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> Dr George Gheverghese Joseph from The University of Manchester says the 'Kerala School' identified the 'infinite series'- one of the basic components of calcu

by vitus 6y ago

> Dr George Gheverghese Joseph from The University of Manchester says the 'Kerala School' identified the 'infinite series'- one of the basic components of calculus - in about 1350. > The discovery is currently - and wrongly - attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries. Um, infinite series existed in the time of the ancient Greeks (even if they went out of their way to avoid using limits). An instance of Archimedes dealing with an infinite geometric series: https://en.wikipedia.org/wiki/The_Quadrature_of_the_Parabola https://en.wikipedia.org/wiki/The_Quadrature_of_the_Parabola Here's the thing, though: phenomena can be rediscovered, with discoveries spaced even hundreds or thousands of years apart (e.g. Pythagorean theorem). And, there's no strong evidence either way regarding Kerala school results 1) making their way to Europe in the 17th century or before, and 2) influencing results by Newton, Leibniz, and more. But even if this is the case, Newton's line about standing on the shoulders of giants is apt -- there's no dispute here that he and Leibniz still had invaluable contributions that led to the development of calculus, or that they built on an existing foundation.

haltingproblem 6y ago
> Here's the thing, though: phenomena can be rediscovered, with discoveries spaced even hundreds or thousands of years apart (e.g. Pythagorean theorem). I agree. We call it the Pythagorean theorem and not haltingproblem's great amazing proof ;) The earliest discoverer is given the credit as long as there is some evidence of the dissemination of the discovery. The Kerala schools shows infinite series with limits and there is transmission as the article documents to Europe. Newton/Liebniz surely formalized and greatly advanced state of the art but what is the harm in giving credit to the Kerala school for the earlier discoveries.
- vitus 6y ago
  (I've flipped the order of some statements, since I think it reads better this way.) > there is transmission as the article documents to Europe The article cites opportunity (Jesuit missionaries) and motive (Gregorian calendar reform), but there's no actual evidence that, say, Clavius actually brought back the full body of the Kerala school's work, or even anything that wasn't related to calendars. "But wait," you might interject. "The article itself states: 'For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.'" But this is an assertion, without any evidence in itself. For instance, gunpowder and paper both spread from China to the Middle East before making their way to Europe. The concept of zero (as a digit) is also widely acknowledged to have originated from India. And even these are just anecdotes, not to be taken as proof or refutation of a broader trend. > The earliest discoverer is given the credit as long as there is some evidence of the dissemination of the discovery. Unfortunately, that's not always the case, especially once the associated names become ingrained. Sometimes there's co-credit even for independent discoveries, something nothing. Some examples, from https://en.wikipedia.org/wiki/List_of_examples_of_Stigler%27s_law https://en.wikipedia.org/wiki/List_of_examples_of_Stigler%27... : - Chernoff bounds were actually named because of a notable paper that used them, even though Chernoff simply failed to credit Rubin because he thought it was a minor lemma (since it's an application of Markov's inequality). - Floyd-Warshall is named after two independent discoverers, even though there's a third independent discoverer. - Gaussian elimination was well-known (and present in textbooks) at the time that he said he used "common elimination". - The Ising model was given to Ising by Lenz, his doctoral advisor. (There are plenty of other instances, e.g. Cooley-Tukey FFT, Reynolds number, Schottky diode.) Some other examples: - Watson and Crick get most of the credit for discovering DNA's structure, even though they leaned heavily on Rosalind Franklin's work (she died from ovarian cancer, probably due to x-ray radiation). - "Arabic numerals" were invented by the Indians.

by vitus 6y ago

haltingproblem 6y ago

> Here's the thing, though: phenomena can be rediscovered, with discoveries spaced even hundreds or thousands of years apart (e.g. Pythagorean theorem). I agree. We call it the Pythagorean theorem and not haltingproblem's great amazing proof ;) The earliest discoverer is given the credit as long as there is some evidence of the dissemination of the discovery. The Kerala schools shows infinite series with limits and there is transmission as the article documents to Europe. Newton/Liebniz surely formalized and greatly advanced state of the art but what is the harm in giving credit to the Kerala school for the earlier discoveries.

vitus 6y ago
(I've flipped the order of some statements, since I think it reads better this way.) > there is transmission as the article documents to Europe The article cites opportunity (Jesuit missionaries) and motive (Gregorian calendar reform), but there's no actual evidence that, say, Clavius actually brought back the full body of the Kerala school's work, or even anything that wasn't related to calendars. "But wait," you might interject. "The article itself states: 'For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.'" But this is an assertion, without any evidence in itself. For instance, gunpowder and paper both spread from China to the Middle East before making their way to Europe. The concept of zero (as a digit) is also widely acknowledged to have originated from India. And even these are just anecdotes, not to be taken as proof or refutation of a broader trend. > The earliest discoverer is given the credit as long as there is some evidence of the dissemination of the discovery. Unfortunately, that's not always the case, especially once the associated names become ingrained. Sometimes there's co-credit even for independent discoveries, something nothing. Some examples, from https://en.wikipedia.org/wiki/List_of_examples_of_Stigler%27s_law https://en.wikipedia.org/wiki/List_of_examples_of_Stigler%27... : - Chernoff bounds were actually named because of a notable paper that used them, even though Chernoff simply failed to credit Rubin because he thought it was a minor lemma (since it's an application of Markov's inequality). - Floyd-Warshall is named after two independent discoverers, even though there's a third independent discoverer. - Gaussian elimination was well-known (and present in textbooks) at the time that he said he used "common elimination". - The Ising model was given to Ising by Lenz, his doctoral advisor. (There are plenty of other instances, e.g. Cooley-Tukey FFT, Reynolds number, Schottky diode.) Some other examples: - Watson and Crick get most of the credit for discovering DNA's structure, even though they leaned heavily on Rosalind Franklin's work (she died from ovarian cancer, probably due to x-ray radiation). - "Arabic numerals" were invented by the Indians.