![]() ![]() The system has fully evolved by about AD 800, when it is adopted also in Baghdad. The Indians use a dot or small circle when the place in a number has no value, and they give this dot a Sanskrit name - sunya, meaning 'empty'. The digits now used internationally make their appearance gradually from about the 3rd century BC, when some of them feature in the inscriptions of Asoka. This seems to have been achieved first in India. In the Babylonian and Mayan systems the written number is still too unwieldy for efficient arithmetical calculation, and the zero symbol is only partly effective.įor zero to fulfil its potential in mathematics, it is necessary for each number up to the base figure to have its own symbol. Zero, decimal system, Arabic numerals: from 300 BC They merely use a dot for 1 and a line for 5 (writing 14, for example, as 4 dots with two lines below them). Like the Babylonians, they do not have separate digits up to their base figure. If this gap is not kept, all the digits before it will appear to be in the wrong column and will be reduced in value by a factor of 60.Īnother civilization, that of the Maya, independently arrives at a place-value system - in their case with a base of 20 - so they too have a symbol for zero. The place-value system necessarily involves a sign meaning 'empty', for those occasions where the total in a column amounts to an exact multiple of 60. For them a number as simple as 222 is the equivalent of 7322 in our system (2 x 60 squared + 2 x 60 + 2). We now take for granted the strange fact that in the number 222 the digit '2' means three quite different things - 200, 20 and 2 - but this idea is new and bold in Babylon.įor the Babylonians, with their base of 60, the system is harder to use. They introduce the place-value concept, by which the same digit has a different value according to its place in the sequence. The Babylonians take one crucial step towards a more effective numerical system. Much later, when time can be accurately measured, the same system is adopted for the subdivisions of an hour. Through the Babylonian pre-eminence in astronomy, their base of 60 survives even today in the 60 seconds and minutes of angular measurement, in the 180 degrees of a triangle and and in the 360 degrees of a circle. Instead, numbers below 60 are expressed in clusters of ten - making the written figures awkward for any arithmetical computation. This is extremely unwieldy, since it should logically require a different sign for every number up to 59 (just as the decimal system does for every number up to 9). The Babylonians use a numerical system with 60 as its base. The scribes of the Egyptian pharaohs (whose possessions are not easily counted) use the system for some very large numbers - unwieldy though they undoubtedly are (see A large Egyptian number). This is essentially the Egyptian system, adapted by Rome and still in occasional use more than 5000 years after its first appearance in human records. If that looks hard to read as 23, glance for comparison at the name of a famous figure of our own century - Pope John XXIII. The Egyptians write from right to left, so the number 23 becomes lll^^ In Egypt, from about 3000 BC, records survive in which 1 is represented by a vertical line and 10 is shown as ^. In the earliest surviving traces of a counting system, numbers are built up with a repeated sign for each group of 10 followed by another repeated sign for 1. When any sort of record is needed, notches in a stick or a stone are the natural solution. ![]() Ten has been the basis of most counting systems in history. ![]() Soon after language develops, it is safe to assume that humans begin counting - and that fingers and thumbs provide nature's abacus. ![]()
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