Language Pulsations: Hindu-Arabic numerals Part II

The figure on the left is counting with Boethian apices; the one on the right uses an additive abacus reckoning system

It was in India that all the crucial numerical ingredients came together to form our numbering system. From here, the decimal place-value system disseminated throughout the Eurasian continent before going on to conquer the world.

Brahmi numerals, 100 AD

The Hindu-Arabic numbers have their origin in India, based on the first nine numerals of Brahmi script, an ancient Indian writing which was probably derived from the Phoenician alphabet. The only numbers in Brahmi writing to have distinct signs were 1-9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and 1000.  All other numerical signs were derived from these.

By 458 AD, there was evidence of Hindu numbers being written from left to right in descending powers of 10. Indian reckoners could have used counting boards with columns pre-inscribed with the number signs to calculate more easily. Each column indicated a different place-value (ones, tens, hundreds, etc.), with the “ones” column in the right of the board and then moving up the powers of ten leftward. This method of writing numbers caught, leaving the numbers going “from left to right” instead of the opposite direction.

Towards the mid-7th century BC people far away from India already knew about the Hindu numeral system. An interesting case is that of Abraham ben Meir ibn Ezra (Rabbi Ben Ezra), a Spanish scholar from Toledo. He borrowed the Indian place-value system, but instead of using the traditional number signs, he represented each with the first nine letters of the Hebrew alphabet (keeping the Indian sign for zero):

The Chinese, having been familiar with the base, only needed to borrow zero (0) from the Indians. Other cultures across Asia (Khmer, Malay, Cham, and Javanese) also took the Indian numbers and adapted them to their own scripts.

Hindu numerals adapted to various Asian scripts

Al-Khowarizimi, founder of algebra. The word “algorism” derives from the Latinized version of his name

Arabs became acquainted with Indian scholarship through trade with and incursion into India. By around 770 the Hindu numerals made their way to the Caliph’s court in Baghdad when an Indian messenger transmitted the works of mathematician and astronomer Brahmagupta. Mohammed ibn-Musa al-Khowarizimi, a Persian scholar and eminent mathematician of his day, found great value in these numbers. Al-Khowarizimi in 825 wrote a book titled On the Calculation with Hindu Numerals. He utilized the numbers in treatises on mathematics and algebra, such as his book Hisab aljabr w’almuqabala, “The Book of Restoration and Equalization,” which was translated into Latin as Algebra et Almucabala.

First row, modern Hindu-Arabic numerals; second, gobar numerals; third, the Eastern Arabic version of the Hindu numerals

The Eastern Arabs were responsible for gradually altering the Hindu numerals to make them look more like Arabic script. Meanwhile, Arabs in Northern Africa possibly learned of the Eastern Arabic numerals around the 9th century and adapted them into a form we would recognize today. Our numbers are direct descendents of these “gobar numerals”:

The Western Arabs referred to their numbers as gobar numerals, an Arabic word meaning ‘dust’ because many of the Arabs wrote their works on sandy dusty slants. It is these dust numerals that are formally and historically considered the direct ancestors of the numerals we use today. (Source)

Excerpt from the Codex Vigilianus (c. 976), the oldest existing European manuscript containing Hindu-Arabic numbers.
Then, European scholars began to translate Arabic texts, including al-Khowarizimi’s treatises. As these works filtered into Europe via Spain, the Hindu-Arabic numerals and their decimal positional numbering system were introduced to the West. These numbers became increasingly popular in Europe through the reckoning practice that involved them being written in apices (“Boethian apices”; see the very first image on this post). Finally, counting boards fell into disuse and Europeans began to calculate on paper, which allowed for further changes in the appearance of written number signs, including zero.
Different symbols used in Europe to represent Hindu-Arabic numbers

The author of this 1459 manuscript presents the Hindu-Arabic numbers alongside Hebrew alphabet and astrology, implying that they are equally arcane.
For centuries, Europeans considered the Hindu-Arabic numbers more esoteric than practical, but intellectual and technological development soon caught up. Fibonnaci studied in Algeria and returned to the Republic of Pisa as a passionate promoter of the Indian numeral system in the 13th century. The printing press accelerated the standardization and acceptance of the numerals, and by the mid-16th century, they were in common use in most of Europe. After fighting through a melee of competing scripts, technologies, and languages, the numerals emerged to take over the world.
I hope you can see that our numbering system is both extremely old and incredibly young — its conceptual roots lie 5000 years in the past, but it only became widely adopted 500 years ago.

Sources

My Linguistics partner-in-crime Andres Garcia was responsible for the majority of the research in this part.

History of Numbers, Gulf Coast Community College

Very cool collection of graphics relating to the development of Hindu-Arabic numerals, Wikimedia Commons

Arabic numerals, Wikipedia

Brahmi numerals, Wikipedia

David Eugene Smith, Louis Charles Karpinski. The Hindu-Arabic Numerals.

Georges Ifrah, From One to Zero: A Universal History of Numbers.

Karl Menninger, Number Words and Number Symbols.

Peter Rudman, How Mathematics Happened: The First 50,000 years.

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