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Multiplying and dividing with Hindu-Arabic numerals and with Roman ones (thonyc.wordpress.com)
103 points by Hooke on Feb 14, 2017 | hide | past | web | favorite | 74 comments

Thank you for this:

"I would point out, as I have already done in my nineteenth-century style over long title, that one should call them Hindu-Arabic numerals, as although we appropriated them from the Islamic Empire, they in turn had appropriated them from the Indians, who created them."

"The Hindu-Arabic number system developed sometime in the early centuries CE and our first written account of it is from the Indian mathematician, Brahmagupta, in his Brāhmasphuṭasiddhānta (“Correctly Established Doctrine of Brahma“) written c. 628 CE. It came into Europe via Al-Khwārizmī’s treatise, On the Calculation with Hindu Numerals from 825 CE, which only survives in the 12th-century Latin translation, Algoritmi de numero Indorum."

You wouldn't believe me if I said so but in Indian schools we were taught it to be "Arabic numerals" with no context of the origin of the modern-day numeral system. I'm not sure if this has changed in the recent years but that is what I was taught anyways. As a child I assumed that the origin of the modern-day numeral system was thanks to the Arabs. It was this whitewashing of anything "Hindu" that really surprises me (especially in a country like India with 70% Hindu populace). It's almost as if Hindus never contributed anything to the field of Science. It was quite later in my life that I was able to read up various articles online and realize that most Mathematical concepts originated from India.

> It's almost as if Hindus never contributed anything to the field of Science

You can thank Thomas Babington Macaulay, the designer of the "Indian education system" for that.

" We must at present do our best to form a class who may be interpreters between us and the millions whom we govern, – a class of persons Indian in blood and colour, but English in tastes, in opinions, in morals and in intellect. To that class we may leave it to refine the vernacular dialects of the country, to enrich those dialects with terms of science borrowed from the Western nomenclature, and to render them by degrees fit vehicles for conveying knowledge to the great mass of the population. "


Wow. Thank you for pointing me to this Wiki. I never knew whitewashing was carried out to this extent by the British. Very sad!

> "my nineteenth-century style over long title"

Heh, much better than a 21st century title like "This numeral system makes multiplying and dividing easier, this may shock you"

“Hindu” is even somewhat misleading, as plenty of early Indian mathematicians were Jain or Buddhist. Likewise “Arabic” is misleading, considering Islamic mathematicians working with such numerals were from a wide variety of ethnic backgrounds, such as Al-Khwarizmi who was Persian.

Anyway, if you’re interested in Indian mathematics, check out this lecture https://www.youtube.com/watch?v=2HmMzhZ8zJg (Sadly I don’t know of any other good online lectures about the subject.)

It is not misleading. Most Mathematical concepts originated from Hindu Mathematicians.

For example, the definition of "Infinity" from the Isha Upanishad (Written in 1st millenium BC. You can find the pronunciation here: https://www.youtube.com/watch?v=0Pn5oo24THM. This was written way before Buddhism or Jainism were founded):

ॐ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते | पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते || ॐ शान्तिः शान्तिः शान्तिः ||

It's literal transliteration:

"Om, That is complete, This is complete, From the completeness comes the completeness If completeness is taken away from completeness, Only completeness remains Om, Peace peace peace"

Jainism or Buddhism were later offshoots of Hinduism (almost centuries after Brahmi numerals were invented). They adopted a lot of Hindu scriptures and practices while rejecting the authority of the Vedas at the same time. Their founders were themselves Hindus. For example: Do you know that Yoga is inadvertently associated with Buddhism even though the origins, scriptures and teachings are from Hinduism?

I would have linked various lectures that talk about Hindu mathematicians but unfortunately they are in Hindi. But there is one video by Dr. Dean Brown on Sanskrit, the Upanishads etc which you can find here: https://www.youtube.com/watch?v=yxzXxQrX2Mc

Another video relevant to this discussion: https://www.youtube.com/watch?v=QxgK0dX872k&list=PL6m6y6YFPj...

With all due respect to the many wonderful Indian mathematicians throughout history, this..

> Most Mathematical concepts originated from Hindu Mathematicians

.. is nonsense. For instance, many core tools of mathematics, measuring systems, astronomy, etc. were developed by Sumerians and Akkadians living in Mesopotamia in 4000–1000 BCE. If you’re curious about it, I recommend this recent book, http://amzn.com/069109182X

Other important advances have been made by Chinese, Greeks, Persians, Arabs, Turks, Italians, English, French, Russians, Germans, Hungarians, Americans, ...

> .. is nonsense. For instance, many core tools of mathematics, measuring systems, astronomy, etc. were developed by Sumerians and Akkadians living in Mesopotamia in 4000–1000 BCE.

It is not "nonsense". Your knowledge of Hindu astronomy is limited. I suggest you to read up on Hindu Astronomy and Measuring systems here: http://www.crystalinks.com/indiastronomy.html

"Ancient India's contributions in the field of astronomy are well known and well documented. The earliest references to astronomy are found in the Rig Veda, which are dated 2000 BC. During next 2500 years, by 500 AD, ancient Indian astronomy has emerged as an important part of Indian studies and its affect is also seen in several treatises of that period. In some instances, astronomical principles were borrowed to explain matters, pertaining to astrology, like casting of a horoscope. Apart from this linkage of astronomy with astrology in ancient India, science of astronomy continued to develop independently, and culminated into original findings, like:

The calculation of occurrences of eclipses Determination of Earth's circumference Theorizing about the theory of gravitation Determining that sun was a star and determination of number of planets under our solar system There are astronomical references of chronological significance in the Vedas. Some Vedic notices mark the beginning of the year and that of the vernal equinox in Orion. This was the case around 4500 BC. Fire altars, with astronomical basis, have been found in the third millennium cities of India.

Yajnavalkya (perhaps 1800 BC) advanced a 95-year cycle to synchronize the motions of the sun and the moon. A text on Vedic astronomy that has been dated to 1350 BC, was written by Lagadha."

Read up on Kalpa and Yuga: https://en.wikipedia.org/wiki/Kalpa_(aeon)#Hinduism and https://en.wikipedia.org/wiki/Yuga

and the "Hindu units of Time": https://en.wikipedia.org/wiki/Hindu_units_of_time

Also read this book on Hindu cosmology and astronomy: https://www.abebooks.com/book-search/title/the-theogony-of-t...

You can find an archive of the entire book for free here: https://archive.org/stream/theogonyofhindoo00bjrn/theogonyof...

Some quotes from the book:

"The antiquity of the Hindoo Astronomy has long been a disputed point among the learned of Europe. Cassini* Bailly,^ Gentil,* and Play/air^ maintain, that there are Hindoo observations extant which must have been made more than 3000 years before Christ, and which evince even then a very high degree of astronomical science."

"Davis, who has also taken up this question, calculates that the celebrated Hindoo astronomer Parasura, judging from the observations made by him, must have lived 1391 years before Christ (Asiatic Researches, vol. ii. p. 288), and consequently had read in the divine book of the heavenly firmament, long before the Chaldees, the Arabs, and the Greeks."

"The religion of the Hindoos, which is called the Brahmin, is the most ancient of the present systems of religion upon the earth, and probably one of the oldest ever known ; in this respect, therefore, it is deserving of a high degree of attention. The doctrine is based upon the books of religion held sacred by the Hindoos, called Vedas, written in the ancient Sanscrit, which bears the same rela- tion to the present dialects of the Sanscrit, the Hindostanee, Bengalee, Tamul, &c, as the Gothic does to the Swedish, and the Latin to the French and Italian, (fhe Hindoos maintain that the Vedas (four books) are contemporary with the creation, and were revealed by Brahma himself) The sacred volume begins with these words : — " (There is only one God, Brahma, omnipotent, eternal, omnipresent, the great soul, of which all other gods are but parts\" Nevertheless the Vedas do not address their hymns to this only God, but to things created by him, as the sun, the moon, the stars, the earth, fire, &c. ; so that this religion, although Monotheistic in its fundamental principle, is tinctured with a kind of Sabceism, which probably constituted the early religion at the time when the ancestors of the Hindoos still dwelt in that country from which they came to India (from 2500 to 3000 years before Christ). The Vedas also contain a Cosmogony, the most ancient that is known."

Also, please don't ignore the fact that most of Hindu knowledge of Mathematics, Astronomy, Science, Philosophy or Religion was transferred by word of mouth for millennia. It was only around 2000-1500 BCE that this knowledge was transferred to scriptures which were written in Devanagari (Sanskrit). Most of these scriptures did not survive, but the knowledge did, because of the stress on rote learning of Mantras (which apart from extolling God and God's virtues also included Scientific/Mathematical concepts). There are many Mantras that have been passed on for generations but the actual scripture is lost.

The problem is that the West had not (and still has not) translated a lot of the Sanskrit scriptures (maybe due to lack of interest) that exist today. The Government of India had setup an ASI (Archaeological Survey of India) to look into translating these scriptures and excavating a lot of ancient cities but due to immense corruption not much progress has happened in this regard. Look up the excavation videos of Submerged City of Dwaraka and why it was abruptly stopped (https://www.youtube.com/watch?v=NVIsjx5X3QM).

I don't think anyone should rely on a site like http://www.crystalinks.com/ for facts. It's filled with pseudoscience, speculations and myths. An alternative source would be nice.

Wikipedia's entry and discussion:


While there is some level of whitewashing going on, there's a lot of hyperbole of what was discovered during the Vedic period.

Not sure why there's even a need to amplify/attenuate the contributions. There are Indian mathematicians today who are making significant contributions. Probably more productive to focus on mathematical developments in general rather than assigning credit to the past. Assigning credit to a culture is problematic. What about the culture enabled the mathematical development?

Perhaps one day we'll move past assigning credit and towards purely developing ideas in the spirit of the Upanishads written in anonymity.

> there's a lot of hyperbole of what was discovered during the Vedic period

Where is the hyperbole? All I see is whitewashing of what was discovered during the Vedic period. If you need to understand what whitewashing means: Abrahamic texts/scriptures are classified as History but Hindu scriptures are classified as "Mythology". If this is not systematic whitewashing explain to me what is.

This is precisely what I call Western whitewashing. You are quoting some random and unscientific paper (Vaimanika Sastra) as part of the Vedic period. That piece of paper (Vaimanika Sastra) was written in 1918 by some unknown (Pandit Subbaraya Shastry) and his paper was put forth by G.R Josyer (another unknown).

How can you compare an unscientific paper written in the close of 20th century with Vedic scriptures (Vedas and the Upanishads) written 2000 years ago?

EDIT: Again, just to confirm we are on the same page: I'm talking about whitewashing of discoveries during the Vedic period. Not papers written in the 20th century by unknowns.

Another quote from the same book ("Science of the Sacred") about Shulba Sutras (https://en.wikipedia.org/wiki/Shulba_Sutras):

"Although Vedic mathematicians are known primarily for their computational genius in arithmetic and algebra, the basis and inspiration for the whole of Indian mathematics is geometry. Evidence of geometrical drawing instruments from as early as 2,500 B.C.E has been found in the Indus Valley. The beginnings of algebra can be traced to the constructional geometry of the Vedic priests, which are preserved in the Shulba Sutras. Exact measurements, orientations, and different geometrical shapes for the altars and arenas used for the religious functions (yajnas), which occupy an important part of the Vedic religious culture, are described in the Shulba Sutras. Many of these calculations employ the geometrical formula known as the Pythagorean Theorem.

This Theorem (c. 540 B.C.E.) equating the square of the hypotenuse of a right angle triangle with the sum of the squares of the other two sides, was utilized in the earliest Shulba Sutras (the Baudhayana) prior to the eighth century B.C.E. Thus, widespread use of this famous mathematical theorem in India, several centuries before its being popularized by Pythagoras, has been documented.

The exact wording of the theorem as presented in the Shulba Sutras is: "The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately". The proof of this fundamentally important theorem is well known from Euclid's time until the present for its excessively tedious and cumbersome nature; yet the Vedas present five different extremely simple proofs for this theorem. One historian, Needham, has stated: "Future research on the history of science and technology in Asia will in fact reveal that the achievements of these peoples contribute far more in all pre-Renaissance periods to the development of world science than has yet been realized.""

> An alternative source would be nice.

Sure. Here is a complete book on Vedāṅga Jyotiṣa (one of the earliest books on Hindu astronomy. It's just 74 pages in total): http://www.worldlibrary.in/articles/Vedanga_Jyotisha


"The Vedāṅga Jyotiṣa, or Jyotiṣavedāṅga (Devanagari वेदाङ्ग ज्योतिष) is one of earliest known Indian texts on astronomy and astrology (Jyotisha). The extant text is dated to the final centuries BCE, but it may be based on a tradition reaching back to about 700-600 BCE. The text is foundational to Jyotisha, one of the six Vedanga disciplines. It was composed by Lagadha.

The Vedanga Jyotisha describes the winter solstice for the period of ca. 1400 BCE. This description has been used to date the Vedanga Jyotisha. According to Michael Witzel, the question is "whether the description as given in the jyotiSa is also the date of the text in which it is transmitted." T. K. S. Sastry[note 1] and R. Kochhar[note 2] suppose that the Vedanga Jyotisha was written in the period that it describes, and therefor propose an early date, between 1370 and 1150 BCE, while David Pingree propose ca. 1180 BCE. The estimation of 1400-1200 BCE has been followed by others, with Subbarayappa adding that the extant form can be possibly from 700-600 BCE."

Ganita, the Sanskrit word for Mathematics, existed since the writing of the Vedas. You can read more about it here: http://veda.wikidot.com/ganita

Even Sulba Sutra (written 8th century BC) explained Pythagorean Theorem before Pythagoras did (6th century BC):

"The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately."

All the Scientific and Astronomical discoveries of Ancient Hindu scientists has been explained beautifully in this book "Science of the Sacred". The Sulba Sutra part is specifically explained in this page of the book:


Define "most".

Edit: I don't mean to take away from your point that Hindu mathematicians contrubuted a significant amount, but I think the word most here is misleading.

"Hindu" refers to people living across the Sindhu (Indus) river. It's a geographic label, not religious one, given by the Persians.

This needs to be emphasised more. In India, the right wing Hindu brigade try very hard to appropriate ancient Indian history as that of the Hindu religion (while also conveniently even denying that it is indeed a religion).

Most modern day Indians do not take the trouble to learn about India (the notion of which was created by the British). If they did they'd realise that speaking about ancient Hindu culture as something that they can associate with is as silly as the British claiming they invented Democracy just because they were part on the roman empire at some point (as also was Greece who actually could make that claim)

> This needs to be emphasised more

This is a well known fact for many in India.

> In India, the right wing Hindu brigade try very hard to appropriate ancient Indian history as that of the Hindu religion (while also conveniently even denying that it is indeed a religion).

This is where you are wrong. There is no "ancient Indian history". "India" was formed in 1947 and if at all there is any history for India it is the past 70 years. We were called Hindustan before 1947. The word Hindustan was not based on the religion that we know today as "Hinduism". The religion was called Sanathan Dharma. The word Hindu however, as was rightly said in the grandparent comment, a name given by the Persian invaders. What the right wingers do propagate is "Hindutvawadi" or that we are all Hindus -> Hindu-Christians, Hindu-Muslims, Hindu-Sikhs, Hindu-Buddhists, Hindu-Jains, Hindu-Sanatanis etc. Hindu being the geographical name of the Country we reside in and Sanathan Dharma/Islam/Christianity/Jainism/Buddhism etc being the actual religion. Does this make sense?

Mahatma Gandhi said the following: "I call myself a Sanatani Hindu, because I believe in the Vedas, the Upanishads, the Puranas, and all that goes by the name of Hindu scripture, and therefore in avataras and rebirth; I believe in the varnashrama dharma in a sense, in my opinion strictly Vedic but not in its presently popular and distorted crude sense; I believe in the protection of cow. I do not disbelieve in murti puja.". Was Mahatma Gandhi a right winger to call himself a "Sanatani Hindu"? Why call himself a "Sanatani Hindu" if Sanatan and Hindu both mean the same? It is very evident that the word Hindu in pre-independence India mean't geographical boundary and the word Hindu post-independence India means religion.

> Most modern day Indians do not take the trouble to learn about India (the notion of which was created by the British). If they did they'd realise that speaking about ancient Hindu culture as something that they can associate with is as silly as the British claiming they invented Democracy just because they were part on the roman empire at some point (as also was Greece who actually could make that claim)

The problem is that no one claims to be "associating" with ancient Hindu culture because the context of the word "Hindu" changed drastically over the past century. What was once a geographical association pre-Independence has now turned into a religious association. It's extremely sad that it has been distorted in this manner all in the name of Secularism.

It's essentially cognate with "Indian" or "Indo-". But "Hindu" has religious connotations in English that "Indo-" does not.

Indo, Hindu, Sindhu all point to geography and not religion.

Hindu only has religious connotations in English because the West chose to recognize the word as a religion. The actual name of the religion is "Sanathan Dharma". I'm sure it was easier to say Hindu than say "Sanathan Dharma".

There is no Wikipedia page for "Sanathan Dharma". The closest I can get is Sanātanī, but it appears this term does not cover significant elements of Hinduism. Wikipedia says that this term was popularized in 1921, but etymonline says "Hinduism" has been present in English since 1786. https://en.wikipedia.org/wiki/San%C4%81tan%C4%AB

Hinduism is ancient, but a living, evolving, and extremely diverse religion. To an outsider, it looks more like a cluster of religions than a unified religion. So it's hard to name appropriately. "Vedic religion" is mostly used for historical traditions more than living ones.

Aryabhatta to Bramhagupta were all pretty much Hindus. Jain or Buddhists might be distinct religions in modern political parlance but were generally considered from the same family of Hinduism.

My feelings about Indian education are re-affirmed in this article: http://www.thehindu.com/features/metroplus/The-Indian-number...

“Akkangalude Charithram deals with everything about numbers; the science and history of digits, ancient culture and tradition which led to the discovery of the number system, and how the political, social and scientific fabric steered India towards the magic world of numbers.

“This book which shows the history, science and uniqueness of the Indian number system can help instill in students a love for Mathematics. The sad part is, many Indians are still unaware that the decimal system originated around their homeland,” said Paulose Jacob.

Then as an Arab you would be truly pissed about how much of the basic sciences were lifted from the Arabic world, without any kind of attribution in modern times.

If there was any contribution by any Arab then it should be attributed. Where did I say otherwise? All I was talking about was contribution by Hindu mathematicians which was not just appropriated (I'm not against this) but their contribution forgotten/neglected (which kinda pisses me off).

In fact, even in another Hackernews post about "Box Breathing" I made a similar comment: https://news.ycombinator.com/item?id=13512908

I'm not against appropriation but, at the same time, I'm also against whitewashing. Does this make sense?

>turn had appropriated them from the Indians, who created them.

What about the connection to numerals in scripts like Brahmi, whose origins are unclear


Who disputes origins of Brahmi numerals? Western indologists? Brahmi numerals and Brahmi script are long considered by Indian scholars as indigenous. The dispute arises only because the Western scholars don't wish to recognise it's indigenous origins. These are imperialistic biases. It's in the same vein as conveniently discarding the word Hindu from Hindu-Arabic numeral system just as part of ongoing whitewash of anything Hindu origin.

The West has not just whitewashed numeral contributions. It has also, atleast during the British colonial rule, spread the false "Aryan invasion theory" to divide north and south India on racial lines.

Maybe its scholars, who have looked into the matter? Not, you know, nationalist bloggers who just want something to claim for their ethnicity.

Many Indian scholars don't accept the Aryan Invasion theory. Are they "nationalist bloggers" just because they don't concur with their Western counterparts? Or maybe, the all-knowing West knows more about Hindu culture than Hindus themselves.

EDIT: Here is a good article written by Dr. Madan Lal Goel (Professor Emeritus of Political Science, University of Florida) on "Myth of Aryan Invasion theory": http://uwf.edu/lgoel/documents/AMythofAryanInvasionsofIndia....

Read the article and come to your own conclusions.

Some quotes for your convenience:

"Hindus collectively have no memory of an Aryan invasion of India that supposedly took place around 1,500 B.C. Hindu epics do not mention any such invasion. Surely, the extensive Hindu literature would describe the Aryan invasions if such had indeed taken place. Swami Vivekananda remarked: “As for the truth of these theories, there is not one word in our scriptures, not one, to prove that the Aryan ever came from anywhere outside of India, and in ancient India was included Afghanistan. There it ends.” (Collected Works, Vol. 3). "

"The recent discovery of the dried-up Saraswati River further negates the Aryan invasion theory. Satellite photography from outer space shows the existence of a dried-up river bed in Northern India. The archeological evidence indicates that the river dried up completely about 1900 B.C., much before 1,500 B.C., the date ascribed to Aryan invasions. Saraswati is mentioned numerous times in the Vedic scriptures of the Aryans, indicating that these people lived in India during very ancient times."

"Recent DNA evidence further negates the Aryan invasion theory. Advances in genetics make it possible to show ancient migrations. It is generally accepted that modern man arose in East Africa about 200,000 years ago. From there, they spread to India about 90,000 years ago taking the southern route to Yemen, Sindh and the Indus region. In India they multiplied and spread to other parts of Asia and Europe. The research is reported in Stephen Oppenheimer, The Real Eve."

There's clear linguistic evidence that Sanskrit (as well as Avestan/Persian, Latin, etc.) is derived from the Indo-European family. This is apparent even today by comparing modern languages such as Hindi and English. This, as you probably know, does not apply to South Indian languages that appear to be linguistically distinct. However, this of course does not say anything about the ethnicity.

In any case, Iranians today identify as Aryans (Iran effectively means the land of Aryans in old Persian, as I understand) and the general western consensus these days seems to deem Indo-Iranians as Aryans especially due to obvious recent historical connotations during which many in the west dissociated from the term.

> There's clear linguistic evidence that Sanskrit (as well as Avestan/Persian, Latin, etc.) is derived from the Indo-European family

Infact the article I linked to suggests otherwise (http://uwf.edu/lgoel/documents/AMythofAryanInvasionsofIndia....):

"An invasion of India from the outside around 1,500 B. C. did not occur. Recent scholarship does not deny that the people in India had relations with other Indo-European people in Asia and Europe. There was a belt stretching from India to the Mediterranean inhabited by a people who spoke related languages, known as the Indo-European languages. Sanskrit is the oldest known language in this family and may appropriately be called as the Mother of Indo-European languages. English is an Indo-European language."

How can Sanskrit be called as the "Mother of Indo-European languages" and still be "derived" from the Indo-European family?

> This is apparent even today by comparing modern languages such as Hindi and English. This, as you probably know, does not apply to South Indian languages that appear to be linguistically distinct.

Again the article I linked to clearly explains this falsehood/whitewashing done by the West:

"Sri Aurobindo (1872-1950), a scholar of Latin and Greek as well as of Sanskrit, debunked this theory of the North-South racial divide in India. He disagreed with the theory that the languages of North and South India are unrelated. Sri Aurobindo’s study of the Tamil led him to discover that the original connection between the Sanskrit and Tamil languages was “far closer and more extensive than is usually supposed.” These languages are “two divergent families derived from one lost primitive tongue.” And, “My first study of Tamil words had brought me to what seemed a clue to the very origins and structure of the ancient Sanskrit tongue.” –See The Secret of the Veda, V 10, the Centenary Edition, p 36, 46. Sri Aurobindo also noted that a large part of the vocabulary of the South Indian languages (Tamil, Kannada, Telugu, Malayalam) is common with Sanskrit."

> How can Sanskrit be called as the "Mother of Indo-European languages" and still be "derived" from the Indo-European family?

Because a language does not pop out of nowhere. A language is simply a relatively standardized register. I'm not asserting that Sanskrit is derived from a Western language (far from it) but that the roots of Sanskrit are shared with roots of various Western languages, which is quite clear.

> Sri Aurobindo also noted that a large part of the vocabulary of the South Indian languages (Tamil, Kannada, Telugu, Malayalam) is common with Sanskrit.

Vocabulary is not very indicative as these can easily be loanwords. As in my other sibling (cousin?) comment consider basic articles and fundamental verbs.


> Vocabulary is not very indicative as these can easily be loanwords. As in my other sibling (cousin?) comment consider basic articles and fundamental verbs.

I understand where you come from. Even if I consider the "linguistic relationship" vs "loanwords" argument as a fact explain to me how Vedic literature got integrated into Sangam literature (I ask this because the context of this discussion is "Aryan Invasion theory")? How is it that the Sangam literature extols Lord Vishnu as "the supreme deity who is the inner controller of the entire universe" if the concepts of Vishnu were Aryan of origin? If there was a clear division between the "Aryan invaders" and the "Dravidian natives" why is it that there is no mention of any such strife in the Vedas/Puranas or even in the Sangam literature (which is considered the oldest literature by the Tamilians)? Also, why does the Sangam literature have Vedic/Puranic stories (stories of Kartikeya, Vishnu, Shiva etc) if the civilizations are so distinct (and supposedly in strife during that period)?

Also, the other big problem with "Aryan Invasion Theory" is that it directly conflicts with a very famous Indian scripture: Ramayana. In the story, which takes place in the Treta Yuga (many hundreds of thousands of years before the supposed "Aryan invasion" took place), the Demon King Ravana of Lanka (modern day Sri Lanka) was killed by Lord Rama (of Ayodhya). Ravana is extolled in the Ramayana as a great worshipper of Lord Shiva and a great Brahmin Vedic scholar who was thorough in all the 4 Vedas. How is this even possible? Aryan Invasion had not taken place during the Ramayana. How is it that Ravana, who was a King of the supposed "Dravidian" Lanka, be a Brahmin Vedic scholar who worshipped Shiva? Why doesn't Ramayana mention that Lanka was a "Dravidian Kingdom" and was invaded by "Aryan Ram"? It's not a small detail that can be missed right?

No. Sanskrit is not derived from Indo-European family. There is absolutely no evidence for that. Nor do South Indian languages appear linguistically distinct. I'm a Kannadiga and many Kannada words are directly derived from Sanskrit. My mother is a Tamilian and a lot of Tamil words are also derived from Sanskrit. This falsehood was spread by the British.

> In any case, Iranians today identify as Aryans (Iran effectively means the land of Aryans in old Persian, as I understand) and the general western consensus these days seems to deem Indo-Iranians as Aryans especially due to obvious recent historical connotations during which many in the west dissociated from the term.

It doesn't matter because India was also called Āryāvarta (Abode of the Aryans) in the Ancient days. This was way before Iran got it's name (possibly in the 3rd century A.D). Iran was called Persia in the olden days.

The word Aryan itself has multiple meanings. The definition of Proto-European Aryan is different from Indo-Aryans of India.

You are confusing loanwords with actual linguistic relationships. I understand Kannada fluently and it's quite plausible that the commonalities with Sanskrit are loanwords compared to more structural or fundamental similarities between Sanskrit and Persian, Latin, etc.

Consider the basic articles (I, you, etc.) or many fundamental verbs, for instance, which at least modern Kannada almost surely does not share.


>Who disputes origins of Brahmi numerals?

I remember reading it in a book with following claims, but i haven't verified any of the sources

1. Brahmi is found throughout the sub-continent and in Ceylon.

2. Brahmi has been traced back to the Phoenician type of writing represented by the inscription in which Mesha, king of Moab (c. 850, BC), records his successful revolt against the kingdom of Israel. It was probably brought into India through Mesopotamia, as a result of the early commerce by sea between Babylon and the ports of Western India. It is the parent of all the modern Indian alphabets.

Rapson, E.J. (2015-04-09). Ancient India Chios Classics. Kindle Edition.

1. I don't see how Ceylon can be the origin. There is no evidence to back this.

2. How can Brahmi numerals have come into India around 850 BC when Sanskrit already existed during that time period. Again, these claims make no sense. Brahmi scripture is considered older than Sanskrit. How can it be introduced after Sanskrit was already popular? The Vedic scriptures (written in Sanskrit) date back to 1500 BC. Why is it so hard to not realise that maybe it was Mesopotamians who accepted the Brahmi numerals and not the other way round?

Indian Laws and constitution is explicit in it's bias against Hindus, very likely under the Church influence on Congress Party and President Sonia Gandhi.

1. 93rd amendment to Indian constitution denies Hindus right to occupation. The term used is "non minority". [1] 2. In India minority in the context of education is defined as anyone who has certificate from a body called NCMEI which by law can not have any Hindu person on its body. 3. Indian government passed a weird law called "Right to Education Law" which actually puts huge burden of regulation on only Hindu schools. All Christian or Muslim run schools despite getting government funding are exempt where as all Hindu schools which are run on 100% private money have to comply. Failure to comply even a minor clause in RTE results in shutting down of the school. Around 10 thousand schools have got notices to shut down. [2] 4. Under RTE government controls the admission criteria of even 100% private schools run by Hindus. A Hindu for example can not start a school for students above 140 IQ. It is not possible for a Hindu to start a school meant for extremely poor kids. Because admission criteria is decided by government. 5. All Hindu schools must give 25% of their seats to government. Government then fills those using a complex lottery system that accounts of people's caste. In case government can not fill the seats those seats must be kept vacant for that batch. 6. Governments can simply exercise eminent domain powers and take over a private school without giving any compensation if the school violates even a minor clause. [4] [5]

All educational institutes in India now have a minority vs non-minority divide. Minority schools have 100% freedom from all government where has majority run schools and colleges have 0% freedom.

Delhi had two major colleges. St. Stephans and Sri Ram. Both were considered so good that their cut-off marks were generally 99%. (You need to get 99% in your 12td Std. exams to get admission). This year the entire system was gamed by a remote school. This school somehow gave 99% marks to most of their kids who then applied and got admitted into Sri Ram. St. Stephans however being a minority school had the freedom to apply any filtering criteria and was not affected at all.


[1] https://realitycheck.wordpress.com/2015/03/22/how-congress-p... [2] https://swarajyamag.com/politics/hindu-run-schools-buckling-... [3] https://swarajyamag.com/politics/more-rte-victims-6-hindu-ru... [4] http://www.hindustantimes.com/delhi/in-a-first-delhi-govt-re... [5] https://realitycheck.wordpress.com/2016/01/07/delhi-schools-...

You now add the results from the right hand column leaving out those were the number on the left is even i.e. rows 2, 4 and 5.

In other words, it's just the shift-and-add algorithm: https://en.wikipedia.org/wiki/Multiplication_algorithm#Shift...

...which can really be done in any number base (and is even "easier" in base 2), so I'm still not convinced.

All we need to carry out the multiplication is the ability to multiply and divide by two! Somewhat simpler than the same operation in the Hindu-Arabic number system!

Maybe it is "simpler" but certainly not faster, because it glosses over the fact that division by 2 of Roman numerals is itself not exactly straightforward.

Roman numerals are a mix of positional and unary-ish "repeated symbol" --- that's what makes them hard to manipulate.

Both doubling and halving on a base ten counting board (e.g. of the style commonly used in Europe up until at least the 16th century; Roman counting boards were presumably recognizably similar, though not much physical evidence remains) are very fast and easy.

To halve any even group of pebbles, just remove half of them. To halve a lone pebble resting on a line (representing some power of ten), just move it downward into the adjacent space. To halve a number in a space (representing 5 times a power of ten), replace it by 2 pebbles on the line below, and one pebble in the space below that. These operations can be done very quickly and fluidly with a bit of practice. Maybe not quite as fast as operating a soroban, but not inordinately much slower either.

Historically nobody performed arithmetic calculations by writing down a bunch of intermediate steps on scratch paper using Roman numerals (for one thing, paper wasn’t available in the time of the Romans and both papyrus and parchment were expensive). Roman numerals are just a way of recording the finished answers to calculations done on an abacus (counting board).

>Historically nobody performed arithmetic calculations by writing down a bunch of intermediate steps on scratch paper

When I was in elementary school we used a slate and chalk. I think this was quite common when paper wasn't abundant.

From what I understand ancient Roman schoolchildren did most of their writing on wax tablets. It’s not clear when writing slates were first used; one of the earliest known examples is apparently 11th century India, though I’m not sure if they used chalk or some other writing material. See https://en.wikipedia.org/wiki/Slate_(writing) https://en.wikipedia.org/wiki/Blackboard

So to correct your statement: this was quite common in the 18th–20th century, well after the introduction of “arithmetic” and Hindu–Arabic numerals, which were popularized in Europe by Leonardo of Pisa’s 1202 book Liber Abaci (mostly material translated from Arabic sources).

Before that (and for a few hundred years after in most parts of Europe), most calculation was done with counting boards.

Here’s a famous 1503 woodcut showing a comparison between arithmetic (“Boethius”) vs. abacus (“Pythagoras”): http://www.maa.org/sites/default/files/images/upload_library...

If you want some up-to-date (and very in-depth) information on ancient Mesopotamian arithmetic, you might be interested in the paper "Floating Calculation in Mesopotamia" [1]. By "floating" the author means what I would call floating-point. If I understand the paper correctly, there were actually two base-60 systems: one for counting (addition and subtraction) and a different one for multiplying and dividing.

[1] http://cdli.ucla.edu/pubs/cdlp/cdlp0005_20160501.pdf

Nothing could have demonstrated the advantage of modern numerals any more than this has. What an awfully cumbersome algorithm shift-and-add is to hand execute.

With things like this (where conversion is trivial), internal use of Roman numerals would be widespread if they were advantageous. They were not, previously. and now the numeral system we use is irrelevant with ubiquitous computers except for readability .

I think the evidence is quite strong that Roman numerals are a poorer numeral system.

I think it's a fair point that the reason dividing MCMLXVI by XXXIX seems daunting is mostly due to lack of familiarity with the notation. Roman numerals jump up in value by factors of 5 then 2, which is 10, so translation to/from base-10 Arabic numerals can be done inline... assuming you ignore the god-awful reverse-order-means-subtraction rule, and the fact that you don't have any letters for fractional numbers or huge numbers.

The post seems to imply you can't do the doubling algorithm with Arabic numerals, but of course that's wrong. It also associates roman numerals with abacus computations, which is probably historically sensible, but to me the columns of the pictured abacus are literally base-10 positional notation and so more akin to Arabic numerals. For the abacus to "really" be like roman numerals, you'd have to remove one bead from each section of the pictured abacus. Representing four (or one, for the top sections) would be done by moving a bead to the next grove in sequence. You'd be able to tell it was a bead from the previous section because every section would be required by law to use a different kind of bead.

It’s not clear how much the “hand abacus” pictured, with its sliding counters in grooves, was used in practice. Most calculations in Roman times were probably done with a free-form counting board with some kind of tokens (for instance “calculi”, i.e. pebbles). We don’t have a lot of surviving evidence though, since a wood/cloth/drawing-on-the-ground counting board with pebbles for counters isn’t exactly the most permanent artifact.

The way such counting boards worked in Europe in the Middle Ages was to put pebbles on horizontal lines representing powers of ten, or in the spaces between the lines representing five times some power of ten. The Roman ones probably weren’t too different.

A proficient abacus user can learn how to do math quickly by exploiting muscle memory and imagining the abacus rather than physically using it.


    perl6 -e 'say Ⅶ * 2'
Nothing hard about this nowadays.

  $  perl6 -e 'say VII * 2'
  ===SORRY!=== Error while compiling -e
  Two terms in a row
  at -e:1
  ------> say VII *⏏ 2
     expecting any of:
         infix stopper
         statement end
         statement modifier
         statement modifier loop
EDIT: One should use https://en.wikipedia.org/wiki/Numerals_in_Unicode#Roman_nume...

Which one requires more computing power and/pr steps (if that is a right question to ask) 72 or VII 2

Decimal numbers along with zero ٠١٢٣٤٥٦٧٨٩ were invented in India. The arabs used them until early days of Islam. Then due to fraud issues with the zero, being just a dot that can easily be overwritten to anything else, the arabs set to invent their own symbols. The new symbol is angles based, zero being a circle has no angles, 1 has a single angle and so on ... The symbols 0123456789 is yet to be adopted by many Arab countries because it was invented post writings of Quran, where it uses the original Hindi symbols.

We (the West) were screwed over by those who brought Arabic numbers into Europe ... They should have reversed their order as they did it ... It makes addition and subtraction easier if you work them right to left as in the original Arabic

How? Isn't that essentially adding and subtracting from the most significant to least significant? Could you demonstrate why it's simpler with an example? 1532 - 879 will be adequate.

Not OP, but I guess it's easier because you work from left to right. At least, I find subtraction/addition easier to do from least to most significant digit, since the results of the less significant digits affect the more significant digits, but not the other way around.

EDIT: To be clear, going from left to right is not inherently 'easier' but it would be more consistent with our direction of writing.

Isn't that what we actually do, though? Everyone is taught to subtract or add least to most. Why would we want to flip anything.

Because then 'least' is on the left, and you work from left to right, in the same way that you read from left to right.

Ah I see. Thought there was more to it consider the "screwed over". Bit dramatic, I thinnk, that fellow.

Yes but it's cause all sorts of angst in the computer architecture world - "little endian" architectures are "pure" in the sense that arabic is with it's embedded numbers, while big-endian systems are this weird mixed artifact of our language with text bytes going from lower to higher addresses and integers going the other way.

Over time we all realised that big-endian systems (IBM, 68k, etc, and our native western languages) were a hack and we've moved to little endian systems (intel, arm, DEC, ...) as sane

Nothing better than a bit of internet drama :)



This comment crosses into religious flamewar, which is not allowed on HN, so please don't post like this.


> the Arabs did everything to kill & destroy civilizations.

We've banned this account for repeatedly violating the rules of this site.

Religious war and race war are not welcome here. Anybody who wants to post or read this kind of thing needs a different web site.

Is this a joke? During the Middle Ages, Europe was a feudal backwater of peasant farmers and small continuously warring kingdoms. Scientific and mathematical knowledge (optics, mechanics, astronomy, medicine, ...) throughout the Muslim world was considerably further developed, and there were well organized and well funded cultural institutions devoted to scientific research (not to mention much wider access to traded luxury goods, more resources devoted to fine arts, greater literary output, much more sophisticated financial/business operations, etc.). If Greek and Roman works hadn’t been preserved in Arabic translation in great libraries in prosperous Islamic cities, many would not survive to today. See e.g. https://en.wikipedia.org/wiki/Islamic_world_contributions_to...

FWIW, Bill Warner's PhD is in math & physics.


Obviously it is that he has no special authority on this subject.


With 20–40 minutes of effort, someone could easily track down a large pile of peer-reviewed scholarly literature examining the contributions of Arab, Persian, Seljuk, etc. mathematicians and scientists of 800–1600 CE, and putting it in historical / scientific context.

But I doubt you really care much, or you would do the same searching for yourself. So it’s not worth the time.

Wikipedia is an aggregator not a source. It's like HN, a useful place to find links to where reputable people have said things.

No, they're probably equally lacking authority. But you cited the PhD as a better authority, when he clearly wasn't, so you sound ridiculous.


No, I don't have an opinion on your weirdly anti-Islam point, but your way of arguing it is disingenuous and unconvincing and it sounds like you have to resort to cherry-picking and touting up obscure sources to support it, so it's probably false.

I just chimed in to criticize the way you argued, in hopes that it would go away. When you said "look here's a guy with a Phd", pretending like his expertise was relevant, and then someone said that his PhD wasn't in a relevant field, you played dumb and wrote "Yes, that's correct. Not sure what your point is.", as though you couldn't perceive that citing someone as an expert when they're not makes you sound obviously uncredible.

"I would like to say "Grow up, dude", but that would be impolite." I'm not sure what would lead you to think it's somehow more polite to talk about saying something like that than actually saying, but, it's definitely not. You don't sound mature for pretending to exercise restraint.

Hindu is the follower of Hinduism , much as muslim is the follower of islam .... but Hindi is a language much as Arabic is one .... It should be Hindi-Arabic numerals :)

Arabic and Hindu also refer to civilizations. The name doesn't come from the languages.

Besides Hindi is relatively new. It did not even exist as a language when the number system was invented.

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