Drishti of Darshans!

Mankind has always contemplated on higher questions of reality, creation, beyond life from the beginning of its existense in a variety of ways. Stability and security paved the way to curiosity and inquiry into various higher dimensions of life. This tradition of inquiry led to the development of various theories of philosophy at different times in different parts of the world. 

The word 'Philosophy' literally means 'love of knowledge' and it is regarded as 'Queen' of all knowledge systems by medieval scholars. It dwells on many questions beyond normal human perception and makes an to answer them in all possible ways. 

 

The word 'Philosophy' in Indian context brings scriptures like Bhagvad Geeta, Upanishads, Vedas to one's mind. But is  the Indian Philosophy confined only to these? Have the Indian Rishis contemplated on other aspects of Philosophy like the Western or Greek schools?

The Indic term for Philosophy is 'Darshan'.

Originating from the root ' Drsh', the word Darshan means ' to see/perceive' as the study of Darshans gives one a perspective to life. Indian Darshan systems have contemplated on practically all topics of human existence in some form or the other. Cognition, Linguistics, Psychology, Atomism, Health, Aesthetics and much more have been discussed over the long tradition existing for thousands of years.

The Indic tradition attributes Vedas to be at the root of all knowledge systems. But strikingly, we have schools of Darshan which don't hold Vedas as the authority and have conflicting views with Vedas ( Heterodox/ Nastik systems).Orthodox systems (Aastik systems) on the other hand consider Vedas as the supreme authority and are considered to originate from Vedas. There are 6 such schools of Indian Philosophy and their main subject matters are:

1. Nyaya : Cognition, Causation, Reality

2.Vaisheshika : Primordial discussion on Atomism, Matter

3. Sankhya: Creation, 3 gunas, Physical reality etc. 

4: Yoga : Mind, Meditation, States of Consciousness 

5.Purva-Mimansa: Linguistics, Analysis of Vedas. 

6: Uttar-Mimamsa: Liberation, Soul, Metaphysics etc. Bhagvad Geeta and Upanishads are a part of this school. 

Contrary to the popular belief, the word Aastik and Naastik in Indic context are meant to signify the ones who consider Vedas to be the supreme authority and the ones which do not. Certain Aastik Darshans don't believe in existense of God (the present day concept of God to be specific), and had full liberty to do so since their advent.

Indian Philosophy has always been a very rich tradition of discussion and contemplation. Considering Indian Darshan to be of a handful of selected scriptures is disregarding this rich tradition of scholars and Rishis. As inquisitive souls of this rich tradition, one needs to realize the benefits of studying these Darshans are way beyond just philosophy and make an attempt to understand their basics. 

Dr. Karan Mittal 

MBBS, MA (Sanskrit) MA (Clinical Psychology). 

To be continued...

The unknown History of Hypotenuse

The unknown History of Hypotenuse

"Sum of squares of two sides of a right-angled triangle is equal to square of its Hypotenuse ".... A theorem which we have learnt all throughout our school days, popularly known as the 'Pythagoras theorem' .
But, was there any reference to this great inseparable theorem of Geometry in ancient India?

The Shulba Sutras of Vedic Literature are the texts of Ancient Indian Geometry. Out of the many available Shulba sutras composed by different Rishis, Baudhayan Shulba sutra (c.800 BCE) has one of the earliest references to this theorem in context of Geometric applications.This was about 300 years before the date of historical Pythagoras of Samos.The verse in the text is as follows:

दीर्घचतुरस्रस्याक्ष्णया रज्जुः पार्श्वमानी तिर्यग् मानी च यत् पृथग् भूते कुरूतस्तदुभयं करोति ॥

A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together.
In other words: a2=b2+c2

Later in the course of time, Apastambha Rishi and Katyayan Rishi also give reference to these rules in their Shulba sutra texts and elaborate them further.

Although by the Sutra (Aphorism) nature of Shulba texts, its difficult to expect any elaboration of these rules in the texts. But, its certain that the composers of Shulba sutras definitely knew about this theorem.
An unique feature about the composers of various Shulba sutras was that all of them were Rishis and have various Ritual texts (Shraut sutras, Grihya sutras) attributed to them apart from these Geometric texts. Another unique feature being, these mathematical findings were made to arrive at accurate dimensions for creating Yagya Vedis for Fire sacrifices ( Such a high standard for perfection even in Religious rituals!!!). Since these fire rituals were necessary for all householders, it would be safe to assume that people in Vedic era knew the application of this theorem in construction of Yagya Vedis atleast.


There are definitely evidences of knowledge of Pythagorean triplets in Babylonian and Egyptian civilizations. Even the historicity of Pythagoras himself is debated in academic circles.
In Indic context,  with the passage of time, many Sutra texts of Ancient Indian literature have disappeared and many still remain untouched as manuscripts in various museums and libraries. There is still a huge amount of literature which needs to be studied and deciphered.

We as a civilization need to acknowledge our contributions to the journey of scientific achievements of mankind and strive to continue this legacy further!

Life of perfect irrational π

Bharat Musings

Life of perfect irrational π

Geometry lessons are always incomplete without the use of the unique number 'π'. As complicated as its multiplication is, so is its tradition of coming to the value of 3.1416.....

The earliest reference to this value is found in civilizations of Egyptians, Babylonians, Chinese and many more. But where is the contribution of India in this tradition? Have we read about the contribution of Indic scholars in this life of Pi or do we assume it to be completely a discovery of west? 

Indian Vedic literature's component 'Shulba Sutras' (c.800 BCE)  are ancient texts of Indian Geometry. Written for construction of altars for Yagya with precise measurements, these texts contain the earliest material of Indian Geometry. Each of the 4 Vedas have multiple Shulba Sutras under their domain attributed to various Rishis like Apastambha, Baudhayan, Manava and many more. 

The earliest approximation to the value of π in the Indic context comes in Shulba Sutras. Manava Shulba Sutras (c.750 BCE) has mention of approximate value of π to 3.125. In the Baudhayana Sulbasutra (c. 800 BCE) , various approximate values given are 676/225, 900/289 etc. In different Sulbasutras, the values 2.99, 3.00, 3.004, 3.029, 3.047, 3.088, 3.1141, 3.16049 and 3.2022 can all be found. There are various values of π given in Mahabharat, Shatpath Brahaman as well. 

Aryabhatta ( c. 400 CE) in his text Aryabhatiya gives the the accurate value of upto 4 decimal places and also mentions it to be an approximation ( recognising the never ending decimal places). The verse in Aryabhatiya is as follows :

चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्त्राणाम्।

अयुतद्वयस्य विष्कम्भस्य आसन्नौ वृत्तपरिणाहः॥

Add 4 to 100, multiply by 8 and add to 62,000. This is approximately the circumference of a circle whose diameter is 20,000.

(100 + 4) x 8 + 62,000 = 62,832

62832÷20000= 3.1416 = π

Later in 14th century, Indian Mathematician, Madhav gave the correct value of π upto 11 decimal places. This was about 300 years before Gregory and Lebnitz proposed the series to arrive at the value of π. Therefore many historians now call this series of numbers as Madhav-Gregory-Lebnitz series. 

Bharat always had a rich tradition of Rishis who have contemplated on Philosophy and Science both together. The expert town planning of Indus Valley civilization points to existence of advanced mathematics in some form as well. It's essential that one recognises this rich scientific Indian heritage and takes pride in being one. 

Dr.Karan Mittal 

MBBS, MA (Clinical Psychology), MA (Sanskrit).

Dharma Musings

 

Musings of a Medic

Dharma is one of the most used as well as misinterpreted terms in Indic context. Conventionally translated as religion, but does this Sanskrit term actually mean religion?
The word Dharma comes from root 'Dhr' which means 'to hold' or 'to sustain'. But what does it actually hold or sustain?
Dharma finds its place in the four Purusharths of Sanaatan Tradition : Dharma, Artha, Kaama, Moksha. If the definition of Dharma is religion, aren't the latter three a part of it?

The meaning attributed to the word Dharma is quite dynamic and has many dimensions to it. Understanding it completely requires a proper understanding of the Sanaatan tradition and its scriptures.
However to begin with, the nearest English equivalent to the word Dharma is 'Duty' or 'Righteousness'. Connecting it with the above etymology, its the Duty or Righteous behavior that upholds or sustains the Cosmic order.
Having many layers to it, Dharma begins at Individuality and lastly encompasses Universality.

A verse in Mahabharat defines Dharma as one that brings evolution of Individuals:

प्रभवार्थाय भूतानां धर्मप्रवचनं कृतम्।
यः स्यात्प्रभवसंयुक्तः स धर्म इति निश्चयः।।

It is the cause of both Preyas (materialistic progress) and Nishreyas (spiritual progress).  Arth ( Economic progress) and Kama (Desire) become worthwhile if bound by tenets of  Dharma. [What a profound way of regularising social order!].
Dharma as a whole has four levels which need to be adhered to:

Vyashti : One's duty towards oneself.
Samshti : One's duty towards society.
Srishti : One's duty towards Nature.
Parmeshti: One's duty towards spiritual progress or God.

All the four aspects are to be taken into account to follow the Dharmic way of life.
Doing religious rituals on a cost of avoiding family responsibilities is not Dharma. Wasting natural resources like electricity, water and not being mindful about the 'Srishti' is not Dharma.

So the popular conception of equating Dharma with Religion was never true. Religious practices could be a component of Dharma but never can constitute it as a whole!!!

Dr. Karan Mittal
MBBS, MA (Clinical Psychology), MA (Sanskrit)