# Abacus

## Contents

## A Brief Historical Sketch on the Abacus

From a historical point of view, human beings have evolved for many reasons. In thise sense, all materials in our daily life are easily adapted by those who are good at applying brand new technologies. Mathematics is no exception to these undeniable rules. Before accepting these rules, we might have been able to calculate simple things - which included adding, subtracting, multiplying and dividing to a certain level - in our head. Beyon the Point, we are still working on a certain level of simple calculation. Even though we could easily have done the calculation in our head, we certainly could not have done it as accurately or as quickly. For some reason, we try to get the correct answer by doing less work. “Nothing could be further from the truth. The Abacus is at once one of the oldest, most enduring, and efficient products of the human mind. The Abacus has served mankind well, aiding him in commerce and invention. It is likely that the abacus was developed independently at different times in different civilizations; The Peruvian Indians, for instance, used a form of abacus for rapid calculation even before the arrival of the white man. The results of computation were recorded by knots tied in a cord.” (Haga, 1964:398) According to the Mathematical Association, a brief history of the abacus is as follows. “The principles of Abacus arithmetic were first developed in the Middle East over 5000 years ago by the Sumerian civilization. This civilization was probably the first to develop the subject of mathematics and their sexagesimal number system which is based on 60 is still with us in the way that we measure angles and time” (The Mathematical Association, 1981:2-3)

Through this practice, we could simply get a correct answer through our own cognitions. “In its earliest form the Abacus was probably a sand table with pebbles being used as counters. From this form it evolved to its modern design with beads moving on rods. This version dates from the Greek and Roman civilizations. The Abacus in its various forms continued to be used in Western Europe until the Middle Ages.” (The Mathematical Association, 1981:2-3) In this sense, we may also need to get a sort of advanced tools to aid our insufficient analytical system. Moreover, we take it for granted that we can easily add, subtract, multiply and divide numbers. Today is difficult to find people who use the Abacus for any reason. Especially, it would be difficult to find any institutions who would teach and learn the Abacus. It seems like the heyday of the Abacus was around 1960~1990, before being the computerization of society. Why was the abacus so popular at that time? We are already getting sick of the answer to this question: to provide efficiency at certain levels of calculation.Even if the spread of the abacus was focused on Asian cultures, it is not completely. According to Haga(1964:398) “At one time the abacus was used in American schools to teach addition and subtraction. It has much to recommend it; it is pretty much cheap, fast, efficient, and versatile.” Furthermore, “one school in California, the abacus was introduced in all second and third grade classes as part of a project to improve speed and accuracy in the handling of numbers.” (Haga, 1964:398)

As we could easily assume, we do not think of the Abacus as a technology to improve speed and accuracy in the handling of numbers. It was just one of the many historical tools for numerical analysis.

## How it works

### Tell me about Abacus: How to use it?

The Abacus consists of five to seven beads on each row. “Two of the beads are above the bar (upper beads) and five are below the bar (lower beads). The upper beads are worth “5” and the lower beads are worth “1”. Each row represents a decimal place. The right-hand row shows 1s (1 to 9) the second row 10s (10 to 90) and so on. To show a number beads are placed against the bar. “(Maxwell, 1981:3) Unlikely the Chinese Abacus, “the Japanese Abacus has only 1 upper and 4 lowers beads.” (Maxwell, 1981:3)

It is because these two beads -- which are located in the most top and bottom -- are not needed at all in terms of the double meaning. Even if the abacus is used to calculate numbers, it is carried out in a series of calculations in terms of “addition and subtraction, simple and long multiplication, and simple and long division, and finding square and cube roots.” (Maxwell, 1981:3)For instructions on how to calculate using the abacus -- see the article [1].

## Remediation

### Technically Speaking on the Abacus

In an information era, we do not need to take notes or memorize advanced rules,since we can use advanced technologies that provide “efficiency and accuracy”. Experts on the abacus know how to encode each number and could easily get the result as well as we could on a modern calculator.There are some limitations regarding the abacus. It cannot calculate every single number. As we already recognized,the Abacus cannot address unlimited nature of numbers. Even if the abacus has been used such an efficient calculator, it is not good enough to use it today.

Even professional specialist working with numbers;may not need to purchase a calculator today.Even more advanced tecehnolgies, like Excel and other programs, have calculating systems embedded.### Digital vs. Analog: To Cybernerd

When we work in analog, we must work on with certain level of commitment and performance to get the results. After going Digital, we may just be a "cybernerd."Even if we have to solve a complicated calculation, we do not need to follow rules on the Abacus. It is easy to just 'click' it and there are no more complicated rules. In this sense,going digital means the part of the process that must be perfomed by the user is becoming less and less than before.

According to Buck-Morss (1989:5), “Benjamin took seriously the debris of mass culture as the source of philosophical truth”(5). “For Benjamin the various remains of nineteenth century culture –buildings, technologies and commodities, but also illustrations and literary texts – served as inscriptions that could lead us to understand in ways in which a culture perceived itself and conceptualized the “Deeper” ideological layers of its construction. As Tom Gunning puts it, “If Benjamin’s method is fully understood, technology can reveal the dream world of society as much as its pragmatic rationalization.” (Huhtamo, 1997:221)

For those who do formal research on history,they cannot dwell on history itself anymore. “In this sense, history belongs to the present as much as it belongs to the past. It cannot claim an objective status it can only become conscious of its ambiguous role as a mediator and a “meaning processor” operating between the present and the past. “(Huhtamo, 1997:221)

## Historical "Arbitrary"

### Between “Obvious” and “Arbitrary”: What is a biased on the Abacus?

Especially, it is obviously good for right-handed people. (See how to multiply on abacus as below)

“…to multiply one need to know ones multiplication tables and how to add on the Abacus. Simple multiplication is fairly straightforward. One puts the multiplier on the left-hand row to remind one what it is and puts the multiplicand on the right-hand side of the Abacus, leaving the right-hand row clear. Then multiply the right-hand digit of the multiplicand.Remove this digit and place the product on the right-hand row that you have left clear.Multiply the next digit of the multiplicand.”(Maxwell,1981:4)

And also in a certain sense, most Asian cultures which have used the Abacus did not much care about left-handed people. What if some little child was left-handed, it is considered an unusual behaviors to fix. In this sense, it is a kind of design convention resulting from the prevalent tendencies of the historical situation. In a common belief in technology, we easily accept technology as a significant force in society. “Referred to as “technological determinism”, this belief affirms that changes in technology exert a greater influence on societies and their processes than any other force.” (Smith, 1994:2) In other words, some sort of “technological determinism” alters the way of thinking within human beings. That paradigm affects the invention of the abacus which is biased for right-handed people.

### The Pedagogical action: The “Arbitrary” Effect

Based upon the idea of “Obvious”, Moore (2004) writes which is a quite reasonable statement below:

“By designating the cultural as arbitrary, Bourdieu reverses the normal perception of things, which is that the sacred objects of high culture are such because of some quality intrinsic to them. From this essentialist point of view they deserve their place and their veneration because of something about them that is ‘real’ – they really are beautiful in the way that knowledge is really true. This, in fact, Bourdieu argues, is an illusion. In truth, the field of culture is arbitrary in that its positions, and the objects that mark them, have no intrinsic justifications or qualities.” (Moore, 2004:447)

Moreover, Bourdieu and Passeron (1977:5) assert “All pedagogic action is, objectively, symbolic violence insofar as it is the imposition of a cultural arbitrary by an arbitrary power.” With the heyday of the Abacus, we could assert all pedagogic action -- related with making an expert which is good at calculating on the Abacus -– contains entirely motivated and explainable traits unlike “cultural arbitrary”

## Number Representation

### Meanings of Skill: Cognitive development Vs. Competition

If you want to be an expert on the Abacus, you need to be well-trained. According to previous research, “a general orientation toward the study of skills and their development is outlined, in which analyses of representation, transfer, and context are used to explore the consequences of developing a specific skill. This general approach is then applied to the study of abacus training and its implications for school achievement and cognitive development.” (Stigler, Chalip and Miller, 1986: 447) There is no exception to the Abacus as well. To develop these skills, there is no way to publicize the abacus as much as possible at the governmental level. (see a picture as below)

“Indeed, in Japan, where abacus lessons are mandatory for third and fourth grades of the primary school, a skilled student can add and subtract faster than by press the buttons, the light wooden beads have been skillfully flicked to give the answer. To gain high skill in the use of the abacus, Japanese children attend private schools and take nationally organized examination” (The Mathematical Association, 1975:18) Even though, slementary schools in Japan have a mandatory course just for the Abacus, it is not good enough for making abacus experts.

Some students who pursue additional training attend after school classes as private lessons. As we get a sense of the competition, “Children who pursue this additional abacus training use their skill primarily for competition, both national and international.”(Stigler, Chalip and Miller: 1986:448)

According to Spitzer (1942:450-451), there are absolutely significant characteristics related to the representation of quantities on the abacus.

- “The markers (beads) can be used to represent various concrete objects – to aid the children secure an understanding of these efficient abstract uses of number.”
- “The value of a number depends on its position – “consider how much more easily position can be explained on abacus.”
- “Closely associated with the ideas discussed in the preceding paragraphs is the abacus can be used to illustrate, namely, the idea of a place-holder or the function of zero.”
- “The number system illustrated by the abacus is the idea of collection.”
- “The use of the abacus is teaching is to illustrate the true nature of carrying and borrowing.”

Even if the Abacus itself is significant to develop cognitive systems, it is not good enough as times go by. As technologies show us what efficiency is.

## Conclusion

### Where do media go to die?

“In this sense, I would like to review Michel Foucault’s determination “to substitute for the enigmatic treasure of ‘things’ anterior to discourse, the regular formation of objects that emerge only in discourse.” (Foucault, 1982:47) Furthermore, Huhtamo(1997:222-223) also asserts “these ‘discursive object’ can, with reasonable purpose, claim a central place in the study of the history of media culture.” and then “Kittler traces the gradual shift form one discursive system to another, drawing on a great variety of inscriptions.” Moreover, “Registering false starts, seemingly ephemeral phenomena and anecdotes about media can sometimes be more revealing than tracing the facts of machines that were patented, industrially fabricated and widely distributed in the society – let alone the lives of their creators – if focus is on the meanings that emerge through the social practices related to the use of technology.” (Hugtamo, 1997:223)

Especially, Marvin asserts “Media are not fixed object: they have no natural edges. There are constructed complexes of habits, beliefs, and procedures embedded in elaborate cultural codes of communication. The history of media is never more or less than the history of their uses, which always lead us away from them to the social practices and conflicts they illuminate.” (Marvin, 1988:8)

To better explain what I have, we could assert the abacus is not used anymore, and also it seems like almost dead and we do not see a variety of remediated ones. Weinberg (1991:43) asserts as below:

“Technology has expanded our productive capacity to greatly that even though our distribution is still inefficient, and unfair by Marxian perspective, there is more than enough to go around. Technology has provided a “fix” – greatly expanded production of goods – which enables our capitalistic society to achieve many of the aims of the Marxist social engineer without going through the social revolution Marx viewed as inevitable.”

Through this Weinberg’s argument, “technology has provided a “fix.” (Weinberg, 1991:43) Technology lets us have efficiency and accuracy without work being performed by the user. But it is too optimistic to overview what technologies have done until now. We should consider what representational characteristic practices are still used and apply to brand new artifacts that satisfy many of users. In the case of the abacus, we needed to work on encodding and decoding to get the result as possible, yet remediated forms of calculations may no longer have an encoding and decoding process. For some reasons, the transparency may no longer be available on calculators these days, yet it must be definitely a well-organized black box. The whole process of remediation lets us have a survived medium in media ecology without any special encoding/decoding efforts by users.

## Works Cited

- Bourdieu,P.and Passeron,J.-C.
*Reproduction in education, society and culture*,London, Sage.1977,p.5.

- Buck-Morss, Susan. The Dialectics of Seeing:Walter Benjamin and the Arcades Project, Cambridge, MA: MIT Press, 1989, p.ⅸ

- Foucault, Michel.
*The Archaeology of Knowledge*, A.M. Sheridan Smith, trans. (London, Tavistock, 1982) p. 47.

- Haga,Enoch J. Don't write off the Abacus, The Clearing House, 38(7), 1964,p.398.

- Huhtamo, Erkki.
*From Kaleidoscomaniac to Cybernerd: Notes towards an Archaeology of the Media*,THE MIT Press, 30(3), 1997. 221-224.

- Marvin, Carolyn.
*When old technologies were new: thinking about Electric Communication in the Late Nineteenth Century*,New York and Oxford; Oxford Univ. Press, 1988, p8.

- Maxwell,R.Perveval.The Chinese Abacus,
*Mathematics in School*, 10(1),1981,2-5.

- Miller,Kevin F. Stigler, James W.Meanings of Skill:Effects of Abacus Expertise on Number Representation,
*Congnition and Instruction*, 8(1), 1991,29-67

- Moore, Rob. Cultural Capital:Objective Probability and the Cultural Arbitrary,
*British Journal of Sociology of Education*, 25(4),2004,445-456

- Smith, Merritt Roe, and Marx, Leo.
*Does Technology Drive History? The Dilemma of Technological Determinism*, The MIT Press,1-35.

- Spitzer,Herbert F. The Abacus in the Teaching of Arithmetic,
*The Elementary School Journal*,42(6),1942,448-451.

- Stigler,James W. Chalip, Laurence, and Miller, Kelvin F. Consequences of Skill:The case of Abacus Training in Taiwan,
*American Journal of Education*. 94(4), 1896,447-479

- The Mathematical Association. The Abacus Today,
*Mathematics in School*, 4(5),1975,18-19.

- Weinberg, Alvin M.
*Can Technology Replace Social Engineering?,Controlloing Technology:Contemporary Issues*,1991,286-290.