Course:ETEC540/2009WT1/Assignments/ResearchProject/TheTechnologyofNumbers

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Introduction

Pythagoras, the Greek philosopher, once stated that everything could be expressed in numbers (Lahanas, n.d.). Numbers are an integral part of our society; they can represent meaning, communicate significance and conotate importance. The evolution of numbers has infiltrated every aspect of society as it has changed the characteristics of reading, writing, language and therefore communication. Even Galileo declared that the very language of nature was mathematics (Nickel, n.d.).

In the following paragraphs, the origin and history of numbers will be discussed, along with the impact the development and application of the numeric system has had on our culture; including our social, educational and commercial systems.


Origin of Numbers

The first and oldest calculating system was the hand (Ifrah, 2000). Then came notches (tally sticks: various dates are debated), pebbles, followed by numbers on strings (Ifrah, 1985). These are all considered memory aids or mnemonic devices, which allowed society to store and record imperative information (ETEC540, 2009). The abacus, (which is a direct descendant from pebble counting: pebble meaning calculus in Latin), was than followed by Roman numerals (Ifrah, 1985). The invention of numbers was not a linear process; some cultures developed numbering systems independent from each other, or tried to improve on an old system when they discovered that it did not meet their needs.

Egyptian, Chinese, Roman, Greek, Mayan, Babylonian, Inca, and Indian numbering system were developed; some of which were base 10, 20 and 60 (Uhl, 2008). Our present numbering system is a base-ten system, which means numbers 0 – 9 are used and multiplied by increasing powers of ten (Uhl, 2008). This is a Hindu-Arabic system developed in 60 AD, which was preceded by the Roman numeral system (Uhl, 2008). The Mayans, Aztecs, Celts, and Basques had a base 20 systems, while the Sumerians and Babylonians had a base 60 system (Ifrah, 2000). This is where the division of 60 seconds in a minute, 60 minutes in an hour and the division of a circle being 360 degrees originated (Ifrah, 2000).

Numbering systems came out of necessary economic and social development, and therefore there are no differences between prehistoric rock paintings, memory aids (mnemonic devices), winter counts, tallies, knotted cords, pictographs or the alphabet; these were all forms of necessary information storage and messaging (ETEC540, 2009).

Changes to Culture

Impact on the Social System.

The technology of numbers has infiltrated every aspect of our culture, and is closely linked to language and the alphabet. “To realize that representation begins with language, actualized in the creation of a reproducible formal structure, is already to apprehend the fundamental tie between language and number[s]” (Zerzan, 2009, p.1). The numerical system has had a substantial impact on the social systems that followed. The meaning behind 1st, 2nd and 3rd place or level 1, 2 and 3 on the salary scale, are some examples.

Numbers have significantly impacted the communication system, and therefore the social structure of society. Whether it is a telephone number, fax number, e-mail address, pager number or cell phone number, it is the basis of many forms of communication. And how a society communicates with one another determines its boundaries and defines its communities. Technology creates a new language in society and along with it a different way of communicating.

Some argue that numbers were more than a cultural invention; that it reflected more of a cognitive evolution (DeCruz, 2006). Whereas others believed that numerical concepts were a gradual accumulation of mathematical knowledge, and therefore the result of cultural evolution (DeCruz, 2006). Regardless, the technology of numbers has evolved to fill the necessary voids of knowledge, information storage, and data analysis.

Impact on the Educational System

The invention of time using numbers altered the educational system. Time allowed the increments of classes. Numbers permitted the use of grades, along with the conditioning of the technology of numbers (Postman, 1992). Grades, IQ and GPA’s communicate to society one’s level of intelligence. Numbers have given us chronological age with various meanings. We start school at age 6, age 16 comes freedom and independence with a driver’s license, and we end school at age 18, at which age we are considered an ‘adult’. Completing these milestones is an expectation of society.

With numbers came the advent of calculation, math and science. “The invention and democratization of our positional number-system has had immeasurable consequences for human society, since it facilitated the explosion of science, of mathematics and of technology” (Ifrah, 2000, p. 594). Scientists have linked math to art and music, and surmise that the language of mathematics involves a particular kind of visual and sensory motor thinking that goes beyond ordinary language (Peat, 1990). Mathematics is considered a unique language related to clear cut criterion that can begin or end communication (Nickel, n.d.).

Numbers allow easy referencing. The dewy decimal system is built into every library while numbering of chapters and verses in the bible allow access to passages. Previously the religious elite would have to read through many papyrus scrolls or manuscripts to locate a specific verse or passage.

Impact on Commercial and Commerce System.

Numbers and time have had a significant effect on the commerce system. “The division of time into regular, predictable units is fundamental to the operation of society” (Weisman, 1995, p.1). For example, the clock was invented by monks in monasteries to provide precision in worship rituals. Now it is a product of capitalism, for without the clock there would be no workday, no standardized production or standardized product (Postman, 1992). Numbers created a clearer way of communicating trade. Quality, quantity and grade of product are all assigned a numerical value, each representing or denoting a specific concept. Grade A eggs or a ton of number 2 grade Winter Wheat has definition and meaning to those in agriculture.

The banking system is number based. Every business transaction has numbers associated with it. Whether it is in the form of pay cheques, taxes, social security numbers, account numbers, property tax roll numbers, hydro account numbers, etc. Credit card numbers are large financial gains for credit card companies, and allows the acquisition of goods that otherwise would not be amassed by the population.

Language of Computers

The creation of numbers allowed the binary system – the language of computers – to be established. Computers have changed every aspect of our culture, including the way we learn and think, acquire education, commerce, our community identities and how we conduct business. Digital books have replaced papyrus rolls, manuscripts and paperbacks. One manufacturer advertises that their digital book holds up to ten bibles, thereby replacing the standard unit of measuring manuscripts, which was sheep (Keep, 2001). Parchment was originally made of sheep and a 160-page book was referred to as a forty sheep book (Keep, 2001).

The advancement of computers has changed the very nature and space of reading and writing, and challenges our concept of knowledge. It has impacted the entertainment and news industry, which is the very mode of communication that feeds society. The long-term effects of computers are still to be seen.

Conclusion

The advent of numbers has had a profound impact on society; from a social, education and commerce viewpoint; providing the foundation of many essential aspects of one’s life. “New technologies alter the structure of our interests: the things we think about. They alter the character of our symbols: the things we think with. And they alter the nature of community” (ETEC540, 2009). Numbers have changed how we communicate, the spaces in which we read and write, how we perceive meaning, store data and organize information. In essence, everything.


References

DeCruz, H. (2006). Why are some numerical concepts more successful than others? An evolutionary perspective on the history of number concepts. Evolution and Human Behavior, 27, 306-323.

ETEC540. (2009). Text technologies: the changing spaces of reading and writing. Retrieved from https://www.vista.ubc.ca/webct/urw/lc5116011.tp0/cobaltMainFrame.dowebct?JSESSIONIDVISTA=Z2RGKkRXyLxB4z8tZMLhcLJc9QkgMbVsZywhJn4GTb7cf2gJSCH9!-170808859!node08.vista.ubc.ca!20001!-1!2016739437!node09.vista.ubc.ca!20001!-1

Flegg, G. (1983). Numbers: Their History and Meaning. New York: Schocken Books.

Glaser, A. (1971). History of Binary and other nondecimal numeration. Pennsylvania: Tomash Publishers.

Ifrah, G. (1985). From one to zero. New York: Viking Penguin, Inc.

Ifrah, G. (2000). The universal history of numbers from prehistory to the invention of the computer. New York: John Wiley & sons, Inc.

Keep, C., McLaughlin, T., & Parmar, R. (2001). The electronic labyrinth. Retrieved from http://www2.iath.virginia.edu/elab/elab.html

Lahanas, M. (n.d.). Pythagoras: The whole thing is a number. Retrieved from http://www.mlahanas.de/Greeks/PythagorasNumber.htm

Nickel, G. (n.d.). Reason’s Nature— The Role of Mathematics. Retrieved from http://sophia-iberia.pbworks.com/f/Reason's+Nature+-+Role+of+Mathematics+G-Nickel+Madrid.pdf.

Peat, D. (1990). Mathematics and the language of nature. Retrieved from http://www.fdavidpeat.com/bibliography/essays/maths.htm

Postman, N. (1992). Technopoly: The surrender of culture to technology. New York: Vintage Books.

Uhl, T. (2008). Evolution of Number Systems. Retrieved from education.uncc.edu/cmste/summer/newcourse9.htm

Weissman, J. (1995). A Brief History of Clocks: From Thales to Ptolemy. Retrieved from 1995http://www.google.com/search?q=A+Brief+History+of+Clocks%3A+From+Thales+to+Ptolemy&rls=com.microsoft:en-us:IE-SearchBox&ie=UTF-8&oe=UTF-8&sourceid=ie7&rlz=1I7SUNA_en

Zerzan, J. (2009). Number: Its Origin and Evolution. Retrieved from http://www.primitivism.com/number.htm