History of Numbers: Essay Introduction
Different versions of the evolution of numbers have led to different outcomes. These include the Egyptian, Babylonians and Hindu-Arabic versions as well as the Mayans, Romans and modern American number systems. The mathematical evolution is the basis of the development history of counting. It is believed that this was before the beginning of the counting systems. (Zavlatsky, 124).
The history of mathematics and counting began with the idea of formulating measurement methods. This was used by the Babylonians/Egyptians. This paper will highlight the evolution history of counting by the Egyptians/Babylonians, the Romans, Hindu-Arabic, and the Mayans' counting systems. The paper will also explain why Western counting systems are so popular today.
The Egyptians/Babylonians Number History
The ancients recognized the measurement in terms of more and less, which led to the need for counting. Although the assumptions of numbers were based on archeological evidence from around 50,000 years ago (Higgins, 87), the background of the counting system is the ancient recognition of more or less in routine activities (Higgins, 87). The need for simple counting was also recognized by ancient people. These ancient people developed other types of number systems, such as more or less and odd numbers. Because people need a way to count groups of people through the increase in population by birth, counting became a necessity. Menninger also claims that pre-historical activities like barter and cattle trading led to the need to count and determine value (105).
Prehistoric people used sticks to count cows. The total number of animals in the world was determined by the allocation and collection of sticks. The mathematical history was formed from the marking of rows of bones, tallying and pattern recognition. This led to the introduction numbers. As shown below, the bones and woods were marked.
The spoken words of prehistoric people are what influenced the evolution of numbers. It has been hard to track down the pattern of numbers between one and ten. Any pattern beyond ten can be easily identified and traced. One example is ein lifon. This prehistoric term meant "one left" and led to eleven. Twelve were derived from the lif which was "two leftovers". (Higgins143). The pattern was extended to nineteen by tracing thirteen from the combination of three and four, which were taken from fourteen. The word "ten times," which is the number of hundred, can be deduced from Ifrah Bello (147). The written words of ancient people, such as notches on stone carvings and knots for count, provided a solid foundation for the evolution in counting.
The Incas used the counting of boards for their record-keeping. The Incas used "quip" to help pre-historic people record their items. Three different colors were used to paint the counting boards. These represented the highest number, the darkest part represented the second-highest level, and the lighter parts represented the stone compartments (Havil 277) The quip could also be used to perform fast mathematical computations (Zavlatsky, 154). The quip generally used knots on cords that were arranged in certain ways to provide certain numerical information. The quip system of information and record keeping has been linked to many mysteries that have yet to be solved. Below are examples of how knots look.
History of the Hindu-Arabic Number History
This is the 21st century's common system for counting and numbers. Al-Brahmi introduced in India the numbers 1, 2, 4, 5, 6, 7, 8, 8 and 9 (Menninger 175). With time, the Brahmi numerals changed. The numerals in the 4th through 6th centuries were, for example, as shown below.
The numerals were eventually extended to 1,2,3,4,5 and 6,7,7,8,9 over time. From Cambodia came the earliest system for using zero. The Saka era saw the introduction of three digits with a dot between (Hays & Schmandt-Besserat, 198). This was the beginning of the evolution in decimal points. Babylonians introduced the positional systems, which established the place value for numerical systems. The Babylonians created the base systems for the numerical using the positional system, which was later further developed by the Indians. Brahmi numerals went through many incarnations before they were able to create the current number system (Higgins, 204).
Gupta numerals are one of the ways that the Hindu-Arabic numbers system evolved to become the most widely used American number version. Researchers are still unsure of the origins and evolution of the Gupta numbers.
The Europeans also adopted the Hindu-Arabic trading system, which meant that travelers could use the Mediterranean Sea to trade (Havil 191). European number evolution was dominated by the Pythagorean and the abacus. Even though both systems declined after a while, the Pythagorean still used "sacred number" The Europeans borrowed the Hindu–Arabic number system over time to create their mathematical number systems (Ifrah 207 and Bello 207). The exact process by which the Europeans adopted Hindu-Arabic systems has yet to be established. The Europeans may have adopted the Hindu-Arabic numbering system because they rely heavily on it to build their strong numerals (Higgins, 210). The positional base system's scope is extensive, and involved conversion of various bases using numerical numbers 10.
History of the Mayan Number
Mexico was home to the Mayan civilization, which developed number and counting systems through rituals. Two ritual systems were used to calculate calendar dates. One for priests, the other for common civilians (Higgins 217). The priestly calendar counting utilized mixed base systems that involved multiples of numerical numbers. The Mayan number system forms the basis of mathematical knowledge. The Mayan system of number used the position of numbers to assign the place value of the combined numbers (Havil 223).
The Mayans used place values of numerical numbers to multiply and add numbers. Ultimately, the Hindu-Arabic and the Mayan number systems contributed highly to the evolution of numbers as opposed to the Egyptians/Babylonians number systems (Menninger 199). The strong features of all other evolutions were incorporated into the Western number system for counting and mathematics to create a solid number system. The American system, which is used in most countries, uses decimal points, place values, and Roman numbers 1-10 (Ifrah 225 and Bello 225). Below is a sketch of what the Mayans called the tabled numbers.
To create a reliable, universally accepted number system, the American version of numbers and count used all the development features from the Mayans, Babylonians and Incas. This is a unique aspect that makes the American system stand apart from all other number systems and counting. The merits of the Mayans Babylonians, Egyptians and Indians must not be underestimated as without them, history would not be complete.
Essay Conclusion on History of Numbers
There is a lot of pre-historical archeological evidence that shows the historical history of counting and number systems. Researchers face a huge challenge when trying to trace the ancient times of number systems and counting. Research on the topic number systems and counting is still ongoing. The Mayans, Hindus, and Babylonians, which rely on Incas development, are the most successful number systems. Prehistoric evidence, such as wood carvings and stones, left mathematical evidence that led to the evolution in counting. There are many methods and arguments for the evolution of numbers. There are therefore no accepted research findings regarding the evolution of numbers and mathematical systems.
Havil, Julian. The Irrationals: A Story of the Numbers You Cant Count on, Princeton: Princeton University Press, 2014. Print.
Hays, Michael, and Denise Schmandt-Besserat. The History of Counting, Broadway: HarperCollins, 1999. Print.
Higgins, Peter. Number Story: From Counting to Cryptography, Gottingen: Copernicus, 2008. Print.
Ifrah, Georges, and David Bello. The Universal History of Number: From Pre-history to the Invention of Computer, Hoboken: Wiley, 2000. Print.
Menninger, Karl. Number Words and Number Symbols; Cultural History of Numbers, Mineola: Dover Publications, 2011. Print.
Zavlatsky, Claudia. Africa Counts; Number and Pattern in Africa Cultures, Chicago: Chicago Review Press, 1999. Print.
East Asian History in the 18th-19th Centuries
William Lloyd Garrison and Slavery in America
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