Void, Sunya, Zero, and the Ancient civilizations…………………..


Glyphs used to represent digits of the Hindu-A...

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[An excerpt, a little introduction to the subject]

Harmony or proportion- numbers, place value and zero

“The proportions that govern the dimensions of Greek temples, the intervals between the columns or the relationships between the various parts of the façade, correspond to the same ratios that govern musical intervals”. The same principles of harmony and proportion applied to all the arts, architecture, although there were differences to the way they were applied.  The numerical ratios, however, were the same, because mathematical values are immutable. This pure mathematics could create the magic for any of the art forms, whatever it was, providing it with an almost immortality or transcendentalism.

The Pythagoreans are credited as being the first to study the relationships between the numbers and sounds. Pythagoras, the 6th century Greek mathematician, mystic, philosopher and scientist has mainly been known to the world, till now, and will remain in the days to come even, for his theorems. However, the Pythagoreans discovered certain pitches and proportions to be more pleasing to people than others, and these discoveries were propagated in the middle ages.

Now this introduction of the relationship between numbers and sound perhaps did some wonder for music. As the sound was first associated with number, there could evolve a pattern in the form of music itself. A pattern is always associated with definite design and with the repetition of it. And there was cyclic order to represent the perfect form.

This order, this repetitive order, was wanting in the world of numbers itself, when the world was even more young. By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a place value, or zero, was indicated by a space between sexagesimal numerals. By 300 BC, a punctuation symbol was co-opted as a place-holder in the same Babylonian system. This Babylonian place-holder was not a true zero, because it was not used alone. The ancient Greece seemed to have been unsure about the status of zero as a number.

The concept of zero as a number, and not merely a symbol for separation was attributed to India. The Indian scholar Pingala (circa 5th– 2nd century BC) used binary numbers in the form of short and long syllables. He and his contemporary Indian scholars used the Sanskrit word Sunya to refer to zero or void. By 130 AD, Ptolemy, the Roman citizen of Egypt who wrote in Greek, was using a symbol for zero within that sexagesimal numeral system. In 498 AD, Indian mathematician and astronomer Aryabhatta initiated the origin of the modern decimal-based place value notation.

The Hindu-Arabic numerals and the positional number system were introduced around 500 AD; and in 825 Ad, it was introduced by a Persian scientist, Al-Khwarizmi, in his book on arithmetic, that synthesized Greek and Hindu knowledge and also contained his own fundamental contribution to mathematics and science including an explanation of the use of zero. It was only centuries later, in the 12th century precisely, that the Arabic numeral system was introduced to the Western world through Latin translation of his Arithmetic.

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