Indian Calendar

 INDIAN CALENDAR

Elements of the Indian Calendar

• Coordinate system

                      

The ecliptic plane is the plane that contains the orbit of the Earth around the Sun

The sun is said to be in a nakshatra or Rasi if the line joining the Earth with Sun goes through that nakshatra (star) or rasi (constellation)

The celestial sphere is an imaginary sphere centered on the Earth used to measure the positions of the stars  through angles Azimuth and Altitude

The moon and almost all the planets are found within a belt of width 8 degrees on either side of the ecliptic plane, and this belt is known as the Zodiac or the Rasichakra

Solar and Lunar Years

• Solar year (Samvatsara) is the time taken by the Earth to complete one revolution around the Sun. That means, after exactly one solar year, the Sun will return to the same star (background of stars). It is equal to 365.2564 days.
• Lunar year (AnuVatsara) is 12 cycles of Full Moon to Full Moon (or New Moon to New Moon). It is equal to 354.3671 days. 
  

Thus, there is a discrepancy of 10.9 days in the Solar and Lunar years. After every Five years the Sun and the Moon come to the same position in the background of stars. This 5-year cycle is used to synchronize the solar and Lunar calendars by adding two Lunar months (Adhika masas).

Five components of Panchanga: These five components uniquely 

• Tithi
• Nakshatra
• Vara
• Karana
• Yoga
  

The Sun moves at the rate of 1 degree per day, with respect to the Earth. The Moon moves at the rate of 13 degrees with respect to the Earth. The difference between the longitudinal positions of the Sun and the Moon is Tithi

The Moon is in the green color longitude (i.e. the line joining centres of Earth and Moon in this longitude). The Sun is in blue color Longitude. The Integer part of the angle between these two longitudes is called TITHI.

The Nakshatra, at any instant, refers to the particular portion of the ecliptic in which the moon is situated. In the above picture, the moon is situated in Nakshatra #3 i.e., Krittika

There are 27 Nakshatras (lunar mansions) in Vedic astrology. They are: 1. Ashvini, 2. Bharani, 3. Krittika, 4. Rohini, 5. Mrigashirsha, 6. Ardra, 7. Punarvasu, 8. Pushya, 9. Ashlesha, 10.Magha, 11.Purva Phalguni, 12.Uttara Phalguni, 13.Hasta, 14. Chitra, 15.Swati, 16.Vishakha, 17. Anuradha, 18. Jyeshtha, 19. Mula, 20. Purva Ashadha, 21. Uttara Ashadha, 22. Shravana, 23. Dhanishtha, 24. Shatabhisha, 25. Purva Bhadrapada, 26.Uttara Bhadrapada, and 27. Revati

Indian Mathematicians

 Indian Mathematicians

1. Panini - Algorithms
2. Pingala - Binary Mathematics
3. Aryabhatta - Square root, cube root, place value system, sine table, quadratic equ., trigonometry
4. Varaha Mihira- Fine ancient Siddhantas, Trigonometric identities, combinatorics, Magic square
5. Bhaskara-I - Indeterminate equations, approximate formula for sine function, astronomy
6. Brahmagupta - Arithmetic with zero and negative numbers, pythogorean triplets, etc
7. Virahanka - Fibonacci numbers, Morci meters,
8. Bhaskara-II - Sine functions, surds, permutations and combinations, ideas of calculus, astronomy
9. Nilakantha Somayaji - Irrationality of pi, BAsic ideas of calculus, PLanetary theory, Sine series

Unique Aspects of Indian Mathematics

 Unique Aspects of Indian Mathematics

Unique features

• Indian mathematics is a seamless blend of poetry, literature, logic, and mathematical thinking weaved into a single work. It is not compartmentalized as in modern education. There is no fear or stress in learning mathematics
• Indian mathematics seamlessly blended into daily life:  Temple inscriptions, literary works, discussions on religion, spirituality, etc
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Vaisesika Darsana

 Vaisesika Darsana

• Mainly deals with 'Exposition of reality'
• Systematic framework to describe all the 'Nameable and knowable' entities
• Kanaada gave 370 sutras to describe the 'second stage of creation' (First stage of creation, as per Indian Tradition, involves creation of ether, time, space and elements- earth, water, fire and air. Second stage of creation involves creation of multitude of physical entities)
• Three-pronged approach
• Uddhesa: Classification framework
• Lakshana: Definition of properties
• Pariksa: Examination using perception and inference
• Framework of Vaisesika school

• Dravyas, guna and karmas have general and special aspects, as given below
  

• Dravya constitutes the basic building block of the physical reality. It can be roughly translated as substance or matter, with more broader scope
• Classification on the basis of extent

• Classification based on occurence as singular or in classes

• Attributes of substances

Attributes are inherent properties associated with the substances (DRAVYA). 

They do not have independent existence nor cause for conjunction or disjunction process

17-24 attributes are identified and classified into three sets.

1)  Attributes related to finite substances- color, taste, smell , touch, fluidity, viscidity, etc

2) Attributes related infinite substances - cognition, pleasure, pain, desire, aversion, volition, merit, demerit, impression and sound

3) Attributes associated with both finite and infinite substances- number, quantity, separateness, conjunction and disjunction

From the above table, we can understand the general properties and special properties. Earth has a special property of smell. Ether has a special property of Sound. Water has a special combination of taste-color-touch

 

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Knowledge Framework and classification

 Knowledge Framework and classification

Expected Outcomes

• Understand the framework for establishing the right knowledge
• Explain the Nyaya Framework

Nyaya Sastra:

• One of the 6 Vedic (Theistic) schools of philosophy 
• It has 528 sutras
• It discusses the rules of reason, logic and epistemology

The knowledge triangle

• Knowledge (jnana) is defined as perception by revelation or manifestation of objects
• Valid Knowledge is called Prama- right perception of an object or "knowing an object as it is"
• Invalid knowledge: Memory, doubt, error or hypothetical meaning

Components of knowledge triangle: 

• Seeker of knowledge is pramatru
• Object of knowledge is prameya: Vaisesika Philosophy addresses this component (Metaphysics)
• Means of knowledge is pramana: Nyaya Philosophy addresses this component (Epistemology)

Nyaya Sutras by Gautama: 

• Considering 16 factors while establishing the right knowledge
• They form the fundamental framework for creating new knowledge and advancing thoughts through logic and arguementation
• Can be used in all fields (literature, grammer, philosophy, etc)

Vaisesika Sastra or darsana by Kanaada:

• There are 12 objects of knowledge- 
• Visesa is "individual or special or distinguishing characteristic"
• It involves classification of individual or atomic elementals and their association with one another
• There are 370 sutras
• This forms the basic science that is applied in "ayurveda" and "Shilpa-sastra"
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Indian Number System

 Indian Number System

(Source: Indian Knowledge System by Mahadevan et al., PHI)

• Historical evidences of Indian Number System
• Decimal Number System: 

• Bhuta-Sankhya System- Representing numbers through popular entities (Bhutas)

Example#1to 3

Example #4

• Katapayadi System

Example #1

Example #2

Example #3

Example #4

Indian philosophical systems

 Indian philosophical systems- Development and unique features

Questions (of existential nature) that inspire philosophical requirement

• Why should one not commit theft? Is it because of the scriptural or saintly or God's injunctions? Why should God give injunctions/ commands? What is the nature of God?
• What is the root cause behind our constant pursuit of happiness, which seems to be the fundamental instinct of all living beings? Who am I? What is my nature?
• What is the nature of the universe? Are there any universal laws that allow for perpetual happiness?

In trying to find the answers to these questions, great personalities arrived at holistic view of world

A Holistic view of world is called DARSANA. View is indicated by the root 'drs' in Darsana. The different 'darsanas' or Schools of philosophy have enriched Indian thinking and formed the basis for all aspects of life including worship, rituals, art, etc

Three subjects of darsanas

• Jiva- Individual living entity whose happiness or distress is the source of enquiry
• Jagat- The universe which provides the context or field
• Isvara- Universal force or Divinity or God who/ which seems to coordinate the Universe

Unique aspects of Indian philosophical thoughts

• Philosophy → Spirituality  → Religion  → Way of living
• Vedic schools of philosophy (six darsanas) and Non-vedic schools (Jaina, Buddhist, Caarvaka)
• All indian schools have some common concepts (karma, samsara, mukthi)
• Ultimate goal of life and the path to reach that is specifically mentioned in all schools of Indian..
• Different schools differ in their epistemological tools (the theory of knowledge, especially with regard to its methods, validity, and scope, and the distinction between belief and opinion) 
• Healthy culture of respectful and peaceful coexistence, inspite of differences in philosophies
• Every aspect of philosophy is subjected to debate.One of the schools give a framework of debates

Vedic Schools of Philosophy

Six Vedic Schools and their salient aspects

1. According to Samkhya system, two basic elements constitute everything in this world, i.e matter (Prakrti) and spirit (Purusa). Purusa is the pure consciousness, sentient, changeless, eternal, and passive. Prakriti is the root cause of all activity including the entire creation
2. Yoga emphasises on the understanding of mind, its various states, its cognitive activities,  and methods to control it.  Yoga provides a structured and practical eight step process to gradually reach a stage of complete cessation of the activites of Chitta.
3. The Nyaya system emphasises on the means of obtaining the right knowledge. Therefore the unique contribution of Nyaya school is its detailed inquiry of knowledge (prama) and valid cognition and its means (Pramana)
4. Vaisesika system deals with the Objects in the reality that is knowable
5. The main aim of Purva mimamsa school is to ascertain the meanings of the Samhita and Brahmana portions of veda which lay importance on the karma, performing rituals, and thereby attaining Dharma as a means of liberation
6. Vedanta schools of philosophy rely on three major texts: Brahma Sutras, Bhagavad-Gita and Upanisads, known as Prasthana-traya, for establishing their tenets.

• Sankaracharya propounded a monistic philosophy, known as advaita, with the conception of the attribute-less God (Nirguna-brahman) as the ultimate reality
• Visistadvaita philosophy of Ramanujacarya, recognises three entities- Matter, Jiva and Isvara
• The dvaita School clearly admits three independent and mutually irreducible substances that make up the universe: The Jivam Jagat and the Isvara.

Non-vedic schools of philosophy

1. Jain school of thought is in line with the vedic schools of philosophy. With syad-vada, Jain philosophers are able to analyse claims made by various systems of thought and show them to be relative assertions of the truth as understood by Jain tradition
2. Buddha's philosophy focusses on the means of ending the suffering of the individuals. It is based on the four Noble truths. The ultimate goal in Buddhist philosophy is to reach Nirvana. Nirvana is not the state reached after death, but something that is attainable in this very life
3. Carvaka school of thought closely maps to the trait of materialism, which emphasises a life of enjoyment based on certain principles and assumptions about life. The concept of rebirth and other world is completely dismissed in this system.