Ancient Indian Texts
sites.google.com
sites.google.com
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.
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.
I too find myself wondering what the world would be like if there were more crossover between the early mathematical cultures. A few pages of Fibonacci's Liber Abaci pretty much transformed European math.
I saw a couple criticisms of the page's overall tone; I wanted to direct people to the stuff I knew was pretty good. I don't know enough about things like the vastu shastra, but I've studied my math history pretty extensively and am more than happy to comment on that.
I'd give you that in its current marketed form it is astrological bullshit, but originally Vastu Shastra was a formal form of science [1] grounded on engineering principles and urban design. All persevering to obtain a 'calm' for the dweller.
One can still infer from the high precision N-S-E-W positioning of fairly huge ancient Hindu temples, historical remains of homes and dwellings, monasteries and other artefacts. Even the 1000+ step staircases in some of the forts and fortresses [2][3], transoceanic bridges [4] suggest the quality of math that was in play.
The choice and placement of stone, wood and metal w.r.t Sun, tropical climate and other ergonomic needs is simply mind blowing. Math has to be at the root of it.
Obviously not many records exist to substantiate the level of skill and academia prevalent at the time. I wish someone undertook a journey to research and substantiate just about "everything" that we have from Egypt to Indonesia (Hindu kingdoms spanned that far, yes!). At the risk of being shooed away by existing pride.
[1] http://en.wikipedia.org/wiki/Vastu_shastra
Even the wikipedia here, for example, says ... "while Vastu had long been essentially restricted to temple architecture..." which is completely wrong, and they defeat it in the third paragraph where they define "the Sanskrit word vastu means a dwelling or house with a corresponding plot of land" which is what Vaastu Shastra was all about, not temples alone.
[2] http://en.wikipedia.org/wiki/File:ChandBaori.jpg
Numerology is just as likely of a root.
http://3.bp.blogspot.com/-qzhiolzuxsw/UK0HEPH7x4I/AAAAAAAAH8...
http://1.bp.blogspot.com/-a7UIHnAfmH0/UK0Ga-RmigI/AAAAAAAAH5...
http://bldgblog.blogspot.com/2012/11/chand-baori.html
http://bldgblog.blogspot.com/2012/11/chand-baori.html
This is just an example. What do you think has higher probability of being used to build this?
1. Math and calculations or 2. Numerology?
"Root" makes it sound like the purpose of building the very nice step well is to prove a mathemathical point. I'd venture to say its primary purpose had something to do with water.
Patterns and repetition is what I see beyond that, which are fairly prevalent in art and architecture exactly because you can get to them by simple experimentation.
Got it. I volunteer to move out of this discussion because you could have as well said that primary purpose of stairs had something to do with going up or down?
Most architecture around the world from Eiffel tower to Pyramids to Angkorvat has something to do with proving a point. Usually the point is that 'we have achieved this engineering marvel, we have the capability to build this'.
By your logic people possibly got to Eiffel tower or Golden gate by simple pattern and repetition, even experimentation, devoid of any math. That's just plain stupid.
Of course math is involved. But those things were not built for the sake of math, their "roots" are in their respective functions (building something impressive, something religious, or crossing a bay).
Edit: I just checked your [4] http://en.wikipedia.org/wiki/Adam%27s_Bridge reference. You seem to be saying that this geological formation ("transoceanic bridge") is about mathematics too, implying it's man-made. If that's the case, we're playing by different rules of what "logic" means, and our discussion is completely pointless, no offense intended.
Yes, there isn't a proof that the bridge in question is man-made. I deliberately put it up there. GSI claims it 'may be man-made' but it stops at that. Here is something you might want to look at: Search about 'floating rocks of India' (Pumice rocks) that have specific gravity lower than sea water.
Once you dig deep into some of it, read through Ramayana and also dive into history of Sri Lanka, I am sure you'll find something really interesting. That's why in the parent comment I wished someone undertook the journey to capture and record "everything" that needs to be explored of history over there.
wait, what?? Clear to elaborate? I know alexander had a huge kingdom, i know gnehis khan conquered a very very large area of land. I know muslims had an ENORMOUS empire but this looks like news to me. So clear to elaborate? Specifics?
[1]http://en.wikipedia.org/wiki/Ashoka [2]http://en.wikipedia.org/wiki/History_of_Indonesia
Btw, I think you are right about the whole area not being in Hindu control at one point in time. The largest Indian kngdom i remember was of Ashoka, and even that din't completely cover all of modern day India+Pakistan (he gave up war right before conquering the south-most tip because he converted to Budhism).
I think Muslims actually ruled all of the south-asian subcontinent at one time. The Mughals
Here is a write up listing some studies and names of books to consider:
http://amlanroychowdhury.webs.com/antiquityofegypt.htm
For far eastern links, read about inter-marriages and relationships for a period of over two millennium between Ayodhya(India) and Seoul (South Korea) [1]. A search on the Kim clan and Princess Heo Hwang-ok and the spread of Buddhist/Hindu culture right up to Japanese coastline can be inferred.
This is kind of the spread of Hinduism in South East Asia [2] before convertists of other religions (like Muslims or Christianity) emanated.
http://en.wikipedia.org/wiki/Angkor_Wat Also try http://en.wikipedia.org/wiki/Hinduism_in_Indonesia
Indian rulers did not have much intentions of ruling outside India but in the ancient world presence of Hinduism had spread to Egypt to Indonesia and even China,Japan. Even though it was not that much successful as Buddhism or Jainism.
God this is going to be a long comment.
I don't know how immersed you are w.r.t Hinduism, which gave birth to, no rather off-shooted other religions like Buddhism & Jainism. Here I can only give a very top-level view to help you make an entry:
There are two epics of the Hindus: The Ramayana and the Mahabharata. Read both, they're brilliant classics. These two epics are stories about rise and fall of political power, affairs, conceit and ensuing wars between leaders of different Hindu kingdoms. Let's say kingdoms of an aggregate land mass we now call India, Sri Lanka, Afghanistan that stretches up to far, far east to places like Cambodia.
I could not confirm how far in the west did Hinduism spread out but will do so given that I am excited about it now.
Both epics are mythology by today's standards, but the stories in each are what Hindus vehemently believe as true. All (not most) of warring cities in both these epics exist inside and outside of India (or sunk under the ocean [1]) even today. I mean literally.
On axis of time, both these two epics are separated from each other by two 'Yugas' [2]. We are living in the Kaliyug where kali == machines and yug == time-frame. Yugas are of varying length, first being Satayug about 1,728,000 million years. Man exists during this period as life forms from scratch in this universe. Alexander was like a fucking second ago when you're talking ages of this length.
I suggest start with Yugas and you'll start seeing math, numbers, conclusions, geometric progressions and astronomy right in there. No need to accept anything is true or false, w.r.t written and confirmed history. But you'll love visiting places, and connecting it with the historical texts.
It goes up the Bohr's model of atom (Paramaṇu), the theory of what nucleus and subatomic particles were about (hell yes!), the nuclear bomb (Brahma Asthra) and how these were used in warfare, negotiation and peace keeping. Several other concepts of what seems similar to magic of quantum physics, treatment of time-space curvature, extraterrestrial life, theory of relativity and additional dimensions of gravitational physics (though refuted by modern practitioners of course) all exist in discussions. May or may not be correct, but the level of thought can be appreciated.
Astronomy, for example, scales to the level of predicting solar cycles, cycles of universe (311.04 trillion years?[3]), variable length of life of man/species, sub-sub-events like the ice age, age of the machines, age of only truth which you will find pretty fascinating to read, if not believable.
Let me just throw in the starting point [2]:
[1] http://en.wikipedia.org/wiki/Dwarka
[2] http://en.wikipedia.org/wiki/Yuga
[3] http://en.wikipedia.org/wiki/Metrics_of_time_in_Hinduism
A humble evidence based look at this: http://en.wikipedia.org/wiki/Cradle_of_civilization#Indian_s...
No known evidence shows anything meaningful in the civilization department happened before 4000BC.
Ayodhya, for example, the city of Ram exists even today [1]. You're an Indian, you'd know it of course. The modern version of this city is considered more than 9000 years old, that's roughly about 7000 BC on wards. Buy a plot of land in Ayodhya, start digging and you'll hit structures and temple tops of another buried city underneath as you go deeper.
[1] http://en.wikipedia.org/wiki/Ayodhya
This cave for example Bhimbetka [2], is between 50,000-200,000 years old. It is mentioned in epic Ramayana which has yet to be dated. Bhimbetka is declared a world heritage site, and gives a proof of homo erectus with skills in the Deccan area that early in time.
Some crazy estimates suggest approximately 100,000 to 900,000 years ago for Ramayana, but then it is a crazy estimate [3] indeed. There are pearls of available proof, mythology and craziness all over the place. Someone needs to connect them together so that we might get a better picture of it. Obviously I don't wish to over state the age of Hinduism, but it is mystic by virtue of its age for sure. It makes me lose my calm, ironically.
http://en.wikipedia.org/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81
http://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and_...
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/
You're saying fight one "propaganda" with another "propaganda"? LOL!
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?
(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...
http://blog.seattlepi.com/bookpatrol/2010/01/29/rare-bamboo-...
I've also seen the long-form bronze inscriptions in museums - but those are the exceptions. That's why they're in museums ;)
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.
Do you mean cultural heritage? I wouldn't call the culture so great now with the corruption in politics, etc.
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
Edit: What I mean by typical: http://youtu.be/RSHFzZmQPj0
Looks pretty accurate to me. All the best science comes from philosophers backed by feelings and visions instead of math.
Similarly, the modern ear hears "relativity" and can't help but think of Einsteinian relativity, but the adjective "Einsteinian" is not redundant as it is not the only idea of relativity. Relativity as a concept also goes back a long way, but it looked more like Galilean relativity (if indeed it was even that formalized, which it probably wasn't), which contains certain contradictions in it which can be determined with pure reasoning, and indeed may have been (see [1]).
The summary leads to misleading ideas about what the Indian philosophers really knew/discovered/thought, if for no other reason than there is no way to accurately summarize the ancient ideas in modern words that briefly; it is not clear to me whether the author of the linked web page is himself confused or being deliberately mendacious.
[1]: http://mathpages.com/rr/s3-07/3-07.htm , and indeed, the entire first half of that book or so. Among this book's many points is that physicists were seriously beginning to consider whether they were going to have to give up on the general idea of relativity until Einstein was able to rescue it.
But we have no evidence of any of this, and therefore we claim that it did not happen. That is not a very rational position to take. It should be clear by now that wonderfuly discoveries often happen in parallel in different geographical locations. Sometimes they are almost forgotten for generations until a historian discovers old documents. There is no good reason to believe that this kind of thing has been going on since Homo Sapiens first came to be.
The only real advantage that we have today is the law of large numbers and the network effect.
The last sentence is manifestly not true (we're not even genetically identical to each other, much less all of us to the earliest example of H. Sapiens, or even the earliest examples of H. Sapiens sapiens.)
And even if it was, the first doesn't follow from it: intellectual capacity may have an upper bound set by genetics, but realizing it is more than genetics, its environment starting in the vary early environment.
And nutrition is, manifestly, a big part of that.
> The only real advantage that we have today is the law of large numbers and the network effect.
And lots of other things; to name just one key one, the adoption of the scientific method which does a lot to help identify the useful ideas from the attractive-but-useless ones. Even if we were no better at thinking up ideas, we are a lot better at validating ideas, and its not just through numbers, its through approach. Because of an idea that was thought up, and widely adopted.
Maybe it's because such a huge population actually has an origin place and story going back quite far? I don't have an origin. I come from some vague stock of medium-tall people with transparent skin in northern europe where the sun don't shine. I've nothing of ancestry to fight for, so I'm not sure I can even understand how they approach the world largely focused on the past.
There are certain people (or very few tv shows) who re-build ancient machines which might not be needed in the current age. Because we acquire knowledge enough to live in a point-of-time.
Money is just "to get things done". Not sure if everyone gets it.
The answer is simple. "Human Thirst for knowledge never ends" and nobody really knows for sure where they are headed.
"The present" which we feel really proud of, will be called ancient and worthless in the future. Because, the knowledge of humans increases with time (or understanding of nature increases with generations, some become dumb over time as well)
"The future" few people have envisioned it (saints in ancient form - who didn't expect anything from anybody but wanted to spread the knowledge, "visionaries" in the current business world - who want to rule the world with money, etc)
"stand the test time" just because they are not accessible doesn't mean they didnt' stand the test time. We keep discovering the same things whichever has been told in the past and the same things will happen in future as well. Its just that we love to call it with different names.
Someone has to connect the dots. Nobody has time in the current world. Everyone just moves on.
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?
It seems like technoliterate civilizations are eventually replaced by fundamentalism then animism, perhaps?
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.
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...
Bhaskaracharya and the man who found zero:
http://jugad2.blogspot.in/2010/06/bhaskaracharya-and-man-who...
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.
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
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
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.
Definitely a Hindutva site.
[1] https://sites.google.com/site/ancientbharat/aeronautics
[2] http://en.wikipedia.org/wiki/Vaim%C4%81nika_Sh%C4%81stra
And, your point is?
That site also has collections about works of legit ancient Indian mathematicians, Vedas etc. So, you are going to disregard them because they're Hindus?
If somebody mentions about these things, then they're said to be peddling this so called Hindu propaganda. Now, THAT'S a real propaganda.
Propaganda: http://en.m.wikipedia.org/wiki/Propaganda
Ambedkar was very diplomatic in his criticisms towards them. Osho was not so kind. See: http://www.osho.com/library/online-library-rigveda-tulsidas-...
You can also see that the site claims that Jyotish is astronomy but it actually means astrology.
Here is the description of Saturn in one of the texts "Parashara Hora Sastra" http://archive.org/stream/ParasharaHoraSastra/BrihatParashar...
29. [Saturn] has an emaciated and long physique, has tawny eyes, is windy in temperament, has big teeth, is indolent and lame and has coarse hair.
What is legit or scientific about it?
Nothing. And no one here is claiming that all parts of these texts are to be taken as absolute fact with empirical proof. Most of it, as you mention, is riddled with imaginary stories probably because scientific discovery was being carried out by religious philosophers of that time.
However, there are parts of these texts that are legitimately impressive, philosophically or scientifically - and a blanket denial of that would be just as unjust as the 'filth'.
I have provided references to show that the basic 4 vedas are tribal in nature and there is no basis to claim them as the origin of other scientific oriented texts. I am not denying all of the texts as bad.
>>>You can also see that the site claims that Jyotish is astronomy but it actually means astrology.
Where? They do mention it as "astrology".
>>>In reality, the scriptures are filled with filth like procedures of sacrificial, bestiality and orgy rituals, calls upon gods to slaughter their enemies (who have stolen their herds), etc.
>>>29. [Saturn] has an emaciated and long physique, has tawny eyes, is windy in temperament, has big teeth, is indolent and lame and has coarse hair.
What is legit or scientific about it?
Have you heard of mythology, euhemerism, and personification? Out of all those stuff on that site, you zeroed-in on sacrificial rituals, description of Saturn, and dismissed everything as "filth"? Then, what is your say on Ganit Shastra, Kaam Shastra, Khagol Shastra to name a few?
Based on that logic, all these below must be filth and their sole purpose is to brainwash people:
http://en.wikipedia.org/wiki/Christian_mythology
http://en.wikipedia.org/wiki/Norse_mythology
http://en.wikipedia.org/wiki/Greek_mythology
Astrology is different from astronomy in the present day, but not in the past.