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.
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]:
"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."
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:
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.
> Brahmagupta was a worshipper of Shiva who lived in Rajasthan. He fits in perfectly well with Indianness both modern and ancient.
What does it matter who they worshiped, unless we want to buy into Hindu nationalism? What about all the vast number of other religions in modern India? What about the secular foundation of modern India?
> 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
Sure. However, the India that is being referred to in the post is the period of Hindu renaissance during which a vast body of philosophical, secular, and scientific literature (including the developments referred to in the article) was produced. That cultural context is carried forward to a large extent in what is India today. Neither of the other countries mentioned carry this context today.
Referring to Indian history and Indian civilization as S.Asian history/civilization is like referring to the Egyptian civilization as the North-east African Civilization, because the Kingdom of Kush also extended into Sudan.
> 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.
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.
Thanks, I was born after the conversion and should have checked. Sadly I can't edit my comment.
I remember being told it was base 60, which fit comfortably with the pounds/shilling system I did have as a kid -- but had I been a 7-year-old programmer like all the kids are these days I probably would have been super excited by 64.
> I remember being told it was base 60, which fit comfortably with the pounds/shilling system I did have as a kid
??? Pounds-shillings-pence weren't base 60: there were 20 shillings in a pound & 12 pennies in a shilling. That did happen to work out to 240 pence to the pound, which happens to be 4 × 60, but it wasn't a base-60 system.
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.
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.
Unfortunately this comment doesn't contain enough substance to prevent a landslide of nationalistic bickering. All: don't do that on this site, please.
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.
Naming is more political than one would imagine. It has only a little to do with actual history.
As a fun example: I grew up calling a water body near my home country as Khaleej Al Arabi. The "Arabian gulf".
It's only when I came to the US that I realised people around the world, thanks to an effective campaign by the Persians, call that same waterbody the Persian Gulf.
Edit: actually, turns out it was the Arab nationalism that preferred to adopt "Arabian gulf" in the 1960s. Turns out I was sold Arab propaganda even after being told about the globally recognized name, that it was a Persian campaign.
It's been more than 10 years now, but I recall a friend of mine (Arab but living in America for a while) showing me websites and Google bombs that propped up content to change the perception that the name was not Arabian gulf but Persian Gulf. It was linked to Persian technologists who wanted to change this perception.
A funny example of this was that in America, if you googled "Arabian gulf", the top result was a fake old school Internet Explorer 404 page with the title "Error: Gulf not found. You may be looking for Persian Gulf"
Propaganda might be a strong word. It was more that some Arabs I knew in the west believed that Persians were trying to change the name, and not that the Arabs were the ones who actually changed it in the 60s.
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.
> 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.
>There's no documented proof that Indian system was descended from another system. The Fountainhead was India. Hence, purely of Indian creation.
You misunderstand my comment. Read it again:
>What we use today is the modified system, it's not purely of Indian creation.
The current numeral system used is not purely of Indian creation. This chart shows the progression of the ancient Indian numeral system to the one in use today:
The ancient Indian system was adopted by Arabic scholars who in turn modified it into an early version of the form used today, although you can see that even after the general forms of the numerals were "settled" they've continued to evolve to become the ones familiar to us now.
So no, not purely of Indian creation, anymore than the modern English alphabet, as noted above, is purely a Phoenician creation. Like most concepts, it's been adopted and modified across the ages.
> There's no documented proof that Indian system was descended from another system. [...] Hence, purely of Indian creation.
If the Babylonians developed a place value number system with a zero in it before the Indians did, then it's more likely the Indians copied it from the Babylonians and changed it to base 10, than it is that the systems were developed independently, because the two civilizations were in close contact with each other. Number systems are exactly the sort of thing that ancient traders would share with each other -- it only needs to happen once during the many hundreds or thousands of such contacts.
The onus of proof is hence on you to prove any such single contact didn't happen before claiming "Hence, purely of Indian origin". It's better to write, as the article did:
> whether the Indians got the idea of a place value system from the Babylonians [...] is simply not known
What's interesting is that there is some evidence that the Brahmi script itself is descended from some variant of Aramaic. The jury is still out among experts whether or not this is the case.
The moral of this is that human history is not as easily partitioned as people would like.
(Before I get accused of being anti-India, I'd like to make it clear that I'm Indian)
You maybe an Indian, but you are no Historian. As such the same logic can be applied to the term "West" or "Western Civilization". While no single civilization, or people create anything original, there are definitely histories of a people, and therefore the accusation of borrowing, using, or obtaining some outside source of inspiration doesn't preclude that people from their own history.
While you are Indian, I often feel that many Indians also tend to lack also unfortunately basic understanding of Indian history, perhaps it's the incessant cultural demand to pursue other subject, so far as to even claim that there's no such thing as "Indian" history, but rather merely the history of different people in a region arbitrarily created by the British.
I'm not accusing you of that, but simply pointing that being Indian doesn't shield you from the accusation of either being "anti-India" or lack of knowledge.
Again, I'm not refuting your claim, merely saying that doesn't preclude, or deny the claim you're responding to. History, while complex, and civilizations more points on a spectrum, than a closed system, doesn't prevent or deny the claim of a civilization claiming a unique, distinct, and separate identity that is used to claim the products of a society.
Nothing is original. If that's you're claim then it's not a valid argument, and doesn't really address the situation other introduce some existentially reductive platitudes.
That's bullshit (sorry), Al Khwarizmi wrote a book with the words Al-Jabr in its title and we translate those words to mean calculation.
> The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala)
What the words meant originally is not entirely clear. Something like to set, adjust, reckon, I reckon.
PS: And as was pointed out, the Author is said to be from Persia
In this case, your comment would be excellent if you'd simply delete that bit. Saying sorry doesn't make it better, because the other person typically doesn't hear that part.
Yes , you are right. The interjection wasn't exactly aimed at the minor mix-up, but the whole comment. The mix-up just made me enthusiastic enough to display my overbearing sense of superior knowledge with glee. That's the same problem the GP had, so it evens out?!
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).
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.
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?
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
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?
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.
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
There is no inferiorty complex, when you get a factual book out of the library you want to read it hoping you know the truth, not what something wanted you to think.
Presumably, if you get a book out of the library about numeric systems, it would have a detailed section on the origin of our current system. And keep in mind that all of history is what someone "wanted you to think" to some degree.
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.
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.
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_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_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.
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.”
