The path that the decimal number system took from India to medieval Europe
thonyc.wordpress.com
thonyc.wordpress.com
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.2015.81882/2015.8188...
2. https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188...
3. https://en.wikipedia.org/wiki/Bakhshali_manuscript
4. https://archive.org/stream/in.ernet.dli.2015.189295/2015.189...
"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."
(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
EDIT: a few enhancements
Source: Sir V.S. Naipaul on East Indians, 1965 http://faroutliers.blogspot.com/2004/10/naipaul-on-east-indi...
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.
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?
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.
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.
The pre-decimalized currency was 16 anna to the rupee and 4 paise to the anna. There was no base-60 denomination.
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.
??? 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.
> 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.
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.
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.
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.
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.
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)
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.
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.
It's an odd combination to have Adunaic and Sindarin in such a name. Maybe it should be Tar-Curunir or Ar-Saruman?
(Much as I like history ... now, not when I was young, there's so much of it!)
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:
https://en.wikipedia.org/wiki/File:Numeration-brahmi_fr.png
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.
https://en.wikipedia.org/wiki/Arabic_numerals https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93A...
> 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
Please don't break the site guidelines like that, when they ask you quite explicitly not to:
When disagreeing, please reply to the argument instead of calling names. "That is idiotic; 1 + 1 is 2, not 3" can be shortened to "1 + 1 is 2, not 3."
https://news.ycombinator.com/newsguidelines.html
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.
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
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.
https://en.m.wikipedia.org/wiki/Persian_Gulf_naming_dispute
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.
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"
https://www.researchgate.net/publication/220437752/figure/fi...
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.
I was googling around now, I didn't realize Trump also used Arabian gulf recently: https://www.google.com/amp/amp.timeinc.net/time/4983604/dona...
It's a hot button topic!
https://cdn.britannica.com/668x448/60/91960-004-42DF23AB.jpg
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
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.
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.
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?
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.