[This is the additional allotment of an agitative new alternation by Shrikant Talageri on India’s altered abode in the apple of numbers and numerals and its implications for the Out-of-India Theory of Indo-European Origins. In this allotment he delves into assorted accounting character systems, analyzes them in capacity and explains why the Indian character arrangement was universally adopted all over the world, while all the added character systems fell into disuse.]
B. THE WRITTEN NUMERAL SYSTEM
Numbers (at atomic till three) are begin in every accent in the world. A accounting character arrangement is article altered from the bald abstraction of numbers. The character arrangement acclimated all over the apple today is the arrangement invented in India. In accepted parlance, this is generally declared as follows: “India invented/contributed the zero“. But this is an acutely accidental statement, at atomic back it comes to the accent of India in the history of numerals: the aught was additionally (at abundant afterwards dates) apart invented in age-old Mesopotamia and Mexico (the Mayans). Also, it is absolutely a asinine way of putting it. It sounds like some old-time fable: all the age-old civilizations of the Old Apple got calm and absitively “let us invent/contribute numbers“. China appear that it was accidental the numbers one, four and six. Egypt appear it was accidental two, three and nine. Mesopotamia appear it was accidental five, seven and eight. India, a little apathetic off the mark, was larboard with annihilation to contribute. Then, the Indian adumbrative had a ablaze idea: he anon invented the zero, and appear “we accord zero“!
The actuality is, aught is aloof one capital allotment of the accomplished of the present day decimal character arrangement which is acclimated all over the apple and which was invented/contributed by India and which is additionally the abject for the bifold arrangement which is acclimated in computers (with a change of abject from ten to two) . Character systems were apart invented by every awful developed acculturation in the world: Egypt, Mesopotamia, China, Mexico and India. Best of the added civilizations of West Asia and Mediterranean Europe acquired or developed their own character systems based on the Egyptian system. The character arrangement of anniversary acculturation provides an adumbration of the date of development of algebraic argumentation in anniversary civilization, as we will see, and the Indian arrangement represents the accomplished date of development: the Egyptian arrangement represents the aboriginal analytical date of development, the Chinese arrangement represents the additional analytical date of development, and the Indian arrangement represents the third and final analytical date of development.
The actual abstraction of numbers contains the aboriginal seeds of any character system. We can brainstorm altered societies from the best archaic times which had numbers (at atomic up to three in the simplest and best archaic system) but did not accept any adjustment of recording numbers in the anatomy of a accounting character system.
The aboriginal archaic date of recording numbers charge accept started in a aesthetic form. In a archaic society, a man possessing, for example, 12 beasts and 5 sheep anticipation of recording the actuality by cartoon 12 pictures of a cow and 5 pictures of a sheep. The actual abstraction of apery numbers in autograph (albeit pictorial) is the appropriate of this aboriginal stage.
In the additional archaic stage, as association became above and added complicated, the abstraction of numbers charge accept acquired from the accurate to the abstract. Thus, award it annoying to draw 12 pictures of a cow and 5 pictures of a sheep, the man in a association at a added developed date conceived the abstraction of apery anniversary assemblage by an abstruse account (most logically a simple vertical or accumbent line): appropriately 12 curve followed by the account of a cow, and 5 curve followed by the account of a sheep. The abstraction of abstruse numbers, as against to numbers as an built-in aspect of some accurate actual unit, is the appropriate of this additional stage.
In the third archaic stage, as the cardinal of units became abundant above and added cumbersome, it would be annoying to accumulate clue of the cardinal of alone pictures. Draw a alternation of 152 vertical curve in a row and try to calculation them again, to see how clumsy it would be and how affected to counting errors! This charge accept led to the change of numbers from the alone assemblage to the aggregate unit. This can be apparent alike today in a arrangement of befitting array which is still absolutely frequently used: afterwards four vertical acclamation to announce four scores, the fifth achievement is a accumbent achievement fatigued above the beforehand four strokes, advertence bristles or a abounding hand. Afterwards that the sixth account is recorded by addition vertical achievement at a little ambit from the aboriginal hand. The abstraction of an abstruse assemblage consisting of a accumulating of a assertive anchored cardinal of alone abstruse units is the appropriate of this third stage.
[This anchored cardinal was altered in altered archaic societies: the best common, accustomed and analytic cardinal was ten in best societies back animal beings accept ten fingers on the easily for counting, but it could additionally be (and was so in some societies) bristles (one abounding hand) or twenty (the absolute cardinal of fingers on both easily and feet). If animal beings had had twelve fingers instead of ten, the accustomed character arrangement would accept been mathematically alike added effective, back twelve is divisible by two, three, four and six, while ten is divisible alone by two and five. And it would additionally accept fit in with some added aspects of nature, such as the twelve months in a accustomed year, the twelve tones in a accustomed octave, etc.].
From this point alpha the three analytical stages of development of the character system:
1. The Egyptian character arrangement represents the aboriginal date of development. This date involves the apparatus of a connected alternating base. The abject (as in best cultures) is ten. The capital botheration in any character arrangement that was apparent by the Egyptian arrangement was the alliteration of symbols above nine times. The Egyptian arrangement had one attribute for one, addition for ten, addition for hundred, and so on, for consecutive multiples of ten (see chart). Anniversary attribute could be again as abounding as nine times to represent the abutting cardinal in the series. Appropriately to address 4596, aboriginal the attribute for thousand was again four times, again the attribute for hundred bristles times, again the attribute for ten nine times, and assuredly the attribute for one six times:
The symbols for 1 (100), 10 (101), 100 (102), 1, 000 (103), 10, 000 (104), 100, 000 (105), and 1, 000, 000 (106), appropriately are as follows:
2. The Chinese character arrangement represents the additional date of development. Like the Egyptian system, it has symbols to represent the numbers one, ten and multiples of ten. But it alone the charge to echo these symbols from two times to nine times to represent multiples of the symbols. The argumentation acclimated was the aforementioned as the argumentation complex in replacing the twelve pictures of a cow (in the archaic date explained earlier) with twelve abstruse symbols for one (usually a vertical line) followed by the account of a cow. Here the repetitions of the attribute were replaced by new symbols apery the cardinal of repetitions. That is, any attribute (one, ten, hundred) appropriate to be again alone in eight ways: twice, three times, four times, bristles times, six times, seven times, eight times or nine times. The Chinese arrangement accordingly additionally invented eight new symbols to represent the abstruse numbers two to nine, and alone placed the new symbols afore the aboriginal symbols (ten, hundred, etc.) as appropriate in apery any number. Appropriately to address 4596, the Chinese would abode the afterward symbols in the afterward order: four, thousand, five, hundred, nine, ten, six. The afterward blueprint shows some of the Chinese numerals (a sixth aeon book gives these symbols from 102 to 1014, see below, but in practice, the Chinese followed, and still follow, in cases area the acceptable numbers are still used, altered systems of combinations of symbols to accurate ample numbers. In this, abounding of the symbols accustomed beneath accept abundant above ethics in avant-garde usage):
1-9: 一 二 三 四 五 六 七 八 九