8 ms·

The path that the decimal number system took from India to medieval Europe

173 points by cossatot 8y ago

amriksohata 8y ago
A lot of Indians got annoyed that they are double barrelled as Hindu Arabic, when the original source was India. The arabs then took it and created other concepts. Its like calling English alphabet English-American.
- jankotek 8y ago
  English alphabet comes from ancient Rome, there is a reason why it is called Latin script....
  - deleted 8y ago
    [deleted]
  - stevula 8y ago
    I think there is a distinction between script and alphabet. English, French, and Spanish all use the Latin script but have different alphabets. For example, the German alphabet includes ß, Spanish includes digraphs (ch, rr).
    - posterboy 8y ago
      ß is also a digraph (ligatur) of ss, confused with sz, hence its name "esszett". > script and alphabet I don't think there is a notable distinction. But sure enough, the ancient Greeks used several alphabets, some different letters ... and different forms for equal letters, which therefore cannot be called the same letters.
- Sangermaine 8y ago
  The English alphabet is a good example of why the Indian complaint doesn't make much sense. The modern English alphabet descends from an ancient Proto-Sinaitic script, which was adopted and transformed over time by the Phoenicians, then the Greeks, then the Romans, then the Anglo-Saxons, and then underwent some further evolution into the script English speakers use today. Of course, this is extremely simplified and the development wasn't this linear, but it's a rough sketch. Just as it would be odd and inaccurate to call the modern English alphabet Proto-Sinaitic or Phoenician, it's inaccurate to call the modern number system Indian because, as you note the "arabs then took it and created other concepts". What we use today is the modified system, it's not purely of Indian creation.
  - godelmachine 8y ago
    There's no documented proof that Indian system was descended from another system. The Fountainhead was India. Hence, purely of Indian creation. It's also a well-known fact that Al-Jabr took some mathematical aspects from India and spread them across the Arabic countries. From there they eventually reached the west. That's how Algebra got its name.
    - jacobolus 8y ago
      > well-known fact that Al-Jabr took some mathematical aspects from India and spread them across the Arabic countries Your “Al-Jabr” (Short for Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala, or The Compendious Book on Calculation by Completion and Balancing) was a book, written by Muḥammad ibn Mūsā al-Khwārizmī, who was Persian. Like other scholars writing in Arabic at the time, he read translations of Greek and Indian sources, while also doing significant original work. The book of his which explained and advocated Indian numerals was a different book (not “Al-Jabr”). We have this in Latin translation so the original title is unknown, but Wikipedia speculatively lists Kitāb al-Jam‘ wat-Tafrīq bi-Ḥisāb al-Hind (The Book of Addition and Subtraction According to the Hindu Calculation). [Edit: I just read the linked blog post which this discussion is ostensibly about, and noticed that the above was already described there. I assume you didn’t read it. You might want to start with that.] If you want to play a game of “whose culture first invented everything”, we can trace a whole heck of a lot back to the Sumerians (and for what we can’t trace, who knows what still lies on some buried cuneiform tablet). But of course there were then crucial additional advancements made by Akkadians, Egyptians, Hellenes, Indians, Chinese, Arabs, Persians, Italians, French, English, Russians, Germans, Hungarians, Canadians, Japanese, ..... Mathematics is international and spreads easily. No culture can uniquely claim to have “invented” something as massive as “algebra”, even if we limit ourselves to topics taught in secondary school.
      - structclass 8y ago
        Again, there is no proof, nor even speculation that the Math in Bharat was descended from any other sub culture. Also, I do not know who said, "math is queen of all sciences". >No culture can uniquely claim to have “invented”? No. It can. It should. And It will.
- sidhu1f 8y ago
  Even calling them Hindu-Arabic would be preferable to the usual custom of labeling them simply Arabic (for e.g. in LaTeX).
- kifachachaf 8y ago
  The numerals used by Al Khawarizmi are not the exact ones used in India back then. Now the problem is Al Khawarizmi is Persian he's not Arab. https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg
- empath75 8y ago
  They arrived in the west via Arabic books, so they were originally just called ‘arabic’. Calling them Hindu/Arabic is at least an improvement.
- baxtr 8y ago
  Even caring about this kind of stuff feels like people have an inferiority complex
  - yumraj 8y ago
    So, if you invent something and tell me about it, you'd be totally fine if I go ahead and claim it as my invention, file a patent, copyright it etc., since you don't suffer from inferiority complex, right?
    - baxtr 8y ago
      I don’t think that is a sound comparison and it’s missing my point Look, I don’t want to insult anyone. That’s just a conclusion I’ve made over the years. My background is also such that my native people always complain about past stuff like that instead of changing the here and now
    - Sangermaine 8y ago
      That analogy is a terrible one for the historical situation we're talking about. The numeral system is a concept that was vastly changed as it passed through different cultures over time. The current system in use is, demonstrably, not the one used in the ancient Indian subcontinent. It is indeed a Hindu-Arabic system because the form we use today arose among Arab scholars who had adapted the older Indian symbols. It's nationalistic nonsense to fight against both the historical reality and the natural flow of ideas over millennia, and does indeed smack of an inferiority complex. It's not a slight or a slur to acknowledge the complexity of the historical reality, and the achievements of ancient Indian peoples are no less impressive, anymore than the Greek adaptation and expansion of older Babylonian geometric concepts diminishes those.
  - thankthunk 8y ago
    Welcome to humanity. You should read up on the centuries old newton-leibniz calculus debate. But regardless, the modern number system is one of the seminal achievements in human history, along with the wheel, alphabet, paper, etc. It shouldn't be too surprising that people want correct attribution/credit.
- jdtang13 8y ago
  This smells exactly like the sort of stuff you'd read in a nationalist-revised history textbook. Hindu Arabic is a fine way to describe it, since, as others have mentioned, it's exactly the Arabic-writing Persians who transmitted the idea to the West. I think this naming is just as permissible as referring to the Latin alphabet as the English alphabet, which is what you just did ;) Also, the word "firangi" means foreigner in Hindi, but it also means "Frankish person". Should Englishmen in India be upset that they are being grouped with the French?
  - amriksohata 8y ago
    Lol at anything being nationalist because people want others to know the truth. Comparing something so fundamental as the discovery of the numerical system to a word in the English dictionary is comparing two very different things
    - posterboy 8y ago
      Well, the Sumerians used sexagesimal, which brings us back on topic, because I've read the fact in Don Knuth - TAOCP 4.
- dang 8y ago
  Unfortunately this comment doesn't contain enough substance to prevent a landslide of nationalistic bickering. All: don't do that on this site, please. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- deleted 8y ago
  [deleted]
nyc111 8y ago
The book mentioned in the comments is very interesting https://www.amazon.com/Money-Changes-Everything-Civilization-Possible/dp/0691178372 https://www.amazon.com/Money-Changes-Everything-Civilization... "William H. Goetzmann in “Money changes everything”, a history of the influence of finance on civilisation from Babylonian times onwards, also credits Leonardo of Pisa with introducing the concept of what we now call Net Present Value in one of his Liber Abbaci problems."
gumby 8y ago
I’ve always been amused that they are called “Arabic” as a cursory glance at the shapes of European and Hindu digits shows the connection while the Arab scripts use such different forms. But the again this is how we get terms like the foods “turkey” and “orange” so there’s no reason to complain. India did also have a (presumably) Babylonian-inspired sexagesimal system as well, as seen for example in the pre-decimalized currency. There was extensive trade between India, the Middle East, and Eastern Africa stretching back thousands of years, and cultural as well as physical goods clearly went both ways.
- kifachachaf 8y ago
  wrong. https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg
  - gumby 8y ago
    Is it? You can see from the picture you posted that the glyphs of the digits from Gwalior have as strong resemblance to contemporary 1, 2, 3, 4/5, 7, 9, and 0 (the 4/5 relation is similar to the evolution of English letters like J, G and Y from the Phoenician/Greek letters) while the current Arabic digits, the east Arabic of that chart, are mostly quite different.
    - v_lisivka 8y ago
      Idea behind modern digits is pretty simple: just count number of angles: http://mathandmultimedia.com/2013/05/23/angles-and-the-hindu-arabic-numerals/ http://mathandmultimedia.com/2013/05/23/angles-and-the-hindu...
- Arnavion 8y ago
  >India did also have a (presumably) Babylonian-inspired sexagesimal system as well, as seen for example in the pre-decimalized currency. The pre-decimalized currency was 16 anna to the rupee and 4 paise to the anna. There was no base-60 denomination.
dang 8y ago
All: since the title was baiting some people into nationalistic arguments, which are off topic here, we replaced it with representative language from the article explaining what it is about. This is a great HN submission! Please don't let the thread slide back into bickering.
forapurpose 8y ago
When we say "India" in an historical context, realize that we're not talking about the place we know today. S. Asian history contains many varying political entities and cultures each covering varying sub-regions of the region covered today by India, Pakistan, and Bangladesh. For much of of the time (I don't remember enough to say how long off the top of my head), the main divide has been between (northern India + Pakistan) and (southern (Tamil?) India), for geographical reasons. Heck, the Indus river, after which India is named, is now in Pakistan. The current countries and their borders date only to 1971, and are unresolved in some places. (The vagueries of history and its crazy etymologies are hardly limited to the subcontinent: Look at the "West Indies" and Native American "Indians" as easy examples. And every piece of real estate in the world has been controlled by more than one political entity, and periodically one of the former owners claims someone else's land on some historical basis.) For those interested in more, it's hard to find a good one-volume scholarly history of the region in English, at least last I looked. Here's the best I found, IMHO: India: A History by John Keay https://www.harpercollins.com/9780007382392/india-a-history https://www.harpercollins.com/9780007382392/india-a-history EDIT: a few enhancements
- justboxing 8y ago
  > For this word "Indian" has been abused as no other word in the language; almost every time it is used it has to be qualified. There was a time in Europe when everything Oriental or everything a little unusual was judged to come from Turkey or India. So Indian ink is really Chinese ink and India paper first came from China. When in 1492 Columbus landed on the island of Guanahani he thought he had got to Cathay. He ought therefore to have called the people Chinese. But East was East. He called them Indians, and Indians they remained, walking Indian file through the Indian corn. And so, too, that American bird which to English-speaking people is the turkey is to the French le dindon, the bird of India. Source: Sir V.S. Naipaul on East Indians, 1965 http://faroutliers.blogspot.com/2004/10/naipaul-on-east-indians-1965.html http://faroutliers.blogspot.com/2004/10/naipaul-on-east-indi...
- adrianratnapala 8y ago
  But still there is nothing wrong with the word "India" in this context. Brahmagupta was a worshipper of Shiva who lived in Rajasthan. He fits in perfectly well with Indianness both modern and ancient. Now it is interesting that the words "India" and "Hindu" are western (mostly Iranian) impositions. Perhaps Brahmagupta would have found the word "Bharat" less alien. But since the topic of the article is about how a particular Indian idea was spread and developed further west, the name is perfectly appropriate. P.S. I also like John Keay's book.
vectorEQ 8y ago
islamic culture cultivated and gathered lots of knowledge, includign that of roman, indian, some african and other cultures. in my opinion their translation efforts have saved a lot of, and furthered a lot of science and research. As europe was plunged into the dark ages, the islamic culture saw an age of light where knowledge was power and there was a big effort for about 1000 years to cultivate and improve understanding of the world around us. alchemy, algebra, algorithm, a lot of words which came from there. though some of the underlying knowledge was gained from translating texts of other cultures, credit goes to these islamic scientists for recognising the importance of these works and improving upon them.
- wahern 8y ago
  1000 years is a stretch. Most of it occurred during the Abbasid Caliphate, which promulgated a school of Islamic scholarship and practice that supported and even promoted the development of worldly knowledge. https://en.wikipedia.org/wiki/Abbasid_Caliphate#Islamic_Golden_Age https://en.wikipedia.org/wiki/Abbasid_Caliphate#Islamic_Gold... Importantly, this school of Islam accepted or at least was tolerant of the idea that God controlled the world indirectly through what we now call natural laws. It's in this age that you saw the theological state financially support philosophy, the collection of foreign philosophic works into libraries, and their study and extension. But an anti-intellectualist school very quickly rose to dominate the landscape, both the scholarship and lay practice. https://en.wikipedia.org/wiki/The_Incoherence_of_the_Philosophers https://en.wikipedia.org/wiki/The_Incoherence_of_the_Philoso... Subsequently, the preservation and advancement of philosophy was a mere echo of the earlier, short-lived era and occurred at the periphery of Islamic power rather than at its center as in the Abbasid Caliphate. The same conflicts played out in Christianity, but fortunately orthodox (small-o) Christianity adopted a natural laws perspective. It's worth pointing out that there was never really a Dark Age in Europe. Rather, the political upheaval merely disrupted Europe's collective memory and severed its rich connections to the rest of Eurasia and Africa. Philosophical and scientific advancements proceeded, but without the benefit of well-understood context about the sources of received knowledge, and with a much diminished inflow of novel advancements. FWIW, I hesitate to refer to the rise of the school which rejected natural laws as "anti-intellectualism". The school has its own internally consistent logic, and I understand why it would be appealing. You can see the appeal by recognizing the similarity with similar movements in Christianity. I don't think it's a coincidence that what we would call anti-intellectualism in the Christian world also coincides with, e.g., iconoclasm, another point of divergence between orthodox scholarship in Islam and Christianity. There's an appealing intellectual purity in reducing everything to a singular axiom that effectively says everything is as God wills it to be and that attempts to systematize his will is (like iconography) an intermediation and a rejection of his agency and presence. But that manner of viewing the world is not hospitable to the nurture of scientific rationalism, which is largely how we understand intellectualism today. Note that I'm not trying to make the claim that Christianity is somehow better or more logical than Islam. As non-orthodox Christian denominations (i.e. the ones which, among other things, lean to biblical literalism) are happy to point out, the pro-intellectual characteristics of orthodox Christianity owe more to its inheritance from Greek and other sources largely orthogonal to the foundational doctrines of Christianity. In other words, orthodox Christianity was more hospitable to science despite itself. Islam shared many of the same influences, it just rejected them where orthodox Christianity syncretized them.
matco11 8y ago
Title of the link is inaccurate. The post refers to the Arabic numerals, not the decimal system - and after all the Roman numerals (which was widely commonal) also follow the decimal system. It should be “the path that Arabic numerals [or Hindu-Arabic numerals] took from India to medieval Europe.”
msravi 8y ago
The earliest use of the decimal system in Hindu mathematics is in the Yajurveda Samhita, where there is a list of numerical denominations given: eka(1), dasha(10), shata(100), sahasra(1000), ayuta(10000), nryuta(100000), ... all the way to 10^12. The list, with slight modifications and additions, is repeated in other Vedic texts [1]. The Yajurveda Samhita dates back to between 2000BCE - 1000BCE. The earliest use of zero as a symbol in Hindu mathematics actually occurs between 300BCE - 200BCE in a work called Chandah Sutra by Pingala. It is used in figuring out the number of combinations of long and short syllables in a verse containing n syllables [2]. The earliest written manuscript that uses zero as a symbol predates both Brahmagupta and Aryabhatta, and is found in the Bakhshali manuscript that is dated between 224CE-383CE [3]. Here are some of the problems tackled in the Bakhshali manuscript [4]: a) Problems involving systems of linear equations b) Indeterminate equations of the 2nd degree c) Arithmetica progressions d) Quadratic equations e) Approximate evaluations of square roots f) Problems of the type x(1-a1)(1-a2)...(1-an)=p 1. https://archive.org/stream/in.ernet.dli.2015.81882/2015.81882.History-Of-Hindu-Mathematics-A-Source-Book-Part-iampii#page/n31/mode/2up https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188... 2. https://archive.org/stream/in.ernet.dli.2015.81882/2015.81882.History-Of-Hindu-Mathematics-A-Source-Book-Part-iampii#page/n97/mode/2up https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188... 3. https://en.wikipedia.org/wiki/Bakhshali_manuscript https://en.wikipedia.org/wiki/Bakhshali_manuscript 4. https://archive.org/stream/in.ernet.dli.2015.189295/2015.189295.The-Bakhshali-Manuscript--Vol-1#page/n25/mode/2up https://archive.org/stream/in.ernet.dli.2015.189295/2015.189...

173 points by cossatot 8y ago

A lot of Indians got annoyed that they are double barrelled as Hindu Arabic, when the original source was India. The arabs then took it and created other concepts. Its like calling English alphabet English-American.

jankotek 8y ago
English alphabet comes from ancient Rome, there is a reason why it is called Latin script....
- deleted 8y ago
  [deleted]
- stevula 8y ago
  I think there is a distinction between script and alphabet. English, French, and Spanish all use the Latin script but have different alphabets. For example, the German alphabet includes ß, Spanish includes digraphs (ch, rr).
  - posterboy 8y ago
    ß is also a digraph (ligatur) of ss, confused with sz, hence its name "esszett". > script and alphabet I don't think there is a notable distinction. But sure enough, the ancient Greeks used several alphabets, some different letters ... and different forms for equal letters, which therefore cannot be called the same letters.
Sangermaine 8y ago
The English alphabet is a good example of why the Indian complaint doesn't make much sense. The modern English alphabet descends from an ancient Proto-Sinaitic script, which was adopted and transformed over time by the Phoenicians, then the Greeks, then the Romans, then the Anglo-Saxons, and then underwent some further evolution into the script English speakers use today. Of course, this is extremely simplified and the development wasn't this linear, but it's a rough sketch. Just as it would be odd and inaccurate to call the modern English alphabet Proto-Sinaitic or Phoenician, it's inaccurate to call the modern number system Indian because, as you note the "arabs then took it and created other concepts". What we use today is the modified system, it's not purely of Indian creation.
- godelmachine 8y ago
  There's no documented proof that Indian system was descended from another system. The Fountainhead was India. Hence, purely of Indian creation. It's also a well-known fact that Al-Jabr took some mathematical aspects from India and spread them across the Arabic countries. From there they eventually reached the west. That's how Algebra got its name.
  - jacobolus 8y ago
    > well-known fact that Al-Jabr took some mathematical aspects from India and spread them across the Arabic countries Your “Al-Jabr” (Short for Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala, or The Compendious Book on Calculation by Completion and Balancing) was a book, written by Muḥammad ibn Mūsā al-Khwārizmī, who was Persian. Like other scholars writing in Arabic at the time, he read translations of Greek and Indian sources, while also doing significant original work. The book of his which explained and advocated Indian numerals was a different book (not “Al-Jabr”). We have this in Latin translation so the original title is unknown, but Wikipedia speculatively lists Kitāb al-Jam‘ wat-Tafrīq bi-Ḥisāb al-Hind (The Book of Addition and Subtraction According to the Hindu Calculation). [Edit: I just read the linked blog post which this discussion is ostensibly about, and noticed that the above was already described there. I assume you didn’t read it. You might want to start with that.] If you want to play a game of “whose culture first invented everything”, we can trace a whole heck of a lot back to the Sumerians (and for what we can’t trace, who knows what still lies on some buried cuneiform tablet). But of course there were then crucial additional advancements made by Akkadians, Egyptians, Hellenes, Indians, Chinese, Arabs, Persians, Italians, French, English, Russians, Germans, Hungarians, Canadians, Japanese, ..... Mathematics is international and spreads easily. No culture can uniquely claim to have “invented” something as massive as “algebra”, even if we limit ourselves to topics taught in secondary school.
    - structclass 8y ago
      Again, there is no proof, nor even speculation that the Math in Bharat was descended from any other sub culture. Also, I do not know who said, "math is queen of all sciences". >No culture can uniquely claim to have “invented”? No. It can. It should. And It will.
sidhu1f 8y ago
Even calling them Hindu-Arabic would be preferable to the usual custom of labeling them simply Arabic (for e.g. in LaTeX).
kifachachaf 8y ago
The numerals used by Al Khawarizmi are not the exact ones used in India back then. Now the problem is Al Khawarizmi is Persian he's not Arab. https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg
empath75 8y ago
They arrived in the west via Arabic books, so they were originally just called ‘arabic’. Calling them Hindu/Arabic is at least an improvement.
baxtr 8y ago
Even caring about this kind of stuff feels like people have an inferiority complex
- yumraj 8y ago
  So, if you invent something and tell me about it, you'd be totally fine if I go ahead and claim it as my invention, file a patent, copyright it etc., since you don't suffer from inferiority complex, right?
  - baxtr 8y ago
    I don’t think that is a sound comparison and it’s missing my point Look, I don’t want to insult anyone. That’s just a conclusion I’ve made over the years. My background is also such that my native people always complain about past stuff like that instead of changing the here and now
  - Sangermaine 8y ago
    That analogy is a terrible one for the historical situation we're talking about. The numeral system is a concept that was vastly changed as it passed through different cultures over time. The current system in use is, demonstrably, not the one used in the ancient Indian subcontinent. It is indeed a Hindu-Arabic system because the form we use today arose among Arab scholars who had adapted the older Indian symbols. It's nationalistic nonsense to fight against both the historical reality and the natural flow of ideas over millennia, and does indeed smack of an inferiority complex. It's not a slight or a slur to acknowledge the complexity of the historical reality, and the achievements of ancient Indian peoples are no less impressive, anymore than the Greek adaptation and expansion of older Babylonian geometric concepts diminishes those.
- thankthunk 8y ago
  Welcome to humanity. You should read up on the centuries old newton-leibniz calculus debate. But regardless, the modern number system is one of the seminal achievements in human history, along with the wheel, alphabet, paper, etc. It shouldn't be too surprising that people want correct attribution/credit.
jdtang13 8y ago
This smells exactly like the sort of stuff you'd read in a nationalist-revised history textbook. Hindu Arabic is a fine way to describe it, since, as others have mentioned, it's exactly the Arabic-writing Persians who transmitted the idea to the West. I think this naming is just as permissible as referring to the Latin alphabet as the English alphabet, which is what you just did ;) Also, the word "firangi" means foreigner in Hindi, but it also means "Frankish person". Should Englishmen in India be upset that they are being grouped with the French?
- amriksohata 8y ago
  Lol at anything being nationalist because people want others to know the truth. Comparing something so fundamental as the discovery of the numerical system to a word in the English dictionary is comparing two very different things
  - posterboy 8y ago
    Well, the Sumerians used sexagesimal, which brings us back on topic, because I've read the fact in Don Knuth - TAOCP 4.
dang 8y ago
Unfortunately this comment doesn't contain enough substance to prevent a landslide of nationalistic bickering. All: don't do that on this site, please. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
deleted 8y ago
[deleted]

nyc111 8y ago

The book mentioned in the comments is very interesting https://www.amazon.com/Money-Changes-Everything-Civilization-Possible/dp/0691178372 https://www.amazon.com/Money-Changes-Everything-Civilization... "William H. Goetzmann in “Money changes everything”, a history of the influence of finance on civilisation from Babylonian times onwards, also credits Leonardo of Pisa with introducing the concept of what we now call Net Present Value in one of his Liber Abbaci problems."

gumby 8y ago

I’ve always been amused that they are called “Arabic” as a cursory glance at the shapes of European and Hindu digits shows the connection while the Arab scripts use such different forms. But the again this is how we get terms like the foods “turkey” and “orange” so there’s no reason to complain. India did also have a (presumably) Babylonian-inspired sexagesimal system as well, as seen for example in the pre-decimalized currency. There was extensive trade between India, the Middle East, and Eastern Africa stretching back thousands of years, and cultural as well as physical goods clearly went both ways.

kifachachaf 8y ago
wrong. https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg
- gumby 8y ago
  Is it? You can see from the picture you posted that the glyphs of the digits from Gwalior have as strong resemblance to contemporary 1, 2, 3, 4/5, 7, 9, and 0 (the 4/5 relation is similar to the evolution of English letters like J, G and Y from the Phoenician/Greek letters) while the current Arabic digits, the east Arabic of that chart, are mostly quite different.
  - v_lisivka 8y ago
    Idea behind modern digits is pretty simple: just count number of angles: http://mathandmultimedia.com/2013/05/23/angles-and-the-hindu-arabic-numerals/ http://mathandmultimedia.com/2013/05/23/angles-and-the-hindu...
Arnavion 8y ago
>India did also have a (presumably) Babylonian-inspired sexagesimal system as well, as seen for example in the pre-decimalized currency. The pre-decimalized currency was 16 anna to the rupee and 4 paise to the anna. There was no base-60 denomination.

dang 8y ago

All: since the title was baiting some people into nationalistic arguments, which are off topic here, we replaced it with representative language from the article explaining what it is about. This is a great HN submission! Please don't let the thread slide back into bickering.

forapurpose 8y ago

When we say "India" in an historical context, realize that we're not talking about the place we know today. S. Asian history contains many varying political entities and cultures each covering varying sub-regions of the region covered today by India, Pakistan, and Bangladesh. For much of of the time (I don't remember enough to say how long off the top of my head), the main divide has been between (northern India + Pakistan) and (southern (Tamil?) India), for geographical reasons. Heck, the Indus river, after which India is named, is now in Pakistan. The current countries and their borders date only to 1971, and are unresolved in some places. (The vagueries of history and its crazy etymologies are hardly limited to the subcontinent: Look at the "West Indies" and Native American "Indians" as easy examples. And every piece of real estate in the world has been controlled by more than one political entity, and periodically one of the former owners claims someone else's land on some historical basis.) For those interested in more, it's hard to find a good one-volume scholarly history of the region in English, at least last I looked. Here's the best I found, IMHO: India: A History by John Keay https://www.harpercollins.com/9780007382392/india-a-history https://www.harpercollins.com/9780007382392/india-a-history EDIT: a few enhancements

justboxing 8y ago
> For this word "Indian" has been abused as no other word in the language; almost every time it is used it has to be qualified. There was a time in Europe when everything Oriental or everything a little unusual was judged to come from Turkey or India. So Indian ink is really Chinese ink and India paper first came from China. When in 1492 Columbus landed on the island of Guanahani he thought he had got to Cathay. He ought therefore to have called the people Chinese. But East was East. He called them Indians, and Indians they remained, walking Indian file through the Indian corn. And so, too, that American bird which to English-speaking people is the turkey is to the French le dindon, the bird of India. Source: Sir V.S. Naipaul on East Indians, 1965 http://faroutliers.blogspot.com/2004/10/naipaul-on-east-indians-1965.html http://faroutliers.blogspot.com/2004/10/naipaul-on-east-indi...
adrianratnapala 8y ago
But still there is nothing wrong with the word "India" in this context. Brahmagupta was a worshipper of Shiva who lived in Rajasthan. He fits in perfectly well with Indianness both modern and ancient. Now it is interesting that the words "India" and "Hindu" are western (mostly Iranian) impositions. Perhaps Brahmagupta would have found the word "Bharat" less alien. But since the topic of the article is about how a particular Indian idea was spread and developed further west, the name is perfectly appropriate. P.S. I also like John Keay's book.

vectorEQ 8y ago

islamic culture cultivated and gathered lots of knowledge, includign that of roman, indian, some african and other cultures. in my opinion their translation efforts have saved a lot of, and furthered a lot of science and research. As europe was plunged into the dark ages, the islamic culture saw an age of light where knowledge was power and there was a big effort for about 1000 years to cultivate and improve understanding of the world around us. alchemy, algebra, algorithm, a lot of words which came from there. though some of the underlying knowledge was gained from translating texts of other cultures, credit goes to these islamic scientists for recognising the importance of these works and improving upon them.

wahern 8y ago
1000 years is a stretch. Most of it occurred during the Abbasid Caliphate, which promulgated a school of Islamic scholarship and practice that supported and even promoted the development of worldly knowledge. https://en.wikipedia.org/wiki/Abbasid_Caliphate#Islamic_Golden_Age https://en.wikipedia.org/wiki/Abbasid_Caliphate#Islamic_Gold... Importantly, this school of Islam accepted or at least was tolerant of the idea that God controlled the world indirectly through what we now call natural laws. It's in this age that you saw the theological state financially support philosophy, the collection of foreign philosophic works into libraries, and their study and extension. But an anti-intellectualist school very quickly rose to dominate the landscape, both the scholarship and lay practice. https://en.wikipedia.org/wiki/The_Incoherence_of_the_Philosophers https://en.wikipedia.org/wiki/The_Incoherence_of_the_Philoso... Subsequently, the preservation and advancement of philosophy was a mere echo of the earlier, short-lived era and occurred at the periphery of Islamic power rather than at its center as in the Abbasid Caliphate. The same conflicts played out in Christianity, but fortunately orthodox (small-o) Christianity adopted a natural laws perspective. It's worth pointing out that there was never really a Dark Age in Europe. Rather, the political upheaval merely disrupted Europe's collective memory and severed its rich connections to the rest of Eurasia and Africa. Philosophical and scientific advancements proceeded, but without the benefit of well-understood context about the sources of received knowledge, and with a much diminished inflow of novel advancements. FWIW, I hesitate to refer to the rise of the school which rejected natural laws as "anti-intellectualism". The school has its own internally consistent logic, and I understand why it would be appealing. You can see the appeal by recognizing the similarity with similar movements in Christianity. I don't think it's a coincidence that what we would call anti-intellectualism in the Christian world also coincides with, e.g., iconoclasm, another point of divergence between orthodox scholarship in Islam and Christianity. There's an appealing intellectual purity in reducing everything to a singular axiom that effectively says everything is as God wills it to be and that attempts to systematize his will is (like iconography) an intermediation and a rejection of his agency and presence. But that manner of viewing the world is not hospitable to the nurture of scientific rationalism, which is largely how we understand intellectualism today. Note that I'm not trying to make the claim that Christianity is somehow better or more logical than Islam. As non-orthodox Christian denominations (i.e. the ones which, among other things, lean to biblical literalism) are happy to point out, the pro-intellectual characteristics of orthodox Christianity owe more to its inheritance from Greek and other sources largely orthogonal to the foundational doctrines of Christianity. In other words, orthodox Christianity was more hospitable to science despite itself. Islam shared many of the same influences, it just rejected them where orthodox Christianity syncretized them.

matco11 8y ago

Title of the link is inaccurate. The post refers to the Arabic numerals, not the decimal system - and after all the Roman numerals (which was widely commonal) also follow the decimal system. It should be “the path that Arabic numerals [or Hindu-Arabic numerals] took from India to medieval Europe.”

msravi 8y ago

The earliest use of the decimal system in Hindu mathematics is in the Yajurveda Samhita, where there is a list of numerical denominations given: eka(1), dasha(10), shata(100), sahasra(1000), ayuta(10000), nryuta(100000), ... all the way to 10^12. The list, with slight modifications and additions, is repeated in other Vedic texts [1]. The Yajurveda Samhita dates back to between 2000BCE - 1000BCE. The earliest use of zero as a symbol in Hindu mathematics actually occurs between 300BCE - 200BCE in a work called Chandah Sutra by Pingala. It is used in figuring out the number of combinations of long and short syllables in a verse containing n syllables [2]. The earliest written manuscript that uses zero as a symbol predates both Brahmagupta and Aryabhatta, and is found in the Bakhshali manuscript that is dated between 224CE-383CE [3]. Here are some of the problems tackled in the Bakhshali manuscript [4]: a) Problems involving systems of linear equations b) Indeterminate equations of the 2nd degree c) Arithmetica progressions d) Quadratic equations e) Approximate evaluations of square roots f) Problems of the type x(1-a1)(1-a2)...(1-an)=p 1. https://archive.org/stream/in.ernet.dli.2015.81882/2015.81882.History-Of-Hindu-Mathematics-A-Source-Book-Part-iampii#page/n31/mode/2up https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188... 2. https://archive.org/stream/in.ernet.dli.2015.81882/2015.81882.History-Of-Hindu-Mathematics-A-Source-Book-Part-iampii#page/n97/mode/2up https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188... 3. https://en.wikipedia.org/wiki/Bakhshali_manuscript https://en.wikipedia.org/wiki/Bakhshali_manuscript 4. https://archive.org/stream/in.ernet.dli.2015.189295/2015.189295.The-Bakhshali-Manuscript--Vol-1#page/n25/mode/2up https://archive.org/stream/in.ernet.dli.2015.189295/2015.189...