Tuesday, September 29, 2009

Fjordman: A Brief History of Zero and Indian Numerals

Fjordman will begin a small series of essays next week with a focus on mathematics and mathematical astronomy. Below are some excerpts from his brief introductory post at the Brussels Journal:

I heard the claim from one European reader that “The Arab world invented the zero, and it’s been downhill ever since.” This is false, but unfortunately not an uncommon mistake. Our numeral system dates back to India during the post-Roman era, but it came to Europe via the medieval Middle East which is why these numbers are called “Arabic” numbers in many European languages. Yet even Muslims admit that they imported these numerals from India. Calling them “Arabic” numerals is this therefore deeply misleading. “Hindu-Arabic” number system could be accepted, but the preferred term should be “Indian numerals.”

The question nevertheless remains why Indians dropped their own multiplicative system and introduced the place-value system, including a symbol for zero. We currently don’t know for sure. Victor J. Katz elaborates in his fine A History of Mathematic, Second Edition:

“It has been suggested, however, that the true origins of the system in India may be found in the Chinese counting board. Counting boards were portable. Certainly, Chinese traders who visited India brought them along. In fact, since southeast Asia is the border between Hindu culture and Chinese influence, it may well have been the area in which the interchange took place. Perhaps what happened was that the Indians were impressed with the idea of using only nine symbols, but they took for their symbols the ones they had already been using. They then improved the Chinese system of counting rods by using exactly the same symbols for each place value rather than alternating two types of symbols in the various places. And because they needed to be able to write numbers in some form, rather than just have them on the counting board, they were forced to use a symbol, the dot and later the circle, to represent the blank column of the counting board. If this theory is correct, it is somewhat ironic that Indian scientists then returned the favor and brought this new system back to China early in the eighth century.”
- - - - - - - - -
Some Sanskrit works were introduced to Europe via Arabic translations. One Latin manuscript begins with the words “Dixit Algorismi,” or “al-Khwarizmi says.” The word “algorismi,” through some misunderstandings became a term referring to various arithmetic operations and the source of the word algorithm. “Zero” derives from sifr, Latinized into “zephirum.” The word sifr itself was an Arabic translation of Sanskrit sunya, meaning “empty.” The English word “sine” comes from a series of mistranslations of the Sanskrit jya-ardha (chord-half). Aryabhata frequently abbreviated this term to jya or jiva. When some Hindu works were translated into Arabic, this word was transcribed phonetically into jiba. But since Arabic is a consonantal alphabet usually written without added short vowels, later writers interpreted the consonants jb as jaib, which means bosom or breast. When an Arabic work of trigonometry was translated into Latin, the translator used the equivalent Latin word sinus, which also meant bosom. This Latin word has become our modern English “sine.”

Leonardo of Pisa (ca. 1170-1240), often known as Fibonacci (son of Bonaccio), was an Italian and the first great Western mathematician after the decline of ancient Greek science. The son of a merchant from the city of Pisa with contacts in North Africa, Leonardo himself travelled much in the region. He is most famous for his masterpiece the Liber abbaci or Book of Calculation. The word abbaci (from abacus) does not refer to a computing device but to calculation in general. The first edition appeared in 1202, and a revised one was published in 1228. This work enjoyed a wide European readership and contained rules for computing with the new Indian numerals. The examples were often inspired by examples from Arabic-language treatises, but filtered through Leonardo’s creative and original genius. Indian numerals faced powerful opposition for generations but were gradually adopted during the Renaissance period, especially by Italian merchants. Their practical advantages compared to the more cumbersome Roman numerals were simply too great to ignore, although Roman numerals are still used for certain limited purposes in the West in the twenty-first century.

Read the rest at the Brussels Journal.


Graham Dawson (Archonix) said...

The fact that they didn't even invent "nothing" stands in stark contrast to the current attempt to claim that arab muslims invented just about everything.

Islam truly is a religion of peace - but the peace of never-changing, never advancing, static, uncreative, unaltered null-life. The peace of dead air and airless wasteland.

Robin Shadowes said...

In fact they actually invented at least one thing, namely islam. We have to give them credit for that. But that is about all they have ever invented. But I guess that makes them more than proud since they do everything in their power to export it.

Oh sorry, I forgot. They also inevented the IPod, the hydron collider, pencillin, electricity, gravity, cars, aeroplanes, oxygene and common sense. And a gazillion more things but mentioning that would make this a very looong posting.

Czechmade said...

jyárdha means simply "the sine of an arc" and there is no need to abbreviate this word, since jyá means simply a bow string in Vedas
(probably connected with Greek bios, the homonym we know as bios=life, a matter of Greek philosophical puns) and later simply the chord of an arc
or exactly the same as jyárdha.

Now jiva (pronounce jeeva) is extremely interesting in this context, since it evokes the same thing as in the presocratic Greek: living, existing, alive (Vedas) causing to live, vivifying m. the principle of life, vital breath, the living or PERSONAL SOUL!!!

Any idea? I just supply raw material...

Czechmade said...

A جیب jaib (in P. pronounced jeb or jīb), The opening at the neck and bosom (of a shirt, &c.); the breast-collar; the heart, bosom; a pocket;--jībi ufq, The sky;--jībi bag̠ẖal, Waistcoat-pocket (m.c.);--jībi ḵẖāṣ, A privy purse.

OK, but b-v is interchangeable in Indian languages without any interference from Arabic

Czechmade said...

And now check the same in purely Persian context:


جان jān (Z. yāna), Soul, vital spirit, mind; self; life; spirit, courage; wind; the mouth; arms; the father of demons; name of a race said to have inhabited the world before Adam; in modern conversation a word of endearment, as ai āqā jān, my dearest master, ʻamma jān, auntie dear;--jānī ādam, (met.) Something rare and wonderful;--jān az kūn dar raftan, (met.) To die;--jān ba dastārcha dādan, To tender one's life; to advance money;--jān bar damīdan, To restore to life;--jān burdan (bīrūn, burdan), To save one's life;--jān bar shukrāna dādan, To advance money;--jān ba-sar (bar sar) būdan, jān ba-lab āma- dan (rasīdan), To be at death's door, to die;--jāni pidar, Soul of (thy) father! my dear son!--jāni pariyān, Wine;--jān taslīm kardan, To give up the ghost, to die;--jāni tū (shumā) u jāni man, Your life and mine, said in entrusting something or somebody very dear to the careful keeping of another; also to express "my safety is bound up in yours";--jāni tū u jāni o, His life is as dear to him as thine to thee; (it implies also) unanimity;--jāni jamāsh, Wine;--jāni jahān, Life of the world;--jāni ḥaiwān, Milk; butter-milk; butter; flesh; honey;--jāni ḵẖẉud faroḵẖtan, To sell one's life, i.e. expose oneself to danger;--jān dādan, To resign one's life; to kill oneself; to spare another's life;--jān dāshtan, To wish, desire, aspire after, endeavour with eagerness;--jān dar āstīn dāshtan, To risk one's life;--jān dar bīnī rasīdan, To be in the utmost straits and bewilderment;--jān dar pay kase afshāndan (baḵẖtan, reḵẖtan, kashīdan), To sacrifice life for another's sake;--jān dar tani kase kardan, To impart life;--jān dar jāni kase kardan, To ransom another's life with one's own;--jān dar sari dil kanī, You ruin your- self in following your heart's desires;--jān dar miyān, Though one's life be at stake;--jān zadan, To breathe out the soul, to expire;--jāni zamīn, Herbage, flowers and fruits;--jān sipurdan, To resign one's breath;--jān shudan (raftan), Life departs;--jāni ʻālam, Life of the world, i.e. Muhammad;--jān kandan, To be in the agonies of death; to die;--jān giriftan, To take away life, to deprive of life;--ba-jān rasīdan, To come to extremities, to be driven to despair;--bar jān qadam nihādan, To renounce all remedy and offer oneself to death.

Czechmade said...

And do not feel tired about these numerous nuances, it is about our soul(s)...and mathematics.