|
|
Post by vkaul1 on Sept 22, 2011 16:34:03 GMT -6
David Mumford (a pretty famous mathematician) en.wikipedia.org/wiki/David_Mumford wrote an excellent review for the book on mathematics in India by Kim Plofer. It shows how Indian mathematics was in fact underestimated by the west and even Arabic scholars. www.ams.org/notices/201003/rtx100300385p.pdfSome good excerpts from the review. Another major root of Indian mathematics is the
work of Paninin.
ini and Pi˙ngala (perhaps in the fifth
century BCE and the third century BCE respectively), described in section 3.3 of Plofker’s book.
Though Panini. is usually described as the great
grammarian of Sanskrit, codifying the rules of the
language that was then being written down for the
first time, his ideas have a much wider significance
than that. Amazingly, he introduced abstract symbols to denote various subsets of letters and words
that would be treated in some common way in
some rules; and he produced rewrite rules that
were to be applied recursively in a precise order.
One could say without exaggeration that he
anticipated the basic ideas of modern computer
science.Chapter 7 of Plofker’s book is devoted to thecrown jewel of Indian mathematics, the work of
the Kerala school. Kerala is a narrow fertile strip
between the mountains and the Arabian Sea along
the southwest coast of India. Here, in a number
of small villages, supported by the Maharaja of
Calicut, an amazing dynasty
17
of mathematicians
and astronomers lived and thrived. A large proportion of their results were attributed by later
writers to the founder of this school, Madhava of
Sangamagramma, who lived from approximately
1350 to 1425. It seems fair to me to compare him
with Newton and Leibniz. The high points of their
mathematical work were the discoveries of the
power series expansions of arctangent, sine, and
cosine. By a marvelous and unique happenstance,
there survives an informal exposition of these
results with full derivations, written in Malayalam,
the vernacular of Kerala, by Jyes
I think we will do disservice to the thoughtful people of the past to freeze ourselves to a rigid 16 th century medieval Indian view. As the thoughtful people in Indian kept on accommodating new discoveries, we can do the same. |
|
|
|
Post by Nitaidas on Sept 28, 2011 11:25:42 GMT -6
David Mumford (a pretty famous mathematician) en.wikipedia.org/wiki/David_Mumford wrote an excellent review for the book on mathematics in India by Kim Plofer. It shows how Indian mathematics was in fact underestimated by the west and even Arabic scholars. www.ams.org/notices/201003/rtx100300385p.pdfSome good excerpts from the review. Another major root of Indian mathematics is the
work of Paninin.
ini and Pi˙ngala (perhaps in the fifth
century BCE and the third century BCE respectively), described in section 3.3 of Plofker’s book.
Though Panini. is usually described as the great
grammarian of Sanskrit, codifying the rules of the
language that was then being written down for the
first time, his ideas have a much wider significance
than that. Amazingly, he introduced abstract symbols to denote various subsets of letters and words
that would be treated in some common way in
some rules; and he produced rewrite rules that
were to be applied recursively in a precise order.
One could say without exaggeration that he
anticipated the basic ideas of modern computer
science.Chapter 7 of Plofker’s book is devoted to thecrown jewel of Indian mathematics, the work of
the Kerala school. Kerala is a narrow fertile strip
between the mountains and the Arabian Sea along
the southwest coast of India. Here, in a number
of small villages, supported by the Maharaja of
Calicut, an amazing dynasty
17
of mathematicians
and astronomers lived and thrived. A large proportion of their results were attributed by later
writers to the founder of this school, Madhava of
Sangamagramma, who lived from approximately
1350 to 1425. It seems fair to me to compare him
with Newton and Leibniz. The high points of their
mathematical work were the discoveries of the
power series expansions of arctangent, sine, and
cosine. By a marvelous and unique happenstance,
there survives an informal exposition of these
results with full derivations, written in Malayalam,
the vernacular of Kerala, by Jyes
I think we will do disservice to the thoughtful people of the past to freeze ourselves to a rigid 16 th century medieval Indian view. As the thoughtful people in Indian kept on accommodating new discoveries, we can do the same. This is good stuff, Vivekji. We do not give the ancient Indians enough credit for scientific achievement. There has been a rising interest in the ancient Indian sciences. We should try to understand those better. Mathematics, medicine, astronomy, linguistics: these are just some of the areas in which India excelled. That part always gets left out of the histories of science. No one ever looks beyond the durn Greeks. |
|
|
|
Post by vkaul1 on Sept 28, 2011 17:41:50 GMT -6
See Nitai ji, the problem is when the traditionalists from the Indic tradition (obviously only the Vedanta tradition because I don't see any other tradition alive in India apart from Tantra and Saivism) just want to go to the other extreme by claiming that all discoveries of modern science were known to people millions of years ago in treta yuga (spacecrafts etc). I also wanted to believe that it is true but did not find evidence, so made it very unlikely. If you see the document above, it is obvious that lot of good work was continued by Panini and then in the Kerala school (13th century CE). So they kept on refining and inventing new things. However, traditional worldview seems to want to freeze reality in the 16th century and look at the modern world as a bunch of crazy schoolboys who know nothing that was not known to people millions of years ago. On the other extreme are people who want to debunk and discredit any meritorious work coming from India. Therefore, we want to go to a balanced view where we give due credit to ancient Indians while not saying that everything in modern science (including quarks and electrons) was known to people in the past in the same way as today. Unfortunately, the balanced view is generally in a minority. Some traditionalists actually opposed surya siddhanta (calling it anti-vedic) and many believed in the flat-earth theory just because of the way they interpreted scriptures literally. Literal interpretation of scripture certainly does much disservice to the Indians of the past and their accomplishments according to me, though in 16th century everybody including the Goswamis perhaps bought into the literal world view (it was the dominant paradigm). Now, we don't function in the same paradigm and have to shift or else get extinct. I appreciate your efforts in this regard.
|
|
|
|
Post by Nitaidas on Sept 29, 2011 10:32:47 GMT -6
See Nitai ji, the problem is when the traditionalists from the Indic tradition (obviously only the Vedanta tradition because I don't see any other tradition alive in India apart from Tantra and Saivism) just want to go to the other extreme by claiming that all discoveries of modern science were known to people millions of years ago in treta yuga (spacecrafts etc). I also wanted to believe that it is true but did not find evidence, so made it very unlikely. If you see the document above, it is obvious that lot of good work was continued by Panini and then in the Kerala school (13th century CE). So they kept on refining and inventing new things. However, traditional worldview seems to want to freeze reality in the 16th century and look at the modern world as a bunch of crazy schoolboys who know nothing that was not known to people millions of years ago. On the other extreme are people who want to debunk and discredit any meritorious work coming from India. Therefore, we want to go to a balanced view where we give due credit to ancient Indians while not saying that everything in modern science (including quarks and electrons) was known to people in the past in the same way as today. Unfortunately, the balanced view is generally in a minority. Some traditionalists actually opposed surya siddhanta (calling it anti-vedic) and many believed in the flat-earth theory just because of the way they interpreted scriptures literally. Literal interpretation of scripture certainly does much disservice to the Indians of the past and their accomplishments according to me, though in 16th century everybody including the Goswamis perhaps bought into the literal world view (it was the dominant paradigm). Now, we don't function in the same paradigm and have to shift or else get extinct. I appreciate your efforts in this regard. Yes, such extremists are foolish and worthy only of ridicule. Still, there are genuine achievements in Indic studies of the various sciences. Certainly they did not have nor did they understand anything like the scientific method. But, they were careful observers of their surroundings and they did make great advancements in understanding them. The literal worldview you are referring to is the Puranic world view which was developed in the context of Puranic studies and production. Outside that framework others were discovering things like the fact that the world is a sphere and circles the sun. But the Puranic scholars only considered the Puranas a valid source of knowledge and they ignored these other savants. It is not much different from what happened in the West. Look at all the trouble Galileo faced. Humans are the same obstinate brutes the world over. We need lots of people working on this problem. We people who really understand the CV philosophy and who are imaginative enough to sift out the false from the true. We need people who really understand modern science and the potentials of discovery there. The biggest task as I see it is to toss out the idea of a dualism and rethink the whole tradition in terms of a thorough-going non-dualism which nevertheless still leaves room for a degree of variegation. What were thought to be two, mind and matter, need to be joined and never separated again. The CV position of Acintya-bhedAbheda is a good starting point, except for the acintya part. We need new ways of making it cintya. Acintya puts up a road block and inhibits progress. Perhaps Baladeva's redefinition of the relationship as vizeSa (not real difference, but a substitue for difference that appears like difference) which he borrowed from Madhva is a good candidate for exploration. Anyway, I can't do it alone. I need help from smart people who refuse to let the wool be pulled over their eyes. |
|
|
|
Post by vkaul1 on Sept 29, 2011 12:42:05 GMT -6
To get lots of people will be really hard because modern science as seen as a challenge that needs to be dismissed by most practitioners of CV. I plan to go to UC Berkeley working on Philosophy and South Asian studies in about 5-6 years. Then, I would want to stay there for about 5-6 years to get my hands dirty in some important subjects in fundamental sciences (neuroscience, evolution and quantum mechanics), philosophy of science and the mind and some Sanskrit texts. A hard task, but I will try
Now some points I had:
1) I had a small question about yoga sutra.
I had a question about the idea of citta (comprised of manas, buddhi and ahamkara) in yoga. Are manas, buddhi and ahamkara only conceptual categories or ontologically different substances? I was thinking if citta is supposed to be an ontologically substance that is comprised of three concepts of manas, buddhi and ahamkara.
Or maybe, it is hard to know from the text how the authors thought of these.
In the Gita do you think intellect, mind and false ego are separate substances or categories? Or the authors did not make such distinctions.
2) Visesa of madhva seems different to what you are saying. Visesa in the madhva system, if I recall correctly, is used to explain that there is no difference between the substance and the attribute, though apparently there is. Perhaps that is what you want to do with the mind and matter. Now the problem is that in the Eastern ideas you have mind (don't know if we can have mind only or to complicate things have more of mind, intellect and as subtle matter (don't know if there is a substance there or just a
concept?) and atma as something completely different.
3) I have this idea that Sri Rupa studied Rasa and created categories for gopis/manjaris so that he can encompass all variegation in the concept of Krsna. Every rasa the humans could imagine at that time had to be found in relation to Krsna (akhila-rasāmṛta-mūrtiḥ) so he build build up the idea of 8 kinds of gopis, sakhas etc and defined names for them. Afterwards everything became like a frozen truths and people do fight over the exact details of the names and the identities of the people in Gaura Lila, exact age of the manjaris etc. Is it alright to understand Sri Rupa as I expressed above?
4) Certainly, buddhist idea of no-self is powerful because an unchanging self idea has to be accepted axiomatically. Perhaps, it is an undecidable question. Even with citti-vritti nirodha is accomplished and someone experiences a state of pure awareness, citta just reflects the pure awareness of the soul. Citta is some way is defined as empirical consciousness (what you experience) and once the vrittis are stopped empirically consciousness reflects the state of the purusha. But obviously purusha can never be proved.
|
|
|
|
Post by vkaul1 on Sept 29, 2011 16:36:08 GMT -6
Another thing I worry about is Rupa Goswami warns against overendeavor (atyāhāraḥ prayāsaś ca) in Upadeshamrita. Perhaps to take us away from jnana but how do we avoid this in our modern world with so much information?
Another thing Amit Goswami tries to break the dualism by positing consciousness as the only reality in which things turn from potentiality to actuality.
|
|
|
|
Post by vkaul1 on Sept 29, 2011 17:28:41 GMT -6
Another thing I worry about is Rupa Goswami warns against overendeavor (atyāhāraḥ prayāsaś ca) in Upadeshamrita. Perhaps to take us away from jnana but how do we avoid this in our modern world with so much information?
Another thing Amit Goswami tries to break the dualism by positing consciousness as the only reality in which things turn from potentiality to actuality. Scientists have it the other way round. So anyway, we will see what do. It seems like the term anivicaraniya is point of strong controversy in advaita. And there is no way to know whether buddhist doctrine of anicca and anatama (though the buddha seems to have made a point not to cling to either no-self or self ) is true. However, anicca seems to be more compatible with modern science, I suppose.
|
|
|
|
Post by Nitaidas on Sept 30, 2011 10:08:29 GMT -6
To get lots of people will be really hard because modern science as seen as a challenge that needs to be dismissed by most practitioners of CV. I plan to go to UC Berkeley working on Philosophy and South Asian studies in about 5-6 years. Then, I would want to stay there for about 5-6 years to get my hands dirty in some important subjects in fundamental sciences (neuroscience, evolution and quantum mechanics), philosophy of science and the mind and some Sanskrit texts. A hard task, but I will try Good plan. Don't lose your way. It is easy to do in that environment. I am not sure what distinction you are looking for here. What is the difference between conceptual categories and substances? They both seem conceptual. Yoga is built on Sankhya so the citta and its subdivisions are regarded as vikaras or transformations of Prakrti. Now are they categories or substances? Neither seems to fit. The answer rests on the meaning of vrtti, (function, operation, existent, turning, etc). The same thing citta acting in one way is buddhi and in another is ahamkara. In Nyaya, of course, the mind is a substance (dravya). But so are the five elements, time, space, and the self. The main trait of a substance is that it has qualities which is another category of Nyaya. No. It is the same. A vizeSa is the substitute for difference. In other words it is not really difference but it appears to be difference. Yes in the East the duality is between self and matter. Those two are the ones that need to be joined. Self is matter and matter is self. Matter is no longer just matter nor is self just self. To say that self is an epiphenomenon of matter is to favor matter over self and vice-versa. Both are wrong. Is it the same problem if we say self is a vizeSa of matter or matter is the vizeSa of the self? If you knew more about the history of alankara sastra you would know better than this. Rupa did not really invent anything. The eight nayikas are already there in the earlier texts. He just applied them to the gopis. He took the ideas of nayaka and nayika that were already highly developed in the previous tradition and applied them to Krsna and the Gopis with appropriate alterations to allow for their divinity. None of it is new. My Sanskrit teacher who was an expert in Alankara-sastra (literary criticism) and had all the major texts memorized at one point, once told me that Rupa had only two original ideas and they were both wrong. He, if anyone ever did, knew the whole of the sastra and was in a good position to make such a judgment. We read Rupa and are surprised at the complexity and richness of his ideas. Unless we read the rest of Alankara-sastra we have no idea how much he owed to his predecessors. The real greats in the Alankara world were Anandavardhana, Abhinavagupta, Mammata Bhatta, Jagannatha Pandita and I would add Bhojaraja, too. Held up next to them Rupa looks pretty uncreative and dull. Another set of IGM and CV misrepresentations we have to learn to overcome. It was too powerful for even the Buddhists. The Mahayanist apparently left it behind pretty early on for a concept of absolute oneness. This is what I have learned from Stcherbatsky. |
|
|
|
Post by Nitaidas on Sept 30, 2011 10:19:53 GMT -6
Another thing I worry about is Rupa Goswami warns against overendeavor (atyāhāraḥ prayāsaś ca) in Upadeshamrita. Perhaps to take us away from jnana but how do we avoid this in our modern world with so much information? Another thing Amit Goswami tries to break the dualism by positing consciousness as the only reality in which things turn from potentiality to actuality. Scientists have it the other way round. So anyway, we will see what do. It seems like the term anivicaraniya is point of strong controversy in advaita. And there is no way to know whether buddhist doctrine of anicca and anatama (though the buddha seems to have made a point not to cling to either no-self or self ) is true. However, anicca seems to be more compatible with modern science, I suppose. I wouldn't call prayAza overendeavor. Another mistranslation. Prayaza is fruitless endeavor, working without result or hope of result. What better fruit could there be than bringing CV up into the modern world? It has been done by just about every generation of CV. But, I think it is even more crucial today. If we are not successful today, CV is fade into history as a lovely religion that once was, like the ancient Greek religion. Of course there will probably always be a few cranks walking around in kaupin thumping their chests and proclaiming they know the truth. |
|
|
|
Post by vkaul1 on Sept 30, 2011 11:32:27 GMT -6
I am not sure what distinction you are looking for here. What is the difference between conceptual categories and substances? They both seem conceptual. Yoga is built on Sankhya so the citta and its subdivisions are regarded as vikaras or transformations of Prakrti. Now are they categories or substances? Neither seems to fit. The answer rests on the meaning of vrtti, (function, operation, existent, turning, etc). The same thing citta acting in one way is buddhi and in another is ahamkara. In Nyaya, of course, the mind is a substance (dravya). But so are the five elements, time, space, and the self.
The main trait of a substance is that it has qualities which is another category of Nyaya.
What about the Gita, the hierachy of mind, intellect and soul there, is it just conceptual or mind and intellect are substances?
No. It is the same. A vizeSa is the substitute for difference. In other words it is not really difference but it appears to be difference. Yes in the East the duality is between self and matter. Those two are the ones that need to be joined. Self is matter and matter is self. Matter is no longer just matter nor is self just self. To say that self is an epiphenomenon of matter is to favor matter over self and vice-versa. Both are wrong. Is it the same problem if we say self is a vizeSa of matter or matter is the vizeSa of the self?
Don't know. We will have to dig in.
If you knew more about the history of alankara sastra you would know better than this. Rupa did not really invent anything. The eight nayikas are already there in the earlier texts. He just applied them to the gopis. He took the ideas of nayaka and nayika that were already highly developed in the previous tradition and applied them to Krsna and the Gopis with appropriate alterations to allow for their divinity. None of it is new. My Sanskrit teacher who was an expert in Alankara-sastra (literary criticism) and had all the major texts memorized at one point, once told me that Rupa had only two original ideas and they were both wrong. He, if anyone ever did, knew the whole of the sastra and was in a good position to make such a judgment. We read Rupa and are surprised at the complexity and richness of his ideas. Unless we read the rest of Alankara-sastra we have no idea how much he owed to his predecessors. The real greats in the Alankara world were Anandavardhana, Abhinavagupta, Mammata Bhatta, Jagannatha Pandita and I would add Bhojaraja, too. Held up next to them Rupa looks pretty uncreative and dull. Another set of IGM and CV misrepresentations we have to learn to overcome.
My idea was actually the opposite Nitai ji. I mean because Rupa has borrowed so much from secular rasa sastra and put the divine play in that context, it is strange to get obsessed with the idea that all the details Rupa provided about the players in rasa lila are accurate in the literal sense (the age of the manjaris, gopis, the number of gopis). There is a lot of symbolism there too describing ineffable experiences as you said before, right? What were the two mistakes Rupa Goswami made?
It was too powerful for even the Buddhists. The Mahayanist apparently left it behind pretty early on for a concept of absolute oneness. This is what I have learned from Stcherbatsky.[/quote]
I meant actually that there is no way to demonstrate and unchanging self because as soon as you are out of the state of pure awareness, you are in a different stateSo even the state of pure awareness becomes transitory. .
|
|
|
|
Post by vkaul1 on Oct 4, 2011 12:24:52 GMT -6
I think Avijit Goswami's idea in many ways resemble those of George Berkeley in that he gets rid of dualism. Bishop Berkeley’s mystic idealism (as Kant aptly christened it)[citation needed] claimed that nothing separated man and God (except materialist misconceptions, of course), since nature or matter did not exist as a reality independent of consciousness. The revelation of God was directly accessible to man, according to this doctrine; it was the sense-perceived world, the world of man's sensations, which came to him from on high for him to decipher and so grasp the divine purpose.[13] God is not the distant engineer of Newtonian machinery that in the fullness of time led to the growth of a tree in the university quadrangle. Rather, my perception of the tree is an idea that God's mind has produced in mine, and the tree continues to exist in the quadrangle when "nobody" is there, simply because God is an infinite mind that perceives all.
|
|
|
|
Post by vkaul1 on Oct 5, 2011 1:50:38 GMT -6
"The Samkhya Karika speaks of manas, buddhi and ahamkara as if they were distinct elements or subtle substances that comprise the individual's psyche. However, I have seen in some of the early Samkhya treatises in the Mahabharata that they are designations given to the functions of the mind. So when the mind is receiving data via the senses it is manas but when it is making judgements on that data it functions as buddhi. The Gita merely repeats the Samkhya listings without seeking to explore their meaning any further. Chitta is an interesting concept that does not usually appear in the Samkhya analyses. It is usually translated as mind but of course that is also given as the meaning of manas. In Yoga discourse I think chitta really means the thought processes or the actions of the mind but different works seem to use the terms in slightly different ways." A scholar wrote this to me.
|
|
