WI: Indian mathematicians develop calculus first

The other thing is that the Kerala school mathematicians were somewhat isolated from any other potential schools of knowledge in Northern or Eastern India. There's no real evidence of communication with anyone outside of Kerala (aside from some fanciful theories about their ideas making it to France through Italy). Leibniz and Newton, 200 years later, were very much part of a broader European mathematical community.

Edit: Incidentally, does anyone know if the Kerala mathematicians knew of or read the work of Bhaskara II, who lived a couple hundred years before they got started? I assume so, but I can't find a source that says so.

Cheers,
Ganesha

It is a very reasonable supposition.
It is also possible that Bhāskara II's work made its way westwards via Arab traders and possibly Leonardo of Pisa (also known as Fibonacci, yes, that guy) may have heard of it (although no proof of that I'm aware of). He introduced the modus Indorum, better known as Arabic numerals to Europe and worked with the leading Arab mathematicians of his time (13th C.). He was definitely a part of the conceptual train that eventually gave birth to Calculus.
 
Then they could do it, and this talk of merchant guilds and modern institutions is an irrelevant detour.

The talk of merchant guilds and institutions concerns what they could do if they developed calculus, namely whether or not such a breakthrough could have been utilized to a practical end. After all, I asked what would have happened if they'd developed calculus first, not whether or not they could've. Although, I'd say that the true key to the usage of mathematical advances lies in academic institutions devoted to a wide range of sciences. The Kerala School was devoted wholly to mathematics and astronomy, and I can't find much about Indian understanding of physics or chemistry. I imagine this would've had a more immediate impact than the lack of merchant guilds.
 
After all, I asked what would have happened if they'd developed calculus first, not whether or not they could've.

Indeed you did, but Flocc's reply read to me, and I see now that I misread, that he was implying that these things were important to the possible development of Calculus.
 
The other thing is that the Kerala school mathematicians were somewhat isolated from any other potential schools of knowledge in Northern or Eastern India. There's no real evidence of communication with anyone outside of Kerala (aside from some fanciful theories about their ideas making it to France through Italy). Leibniz and Newton, 200 years later, were very much part of a broader European mathematical community.

Edit: Incidentally, does anyone know if the Kerala mathematicians knew of or read the work of Bhaskara II, who lived a couple hundred years before they got started? I assume so, but I can't find a source that says so.

Cheers,
Ganesha

As always, solid textual evidence is ridiculously hard to find when dealing with South India.
 
The talk of merchant guilds and institutions concerns what they could do if they developed calculus, namely whether or not such a breakthrough could have been utilized to a practical end. After all, I asked what would have happened if they'd developed calculus first, not whether or not they could've. Although, I'd say that the true key to the usage of mathematical advances lies in academic institutions devoted to a wide range of sciences. The Kerala School was devoted wholly to mathematics and astronomy, and I can't find much about Indian understanding of physics or chemistry. I imagine this would've had a more immediate impact than the lack of merchant guilds.

Yup- that was my point. Philosophy (of all sorts, scientific and metaphysical) in India always tended to be treated more along the lines of esoteric pure knowledge, so to speak.

Where Newton came up with a theory he could publish his findings to various learned societies (recorded for anyone literate to see). If someone in Kerala came up with a theory, he'd have it discussed within a small and cloistered group of academics. It's as if Oxford and Cambridge were run like isolated monasteries.

It's also struck me that a scientific lingua franca (in Latin) was another advantage Europe had. From what I can tell the Kerala School mathematicians wrote in Malayalam which wouldnt be understood outside Kerala.
 
Yup. I think the key is whatever it was that tipped the balance from guilds into more modern institutions. I'd argue that the key is probably something to do with with the upheaval brought by the Black Death and the Reformation.

Black Death, Renaissance and Reformation had certainly a lot of importance. However I believe that the tipping point was the discovery of the Americas: the availability of new and untapped resources, including many staple food not known before, and the increase to commerce which came very fast. That's geography (or luck)
 
Black Death, Renaissance and Reformation had certainly a lot of importance. However I believe that the tipping point was the discovery of the Americas: the availability of new and untapped resources, including many staple food not known before, and the increase to commerce which came very fast. That's geography (or luck)

That's also true but the food explosion also had major effects on Asia- China went through a massive population boom due to maize, for example. The transpacific columbian exchange was just as huge as the transatlantic one.

I don't think it had as much of an effect on India (potatoes and maize were adopted but never became more than supplementary crops) but the point stands.

You could, however, argue, that the shifting of the global trade routes to transatlantic/transpacific trade led to a relative sidelining of the Indian Ocean trade and a decline in the maritime societies of South India.
 

dead_wolf

Banned
Speaking of institutions, would the development of calculus in India really change much? It seems like it'd just be an interesting hobby for a very select few. There wasn't the same open air of exchange of ideas in India as there was in Europe at the same time.
 
That's also true but the food explosion also had major effects on Asia- China went through a massive population boom due to maize, for example. The transpacific columbian exchange was just as huge as the transatlantic one.

I don't think it had as much of an effect on India (potatoes and maize were adopted but never became more than supplementary crops) but the point stands.

You could, however, argue, that the shifting of the global trade routes to transatlantic/transpacific trade led to a relative sidelining of the Indian Ocean trade and a decline in the maritime societies of South India.

IIRC the population boom in China came in the 17th century and they certainly benefited from new foods from the Americas (not just maize but also potatoes).
The point to explore however is why this population boom did not bring major changes to Chinese society: Ian Morris claims that China was in a high-equilibrium trap. Maybe it's because the social structure was too strong, there was no foreign commerce (in the European sense) and the bonus of new staple foods was not enough to break the hard ceiling.

I have two questions to ask you however: leaving China aside, why the impact of maize and potatoes was so limited in India? and why the arrival of the Portuguese did not kick off a revival of maritime and commercial societies in India? I don't think it should have been so difficult for the western coast of India to imitate the Portuguese naos and also naval artillery should be easy enough to copy.
 
Yup- that was my point. Philosophy (of all sorts, scientific and metaphysical) in India always tended to be treated more along the lines of esoteric pure knowledge, so to speak.

Where Newton came up with a theory he could publish his findings to various learned societies (recorded for anyone literate to see). If someone in Kerala came up with a theory, he'd have it discussed within a small and cloistered group of academics. It's as if Oxford and Cambridge were run like isolated monasteries.

It's also struck me that a scientific lingua franca (in Latin) was another advantage Europe had. From what I can tell the Kerala School mathematicians wrote in Malayalam which wouldnt be understood outside Kerala.

Agreed. The point about the lack of a common language is also really interesting - I don't know why I never noticed that before, but you're right. Obviously it must have helped Europe to some extent (probably to a large extent) that many literates and scientists in almost every country wrote and read in the same language.

As for the general lack of communication, what was the medium of writing in India at the time of the beginning of the Kerala school? Were they using paper, or was that introduced later (around the same time as Europe)? Sources (again!) are difficult to find.

IIRC the population boom in China came in the 17th century and they certainly benefited from new foods from the Americas (not just maize but also potatoes).
The point to explore however is why this population boom did not bring major changes to Chinese society: Ian Morris claims that China was in a high-equilibrium trap. Maybe it's because the social structure was too strong, there was no foreign commerce (in the European sense) and the bonus of new staple foods was not enough to break the hard ceiling.

I have two questions to ask you however: leaving China aside, why the impact of maize and potatoes was so limited in India? and why the arrival of the Portuguese did not kick off a revival of maritime and commercial societies in India? I don't think it should have been so difficult for the western coast of India to imitate the Portuguese naos and also naval artillery should be easy enough to copy.

Simply because maize and potatoes won't grow well in India. While northern China has a temperate climate, there's very little land in India that grows anything other than tropical and subtropical crops (the Punjab being a big exception, but wheat was already dominant there). Some crops were huge successes (like chili peppers) but aren't primary food sources.

As for the imitation of naval structures, it would be possible for Indian states to make say, 1 gunboat, but turning out dozens of high-quality ships requires institutional structure, something that was often lacking. The Portuguese and Dutch were occasionally defeated by Indian fleets (see the Battle of Colachel and Kanhoji Angre) but there was no chance of large-scale victories.

Cheers,
Ganesha
 

Sulemain

Banned
All this talk of Indian maths and science and such makes me wonder how we (The Brits) came to control such a proud, prosperous, productive land. And yes, I know it was due to divide and conquer and to the application of superior infantry tactics and such, but still! One of history's unlikelier occurrences.

Of course, the withdrawal of China from the Indian Ocean leaving the door open for Portuguese (later Dutch then British) dominance didn't help. Did any Indian state develop there own navy/navies?
 
Agreed. The point about the lack of a common language is also really interesting - I don't know why I never noticed that before, but you're right. Obviously it must have helped Europe to some extent (probably to a large extent) that many literates and scientists in almost every country wrote and read in the same language.

As for the general lack of communication, what was the medium of writing in India at the time of the beginning of the Kerala school? Were they using paper, or was that introduced later (around the same time as Europe)? Sources (again!) are difficult to find.



Simply because maize and potatoes won't grow well in India. While northern China has a temperate climate, there's very little land in India that grows anything other than tropical and subtropical crops (the Punjab being a big exception, but wheat was already dominant there). Some crops were huge successes (like chili peppers) but aren't primary food sources.

As for the imitation of naval structures, it would be possible for Indian states to make say, 1 gunboat, but turning out dozens of high-quality ships requires institutional structure, something that was often lacking. The Portuguese and Dutch were occasionally defeated by Indian fleets (see the Battle of Colachel and Kanhoji Angre) but there was no chance of large-scale victories.

Cheers,
Ganesha

Persian was the cosmopolitan language of India for a long while and while Vijayanagar and its successors didn't use it, the Deccan Sultanates did.

In terms of developing a proper navy, Indian traders did have interests in a lot of areas, and Akbar himself expressed interest in buying a large Portuguese ship- which might have perhaps been reverse engineered into a small fleet. If that interest is shared with the nobles- perhaps the Siddis of Gujarat see a way to expand their power through control of more ships- then construction of a fleet might be encouraged.
 
All this talk of Indian maths and science and such makes me wonder how we (The Brits) came to control such a proud, prosperous, productive land. And yes, I know it was due to divide and conquer and to the application of superior infantry tactics and such, but still! One of history's unlikelier occurrences.

Initially, it was simply offering some nobles a better deal than the Mughal Empire- that bloomed into the Unlikely Empire of British India over time. :p
 
Persian was the cosmopolitan language of India for a long while and while Vijayanagar and its successors didn't use it, the Deccan Sultanates did.

In terms of developing a proper navy, Indian traders did have interests in a lot of areas, and Akbar himself expressed interest in buying a large Portuguese ship- which might have perhaps been reverse engineered into a small fleet. If that interest is shared with the nobles- perhaps the Siddis of Gujarat see a way to expand their power through control of more ships- then construction of a fleet might be encouraged.

I gather that prior to that, Sanskrit and to a lesser extent Pali pretty much operated like Latin in being the common languages of cultivated use among Indian intellectual circles.
However, I also get the impression that this was much less the case in Kerala and Tamilnad. Fascinating topic, by the way.
 
I think one of the key points is that India lost its status as a waypoint between the Middle East/Europe and China as the Europeans (and especially the Portuguese) developed ships capable of much longer-distance journeys on the open ocean. After a certain point, the Portuguese presence in India was about convenience and not necessity.

Trade across the Indian ocean was traditionally coastal and therefore controlled by many local entities. However, once the open ocean came into play, Indian states lost the ability to tax and control trade across the Indian ocean, leading to a decline in revenue and power. If Indian nobles decide at that point to contest the Portuguese, Dutch (and later British) for control of the sea, that's when they need to build - before the Europeans are too much established to get rid of. By the time the Marathas are around, it's too late.

I gather that prior to that, Sanskrit and to a lesser extent Pali pretty much operated like Latin in being the common languages of cultivated use among Indian intellectual circles.
However, I also get the impression that this was much less the case in Kerala and Tamilnad. Fascinating topic, by the way.

It also depends on the time period. Sanskrit is a liturgical language foremost and a language of cross-cultural communication secondarily. As Badshah mentioned, once the Delhi Sultanate was established, Persian was far more in vogue across North India. Bengali underwent a lot of use early on in the 14th and 15th centuries as well in Eastern India.

Cheers,
Ganesha
 
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One of the problems with earlier calculus is that, initially, its magic, to oversimplify.

Newton used 'infinitesmals' which dont exist (OK, so Robinson in the 1970s managed to create an eqivalent), so you have to do a lot of handwaving. Its not until a century or so later that theres actually a foundation underneath the structure.

Archimedes was halfway there. The Indians and Chinese were, too. But the level of handwavium needed to get your results probably made some of them give up.
 
IIRC the population boom in China came in the 17th century and they certainly benefited from new foods from the Americas (not just maize but also potatoes).
The point to explore however is why this population boom did not bring major changes to Chinese society: Ian Morris claims that China was in a high-equilibrium trap. Maybe it's because the social structure was too strong, there was no foreign commerce (in the European sense) and the bonus of new staple foods was not enough to break the hard ceiling.

I've read that concurrently there was a crash in fertility brought about by intensive tobacco cultivation in South China. They sort of cancelled each other out.

I have two questions to ask you however: leaving China aside, why the impact of maize and potatoes was so limited in India? and why the arrival of the Portuguese did not kick off a revival of maritime and commercial societies in India? I don't think it should have been so difficult for the western coast of India to imitate the Portuguese naos and also naval artillery should be easy enough to copy.


As for why the impact was limited- no idea. South India certainly doesn't have the best climate for maize or potatoes but I'm not sure why they never really took off in the North.

As for a revival- because the Portuguese initiated a comprehensive campaign to crush any potential opposition. It's hard to build up a naval force when your trade and maritime capabilities are repeatedly smashed by Portuguese forces before you can build them up.

You do see some evidence of Indian shipbuilding capabilities recovering int he 17th C when the Malayalee kingdom of Travanacore beat the Dutch in a minor war but this is a couple of centuries after the period in question.
 
Persian was the cosmopolitan language of India for a long while and while Vijayanagar and its successors didn't use it, the Deccan Sultanates did.

Of North India, yes- the nobility of the Deccan sultanates used Persian and Urdu but the academics aren't genrally going to be part of this social class. Persian was never a lingua franca in South India. In any case Kerala was never under the sway of the Deccan sultanates- it's even further South an in a totally different cultural sphere where Tamil and Malayalam were the main languages.
 
I gather that prior to that, Sanskrit and to a lesser extent Pali pretty much operated like Latin in being the common languages of cultivated use among Indian intellectual circles.
However, I also get the impression that this was much less the case in Kerala and Tamilnad. Fascinating topic, by the way.

Yup- it's important not to lump India together as a whole. You're right in that even liturgicaly Kerala and Tamilnad tended to lean towards Classical Tamil.
 
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