
The path that the decimal number system took from India to medieval Europe - cossatot
https://thonyc.wordpress.com/2018/05/03/as-easy-as-123/
======
dang
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.

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msravi
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.2015.81882/2015.8188...](https://archive.org/stream/in.ernet.dli.2015.81882/2015.81882.History-
Of-Hindu-Mathematics-A-Source-Book-Part-iampii#page/n31/mode/2up)

2\.
[https://archive.org/stream/in.ernet.dli.2015.81882/2015.8188...](https://archive.org/stream/in.ernet.dli.2015.81882/2015.81882.History-
Of-Hindu-Mathematics-A-Source-Book-Part-iampii#page/n97/mode/2up)

3\.
[https://en.wikipedia.org/wiki/Bakhshali_manuscript](https://en.wikipedia.org/wiki/Bakhshali_manuscript)

4\.
[https://archive.org/stream/in.ernet.dli.2015.189295/2015.189...](https://archive.org/stream/in.ernet.dli.2015.189295/2015.189295.The-
Bakhshali-Manuscript--Vol-1#page/n25/mode/2up)

------
nyc111
The book mentioned in the comments is very interesting
[https://www.amazon.com/Money-Changes-Everything-
Civilization...](https://www.amazon.com/Money-Changes-Everything-Civilization-
Possible/dp/0691178372)

"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."

------
forapurpose
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

~~~
adrianratnapala
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.

~~~
forapurpose
> 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?

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gumby
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.

~~~
Arnavion
>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.

~~~
gumby
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.

~~~
eadmund
> 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.

~~~
gumby
A crown was five shillings and was about the largest coin I was going to get
my hands on :-)

------
amriksohata
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.

~~~
baxtr
Even caring about this kind of stuff feels like people have an inferiority
complex

~~~
yumraj
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?

~~~
Sangermaine
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.

------
vectorEQ
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
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...](https://en.wikipedia.org/wiki/Abbasid_Caliphate#Islamic_Golden_Age)

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...](https://en.wikipedia.org/wiki/The_Incoherence_of_the_Philosophers)
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.

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matco11
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.”

