A comment by Aravindhan

 I do not know whether I learnt any thing from keeping a blog. There are some comments I seem to keep going back to by BenjaminFranklin, Nabokov, and others. Another constant is a comment by Aravindhan in forum Hub in May 2005. The link does not work in some places)and so I am pasting his full comment here:
Quote Originally Posted by gaddeswarup
An article in this direction is written by a Swiss Samskrit scholar Johannes Bronkhorst : "Panini and Euclid:Reflections on Indian Geometry", which appeared in Journal of Indian Philosophy, 29, pp 43-80, 2001. I do not have a URL to this but if anybody is interested, I can send a pdf file of the article.
I've read Bronkhorst's paper. I think he identifies an important problem, and does it well, but misidentifies its cause. He seems to suggest that the problem could have been that science was influenced by grammatical methodology (though there is no clear evidence for this). In my opinion, it was much deeper than that. 

Panini's grammar, from a methodological perspective, embodies two trends. The first is the trend towards the primacy of exegesis in scholarly discourse. For some reason, texts by renowned scholars came to have a very special status, eventually becoming a source of knowledge equal to or superior than observation. The second trend is the increasing importance of inductive reasoning, where you used specific examples to derive generalised rules. Taken together, these are capable of producing devastating errors.

But Panini's grammar did not create these trends, nor were they confined to grammatics. You find them equally in philosophical works of the period which - unlike earlier texts - only try to interpret, expound on and clarify the meanings of existing texts; and even the original work that is done still seeks support in interpretation of existing texts. 

We see exactly the same disease in the mathematics of the period. Bhaskara tries to argue mathematics using rules of mimamsa. Mimamsa, for heaven's sake! And proofs - where they are provided - tend to be anecdotal, rather than deductive. Bronkhorst argues that philosophy in that period understood the concept of proof. He's right, technically speaking, but the form of proofs they used lacked rigour and routinely accepted exegetic and anectdotal evidence as "proof". Just as the mathematicians did.

So I don't think Bronkhorst adequately looks at what was happening in other disciplines. I think there is a readily available explanation for why the problems he identifies happened in Ancient India, as I've tried to outline above. 

There is also a clear parallel with certain modern trends (not just confined to India), where ancient knowledge is being venerated without much independent inquiry. I would like to quote one passage from Bronkhorst's paper:

Aryabhatta is wrong where he gives the volume of a pyramid as: "Half the product of the height and the [surface of the triangular base] is the volume called 'pyramid'." The correct volume of a pyramid is a third, not half, of the product here specified... The same is true of Aryabhatta's incorrect rule for the volume of a sphere.
These errors are discussed in greater detail in a 1985 paper published in a French journal. It tends to flabbergast people because the idea that Sanskrit texts might actually be wrong is not something people think about (which is absurd - no human science can ever be wholly right about everything at any point of time). 

And that, I think, is the biggest danger in the current trend of constantly exalting ancient works. Science (and any other field of inquiry) progresses best when it is most open and least dogmatic. Which is why (in my opinion) Indian science didn't progress beyond a point - and why even mathematicians as obviously gifted as Aryabhatta and Bhaskara made such glaring errors.