William Dalrymple is one of the finest historians and authors who has previously brought to life the story of East India Company and how it led to British India.
In this book, he focuses on, among other things, how Buddhism spread all over.
It's a fascinating topic. He also has a very successful podcast [1][2] -- with his co-host Anita Anand -- The Empire Podcast, which chronicles the rise and fall of empires. Highly educational, not to mention entertaining.
I second the podcast recommendation. Empire pod has been truly worth every bit of the time. I am currently on the episode about History of coffee - ethiopia, ottoman turks etc.
Hmmm, interesting that you give agency for 75 years of history to those in China, but not in India. Are you claiming there is some racial superiority of the Han over Hindu? Couldn't you also argue that the rise of debt based mercantilist growth in China and subversion of Maoist Communism was a devious western European plan? Is that due to some inherent Aryan superiority that makes them responsible for every modern condition, or is it that devious plans put in place 50 years ago by Henry Kissinger and Winston Churchill have just come to fruition?
Ok, so Kissinger and Churchill. Thanks for the clarification.
I'm sure you're aware of the Indo-Soviet cooperation treaty of '71. Those sneaky anglophones strike again. I'm surprised you've been fooled by their clever subterfuge in China. The current business conditions there are everyone's fault but their own. For reference it all started with tricking Deng into supporting the Khmer Rouge and embarassingly invading Vietnam in '78.
I assume The West is also responsible for the Wagner Group in Africa, but not for the fall of apartheid in South Africa. I just want to get the collective guilt right.
I am sure Sachar committee would have loved to hear about these Islamic overlords oppressing Muslims in India or having last Muslim majority state having statehood taken away
This has basically nothing to do with the parent comment about Muslim "overlords" treating Indians badly. It's more about how superstitions and belief without applied logic can restrict avenues to worldly success
You have not understood my and the parent's comment i was responding to.
You have to know what the "Sachar Committee" was and its recommendations, to understand why the parent sarcastically referred to it in its comment. My comment will then become clear.
Pervez Hoodbhoy has spent a lifetime (and much reviled for it in Pakistan and by most Muslims all over the world) trying to shine a light on why the Islamic culture/society has fallen behind dramatically in Scientific/Economic/Social progress in the 21st century and become regressive/backward. The video i linked to gives a snippet and you can find more detailed analysis in his longer videos (available on Youtube) and books.
Because he and many other online-only viewpoint pushers only considers the situations where he and his in-group are the victim, not the other way around
In the West the numerals we use are known as "Arabic numerals" because it came from the middle east. But in the middle east the same numerals are known as "Indian numerals" because that's where they got it from.
Similarly, algebra came from the middle east where it was called "al-Jabr" [1], but they in turn got it from India [2].
The invention of calculus is traditionally attributed to Isaac Newton and Gottfried Leibniz. But this book [3] says calculus was brought into being in India in the 14th century by a mathematician named Madhava.
Years ago I worked on a site which was translated into Arabic. Some of the early partners were adamant that we needed to use the Indic numerals everywhere, so I had localized all of our UI, including some JavaScript widgets and worked with a third-party to localize their embed. A few years later, they had a larger conference with a wider swath of the Arabic-fluent world represented and pretty much everyone said we should use what the English-speaking world calls Arabic numerals because most people were more familiar with them than the Indic numeral variants they didn’t use, and computers were making that even more pronounced.
It's difficult to call Madhava's work calculus as we know it. He and his school certainly made huge contributions to analysis of infinite series, but they did not develop that into a unifying framework. It's important to note that no mathematics is done in a vacuum, if Newton/Leibniz "invented" Calculus, it's by building on top of hundreds of years of work done throughout the world.
I encountered this topic a while, back and had a deep look into it, I will be sharing my insights and formed opinion based on the facts that I encountered.
@Dx51Q
I appreciate your perspective, but I'd like to clarify a few points regarding Madhava's contributions to calculus. While it's true that Madhava and his school may not have created a unifying framework like Newton and Leibniz did, their work laid crucial groundwork for what we now consider calculus. Madhava is credited with developing infinite series for trigonometric functions such as sine and cosine, which are equivalent to the Taylor series we use today.
For example, his series for sin(x) and cos(x) predate those discovered in Europe by over 200 years[1][2].
His followers, like Jyeṣṭhadeva, further elaborated on these concepts in texts like the Yuktibhāṣā, providing proofs and demonstrating their applications[3][5]. Moreover, Madhava's methods for approximating pi were remarkably accurate, achieving values correct to 11 decimal places, showcasing his advanced understanding of numerical analysis[2][4].
This indicates that he was indeed engaging with concepts foundational to calculus, such as limits and convergence. Thus, while Madhava's work may not fit neatly into the modern definition of calculus, it represents a significant and sophisticated mathematical tradition that deserves recognition as a precursor to later developments in the field.
While we are on this topic, we can stop for a second and ponder on why the ancient Indians needed these mathematical formulation. The answer is astronomy, and thus needing a language/framework to understand the cosmos, i.e. mathematics.
Additionally, I wanted to share some interesting insights about the Jesuit transmission of both calculus and the Gregorian calendar from Kerala to Europe. The Jesuit missionaries were not only spreading Christianity through their work, but they were scholars in their own right and could see the value of the advance mathematics they encountered by the Kerala (India) school of mathematics by madhava and the advanced calendar, more accurate than the julian calendar used in Europe at the time.
Jesuit missionaries, especially Matteo Ricci, were really fascinated by the advanced mathematical knowledge coming from the Kerala school. They connected with local scholars, like Brahmins and Kshatriyas, to learn about their mathematical concepts, including those found in texts like the Yuktibhāṣā and Tantrasangraha [5]. This collaboration was part of the Jesuits' efforts to understand local cultures and improve their missionary work. It’s fascinating to think that this exchange not only contributed to the Gregorian calendar reform in 1582 but also helped introduce key calculus concepts into European mathematics.
As to why this is not common knowledge, it’s partly the British colonial policies that muddied the waters and/or suppressed the source of information. But If one looks at it with time, the evidence is there
Going to preface this by saying that it's completely uncontroversial that the Kerala school discovered a lot of foundational mathematical concepts independently and in many cases earlier than Europeans, but the evidence for any transmission of those ideas to europe is _extremely_ thin, and you can see the organic development of it mostly within Europe in the textual record after the introduction of Arabic numbers and Arabic mathematical texts to Europe (which of course themselves where _hugely_ influenced by Indian mathematics themselves).
You can of course make the argument that colonialist historians are motivated to erase the contributions of foreign mathemeticians, but the _mathematicians themselves_ were not shy about crediting the influence of arabic philosophers and mathematicians, so it would have to be explained why they were fine with crediting al-Khwārizmī but drew the line at crediting Madhava. If they did have direct access to the works of the Kerala school, they'd have developed Calculus much more quickly, that's for sure.
It's very possible that there was some extremely vague indirect transmission through word of mouth where the source was obscure even to the mathematicians themselves, but I think it's hard to make the argument that "if not for Madhava, calculus would not have been discovered in Europe." There were many scientists and mathematicans all circling around the same problems and several of them solved aspects of it independently at the same time from different directions.
And the idea that _Euler_ only discovered power series with help from Indian mathematics is ridiculous. You can see in his own books and his correspondence with others how he gradually worked them out from first principles over time. There's no mystery as to where it came from. If he had just read about them from a book, he would have used them and not spent several years trying to figure it out.
The development of math in Europe was _absolutely_ dependent on the introduction of Indian mathematical ideas through Arabic texts, though.
The claim of "extremely thin evidence" for the transmission of Kerala mathematics to Europe by Jesuits is far from accurate. In fact, there's a wealth of circumstantial evidence supporting this possibility. Jesuits were present in Kerala from 1540-1670, with many, like Matteo Ricci, being highly trained mathematicians tasked with studying Indian sciences.
We have clear documentation of their interest in local mathematics, astronomy, and timekeeping, even incorporating subjects like jyotisa into their curricula. Numerous examples show Jesuits actively gathering and transmitting knowledge, from Ricci's inquiries about Indian calendars to Schreck's astronomical observations sent to Kepler.
Their close relationships with the Court of Cochin provided access to valuable mathematical manuscripts, and there's evidence of collaboration with Brahmins in translating Sanskrit works.
The Jesuits were strongly motivated by practical needs in navigation and calendar reform. Moreover, Marin Mersenne's extensive correspondence network demonstrates that awareness of Indian mathematical knowledge was circulating in Europe. Intriguingly, there are methodological similarities between Kerala mathematics and later European developments, such as parallels between methods used by Wallis and those in the Yuktibhasa.
I believe it's crucial to consider the historical context of knowledge transmission between cultures, which often involved clandestine methods. A prime example is the case of Robert Fortune, a Scottish botanist, who in 1848 undertook a covert mission for the British East India Company. Fortune, disguised as a Chinese merchant from a distant province, infiltrated China's heavily guarded tea-growing regions. His objective was to acquire tea plants and seeds, along with the closely guarded secrets of tea production. Fortune's mission was successful; he managed to remove thousands of tea plants and seeds from China, effectively ending the Chinese monopoly on tea production.
This act of industrial espionage had far-reaching consequences, leading to the establishment of vast tea plantations in India and Ceylon (now Sri Lanka), and fundamentally altering the global tea trade. While this example pertains to botany rather than mathematics, it illustrates the lengths to which nations went extract knowledge.
(Source: Joseph, G. G. (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton University Press.)
The thing is, circumstantial evidence that transmission could have happened, though suggestive, isn't positive evidence that it did happen. The absence of such direct evidence such as translations or quotations from relevant Indian works in Europe is even emphasized in Joseph's book that you give as ref.
The claim that Madhava "laid crucial groundwork" for the development of calculus in Europe needs to be backed up with some argument saying exactly what was transmitted and when. The problem with simply observing that his results on infinite series for arctan, sin and cos reappeared in Europe much later is that this doesn't rule out independent discovery in Europe. And the case for independent discovery is strong, because we have the documentary evidence of the logic of discovery: Newton and Gregory both obtained these series from the general binomial series, seemingly independently of each other, and to my knowledge Madhava didn't have this result.[0] They're both clearly basing their works on documented predecessors (who happen to be European) such as Wallis, Fermat, Descartes, Viete, and others, so the trajectory of how the results were obtained seems to be accounted for.
So what was the crucial groundwork, and when was it transmitted? There might have been something (e.g. your suggestion about parallels between Wallis and the Yuktibhasa), but I haven't seen a strong argument that gives these details. I would be fascinated if there were though.
[0] Stillwell 2010 Mathematics and its History (3rd ed.)
- Stillwell is sympathetic to the Kerala school, is very clear in assigning Madhava priority on the arctan, sin and cos series, but concludes, along with most historical scholarship, that it seems there was no transmission of these results to Europe
Transmission of the calculus from Kerala to Europe: "...we propose to adopt a legal standard of evidence good enough to hang a person for murder." See document for (1) motivation, (2) opportunity, (3) circumstantial evidence, and (4) documentary
evidence.
Thanks, it's interesting and gives some suggestive information about the motivations concerning navigation and calendrical reform.
It has some severe weaknesses when trying to make the case for influence on mathematics, though.
The authors mention Pell's equation x^2+Ny^2=1, and the method given by Bhaskara II to find solutions x,y for arbitrary N (though others note the method was given earlier by Jayadeva).[0] Bhaskara gives the example of N=61. Fermat, in a letter to his friendly rival Frenicle, also gives the example N=61 as a challenge. Now, if 61 were arbitrary in this context, then this would be something like a smoking gun showing almost certain influence. However, 61 is very special here, because the smallest solutions x and y that satisfy the equation are suddenly much larger for 61 than for any smaller N (they're of order 10^10). The authors of the paper don't mention this crucial detail. Fermat also challenges his pal with N=109, which has similarly huge minimal solutions (order 10^15), and which Bhaskara does not give. Fermat writes that he's chosen smallish values of N, "pour ne vous donner pas trop de peine," so he's obviously chosen these values precisely because they're fiendishly difficult, and that's no doubt why Bhaskara also chose 61 as an example, and that's adequate explanation for why the same value shows up in the two places. Fermat had been working on number theory for some decades prior to this point, and his correspondence shows him working through simpler versions of this and related problems, making many original contributions along the way.[0]
The example the authors give about influence on calculus has similar weaknesses. The example they give involves using the sum of the kth powers to integrate x^k. They write that "the formula had no natural epistemological basis in European mathematics," which almost made me spit out my tea because it suggests the authors haven't heard of Archimedes, who used exacly this method with k=2 to give his quadrature of the parabola, and this was well known in Europe at the time (although his works had only really been rediscovered in Europe in the 1500s). The Arab mathematician Al-Haytham had extended the method with k=1,2,3, and 4 in the 10-11th cenury, Cavalieri in 1635 had calculated up to k=9 and conjectured the integral was (1/(k+1))x^(k+1), before Fermat, Pascal, and Roberval gave their proofs of this general relation.[1][2] This last point especially means I don't understand what the authors of the paper mean when they say "the European mathematicians were unable to prove the formula or provide a rigorous rationale for it within their epistemology." ... They did give proofs, and what they were doing was completely intelligible within the historical development leading up to that time.
These are the points I know about, and they don't fill me with confidence about the authors' other judgements.
[0] Andre Weil 1984 Number Theory: An approach through history (ch.1 section 9 mentions Jayadeva and see ch.2 on Fermat, esp. sections 12 and 13)
[1] Edwards 1979 The Historical Development of the Calculus (p.109ff.)
[2] Stillwell 2010 Mathematics and its History (section 9.1)
Firstly, your claim about Stillwell's "conclusion" is a misrepresentation. Stillwell makes no such conclusion about the lack of transmission. In fact, he explicitly states that the Kerala school knew these mathematical series before 1540. This selective reading and distortion of Stillwell's work is intellectually dishonest and undermines genuine historical inquiry.
The Jesuits sent to India weren't not your typical bible thumpers; they were highly trained mathematicians and astronomers with a specific mission to study and acquire Indian mathematical and astronomical knowledge. The primary motivation for Europeans to import knowledge from India wasn't mere academic curiosity - it was a matter of practical necessity, particularly in navigation. By the mid-16th century, Europeans were grappling with significant errors in their calendar calculations. The true solar year was about 11.25 minutes shorter than the assumed 365.25 days, an error that had compounded over centuries, leading to serious discrepancies in timekeeping and navigation. Matteo Ricci, the Jesuit astronomer and mathematician in a letter from India to Giovanni Battista Maffei (Italian mathematician) he states that he requires the assistance of an “intelligent Brahmin or an honest Moor” to help him understand the local ways of recording and measuring time.
If one wants a smoking gun—a direct admission of knowledge transfer—is either naïve or deliberately obtuse. Do you also believe that tea plants magically teleported from China to India? The British East India Company's industrial espionage in China's tea industry parallels the Jesuits' activities in India perfectly. Both were covert operations aimed at acquiring valuable "know-how" for economic and strategic gain. Do we have a signed confession from Robert Fortune or his kin admitting to tea espionage?
The cumulating circumstantial evidence isn't just substantial—it's overwhelming. We have documented records of Jesuits studying Indian texts, teaching Indian concepts, and corresponding with European mathematicians (see my other comment for examples). The methodological similarities between Kerala mathematics and later European work, like the striking parallels between Wallis and the Yuktibhasa (15th century), where Wallis (in 17th Century) is using the exact expression and reasoning as given in the Yuktibhasa, aren't coincidences—they're smoking guns.
Your dismissal of this substantial body of evidence goes beyond healthy skepticism. It appears to disregard the complex realities of historical knowledge transfer risks coming off as a deliberate attempt to erase non-European contributions to mathematical history.
>The primary motivation for Europeans to import knowledge from India wasn't mere academic curiosity - it was a matter of practical necessity, particularly in navigation.
If the Europeans needed help from Indians "particularly in navigation", then why did the Indians never navigate to Europe before Europeans navigated to India?
Also, in your opinion, did the Europeans continue to copy math from India after they copied calculus or did European civilization suddenly start discovering most of the world's important new math and physics (including refinements of calculus and most of the math and physics that requires calculus) while Indian civilization suddenly slowed way down in the rate at which it discovered important new math?
> Stillwell makes no such conclusion about the lack of transmission
Stillwell: "It is sad that the Indian series became known in the West too late to have any influence or even to become well known until recently." (p. 184, 3rd ed.)
It's quite revealing and ironic that your approach to disagreement and request for concrete evidence is to make false accusations of intellectual dishonesty, dance around the issue making irrelevant analogies to tea, and use emotional rhetoric about "erasing non-European contributions".
I'm fascinated by non-European contributions to maths, science and philosophy because they're substantial and under-recognized historically, but I want actual evidence. Obviously the Jesuits were transmitting some knowledge to Europe, but if you make the stronger claim that Indian mathematicians laid crucial groundwork for calculus, then demonstrate it. That would be intellectually honest and a far better service to the history of Indian mathematics.
What you mention about Wallis and the Yuktibhasa (actually 16th century) is potentially interesting, but you decline to make a concrete case for it and just make vague statements about "striking parallels". Well, let's hear it.
p.s. you're wrong about tea as well: it was cultivated in Assam for centuries before the British were there - history can be complicated;
Any one who knows his/her tea, opium, coffee and chocolate knows a lot about the world. I don't know enough about cocaine to comment on it.
The battle for and between tea and opium is truly bizarre. Today we have war against drugs, the British were fighting for the opposite -- to make China hooked on opium (to counterbalance the import cost of tea) and then blame China -- you opium addled lesser civilization.
Not in any mathematically significant way, except for the big endian little endian swap. In Indian system the units is specified first, then the 10s then the hundreds and so on. Arabs took the same system but they wrote right to left. That's why we write the numbers the way we do.
Anyone interested in Indian history and its interaction with the world should check out the Odd Compass channel on YouTube (https://www.youtube.com/@OddCompass) - it's really well done, entertaining and just makes you appreciate the world a little more - especially how interconnected we've all been, especially through trade.
I love this channel! The videos are well made narratively while still preseving the facts and citing sources. Almost the ideal combo of being academic and entertaining
> The great mathematician Aryabhata (476-550), in his masterwork composed when he was only 23, covers square and cube roots, the properties of circles and triangles, algebra, quadratic equations and sines, and contains a decent approximation of the value of pi at 3.1416.
While we praise Aryabhatta man, i would like to shed some lights on Madhava of Sangamagrama c. 1340 - c. 1425 CE from India who less well known
Key Contributions
Infinite Series and Trigonometry
Discovered power series expansions for trigonometric functions:
Madhava's Sine Series: Infinite series representation for the sine function.
Madhava's Cosine Series: Infinite series representation for the cosine function.
Madhava–Gregory Series: Series for the arctangent function, predating James Gregory by over 200 years.
Calculus and Mathematical Analysis
Laid early foundations of calculus through: 200 years before Newton or leibniz
Methods of term-by-term integration and iterative techniques for solving transcendental equations.
Concepts related to the area under curves, similar to integral calculus.
Introduction of convergence tests for infinite series.
Creation of trigonometric tables with accurate sine and cosine values.
The Jesuit missionaries in India played a crucial role in the transmission of advanced Indian mathematical and astronomical knowledge to Europe by learning local languages, collaborating with local scholars, and documenting key works, thereby significantly influencing the development of mathematics in the West.
Which suggests a long oral and|or easily destroyed "document" tradition of teachings being passed down which came to Aryabhata who compiled such things in a manner that survived.
The sophistication of Babylonian mathematics boggles my mind. I am sure a credible science fiction story could be told where the Babylonians are a sophisticated alien race making Earth their home.
However, "the same kind of mathematics" rings dismissive. Trigonometry as we know it, came to its own and flourished in the middle ages in Indian, Arab and Persian civilizations. I am not aware of Babylonic trigonometry.
The story of the name of sin is itself quite interesting. It was half a 'jyay' (meaning chord subtended by an angle) in India. Through transliteration it became 'jayb' to the Arabs. Or the Europeans who were translating the Arabic mathematical literature derived from India, transliterate it as 'jayb', a phonetically similar bonafide Arabic word, that to this day is used to mean, a pocket/wallet/cavity. So pocket becomes sinus in Latin and then it evolves into just 'sin'. I think it was Napier who gave the name that we use.
Cultivation of geometry by Indian scholars go further in the past, to about 8th century BC as recorded in Sulbasutra.
You might be interested to know that combinatorics was also a hot topic among the Indian mathematicians. What we know as Fibonacci goes back far in the past, to Pingala (250 BC +/- 50). Pingala had worked out the binary numeral system and the 'Fibonacci' series.
What I am really keen to know is the mathematics of the Indus valley civilization, they were contemporaries of the Babylonians. Scarce little is known about their mathematics.
> However, "the same kind of mathematics" rings dismissive.
That's on you if you read it that way;
There are other sources, but sticking with the wikipedia article already linked (which references other sources):
* The Babylonian astronomers kept detailed records of the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere.
"angular distances measured on spheres" is the domain of trigonometry, how deep is a matter of debate but trigonometry it is.
* They also used a form of Fourier analysis to compute an ephemeris (table of astronomical positions), which was discovered in the 1950s by Otto Neugebauer.
That seems reasonably advanced.
* Tablets kept in the British Museum provide evidence that the Babylonians even went so far as to have a concept of objects in an abstract mathematical space. The tablets date from between 350 and 50 B.C.E., revealing that the Babylonians understood and used geometry even earlier than previously thought. The Babylonians used a method for estimating the area under a curve by drawing a trapezoid underneath, a technique previously believed to have originated in 14th century Europe.
Neugebauer's books are a fantastic resource. I am mostly familiar with their contents.
I am aware of Babylonian's contribution to positional astronomy. If I remember right, Hipparchus, considered the father of trigonometry, was familiar with Babylonian astronomy. Contemporaneous (meaning Hipparchus's times) Greek astronomy was not as accurate in comparison.
However, I have missed the Fourier series that you mention or any record that shows trigonometric manipulation or working out the values of the trigonometric functions. If you have a reference I would love to read, perhaps a specific Neugebauer book. Almagest model too can be considered a crude Fourier decomposition. So I am quite keen to learn about this Fourieresque decomposition that you speak of.
If ancient trigonometry interests you, you should definitely checkout Indian scholars of the middle ages. Neugebauer covers some of that in his books. Glen Van Brummelen is another good resource.
Awareness of angle measurement is not yet trigonometry, that would amount to saying Euclid's Elements- I has trigonometry. Trigonometry, whether planar or spherical becomes trigonometry with the awareness of trigonometric functions, their evaluations and trigonometric identities.
> > However, "the same kind of mathematics" rings dismissive.
> That's on you if you read it that way;
Yes I do. The 'same kind of mathematics' is too broad a brush stroke that can easily sweep away any form of mathematical originality and novelty. As a characterization it is somewhere between 'vapid' and 'not very useful'.
We do agree about how mind-bogglingly sophisticated Babylonian math was. They had Algebra that the Greeks didn't, and as you noted had figured out the technique of area under the curve well before Archimedes ... another person who seems centuries ahead of his times.
I think it’s important to clarify that describing the Babylonian method of estimating the area under a curve using trapezoids as "proto-integration" or "pre-calculus" might be a bit misleading. While their approach demonstrates an impressive grasp of geometry and an early method for approximating areas, it doesn't quite align with the formal development of calculus that emerged centuries later.
Madhava of Sangamagrama, a 14th-century Indian mathematician, made groundbreaking contributions to calculus that were far more advanced. He is known for discovering infinite series expansions for trigonometric functions such as sine, cosine, and arctangent, as well as deriving power series for π. His work included innovative methods for numerically approximating π to remarkable precision. In comparison, Madhava's achievements represent a significant evolution in mathematical thought. While the Babylonians were certainly ahead of their time, their techniques were still relatively basic when juxtaposed with the sophisticated concepts introduced by Madhava. His work laid critical groundwork for the later development of calculus by figures like Newton and Leibniz.
The Babylonians, while advanced for their time, were still operating in a more primitive mathematical framework. So while the Babylonians showed an inkling of ideas that would later blossom into calculus, it's an overstatement to equate their methods directly with calculus. Madhava's work represents a much more mature and developed understanding of these concepts. The Babylonians were pioneers, but Madhava was a revolutionary in comparison. Let's give credit where it's due!
Did not expect to see this here. But I have been looking forward to this book for a while. I’m a big fan of William Darlymple. The Anarchy is my favorite of his.
I picked it up from the title alone because I was on a medieval history kick and I unreasonably expected it to be about... "The Anarchy"... you know, the period of history that actually goes by that name... but no. I was surprised and disappointed to find it was about The East India Company which I didn't have much of a hankering after. I still feel cheated!
Wow reading the comments here, there is so much in terms of invention and contribution that I wasn’t taught (in American schools). Given the importance of some of these contributions, I feel a bit shocked at how much is left out of our education in America (and I assume Europe) about what other cultures have provided. India in particular feels like a blind spot - they’re the largest country by population but also conspicuously missing. All you hear about is Gandhi, and even that is not covered well (in terms of the politics of colonization or the partition of India). It feels to me like it is purposeful - how else do you explain skipping out on all these math inventions that are critical to the modern world?
Many things are not taught in school, because basic education is short, and a lot of it happens before people's cognitive abilities have fully developed. The average kid probably spends about a year learning about society and culture, and much of it must be devoted to topics that are relevant to daily life in their own society.
Back in Finland some decades ago, there was pretty decent coverage of India in three topics: world religions and the history of religion; European explorers, colonialism, and imperialism; and "modern" history with Gandhi, Nehru, the partition, and the wars. There were also some passing mentions in other topics. Overall, we probably spent more time on Indian history than American history.
> and a lot of it happens before people's cognitive abilities have fully developed.
This is sort of trivially true, in that there is generally literally no point at which a person's cognitive abilities are "fully developed" (cognitive abilities being non-uniform in development, and some aspects of cognitive ability tending to continue developing until very late in life, long after most of the rest have been declining for quite a long time.)
The West hardly knows anything "true" of India; almost everybody looks at it only through a narrow perspective and thus are "incorrect".
The History of India is a multi-branched tree with the main branches being; a) Oral Tradition b) Linguistic Tradition c) Philosophical/Religious Tradition d) Literature/Poetry e) Mythologies f) Historical writings g) Writings by other cultures/civilizations h) Archeology. All of them have to be studied to get an idea of what India was/is.
1) A good book to start with is A.L.Basham's The Wonder That Was India: A Survey of the Culture of the Indian Sub-Continent Before the Coming of the Muslims.
Not just that! For many hundreds of years there were over 250 ships a year trading between India and Rome, and tariffs on that trade alone accounted for 25% of the Roman Empire’s tax revenue. Among many other things, India fed the demand for transparent clothing, which was all the rage in the Roman Empire during that period.
I’ve been fascinated with Indian history (mostly for selfish reasons to understand my lineage). My oversimplified summary has been,
India has had 3 major golden ages in its history.
The earliest was during the Mauryan Period. This is the age Dalrymple is talking about, the time of Aryabhatta, the popularization of Buddhism, arguably the time when most of the Indian epics were written (dating them has become notoriously political to the point that discerning the truth is hard now). This is the age Indian nationalists stress on, and the left wing tries to ignore. This age declines because the empire got too big, lost control and slowly disintegrated.
The second age was during the Islamic golden age for India which the right tries to ignore and left stress on. My general sense is that there was a golden age of architecture, poetry and arts and probably not so much in Science. The Taj Mahal for instance was built during this time. This age declined mostly due to wars, the Mughal rulers were never successful in fully unifying India, even to the extent the Mauryans did. They fought consistent wars against pockets of resistance in the South, and towards the end began losing these wildly expensive wars (leading to a brief reign by Shivaji)
The third golden age which no one wants to admit (left or right) is the British Golden age. There really was a renaissance in Indian thought in arts, science during British rule. This was when Indian history was “rediscovered”, first by British orientalists and then by mostly Indian Bengalis. CV Raman won the Nobel prize in science, Tagore won the Nobel prize in literature, Ramanujan etc, the names are numerous. The British rule also was the largest and most stable unification of India till the modern times. After 1850s there were almost no pockets of military resistance against the British rule. The British age declined with WW1 and WW2, and ended with Indian independence.
Post independence was not a smooth going party. If you came to India during 1980s, you could argue independence had been a disaster with everything getting worse post independence. But since 1990s economic liberalization India has a new ish golden age with unique characteristics. Who knows how long this will continue and when it will inevitably end
I don't think British India can be described as a Golden Age, when it was arguably the biggest transfer of wealth in history. When the British started colonizing India, its share of the World GDP was approximately between 1/5 and 1/4. So it was a major player. When they left, GDP share was a mere 4/100. Under British rule, India experienced massive de-industrialization. For example, the UK disassembled most of the handloom industry.
By golden age I only focus on top of the line Science, Art, Architecture etc which is a what a lot of people intuitively focus on since that is what we remember a period by. What rule was best for the common population is unclear.
It might have been the Mauryas but we don’t have enough details of how the common man lived in the Mauryan empire. The arthashastra seems like our best source. Both the Mughals and the British had their share of evils against the common population but my sense is that if you were Hindu you were better off in the British empire than the Mughal Empire except for the rare tolerant Mughal ruler (eg ; Akbar).
The Mauryans and Mughals settled and did not rule with the goal of extracting / plundering. The British EIC did the latter. Arts and culture can prosper sustainably only when basic needs are well met, otherwise it is only the privileged that can dream of arts.
> if you were Hindu you were better off in the British empire than the Mughal Empire except for the rare tolerant Mughal ruler
Unless you were Bengali Hindu, I guess?
An undeniable difference between the British Raj and the Mughals is, the British were colonizers; the country as a whole suffered due to imperialism. One other user points out in this thread about the upending of socio-economic fabric under the Raj. Not really a "Golden Age" by any measure.
You forgot the Gupta Empire from mid 3rd century CE to mid 6th century CE. Aryabhatta - the famous mathematician was a product of this age.
The empire unfortunately promulgated the extensive spread of Buddhism, became pacifist and passive and was easily invaded and looted by invaders from Central Asia. The late Gupta empire's army was a joke - only existed on paper.
The fall of Indian civilization from the 7th century on-wards is very painful to read. No military of any note - Islamic invaders would regularly invade and loot and burn great temples and libraries every few years with little to no trouble. Foundational records and knowledge of ancient India was utterly annihilated. So much critical informational on Aryuveda, astronomy, mathematics and the physical sciences was lost forever. Some libraries were so huge, they burned for days.
Islam was at the height of its military era at the time and easily destroyed and annexed other passive cultures. Lots of journals of invaders from that time that documented their utter contempt for peoples who couldn't defend themselves.
The West had learned this lesson early and well from the Roman era: Si vis pacem, para bellum.
> CV Raman won the Nobel prize in science, Tagore won the Nobel prize in literature, Ramanujan etc, the names are numerous.
So golden age of India was when the country with a seventh of the world's population won 2 nobel prizes over 5 decades ?
> The British rule also was the largest and most stable unification of India till the modern times. After 1850s there were almost no pockets of military resistance against the British rule.
Mughal and Gupta empires lasted over 3 centuries, Mauryan empire a little under 1.5 centuries. By comparison, east india company rule lasted a century and the British crown's rule less than that. So again completely incorrect.
> The third golden age which no one wants to admit (left or right) is the British Golden age.
There's your hint: if people on both sides of the aisle don't "want to admit" something, maybe it doesn't make sense. Not to mention a slap in the face of billions of Indians.
> The British age declined with WW1 and WW2, and ended with Indian independence.
Thank god for that decline, otherwise Indian taxpayers would have been funding Brexit and the crumbling British economy right now.
> My oversimplified summary has been
This is not a summary, it's a lazy opinion backed by little research.
Have you read any books at all by Indians who lived through the British empire. Maybe start with “My Experiments with Truth” by Gandhi. The caricature that some modern Indians have made of the British empire would make even Gandhi turn in his grave.
But if you want to read something really heretic, maybe try reading An autobiography of an unknown Indian by Niraj Choudhary. Choudhary was a British raj supporter, as in an Indian who opposed Indian independence. Does that shock you? There were actually quite a lot of them, more than you’d expect.
Then if you want to get really metal, read in his own words, by Subedar Sitaram Pande. Sitaram Pande, was a soldier for the bengal army, for the British empire from 1812 to 1860, it’s one of the rare first author accounts we get of an Indian in that era. It will give you a glimpse of how an Indian at that time thought generally (hint: it was far more dominated by caste than you’d expect), how he viewed the empire and his relation to it. At that point I would say you are ready to try to understand Indian history that is not an avengers movie plot.
I would follow it with CK Majumdars history of modern India, one of the best historians so committed to the truth that Nehru had to throw him out of the government and try to prevent him from writing his book. Don’t worry, he’s not an heretic, he was an Indian freedom fighter, but you will find that he was far more honest about his life under Britain, under Indian national Congress and the state of the country in different periods of time (he also has a 12 volume set covering India for over 2000 years that I never had a chance to complete).
Please don't cross into personal attack or flamewar. Your post here is a noticeable step in those directions, and we're trying for the opposite on this site. (I'm not saying that the parent comments were perfect either but degrees matter.)
>Mauryan empire a little under 1.5 centuries. By comparison, east india company rule lasted a century and the British crown's rule less than that
This is a very dishonest way to obscure the actual facts.
Direct rule from Britain lasted for almost 90 years: 1858 to 1947. Even by your numbers then, that's 190 years: longer than the Mauryan empire's whole lifespan, and much closer to that of the Mughals. From there the question remains whether it's the longest "unification", and this mostly comes down to exactly when each of the aforementioned empires could be considered to have "unified" India.
By any definition the Mughals united the subcontinent by 1707AD at the latest: but by 1751, less than fifty years on, their effective domain had declined to a few pockets in Rajputana and Bengal.
The Guptan Empire on the other hand, while certainly a key predecessor to later Indian states and a major unifying force in the northern half of the subcontinent, never conquered the southern half -- what is today Karnakata, Kerala, and Tamil Nadu never entered their control. The closest they got was ~420AD after the south-eastern conquests of Chandragupta II, but again within fifty years they again lost control of today's Orissa, and even lost large swathes of north+western India to invasions from the steppe.
You call GP's post "a lazy opinion backed by little research", but when you dig into the facts I can't see how you could argue that his claim is incorrect. The British Raj alone seems to qualify as the longest-lasting unification of India before the modern Indian state, and if you include any part of the EIC's rule then it's indisputably so.
Mughals did not unite the subcontinent at any time. Even at its peak, Kerala, parts of Tamil Nadu and Sri Lanka was out of its influence.
Parts of Kerala became British territories after 1804.
“In fact, Buddhism, which had flourished in Bharat for 1600 years, suddenly vanished almost completely as soon as Muslims became masters of Delhi and started raiding the plains of Ganga.” Citation needed?
1) https://en.wikipedia.org/wiki/Decline_of_Buddhism_in_the_Ind... - From 986 CE, the Turks started raiding northwest India from Afghanistan, plundering western India early in the eleventh century. Forced conversions to Islam were made, and Buddhist images smashed, due to the Islamic dislike of idolatry. Indeed in India, the Islamic term for an 'idol' became 'budd'. — Peter Harvey, An Introduction to Buddhism ... According to William Johnston, hundreds of Buddhist monasteries and shrines were destroyed, Buddhist texts were burnt by the armies, monks and nuns killed during the 12th and 13th centuries in the Gangetic plains region. The Islamic invasions plundered wealth and destroyed Buddhist images ... The decline of Buddhism in the Indian subcontinent coincides with the spread of Islam in that part of the world, especially due to the Islamic invasions that occurred in the late 12th century. See sections "Turkic Invasions" and "Decline under Islamic Rule".
Buddhism was the tranquilizing death of India. You can argue that Islamic invaders would have conquered India anyways - but with Buddhism they rarely even had to fight!
Their puzzlement is even captured in several journals where they could range for hundreds of miles and loot/burn with little to no resistance. And do it once again a few years later!
There is a stronger argument to be made that it was because of the establishment of Buddhism as the de-facto state philosophy/religion/practice in North/Northwest part of India that the Islamic invaders could conquer India. Buddhism for all its intellectual/ethical/moral strengths was not a pragmatic religion. It ignored the realities of Life in favour of higher ideals in a context ill-suited to its survival and hence paid the price at the hands of barbaric muslim invaders. This happened through the elevation of Ahimsa into an all-encompassing tenet of state policy which severely sapped the Martial Spirit of the population and thus could offer no resistance to invaders bent on genocide. Prior to Buddhism (and Jainism) while Ahimsa was considered one of the central pillars of Hinduism its limitations in the practical world were acknowledged and Kings were expected to protect by force if necessary, those practicing Ahimsa as a way of life. With this gone, North/Northwest India was easy prey to barbaric muslim invaders who did not play by the same rules.
During their conquest of Sindh, the Arabs brought the non-Muslims into the category of ahl al-kitab, considering them ahl al-dhimmah (protected subjects) and thus practicing a certain amount of non-interference in their religious lives under the condition that they fulfil a number of obligations that came with this status. Since both Buddhism and Hinduism are literate religions with scriptures, the precedent of assimilating Zoroastrians into the category of ahl al-kitab was extended to them as well. The dhimmis were obligated to pay the jizya for following their ancestral religion. The historian Al-Baladhuri notes a decision by Muhammad bin Qasim in relation to a Buddhist vihara and Aror that after conquering the city through a treaty (sulh) he agreed not to kill the people and enter their temple, in addition to imposing kharaj on them.[29] The Buddhists had petitioned the Arabs for the right to restore one of their temples and it was granted by Al-Hajjaj ibn Yusuf. However, this decision was later violated by the Pact of Umar and subsequent Muslim law codes which prohibited the restoration of existing non-Muslim religious structures as well as the building of new ones. Despite this fact, Buddhist inscriptions were still being recorded in the eleventh century.[28] Some Buddhists also fled and emigrated from Muslim-ruled areas into other regions. Unlike Brahmanical worship, Buddhism rapidly declined in Sindh after the eighth century and it virtually disappeared by the eleventh century.
You've broken the site guidelines repeatedly and badly in this thread. We have to ban accounts that do this, so if you'd please review https://news.ycombinator.com/newsguidelines.html and stick to the rules when posting here, we'd appreciate it.
That means no personal attacks and no religious flamewar, among other things.
I don't doubt that you know a lot about this and other topics but we need you to make your substantive points thoughtfully and respectfully.
I understand your point (the letter) but disagree with its spirit.
One should not tolerate attempts to intentionally "sweep under the rug" documented genocides and distort History just because it involves someone's Religion (their in-group). It is easy to be blind to genocides if one is not forced to face up to them, admit their faults and change their ways. Else the vicious cycle keeps spinning to the detriment of Society as a whole. Hence my forceful attempt to show up a person who intentionally was downplaying documented genocides. Note that most of my data/articles are from wikipedia (curated database and hence less susceptible to fake news/specific narratives/gaming) and not some opinion piece to push a narrative.
As you are very well aware, there are insidious groups trying to game the system at HN (and elsewhere) to push their narratives. They are not interested in the Truth/Factual Data/Social Accountability etc. but are only interested in distorting reality to their benefit (see Orwell's essay on Nationalism). These people/groups need to be called out forcefully even if it means not obeying all rules of etiquette. It is in that spirit that i wrote my comments.
> there are insidious groups trying to game the system at HN (and elsewhere) to push their narratives.
This sort of perception is common and has been common on HN for well over a decade, but I've rarely seen any evidence to support it. What there is evidence for—plenty of it—is users with different backgrounds misperceiving each other's comments as astroturfing/shilling/etc. because they simply can't imagine anyone holding those other views in good faith.
The odds are high that this is what you're encountering. It's not some shady misinformation group; it's simply people with very different backgrounds than your own, who hold opposite views for legit reasons, just like you hold your own views for legit reasons. These are difficult historical topics that there's no consensus on.
Here are a couple of long explanations I posted about this in the past:
The Minority Rule, often associated with Nassim Nicholas Taleb, refers to a principle in which a small, intransigent minority can have a disproportionate impact on the behavior of a larger group, eventually leading the majority to adopt the preferences or practices of that minority. This occurs because the minority is highly committed to a particular preference or practice and is unwilling to compromise, while the majority is more flexible and willing to accommodate the minority's demands to avoid conflict or inconvenience.
Key Points of the Minority Rule:
Intransigence: The minority is unwavering in its position and refuses to accept alternatives.
Flexibility of the Majority: The majority is more flexible and often prefers to avoid confrontation or inconvenience, leading them to adopt the minority's preference.
Asymmetric Impact: Even though the minority is smaller, its rigid stance can lead to a situation where the majority conforms to the minority's preferences.
Examples:
Cultural Practices: In a mixed group, if a small number of individuals strictly follow a particular dietary rule (e.g., kosher or halal), the larger group might choose to accommodate these restrictions, leading to everyone adopting the more restrictive practice.
Regulations and Standards: Sometimes, a regulation or standard that applies to a small subset of people (e.g., accessibility requirements) becomes the norm for everyone because it’s easier or more efficient to have a single standard.
Implications:
The minority rule highlights how committed minorities can exert significant influence over larger groups, often shaping social norms, practices, and even laws. This can be both positive (e.g., ensuring certain ethical standards) and negative (e.g., stifling diversity of thought or practice).
Nice writeups. While most of your reasoning/logic are valid i think you are missing a few crucial viewpoints which should be incorporated into your "HN filtration and decision-making" process.
I presume you know of Nassim Taleb's "The Minority Rule", if not see his article The Most Intolerant Wins: The Dictatorship of the Small Minority - https://medium.com/incerto/the-most-intolerant-wins-the-dict... and video explanation https://www.youtube.com/watch?v=MwlW2aamDFc Any system can be gamed by an intransigent group by applying this rule under the guise of victimhood/false equivalence/even-handedness/appeal to authority/religion/PC/DEI/etc. Various language techniques like phrasing/tone/insinuation/instigation/support/oppose/etc. can be used to lead/sway/hint/push towards the group's viewpoint irrespective of Truth/Reality. In today's world all Human topics involve Politics/Propaganda/Manipulation/Spin/Gaslighting/etc. whether we like it or not. The effects of "events" (eg. HN comments) in these domains are non-linear (pareto/power law/etc.) and hence a single outlier can ruin everything i.e. you don't need an actual "shady misinformation group".
I am not sure how HN does its moderation but i can guarantee that the above is happening in one form or another. I have seen this in threads to do with Russia-Ukraine war, Israel-Palestine issue, Boeing issues etc.
As an example, you say; "These are difficult historical topics that there's no consensus on." which is factually incorrect given the wikipedia links i had posted. You have been manipulated to disregard Truth in the guise of even-handedness :-)
You realize I belong to an Ahmedi family? What kind of insidious “ingroup” is that in Pak context? Please tell that to any Pakistani who will collapse in peals of laughter.
As an Indian, it is extremely naive and childish to dismiss any consideration of the British rule as a "slap in the face". The British introduced electricity, railways, capitalism and a thousand other things we take for granted behind those saffron-tinted glasses.
Hell, the British Raj was what unified India into a single national identity. It was more fractured than the European continent otherwise.
Good summary, even if I disagree with the 3rd piece being called a golden age. But my question is why ignore the cholas, pallavas and pandyas? Only because they didn’t capture the whole subcontinent? Our schools history books were Delhi centric but we don’t have to be going forward. Those 3 empires had a lot of arts and culture too - and in terms of impact, they spread to parts of SE Asia too.
That's the specialty of a centralized state. There is a heavy push towards homogenizing Indian culture often at the cost of regional subcultures since almost 1947.
I hear what you’re saying, but this idea of a golden age under rule by some outside force is often the positive take about many historical periods where someone who committed significant crimes (invasions, genocides, etc) is then praised hundreds of years later because of the positive effect they had for the economy or whatever. Julius Caesar is one such example that comes to mind.
But I feel that approach sometimes discounts what the country and its people could have achieved on their own if they were not invaded. For example, the Taj Mahal is just one building in India. There are lots of other structures that exist that were not built under rule from outside invaders, but they never get attention (at least I’ve not heard of them). With Britain - you mentioned that they unified India and brought stability but how true is that if you compare it to the period of India much earlier? India was rocked by Islamic invasions (which led to the Mughal period) and colonized by those Islamic rulers for hundreds of years. That’s what the European colonizers took over. Is that really a fair period to compare against? India basically spent a millennium ruled by one outside genocidal invader or the other. I am guessing the period before that was more peaceful and not in need of some outside unifying force to feel ‘stable’.
They never reached the highs reached by the Mauryan Empire, but were still a period of relatively prosperity and stability compared to what immediately followed (until the Mughals came)
I guess the author, a historian, writes about ancient Indian mathematical contributions (a science of which he has no expertise presumably). These historical references I have learnt in various mathematical texts (the story of Fibonacci and al khwarizmi) - the journey across multiple centuries, of these innovations made by Aryabhata or Brahmagupta.
As an Indian, and as a math aficionado (and degree holder) - I wonder, that was about 1500 years ago. In that era, a discovery (as you can read it) took 500 years to move from Arabia to Europe, thanks to Fibonacci's writing. Contrast it to today's instant dissemination of information and breakthroughs. Yes those were the glory days of Indian civilization. We have a Ramanujan every 100 years in India. Breakthrough ideas (earthshaking ones like the concept of 0) emerging out of India are few and far between. Around 1000 years ago, the fountain of (world-changing) creativity and ideas seems to have dried up, as far as India is concerned. Maybe it was the invaders , easy to blame everything on outsiders, though - what is India today was 600 or 400 odd kingdoms, frequently warring each other - so turmoil was always there. And if you were a reclusive monk in a forest with a bunch of students, no Brit or Mughal dude was stopping you from innovating. So, the big question is - can we explain why genius ideas stopped (without blaming British, or Mughals etc) - because thanks to Indian's instincts, the first step is to blame the Brits/Mughals , so problem solved, proved, ostrich is happy in the sand.
I can only indulge in thought exercises , like : Aryabhata and Brahmagupta didn't have computers, didn't even have pencil and paper. They just sat there and thought. For months, or years. Or maybe they were walking. And gazed at the stars and observed and observed. And most likely, and importantly debated orally : endlessly with their teachers (in a monastery type place class sizes were small), peers- I believe this was a time in India's cultural history when debating, and disagreeing were positive things. In modern India, intellectualism has taken a back seat. To disagree is to be unpatriotic even. (Nalanda University comes to mind https://en.wikipedia.org/wiki/Nalanda_mahavihara - not its modernized recreation which is likely going to be hardly attempting to break the mold). WhatsApp - the destroyer of brain cells by atrophy , has a grip on every mind.
We read about the great Greek debates. We see videos of Tibetan buddhist monks practice debating in a monastery. Surely this kind of debating, face-to-face is missing in today's world (without getting angry) - this is the equivalent of the modern cafe in Paris or Vienna, with Godel and co. debating . This debating society , was Nalanda back a thousand years until invaders burnt every manuscript down and slaughtered every monk almost - except the manuscripts the Chinese monks took back to the Emperor in China - they are the only written records of life that remain, that and some arabic ones.
Yet I hope new lotuses will bloom from India - we can never predict where the next genius or breakthrough idea will emerge from - why not Africa?
I think it's just that industrialization, the computer, and the Internet were such massive juice that even if you have a brilliant mind it doesn't matter because the guy with that tool can take anything you think of and make it better. Each of these is a step up so huge that no mind can match it. So you have to match the tool first before the minds start mattering.
The oral tradition was certainly strong but there was no dearth as such of writing instruments. What makes their work not easy to access is their poetic symbolism, sun is one, moon is two and so on. These symbolisms were not even one to one, thus always leaving a window a doubt about what they really meant in their verses.
Since you mention Fibonacci, you may know what we call Fibonacci series was worked out around 250 BC by Pingala as an exercise in enumerating meter of verse
The question is why has that innovation of breakthrough ideas dried up. Past glory is small consolation, or none at all. How long will we keep sharing these 1000-year old memes in 'modern' India? Maybe innovation still happens (likely) - but no one recognizes it, and it gets lost in the endless clamor and noise of meaningless rituals that define religion in India today - or there may be no ecosystem to surface it, ie bring to market.
What religion/culture was then in the time of Aryabhata (which no one really knows I suppose) - is very likely totally different than what it is today , i.e. a way to impose majority opinions with zero debate. Because Aryabhata and others created works which made it through the centuries of strife, they survived, they had an ecosystem that supported the genius - which seems to be lacking now in Modern India - which might explain why it has dried up - i.e. Indians aspirations are far less lofty, the bar is set quite low - because there is no lack of money, there is no lack of tools. Whether now, or 1000 years ago, they were recognized as authoritative, transformative works - do we have the current generation creating anything (to which the average Indian response is the last 70 years of liberal rule has to be ruled out, and undone first).
> Past glory is small consolation, or none at all.
I think its far worse. Current and in power ideology has co-opted scientific progress for romanticizing about a past, often fictional. That's why we have government patronage of fraudulent medicine-men and their medicine such as coronil that was supposed to ward off coronavirus and simultaneously fight the evil conspiracies of the western civilization that denied them their due glory.
I also misunderstood an aspect of your original comment. I thought you were waxing romantically eloquent -- look they had no pencil and paper and they would just gaze poetically at the heavens and maths would happen in their brains... just imagine what would have happened had they been given paper.
Hence my comment, that lack of writing material was not holding them back.
The Manusmriti - if you ignore the social aspects of it has a calculation for the age of the universe. The very first chapter has it. I think it computes to about 12 billion years - close to what modern science brings it out to be.
While manu discouraged widow remarrige he advocated for a share of property for a married woman who has an extra-marital affair. The norm the world around at that time was death by stoning.
I don't see why it wouldn't be. Conscious thought is only the tip of the iceberg; even Western thought has a long tradition of noting that Eureka moments come during periods when you are not rationally engaging with the topic. See for example
That is the belief. But deep meditation is elusive. You need to understand the relationship between yourself and your Mantra.
One of the best explanations of Mantras and meditation are by Dr Robert Svoboda (for any audience more familiar with English than Sanskrit/hindi). Granted he trained under an Aghori which isn’t traditionally the path most folks would take. But his explanations are exemplary.
Dalrymple has a uniquely addictive style of writing that very few history writers do. I can't recall any other nonfiction book becoming such a page-turner for me as his "Anarchy" did. Terrific writer.
It's a fine surprise that I just ordered the book independently and then discovered the podcast and found the book being discussed on HN all in the same day. Pretty nice coincidence.
Very good writer, but he personally wound me up with his public "Great Escape" from India during the pandemic and laid himself open to the criticism that followed, of being a fairweather friend.
What exactly is the criticism here? He didn't strand himself in a particular densely populated foreign country while COVID lockdowns were happening across the world? He would be a better friend to India if he stayed there, contracted COVID, and put more strain on their healthcare system to the detriment of actual citizens?
His words, in the context of Indian, Britishness, colonialism, his own writing and the suffering of those he had left behind - he himself apologised for the message "being tone deaf & reeking with privilege" and I think it was quite reasonable that people were irritated by his posts of palm trees and sunny beaches while so few others had the choice.
And secondly, he lives there, it was not a "foreign" country and he was not "stranded". He lives there.
William Dalrymple is one of the finest historians and authors who has previously brought to life the story of East India Company and how it led to British India. In this book, he focuses on, among other things, how Buddhism spread all over.
It's a fascinating topic. He also has a very successful podcast [1][2] -- with his co-host Anita Anand -- The Empire Podcast, which chronicles the rise and fall of empires. Highly educational, not to mention entertaining.
Recommended!!
[1] Empire Podcast - Apple - https://podcasts.apple.com/gb/podcast/empire/id1639561921 [2] On Spotify - https://open.spotify.com/show/0sBh58hSTReUQiK4axYUVx?si=45f5...
I second the podcast recommendation. Empire pod has been truly worth every bit of the time. I am currently on the episode about History of coffee - ethiopia, ottoman turks etc.
I'm guessing that Anita Anand is not the one that was the Canadian Minister of Defense...
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Hmmm, interesting that you give agency for 75 years of history to those in China, but not in India. Are you claiming there is some racial superiority of the Han over Hindu? Couldn't you also argue that the rise of debt based mercantilist growth in China and subversion of Maoist Communism was a devious western European plan? Is that due to some inherent Aryan superiority that makes them responsible for every modern condition, or is it that devious plans put in place 50 years ago by Henry Kissinger and Winston Churchill have just come to fruition?
Just asking questions.
The West controlled India to a degree that was thankfully not the case in China. This is basic history that the OP literally referenced
> Just asking questions.
Nobody is fooled. Have the courtesy to say what you mean instead of insinuating disgusting aspersions
Ok, so Kissinger and Churchill. Thanks for the clarification.
I'm sure you're aware of the Indo-Soviet cooperation treaty of '71. Those sneaky anglophones strike again. I'm surprised you've been fooled by their clever subterfuge in China. The current business conditions there are everyone's fault but their own. For reference it all started with tricking Deng into supporting the Khmer Rouge and embarassingly invading Vietnam in '78.
https://en.wikipedia.org/wiki/Sino-Vietnamese_War
I assume The West is also responsible for the Wagner Group in Africa, but not for the fall of apartheid in South Africa. I just want to get the collective guilt right.
I am sure Sachar committee would have loved to hear about these Islamic overlords oppressing Muslims in India or having last Muslim majority state having statehood taken away
The Pakistani Scientist Pervez Hoodbhoy's (https://en.wikipedia.org/wiki/Pervez_Hoodbhoy) writing's and videos on Youtube are self-explanatory.
See for example; https://www.youtube.com/watch?v=a9qGcghkDsc
This has basically nothing to do with the parent comment about Muslim "overlords" treating Indians badly. It's more about how superstitions and belief without applied logic can restrict avenues to worldly success
You have not understood my and the parent's comment i was responding to.
You have to know what the "Sachar Committee" was and its recommendations, to understand why the parent sarcastically referred to it in its comment. My comment will then become clear.
Pervez Hoodbhoy has spent a lifetime (and much reviled for it in Pakistan and by most Muslims all over the world) trying to shine a light on why the Islamic culture/society has fallen behind dramatically in Scientific/Economic/Social progress in the 21st century and become regressive/backward. The video i linked to gives a snippet and you can find more detailed analysis in his longer videos (available on Youtube) and books.
My friend’s father was Hoodbhoy’s class fellow at MIT but thanks for the links.
Fail to see the relevance but here is another one; Are Muslim Attitudes Tuned For Economic Progress? by Dr. Jamshed Uppal - https://www.youtube.com/watch?v=P1zaQgIEJ4s
I think he meant the Indians working in the Middle East.
Because he and many other online-only viewpoint pushers only considers the situations where he and his in-group are the victim, not the other way around
In the West the numerals we use are known as "Arabic numerals" because it came from the middle east. But in the middle east the same numerals are known as "Indian numerals" because that's where they got it from.
Similarly, algebra came from the middle east where it was called "al-Jabr" [1], but they in turn got it from India [2].
The invention of calculus is traditionally attributed to Isaac Newton and Gottfried Leibniz. But this book [3] says calculus was brought into being in India in the 14th century by a mathematician named Madhava.
[1] https://en.wikipedia.org/wiki/Al-Jabr
[2] https://www.theguardian.com/world/article/2024/sep/01/hidden...
[3] https://www.nytimes.com/2024/07/24/books/review/the-secret-l...
The Arabic-Indic numerals are especially neat because you can see how they evolved as they spread:
https://persianlanguageonline.com/wp-content/uploads/2023/07...
Years ago I worked on a site which was translated into Arabic. Some of the early partners were adamant that we needed to use the Indic numerals everywhere, so I had localized all of our UI, including some JavaScript widgets and worked with a third-party to localize their embed. A few years later, they had a larger conference with a wider swath of the Arabic-fluent world represented and pretty much everyone said we should use what the English-speaking world calls Arabic numerals because most people were more familiar with them than the Indic numeral variants they didn’t use, and computers were making that even more pronounced.
It's difficult to call Madhava's work calculus as we know it. He and his school certainly made huge contributions to analysis of infinite series, but they did not develop that into a unifying framework. It's important to note that no mathematics is done in a vacuum, if Newton/Leibniz "invented" Calculus, it's by building on top of hundreds of years of work done throughout the world.
Fibonacci himself, who popularised their use, explicitly mentioned that they were from India. Somehow this was muddied in later secondary sources.
I encountered this topic a while, back and had a deep look into it, I will be sharing my insights and formed opinion based on the facts that I encountered.
@Dx51Q I appreciate your perspective, but I'd like to clarify a few points regarding Madhava's contributions to calculus. While it's true that Madhava and his school may not have created a unifying framework like Newton and Leibniz did, their work laid crucial groundwork for what we now consider calculus. Madhava is credited with developing infinite series for trigonometric functions such as sine and cosine, which are equivalent to the Taylor series we use today. For example, his series for sin(x) and cos(x) predate those discovered in Europe by over 200 years[1][2].
His followers, like Jyeṣṭhadeva, further elaborated on these concepts in texts like the Yuktibhāṣā, providing proofs and demonstrating their applications[3][5]. Moreover, Madhava's methods for approximating pi were remarkably accurate, achieving values correct to 11 decimal places, showcasing his advanced understanding of numerical analysis[2][4].
This indicates that he was indeed engaging with concepts foundational to calculus, such as limits and convergence. Thus, while Madhava's work may not fit neatly into the modern definition of calculus, it represents a significant and sophisticated mathematical tradition that deserves recognition as a precursor to later developments in the field.
While we are on this topic, we can stop for a second and ponder on why the ancient Indians needed these mathematical formulation. The answer is astronomy, and thus needing a language/framework to understand the cosmos, i.e. mathematics.
Additionally, I wanted to share some interesting insights about the Jesuit transmission of both calculus and the Gregorian calendar from Kerala to Europe. The Jesuit missionaries were not only spreading Christianity through their work, but they were scholars in their own right and could see the value of the advance mathematics they encountered by the Kerala (India) school of mathematics by madhava and the advanced calendar, more accurate than the julian calendar used in Europe at the time.
Jesuit missionaries, especially Matteo Ricci, were really fascinated by the advanced mathematical knowledge coming from the Kerala school. They connected with local scholars, like Brahmins and Kshatriyas, to learn about their mathematical concepts, including those found in texts like the Yuktibhāṣā and Tantrasangraha [5]. This collaboration was part of the Jesuits' efforts to understand local cultures and improve their missionary work. It’s fascinating to think that this exchange not only contributed to the Gregorian calendar reform in 1582 but also helped introduce key calculus concepts into European mathematics.
As to why this is not common knowledge, it’s partly the British colonial policies that muddied the waters and/or suppressed the source of information. But If one looks at it with time, the evidence is there
Citations: [1] https://www.linkedin.com/pulse/madhava-man-who-taught-trigon... [2] https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama [3] https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ [4] https://en.wikipedia.org/wiki/Madhava_series [5] https://indicmandala.com/the-kerala-school-european-mathemat...
Going to preface this by saying that it's completely uncontroversial that the Kerala school discovered a lot of foundational mathematical concepts independently and in many cases earlier than Europeans, but the evidence for any transmission of those ideas to europe is _extremely_ thin, and you can see the organic development of it mostly within Europe in the textual record after the introduction of Arabic numbers and Arabic mathematical texts to Europe (which of course themselves where _hugely_ influenced by Indian mathematics themselves).
You can of course make the argument that colonialist historians are motivated to erase the contributions of foreign mathemeticians, but the _mathematicians themselves_ were not shy about crediting the influence of arabic philosophers and mathematicians, so it would have to be explained why they were fine with crediting al-Khwārizmī but drew the line at crediting Madhava. If they did have direct access to the works of the Kerala school, they'd have developed Calculus much more quickly, that's for sure.
It's very possible that there was some extremely vague indirect transmission through word of mouth where the source was obscure even to the mathematicians themselves, but I think it's hard to make the argument that "if not for Madhava, calculus would not have been discovered in Europe." There were many scientists and mathematicans all circling around the same problems and several of them solved aspects of it independently at the same time from different directions.
And the idea that _Euler_ only discovered power series with help from Indian mathematics is ridiculous. You can see in his own books and his correspondence with others how he gradually worked them out from first principles over time. There's no mystery as to where it came from. If he had just read about them from a book, he would have used them and not spent several years trying to figure it out.
The development of math in Europe was _absolutely_ dependent on the introduction of Indian mathematical ideas through Arabic texts, though.
The claim of "extremely thin evidence" for the transmission of Kerala mathematics to Europe by Jesuits is far from accurate. In fact, there's a wealth of circumstantial evidence supporting this possibility. Jesuits were present in Kerala from 1540-1670, with many, like Matteo Ricci, being highly trained mathematicians tasked with studying Indian sciences. We have clear documentation of their interest in local mathematics, astronomy, and timekeeping, even incorporating subjects like jyotisa into their curricula. Numerous examples show Jesuits actively gathering and transmitting knowledge, from Ricci's inquiries about Indian calendars to Schreck's astronomical observations sent to Kepler. Their close relationships with the Court of Cochin provided access to valuable mathematical manuscripts, and there's evidence of collaboration with Brahmins in translating Sanskrit works.
The Jesuits were strongly motivated by practical needs in navigation and calendar reform. Moreover, Marin Mersenne's extensive correspondence network demonstrates that awareness of Indian mathematical knowledge was circulating in Europe. Intriguingly, there are methodological similarities between Kerala mathematics and later European developments, such as parallels between methods used by Wallis and those in the Yuktibhasa.
I believe it's crucial to consider the historical context of knowledge transmission between cultures, which often involved clandestine methods. A prime example is the case of Robert Fortune, a Scottish botanist, who in 1848 undertook a covert mission for the British East India Company. Fortune, disguised as a Chinese merchant from a distant province, infiltrated China's heavily guarded tea-growing regions. His objective was to acquire tea plants and seeds, along with the closely guarded secrets of tea production. Fortune's mission was successful; he managed to remove thousands of tea plants and seeds from China, effectively ending the Chinese monopoly on tea production. This act of industrial espionage had far-reaching consequences, leading to the establishment of vast tea plantations in India and Ceylon (now Sri Lanka), and fundamentally altering the global tea trade. While this example pertains to botany rather than mathematics, it illustrates the lengths to which nations went extract knowledge.
(Source: Joseph, G. G. (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton University Press.)
The thing is, circumstantial evidence that transmission could have happened, though suggestive, isn't positive evidence that it did happen. The absence of such direct evidence such as translations or quotations from relevant Indian works in Europe is even emphasized in Joseph's book that you give as ref.
The claim that Madhava "laid crucial groundwork" for the development of calculus in Europe needs to be backed up with some argument saying exactly what was transmitted and when. The problem with simply observing that his results on infinite series for arctan, sin and cos reappeared in Europe much later is that this doesn't rule out independent discovery in Europe. And the case for independent discovery is strong, because we have the documentary evidence of the logic of discovery: Newton and Gregory both obtained these series from the general binomial series, seemingly independently of each other, and to my knowledge Madhava didn't have this result.[0] They're both clearly basing their works on documented predecessors (who happen to be European) such as Wallis, Fermat, Descartes, Viete, and others, so the trajectory of how the results were obtained seems to be accounted for.
So what was the crucial groundwork, and when was it transmitted? There might have been something (e.g. your suggestion about parallels between Wallis and the Yuktibhasa), but I haven't seen a strong argument that gives these details. I would be fascinated if there were though.
[0] Stillwell 2010 Mathematics and its History (3rd ed.)
- Stillwell is sympathetic to the Kerala school, is very clear in assigning Madhava priority on the arctan, sin and cos series, but concludes, along with most historical scholarship, that it seems there was no transmission of these results to Europe
I found this paper interesting: https://ckraju.net/Joseph/Manchester-paper.pdf
Transmission of the calculus from Kerala to Europe: "...we propose to adopt a legal standard of evidence good enough to hang a person for murder." See document for (1) motivation, (2) opportunity, (3) circumstantial evidence, and (4) documentary evidence.
Thanks, it's interesting and gives some suggestive information about the motivations concerning navigation and calendrical reform.
It has some severe weaknesses when trying to make the case for influence on mathematics, though.
The authors mention Pell's equation x^2+Ny^2=1, and the method given by Bhaskara II to find solutions x,y for arbitrary N (though others note the method was given earlier by Jayadeva).[0] Bhaskara gives the example of N=61. Fermat, in a letter to his friendly rival Frenicle, also gives the example N=61 as a challenge. Now, if 61 were arbitrary in this context, then this would be something like a smoking gun showing almost certain influence. However, 61 is very special here, because the smallest solutions x and y that satisfy the equation are suddenly much larger for 61 than for any smaller N (they're of order 10^10). The authors of the paper don't mention this crucial detail. Fermat also challenges his pal with N=109, which has similarly huge minimal solutions (order 10^15), and which Bhaskara does not give. Fermat writes that he's chosen smallish values of N, "pour ne vous donner pas trop de peine," so he's obviously chosen these values precisely because they're fiendishly difficult, and that's no doubt why Bhaskara also chose 61 as an example, and that's adequate explanation for why the same value shows up in the two places. Fermat had been working on number theory for some decades prior to this point, and his correspondence shows him working through simpler versions of this and related problems, making many original contributions along the way.[0]
The example the authors give about influence on calculus has similar weaknesses. The example they give involves using the sum of the kth powers to integrate x^k. They write that "the formula had no natural epistemological basis in European mathematics," which almost made me spit out my tea because it suggests the authors haven't heard of Archimedes, who used exacly this method with k=2 to give his quadrature of the parabola, and this was well known in Europe at the time (although his works had only really been rediscovered in Europe in the 1500s). The Arab mathematician Al-Haytham had extended the method with k=1,2,3, and 4 in the 10-11th cenury, Cavalieri in 1635 had calculated up to k=9 and conjectured the integral was (1/(k+1))x^(k+1), before Fermat, Pascal, and Roberval gave their proofs of this general relation.[1][2] This last point especially means I don't understand what the authors of the paper mean when they say "the European mathematicians were unable to prove the formula or provide a rigorous rationale for it within their epistemology." ... They did give proofs, and what they were doing was completely intelligible within the historical development leading up to that time.
These are the points I know about, and they don't fill me with confidence about the authors' other judgements.
[0] Andre Weil 1984 Number Theory: An approach through history (ch.1 section 9 mentions Jayadeva and see ch.2 on Fermat, esp. sections 12 and 13)
[1] Edwards 1979 The Historical Development of the Calculus (p.109ff.)
[2] Stillwell 2010 Mathematics and its History (section 9.1)
Firstly, your claim about Stillwell's "conclusion" is a misrepresentation. Stillwell makes no such conclusion about the lack of transmission. In fact, he explicitly states that the Kerala school knew these mathematical series before 1540. This selective reading and distortion of Stillwell's work is intellectually dishonest and undermines genuine historical inquiry.
The Jesuits sent to India weren't not your typical bible thumpers; they were highly trained mathematicians and astronomers with a specific mission to study and acquire Indian mathematical and astronomical knowledge. The primary motivation for Europeans to import knowledge from India wasn't mere academic curiosity - it was a matter of practical necessity, particularly in navigation. By the mid-16th century, Europeans were grappling with significant errors in their calendar calculations. The true solar year was about 11.25 minutes shorter than the assumed 365.25 days, an error that had compounded over centuries, leading to serious discrepancies in timekeeping and navigation. Matteo Ricci, the Jesuit astronomer and mathematician in a letter from India to Giovanni Battista Maffei (Italian mathematician) he states that he requires the assistance of an “intelligent Brahmin or an honest Moor” to help him understand the local ways of recording and measuring time.
If one wants a smoking gun—a direct admission of knowledge transfer—is either naïve or deliberately obtuse. Do you also believe that tea plants magically teleported from China to India? The British East India Company's industrial espionage in China's tea industry parallels the Jesuits' activities in India perfectly. Both were covert operations aimed at acquiring valuable "know-how" for economic and strategic gain. Do we have a signed confession from Robert Fortune or his kin admitting to tea espionage?
The cumulating circumstantial evidence isn't just substantial—it's overwhelming. We have documented records of Jesuits studying Indian texts, teaching Indian concepts, and corresponding with European mathematicians (see my other comment for examples). The methodological similarities between Kerala mathematics and later European work, like the striking parallels between Wallis and the Yuktibhasa (15th century), where Wallis (in 17th Century) is using the exact expression and reasoning as given in the Yuktibhasa, aren't coincidences—they're smoking guns.
Your dismissal of this substantial body of evidence goes beyond healthy skepticism. It appears to disregard the complex realities of historical knowledge transfer risks coming off as a deliberate attempt to erase non-European contributions to mathematical history.
>The primary motivation for Europeans to import knowledge from India wasn't mere academic curiosity - it was a matter of practical necessity, particularly in navigation.
If the Europeans needed help from Indians "particularly in navigation", then why did the Indians never navigate to Europe before Europeans navigated to India?
Also, in your opinion, did the Europeans continue to copy math from India after they copied calculus or did European civilization suddenly start discovering most of the world's important new math and physics (including refinements of calculus and most of the math and physics that requires calculus) while Indian civilization suddenly slowed way down in the rate at which it discovered important new math?
> Stillwell makes no such conclusion about the lack of transmission
Stillwell: "It is sad that the Indian series became known in the West too late to have any influence or even to become well known until recently." (p. 184, 3rd ed.)
It's quite revealing and ironic that your approach to disagreement and request for concrete evidence is to make false accusations of intellectual dishonesty, dance around the issue making irrelevant analogies to tea, and use emotional rhetoric about "erasing non-European contributions".
I'm fascinated by non-European contributions to maths, science and philosophy because they're substantial and under-recognized historically, but I want actual evidence. Obviously the Jesuits were transmitting some knowledge to Europe, but if you make the stronger claim that Indian mathematicians laid crucial groundwork for calculus, then demonstrate it. That would be intellectually honest and a far better service to the history of Indian mathematics.
What you mention about Wallis and the Yuktibhasa (actually 16th century) is potentially interesting, but you decline to make a concrete case for it and just make vague statements about "striking parallels". Well, let's hear it.
p.s. you're wrong about tea as well: it was cultivated in Assam for centuries before the British were there - history can be complicated;
> A prime example is the case of Robert Fortune, a Scottish botanist, who in 1848 undertook a covert mission for the British East India Company.
For anyone else reading, I'll mention that I found this book extremely engaging:
Rose, Sarah. For All the Tea in China: Espionage, Empire, and the Secret Formula for the World's Favourite Drink.
Any one who knows his/her tea, opium, coffee and chocolate knows a lot about the world. I don't know enough about cocaine to comment on it.
The battle for and between tea and opium is truly bizarre. Today we have war against drugs, the British were fighting for the opposite -- to make China hooked on opium (to counterbalance the import cost of tea) and then blame China -- you opium addled lesser civilization.
The Arabic numerals are called Arabic because the Europeans got them from North African Arabs. They are different to the Indian numerals.
> They are different to the Indian numerals.
Not in any mathematically significant way, except for the big endian little endian swap. In Indian system the units is specified first, then the 10s then the hundreds and so on. Arabs took the same system but they wrote right to left. That's why we write the numbers the way we do.
Anyone interested in Indian history and its interaction with the world should check out the Odd Compass channel on YouTube (https://www.youtube.com/@OddCompass) - it's really well done, entertaining and just makes you appreciate the world a little more - especially how interconnected we've all been, especially through trade.
I love this channel! The videos are well made narratively while still preseving the facts and citing sources. Almost the ideal combo of being academic and entertaining
Thanks for sharing! Sounds like a great recommendation.
> The great mathematician Aryabhata (476-550), in his masterwork composed when he was only 23, covers square and cube roots, the properties of circles and triangles, algebra, quadratic equations and sines, and contains a decent approximation of the value of pi at 3.1416.
TIL...
The man was certified genius, here are some more of his contributions to the world
- Invention of Zero - Decimal Place-Value System - Astronomical Calculations - Understanding of Negative Numbers
here is a good YouTube video on this subject https://www.youtube.com/watch?v=jgjcy04PDRM
While we praise Aryabhatta man, i would like to shed some lights on Madhava of Sangamagrama c. 1340 - c. 1425 CE from India who less well known
Key Contributions
Infinite Series and Trigonometry Discovered power series expansions for trigonometric functions: Madhava's Sine Series: Infinite series representation for the sine function. Madhava's Cosine Series: Infinite series representation for the cosine function. Madhava–Gregory Series: Series for the arctangent function, predating James Gregory by over 200 years.
Calculus and Mathematical Analysis Laid early foundations of calculus through: 200 years before Newton or leibniz Methods of term-by-term integration and iterative techniques for solving transcendental equations. Concepts related to the area under curves, similar to integral calculus. Introduction of convergence tests for infinite series. Creation of trigonometric tables with accurate sine and cosine values.
The Jesuit missionaries in India played a crucial role in the transmission of advanced Indian mathematical and astronomical knowledge to Europe by learning local languages, collaborating with local scholars, and documenting key works, thereby significantly influencing the development of mathematics in the West.
The same kind of math found on Babylonian clay tablets from 2,000 years earlier then?
https://en.wikipedia.org/wiki/Babylonian_mathematics
Which suggests a long oral and|or easily destroyed "document" tradition of teachings being passed down which came to Aryabhata who compiled such things in a manner that survived.
https://en.wikipedia.org/wiki/Babylonian_mathematics
The sophistication of Babylonian mathematics boggles my mind. I am sure a credible science fiction story could be told where the Babylonians are a sophisticated alien race making Earth their home.
However, "the same kind of mathematics" rings dismissive. Trigonometry as we know it, came to its own and flourished in the middle ages in Indian, Arab and Persian civilizations. I am not aware of Babylonic trigonometry.
The story of the name of sin is itself quite interesting. It was half a 'jyay' (meaning chord subtended by an angle) in India. Through transliteration it became 'jayb' to the Arabs. Or the Europeans who were translating the Arabic mathematical literature derived from India, transliterate it as 'jayb', a phonetically similar bonafide Arabic word, that to this day is used to mean, a pocket/wallet/cavity. So pocket becomes sinus in Latin and then it evolves into just 'sin'. I think it was Napier who gave the name that we use.
Cultivation of geometry by Indian scholars go further in the past, to about 8th century BC as recorded in Sulbasutra.
https://personal.math.ubc.ca/~cass/courses/m309-01a/kong/sul...
You might be interested to know that combinatorics was also a hot topic among the Indian mathematicians. What we know as Fibonacci goes back far in the past, to Pingala (250 BC +/- 50). Pingala had worked out the binary numeral system and the 'Fibonacci' series.
https://en.wikipedia.org/wiki/Pingala
What I am really keen to know is the mathematics of the Indus valley civilization, they were contemporaries of the Babylonians. Scarce little is known about their mathematics.
> However, "the same kind of mathematics" rings dismissive.
That's on you if you read it that way;
There are other sources, but sticking with the wikipedia article already linked (which references other sources):
* The Babylonian astronomers kept detailed records of the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere.
"angular distances measured on spheres" is the domain of trigonometry, how deep is a matter of debate but trigonometry it is.
* They also used a form of Fourier analysis to compute an ephemeris (table of astronomical positions), which was discovered in the 1950s by Otto Neugebauer.
That seems reasonably advanced.
* Tablets kept in the British Museum provide evidence that the Babylonians even went so far as to have a concept of objects in an abstract mathematical space. The tablets date from between 350 and 50 B.C.E., revealing that the Babylonians understood and used geometry even earlier than previously thought. The Babylonians used a method for estimating the area under a curve by drawing a trapezoid underneath, a technique previously believed to have originated in 14th century Europe.
This is proto-integration, pre-caclulus, etc.
Neugebauer's books are a fantastic resource. I am mostly familiar with their contents.
I am aware of Babylonian's contribution to positional astronomy. If I remember right, Hipparchus, considered the father of trigonometry, was familiar with Babylonian astronomy. Contemporaneous (meaning Hipparchus's times) Greek astronomy was not as accurate in comparison.
However, I have missed the Fourier series that you mention or any record that shows trigonometric manipulation or working out the values of the trigonometric functions. If you have a reference I would love to read, perhaps a specific Neugebauer book. Almagest model too can be considered a crude Fourier decomposition. So I am quite keen to learn about this Fourieresque decomposition that you speak of.
If ancient trigonometry interests you, you should definitely checkout Indian scholars of the middle ages. Neugebauer covers some of that in his books. Glen Van Brummelen is another good resource.
Awareness of angle measurement is not yet trigonometry, that would amount to saying Euclid's Elements- I has trigonometry. Trigonometry, whether planar or spherical becomes trigonometry with the awareness of trigonometric functions, their evaluations and trigonometric identities.
> > However, "the same kind of mathematics" rings dismissive.
> That's on you if you read it that way;
Yes I do. The 'same kind of mathematics' is too broad a brush stroke that can easily sweep away any form of mathematical originality and novelty. As a characterization it is somewhere between 'vapid' and 'not very useful'.
We do agree about how mind-bogglingly sophisticated Babylonian math was. They had Algebra that the Greeks didn't, and as you noted had figured out the technique of area under the curve well before Archimedes ... another person who seems centuries ahead of his times.
I think it’s important to clarify that describing the Babylonian method of estimating the area under a curve using trapezoids as "proto-integration" or "pre-calculus" might be a bit misleading. While their approach demonstrates an impressive grasp of geometry and an early method for approximating areas, it doesn't quite align with the formal development of calculus that emerged centuries later.
Madhava of Sangamagrama, a 14th-century Indian mathematician, made groundbreaking contributions to calculus that were far more advanced. He is known for discovering infinite series expansions for trigonometric functions such as sine, cosine, and arctangent, as well as deriving power series for π. His work included innovative methods for numerically approximating π to remarkable precision. In comparison, Madhava's achievements represent a significant evolution in mathematical thought. While the Babylonians were certainly ahead of their time, their techniques were still relatively basic when juxtaposed with the sophisticated concepts introduced by Madhava. His work laid critical groundwork for the later development of calculus by figures like Newton and Leibniz.
The Babylonians, while advanced for their time, were still operating in a more primitive mathematical framework. So while the Babylonians showed an inkling of ideas that would later blossom into calculus, it's an overstatement to equate their methods directly with calculus. Madhava's work represents a much more mature and developed understanding of these concepts. The Babylonians were pioneers, but Madhava was a revolutionary in comparison. Let's give credit where it's due!
>contains a decent approximation of the value of pi at 3.1416.
I read this somewhere earlier, in some article about the history of mathematics, maybe Indian, Chinese, or both:
Take the number 113355 (easy to remember). Split it down the middle to get 113 and 355. Divide the latter by the former. E.g. in the Python shell:
> print (355/113)
Result:
3.1415929203539825
which is a slightly closer approximation to pi than 3.1416.
That's nice! Another one is remembering the phrase: Can I have a large container of coffee please sir.
That's nicer! TIL. :)
Googled it.
Here is a result that explains it, since some of the others seem vague:
https://www.reddit.com/r/todayilearned/comments/l6icp/til_yo...
But please has 6 letters?
Check this one: "Now I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics"
head = spin.
from early pg essay. :)
now i need to write a python program to count the letters in the words and map them to pi's official digits, to check your 'formula'.
;)
easy as pi.
https://en.m.wikipedia.org/wiki/List_of_Indian_mathematician...
Did not expect to see this here. But I have been looking forward to this book for a while. I’m a big fan of William Darlymple. The Anarchy is my favorite of his.
I picked it up from the title alone because I was on a medieval history kick and I unreasonably expected it to be about... "The Anarchy"... you know, the period of history that actually goes by that name... but no. I was surprised and disappointed to find it was about The East India Company which I didn't have much of a hankering after. I still feel cheated!
https://en.wikipedia.org/wiki/The_Anarchy
And still, it’s one of the greatest works of popular history ever written.
Wow reading the comments here, there is so much in terms of invention and contribution that I wasn’t taught (in American schools). Given the importance of some of these contributions, I feel a bit shocked at how much is left out of our education in America (and I assume Europe) about what other cultures have provided. India in particular feels like a blind spot - they’re the largest country by population but also conspicuously missing. All you hear about is Gandhi, and even that is not covered well (in terms of the politics of colonization or the partition of India). It feels to me like it is purposeful - how else do you explain skipping out on all these math inventions that are critical to the modern world?
Many things are not taught in school, because basic education is short, and a lot of it happens before people's cognitive abilities have fully developed. The average kid probably spends about a year learning about society and culture, and much of it must be devoted to topics that are relevant to daily life in their own society.
Back in Finland some decades ago, there was pretty decent coverage of India in three topics: world religions and the history of religion; European explorers, colonialism, and imperialism; and "modern" history with Gandhi, Nehru, the partition, and the wars. There were also some passing mentions in other topics. Overall, we probably spent more time on Indian history than American history.
> and a lot of it happens before people's cognitive abilities have fully developed.
This is sort of trivially true, in that there is generally literally no point at which a person's cognitive abilities are "fully developed" (cognitive abilities being non-uniform in development, and some aspects of cognitive ability tending to continue developing until very late in life, long after most of the rest have been declining for quite a long time.)
The West hardly knows anything "true" of India; almost everybody looks at it only through a narrow perspective and thus are "incorrect".
The History of India is a multi-branched tree with the main branches being; a) Oral Tradition b) Linguistic Tradition c) Philosophical/Religious Tradition d) Literature/Poetry e) Mythologies f) Historical writings g) Writings by other cultures/civilizations h) Archeology. All of them have to be studied to get an idea of what India was/is.
1) A good book to start with is A.L.Basham's The Wonder That Was India: A Survey of the Culture of the Indian Sub-Continent Before the Coming of the Muslims.
The Book: https://archive.org/details/TheWonderThatWasIndiaByALBasham_...
The Author : https://en.wikipedia.org/wiki/Arthur_Llewellyn_Basham
2) For a modern idiosyncratic and funny take, see Sam Miller's book A Strange Kind of Paradise: India through Foreign Eyes.
Not just that! For many hundreds of years there were over 250 ships a year trading between India and Rome, and tariffs on that trade alone accounted for 25% of the Roman Empire’s tax revenue. Among many other things, India fed the demand for transparent clothing, which was all the rage in the Roman Empire during that period.
More inclusive approach to education is needed
I’m reading this right now, and it’s excellent. Some amazing stories in there, like that of Wu Zetian, the real life Mother of Dragons:
https://en.m.wikipedia.org/wiki/Wu_Zetian
I’ve been fascinated with Indian history (mostly for selfish reasons to understand my lineage). My oversimplified summary has been, India has had 3 major golden ages in its history.
The earliest was during the Mauryan Period. This is the age Dalrymple is talking about, the time of Aryabhatta, the popularization of Buddhism, arguably the time when most of the Indian epics were written (dating them has become notoriously political to the point that discerning the truth is hard now). This is the age Indian nationalists stress on, and the left wing tries to ignore. This age declines because the empire got too big, lost control and slowly disintegrated.
The second age was during the Islamic golden age for India which the right tries to ignore and left stress on. My general sense is that there was a golden age of architecture, poetry and arts and probably not so much in Science. The Taj Mahal for instance was built during this time. This age declined mostly due to wars, the Mughal rulers were never successful in fully unifying India, even to the extent the Mauryans did. They fought consistent wars against pockets of resistance in the South, and towards the end began losing these wildly expensive wars (leading to a brief reign by Shivaji)
The third golden age which no one wants to admit (left or right) is the British Golden age. There really was a renaissance in Indian thought in arts, science during British rule. This was when Indian history was “rediscovered”, first by British orientalists and then by mostly Indian Bengalis. CV Raman won the Nobel prize in science, Tagore won the Nobel prize in literature, Ramanujan etc, the names are numerous. The British rule also was the largest and most stable unification of India till the modern times. After 1850s there were almost no pockets of military resistance against the British rule. The British age declined with WW1 and WW2, and ended with Indian independence.
Post independence was not a smooth going party. If you came to India during 1980s, you could argue independence had been a disaster with everything getting worse post independence. But since 1990s economic liberalization India has a new ish golden age with unique characteristics. Who knows how long this will continue and when it will inevitably end
I don't think British India can be described as a Golden Age, when it was arguably the biggest transfer of wealth in history. When the British started colonizing India, its share of the World GDP was approximately between 1/5 and 1/4. So it was a major player. When they left, GDP share was a mere 4/100. Under British rule, India experienced massive de-industrialization. For example, the UK disassembled most of the handloom industry.
> I don't think British India can be described as a Golden Age, when it was arguably the biggest transfer of wealth in history.
It _was_ the Golden Age ... for the Brits! :-D
By golden age I only focus on top of the line Science, Art, Architecture etc which is a what a lot of people intuitively focus on since that is what we remember a period by. What rule was best for the common population is unclear.
It might have been the Mauryas but we don’t have enough details of how the common man lived in the Mauryan empire. The arthashastra seems like our best source. Both the Mughals and the British had their share of evils against the common population but my sense is that if you were Hindu you were better off in the British empire than the Mughal Empire except for the rare tolerant Mughal ruler (eg ; Akbar).
The Mauryans and Mughals settled and did not rule with the goal of extracting / plundering. The British EIC did the latter. Arts and culture can prosper sustainably only when basic needs are well met, otherwise it is only the privileged that can dream of arts.
> if you were Hindu you were better off in the British empire than the Mughal Empire except for the rare tolerant Mughal ruler
Unless you were Bengali Hindu, I guess?
An undeniable difference between the British Raj and the Mughals is, the British were colonizers; the country as a whole suffered due to imperialism. One other user points out in this thread about the upending of socio-economic fabric under the Raj. Not really a "Golden Age" by any measure.
You forgot the Gupta Empire from mid 3rd century CE to mid 6th century CE. Aryabhatta - the famous mathematician was a product of this age.
The empire unfortunately promulgated the extensive spread of Buddhism, became pacifist and passive and was easily invaded and looted by invaders from Central Asia. The late Gupta empire's army was a joke - only existed on paper.
The fall of Indian civilization from the 7th century on-wards is very painful to read. No military of any note - Islamic invaders would regularly invade and loot and burn great temples and libraries every few years with little to no trouble. Foundational records and knowledge of ancient India was utterly annihilated. So much critical informational on Aryuveda, astronomy, mathematics and the physical sciences was lost forever. Some libraries were so huge, they burned for days.
Islam was at the height of its military era at the time and easily destroyed and annexed other passive cultures. Lots of journals of invaders from that time that documented their utter contempt for peoples who couldn't defend themselves.
The West had learned this lesson early and well from the Roman era: Si vis pacem, para bellum.
> CV Raman won the Nobel prize in science, Tagore won the Nobel prize in literature, Ramanujan etc, the names are numerous.
So golden age of India was when the country with a seventh of the world's population won 2 nobel prizes over 5 decades ?
> The British rule also was the largest and most stable unification of India till the modern times. After 1850s there were almost no pockets of military resistance against the British rule.
Mughal and Gupta empires lasted over 3 centuries, Mauryan empire a little under 1.5 centuries. By comparison, east india company rule lasted a century and the British crown's rule less than that. So again completely incorrect.
> The third golden age which no one wants to admit (left or right) is the British Golden age.
There's your hint: if people on both sides of the aisle don't "want to admit" something, maybe it doesn't make sense. Not to mention a slap in the face of billions of Indians.
> The British age declined with WW1 and WW2, and ended with Indian independence.
Thank god for that decline, otherwise Indian taxpayers would have been funding Brexit and the crumbling British economy right now.
> My oversimplified summary has been
This is not a summary, it's a lazy opinion backed by little research.
Have you read any books at all by Indians who lived through the British empire. Maybe start with “My Experiments with Truth” by Gandhi. The caricature that some modern Indians have made of the British empire would make even Gandhi turn in his grave.
But if you want to read something really heretic, maybe try reading An autobiography of an unknown Indian by Niraj Choudhary. Choudhary was a British raj supporter, as in an Indian who opposed Indian independence. Does that shock you? There were actually quite a lot of them, more than you’d expect.
Then if you want to get really metal, read in his own words, by Subedar Sitaram Pande. Sitaram Pande, was a soldier for the bengal army, for the British empire from 1812 to 1860, it’s one of the rare first author accounts we get of an Indian in that era. It will give you a glimpse of how an Indian at that time thought generally (hint: it was far more dominated by caste than you’d expect), how he viewed the empire and his relation to it. At that point I would say you are ready to try to understand Indian history that is not an avengers movie plot.
I would follow it with CK Majumdars history of modern India, one of the best historians so committed to the truth that Nehru had to throw him out of the government and try to prevent him from writing his book. Don’t worry, he’s not an heretic, he was an Indian freedom fighter, but you will find that he was far more honest about his life under Britain, under Indian national Congress and the state of the country in different periods of time (he also has a 12 volume set covering India for over 2000 years that I never had a chance to complete).
Sitaram Pande's book - https://archive.org/details/fromsepoytosubed0000sita
Choudhary's Autobiography of an unknown Indian
https://archive.org/details/autobiographyofu0000nira
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Please don't cross into personal attack or flamewar. Your post here is a noticeable step in those directions, and we're trying for the opposite on this site. (I'm not saying that the parent comments were perfect either but degrees matter.)
https://news.ycombinator.com/newsguidelines.html
>Mauryan empire a little under 1.5 centuries. By comparison, east india company rule lasted a century and the British crown's rule less than that This is a very dishonest way to obscure the actual facts.
Direct rule from Britain lasted for almost 90 years: 1858 to 1947. Even by your numbers then, that's 190 years: longer than the Mauryan empire's whole lifespan, and much closer to that of the Mughals. From there the question remains whether it's the longest "unification", and this mostly comes down to exactly when each of the aforementioned empires could be considered to have "unified" India.
By any definition the Mughals united the subcontinent by 1707AD at the latest: but by 1751, less than fifty years on, their effective domain had declined to a few pockets in Rajputana and Bengal.
The Guptan Empire on the other hand, while certainly a key predecessor to later Indian states and a major unifying force in the northern half of the subcontinent, never conquered the southern half -- what is today Karnakata, Kerala, and Tamil Nadu never entered their control. The closest they got was ~420AD after the south-eastern conquests of Chandragupta II, but again within fifty years they again lost control of today's Orissa, and even lost large swathes of north+western India to invasions from the steppe.
You call GP's post "a lazy opinion backed by little research", but when you dig into the facts I can't see how you could argue that his claim is incorrect. The British Raj alone seems to qualify as the longest-lasting unification of India before the modern Indian state, and if you include any part of the EIC's rule then it's indisputably so.
Mughals did not unite the subcontinent at any time. Even at its peak, Kerala, parts of Tamil Nadu and Sri Lanka was out of its influence. Parts of Kerala became British territories after 1804.
https://frontline.thehindu.com/arts-and-culture/literature/i...
The man was a card-carrying Marxist member of CPI with his own agenda and hence all of his "scholarship" is highly suspect.
https://koenraadelst.blogspot.com/2014/08/an-eminent-histori... - Read the conclusion first and then follow the tear down from the beginning of the article.
https://hindupost.in/history/how-leftist-historian-d-n-jha-d...
“In fact, Buddhism, which had flourished in Bharat for 1600 years, suddenly vanished almost completely as soon as Muslims became masters of Delhi and started raiding the plains of Ganga.” Citation needed?
Plenty of citations/articles/books/links here;
1) https://en.wikipedia.org/wiki/Decline_of_Buddhism_in_the_Ind... - From 986 CE, the Turks started raiding northwest India from Afghanistan, plundering western India early in the eleventh century. Forced conversions to Islam were made, and Buddhist images smashed, due to the Islamic dislike of idolatry. Indeed in India, the Islamic term for an 'idol' became 'budd'. — Peter Harvey, An Introduction to Buddhism ... According to William Johnston, hundreds of Buddhist monasteries and shrines were destroyed, Buddhist texts were burnt by the armies, monks and nuns killed during the 12th and 13th centuries in the Gangetic plains region. The Islamic invasions plundered wealth and destroyed Buddhist images ... The decline of Buddhism in the Indian subcontinent coincides with the spread of Islam in that part of the world, especially due to the Islamic invasions that occurred in the late 12th century. See sections "Turkic Invasions" and "Decline under Islamic Rule".
2) https://en.wikipedia.org/wiki/Persecution_of_Buddhists - See sections "Persecution by Muslim Empires" and "Persecution by Muslims".
3) And for good measure also read https://en.wikipedia.org/wiki/Persecution_of_Hindus
Buddhism was the tranquilizing death of India. You can argue that Islamic invaders would have conquered India anyways - but with Buddhism they rarely even had to fight!
Their puzzlement is even captured in several journals where they could range for hundreds of miles and loot/burn with little to no resistance. And do it once again a few years later!
There is a stronger argument to be made that it was because of the establishment of Buddhism as the de-facto state philosophy/religion/practice in North/Northwest part of India that the Islamic invaders could conquer India. Buddhism for all its intellectual/ethical/moral strengths was not a pragmatic religion. It ignored the realities of Life in favour of higher ideals in a context ill-suited to its survival and hence paid the price at the hands of barbaric muslim invaders. This happened through the elevation of Ahimsa into an all-encompassing tenet of state policy which severely sapped the Martial Spirit of the population and thus could offer no resistance to invaders bent on genocide. Prior to Buddhism (and Jainism) while Ahimsa was considered one of the central pillars of Hinduism its limitations in the practical world were acknowledged and Kings were expected to protect by force if necessary, those practicing Ahimsa as a way of life. With this gone, North/Northwest India was easy prey to barbaric muslim invaders who did not play by the same rules.
In Sindh Buddhist regions yielded peacefully to Muslims as opposed to Hindus/Raja Dahir
https://news.ycombinator.com/item?id=41537302
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I’m not cherry picking, I’m citing this book - https://brill.com/display/title/2198
https://archive.org/details/religion-and-society-in-arab-sin...
From https://en.wikipedia.org/wiki/Persecution_of_Buddhists :
During their conquest of Sindh, the Arabs brought the non-Muslims into the category of ahl al-kitab, considering them ahl al-dhimmah (protected subjects) and thus practicing a certain amount of non-interference in their religious lives under the condition that they fulfil a number of obligations that came with this status. Since both Buddhism and Hinduism are literate religions with scriptures, the precedent of assimilating Zoroastrians into the category of ahl al-kitab was extended to them as well. The dhimmis were obligated to pay the jizya for following their ancestral religion. The historian Al-Baladhuri notes a decision by Muhammad bin Qasim in relation to a Buddhist vihara and Aror that after conquering the city through a treaty (sulh) he agreed not to kill the people and enter their temple, in addition to imposing kharaj on them.[29] The Buddhists had petitioned the Arabs for the right to restore one of their temples and it was granted by Al-Hajjaj ibn Yusuf. However, this decision was later violated by the Pact of Umar and subsequent Muslim law codes which prohibited the restoration of existing non-Muslim religious structures as well as the building of new ones. Despite this fact, Buddhist inscriptions were still being recorded in the eleventh century.[28] Some Buddhists also fled and emigrated from Muslim-ruled areas into other regions. Unlike Brahmanical worship, Buddhism rapidly declined in Sindh after the eighth century and it virtually disappeared by the eleventh century.
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You've broken the site guidelines repeatedly and badly in this thread. We have to ban accounts that do this, so if you'd please review https://news.ycombinator.com/newsguidelines.html and stick to the rules when posting here, we'd appreciate it.
That means no personal attacks and no religious flamewar, among other things.
I don't doubt that you know a lot about this and other topics but we need you to make your substantive points thoughtfully and respectfully.
@dang;
I understand your point (the letter) but disagree with its spirit.
One should not tolerate attempts to intentionally "sweep under the rug" documented genocides and distort History just because it involves someone's Religion (their in-group). It is easy to be blind to genocides if one is not forced to face up to them, admit their faults and change their ways. Else the vicious cycle keeps spinning to the detriment of Society as a whole. Hence my forceful attempt to show up a person who intentionally was downplaying documented genocides. Note that most of my data/articles are from wikipedia (curated database and hence less susceptible to fake news/specific narratives/gaming) and not some opinion piece to push a narrative.
As you are very well aware, there are insidious groups trying to game the system at HN (and elsewhere) to push their narratives. They are not interested in the Truth/Factual Data/Social Accountability etc. but are only interested in distorting reality to their benefit (see Orwell's essay on Nationalism). These people/groups need to be called out forcefully even if it means not obeying all rules of etiquette. It is in that spirit that i wrote my comments.
> there are insidious groups trying to game the system at HN (and elsewhere) to push their narratives.
This sort of perception is common and has been common on HN for well over a decade, but I've rarely seen any evidence to support it. What there is evidence for—plenty of it—is users with different backgrounds misperceiving each other's comments as astroturfing/shilling/etc. because they simply can't imagine anyone holding those other views in good faith.
The odds are high that this is what you're encountering. It's not some shady misinformation group; it's simply people with very different backgrounds than your own, who hold opposite views for legit reasons, just like you hold your own views for legit reasons. These are difficult historical topics that there's no consensus on.
Here are a couple of long explanations I posted about this in the past:
https://news.ycombinator.com/item?id=35932851 (May 2023)
https://news.ycombinator.com/item?id=27398725 (June 2021)
You'll find links here to many years' worth of other explanations: https://hn.algolia.com/?sort=byDate&dateRange=all&type=comme....
If you read some of those explanations and still have a question that I haven't answered there, I'd be happy to take a crack at answering it.
Here is a very good summary from Youtube on "The Minority Rule" - https://www.youtube.com/watch?v=MwlW2aamDFc;
The Minority Rule, often associated with Nassim Nicholas Taleb, refers to a principle in which a small, intransigent minority can have a disproportionate impact on the behavior of a larger group, eventually leading the majority to adopt the preferences or practices of that minority. This occurs because the minority is highly committed to a particular preference or practice and is unwilling to compromise, while the majority is more flexible and willing to accommodate the minority's demands to avoid conflict or inconvenience.
Key Points of the Minority Rule:
Intransigence: The minority is unwavering in its position and refuses to accept alternatives.
Flexibility of the Majority: The majority is more flexible and often prefers to avoid confrontation or inconvenience, leading them to adopt the minority's preference.
Asymmetric Impact: Even though the minority is smaller, its rigid stance can lead to a situation where the majority conforms to the minority's preferences.
Examples:
Cultural Practices: In a mixed group, if a small number of individuals strictly follow a particular dietary rule (e.g., kosher or halal), the larger group might choose to accommodate these restrictions, leading to everyone adopting the more restrictive practice.
Regulations and Standards: Sometimes, a regulation or standard that applies to a small subset of people (e.g., accessibility requirements) becomes the norm for everyone because it’s easier or more efficient to have a single standard.
Implications: The minority rule highlights how committed minorities can exert significant influence over larger groups, often shaping social norms, practices, and even laws. This can be both positive (e.g., ensuring certain ethical standards) and negative (e.g., stifling diversity of thought or practice).
Nice writeups. While most of your reasoning/logic are valid i think you are missing a few crucial viewpoints which should be incorporated into your "HN filtration and decision-making" process.
I presume you know of Nassim Taleb's "The Minority Rule", if not see his article The Most Intolerant Wins: The Dictatorship of the Small Minority - https://medium.com/incerto/the-most-intolerant-wins-the-dict... and video explanation https://www.youtube.com/watch?v=MwlW2aamDFc Any system can be gamed by an intransigent group by applying this rule under the guise of victimhood/false equivalence/even-handedness/appeal to authority/religion/PC/DEI/etc. Various language techniques like phrasing/tone/insinuation/instigation/support/oppose/etc. can be used to lead/sway/hint/push towards the group's viewpoint irrespective of Truth/Reality. In today's world all Human topics involve Politics/Propaganda/Manipulation/Spin/Gaslighting/etc. whether we like it or not. The effects of "events" (eg. HN comments) in these domains are non-linear (pareto/power law/etc.) and hence a single outlier can ruin everything i.e. you don't need an actual "shady misinformation group".
I am not sure how HN does its moderation but i can guarantee that the above is happening in one form or another. I have seen this in threads to do with Russia-Ukraine war, Israel-Palestine issue, Boeing issues etc.
As an example, you say; "These are difficult historical topics that there's no consensus on." which is factually incorrect given the wikipedia links i had posted. You have been manipulated to disregard Truth in the guise of even-handedness :-)
You realize I belong to an Ahmedi family? What kind of insidious “ingroup” is that in Pak context? Please tell that to any Pakistani who will collapse in peals of laughter.
I like Xkcd's take on certain games: https://www.explainxkcd.com/wiki/index.php/2833:_Lying
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As an Indian, it is extremely naive and childish to dismiss any consideration of the British rule as a "slap in the face". The British introduced electricity, railways, capitalism and a thousand other things we take for granted behind those saffron-tinted glasses.
Hell, the British Raj was what unified India into a single national identity. It was more fractured than the European continent otherwise.
> The British introduced electricity, railways, capitalism and a thousand other things we take for granted behind those saffron-tinted glasses.
Some people love being a slave, but that is not a requirement for having electricity, railways or capitalism. Just look at any other country.
> naive, childish, saffron-tinted glasses.
A brain with less self-righteousness has more space for common sense and logic.
Good summary, even if I disagree with the 3rd piece being called a golden age. But my question is why ignore the cholas, pallavas and pandyas? Only because they didn’t capture the whole subcontinent? Our schools history books were Delhi centric but we don’t have to be going forward. Those 3 empires had a lot of arts and culture too - and in terms of impact, they spread to parts of SE Asia too.
That's the specialty of a centralized state. There is a heavy push towards homogenizing Indian culture often at the cost of regional subcultures since almost 1947.
> you could argue independence had been a disaster with everything getting worse post independence
There hasn't been a single famine in india since independence. The last one was the bengal famine of 1943. India became independent in 1947.
And, it should be on track to become the world’s largest economy by 2075 - which historically it and China always have been.
I hear what you’re saying, but this idea of a golden age under rule by some outside force is often the positive take about many historical periods where someone who committed significant crimes (invasions, genocides, etc) is then praised hundreds of years later because of the positive effect they had for the economy or whatever. Julius Caesar is one such example that comes to mind.
But I feel that approach sometimes discounts what the country and its people could have achieved on their own if they were not invaded. For example, the Taj Mahal is just one building in India. There are lots of other structures that exist that were not built under rule from outside invaders, but they never get attention (at least I’ve not heard of them). With Britain - you mentioned that they unified India and brought stability but how true is that if you compare it to the period of India much earlier? India was rocked by Islamic invasions (which led to the Mughal period) and colonized by those Islamic rulers for hundreds of years. That’s what the European colonizers took over. Is that really a fair period to compare against? India basically spent a millennium ruled by one outside genocidal invader or the other. I am guessing the period before that was more peaceful and not in need of some outside unifying force to feel ‘stable’.
Taj Mahal is nothing compared to ajanta and elloracaves. Whoever elected Taj Mahal as one of the 7 wonders was an idiot in my view
Even more grandiose is the temple at Tanjavur built by the Chola king. Its dome is taller than Qutub Minar and is wider than the Taj Mahal.
What do you think about Gupta india
They never reached the highs reached by the Mauryan Empire, but were still a period of relatively prosperity and stability compared to what immediately followed (until the Mughals came)
I don't think anything about it (due to not having enough info about it), but Wikipedia does:
https://en.m.wikipedia.org/wiki/Gupta_Empire
You missed Gupta.. but I too consider Islamic/Mighal as well as British time too Golden period from world progress perspective.
If Invasions and colonization were golden age we should continue that tradition throughout the world. /s
I guess the author, a historian, writes about ancient Indian mathematical contributions (a science of which he has no expertise presumably). These historical references I have learnt in various mathematical texts (the story of Fibonacci and al khwarizmi) - the journey across multiple centuries, of these innovations made by Aryabhata or Brahmagupta.
As an Indian, and as a math aficionado (and degree holder) - I wonder, that was about 1500 years ago. In that era, a discovery (as you can read it) took 500 years to move from Arabia to Europe, thanks to Fibonacci's writing. Contrast it to today's instant dissemination of information and breakthroughs. Yes those were the glory days of Indian civilization. We have a Ramanujan every 100 years in India. Breakthrough ideas (earthshaking ones like the concept of 0) emerging out of India are few and far between. Around 1000 years ago, the fountain of (world-changing) creativity and ideas seems to have dried up, as far as India is concerned. Maybe it was the invaders , easy to blame everything on outsiders, though - what is India today was 600 or 400 odd kingdoms, frequently warring each other - so turmoil was always there. And if you were a reclusive monk in a forest with a bunch of students, no Brit or Mughal dude was stopping you from innovating. So, the big question is - can we explain why genius ideas stopped (without blaming British, or Mughals etc) - because thanks to Indian's instincts, the first step is to blame the Brits/Mughals , so problem solved, proved, ostrich is happy in the sand.
I can only indulge in thought exercises , like : Aryabhata and Brahmagupta didn't have computers, didn't even have pencil and paper. They just sat there and thought. For months, or years. Or maybe they were walking. And gazed at the stars and observed and observed. And most likely, and importantly debated orally : endlessly with their teachers (in a monastery type place class sizes were small), peers- I believe this was a time in India's cultural history when debating, and disagreeing were positive things. In modern India, intellectualism has taken a back seat. To disagree is to be unpatriotic even. (Nalanda University comes to mind https://en.wikipedia.org/wiki/Nalanda_mahavihara - not its modernized recreation which is likely going to be hardly attempting to break the mold). WhatsApp - the destroyer of brain cells by atrophy , has a grip on every mind.
We read about the great Greek debates. We see videos of Tibetan buddhist monks practice debating in a monastery. Surely this kind of debating, face-to-face is missing in today's world (without getting angry) - this is the equivalent of the modern cafe in Paris or Vienna, with Godel and co. debating . This debating society , was Nalanda back a thousand years until invaders burnt every manuscript down and slaughtered every monk almost - except the manuscripts the Chinese monks took back to the Emperor in China - they are the only written records of life that remain, that and some arabic ones.
Yet I hope new lotuses will bloom from India - we can never predict where the next genius or breakthrough idea will emerge from - why not Africa?
I think it's just that industrialization, the computer, and the Internet were such massive juice that even if you have a brilliant mind it doesn't matter because the guy with that tool can take anything you think of and make it better. Each of these is a step up so huge that no mind can match it. So you have to match the tool first before the minds start mattering.
>didn't even have pencil and paper.
The oral tradition was certainly strong but there was no dearth as such of writing instruments. What makes their work not easy to access is their poetic symbolism, sun is one, moon is two and so on. These symbolisms were not even one to one, thus always leaving a window a doubt about what they really meant in their verses.
Since you mention Fibonacci, you may know what we call Fibonacci series was worked out around 250 BC by Pingala as an exercise in enumerating meter of verse
https://en.wikipedia.org/wiki/Pingala
The question is why has that innovation of breakthrough ideas dried up. Past glory is small consolation, or none at all. How long will we keep sharing these 1000-year old memes in 'modern' India? Maybe innovation still happens (likely) - but no one recognizes it, and it gets lost in the endless clamor and noise of meaningless rituals that define religion in India today - or there may be no ecosystem to surface it, ie bring to market.
What religion/culture was then in the time of Aryabhata (which no one really knows I suppose) - is very likely totally different than what it is today , i.e. a way to impose majority opinions with zero debate. Because Aryabhata and others created works which made it through the centuries of strife, they survived, they had an ecosystem that supported the genius - which seems to be lacking now in Modern India - which might explain why it has dried up - i.e. Indians aspirations are far less lofty, the bar is set quite low - because there is no lack of money, there is no lack of tools. Whether now, or 1000 years ago, they were recognized as authoritative, transformative works - do we have the current generation creating anything (to which the average Indian response is the last 70 years of liberal rule has to be ruled out, and undone first).
> Past glory is small consolation, or none at all.
I think its far worse. Current and in power ideology has co-opted scientific progress for romanticizing about a past, often fictional. That's why we have government patronage of fraudulent medicine-men and their medicine such as coronil that was supposed to ward off coronavirus and simultaneously fight the evil conspiracies of the western civilization that denied them their due glory.
I also misunderstood an aspect of your original comment. I thought you were waxing romantically eloquent -- look they had no pencil and paper and they would just gaze poetically at the heavens and maths would happen in their brains... just imagine what would have happened had they been given paper.
Hence my comment, that lack of writing material was not holding them back.
The fact that checking primality has a deterministic algorithm is a recent Indian breakthrough.
They did have ink and papyrus.
The Manusmriti - if you ignore the social aspects of it has a calculation for the age of the universe. The very first chapter has it. I think it computes to about 12 billion years - close to what modern science brings it out to be.
While manu discouraged widow remarrige he advocated for a share of property for a married woman who has an extra-marital affair. The norm the world around at that time was death by stoning.
I don’t agree with Manu’s societal directives. I guess it was a feature of its time and Hinduism currently is worse for it.
My interest is the first chapter where he elaborates on the chronology of the universe.
Is it possible to find out universal secrets through deep meditation?
I don't see why it wouldn't be. Conscious thought is only the tip of the iceberg; even Western thought has a long tradition of noting that Eureka moments come during periods when you are not rationally engaging with the topic. See for example
https://en.wikipedia.org/wiki/Eureka_(word)
https://en.wikipedia.org/wiki/Eureka_effect
That is the belief. But deep meditation is elusive. You need to understand the relationship between yourself and your Mantra.
One of the best explanations of Mantras and meditation are by Dr Robert Svoboda (for any audience more familiar with English than Sanskrit/hindi). Granted he trained under an Aghori which isn’t traditionally the path most folks would take. But his explanations are exemplary.
Not from a Jedi.
The Guardian also published a promotional piece for this book if you can't get past the paywall of TFA.
https://www.theguardian.com/world/article/2024/sep/01/hidden...
Dalrymple has a uniquely addictive style of writing that very few history writers do. I can't recall any other nonfiction book becoming such a page-turner for me as his "Anarchy" did. Terrific writer.
Anyone know why the hardcover isn’t available until April 2025?
I was super excited to read this book but I hate buying kindle books as it’s easier to share real books.
What do you mean? Amazon has the hardcover listed for sale.
It available from Amazon UK and they will ship it to the US.
I have already bought hardcover on Amazon India
https://archive.ph/kcVok
Tangential but interesting - see also Sam Miller's idiosyncratic and funny book A Strange Kind of Paradise: India through Foreign Eyes.
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It's a fine surprise that I just ordered the book independently and then discovered the podcast and found the book being discussed on HN all in the same day. Pretty nice coincidence.
Very good writer, but he personally wound me up with his public "Great Escape" from India during the pandemic and laid himself open to the criticism that followed, of being a fairweather friend.
What exactly is the criticism here? He didn't strand himself in a particular densely populated foreign country while COVID lockdowns were happening across the world? He would be a better friend to India if he stayed there, contracted COVID, and put more strain on their healthcare system to the detriment of actual citizens?
His words, in the context of Indian, Britishness, colonialism, his own writing and the suffering of those he had left behind - he himself apologised for the message "being tone deaf & reeking with privilege" and I think it was quite reasonable that people were irritated by his posts of palm trees and sunny beaches while so few others had the choice.
And secondly, he lives there, it was not a "foreign" country and he was not "stranded". He lives there.