Bhagavana Mahavira and his Relevance in Modern Times

Author(s): Narendra Bhanavat, Prem Suman Jain, V P Bhatt
Publisher: Akhil Bharat Varshiya Sadhumargi Jain Sangh

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Mathematical Foundations of Jaina Karma System
II. Basic Concepts and Principles :
Let us concentrate first on a mundane soul along with all its Karmic bonds with matter-particles. (The case of many souls may be treated on statistical lines). Relative to generation the bond relation is ab-aeterno, and the correspondence is one-many. 5
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Owing to procreation through becomings (Bhāvas) of a mundane soul, kinetic effect (kriya) alongwith potential effect (Pariņāma) may be called Karma.6 The matter-particles procreated to effect (Pariņāma) at the very instant (Samaya) due to the instrumental cause may also be called Karma. The matter particles then get transformed into five types of bodies. The mundane soul is also procreated to change due to instrumental cause of the Karmic matter at the very instant. This is specific causality.
Thus the relation between a mundane soul and its Karma is conjugate, and becomings of each, form mutual images or mappings. Karma of a soul may therefore be treated mathematically in various types of spaces-one being that of the becomings of a soul and its dual, the second being that of the becomings of Karma-bound matter-particles and its dual, and the third being the space of the Karma-particles along with its dual. As will be clear later, these spaces will be found to be having properties of neo-linear spaces of operands, operators and transforms. For interactions they may be
non-linear.
The topology of becoming-spaces of a soul in general, becomes the subject of the totality of five distinctive types of its becomings.7 The becomings of controls of a soul, which manifest owing to subsidence of its corresponding Karmas are called subsidence-becomings (Aupaśamika Bhavas). The becomings of controls of a soul, which manifest due to annihilation of its corresponding Karmas are known as annihilation - becomings (Kṣāyika-Bhāva). The becomings of controls of a soul, which manifest because of combinatorial situations of annihilation and subsidence of its corresponding Karmas are annihilation-cum-subsidence becomings (Kṣayopaśamika-Bhāvas). The becomings of controls of a soul, which manifest due to rise of Karmas instrumental in their creation (generation) are called risebecomings (Audayika-Bhava). Whereas the becomings of controls of a soul, happening without any relation to rise, subsidence, annihilation, annihilation-cum-subsidence are recognized as effectual (Pāriņāmika) becomings.