Algorithm

* The word "Algorithm":


Al-Khwarizmi, an eminent 9th century Arab scholar, played important roles in importing knowledge on arithematic and algebra from India to the Arabs. In his work, De numero indorum (Concerning the Hindu Art of Reckoning), it was based presumably on an Arabic translation of Brahmagupta where he gave a full account of the Hindu numerals which was the first to expound the system with its digits 0,1,2,3,...,9 and decimal place value which was a fairly recent arrival from India. Because of this book with the Latin translations made a false inquiry that our system of numeration is arabic in origin. The new notation came to be known as that of al-Khwarizmi, or more carelessly, algorismi; ultimately the scheme of numeration making use of the Hindu numerals came to be called simply algorism or algorithm, a word that, originally derived from the name al-Khwarizmi, now means, more generally, any peculiar rule of procedure or operation. The Hindu numerals like much new mathematics were not welcomed by all. Click here for details.

* Representing Large numbers:


Mathematicians in India invented the base ten system in ancient times. But research did not stop there. The practice of representing large numbers also evolved in ancient India. The base ten system of calculation that uses nine numerals and the zero stood as an efficient way to represent numbers ranging from a very small decimal to an inconceivably large number. The biggest number known to Greeks was the myriad (10,000) whereas the Chinese, until recent times, had 10,000 as the largest unit of enumeration and the ancient Arabs knew only until 1,000. The notion of representing large numbers as powers of 10, one that was invented in India, turned out to be extremely handy. The Yajur Veda Samhitaa, one of the Vedic texts written at least 1,000 years before Euclid lists names for each of the units of ten upto the twelfth power [See 1]. Later other Indian texts (from Buddhist and Jaina authors) extended this list as high as the 53rd power, far exceeding their Greek contmporaries, mainly because of the latter's handicap of not being able to accept the fundamental Mathematical notion of abstract numerals. The place value system is built into the Sanskrit language and so whereas in English we only use thousand, million, billion etc, in Sanskrit there are specific nomenclature for the powers of 10, most used in modern times are dasa (10), sata (100), sahasra (1,000=1K), ayuta (10K), laksha (100K), niyuta (106=1M), koti (10M), vyarbuda (100M), paraardha (1012) etc. Results of such a practice were two-folds. Firstly, the removal of special imporatance of numbers. Instead of naming numbers in grops of three, four or eight orders of units one could use the necessary name for the power of 10. Secondly, the notion of the term "of the order of". To express the order of a particular number, one simply needs to use the nearest two powers of 10 to express its enormity.

Evidences of using very large numbers have been found in the Vedas which are ancient Hindu scriptures. Vedas are the most ancient written texts written in any Indo-European language. They were written in Sanskrit from around 500BC, although traces go back to 2000BC [See 4]. In the Taittiriya Upanishad, which is a part of the third Veda, Yajur Veda, there is a section (anuvaka), that extols the "Beatific Calculus" or a quasi-mathematical relationship between bliss of a young man, who has everything in the world to the bliss of the Brahman, or "realization". Translated roughly as follows, summarized from one done by Max Muller, firstly it says that fear is all-pervasive. It continues by assuming that a young, good man who is fit, healthy and strong, and has all the wealth in the world, is one unit of human bliss. The anuvaka provides a precise calculation of a series of multiplications by 100 to give number 10010 units of human bliss that can be had when one attains Brahman. The previous anuvaka exhorts the aspirants to be fearless and strong, as only such a person may realize the absolute within.

* "... true birthplace of our numerals": Georges Ifrah:


Famed French scholar Georges Ifrah spent years travelling and studying the mystery of the evolution of numbers. While it is hard to prove that India is truly the birthplace of our modern numerals, in my brief survey of the topic, it seems that there is no better authority in the field other than Ifrah. I would refer the interested reader to his authoritative book [See 4] to get a crisp, yet convincing account supporting his claims. Ifrah provides a total of 45 pieces of evidences, supported by numerous research work from contemporary scholars. Of the 45, 17 are from scholarly work from Europe that includes work of scholars like Laplace, Fibonacci, and Adelard of Bath, and 28 are from work from Arabic sources that includes work of scholars like al Biruni. He refers to 24 evidences from scriptures from India, whose dates range from 1150 BC until 458 BC, when the Jaina text Lokavibhaaga dates back to. Of particular interest was the work by Bhaskaracharya (1150 BC) where he makes a reference to zero and the Indian place-value system as being creations of Brahma, indicating that by that time they were considered "to have always been used by humans, and thus to have constituted a "revelation" of the divinities", [See 4]. Ifrah goes on to explain, with furious objectivity aided by a plethora of evidences that are not isolated pieces of information, but "a huge collection of proofs from all disciplines, dating from the most significant eras", to establish his claim. He also shows how the numerals evolved to look as they look today. His suggested pathway to the modern numerals is:

* Brahmi (often called the "mother" of all Indian writing) numerals

* Shaka, Kushana inscriptions

* Gupta style

* Nagari style

* Arabic from the "Gubar" style

* European late middle ages (cursive forms of the Algorisms)

* modern.

Ifrah salutes the Indian researchers saying that the "...real inventors of this fundamental discovery, which is no less important than such feats as the mastery of fire, the development of agriculture, or the invention of the wheel, writing or the steam engine, were the mathematicians and astronomers of the Indian civilisation: scholars who, unlike the Greeks, were concerned with practical applications and who were motivated by a kind of passion for both numbers and numerical calculations."

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