Cf. 9 (a). - (2s - id...(1.3) parisaMvAda-4

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On Contribution of Jainology to Indian Karma Structures 209 The bond fluent of third super-vector-vector group of the first geometric regression of first configuration is: B31 v-2sd *(2s+1)d++w4s - 1 etc., till v/2 1 number of particles are not obtained. - B1, 1 nl W3S Thus the bond fluent of the nth super-vector-group of first geometric regression of the first configuration is +wns +1 Wns v (n - 1)sd BI B12=w(n+1)s+w(n+1)s +1 V d 2 2 Similarly n2 2 +w3s+! V B22-d V ...(2.5) The bond fluent of first super-vector group of second geometric regression of first configuration is 2 + v-((n-1)s+1} di 15 d 2(n-1) s. 2 +w(n+2)s+1 V W2ns + s - 1 V 2- (ns-1) (+1) V- (3s-1)d +...+w(n+1)s+s-1 V d +w2ns+1 V 2 ... 2 And the bond fluent of nth super-vector group of the second geometic regression of first configuration is =W2ns -- (s - 1) +...+w(n+2)s+s-1 V d 27-1 27-1 +w(n+1)s - 1 v (ns-1)}d B}11 =W { (? - 1)n+1} s s+w{(7-1)n+1} s+1 +W V V 27-1 2 (s-1) 27-1-(3-1) d 2 d [(n - 1) (s+1)] -- +...+ +...+W{-1)n+1} s+s-1 V d 27-I ...(2.4) Similarly the bond fluent of first, second etc. super-vector groups of rth geometric regression of first configuration are given as follows: 2s(28-1)-2 d .... (2.7) ...(2.6) ....(2.8) ...(2.9) parisaMvAda -4

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380 jainavidyA evaM prAkRta : antarazAstrIya adhyayana (y - 3) B! =W{(7-1)n +2 )s.iwl(-1)(n+2) 1s+1, - S +W d t ... -s d $+1) + .. twly-1)n +2 ) 5+(S-1) ... (2.10) d +wyns +1 ny Wyns - (n-1) - T- ((n-1) +1} 2 . 27-14... +...+wyns+s-1 ns ....(2.11) 2? Similarly, the bond Aluent, for second, third & upto one hundred forty eighth configuration may be depicted through the B's. There will be difference in the values of r, d, v, s, and they be shown as variables in manipulation of different configuration, but the structures for all configurations will be grouped as above matrices' summation. Thus in the second super-vector group of the third geometric regression of Ca th configuration of karma will be given as under : BSAG Ew2i * +w2i*sa2+1 Co Go + w 3i* sa-1 .... (2.12) Where Sa will denote the total number of super-vector groups contained in a geometric regression Gy corresponding to Ca th configuration of karma as shown above. The total number of W's above will denote the numbers of instants in the set (set) of life-time stay of the karma bond corresponding to a particular configuration and this will be denoted by cardinal of the set ss family, for a particular geoinetric regression. parisaMvAda-4

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On Contribution of Jainology to Indian Karma Structures 211 Thus the number of nisusus, represented by Bac will be B. r for a particular configuration and for all contigurations it will be B. y -a, constituting a three dimensional matrix. For an input of instant effective-bond B or due to charge of Yoga16. B's say x B, shall also have the same total number of W's, i. e., B. 7. a although the other quantities will have an over all charge proportional to x. Let the product B y a be denoted by y. Then the charge in the y the nisus Wy till it decays shall be ay oray Z (t). Similarly change in the next will be a y., ZY-1 (t) and so on. In the and the total charge in the input column (in the karma life-time structure) in r instants will be zero if it is time-invarient, that is if ay Zy (t)+ ay-, Z9-1 (t) + ............ + do=0 (2.13) Similar situation may arise for all state columns, but when there are changes, matters for solutions will become very complicated and require a computers technique in graphics of events for manipulation. As the instant-effective-bond can be put as an input-values vectors column, the whole change may be denoted by dB/dt also, as an instant, of d(xB)/dt in special Yoga and Kasaya circumstances. The geometric regressions could also be put in a matrix form. Thus the nth geometric regression of karmic matter separate from indivisible corresponding-sections could be written in the form bus The Puth sometimes regression of karmic matter separa ld - (2w - 1) - n on-1 on-1 2n 2n. (w V-1d 2 -1 -1" (W/9 1)) . ---> 21-{w-1)-1 ... (2.14) 2n-1 15. Cf. 7, op. cit. 16. Cf. 9 (a) parisaMvAda-4

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212 jainavidyA evaM prAkRta : antarazAstrIya adhyayana when basic vectors in terms of the fractional multiples of V as elements, regressive with fractional multiple of basic vectors d as common difference, vector group (or simply vectors was numbers of rows) and tensors s as number of columns starting from extreme right lowest corner represent n various geometric regressions. Similarly, following matrices, have the same number w of rows and the numbers of columns, as above, have i as a notation for indivisible-corrsponding-sections, and represent the imparlation intensities associated with each basic vector of the corresponding elements of the atove matrices according to the position in the rows & columns. The n th geometric regression of the recoil (anubhaga) intensity-- is given by nsi+ (w - 1),..., ((n-1) s+2) i+(w - 1), ((n-1) s+1)i+(w - 1), . nsi +1 ..., ((n-1) s+2) i+1 ((n-1) s+1)i+1 ... (2.15) Lnsi ..., (n-1) s+2)'i ((n -- 1) s+1) i All the above matrices are in correspondence with a particular configurational structure in relation to karmic bonds etc. Further the equation (2.13) may be written as 2 (t) = Az (t) (2.16) or d zy (t) dir ?, (t) 0 0 1 0 0 1 0...O 0...0 Zy (t) 2y-(t) 7 ....(2.17) L2, (t) zi(t) -a, -a, -a,...ay. 2 2 (t) The solution of the above matric differential equation give z (t) = e.it z (0) = 0 (t) z (0) where z (0) is z (t) at t=0, and eft=(t) (2.18) is called tracnition matric which is a y x y square matric by $(t) = .. 0 1 0 0 0 0 0 0 1 0 0.0 ...... (2.19) -a, -a, -22 ..-ay-1 parisaMvAda-4

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On Contribution of Jainology to Indian Karma Structures 213 Mark that e 4t could also be expanded in the form of a uniformly convergent series e4t-1+At+... .. (2.20) subject to the conrition 11 A" 1 A lt In (2.21) Thus the instant-effective-bond comes as an input wave group, goes as an output-wave group, and what stays is the statewave group, in bond, in tensorial forms as above. A more elaborate form of derivation of the differential equation & its solution may be sought, by assuming the form of a variable nisus in the triangular matrix for statetransition phenomera. We may also represent the input wave or output wave group as in place of Bac with the matrix form as detailed S8 G above, as a wave tensorial function of Yoga and kasaya as well as time. If Yoga and Kasaya are kept constant, the wave function may be said to Satisfy (v, 4) 02 $+$2 (v, i) 4 = $(v, i) ....... (2.22) at du 69,6 could also be constants in tensorial form for certain fixed values of V and i; the threshold creator quanta of karmic matter mass & its intensity of recoil energy. The karmic wave contains mass and energy in subtle forms as above. We know that the configuration will take the shape of waves, for according to Jaina school an ultimate particle, at on instant, hy virtue of velocity could be present at more than one point in space. In any configuration it has a momentum and energy of recoil. Thus the solution of the above wave equation shall have a more complicated form, in exponential than as that anticipated in (2.18), its coefficients being calculated from the elements of the the state-triangular matrix. They may be regarded as a gunahani spard haka or a sum of var ganas. Thus the waves here may also be regarded as sum of wavelets in form of Set of var ganas, etc. or also in form of set of nisekas, which drops out utimately after its life time, giving out unpulses. Thus the samaya oftrata

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jainavidyA evaM prAkRta : antarazAstrIya adhyayana prabaddha wave can be very properly given in terms of the multiple periodic waves, having their different periods of use as well as decay, depending upon various operators, known as (i) time (ii) Yoga (iii) Kasaya (iv) adhah pravrtta karama (low tended activity) (v) apurva karana (invariant activity) and so on. Thus the manipulation of the karma system could be effected either through matrix mechanics (triangular state matrix, column input matrix, row output matrix) for different configuration, as well as through wave mechanics, with the help of differential equations comprising of various operators, operands and transformas. The remaining study is left for future, after a deeper probe in the search for the appropriate modern tools of mathematics. 3. Structures in Phases of Bios 214 The bios remains in the phases of Yoga upto the thirteenth control station (gunasthana), after which it is free Yoga. The phare of kasaya remain up to the ksinakasaya or twelfth control station. The descriphon of Yoga and kasaya structures have been detailed in a previous paper on system theory (System Theory) in Jaina School of Mathematics. In this paper a survey of the above is given. The eperational Yoga stations are of three types (1) upapada (2) ekanta vrdhhi (3) parinama.17 All the Yoga stations are innumerate part of the Jagasreni (set of points in a world line.) Every station of Yoga is classified into five subtypes of structures responsible for configuration (Prakrti) and point (particle)(pradesa) bonds: 1) varga 2) var gana 3) spardhaka 4) gunahani 5) avishagapraticcheda1. They may be called basic vector, vector-group, supervector-group, geometric regression and indivisible-corresponding-section respectively. They have the same structure as the karmic matters, as shown previously; showing group equivalence and harmony in vibration, motion or intensity of recoil. Now these phases are worthy of attention, which are the cause of perturbations or modification in the state matrix. First the details of the low-tended activity (adhah pravrtti karan) are taken up19. The 17. Cf. 1 (d), Gommatasara, Karmakanda, VV. 218-242. 13. Cf. ibid, VV. 223-231. 19. (a) Cf. 1 (d), Gommatasara, Jivakanda, VV. 48-57. (b) Cf. 1 (d), Gommatasara, Karmakanda, VV. 896-912 (c) Cf. 1 (d) Labdhisara, VV. 33-165, & c. parisaMvAda-4

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On Contribution of Jainology to Indian Karma Structures 215 period is Inter-muhurta (*) (numerate avalis: set of instants ranging from an instant greater than avali to fortyeight minutes less two instants. Bhinna muhurta is a muhurta less an instant. The number of parinamas is innumerate universes (set of points), with similar increment, in flow of time. This activity may be for annihilation-sameliness (ksayika-samyaktva, for parting with endless-bonding of affection (anantanubandhi Kasaya), for subsidence or annihilation of mixed or disposition delusion (desa or sakalacaritra). The bonding of lifetime is also altered proportionately, in ratio of innumerate part of Palya, decreasing in every section of timeinterval of Inter-muhurtas. This results in infinite-times purity, bonding of infinite times of graceful recoil intensity bonding of infinitesimal part of ungraceful recoil intensity, and numerate thousand terms reduction in life-time bonding. The protract (anukrsti) structure of the parinamas (resulting phases) is calculated as follows : 20 The progression is arithmetical and the following formulas are applied in manipulation. SARV ADHANA is the sum, gaccha is number of (*) Gf. Dhavala 3/1,2,6/67/6. Cf, also 3/1,2,6/69,5 for approximate Muhurta, which may be greater than a muhurta, and may also be called antarmuhurta. Terms, adi is the first term, caya is the common difference. in which the formulas appear are: Sarvadhana or sredhiyoga gaccha 2 caya-sredhiyoga-(gaccha) (adi) (gaccha)2-gaccha 2 20. [2 (adi)+( gaccha - 1) caya] = Sredhiyoga 1 (approximately) there, Samkhyata is to be (gaccha)2 samkhyata solved for by the method of indeterminate analysis) X caya dhana = [sarvadhana -- (gaccha (adi)} - adi= sarvadhana - cayad hana gaccha adi dhana Sar vad hana-cayad hana =adix gaccha Cf. 19 (a), op. cit. The form parisaMvAda -4

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23EUR jainavidyA evaM prAkRta : antarazAstrIya adhyayana For illustrating the general and protract structures the following working symbolism is adopted : Jagasreni (world. line) Asamkhyata (innumerate) Samkhyata (numerate) Avali (tail) For the general structure, the following data is available : Number of terms Rsss L'd Common differences (Rsss) (Rsss) (s) Sum of common differences L' d (Rsss - 1) (caya dhana) (Rsss) s (2) Sum of first term L'd [1 + Rsss (25 - 1)] (adid hana) (Rsss) () 2) Quantum of Parinamas L'd [1+Rsss (28 - 1)] at first instant (Rsss) (Rsss) (s) (2) Quantum of Parinamas L3d Rsss (25+1)-1 at last instant (Rsss) (RSS) (s) (2) It is understood at present that these values could be obtained through indeterminate analysis, for the formulas form linear equations in more than one unknown, the solutions being in positive integers alone. The method has been discussed by Mahaviracarya in GS. S. (miscellaneous treatment) chaper on various by pesof kuptikaras (indeterminate analysis) (6.79 , et seq.) Data for the protract structure is as follows : Common difference L' a (Rsss) (Rsss) (s s) (Rss) Sum of common differences L' a (Rss - 1) (caja dhana) (Rsss) (Rsss) (s) (2) Difference of sarvad hana and L' a [2+Rss ( s (2s - 1)-1}] cayad hana (Rsss) (Rsss) (s) (2) First portion in relation to L' a [2 + Rss ( s (25 - 1)-1)] first instant (Rsss) (Rsss) (s) Rss) (-) Last portion in relation to first L3 a [Rss {s (28 - 1)+1)] instant (Rsss) (Rsss) (s) (Rss) (2) parisaMvAda-4

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On Contribution of Jainology to Indian Karma Structures La [Rsss (2s+1) - 1] (Rsss) (Rsss) (s) (2) Whole quantum of parinamas in relation to last instant First portion in relation to last instant Last portion in relation to last instant 21. The minimum protract portion in relation to first instant is L3 a Rss {s (2s - 1) ~ 1 } - 2] (Rsss) (Rsss) (s) (2) (Rss) L3 a F2 s In the above Parinamas there is six-station set: or F2 s F* * (F+). Cf. ibid. 16 L'a L3 a Rss s (2s+1)-1}] (Rsss) (Rsss) (s) (2) (Rss) La a [Rss is (2s+1)+1 -2] (Rsss) (Rsss) (s) (2) (Rss) where F is Finger (angula) set of points F+1 a F+1 a The structure for the unprecedent activity is similar, but without protract structure. There is the structure for the invariant activity.(21) It is not understood, how the mathematical correlation has been set up between the structures of the state karmic matrix and the above activity structures. The simultaneity of phases of bios and karmio matter without a difference of even an instant is also not explanable in the similar way as is the indivisibility of an instant during the motion of a particle or bios. F+1 F-1 a 217 parisaMvAda -4