History of Numbers: From Mynan to the Arabic Numeral System - Coursework Example

HISTORY OF NUMBERS No one in this world can deny the importance of the fact that numbers have played an important role in the development of the human civilization. Numbers are ubiquitous; from the paltry calculations of our shopping expenses to the critical calculations in science and technology, a world without numbers is unimaginable. This essay delves into the history of numbers right from the crude rock age symbols to the modern day decimal numbers. It is a well-established fact that the modern day number system was transmitted to Europe by the Arabs, who in turn adopted it from the Indians. The Indians were the inventor of the number ‘zero’ and the other numerals as well but the place value system of decimal is credited to have been a contribution of the Babylonians and it has eventually become the system which is prevalent today. The ancient record of numbers comes from the fossils of bones and other artifacts which show ‘tally’ marks. These tally marks have been accepted to have been kept as a count of the number of days, the lunar cycle, animals etc. Archaeological inscriptions depicting symbols like triangles and circles which are said to have been symbolic of numbers have also been excavated and found across many places in Africa and Asia. For example, Figure 1: Some ancient numbers In the picture one can clearly observe that the number is depicted by exactly depicting the number of objects that it possibly represents. Such a system was pre-dominant for quite a long time in the ancient prehistoric world before man realized the ‘limit of four’. The Limit of Four is defined as the inability of the human mind to numerate. Simply put, the human mind cannot be mindful of more than 4 symbolic numeral representations of any kind. Beyond 4, quantities are vague for our eyes alone cannot tell us how many things there are. As a result of which, various civilizations came up with various solutions. The Cretans in the 12th Century BC came up with the numerals in the linear script which were essentially like tally marks in which the higher numbers were represented in groups of 4. The Egyptians followed suit and in the 3rd Century BC they came up with the similar system of numbers in the elephantine script which were also essentially like tally marks and in which the higher numbers were represented in groups of 3. Similarly in Europe in England they had the system of ‘Five Barred Gate’ which was quite similar to the ‘tally marks’ system like the afore-mentioned two systems but when powers of 5 were achieved the tally marks would be stricken out giving them the appearance of a ‘barred gate’ and hence the nomenclature. Consequently, the number 10 was represented by two such barred gates and so on. In New Guinea, the Elema tribal people had a different system altogether. They had nominated the parts of body with different numbers, for example the finger digits represented the numbers 1 to 10 and the right knee stood for the number 27 etc. As civilizations progressed there was felt a need to have an additive numeral system, where each character has a value independent of its position in its representation. The Greek and the Roman Numeral System was an example of this concept. The Greek adopted specific symbols where as the Romans used the alphabets of their script as numbers. Figure 2: Greek Numerals And, almost all of us have come across Roman numbers in our lives. Some examples are given as follows: I-1, II-2, III-3, IV-4, 5-V, 6-VI, 10-X, 11-XI, 18-XVIII, 20-XX, 29-XXIX, 50-L, 75-LXXV, 100-C, 500-D, 1000-M etc. As one can guess, the problem felt with the positional numeral system was that it was very cumbersome to represent large numbers and esp. do mathematical calculations with them. Therefore, the quest to have a number system which could have had portable representation was still on. Gradually, humans began to realize that there was a need to have a number system with a set of digits which could represent almost any conceivable number. This led to the discovery of positional notation. The Mayans and the Incas were the first to have discovered this positional notation. They adopted a number system denoted by dots and bars. The place starting from right denoted the various notational places. The number could then by understand by suitable calculations (multiplication and addition). The Babylonians however had a very refined number system as compared to the Mayans/Incas. They had a number system which was till the scale of 60 starting from obviously 1. Any number higher than that was a repetition of the digits in their appropriate notational place so as to wholly denote a number. Eventually, the place value system that we use today can be credited to the Babylonians wholly. The problem of the positional notation was to represent the tens, hundreds, thousands, etc. Also, by this time none of the civilizations had thought of the number ‘zero’. There was however felt the need to represent ‘nothing’ and the concept of empty and nothing became synonymous. The Babylonians realized that and they left blank spaces wherever they needed zero. Again, there was felt a need to have a number system which possessed a well-defined zero. This is where the Indians made the biggest contribution in the history of mankind. The Indians can be credited to have developed the modern number system which we use today. Because of the lack of authentic archaeological evidences, not much is known about how ancient Hindu mathematics was developed. Traces of application of mathematical esp. geometrical concepts in construction, town-planning, immaculate drainage system etc. have been found in the Indus Valley Civilization excavations.which clearly indicates that the level of mathematics and sciences was higher in this part of the world during that time when compared to anywhere else in the world. The Indus Valley People had systems of writing, counting, weighing and measuring, and they dug canals for irrigation which required basic knowledge of mathematics and sciences. The Hindu Numeral System was very much indirectly influenced by the ancient Chinese system and to some extent can be said to be its continuance. The Hindu system came up with a pure place value system which demanded a digit to represent the missing denomination. for ‘nothingness’, the zero. The first significant recorded astronomical work was Surya Siddhanta (Knowledge of the Sun) which was written about the beginning of the 5th Century BC. There was a paradigm shift from religion to astronomy in terms of the use of mathematics. In the beginning of the first century AD, Indians began to develop scripts like Brahmi, Kharosthi etc. The Brahmi script, is of great signinficance to any mathematician, as it was in this script that the first traces of the number system which we use today are found. Given below is the specimen of the various symbols and their numeric value representation. Figure 3: The Brahmi Numerals The Brahmi numerals were written from left to right, unlike in Kharosthi. As can be seen above, the numbers two and three were represented by repetitions of the horizontal stroke for one. Similarly, there were different symbols from four to nine, ten and multiples of ten upto ninety, and for hundred and thousand. In the later part of the timeline, research and development in the field of astronomy which really fostered the development of mathematics and numbers. Then, in the seventh century AD, these Brahmi numbers got refined and developed in to the Nagari numerals. These numerals (picture given below) have quite a semblance with the modern day numbers. You can notice how the horizontal strokes for one, two and three joined together to form the numerals. It was in this script that the first mention of ‘zero’ denoting nothingness was recorded. The invention of the number ‘zero’ is now considered to be a milestone in the history of mankind. Figure 4: Nagari numerals Figure 5: Evolution of Nagari numbers from Brahmi numbers This Indian numeral system was the basis of many works of science and mathematics by scholars like Aryabhata, Bhaskara, Mahavira etc. An Indian astronomical textbook which employed the use of the decimal place value system: Siddhanta by Brahmagupta was brought to Baghdad towards the end of the eighth century and translated into Arabic. This translation had a profound impact starting from the Arabic world and eventually spreading out to Europe and the whole of the West at a time when the Greek numeral system was rampant in these parts of the world. There are substantial evidences to prove that the Hindu numerals were known in the Arabic world as early as the seventh century AD. The great Arab mathematician Al-Khwarizmi had become familiar with the Hindu system by studying Brahmagupta’s Siddhanta. The knowledge of the Hindu numeral system spread from the Arabs of the West in Spain before the end of the tenth century. The earliest number script which came from Northern Spain which was a modified version of the Hindu numerals was in the year 976 AD. These Hindu-Arabic numerals as they came to be known about were not easy to influence the European counterparts, especially the Romans. As always, people resist change of any kind and it took quite some time for the Hindu-Arabic numerals to find general acceptance among the people. It is logical in the sense that what may appear normal and acceptable to us didn’t appear the same way to people in the past. For them a change in the number system, meant not only learning that new system but also changing the way they wrote and introducing new symbols to their script which obviously had foreign traits. Especially, the number zero was befuddling to many. People found it difficult to comprehend how could a number which meant ‘nothing’ when it stood to the right of a number could increase its value ten-fold. However, in midst of all this tendency of not wanting to accept the new system of numbers there were many European scholars and Mathematicians who found it very convenient to adopt this new system. The Italian mathematician Fibonacci in his book, the Liber Abaci, explained Arab arithmetic and algebra, and strongly recommended the use of the Hindu-Arabic numeral system. So, ultimately it can be said that it was the mathematicians and not the astronomers, who ultimately ensured the almost universal adoption of the Hindu-Arabic numerals. In all, it can be said that our modern number system was a conjunction of a number of great ideas/concepts which underwent a lot of honing and brushing to reach to their current state. Firstly, it was the idea of attaching to each basic figure graphical signs which stood solely for the numerical unit and has no intuitive association with it. It was important to detach these figures of any kind of visual unit/s that they may evoke in the mind of the perceiver. The numbers are supposed to just invoke the meaning of the figure that they represent and nothing else. Secondly, it was the place value system that is the most important trait of the modern number system. The principal of positional notation has not only helped in condensing the numerals but also in their easier representation and ease in calculations. Lastly, it would definitely be the ‘zero’, the null number which filled the spaces of empty numbers and yet had a meaning attached to it as well. REFERENCES Docs.google.com (n.d.) Powered by Google Docs. [online] Available at: https://docs.google.com/viewer?a=v&q=cache:r116zVvEWrQJ:motivate.maths.org/conferences/conf67/HistoryNumbers.ppt+history+of+numbers&hl=en&gl=in&pid=bl&srcid=ADGEESiJXA-3qK9ivE6FgoPn2cCxVMWSVvn7pcsAEY0fszXyTVyPGNdLoJa36RWvBJCn5qAXr7LzyICbJmfkWCEHVgcBGThrbEMR-dgtIVgX2lDb5a5pqM7rECm7nJKqGcbL-Z25FsAP&sig=AHIEtbS34PWQaDpa-8o_ZXBJ166z0_KK6g [Accessed: 15 Apr 2012]. Home.c2i.net (n.d.) NUMBERS: THEIR HISTORY AND MEANING. [online] Available at: http://home.c2i.net/greaker/comenius/9899/indiannumerals/india.html [Accessed: 15 Apr 2012]. Read More

In New Guinea, the Elema tribal people had a different system altogether. They had nominated the parts of body with different numbers, for example the finger digits represented the numbers 1 to 10 and the right knee stood for the number 27 etc. As civilizations progressed there was felt a need to have an additive numeral system, where each character has a value independent of its position in its representation. The Greek and the Roman Numeral System was an example of this concept. The Greek adopted specific symbols where as the Romans used the alphabets of their script as numbers.

Figure 2: Greek Numerals And, almost all of us have come across Roman numbers in our lives. Some examples are given as follows: I-1, II-2, III-3, IV-4, 5-V, 6-VI, 10-X, 11-XI, 18-XVIII, 20-XX, 29-XXIX, 50-L, 75-LXXV, 100-C, 500-D, 1000-M etc. As one can guess, the problem felt with the positional numeral system was that it was very cumbersome to represent large numbers and esp. do mathematical calculations with them. Therefore, the quest to have a number system which could have had portable representation was still on.

Gradually, humans began to realize that there was a need to have a number system with a set of digits which could represent almost any conceivable number. This led to the discovery of positional notation. The Mayans and the Incas were the first to have discovered this positional notation. They adopted a number system denoted by dots and bars. The place starting from right denoted the various notational places. The number could then by understand by suitable calculations (multiplication and addition).

The Babylonians however had a very refined number system as compared to the Mayans/Incas. They had a number system which was till the scale of 60 starting from obviously 1. Any number higher than that was a repetition of the digits in their appropriate notational place so as to wholly denote a number. Eventually, the place value system that we use today can be credited to the Babylonians wholly. The problem of the positional notation was to represent the tens, hundreds, thousands, etc. Also, by this time none of the civilizations had thought of the number ‘zero’.

There was however felt the need to represent ‘nothing’ and the concept of empty and nothing became synonymous. The Babylonians realized that and they left blank spaces wherever they needed zero. Again, there was felt a need to have a number system which possessed a well-defined zero. This is where the Indians made the biggest contribution in the history of mankind. The Indians can be credited to have developed the modern number system which we use today. Because of the lack of authentic archaeological evidences, not much is known about how ancient Hindu mathematics was developed.

Traces of application of mathematical esp. geometrical concepts in construction, town-planning, immaculate drainage system etc. have been found in the Indus Valley Civilization excavations.which clearly indicates that the level of mathematics and sciences was higher in this part of the world during that time when compared to anywhere else in the world. The Indus Valley People had systems of writing, counting, weighing and measuring, and they dug canals for irrigation which required basic knowledge of mathematics and sciences.

The Hindu Numeral System was very much indirectly influenced by the ancient Chinese system and to some extent can be said to be its continuance. The Hindu system came up with a pure place value system which demanded a digit to represent the missing denomination. for ‘nothingness’, the zero. The first significant recorded astronomical work was Surya Siddhanta (Knowledge of the Sun) which was written about the beginning of the 5th Century BC. There was a paradigm shift from religion to astronomy in terms of the use of mathematics.

In the beginning of the first century AD, Indians began to develop scripts like Brahmi, Kharosthi etc. The Brahmi script, is of great signinficance to any mathematician, as it was in this script that the first traces of the number system which we use today are found.

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