Concept of zero in various ancient civilisations?

Answer 1

0 (zero; BrE: /ˈzɪərəʊ/, zirr-oh or AmE: /ˈziːroʊ/, zeer-oh) is both a number[1] and the numerical digit used to represent that number in numerals. It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems. In the English language, 0 may be called zero, nought or (US) naught ( /ˈnɔːt/), nil, or - in contexts where at least one adjacent digit distinguishes it from the letter "O" - oh or o ( /ˈoʊ/). Informal or slang terms for zero include zilch and zip.[2] Ought or aught ( /ˈɔːt/) have also been used historically.[3]

Mesopotamia

By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by aspace between sexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish(dating from about 700 BC), the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges.[8]

The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60), looked the same because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them.

India

The concept of zero as a number and not merely a symbol for separation is attributed to India, where, by the 9th century AD, practical calculations were carried out using zero, which was treated like any other number, even in case of division.[9][10] The Indian scholar Pingala (circa 5th-2nd century BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse Code.[11][12] He and his contemporary Indian scholars used the Sanskrit word śūnya to refer to zero or void. The use of a blank on a counting board to represent 0 dated back in India to 4th century BC.[13] In 498 AD, Indian mathematician and astronomer Aryabhata stated that "sthānāt sthānaṁ daśaguņaṁsyāt"[14] (literally, "place to place in ten times in value"),[citation needed] i.e. "from place to place each is ten times the preceding"[14] which is the origin of the modern decimal-based place value notation.[citation needed]

The oldest known text to use a decimal place-value system, including a zero, is the Jain text from India entitled the Lokavibhâga, dated 458 AD, where shunya ("void" or "empty") was employed for this purpose.[15] The first known use of special glyphs for the decimal digits that includes the indubitable appearance of a symbol for the digit zero, a small circle, appears on a stone inscription found at the Chaturbhuja Temple[disambiguation needed] at Gwalior in India, dated 876 AD.[16][17] There are many documents on copper plates, with the same small o in them, dated back as far as the sixth century AD, but their authenticity may be doubted.[8]

China

Since the 4th century BC, counting rods were used in China for decimal calculations including the use of blank spaces.[vague]

The Nine Chapters on the Mathematical Art of 213 B.C.[18] instructed "[when subtracting] subtract same-signed numbers,[vague] add differently signed numbers, subtract a positive number from zero to make a negative number, and subtract a negative number from zero to make a positive number."[19] The word wúrù (無入) (rendered here as zero, its standard translation by mathematical historians) literally means "no entry" or "null enters".[vague]

Along with negative numbers, Chinese mathematicians understood zero[when?], and some of them indicated it with wúrù(無入 "no entry"), kōng (空 "empty") and the frame-like symbol[vague] 口/囗,[vague] Gautama Siddha introduced the symbol 0[vague] in the 8th century.[20][21]

Ch'in Chu-shao's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol for zero,[22] and Chinese authors were familiar with the idea of negative numbers well before the fifteenth century[when?] when they became well established in Europe.[22]

The Arab world

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-Khwārizmī,[23] in his book on arithmetic. This book 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, that the Arabic numeral system was introduced to the Western world through Latin translations of his treatise Arithmetic.

Greeks and Romans

Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "How can nothing be something?", leading to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero.

Example of the early Greek symbol for zero (lower right corner) from a 2nd century papyrus

By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not just as a placeholder, this Hellenistic zero was perhaps the first documented use of a number zero in the Old World. However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.)-they were not used for the integral part of a number. In later Byzantine manuscripts of Ptolemy's Syntaxis Mathematica (also known as the Almagest), the Hellenistic zero had morphed into the Greek letter omicron (otherwise meaning 70).

Another zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nullameaning "nothing", not as a symbol. When division produced zero as a remainder, nihil, also meaning "nothing", was used. These medieval zeros were used by all future medieval computists (calculators of Easter). The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725.

The Americas

The back of Olmec stela C from Tres Zapotes, the second oldest Long Count date discovered. The numerals 7.16.6.16.18 translate to September, 32 BC (Julian). The glyphs surrounding the date are thought to be one of the few surviving examples ofEpi-Olmec script.

The Mesoamerican Long Count calendar developed in south-central Mexico and Central America required the use of zero as a place-holder within itsvigesimal (base-20) positional numeral system. Many different glyphs, including this partial quatrefoil--were used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36 BC.[24] Since the eight earliest Long Count dates appear outside the Maya homeland,[25] it is assumed that the use of zero in the Americas predated the Maya and was possibly the invention of theOlmecs. Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the 4th century BC, several centuries before the earliest known Long Count dates.

Although zero became an integral part of Maya numerals, it did not influence Old World numeral systems. Quipu, a knotted cord device, used in theInca Empire and its predecessor societies in the Andean region to record accounting and other digital data, is encoded in a base ten positional system. Zero is represented by the absence of a knot in the appropriate position.