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Mushin Comedian Username: Mushin Post Number: 1343 Registered: 05-2015 Posted From: 219.74.71.214 Rating: N/A |
http://www.thehindu.com/news/cities/chennai/indian-music-mat hematically-deep/article8056375.ece Renowned mathematician strongly advocates including music in school curriculum. Making a strong case for including classical Indian music in the school curriculum, renowned mathematician Manjul Bhargava said it âcan help the country produce not just better artists, but better scientists, judges, innovators and in general, better humans.â To drive home the point that music make individuals highly creative, he quoted Steve Jobs, famous for his products that married top-notch aesthetics and engineering. âWhen asked how Macintosh had revolutionised computing, Steve Jobs remarked that it was because he loved to hire computer scientists who were also trained in fine arts, who showed far greater innovative ability,â he said. Addressing the Sadas of the Music Academy and conferring the Sangita Kalanidhi award on vocalist Sanjay Subrahmanyan, Mr. Bhargava, tabla player himself, said classical Indian music was mathematically deep and aesthetically complex and was an extremely expressive art. Mr. Bhargava, the R. Brandon Fradd Professor of Mathematics, Princeton University, said there was something about classical music that made one more creative even in other endeavours, reiterating that great mathematicians including Srinivasa Ramanujan and C.S. Seshadri had a classical musical background. Mr. Bhargava explained what many people were not aware was that Bharatha's Natyasastra and Sharagadeva's Sangita-ratnakara, the two groundbreaking works on music were also groundbreaking works on mathematics. Let us try to make classical Indian music part of school curriculum to make sure that this form of art continues to evoke the best from our young people,â he said. President of the Academy N. Murali said the Academy intended to make its contribution very soon to flood relief and rebuilding, including to musicians, affected by the recent floods. Sanjay Subrahmanyam said the two week of concerts and lecture demonstrations were self-fulfilling and rewarding experience. Earlier, Mr. Bhargava conferred Sangita Kala Acharya award on vidvan T.H. Subash Chandran and Mysore G.N. Nagamani Srinath. TTK awards were given to nagaswaram player Seshampatti T. Sivalingam and veena player Kamala Aswathama (not present due to ill health). The musicologist award went to Gowri Kuppuswamy. | ||
Mushin Comedian Username: Mushin Post Number: 1342 Registered: 05-2015 Posted From: 219.74.71.214 Rating: N/A |
 thanks for sharing....manjul bhargava never shys away from acknowledging scientific temper in ancient India..he even explained how some sanskrit verses proved fibonacci series https://youtu.be/2MCK3eVwTw4?t=15m54s | ||
Teluguhero Comedian Username: Teluguhero Post Number: 1722 Registered: 04-2008 Posted From: 63.151.12.167 Rating: N/A |
http://www.rediff.com/news/special/did-india-discover-pythog oras-theorem-a-top-mathematician-answers/20150109.htm Did India discover Pythagoras theorem? A top mathematician answers The Pythagoras theorem 'should either be an Egyptian theorem if you look at the standard of just having an idea about it, an Indian theorem if you're looking for a complete statement of it, or a Chinese theorem if you're looking for the proof of it,' Fields Medal winner and Princeton University Professor Dr Manjul Bhargava tells P Rajendran/Rediff.com It's really a subtle question -- where the Pythagorean theorem first originated," says Dr Manjul Bharagava, winner of the Fields Medal, the world's top prize in mathematics, when asked about the controversy over the claims of Indian origins of the theorem by Dr Harsh Vardhan, India's minister of science and technology. Dr Vardhan, a surgeon by training, made the claim at the 102nd Indian Science Congress in Mumbai, which also hit headlines for claims that included assertions of ancient inter-planetary flight, of herbal pastes being used on the feet to find underground water, ways to use dung with herbs and egg white to make natural plastics, and the performance of reconstruction plastic surgery 3,500 years ago. The Pythagorean theorem, which could be tested in a more evidence-based model, states that the square of the hypotenuse of a right triangle is the sum of the squares of its two legs. (usually framed as a2 + b2 = c2), where and c is the length of the hypotenuse, and a and b are the lengths of the two other sides. It is credited to Pythagoras of Samos, a mathematician, philosopher and religious leader. "It depends on what you mean (where the Pythagorean theorem first originated)," says Dr Bhargava, the Brandon Fradd professor of mathematics at Princeton University, adding that there are different levels of knowledge of the theorem. "One is the one that originates in 2,500 BC in Egypt," he adds. "There's no statement of the theorem anywhere, but there is some knowledge that seems to be indicated of it because there are (Pythagorean) triples (when the length of the three sides are whole numbers, such as 34, and 5)." While these are not written down, these ratios that satisfy the theorem can be seen in structures there. "These numbers that come up in 2,500 BC are like 3, 4, 5 and 5, 12, 13 -- some small triples that show some knowledge," says Dr Bhargava. "These could easily have come by trial and error or coincidences. There's no written evidence. There's a big probability that they had knowledge of it, but there's no hard evidence; it's more speculation." If the idea was just that "there's some inkling that something like the Pythagorean theorem is true, that definitely goes back to 2,500 BC," he says. According to Dr Bhargava, "The first systematic systems of listing a2 + b2 = c2 happens in the Plimpton tablets, which happen in about 1,800 BC (in Mesopotamia, or the modern-day Arab world). That shows a systematic understanding of producing solutions to that equation. That shows much more likelihood of knowledge of the Pythagorean theorem in a more general framework. But again there's no written statement of the theorem." He agrees that the very large triples seen on the tablets suggest that a good understanding of the idea is more likely. "I would guess they had a knowledge of the Pythagorean theorem," Dr Bhargava says, adding, "If you're looking for hard scientific evidence, it's completely conceivable that they were just looking at algebraic solutions to the equation a2 + b2 = c2 without any geometric connection because there's no... picture, no reference to any triangle. it's just an abstract equation: a2 + b2 = c2... There's not clear evidence that geometry was behind what they were doing -- although it's entirely possible." "These are the difficulties with history -- because we don't have a complete record of what they knew, we just have a little glimpse. But a2 + b2 = c2 comes naturally for number theorists, even when they're not thinking about triangles." Arguing again that there are different standards for empirical evidence, Dr Bhargava says, "If you're happy with a systematic solution to the equation that come up in the Pythagorean theorem even though there's not a complete statement, one would say it came up with the Babylonians in Mesopotamia around 1,800 BC." "Another standard would involve," he adds, "the requirement of a document that explicitly states the Pythagorean theorem -- the geometric theorem. That first occurs about 800 BC in India in the Shuba Sutra of Baudhayan." "There's the first explicitly written theorem that ways that if you have a right triangle, the square of the length of the hypotenuse is the sum of the square of the length of the two legs. That is written for the first time as a theorem for a general triangle in the Shuba Sutra of Baudhayan... At least, that's the first recorded instance." "In that sense, if you want hard scientific evidence, it's accurate to say that the Pythagorean theorem was first (recorded) in India in about 800 BC. Another standard could go beyond a mere statement," says Dr Bhargava. "One can go further than that -- which is the standard that mathematicians often use -- that while it's nice to have the explicit statement but if there's no proof well, then, maybe they (the ancient culture being studied) didn't know it," he says. "The Shuba Sutras do contain proofs in some special cases and contain numerical proofs in general, but the first actual rigorous proof of the Pythagorean theorem that's on record originates in China -- after the Shuba Sutra." "So in China in school textbooks they often call it the Gougu theorem. And that was first given in a Chinese manuscript some years later (the Zhou Bi Suan Jing, the material for which dates back to sometime between the 1046 BC and 256 BC)." "So maybe the statement of the theorem went from India to China, but the actual proof -- the complete, rigorous proof -- was given in China, at least as far as written records go. That's why the Chinese ... (named) the Pythagorean theorem after the person who first proved it (and) who was in China." According to Dr Bhargava, all these layers of information suggested the question of who discovered the theorem is not a well-defined one. "It depends on what standard you are using," he says. "But a very natural one for the common people is, well, where was it first stated explicitly. And for that India is the correct answer and it's certainly reasonable to say the Pythagorean theorem originated in India. But if you want to be really rigorous and (ask) who first totally understood even the proof of that then it would naturally be the Chinese." Dr Bhargava feels there is something to draw from the discussion. "The Pythagoras theorem is clearly the wrong name; that's clear," he says, laughing. "He (Pythagoras) clearly stated it way after it was stated in India. It is not clear that he proved it at all. From neither perspective -- the statement or the proof -- is the 'Pythagorean theorem' a correct name." "It should either be an Egyptian theorem if you look at the standard of just having an idea about it, an Indian theorem if you're looking for a complete statement of it, or a Chinese theorem if you're looking for the proof of it," he adds. Dr Bhargava agrees that nomenclature can be driven by more chauvinistic needs. "I think sometimes some nationalism, if it inspires them (students) to go into that subject and do well, it's OK as long as it's not false. And all these countries have a thoroughly legitimate claim to say the Pythagorean theorem is invented there. And they are all correct, depending on what standard they implement." Image: Professor Manjul Bhargava at Princeton. Kind courtesy: The Bhargava family | ||
Tilak Legend Username: Tilak Post Number: 36792 Registered: 02-2012 Posted From: 183.83.48.28 Rating: N/A |
sure, I get what you are saying! But we havent graduated to the level of fighting over star dust yet!  makes sense while talking from a universal realm of things .. 99% National - 1% Glocal | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3253 Registered: 10-2008 Posted From: 49.205.61.47 Rating: N/A |
I am saying 'how it is', not trying for an 'how it is supposed to be', hope you get the difference. And I dont want to invest any time on judging the morals of a biased person (be it towards caste or country). neeku hinduism istam kabatti ala try chesta. fritjof capra in his book talks about nataraja and bigbang, think how small things like country/religion/civilization will be compared to that 'shiva' thang which will take care of keeping the rhythm across multiple galaxies and hundreds of billions of years! | ||
Tilak Legend Username: Tilak Post Number: 36791 Registered: 02-2012 Posted From: 183.83.48.28 Rating: N/A |
interesting take .. so people who are proud about India's past must be the ones "belonging to the castes of their pioneer ancestors?" ante .. our caste is the only and primordial identity to own/disown something? 99% National - 1% Glocal | ||
Last_avataar Side Hero Username: Last_avataar Post Number: 6856 Registered: 09-2012 Posted From: 184.101.253.70 Rating: |
Political Stability, Money factors in society are important for development of any field When Kkings were there, thats when all the so called scientists flourished in India , as there was peace in scoiety When survival and slavery comes into picture for 1000s of years coupled by irrational religious practices , thats when India lost in the race , others gained even the so called rationalists always target Hinduism , instead of developing something good for society Pure sciences are required backed by good and free environment to research, then people can create something | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3250 Registered: 10-2008 Posted From: 49.205.61.47 Rating: N/A |
Wrong! Yes, we fought with other animals for life. But, men conquered the animals the moment they knew how to make a 'tool' and 'use' the tool.
Aliens? I am out after this! Anyway, you think you are any different than 'outer space'. No, we are along with any 'aliens' are dust particles with consciousness(talking about humans, not sure about aliens' consiousness), which came from borrowed energies from smaller galaxies and essentially irrelevant in the bigger course of events. I am not saying this, western sciences claim this. | ||
Confused Junior Artist Username: Confused Post Number: 25 Registered: 02-2011 Posted From: 73.173.237.248 Rating: N/A |
I agree to the above statement, it is the negative effect of industrial civilization. But still for the humans to exist they have to use machines. Remember primitive humans would not have survived if he did not think about using machines to counter stronger living beings around him. May be the science in today's world works the same way i.e. to protect us from aliens invading from outer space in future. | ||
Mushin Comedian Username: Mushin Post Number: 1334 Registered: 05-2015 Posted From: 17.150.218.4 Rating: N/A |
Calculus was thought to be a purely European invention (as we are taught at school even now) associated with the names of Newton and Leibnitz, but it was not. Many important parts of it, at least, were known in Indian ganita centuries earlier. This included the infinite series, for example, of the Taylor-Mclaurin type, second-order difference schemes, the idea of limits and so on. Correspondingly, it cannot be said that Archimedes (or some other Greek) started science (compare Bacon); nor did it all start in India, for some little science must have been there even at very early times. There were different contributions from different cultures. Ideas did travel (both ways), but not all of them were accepted along their way by local cultures. For example Indians borrowed the idea of epicycles from the Greeks, but used it very differently: The smaller circle moving along the circumference of the bigger one could keep changing its diameter. | ||
Mushin Comedian Username: Mushin Post Number: 1333 Registered: 05-2015 Posted From: 17.150.218.4 Rating: |
Indic methodology was primarily based on observation, experience (pratyaksha, anubhava), inference and skill (anumana, yukti). The Greek conception was based on deductive two-valued (yes or no type) Aristotelian logic, often following from stated axioms considered 'true' or self-evident (typified by Euclid). | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3245 Registered: 10-2008 Posted From: 49.205.61.47 Rating: N/A |
First off I dont sign up for 'everything happens for a reason' line. But it is indeed a clever line, It is essentially twisted version of "their will be 'repercussions' for every 'action'". Ignoring that part, I have already answered that question: 'any LUXURY to humans is addictive' Industrial civilization made humans blind towards reality as they can't get out of cozy,comfort zone. | ||
Mushin Comedian Username: Mushin Post Number: 1332 Registered: 05-2015 Posted From: 17.150.218.4 Rating: N/A |
Some Indians take the extreme view that everything was known to our ancients, but others go to the opposite extreme and consider everything Indian was superstition and rubbish (an imperial British view typified by Macaulay's comment about how one shelf of good European books was worth the whole literature of India and Arabia).  | ||
Mushin Comedian Username: Mushin Post Number: 1331 Registered: 05-2015 Posted From: 17.150.218.4 Rating: N/A |
http://www.rediff.com/news/interview/why-and-how-did-science -in-india-stagnate/20150814.htm Part 1 of the interview...excellent objective analysis of Aryabhatta,Brahmagupta,Varahamihir etc... | ||
Confused Junior Artist Username: Confused Post Number: 24 Registered: 02-2011 Posted From: 73.173.237.248 Rating: N/A |
They say everything happens for a reason, why do u think industrial civilization happened to Man? | ||
Mushin Comedian Username: Mushin Post Number: 1330 Registered: 05-2015 Posted From: 17.150.218.4 Rating: N/A |
yeah...u did objective analysis annai....kontha mandi sollu posts esaru  | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3243 Registered: 10-2008 Posted From: 49.205.61.47 Rating: N/A |
I tried no? | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3242 Registered: 10-2008 Posted From: 49.205.61.47 Rating: |
biased journalist ki scientist ki polika? if you observe worldwide, historians are more biased and 'search for a reason to support something in their mind' compared to scientists. | ||
Telugu_times Legend Username: Telugu_times Post Number: 46330 Registered: 02-2008 Posted From: 69.219.231.201 Rating: N/A |
ee paki journalist kurrodu balay comedy sesthaadu inkedho video lo, mana mokaalaki, ee rojuki, oka car wiper kooda invent cheyyaledhu annaadu lol Ignore spam. | ||
Mushin Comedian Username: Mushin Post Number: 1329 Registered: 05-2015 Posted From: 17.150.218.4 Rating: N/A |
perfectly put...ee thread lo posts ee example....objective analysis cheyaru...aa bongule India lo em ledhu antaru ledha ababababababa ancient Indians thopulu antaru.... | ||
Telugu_times Legend Username: Telugu_times Post Number: 46329 Registered: 02-2008 Posted From: 69.219.231.201 Rating: N/A |
https://www.youtube.com/watch?v=jamDZk8ynt4 Ignore spam. | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3241 Registered: 10-2008 Posted From: 49.205.61.47 Rating: N/A |
for the first time in recorded history, west is leading. But, they took the shortcut route and hence it is deadly. krishna side, chinna pillala aatallo "thondi aata" antaru -cheating, adi ippudu west aadutunnadi, andarito aadistunnadi. | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3240 Registered: 10-2008 Posted From: 49.205.61.47 Rating: N/A |
I forgot add one more important thing: 5. Presentation - once the corporate started, presentation took precedence than goods. This will have huge impact on the way humans think about a particular civilization | ||
Telugu_times Legend Username: Telugu_times Post Number: 46327 Registered: 02-2008 Posted From: 69.219.231.201 Rating: N/A |
ee self boasting ki emundhi lay go to nalla vaalla sites, vaalla list chaanthaadu antha untadhi go to secular vaalla sites, vaalla list kooda chaanthaadu antha untadhi cut chesthey, jews and christians no where near the reach of others Ignore spam. | ||
Mario_puzo Side Hero Username: Mario_puzo Post Number: 3238 Registered: 10-2008 Posted From: 49.205.61.47 Rating: N/A |
These thinking patterns i think are in existence because of the following reasons: 1. caste system. -the castes that were never part of any significant 'science' in ancient India and now part of it, would never love to acknowledge the past as science. 2. Blind support (from bhakti movement times?) -some castes started not questioning anything and blindly started following it, may be they thought: only way to protect something is, by not questioning it, LOL. 3. post industrial civilization - any LUXURY to humans is addictive. Machines are all about making humans lazy. Understandably India along with the world was bewildered when a machine started doing something that cant be done in a life time. Remember the scene in avatar where Jake arrives on a "turuk-makdo" and the entire civilization bows to him in shock. 4. British infused 'i am inferior' mantra onto our nerves. I can understand it. Rajkumar nela rojulu veerappan gun kinda unte, 'veerappan manchi vadu' laga anipistadu, baitiki ala cheppadam kadu, rajkumar ki alage anipistundi-pinchali. Whether or not India had science is not a burning question any more for me (may be because, I have answers now). Also I can confidently say, down the line this line of western philosophy towards life will be ridiculed and the followers of it will be cursed by future humans for depleting the resources and for living 'life of someone else' in the name of luxury. | ||
Vishvak Side Hero Username: Vishvak Post Number: 2329 Registered: 01-2007 Posted From: 72.192.34.77 Rating: |
http://arabiangazette.com/wp-content/uploads/2012/09/work-de signation-limitation.gif Vi veri universum vivus vici My Blog: The Power Of One | ||
Tilak Legend Username: Tilak Post Number: 36790 Registered: 02-2012 Posted From: 183.83.48.28 Rating: N/A |
kondaru bongule anaru .. just single star vesi jaarukuntaru calm ga .. 99% National - 1% Glocal | ||
Vishvak Side Hero Username: Vishvak Post Number: 2328 Registered: 01-2007 Posted From: 72.192.34.77 Rating: N/A |
Strange enti ante, Jules Verne ni ahead of times think chesedu antaru... Ade Mahabharatam/Ramayanam quote cheste bongule antaru... Vi veri universum vivus vici My Blog: The Power Of One | ||
Tilak Legend Username: Tilak Post Number: 36787 Registered: 02-2012 Posted From: 183.83.48.28 Rating: |
Do you mean to say .. the concept of Ganesha's birth is fiction?
99% National - 1% Glocal | ||
Ysr2009 Side Hero Username: Ysr2009 Post Number: 4025 Registered: 03-2014 Posted From: 129.135.0.19 Rating: |
Even now, Asians are not known any CREATIVE ideas. We are just SERVICE MAINTANANCE people. | ||
Ysr2009 Side Hero Username: Ysr2009 Post Number: 4024 Registered: 03-2014 Posted From: 129.135.0.19 Rating: |
Why so much fake chest thumping yaar? India was ruled by Invaders for 1000 years. We didn't achieve anything in that period. All the scientific breakthroughs came from West. | ||
Chillarodu Side Hero Username: Chillarodu Post Number: 8195 Registered: 03-2008 Posted From: 128.103.224.124 Rating: N/A |
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Bumper Side Hero Username: Bumper Post Number: 7410 Registered: 07-2014 Posted From: 199.168.151.87 Rating: N/A |
SC lo kuchoni baga think chesinappudu naku kuda koni thoughts vachai. one og the thought below: ma universe ki mana body ki baga comparison undhi. We dont know anything about wats going on inside. universe might also dont know whats going on inside. We have hair, universe has trees If we feel thirsty we drink water, If universe feels thirsty there are rains and floods etc. Dini batti oka vishyam enti ante manalo em jarugtundo telusu kunte mana universe gurunchi telusu kunatte Snakes in Your backyard won't bite only your neighbours. #Hillary Clinton | ||
Confused Junior Artist Username: Confused Post Number: 23 Registered: 02-2011 Posted From: 150.148.14.4 Rating: |
Indian history does not show anything about materialistic part of science, but definitely India led the spiritual part of science. Our ancient people spent lot of time thinking about how our mind and body works. | ||
Teluguvaadu Junior Artist Username: Teluguvaadu Post Number: 451 Registered: 11-2012 Posted From: 59.99.157.21 Rating: |
Yah yah ... 10000 years back, India lo plastic surgery chesevaru ani Modi ji chepparu... http://indianexpress.com/article/india/india-others/pm-takes -leaf-from-batra-book-mahabharat-genetics-lord-ganesha-surge ry/ Around 5000+ years ago, Mahabharata time lo Internet TV undedi, thats how Sashirekha and Ambimanyudu used to communicate...Mayabazar lo choosanu. | ||
Sirish Junior Artist Username: Sirish Post Number: 373 Registered: 02-2015 Posted From: 72.208.10.129 Rating: |
thaaths neths | ||
Ruj Hero Username: Ruj Post Number: 18828 Registered: 03-2007 Posted From: 170.202.122.2 Rating: |
'Some Indians take the extreme view that everything was known to our ancients, but others go to the opposite extreme and consider everything Indian was superstition and rubbish.'<<< baa seppad | ||
Gringo Side Hero Username: Gringo Post Number: 3197 Registered: 10-2014 Posted From: 72.15.229.180 Rating: |
Who is leading today is all that matters now | ||
Farmer Side Hero Username: Farmer Post Number: 2109 Registered: 04-2015 Posted From: 162.252.85.172 Rating: |
LOL | ||
Bunty717 Moderator Username: Bunty717 Post Number: 47716 Registered: 02-2008 Rating: |
prob is aa lead maintain cheyalekapoyemu .. | ||
Tilak Legend Username: Tilak Post Number: 36780 Registered: 02-2012 Posted From: 183.83.48.28 Rating: |
Awesome 99% National - 1% Glocal | ||
Teluguhero Comedian Username: Teluguhero Post Number: 1721 Registered: 04-2008 Posted From: 63.151.12.167 Rating: |
http://www.rediff.com/news/interview/for-1400-years-india-le d-the-world-in-science/20160125.htm For 1,400 years India led the world in science Professor Roddam Narasimha has been closely associated with aerospace technology development in India, at both technical and policy-making levels. Between 1977 and 1979, he was the Chief Project Coordinator at Hindustan Aeronautics Limited and led a joint HAL-NAL-IISc team carrying out early conceptual studies of the Light Combat Aircraft. Under his leadership, the National Aerospace Laboratories made the first parallel computer in the country in 1986 and fabricated and flew the first fibre glass aircraft in the country. As a member of then prime minister Rajiv Gandhi's Scientific Advisory Council he was instrumental in establishing a major parallel computing initiative in the country. Dr Narasimha, below, left, has been widely honoured for his research work as well as his scientific leadership. He is a Fellow of the Royal Society, a Foreign Associate of both the US National Academy of Engineering and the US National Academy of Sciences. He is also an Honorary Member of the American Academy of Arts and Sciences, and has been a Fellow of the American Institute of Aeronautics and Astronautics. In India his distinctions include the Bhatnagar Prize, the Gujarmal Modi Award, the Ramanujan Award, the Aryabhata Award, and the Padma Bhushan. And these are just the tip of the iceberg as far as his many achievements are concerned. In this interview with Shivanand Kanavi, he discusses how India once led the world in the fields of science and maths and how the West overtook India on these fronts. Was all Indic science rational? No, we have already talked about Brahmagupta, for example. However, I gradually came to the conclusion that classical Indic science was indeed generally rational, but it was rationality of a different kind; and it did have conflicts with mythology. We must however remember that, although Newton is generally seen as rational about his science, he did not consider it as important as what he secretly wrote about theology. Not many know or remember that. Around that time and later in Europe, the possible existence of great ancient civilisations in Asia and Africa became a serious issue as estimates of their age were approaching the Biblical date of Creation. If you compared the views expressed in Europe during the so called Dark Ages there (before the Renaissance), Indian science was perhaps more rational than the European science of the time. Nobody tried or convicted Aryabhata just because he said Rahu-Ketu is nonsense. At the same time Brahmagupta's criticism did not affect his reputation as a brilliant scientist. Both of them, I believe, were computational positivists, so their other views seem to have been seen as secondary, lost in the indifference of traditional Indic tolerance of different views. So how long did this classical science last, and when and why did it end? Some 20 years ago, I came across Joseph Needham, a distinguished British scientist who had studied Chinese science and technology in great depth and also wrote a bit on the side about Indic science. He concluded that as the West got to know more about Eastern science, the question that demanded an answer was why neither China nor India gave birth to modern science, despite the fact that they were ahead of the West in science and technology for 1,400 years (say 200 CE to 1600 CE). Why was modern science born in Pisa and not in Patna or Peking, Needham asked. It was the first time that I had seen a distinguished Western scholar acknowledge so readily that India and China had earlier been ahead for 1,400 years. This question is not much discussed in India. Some Indians take the extreme view that everything was known to our ancients, but others go to the opposite extreme and consider everything Indian was superstition and rubbish (an imperial British view typified by Macaulay's comment about how one shelf of good European books was worth the whole literature of India and Arabia). It slowly became clear to me that both sides were wrong: The history of science is not linear -- it is chequered. The European Dark Ages were anything but dark in India. Our Dark Ages have been the last several centuries. A study of European opinion in the 15th, 16th centuries leads to the conclusion that Europe was becoming aware at that time that the East had been ahead of them. They had encountered the more advanced Arabs during the crusades, Indian numerals and algebra in the 16th, 17th centuries, Chinese technologies in between and they began to see advances in Asia which they did not know about. If you read Francis Bacon, you will see that he recognised the power of new inventions like the printing press, the nautical compass and gun powder (all from China, as we now know) -- inventions that had changed the world more than any empire, sect or star, he said, and then there was sugar, which came from India. He was dazzled by them, just as I was dazzled by all the things that the West had done when I first went to the US. Bacon blamed the Greeks for the sad state of European knowledge. He called them a set of quacks and charlatans; his criticisms of Plato and Aristotle were scathing. Europe had taken the wrong path and had to change. It is almost like what some Indians began to say in the 19th and 20th centuries as our classical epistemology collapsed: 'All that we have learnt is worthless.' As one begins to analyse classical Indic and European texts, it becomes clear that, deep down, at a fundamental level, it is all really about how one acquires reliable new knowledge, ie about epistemology. In the 17th century, Newton almost implemented what Bacon had said. What changed at that time? The standard Western answer is mathematicisation of science, but that characterisation is misleading. It depends on what you mean by mathematicisation. Surely one cannot say that ancient Greeks and Indians were not mathematical? Actually, what happened in the 16th, 17th centuries was that the meaning of mathematics changed. Till then, it was geometry and Euclid in Europe (borrowed back, incidentally, from the Arabs and their Arabic translations from the Greek a few centuries earlier). After the 16th century it began to include numbers and algebra, both of which had come from India. Algebra or beeja-ganita had developed into a 'new maths' and was transmitted to Europe through creative Arabs and Persians; and the trajectory of that diffusion can now be traced fairly well. The word algebra started getting used in Europe in the 15th, 16th centuries and slowly grew in usage, even as the use of the word geometry declined. Indeed, the new mathematics even affected geometry, leading to what we now call analytical geometry. Thus what really happened in Europe then was the algebraisation of mathematics and (a little later) of the exact sciences like physics. As renowned mathematical physicist Hermann Weyl said, Europe moved away from Greek ideas to follow a path that had originated in India, where the concept of number had been considered logically prior to the concept of geometry. I believe this was a strong factor in the revival of science in Europe. Bacon's formula of knowledge = power (in contrast to the Indic equation knowledge = salvation) translated to growing power over the East. The European languages did not have a word for algebra at the time so they took over the Arabic word al jabr, just as we too have taken over television, radio, etc, from English. Descartes once referred to algebra as 'barbarous': It was clearly not a direct Greek or European legacy. Francis Bacon realised that much new knowledge had come from outside the European culture area -- presumably the East. What is the concept of beeja and ganita, which you have spoken of recently as 'Indic concepts that changed the world'? Ganita is literally reckoning, counting and manipulating numbers; gan is 'to count' in Sanskrit. In the West a mathematician was, and was called, a 'geometer' for long; and in India a mathematician was a gan aka, a numerist. India was number-centric. Bhaskara said beeja-ganita (algebra) is avyakta-ganita, ie ganita with unmanifest (unknown) quantities which need to be found out from the data available and so made to become vyakta, 'known.' That unknown, the hidden, is beeja. Thus computing with the unknown so that it becomes known is beeja ganita, which went as algebra to Europe through the Arabs (who made their own creative contributions). It appears as if the modern scientific revolution in Europe was a response to the inventions, both mathematical and technological, that went from the East through the Arabs. These inventions dazzled the Europeans, just as their inventions in turn dazzled us 200 or 300 years later. So what was the difference between Europe and India in the way science was done? Neelakantha, a 15th-16th century mathematician-philosopher from Kerala, explicitly tells us how to do science. I had been trying to infer from Aryabhata and Bhaskara what their attitude towards science and mathematics might have been and then I came to know about the Kerala school and Neelakantha's Jyotirmimamsa (which unfortunately has not yet been translated into English). He actually talks about epistemology, ie the science of knowledge-making, and describes what methods lead to the generation of valid, reliable and belief-worthy knowledge. Neelakantha's views throw light on where Indians and Westerners differed in their epistemology. Indic methodology was primarily based on observation, experience (pratyaksha, anubhava), inference and skill (anumana, yukti). The Greek conception was based on deductive two-valued (yes or no type) Aristotelian logic, often following from stated axioms considered 'true' or self-evident (typified by Euclid). In the 15th-6th centuries, a fusion seems to have started taking place between the two in Europe. Though Indians were in touch with the Greeks, at least since the times of Alexander, they only borrowed some tools from them, but did not accept their philosophy or ideology. After having rubbished Greek philosophy, Francis Bacon went on to invent a kind of hybrid that combined experience, observation (in particular through experimentation) with inference of axioms. Axioms thus ceased to be self-evident truths and became instead tentative inferences. This method began to be used with Newton and led to what has spectacularly become the global enterprise of 'modern' science. In his great work Principia Mathematica Philosphiae Naturalis (The Mathematical Principles of Natural Philosophy) -- perhaps the biggest ever game-changer in the world of science -- Newton starts like Euclid in the first book, stating and discussing three 'axiom' (his three laws of motion); the rest is full of theorems, lemmas, QED, etc. In the third book he changes gear, introduces numbers from observations and inferences from them in the light of the axioms and results of Books I and II. Book III (of Principia-Ed) seems to me, partly Indic in style, because of the use of inference: QIE (what may be inferred) often replaces the Euclidean QED (what had to be demonstrated). Newton presumably realised that the third book is not in the Greek spirit, so he inserts a short prefatory note on 'The Rules of Philosophical Reasoning' before embarking on Book III, where he justifies his new procedure. He sets out and explains four (new) rules, which have very little to do with the Greeks. But there are also curious commonalities between India and Europe. Calculus was thought to be a purely European invention (as we are taught at school even now) associated with the names of Newton and Leibnitz, but it was not. Many important parts of it, at least, were known in Indian ganita centuries earlier. This included the infinite series, for example, of the Taylor-Mclaurin type, second-order difference schemes, the idea of limits and so on. Correspondingly, it cannot be said that Archimedes (or some other Greek) started science (compare Bacon); nor did it all start in India, for some little science must have been there even at very early times. There were different contributions from different cultures. Ideas did travel (both ways), but not all of them were accepted along their way by local cultures. For example Indians borrowed the idea of epicycles from the Greeks, but used it very differently: The smaller circle moving along the circumference of the bigger one could keep changing its diameter. This would have shocked the Greeks because for them it would spoil the symmetry and beauty of a model based on just circles. To the Indians, however, the resulting kinky ellipse-like curve was computationally simpler and more efficient. It was the sort of thing that Bhaskara said would bring aananda to the ganakas! Indians never really took to Euclid till it came out of Macaulay's bookshelf into the educational system he prescribed for India in the 19th century. In the Indic Nyaya system of knowledge creation (although it makes no reference to the Greeks), the method of hypothesis to conclusion based on (deductive) logic is frowned upon, because the basis for taking the hypothesis as a given truth could not be justified. You have to compare it with or base it on observation. This is where Bacon made his leap, coupling hypothesis and inference. Pratyaksha (observation, including experiment) was the number one pramaana (source of valid knowledge) in all schools of Indian philosophy; it was universally accepted. This must have been one of the few things that all of them agreed on! The second was anumaana (inference), accepted by every school except the Lokaayatas. As Neelakantha says, knowledge arises pratyakshena anumaanena -- from observation and from inference. What about the aagamic pramaana? After getting an interesting mathematical result, Neelakantha says etatsarvamyukti-moolam, natuaagama-moolam: all of this (comes) from intelligent reasoning, not from the aagamas. Such a statement could not have been safely made in the Europe of his time (1500 CE). Aagama can also be taken as existing accumulated knowledge rather than scriptural, an important if not decisive source of knowledge. The aagamas were indeed accepted as a third pramaana in some Indic philosophical systems. What you mention is close to what the Saamkhya philosophers call aapta vacana (the word of the trustworthy), which they accept as the third pramaana after pratyaksha and anumaana, but they make it clear that Vedic knowledge is not privileged, because it is also essentially human in origin, so potentially fallible like any human work. In Nireeshwara Saamkhya they say there is no evidence (pramaana-abhaava) for God. Of course, they don't say that there is no God, only that there is no evidence for it. Classical Indic scientists rarely appealed to scriptural knowledge in their science; however many of them, including Neelakantha, were also very accomplished Vedic scholars. In general, the great scientists (Charaka, Bhaaskara) had respect for Saamkhya thinking. How can you say all this was not rational? The history of ideas, it seems to me, is chequered, and that makes it fascinating -- more fascinating than that of kings and battles. |
