BINARY NUMBERS IN INDIAN ANTIQUITY By B. Van Nooten I. PRELIMINARY Binary numbers have in recent time become indispensable for the workings of the digital computer since they allow the representation of any whole number in terms of two markers: "on" (1) and "off" (0). I have found good reason to believe that the rudiments of binary calculation were discovered in India well in advance of their discovery by the German philosopher Gottfried Leibniz in 1695. Historians of Indian mathematics have for many decades recognized the contributions of the Indian mathematicians from as early as the time that the handbooks for constructing Vedic altars were com- posed (5th century B.C. ?). The better known contributions date from the period of the schools of Ujjain, Kusumapura and Mysore, from the fifth century A.D. until the eleventh. The discovery of the binary number may have escaped attention because its formulation is not contained in any of the strictly mathematical treatises of the Indian tradition.1Instead, I discovered it is an entirely different branch of science, the chandah.,sastra, or "science of verse meters". II. THE SANSKRIT METRICAL TRADITION Pingala The Vedic tradition ascribed a great, almost mystical significance to the meters of the sacrificial chants. Careful studies were made not only of the meters of the chant, but also of its language, prosody, proper place and proper time of recitation. The methodology developed to study and analyze meters became a respected field of study from a very early time onward. In this tradition the earliest comprehensive treatise on Vedic and Sanskrit meters that has been preserved is the Chandah sastra by Piingala. Though most of the work is purely descriptive and is devoted to sorting out and classifying the meters according to their structure, in its eighth chapter occur a few brief statements that purport to establish a more general theory for dealing with the classification of meter. These statements, or sutras treat of the classification of metrical feet in a manner that suggests that Pingala was aware of the binary number. They have not been the subject of any special study in the West since the edition and translation of the Chandah sastra by Albrecht Weber in 1863. They form the subject of this paper and I hope to show that in a devious and unexpected manner Pingala has succeeded in introducing the binary number as a means for classifying metrical patterns. Pingala's Chandah sastra fits into the literary genre of sutras, or series of aphorismic statements that are memorized and serve as ‘aides- memoires’ for a more complete theoretical exposition that is usually supplied by an explanatory commentary. The Chandah sastra itself consists of some 310 brief sutras divided over eight books and it�treats of the structure and nomenclature of meters. The main commentary on the Chandah sutra is Halayudha's 13th century Mrta- samjivini. From an earlier date (8th century ?) we have Kedara's Vrttaratnakara, an independent work based on Pingala, but dealing with non-vedic meters only. The text-critical problems associated with the Chandah~sastra are similar to those of most ancient Indian literary works. We do not know who the author Pingala was, we do not know where he lived, when his work was composed and finally, whether the work going by his name was really all his, or a product of his school, or a conglomerate of text fragments assembled at one time and thenceforth transmitted under his name. Part of the evidence of its date is internal, part external. The text-critical work has been done almost exclusively by Albrecht Weber. The main evidence for Pingala's date is external: his treatise is mentioned by the commentator Sabara on Mimfamsasutra who has been assigned to the 4th century A.D. The treatise as we have it now is probably a composite. However, the passage where the binary system is developed is to all likelihood part of the original work, and not an addition by a later metrist. Source: http://bit.ly/2xJAwfX

Dear Rare Book Society, may I suggest that when you link to a book at Archive.org, you *also* add the bibliographical details of the book in the "Review" section of the Archive.org entry? That way, searching at Archive.org will gradually get more accurate and successful.

Team do you have a copy of the book "Gajasasthra" I would like to have one!

Naveen

Can you help me finding a book named sushruta krishi samhita

Thanx

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