The Effect Zero Had on Calculation - Coursework Example

The effect of zero The effect zero had on calculation Introduction “The path that leads to the discovery of "0" lies only in the most advanced typeof number system, which is called "positional" because the value of a character depends on its position. As far as we know, the positional concept has emerged in only four places: c.2000 B.C.E., in Babylon; around the start of the Common Era, in China; between the 4th and 9th centuries C.E. among the Mayan astronomer-priests; and in India” (Douglas Harper, 2001) As the meaning of zero implies the exact information about the discovery of ‘zero’ is also a big zero among mathematicians and historians. Lots of claims are there for the fatherhood of zero. But still it is unclear for the historians about the exact person who discovered zero or the country where it is originated. “Through all its history, despite the rejection and the exile, zero has always defeated those who opposed it”( Charles Seife , p.3) The number zero as we know it was conceived by the Hindus from India.  The Hindus were the first to recognize a mathematical representation of concept of no quantity. Zero must be distinguished from nothingness (null).  Undoubtedly it was the inability of earlier peoples to perceive this distinction which accounts for their failure to introduce the zero. (Morris Kline, 2001), The effect of zero 2 Introduction of zero- ancient counting systems When we analyze ancient number system we can see that some of the counting systems made use of the number zero while some others were unaware of the number zero. The present number system which consists of digits from 0, 1, 2, 3, 4… etc is the contribution “Arabic numbers” system. “Arabic numbers are also called Hindu-Arabic numbers. This is a better name as it was the Hindus in India who invented the system from about the 4th century BC onwards. This number system spread to the Middle East in about the 9th century AD, where it was used by Arab mathematicians and astronomers. Arabic numbers then spread to Europe. They soon realized how much easier it was to do calculations with Arabic numbers. Now Arabic numbers are generally used throughout the world for calculation, although systems such as Roman, Greek and Chinese are still used for formal purposes. (Jo Edkins, 2006- Arabic Numerals) “The Greeks were used letters as symbols for representing numbers. But this method requires 27 letters and there were only 24 letters in the Greek alphabets. So they used three extra symbols for the missing letters. They never used zero and hence their arithmetic calculations were more complicated.” (Jo Edkins, 2006, Greek Numbers) “The Babylonian number system was similar to the Egyptian number system in many ways. They used two ones to represent two; three ones for three, and so on, up to nine. Ten was represented with a different symbol. Twenty represented with two tens and thirty with three tens and so on. However, something strange happened at sixty (see below). The symbol for sixty seems to be exactly the same as that for one. Sixty one is sixty and one, which therefore looks like one and one, and so on. They never used zero as a number and they never found any The effect of zero 3 difficulty in dealing with their number system even in the absence of zero.” (Jo Edkins, 2006, Babylonian Numbers) “The Egyptians used a simple line to represent 1 and two lines to represent two and so on up to nine. They introduce a new symbol for ten and then they added lines to represent next numbers. Hundred represented with a new symbol and so on. The Egyptians also had symbols for fractions. But they didnt have a symbol for zero.” Egyptians used some kind of pictures or objects to represent numbers. Considering the easiness with which at present we are handling the Arabic numbers, the Egyptian numbers are more difficult to handle. See the table below. 1 - 10 -100 -1,000 -10,000 -100,000 -1,000,000 Infinity (Jo Edkins 2006, Ancient Egyptian Numbers) The number infinity is similar to a circle which means that if you go behind this number you will just ended up like rotating around a circle. In other words you will never see the end. The effect of zero 4 Comparison of usage of zero in the ancient period ‘Babylonians are believed to be the first users of zero as a position marker for representing an empty space in a sequence of numbers. In Greece the zero was used by astronomers only. Some theories suggest that “O” represents the first letter of Greek word “Omricon” which means nothing. On the other hand Indians are believed to be the creators of zero as a number. The Indian trio of mathematicians, Brahmagupta, Mahavira and Bhaskara struggled to slot this symbol into their developing decimal number system though they succeeded in many other aspects of decimal number system.’ (A Countdown to Zero) The effect of zero had on calculations and representation of numbers The Indian mathematician Brahmagupta, was succeeded in forming most of the rules of arithmetic involving zero. “He explained that given a number then if you subtract it from itself you obtain zero. He gave the following rules for addition which involve zero:- 1. The sum of zero and a negative number is negative 2. The sum of a positive number and zero is positive 3. Tthe sum of zero and zero is zero.” (J J OConnor and E F Robertson, 2000) “Dividing by zero, on the other hand, proved to be a more troublesome pursuit and is still causing headaches today. Divide by zero and computers crash, civilisation crumbles and maths teachers reach for the sherry bottle”. (A Countdown to Zero) In fact one of the oldest mysteries of mathematics yet to be solved though technology and computation methods improved immensely using super computers. Most of the mathematical problems were answered; but still The effect of zero 5 division of a number by zero remains a question seems to be with no answers yet and in near future as well. “The work of Brahmagupta, Mahavira and Bhaskara to put zero on an equal footing with other numbers didn’t survive the voyage westward” (Robert Kaplan, Ellen Kaplan p.108) “There are two uses of zero mainly. It can be used as an empty space indicator in place value number system and a number itself. In a number like 2009, the zeros are used so that the positions of 2 and 9 are correct. In other words the place value of 2 will never be 1000 and that of 9 will never be unity unless the two zeros are there in between these numbers.” (Morris Kline, 2001) “Most of the common people believe that the meaning of zero is “nothing”. Actually it is not correct fully. Suppose two persons; one scored zero mark in an examination while the other not even appear for the examination. We can say that both of them secured zero marks. In this example the mark scored by the first person is zero and it has a meaning other than nothing as he attended the examination. But for the second person the meaning of zero is nothing as he has not attended the examination”. (Morris Kline, 2001) Conclusion Amidst the advancement of science and technology and every aspects of improved human life, zero still remains as a mystery. The origin of zero, the meaning of zero, some of the calculations with zero, all are still debatable. The Indians are believed to be the introducers of zero in the decimal number system. The Babylonians, Chinese etc were aware of zero apart from the Indians in ancient times. Zero represents emptiness and at the same times a decimal number as well. The effect of zero 6 References 1. Charles Seife, Zero, The Biography of a Dangerous Idea, Publisher: Oxford University Press, USA (December 7, 2000), Retrieved on 22/1/09, 2. Robert Kaplan, Ellen Kaplan, The Nothing that Is: A Natural History of Zero Publisher: Penguin (Non-Classics) (September 5, 2000) Retrieved on 22/1/09, 3. J. J. OConnor and E F Robertson(November 2000), A history of Zero, Retrieved on 22/1/09, < http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html> 4. Douglas Harper, November 2001, History of Zero, Retrieved on 22/1/09, < http://www.etymonline.com/zero.php> 5. Jo Edkins, 2006, Arabic Numerals, Retrieved on 22/1/09, < http://gwydir.demon.co.uk/jo/numbers/arab/index.htm> 6. Jo Edkins 2006 Greek Numbers, Retrieved on 22/1/09, The effect of zero 7 7. Jo Edkins 2006 Babylonian Numbers, Retrieved on 22/1/09, 8. Jo Edkins 2006, Ancient Egyptian Numbers, Retrieved on 22/1/09, < http://gwydir.demon.co.uk/jo/numbers/egypt/intro.htm> 9. A Countdown to Zero, Retrieved on 22/1/09, 10. Morris Kline, 2001, Zero History, Retrieved on 22/1/09, < http://www.geocities.com/borhoo/History.htm> Read More