The Indic Mathematical Tradition 6000 BCE To ?

[Sunder]

<!--QuoteBegin-Pandyan+Jun 19 2008, 11:16 PM-->QUOTE(Pandyan @ Jun 19 2008, 11:16 PM)<!--QuoteEBegin-->It seems like most of the ancient mathematicians were Brahmin, are there examples of other castes being mathematicians?
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Does it really matter what caste anyone belonged to or to dig into the 'influence of caste system on Indian mathematics'? at most this knowledge will serve the purpose of gloating or to drive a wedge further between the already fragile society. Is there any other reason to know the castes of mathematicians other than knowing them as Dharmic fold or Indians?

[Bodhi]

<!--QuoteBegin-Husky+Jun 20 2008, 06:40 PM-->QUOTE(Husky @ Jun 20 2008, 06:40 PM)<!--QuoteEBegin--><!--QuoteBegin-Pandyan+Jun 19 2008, 11:16 PM--><div class='quotetop'>QUOTE(Pandyan @ Jun 19 2008, 11:16 PM)<!--QuoteEBegin-->It seems like most of the ancient mathematicians were Brahmin, are there examples of other castes being mathematicians?[right][snapback]83046[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->(Insert: there were also Jaina mathematicians in our history.)

Don't know the answer to your question. But just to state the obvious: any Hindu's accomplishments are <i>all</i> Hindus' accomplishments. They were meant for all Hindus.
[right][snapback]83074[/snapback][/right]
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hemachandra, one of the scholars/mathematician, was born from a jaina mother (likely kshatriya) and a brAhmaNa father.

But I shall second wholeheartedly what Sunder said.

[Hauma Hamiddha]

From what we can glean the majority were brAhmaNa-s. This was followed by vaishya-s. The jaina mathematicians were mainly vaishya-s and then there were several kShatriya-s too. Both in the chera country and in Rajasthan we had multiple kShatriya-s

[Pandyan]

This question simply arose out of curiosity, that's all. I was looking at a list of Indian Mathematicians and most of them seemed to be Brahmins. Me, not being a Brahmin, wanted to know if there were contributions from other castes as well.

[G.Subramaniam]

<!--QuoteBegin-Pandyan+Jun 20 2008, 08:47 PM-->QUOTE(Pandyan @ Jun 20 2008, 08:47 PM)<!--QuoteEBegin-->This question simply arose out of curiosity, that's all. I was looking at a list of Indian Mathematicians and most of them seemed to be Brahmins. Me, not being a Brahmin, wanted to know if there were contributions from other castes as well.
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http://en.wikipedia.org/wiki/Indian_mathematics

Jaina Mathematics (400 BCE - 200 CE)

Although Jainism as a religion and philosophy predates its most famous exponent, Mahavira (6th century BC), who was a contemporary of Gautama Buddha, most Jaina texts on mathematical topics were composed after the 6th century BCE. Jaina mathematicians are important historically as crucial links between the mathematics of the Vedic period and that of the "Classical period."

A significant historical contribution of Jaina mathematicians lay in their freeing Indian mathematics from its religious and ritualistic constraints. In particular, their fascination with the enumeration of very large numbers and infinities, led them to classify numbers into three classes: enumerable, innumerable and infinite. Not content with a simple notion of infinity, they went on to define five different types of infinity: the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere, and the infinite perpetually. In addition, Jaina mathematicians devised notations for simple powers (and exponents) of numbers like squares and cubes, which enabled them to define simple algebraic equations (beezganit samikaran). Jaina mathematicians were apparently also the first to use the word shunya (literally void in Sanskrit) to refer to zero. More than a millennium later, their appellation became the English word "zero" after a tortuous journey of translations and transliterations from India to Europe . (See Zero: Etymology.)

In addition to Surya Prajnapti, important Jaina works on mathematics included the Vaishali Ganit (c. 3rd century BCE); the Sthananga Sutra (fl. 300 BCE - 200 CE); the Anoyogdwar Sutra (fl. 200 BCE - 100 CE); and the Satkhandagama (c. 2nd century CE). Important Jaina mathematicians included Bhadrabahu (d. 298 BCE), the author of two astronomical works, the Bhadrabahavi-Samhita and a commentary on the Surya Prajinapti; Yativrisham Acharya (c. 176 BCE), who authored a mathematical text called Tiloyapannati; and Umasvati (c. 150 BCE), who, although better known for his influential writings on Jaina philosophy and metaphysics, composed a mathematical work called Tattwarthadhigama-Sutra Bhashya.

[Husky]

<!--QuoteBegin-Pandyan+Jun 20 2008, 08:47 PM-->QUOTE(Pandyan @ Jun 20 2008, 08:47 PM)<!--QuoteEBegin-->Me, not being a Brahmin, wanted to know if there were contributions from other castes as well.[right][snapback]83086[/snapback][/right]<!--QuoteEnd--><!--QuoteEEnd-->You're a Hindu/Dharmic. That's all that's necessary to know, and it's certainly all that is necessary in order to have an equal share in it. Never let anyone convince you differently.

Everything any Hindu ever did is our inheritance. The Shaivite dynasty in Afghanistan (Shahiyas) kept islam at bay? We are Hindus, they were Hindus - therefore we are their only direct descendants and are so in the only sense that matters. The rest is nitpicking about details (distance, time). The Chozhas and Pandyas - your chosen username! - built Tamizh Hindu Kovils? Hence Kashmiri and Bengali Hindus can boast with equal shamelessness about the magnificent Temples their ancestors of TN built.
This has always been Hindu/Dharmic mentality. That's why when the older members of my family narrated episodes from the Itihasas and Puranas, they tell it in the way that comes naturally to us all: "Then, our Rama and Sita left for the forest accompanied by Lakshmana." My family is neither from Ayodhya nor descended from Rama nor are they Kshatriyas. (Of course, Rama is <i>also</i> "our" in a different sense.) Similar for the retellings of how Pandavas did this and that (Kauravas are never "our", of course <!--emo&--><img src='style_emoticons/<#EMO_DIR#>/smile.gif' border='0' style='vertical-align:middle' alt='smile.gif' /><!--endemo-->) and for how various Rajas of TN built Kovil X for Umachi or fought Rakshasa Y according to local historical traditions.

Whatever our Hindu ancestors did - regardless of their community - is the heritage of all Hindus. The background of a historical Dharmic is immaterial. (The only time this is brought up is when people get brainwashed into saying community X did not contribute.)
What they did is all of ours by right. All the people who served our country and Dharma in their many ways - whether they are named and remembered by name today or whether they worked anonymously (and regardless of how insignificant they imagined their own contributions were at the time) - all those people are our ancestors. And everything they did mattered and matters to us, and it's inconsequential how grand their efforts may or may not have turned out some centuries down the track (remember that humans contribute in small ways as well as large, though people tend to notice only the large kind). What they did and/or achieved is a maalai ("garland") for our Dharma. And we are the inheritors of that. No one else.

For instance, I have no reservations about mentioning how everything that the Reddy Kings did (all the way in AP) are the work of my Hindu ancestors. Because they are. Therefore it is not wrong for me to state the obvious.

So what I'm saying is: You have every right to ownership. No one can deny it you. Take it then.

[Bharatvarsh]

Can anyone shed light on ancient Hindu theories on "light" or give any referrals. I mean, was there awareness in India about the refraction of white light as Newton demonstrated etc.

[Husky]

<!--QuoteBegin-Bharatvarsh+Jun 21 2008, 07:25 AM-->QUOTE(Bharatvarsh @ Jun 21 2008, 07:25 AM)<!--QuoteEBegin-->Can anyone shed light on ancient Hindu theories on "light" or give any referrals. I mean, was there awareness in India about the refraction of white light as Newton demonstrated etc.
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<!--QuoteEnd--><!--QuoteEEnd-->Don't know. But the following is sort of related to light:

Brhatsamhita, chapter 35. ("6th century CE")
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The multi-coloured rays of the Sun,
being dispersed in a cloudy sky,
are seen in the form of a bow,
which is called the Rainbow.
<!--QuoteEnd--><!--QuoteEEnd-->Last line in the Samskritam text reads like (don't know if I have transliterated the characters correctly):
<i>ye drshyante tadindradhanuH</i>. Last bit, "Indra's bow"?

Sayanaacharya comments on the rik-samhita 1.50.4:
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->"It is rememembered that the sunlight travels 2,202 yojanas in half a nimisha."<!--QuoteEnd--><!--QuoteEEnd-->Calc given:<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->1 yojana = 9 miles
110 yards = 9.6025 miles
2,202 yojanas = 21,144.705 miles
Time taken = 1/2 nimisha = 1/8.75 (seconds) = 0.114286 seconds
Thus speed of light = 1,85,016.169 miles/second
Modern value = 1,86,000 miles/second
[Michaelson and Morley discovered the velocity of light in the 19th century AD.]
<!--QuoteEnd--><!--QuoteEEnd-->Q: Is 1 yojana exactly 9 miles?

Aryabhatiyam-GolapaadaH 37 - "499CE" on the cause of eclipse:
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The moon covers the sun and the great shadow of the earth covers the moon.<!--QuoteEnd--><!--QuoteEEnd-->
The above taken from the book "Science in Samskrit".

[G.Subramaniam]

In those days, the brahmins were supported financially and socially by the rest of the community, who in fact provided the infrastructure and a non-hostile environment which allowed the brahmins to do their research
The entire Dharmic society therefore has credit,

edited

[Husky]

Just to clarify what I meant in #126 when I said that all Hindus have an equal share in all Hindus' accomplishments:
What I meant was in the sense of members of a family cutting up vegetables to go into a vegebroth. The entire vegebroth is the ultimate goal of everyone: that they can all together partake of that. No one cares how many vegetables each person put in there, since the goal is to make the broth and eat it together and for the whole family to be satisfied with it.
(If in the above we make broth=Moksha, my pathetic analogy may be more sensible than I had anticipated it could be when I cooked it up.)

In that sense alone did I mean that any Hindu's actions in serving Dharma (including Hindus' accomplishments) belong to all Hindus/Dharmics.


(I therefore did not mean 'share' as in like a grateful acknowledgement that comes at the start of someone's thesis, listing the people who helped/inspired/contributed.)

[G.Subramaniam]

deleted

[Bharatvarsh]

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->In ancient India, the philosophical schools of Samkhya and Vaisheshika, from around the 6th – 5th century BCE, developed theories on light. According to the Samkhya school, light is one of the five fundamental "subtle" elements (tanmatra) out of which emerge the gross elements. The atomicity of these elements is not specifically mentioned and it appears that they were actually taken to be continuous.

According to the Vaisheshika school, motion is defined in terms of the movement of the physical atoms and it appears that it is taken to be non-instantaneous. Light rays are taken to be a stream of high velocity of tejas (fire) atoms. The particles of light can exhibit different characteristics depending on the speed and the arrangements of the tejas atoms. Around the first century, the Vishnu Purana refers to sunlight as "the seven rays of the sun".

Later in 499, Aryabhata, who proposed a heliocentric solar system of gravitation in his Aryabhatiya, wrote that the planets and the Moon do not have their own light but reflect the light of the Sun.[citation needed]

The Indian Buddhists, such as Dignāga in the 5th century and Dharmakirti in the 7th century, developed a type of atomism that is a philosophy about reality being composed of atomic entities that are momentary flashes of light or energy. They viewed light as being an atomic entity equivalent to energy, similar to the modern concept of photons, though they also viewed all matter as being composed of these light/energy particles.

http://en.wikipedia.org/wiki/Science_and_t...n_ancient_India<!--QuoteEnd--><!--QuoteEEnd-->

[Bharatvarsh]

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->The Àryabhatiya of Àryabhata: The oldest exact astronomical constant?

© 1998 by James Q. Jacobs

http://www.jqjacobs.net/astro/aryabhata.html<!--QuoteEnd--><!--QuoteEEnd-->
Interesting article, at the end he asks some questions, I am no expert on this subject, perhaps knowledgable people can email him if they know the answers.
<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->SOME QUESTIONS:

At this rewriting, Jan. 1, 2001, I still await some answers to the questions posed below. This may be indicative of the answers. To date I have found no indication of older accurate astronomical constants or published indications of modern writers noticing the accuracy of the data discovered in the Indian sources.

Do you know of any source previously noticing and publishing the accuracy of Àryabhata's ratio?
Do you know of any older record reflecting such an accurate astronomic ratio? From India? In Sanskrit? From other parts of the world?
Do you know of any astronomic record reflecting such an accurate astronomic ratio prior to the last two centuries?
When did modern astronomers first arrive at an astronomic ratio of comparable accuracy?
The WWW is interactive. You can contribute to this niche of knowledge. If you can comment on or answer any of the questions posed please e-mail me your data: Contact. If your contribution is used to update this material, you will be credited. I do not read Sanskrit. If you do, and you have read the original works, your contributions will be especially appreciated.

FURTHER COMMENTS

2007.08.22. In response to the questions above, I have received few replies in nearly a decade now. Today I received an interesting observation from Clive Ross. In part, Mr. Ross wrote:

Earth years 1,582,237,500/365.256336 = 4,331,855.04 years. Now we know that nobody recorded planet motion for 4,331,855.04 years, therefore the number is significant.it is relevant to something. Evaluating: Jupiter orbits the Sun in 4332.5 days .compare to the number of Earth days chosen by the author when converted to Earth years. 4,331,855.04 . 1000 times the days for Jupiter to orbit the Sun.! <!--QuoteEnd--><!--QuoteEEnd-->

[G.Subramaniam]

Update on vedic math

I have reviewed a lot of texts

and the best book is
the 3 volume ( 3 x $10 ) teachers manuals by Kenneth Williams
available from vedicbooks.net

Much better than kumon etc

Goes all the way into algebra and trignometry

[Bodhi]

<span style='color:red'>Science of fingerprinting in ancient India</span>

Sir William Herschel (1833-1917), an English officer, started studying fingerprints when he was posted in India during the later half of nineteenth century. He propounded the concept of ridge persistency, according to which the patterns of criss-cross lines on the fingertips or palms of an individual remain unchanged from birth till death. He also made it mandatory for the natives to impress their handprints or fingerprints on official documents. Word quickly spread that Herschel was the first pioneer to recognize the utility of fingerprints for identification purposes. However, this was fallacy, for Indians knew about the science of fingerprinting much before the English had an inkling of it.

"Indian civilization and the science of fingerprinting" by G S Sodhi and Jasjeet Kaur, Indian Journal of Traditional Knowledge, Vol. 2(2), April 2003, pp. 137-147

===

Mods, either please change the subject of the thread to "Scientific Progress in Ancient India", or if it were desirable to have a dedicated thread for mathematics (quite understandable) then please consider starting a thread on "Scientific Progress in Ancient India"... or is there already a thread like that>

[Bodhi]

On the mathematical significance of the dimensions of the Delhi Iron Pillar

R. Balasubramaniam
Department of Materials and Metallurgical Engineering
Indian Institute of Technology, Kanpur 208 016, India

The dimensions of the 1600-year-old Delhi Iron Pillar have been re-analysed in light of new scholarship on the traditional Indian unit of measurement. The dimensions of the pillar can be well reconciled considering the basic unit of measurement as 17.63 mm. The low percentage errors between the theoretical and actual measurements provide further support to this analysis. The significant mathematical ratios embedded in the relative dimensions of the pillar have also been set forth. The close association of the basic unit of measurement and the mathematical ratios with those of the Harappan civilization offers evidence for continuity of scientific ideas and traditions from the Harappan civilization to
the Ganga civilization. Analysis of dimensions of the characters of the Gupta–Brahmi inscription revealed the possible use of the decimal system.

http://www.ias.ac.in/currsci/sep252008/766.pdf

[Guest]

I ave tried to make sense of the particular ethos of the Indic and have tried to decipher the common characteristics of the pramana or the episteme with which he created his weltanschuung I presented this at Himachal pradesh u to a fairly diverse audience of students and faculty. The presentation can be viewed at

http://www.scribd.com/doc/12723723/Indic-I...patibility-Mode

I would like to have the comments of the fairly high number of heavyweights who frequent this forum, on
1. whether the tale hangs together2. are there any glaring lacunae in the assumptions or assertions

Of course i have restricted my remarks to the narrow field of subjects that i have some knowledge of

Thank you in advance

[Bharatvarsh]

<!--QuoteBegin-->QUOTE<!--QuoteEBegin-->A report in Pune Mirror by Piali Banerji

Not Newton, but Madhava!

Prof K Ramasubramanian of IIT-Bombay has news for us that we´d all love to hear. His recently released two-volume translation of the Ganita-Yukti-Bhasa by Jyesthdeva points to the fact that some subsets of calculus existed in Indian manuscripts almost two centuries before Isaac Newton published his work. And that an Indian mathematician and astronomer Nilakantha Somayaji spoke, in parts, about a planetary model, credited to Tycho Brahe almost a century later.

Chak de India? "Let´s not get over-excited," laughs Ramasubramanian. "Let´s present the facts instead."
Presenting excerpts of a conversation with the professor - a physicist and Sanskrit scholar, who has been working on the history of science for years now.

How old is the Ganita-Yukti-Bhasa?
It was published some time between 1530 and 1540. However, what´s important is that the material in this book is far older. For, the author makes it clear that his manuscript only explains in detail the work described in the Tantra Sangraha by Nilakantha Somayaji. So the work spoken about is actually much older, as Nilakantha in the 15th century.

What is the Ganita-Yukti-Bhasa about? 
It is divided into 15 chapters. Seven chapters are devoted to mathematics, and eight to astronomy. (By the way, it´s written in Malayalam, not Sanskrit. And I´ve translated it along with M D Srinivas and M S
Sriram.)

And the Tantra Sangraha?
The Tantra Sangraha is a treatise on astronomy and related mathematics in elegant verse form, in Sanskrit. It consists of 432 verses.

How much of Tycho Brahe´s theory existed in this ancient manuscript?
Well, in the Tantra Sangraha, Nilakantha talks about a planetary model where five planets, which can be seen with the naked eye - Mercury, Venus, Mars, Jupiter and Saturn - move around the sun, which in turn moves around the earth. The fact remains that a century later, Tycho Brahe published the same planetary model and was credited for it, since no one knew of Nilakantha´s work.

The Ganita-Yukti-Bhasa also points to the fact that first work on calculus began in India?
Well, the Ganita-Yukti-Bhasa attributes its mathematical models work to Madhava, who lived from 1340 to 1420. That´s way ahead of Newton. But it would be too sweeping a statement to say that this was the first work on calculus. Yes, some of the notions described in the book form a subset of calculus. That´s a fact.

Could you give an example?
The infinite series for the pi, the arc tangent, the sine and cosine functions. The value of the pi, for instance - expressing quantity in the form of an infinite series, came two centuries before calculus was formally developed by Newton and Leibniz. In a different context, perhaps, and expressed in a different way. But it did exist. Obtaining a fast convergent from a slow convergent is a major development in mathematical analysis. This too existed in this book, though in a different way.

How is it different?
Madhava and Nilakantha don´t take a formalistic approach to mathematics, the way we do now, having followed Euclid´s method of mathematics. Euclid´s method is a formal, deductive approach. This is a different approach. Now we need to question whether the formalistic approach is the only approach, or the `correct´ approach. And it´s a very fundamental question.

So what´s the relevance of these findings?
It´s not to show the superiority of Indian mathematicians. I´m only interested in presenting the correct history of the evolution of mathematics.

Can we get credit for the work of our ancient mathematicians?
Our mathematicians haven´t got their due credit due to two reasons. One is that the western world is largely ignorant of ancient Indian work. The second is that some very tall and inappropriate claims have been made about Indian work, in the past. For instance, there was a claim that differential equations existed in Vedic mathematics. Such tall claims only put us back and we´re not taken seriously.

Can saving the Sanskrit language in India put things right to some extent?
I don´t think the Sanskrit language is under threat in India. The language can be saved. It´s Sanskrit scientific texts that really need saving.

What are you working on next?
I´m working on other works of Nilakantha.

http://www.mumbaimirror.com/net/mmpaper.as...216155316003718<!--QuoteEnd--><!--QuoteEEnd-->

[acharya]

<b>History 2D: Science, Magic, and Religion, Lecture 1, UCLA

SINCE IN HISTORY
Lecture Title: "Course Introduction"</b>

March 31st, 2009

Professor Courtenay Raia lectures on science and religion as historical phenomena that have evolved over time. Examines the earlier mind-set before 1700 when into science fitted elements that came eventually to be seen as magical. THe course also question how Western cosmologies became "disenchanted." Magical tradition transformed into modern mysticisms is also examined as well as the political implications of these movements. Includes discussion concerning science in totalitarian settings as well as "big science" during the Cold War.

Spring 2009

http://www.youtube.com/watch?v=K3Zx-qcNZf4

[ramana]

In a book called "The Post Colonial Studies Reader" edited by Ashcroft, Griffiths and Tiffin, published by Routledge, there is a chapter called, "Western Mathematics: The Secret Weapon of Imperialism" by Alan Bishop.

Kaushal and Acharya will give you pdf of the book at next IF-BRF mtg.