Jain Ganit Vigyan Ki Shodh Dishaye

Here's a comprehensive summary of the provided Jain text, focusing on its exploration of Jain mathematics and its research directions, as presented by Lakshmichandra Jain in "Jain Ganit Vigyan ki Shodh Dishaye" (Research Directions in Jain Mathematics and Science):

Overall Theme:

The book, "Jain Ganit Vigyan ki Shodh Dishaye," by Lakshmichandra Jain, aims to highlight the rich and advanced mathematical and scientific concepts within Jain scriptures, particularly those related to cosmology, astronomy, and the theory of karma. It emphasizes the need for further research into these ancient texts, arguing that they contain profound insights comparable to, and in some cases predating, modern scientific theories.

Key Areas of Jain Mathematics and Science Explored:

The text discusses the development and research directions in Jain mathematics and science across several key areas:

1. Historical Context and Previous Research:

   • The author begins by acknowledging existing research on Jain mathematics, citing scholars like B.B. Datta, A.N. Singh, L.C. Jain, and others. These scholars laid the groundwork for understanding Jain mathematics historically and conceptually.
   • The text notes that much of this research was conducted in institutions lacking extensive Jain manuscript collections, underscoring the challenges faced.
   • It also highlights the contributions of figures like Pandit Todermal, whose extensive commentaries on works like Gommatasara are considered invaluable for research.

2. Laukik (Secular) vs. Lokottar (Transcendental) Mathematics:

   • The book differentiates between Laukik mathematics, which focuses on practical applications like astronomy (developed by Mahaviracharya, Sridharacharya, and King Adity Thakkara Pheru), and Lokottar mathematics, which deals with abstract concepts, particularly within the framework of karma theory.
   • Lokottar mathematics is found in texts like Tiloy Pannatti, Shatkhandagama, Mahabandha, and Kashaya Pahuda, which lay the foundation for understanding the mathematical aspects of karma.

3. Transcendental Mathematics and its Research Directions:

   • The Concept of Infinity (Ananta): A significant focus is placed on the Jain treatment of infinities. The text details various types of infinites ( द्रव्य, क्षेत्र, काल, भाव - substance, space, time, and disposition) and their magnitude (अल्प-बहुत्व - less-greater). It asserts that the Jain approach to infinities, particularly their quantification and classification, is a pioneering effort.
     • Comparison to Western Mathematics: The book draws parallels between Jain concepts of infinity and the work of European mathematicians like Zeno (460 BC), Hui Shih (5th century BC), Galileo (1564-1642), and Georg Cantor (1845-1918). It suggests that Jain texts discuss concepts similar to Cantor's set theory and the well-ordering theorem centuries earlier, driven by the need to explain karma theory.
   • Mathematical Methods: The text outlines various specific mathematical methods employed in Jain scriptures:
     • Use of various symbols and notations (Tiloay Pannatti, Ankganita Sangraha).
     • Decimal systems and place-value systems.
     • Methods for writing decreasing multiplier quantities.
     • Salaga Ganana (a method of counting with strings or rods) and its potential for developing function-of-function concepts.
     • One-to-one, one-to-many, and many-to-many interaction methods.
     • Methods of expansion and summation for multiplication and squaring.
     • Spatial and temporal application methods.
     • Various divisions and operations within squared and higher powers.
     • Representation of infinite, innumerable, and countable quantities using "Dhara" (streams or sequences), including concepts of transfinite sets.
     • Units of measurement like suchyanga, jagrashreni, antarmuhurta, palya, sagar, avibhagi pratichchhed (indivisible point), pradesh, and samaya.
   • Cosmology and Astronomy: Jain cosmology is described as possessing intricate mathematical frameworks for determining the angular measurements of celestial bodies, distances, sizes, and movements. The text suggests these methods are distinct from Greek approaches.
   • Karma Theory and System Theory: The book strongly emphasizes the mathematical underpinnings of karma theory, viewing it as a precursor to modern "System Theory."
     • Key Postulates of Karma Science: The text enumerates core principles that form the basis of karma science, including:
       • The theory of infinities and their magnitude.
       • The concept of maximum and minimum acceleration based on the indivisibility of time, leading to quanta of time and space.
       • The indivisibility of the pudgala (matter) atom and its quantitative properties.
       • The concept of multiple atoms occupying the same space.
       • The interdependence and mutual non-existence of qualities in substances.
       • The concept of "Bandha" (bondage) of atoms based on energy levels.
       • Causality, relating past and future time sequences.
       • The principle of mutual concession or cooperation of matter with other substances.
       • General properties of matter beyond specific qualities like color, taste, smell, and touch.
       • The existence of kriyavati (energetic) and bhavavati (dispositional) powers only in soul and matter.
       • Adhyavasaya (mental states like yoga and delusion) as input functions leading to changes in gunasthanas (stages of spiritual development) as output functions.
       • The relationship between asrava (influx of karma) and nirjara (shedding of karma) as states.
     • Jain System Theory: The text argues that Jain karma theory is a form of system theory, more comprehensive than Western counterparts due to its inclusion of principles like bondage.

4. Comparisons with Other Civilizations:

   • The author draws parallels and contrasts between Jain mathematical concepts and those found in ancient Greek, Chinese, and Babylonian civilizations.
   • It notes that while some concepts might appear in different cultures simultaneously, the Jain scriptures provide a structured and comprehensive system, particularly for explaining karmic phenomena.
   • The text suggests that the universal diffusion of similar ideas across vast distances points to a common, albeit unknown, source of inspiration.

5. Research Gaps and Future Directions:

   • Need for Publication: The author stresses the urgent need to publish the vast content found in commentaries like those by Pandit Todermal.
   • Interdisciplinary Research: The book advocates for interdisciplinary research that integrates Jain mathematics and science with modern scientific theories, particularly in areas like quantum mechanics, relativity, and set theory.
   • Developing Mathematical Tools: It calls for the development of new mathematical tools to fully comprehend the depth of Jain concepts, especially concerning infinities and their application in karma theory.
   • Exploring "Dhara" Sequences: Further research is needed into the "Dhara" sequences described in Jain texts for locating transfinite sets.
   • Re-evaluation of Historical Figures: The book suggests a re-evaluation of historical figures like Pythagoras and Confucius in light of possible influences from Indian traditions.

Conclusion:

"Jain Ganit Vigyan ki Shodh Dishaye" serves as a powerful call to action for scholars and researchers. It asserts that Jain scriptures contain a sophisticated and ancient system of mathematics and science that predates many modern discoveries. By delving into these texts, the author believes, we can not only gain a deeper appreciation for India's intellectual heritage but also find valuable insights and frameworks that can contribute to contemporary scientific understanding, particularly in the realms of abstract mathematics and theoretical physics. The book positions Jain karma theory as a foundational "System Theory" with profound implications for understanding the universe and its operations.