If you take a look at the math subsection (https://sites.google.com/site/ancientbharat/math) be aware that Brahmagupta was a beast of a mathematician. His sucessors, the two Bhaskaras, were ridiculously good as well. Their names aren't nearly as big as any of the European mathematicians you know, but they were powerhouses of math during Europe's dark ages.
Brahmagupta was pretty much the first recorded dude to use 0 in math, so he's got that going for him, and the only issue people take with his work is that he was weak around the indeterminate forms (e.g. claiming 0/0 = 0)[1]. His work on Pell's equation is pretty awesome too, but then we're veering into more esoteric mathematics, so I digress.
Bhaskara II invented a rough and early verison of differential calculus to calculate instaneous rates of change in the mid 1100s. Newton finished his Method of Fluxions in 1671. (Newton's work was independent of Bhaskara II's and is said to be far more rigourous with greather breadth and depth of usage and applications; I haven't read enough of either to be an honest source, but the claim seems reasonable.)
[1]For an ancient, though, this is understandable. We know that 0⨯0 = 0, that b|a iff a = b⨯k, and that a = bq + r, so it's reasonable to assume that since 0 = 0⨯0 + 0 and 0|0, that 0/0 = 0. (Phew!) When you pretty much codify 0 in math, I'll cut you a break on that one.
The 'problem' with Indian math was the general aversion (or ignorance) of the importance of the method of proof. The more well known works of Greek mathematics were great in emphasizing the importance of the concept of mathematical proof. Yet, Greek mathematics, with the exception of Archimedes and Diophantus had an aversion for arithmetic (especially the concept of infinity and infinitesimals) and algebra and an over-reliance on geometry[1]. Engaging in a bit of counter-factuals, if either of the following had happened: (1) Indians picking up on the method of proof, (2) Greeks adopting more arithmetic and algebra, history of mathematics may have looked significantly different than today.
However, the OP link has a ton of apologist/revisionist history with insufficient archaeological evidence mixed in with a little bit of the good stuff. Example: references to vastu shastra, which is astrological woo.
[1] Eric Temple Bell, 'The Development of Mathematics,' Dover, 1992.
//Ancient India was a land of sages, saints and seers as well as a land of scholars and scientists. Rishis were the sages who built our great culture. They devoted their life, energy and experience for the welfare of people. They wrote Vedas - the manual of vibrations. Following this many field of science evolved in India.
//
This is typical hindutva propaganda, where they claim that anything and everything originated from Vedic scriptures, which are for welfare of people.
The dates of ancient texts from India are claimed over a whole wide range. There is as much as 2,000 years of divergence between the earliest speculative date and absolutely attested known date for the Vedas, for example. A good outline of the issues in historiography of India can be found in Mathematics in India by Kim Plofker[1], who was trained both as a mathematician and Sanskrit scholar. Not always knowing when a particular text was composed has a lot of influence on knowing or not knowing which ideas appeared in what era in the development of science and mathematics in India.
(One difference between India and either China or the near east is that the writing materials used in India, often plaited sheets of palm leaves, were much less durable than the silk sheets or bamboo slats used in China, or the fired clay tablets or papyrus sheets or parchment hides used in the near east. So many of the earliest writings from India have perished, while remarkably old writings still exist from either China or Sumer.)
The oldest writings in China are not much more than 2,000 years old. Maybe you're thinking of oracle bones & bronze inscriptions? But those are rarely more than a sentence or two in isolation.
You may have picked up on the author's not-so-subtle self-congratulation in the use of the phrase: "our great culture".
There is a lot of wonderful material to be absorbed in the ancient texts of India, but the text of that page has a strong Hindu religious nationalist tone (which in Indian languages is called "Hindutva", or "Hindu-ness").
The vast (in time and space), and diverse Indian culture that produced these works was far more tolerant and open to the world's ideas than the apparent mindset of the individual(s) who created this site.
So try to enjoy the actual linked texts, but observe, and then ignore the religious nationalism that seems to have inspired the site.
This sort of topic has come up before, and to put it gently, blog posts like these have been lacking in context and substance. See a previous HN post:
https://news.ycombinator.com/item?id=4154755
Also see a previous HN post about a PNAS publication that talks about the people from current-day South India 4000 years ago (while South Indians' language is not based on Sanskrit, and 4000 years ago far predates the time period mentioned in the original post):
https://news.ycombinator.com/item?id=5078076
Yep ... I know that eye glasses and cataract surgery were done there first (the ruined lens was poked out of place with a copper wire, then a pair of glasses became the primary lens and the cornea became the secondary lens). And obviously you needed to be able to produce glass to make eye glasses. There was also early production of stainless steel.
I'm not as well-versed in Indian history as I should be ... with that kind of science, you would have expected a dominant technical culture but why was this knowledge lost instead?
>>you would have expected a dominant technical culture but why was this knowledge lost instead?
One word, Entropy!
As an Indian, I can tell you India has seen many cycles of ups and downs. And its not just mere technical culture, there is tons of other things. Food, literature, language, poetry, food, clothes, music, religions, philosophy and what not. I don't know any other country in the world comes close to matching this. Buddha arrived in India in around 500 BC. And that was one of India's peak times in Spiritual and philosophical tradition.
There are languages that are totally extinct, cultures that have faded away. Massive amounts of literature lost completely to mankind.
But Mainland India has been invaded many times, colonized, bulk of its wealth plundered. Add to this the overall entropy of the system.
A simple question to you would be like this. Can you be sure US will remain the world super power 200 years from now.
If there is a lesson to be learnt, it is that one should be humble about the notion of being the first to invent anything. I'm pretty sure the many of the concepts expressed in these texts go further back in time without any record. Everything is an addition or evolution of the past, regardless of whether it is explicitly or wittingly so.
I pass no comment on the site, but on assertions here about hindutva as hindu religious propaganda/nationalism. This is incorrect, hindutva does not proscribe or prescribe any religion.
Veer Savarkar's pamphlet on which modern notions of hindutva are based on can be read at [1]
Sarvakar includes all Indian religions in the term "Hinduism" and outlines his vision of a "Hindu Rashtra" (Hindu Nation) as "Akhand Bharat" (United India), stretching across the entire Indian subcontinent.
Hindu in the context of hindutva is not religious. It speaks about a common identity for a united nation. Savarkar's writing need to be read in the context of the period that they were written, English oppression and the fight for independence, before the idea of a muslim state, Pakistan were first proposed. During this time, India, Pakistan, Bangladesh were one nation commonly know not as India, but Hindustan. Hindustan represented not a Hindu state, but a country where people who shared the hindu ethos reside.
At the level of practice, the Hindutva or Hindu ethos, outlook boils down to upholding righteousness (Sat-guna) and fighting ignoble attitudes (Dur-guna).
Quoting Savarkar, "We Hindus are bound together not only by the tie of the love we bear to a common fatherland and by the common blood that courses through our veins and keeps our hearts throbbing and our affections warm, but also by the tie of the common homage we pay to our great civilization - our Hindu culture"
Modern India was founded at independence on the same beliefs, in the quote above replace hindus by India and hindu culture by Indian culture.
Please read the literature on the subject and not what is simply presented on modern pop culture.
"Bhaskara II gives the value of pi as 22/7 in the book but suggest a more accurate ratio of 3927/1250 for use in astronomical calculations."
I also remembered reading somewhere that some ancient Indians had a simple formula for pi that was somewhat accurate; take the first 3 odd positive integers, twice each, as one single number, split it down the middle, and divide the right half by the left half, i.e. 113355 => 355/113 = ~pi.
So I checked, using Python:
$ python
>>> from math import pi
>>> pi
3.141592653589793
>>> print 3927.0/1250
3.1416
>>> print 355.0/113
3.14159292035
The approximation that uses 113355 matches pi (from Python) upto 6 decimal places.
As someone who put in the years required to learn Classical Latin and Attic Greek I can but only heed you to make very, very sure you are willing to invest the enormous amount of time required to learn an ancient language.
If you have a normal job, wife and children, and can't find at minimum 2 hours out of your day to dedicate to language study, then don't bother. You will never read any Sanskrit at a comfortable pace if you can't commit to such an investment. I'm talking about picking up a book and not hitting an unknown word 3 times a sentence. You'll need at minimum 2 years of a full time schedule like before it even becomes fun.
It's the unfortunate and sad reality about the time commitment required in learning ancient languages to the level of fluency.
This is a hoax. The article reproduced there does exist though: it was published in an artificial intelligence journal in 1985 and made no reference to NASA, except for the fact that the author worked at the NASA Ames Research Center. You can find it there: http://www.aaai.org/ojs/index.php/aimagazine/article/view/46...
A quick search on internet for "sanskrit nasa" shows that all occurences are either copies, extracts or translations of this article taken out of its context. The belief that NASA has used sanskrit seems to come from this internet echo chamber.
I could find no reference about it on any NASA website, nor any other articles written by this Rick Briggs. I was able to find only one other article on sanskrit and AI, quoting the one by Briggs, dated to 1987: http://www.cedar.buffalo.edu/~srihari/papers/KRIS87.pdf
Indian culture was always inclusive in nature right from its point of origin.but now we only see it becoming exclusive and narrow concentrating only on the Hindu side of the culture.
Ancient texts should be considered as a philosophy rather than science, because almost nothing was formally proved that time, but lots of phenomena were correctly inferred or guessed.
Most famous insights, of course, were these about the nature of mind from the Upanishads, which uses state of sleep, deep-sleep (without dreams) and wakefulness as metaphors to illustrate what we now call "models of the world", "contexts", "cognitive dissonance", "frames of reference", or just the role of the mind (consciousness) in cognition - how we constantly distort, reinterpret and even ignore perceived reality.
Roughly, it was a notion clarified later by Buddha - "Life is shaped by our mind, we become what we think", the notion that all our (at least psychological) "suffering" begins (and ends) inside our skulls and doesn't exist in the world outside.
Another great notion was one of the Dzongchen sect of Tibetan Bon tradition, when they use analogy of a mirror to how our mind should "work" - as a mirror isn't affected by what it reflects, so the mind in its "primordial" (original, such that of a child) state is just a "tool" to "do everything", including things done by Buddha or Einstein.
More recent marvels from India including "Want to see a God - look between two thoughts" by "modern" saint Ramakrishna, which is "in continuum" back to Upanishads.
In short, in decent texts composed by highly intelligent authors (including so-called fiction) there is a possibility to find correct inferences and guesses for almost every observable phenomena, if your own mind is lucid enough.
I'm really confused by the comments that say the tone of this site is "Hindu nationalist". I see no mention of the word "Hindu" in the entire page. In fact, it's as far from politicized text as possible. Not everything on the web has some hidden meaning or subtext.
[+] [-] pflats|12 years ago|reply
Brahmagupta was pretty much the first recorded dude to use 0 in math, so he's got that going for him, and the only issue people take with his work is that he was weak around the indeterminate forms (e.g. claiming 0/0 = 0)[1]. His work on Pell's equation is pretty awesome too, but then we're veering into more esoteric mathematics, so I digress.
Bhaskara II invented a rough and early verison of differential calculus to calculate instaneous rates of change in the mid 1100s. Newton finished his Method of Fluxions in 1671. (Newton's work was independent of Bhaskara II's and is said to be far more rigourous with greather breadth and depth of usage and applications; I haven't read enough of either to be an honest source, but the claim seems reasonable.)
[1]For an ancient, though, this is understandable. We know that 0⨯0 = 0, that b|a iff a = b⨯k, and that a = bq + r, so it's reasonable to assume that since 0 = 0⨯0 + 0 and 0|0, that 0/0 = 0. (Phew!) When you pretty much codify 0 in math, I'll cut you a break on that one.
[+] [-] shas3|12 years ago|reply
However, the OP link has a ton of apologist/revisionist history with insufficient archaeological evidence mixed in with a little bit of the good stuff. Example: references to vastu shastra, which is astrological woo.
[1] Eric Temple Bell, 'The Development of Mathematics,' Dover, 1992.
[+] [-] unmole|12 years ago|reply
[+] [-] pramalin|12 years ago|reply
This is typical hindutva propaganda, where they claim that anything and everything originated from Vedic scriptures, which are for welfare of people.
Before buying into it, I would suggest the readers to review the works of Dr. Ambedkar such as Riddle In Hinduism. http://www.ambedkar.org/riddleinhinduism/
[+] [-] s-topper|12 years ago|reply
You're saying fight one "propaganda" with another "propaganda"? LOL!
[+] [-] the__prestige|12 years ago|reply
[+] [-] xerophtye|12 years ago|reply
Eh? What gives? How can people believe that?
PS: I thought the original Aryans brought the Vedas with them from central Asia, instead of the Rishis of India writing them. No?
[+] [-] tokenadult|12 years ago|reply
(One difference between India and either China or the near east is that the writing materials used in India, often plaited sheets of palm leaves, were much less durable than the silk sheets or bamboo slats used in China, or the fired clay tablets or papyrus sheets or parchment hides used in the near east. So many of the earliest writings from India have perished, while remarkably old writings still exist from either China or Sumer.)
[1] http://www.amazon.com/Mathematics-India-Kim-Plofker/dp/06911...
[+] [-] maaku|12 years ago|reply
[+] [-] djdj123|12 years ago|reply
There is a lot of wonderful material to be absorbed in the ancient texts of India, but the text of that page has a strong Hindu religious nationalist tone (which in Indian languages is called "Hindutva", or "Hindu-ness").
The vast (in time and space), and diverse Indian culture that produced these works was far more tolerant and open to the world's ideas than the apparent mindset of the individual(s) who created this site.
So try to enjoy the actual linked texts, but observe, and then ignore the religious nationalism that seems to have inspired the site.
[+] [-] unknown|12 years ago|reply
[deleted]
[+] [-] eklavya|12 years ago|reply
[+] [-] smoyer|12 years ago|reply
Do you mean cultural heritage? I wouldn't call the culture so great now with the corruption in politics, etc.
[+] [-] unknown|12 years ago|reply
[deleted]
[+] [-] elangoc|12 years ago|reply
Also see a previous HN post about a PNAS publication that talks about the people from current-day South India 4000 years ago (while South Indians' language is not based on Sanskrit, and 4000 years ago far predates the time period mentioned in the original post): https://news.ycombinator.com/item?id=5078076
[+] [-] unmole|12 years ago|reply
Edit: What I mean by typical: http://youtu.be/RSHFzZmQPj0
[+] [-] seiji|12 years ago|reply
Looks pretty accurate to me. All the best science comes from philosophers backed by feelings and visions instead of math.
[+] [-] managuru|12 years ago|reply
[+] [-] s-topper|12 years ago|reply
[+] [-] smoyer|12 years ago|reply
I'm not as well-versed in Indian history as I should be ... with that kind of science, you would have expected a dominant technical culture but why was this knowledge lost instead?
[+] [-] kamaal|12 years ago|reply
One word, Entropy!
As an Indian, I can tell you India has seen many cycles of ups and downs. And its not just mere technical culture, there is tons of other things. Food, literature, language, poetry, food, clothes, music, religions, philosophy and what not. I don't know any other country in the world comes close to matching this. Buddha arrived in India in around 500 BC. And that was one of India's peak times in Spiritual and philosophical tradition.
There are languages that are totally extinct, cultures that have faded away. Massive amounts of literature lost completely to mankind.
But Mainland India has been invaded many times, colonized, bulk of its wealth plundered. Add to this the overall entropy of the system.
A simple question to you would be like this. Can you be sure US will remain the world super power 200 years from now.
[+] [-] tomrod|12 years ago|reply
It seems like technoliterate civilizations are eventually replaced by fundamentalism then animism, perhaps?
[+] [-] the__prestige|12 years ago|reply
[+] [-] taway121|12 years ago|reply
Veer Savarkar's pamphlet on which modern notions of hindutva are based on can be read at [1]
Sarvakar includes all Indian religions in the term "Hinduism" and outlines his vision of a "Hindu Rashtra" (Hindu Nation) as "Akhand Bharat" (United India), stretching across the entire Indian subcontinent.
Hindu in the context of hindutva is not religious. It speaks about a common identity for a united nation. Savarkar's writing need to be read in the context of the period that they were written, English oppression and the fight for independence, before the idea of a muslim state, Pakistan were first proposed. During this time, India, Pakistan, Bangladesh were one nation commonly know not as India, but Hindustan. Hindustan represented not a Hindu state, but a country where people who shared the hindu ethos reside.
At the level of practice, the Hindutva or Hindu ethos, outlook boils down to upholding righteousness (Sat-guna) and fighting ignoble attitudes (Dur-guna).
Quoting Savarkar, "We Hindus are bound together not only by the tie of the love we bear to a common fatherland and by the common blood that courses through our veins and keeps our hearts throbbing and our affections warm, but also by the tie of the common homage we pay to our great civilization - our Hindu culture"
Modern India was founded at independence on the same beliefs, in the quote above replace hindus by India and hindu culture by Indian culture.
Please read the literature on the subject and not what is simply presented on modern pop culture.
[1] http://www.savarkar.org/content/pdfs/en/essentials_of_hindut...
[+] [-] selimthegrim|12 years ago|reply
[+] [-] vram22|12 years ago|reply
Bhaskaracharya and the man who found zero:
http://jugad2.blogspot.in/2010/06/bhaskaracharya-and-man-who...
[+] [-] vram22|12 years ago|reply
http://en.wikipedia.org/wiki/Lilavati
I noticed this at that page:
"Bhaskara II gives the value of pi as 22/7 in the book but suggest a more accurate ratio of 3927/1250 for use in astronomical calculations."
I also remembered reading somewhere that some ancient Indians had a simple formula for pi that was somewhat accurate; take the first 3 odd positive integers, twice each, as one single number, split it down the middle, and divide the right half by the left half, i.e. 113355 => 355/113 = ~pi.
So I checked, using Python:
$ python >>> from math import pi >>> pi 3.141592653589793
>>> print 3927.0/1250 3.1416
>>> print 355.0/113 3.14159292035
The approximation that uses 113355 matches pi (from Python) upto 6 decimal places.
[+] [-] Jonovono|12 years ago|reply
I have wanted to learn Sanskrit for a long time, and I think the stuff you could read after learning that would be interesting.
And then there is NASA (apparently) using Sanskrit for AI: http://www.vedicsciences.net/articles/sanskrit-nasa.html
[+] [-] laichzeit0|12 years ago|reply
If you have a normal job, wife and children, and can't find at minimum 2 hours out of your day to dedicate to language study, then don't bother. You will never read any Sanskrit at a comfortable pace if you can't commit to such an investment. I'm talking about picking up a book and not hitting an unknown word 3 times a sentence. You'll need at minimum 2 years of a full time schedule like before it even becomes fun.
It's the unfortunate and sad reality about the time commitment required in learning ancient languages to the level of fluency.
[+] [-] aktiur|12 years ago|reply
This is a hoax. The article reproduced there does exist though: it was published in an artificial intelligence journal in 1985 and made no reference to NASA, except for the fact that the author worked at the NASA Ames Research Center. You can find it there: http://www.aaai.org/ojs/index.php/aimagazine/article/view/46...
A quick search on internet for "sanskrit nasa" shows that all occurences are either copies, extracts or translations of this article taken out of its context. The belief that NASA has used sanskrit seems to come from this internet echo chamber.
I could find no reference about it on any NASA website, nor any other articles written by this Rick Briggs. I was able to find only one other article on sanskrit and AI, quoting the one by Briggs, dated to 1987: http://www.cedar.buffalo.edu/~srihari/papers/KRIS87.pdf
[+] [-] nitin1213|12 years ago|reply
[+] [-] anovikov|12 years ago|reply
[+] [-] dschiptsov|12 years ago|reply
Most famous insights, of course, were these about the nature of mind from the Upanishads, which uses state of sleep, deep-sleep (without dreams) and wakefulness as metaphors to illustrate what we now call "models of the world", "contexts", "cognitive dissonance", "frames of reference", or just the role of the mind (consciousness) in cognition - how we constantly distort, reinterpret and even ignore perceived reality.
Roughly, it was a notion clarified later by Buddha - "Life is shaped by our mind, we become what we think", the notion that all our (at least psychological) "suffering" begins (and ends) inside our skulls and doesn't exist in the world outside.
Another great notion was one of the Dzongchen sect of Tibetan Bon tradition, when they use analogy of a mirror to how our mind should "work" - as a mirror isn't affected by what it reflects, so the mind in its "primordial" (original, such that of a child) state is just a "tool" to "do everything", including things done by Buddha or Einstein.
More recent marvels from India including "Want to see a God - look between two thoughts" by "modern" saint Ramakrishna, which is "in continuum" back to Upanishads.
In short, in decent texts composed by highly intelligent authors (including so-called fiction) there is a possibility to find correct inferences and guesses for almost every observable phenomena, if your own mind is lucid enough.
[+] [-] yarou|12 years ago|reply
[+] [-] chattoraj|12 years ago|reply
Definitely a Hindutva site.
[1] https://sites.google.com/site/ancientbharat/aeronautics
[2] http://en.wikipedia.org/wiki/Vaim%C4%81nika_Sh%C4%81stra
[+] [-] pinkskip|12 years ago|reply