Nemichandra Acharya Ki Khagol Vidya Evam Ganit Sambandhi Manyataye - Book Summary

Here is a comprehensive summary in English of the provided Jain text, "Nemichandra Acharya ki Khagol vidya evam Ganit Sambandhi Manyataye" by Lakshmichandra Jain:

This article explores the astronomical and mathematical beliefs of Acharya Nemichandra Siddhantachakravarti, a prominent Jain scholar of the 11th century, within a modern context. The author, Lakshmichandra Jain, highlights Nemichandra's significant contribution in mathematically systematizing the remaining aspects of the Jain doctrine concerning karma, laying a foundation for future generations. His works are praised for their completeness, orderliness, comprehensibility, utility, and historical importance, incorporating unique traditional knowledge that often stood in contrast to other Indian philosophical schools.

Cosmology (Khagol Vidya):

The text begins by defining cosmology as the study of the universe's depths and structural units, addressing questions about the location, existence, state, past, future, and causes of change for celestial bodies. It traces the historical development of these inquiries from ancient Greece, India, and China, noting the shift from explanations involving divine or supernatural powers to a focus on causality.

Causality and Jainism: Jainism, in particular, is presented as having deeply studied the yogya (control) over events. All occurrences related to pudgala (matter) were understood under the law of causation. This law also extended to the interaction between pudgala and jiva (soul), governed by karma and other subtle states. The author emphasizes that this causal framework is meaningful only when the continuity of past, present, and future events is precisely quantified and organized mathematically.
Historical Context of Cosmology: The article briefly surveys the history of scientific inquiry, mentioning:
- Thales (600 BCE) predicting eclipses through calculation.
- Pythagoras (540 BCE) linking everything to numbers and geometry, including musical harmonies.
- Socrates (415 BCE) strengthening inductive reasoning.
- Zeno (450 BCE) analyzing motion through paradoxes of infinity.
- Democritus (410 BCE) establishing atomism.
- Aristotle (384-322 BCE) developing logical propositions.
- Plato (427-347 BCE) laying the groundwork for mathematics.
- Eudoxus (370 BCE) measuring the Earth's circumference.
- Ptolemy (2nd century CE) explaining planetary motion through complex circles.
- Diophantus (275 CE) founding mechanics and statics.
- Confucius and Lao Tzu in China attempting to scientificize philosophical aspects.
- Newton (1642-1727 CE) revolutionizing physics with laws of motion and calculus, explaining celestial movements through gravitation.
- Maxwell, Lorentz, and Einstein exploring electromagnetism and relativity, with Einstein using four-dimensional geometry to explain gravity and electromagnetic forces, making relativity the basis of cosmology.
- Planck's Quantum Theory introduced the idea of discrete steps in nature and probabilistic outcomes, a concept that challenged deterministic causality.
- Heisenberg and Schrödinger further developed quantum mechanics, explaining the subatomic world.
Einstein's Theories: Einstein's concepts of space-time curvature, his belief that God doesn't play dice, and his view of the universe as a "soap bubble" are discussed. The idea that the universe might expand or contract with its matter content is also touched upon.
Modern Discoveries: The article mentions modern astronomical tools like telescopes, radar, and satellites, as well as advancements in understanding nuclear energy, the sun's fusion processes, and the life cycles of stars. The discovery of pulsars, quasars, and black holes, along with the age of moon rocks and the Big Bang theory, are presented as contemporary developments in cosmology.

Nemichandra's Astronomical Works and Beliefs:

Nemichandra's cosmological views are primarily found in two works:

Dravyasangraha (approx. 58 verses): Also known as Brihad Dravyasangraha, this is often the starting point for studying Jainism. It introduces the concepts of naya (standpoints), dravya (substance), and the initial principles of cosmology.
Trilokasara (approx. 1014 verses): This work is a more detailed exposition of Jain cosmology.

The author notes that information on cosmology is also present in Gommatasara and Labdhisara.

Jiva and Ajiva: The fundamental Jain division of the universe into jiva (soul) and ajiva (non-soul) is discussed. The nature of the jiva is explained through vyavahar naya (practical standpoint) and nishchaya naya (absolute standpoint). While the former describes the jiva with senses, lifespan, and breath, the latter asserts its pure consciousness, knowledge, and perception.
Jiva as a Machine (Yantravat): A significant achievement highlighted is the concept of the jiva acting like a machine (yantravat). This implies that the jiva's karmic processes can be understood through a framework akin to physical mechanisms, involving the influx (asrava) and bondage (bandha) of karmic particles, their disintegration (nirjara), and their ripening (udaya). This perspective can form the basis for studying the flow of atoms, their energy, states, and the results they yield to souls.
Development of Senses: The gradual development of senses from one-sensed to five-sensed beings is mentioned, along with the classification of beings as sthavara (immobile) and trasa (mobile), and sanjni (sentient) and asanjni (non-sentient).
Pudgala (Matter): Pudgala is identified as matter, with its fundamental unit being the anu (atom). The text asserts that Jain atoms cannot transform into pure energy, although atoms have infinite energy surfaces and can undergo changes. Energy and mass are seen as distinct but related.
Other Ajiva Substances: The ajiva substances relevant to cosmology are Dharma, Adharma, Akasha, and Kala.
- Dharma and Adharma: These are described as abstract, unseen substances that facilitate motion (dharma) and rest (adharma) for jiva and pudgala, respectively. They are compared to ether and inertia in physics. While Einstein removed ether from physics due to inconsistencies, the text argues that Dharma and Adharma are crucial for maintaining the ordered structure of the universe (loka). Without them, the universe would become too dispersed.
- Akasha (Space): Akasha provides space for all substances. Lokakasha (occupied space) is infinite and characterized by kalānu (time atoms).
- Kala (Time): Time is described as the cause of transformation (vartana hetutva).
Units of Measurement: The text discusses units like pradesha (space-points) and kala (time), emphasizing the Jain concept that a single pradesha can contain infinitely many atoms. This relates to the mathematical concept of compactness. Time is defined by the movement of an atom, with the slowest and fastest speeds implied.
Paradox of Simultaneity: A scientific paradox is presented: how a particle, while moving, can occupy multiple pradeshas simultaneously. This is linked to modern quantum mechanics and the uncertainty principle.
Numerical Systems: The complex system of numerical representation, including sankhyeya (countable), asankhyeya (uncountable), and ananta (infinite), is discussed. The concept of "degrees" of infinity, the comparison of infinities, and the alpabahutva (relative smallness/largeness) of infinities are highlighted, noting their early development in Jain texts even before Western mathematicians like Georg Cantor.
Types of Measurement (Mana): Jain philosophy recognized two types of measurement: laukika (worldly) and lokottara (transcendental).
- Laukika: Includes measurements of volume (prasta), weight (unmana), quantity (avmana), numbers (ganimana), precious substances (pratimana), and value (tatpratimana).
- Lokottara: Consists of four dimensions: dravyamana (substance measurement), kshetramana (space measurement), kalamana (time measurement), and bhavamana (state/consciousness measurement). These transcendental measurements, with their minimum (jaghanya) and maximum (utkrishta) values, are considered extraordinary and comprehensive.

Mathematical Beliefs:

Nemichandra's mathematical beliefs are deeply intertwined with geometry and numerical systems.

Geometry (Rekhaganita): The text highlights the importance of geometry, comparing the Jain approach to that of the Greeks in simplifying mathematics. The concept of calculating square roots, like √2, through geometric representation in right-angled triangles is mentioned.
Numerical Units and Concepts:
- Suchyagula: Refers to the number of pradeshas that can fit into an "Agula" (finger-breadth) in a linear sequence.
- Pratara-agula: The number of pradeshas within a square Agula.
- Ghanangula: The number of pradeshas within a cubic Agula.
- Jaga-shreni: The number of pradeshas filling the cosmic ladder.
- Jaga-pratara and Ghana-loka: These refer to the number of pradeshas in the flat and cubic universe, respectively.
Palya and Sagaropama: These are described as units of time measurement, representing immense durations calculated through specific methods of making pits and filling them. They serve as upama pramana (analogical measures) to quantify other aspects of reality.
The Concept of Infinity: The Jain understanding of infinity, with its distinct categories and relative magnitudes, is presented as a unique contribution. The ability to systematically list and compare different types of infinities within sequences (dhara) is considered a significant achievement.
Extremals (Jaghanya and Utkrishta): The concept of minimum (jaghanya) and maximum (utkrishta) values is a cornerstone of Nemichandra's system, applied to time, space, motion, knowledge, and consciousness. The text draws parallels between these Jain concepts and modern scientific principles like Maupertuis's principle of least action, Fermat's principle of least time, and the extremal principles used in complex scientific laws today. These principles are seen as underlying nature's selection of specific events or paths.
Astrology and Geography: The text touches upon Jain astrological and geographical calculations, mentioning the systems for calculating eclipses, planetary movements, and the structure of the cosmos (loka). The debate on the interpretation of geographical elements like Meru Parvata and the celestial maps is acknowledged.
Deva and Deviya (Deities): The mention of deities (Deva, Devi) in Jain cosmology is explained not as supernatural beings in the conventional sense, but as beings who act according to their karma. Rahu, for example, is described as a name for a celestial vehicle used in calculations.

Conclusion:

Lakshmichandra Jain concludes by emphasizing the profound scientific and mathematical insights contained in Nemichandra Acharya's works. He calls for further scientific study of these texts, suggesting that their extensive commentaries can be invaluable resources. The article highlights the remarkable foresight and analytical depth of Jain philosophy, particularly in its advanced understanding of cosmology and mathematics centuries ago.