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 These historical references I have learnt in various mathematical texts (the story of Fibonacci and al khwarizmi) - the journey across multiple centuries, of these innovations made by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.
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?