That's regrettable yes, as any centrism. But people interested in epistemology certainly are aware of major contributions to sciences by Indian thinkers.
Biased coverage is unfortunately rather widespread in more general media. And rise of nationalisms don't help in the matter. Which is true for western and eastern countries by the way.
Regarding a case of several millennia of prior art, there is Pāṇini, who employed metalanguage long before the idea become of interest in western side.
Although western centrism is definitely a thing, the link you provided states that temple, for example, was started in the 16th century. The article link is about something from 2800BC
I don’t know if it’s related to Western-centrism or not, but I recall thinking it was weird that my English-speaking colleagues do not know the formula to solve second-degree polynomials as the “Bhaskara formula”, as we call it in Brazil.
By the way, Wolfram’s website has an interesting summary of the history of this formula.[0]
Depends on the details of how you define calculus. Archimedes was doing integration, Descartes was evaluating slopes and tangents of algebraic curves. Isaac Barrow had a good grasp of fundamental theorem of calculus -- that differentiation and integration are inverse operations. Brook Taylor did Taylor series before Newton.
Newton and Leibnitz get credit because they placed calculus as a general technique that is immensely broadly applicable not just for extrapolating the tangent function or the sin function as a series, but to any function that's smooth in some sense.
They worked out the details that do not depend on the specifics of the function and called them out as rules/results of broad applicability. Especially how to push the differential and integral operations through +,-,×,÷ and function composition sign. It did not matter what the function was as long as it was built up from those operations.
I am familiar with the work of Kerala school and also of Aryabhatta's work on using differential coefficients to extrapolate the sin function (this being much before Kerala school), his work on difference equations.
Rather than getting caught up with us versus them narratives , spend some time learning about the beauty of math and how different cultures have thought about them in such creative ways. Otherwise you risk sounding ignorant and rageful conspiracy monger.
The inaccuracies in the Hindu calendar is and was a lot more than the Julian calendar. The Julian calendar assumed that a year was 365 1/4 the day. This is slightly inaccurate and therefore there was a need to correct for the leap day that's added every 4 years by skipping it every 100 years, adding it back every 400 years. At time of Gregorian correction it was off by 10~11 days because of an error of 10 minutes in their estimate of the length of an year.
Hindu civilization's estimate of the length of an year, although remarkably accurate for its time, was less accurate than the estimate of 365 1/4th. Usually the length of an year has been overestimated, making the Hindu calendar lose accuracy quicker. These errors were order of a day per year versus off by about 10 minutes like the Julian calendar.
This was less of a problem historically because Ujjain observatory would correct the calendar time time using accurate observation of the Equinox. Since the fall of Ujjain observatory the Hindu calendar has been accumulating drift error for centuries.
The current state is such that we can, with great authority, give an exact measure of each "years" length, with every one bieng unique.
You touch on but dont quite state that math is a usefull game, but miss that reality does not use math consistantly, and we force arbitrary units and measures onto what we are trying to understand, but are still clueless as to what the nature of reality is, and how it works.
Testable theorys are thin on the ground now,Newton and his peers, past,present,here, and there, would be and are, unsatisfied with the meager conclusions we have, sure we can sincronise, and our tools and toys are wonderfull, but the universe remains,theoretical.
It takes my breath away how consistent the mean length of a day is and how accurately we can measure it. So accurately that if it deviates by mere tens of milliseconds, and it does, we can notice it.
It boggles my mind that a hunk of rock made up of differing densities, with so much of salty water sloshing around, Moon exerting her brakes, bombardments by extraterrestrial matter, Earth still remains so consistent. Of course, this is not surprising if one does the math.
Yes math and physics are different. It's the the fact that math can model the physics so accurately at all that it's breathtaking.
> Blatant Western-centrism within academia (and the strange, almost primitive-hatred for living ancient-cultures) perhaps hasn't led either to the recognition of "ancient" monuments in India or its scientific/astronomical outputs.
Enough with this bullshit please? There are genuine reasons why the knowledge of the calculus of ancient Kerala didn't travel outside India during the late middle ages.
It is a fact that Madhava a mathematician and astronomer from the late middle ages, came up with calculus, and established the Nila School of Mathematics in Kerala. For some reason, the book (Yuktibhasa) that discusses this math is written in the local language Malayalam. Most scholars at the time only understood Sanskrit, including later Western scholars who were unable to find good Malayalam book. Because of this, it was difficult to have the works translated, especially since the works describe formal proofs of concepts like series expansion, which was not even known in the Northern India at the time.
Kerala was also under Portuguese rule at the time and was frequently faced with wars, so the school gradually declined and the math culture sort of died out.
The Mathematics of India by P.P. Divakaran discusses these themes.
P.S: Most of what I've said here is taken from this Numberphile video of another mathematician discussing the life and work of P.P. Divakaran (who recently passed away)
https://www.youtube.com/watch?v=G23Jx0kPCSI
That's regrettable yes, as any centrism. But people interested in epistemology certainly are aware of major contributions to sciences by Indian thinkers.
Biased coverage is unfortunately rather widespread in more general media. And rise of nationalisms don't help in the matter. Which is true for western and eastern countries by the way.
Regarding a case of several millennia of prior art, there is Pāṇini, who employed metalanguage long before the idea become of interest in western side.
https://en.wikipedia.org/wiki/P%C4%81%E1%B9%87ini
Although western centrism is definitely a thing, the link you provided states that temple, for example, was started in the 16th century. The article link is about something from 2800BC
The article is about more than just that one monument and has a few contemporary examples as well.
I don’t know if it’s related to Western-centrism or not, but I recall thinking it was weird that my English-speaking colleagues do not know the formula to solve second-degree polynomials as the “Bhaskara formula”, as we call it in Brazil.
By the way, Wolfram’s website has an interesting summary of the history of this formula.[0]
[0]: https://mathworld.wolfram.com/QuadraticEquation.html
Interesting that it is called Bhaskara formula.
In India and also in general it's called Sridharacharya formula or method. It's named after the Indian algebraist Sridhar
https://en.wikipedia.org/wiki/Sridhara
whom Bhaskara quotes extensively.
Depends on the details of how you define calculus. Archimedes was doing integration, Descartes was evaluating slopes and tangents of algebraic curves. Isaac Barrow had a good grasp of fundamental theorem of calculus -- that differentiation and integration are inverse operations. Brook Taylor did Taylor series before Newton.
Newton and Leibnitz get credit because they placed calculus as a general technique that is immensely broadly applicable not just for extrapolating the tangent function or the sin function as a series, but to any function that's smooth in some sense.
They worked out the details that do not depend on the specifics of the function and called them out as rules/results of broad applicability. Especially how to push the differential and integral operations through +,-,×,÷ and function composition sign. It did not matter what the function was as long as it was built up from those operations.
I am familiar with the work of Kerala school and also of Aryabhatta's work on using differential coefficients to extrapolate the sin function (this being much before Kerala school), his work on difference equations.
Rather than getting caught up with us versus them narratives , spend some time learning about the beauty of math and how different cultures have thought about them in such creative ways. Otherwise you risk sounding ignorant and rageful conspiracy monger.
The inaccuracies in the Hindu calendar is and was a lot more than the Julian calendar. The Julian calendar assumed that a year was 365 1/4 the day. This is slightly inaccurate and therefore there was a need to correct for the leap day that's added every 4 years by skipping it every 100 years, adding it back every 400 years. At time of Gregorian correction it was off by 10~11 days because of an error of 10 minutes in their estimate of the length of an year.
Hindu civilization's estimate of the length of an year, although remarkably accurate for its time, was less accurate than the estimate of 365 1/4th. Usually the length of an year has been overestimated, making the Hindu calendar lose accuracy quicker. These errors were order of a day per year versus off by about 10 minutes like the Julian calendar.
This was less of a problem historically because Ujjain observatory would correct the calendar time time using accurate observation of the Equinox. Since the fall of Ujjain observatory the Hindu calendar has been accumulating drift error for centuries.
The current state is such that we can, with great authority, give an exact measure of each "years" length, with every one bieng unique. You touch on but dont quite state that math is a usefull game, but miss that reality does not use math consistantly, and we force arbitrary units and measures onto what we are trying to understand, but are still clueless as to what the nature of reality is, and how it works. Testable theorys are thin on the ground now,Newton and his peers, past,present,here, and there, would be and are, unsatisfied with the meager conclusions we have, sure we can sincronise, and our tools and toys are wonderfull, but the universe remains,theoretical.
unless you bump your toe on part of it.
It's the other way around.
It takes my breath away how consistent the mean length of a day is and how accurately we can measure it. So accurately that if it deviates by mere tens of milliseconds, and it does, we can notice it.
It boggles my mind that a hunk of rock made up of differing densities, with so much of salty water sloshing around, Moon exerting her brakes, bombardments by extraterrestrial matter, Earth still remains so consistent. Of course, this is not surprising if one does the math.
Yes math and physics are different. It's the the fact that math can model the physics so accurately at all that it's breathtaking.
4 replies →
> Blatant Western-centrism within academia (and the strange, almost primitive-hatred for living ancient-cultures) perhaps hasn't led either to the recognition of "ancient" monuments in India or its scientific/astronomical outputs.
Enough with this bullshit please? There are genuine reasons why the knowledge of the calculus of ancient Kerala didn't travel outside India during the late middle ages.
It is a fact that Madhava a mathematician and astronomer from the late middle ages, came up with calculus, and established the Nila School of Mathematics in Kerala. For some reason, the book (Yuktibhasa) that discusses this math is written in the local language Malayalam. Most scholars at the time only understood Sanskrit, including later Western scholars who were unable to find good Malayalam book. Because of this, it was difficult to have the works translated, especially since the works describe formal proofs of concepts like series expansion, which was not even known in the Northern India at the time.
Kerala was also under Portuguese rule at the time and was frequently faced with wars, so the school gradually declined and the math culture sort of died out.
The Mathematics of India by P.P. Divakaran discusses these themes.
P.S: Most of what I've said here is taken from this Numberphile video of another mathematician discussing the life and work of P.P. Divakaran (who recently passed away) https://www.youtube.com/watch?v=G23Jx0kPCSI
We probably move in similar circles because not everyone will be familiar with Prof Divakaran's passing.