My Personal History of Abacus: From Physical to Mental

I’d like to talk about abacus—an ancient cognitive artifact that is still widely used in China. I began learning abacus to do arithmetic since I was six and interestingly, as time went on, there emerged a virtual abacus in my mind every time I need to calculate, which directly manifests the ideal-material-duality of artifacts mentioned by John Dewey, Marx, and Hegel[i].

1. Abacus as a Cognitive Artifact

According to Donald A. Norman, “a cognitive artifact is an artificial device designed to maintain, display, or operate upon information in order to serve a representational function[ii].” I will discuss how abaci fit in this definition.

The function of abaci is to do elementary arithmetic, specifically, using beads and their dynamic spatial relationships to represent numbers and their logic relationships. I used to play a 1/4 abacus that was suited to decimal calculation. It consisted of a wooden frame with beads sliding on vertical rods. Each rod was divided into two parts by a horizontal bar, above which each of the beads represents the number of five, while the lower beads represent ones.

The structure of an abacus. Source:

The structure of an abacus. Source:

An abacus could maintain and display information. As long as it stays undisturbed, the number represented by it will be recognized by anyone who knows the rules, even though he/she might not know what the number represents, say, the quantity of cows or the revenue of a pawnshop. Even if the positions of beads are disturbed—they are really apt to be messed up—it still maintains and displays the information of the initial state plus the action of disturbance.

Moreover, abaci could be used to operate information. Sets of rules must be learned in order to do that. For example, adding seven to a place involves following rules:

  • If the place you want to add seven has less than three lower beads in up position, then move other two lower beads to up position, and then:
    • If the upper bead is in its default state, i.e. the up position, then, move it to the low position;
    • If the upper bead is already in low position, move it to up position, and add one to the left place;
  • If the place you want to add seven has at least three lower beads in up position, then move three of them to low position, and add one to the left place.

Sounds tricky. A table of pithy formula, however, is used for memorizing the rules, in which, the entry for adding seven is simply “七去三进一,七上二去五进一”. Thus, playing abacus achieves two things:

  • From a system view, abacus offloads people’s cognitive efforts, which are limited in multi-digit and long serial calculation by unaided brain capacities, and ultimately enhances the aggregated system performance.
  • From an individual view, the initial tasks are changed, replaced by a serial of more physical new tasks as follows:
    • remembering the pithy formula (a process called precomputation by Edwin Hutchins);
    • moving the beads accordingly;
    • and translating the final state of beads into numbers.

2. Distributed Cognition of Abacus

Abacus has a long history in China, dating back to 2nd century BC. The shape, configuration, and formula have also evolved a long period to form the modern state. There are many stories, arts, and even music around the theme of abaci. For example, in the long scroll of Along the River During the Qingming Festival painted by Zhang Zeduan during Song dynasty, an abacus appeared on the counter of a medicine store[iii], as shown in the red circle below. Abacus has become a symbol for accounting in China and part of their cognitive process. Actually, in the absence of electronic calculator, learning abacus is an essential part in accountant training programs decades ago.

An abacus in Along the River During the Qingming Festival painted by Zhang Zeduan

An abacus in Along the River During the Qingming Festival painted by Zhang Zeduan

So, from a distributed cognition perspective, the cognitive processes involved in abacus do not only exist in individuals’ mind, but also distribute across social groups, through time, and in its unique culture.

3. My Mental Abacus

As Hollan, Hutchins and Kirsh mentioned in their Distributed Cognition: Toward a New Foundation for Human-computer Interaction Research, distribution of cognitive process may involve coordination between internal and external structure [iv]. This reminds me of my mental abacus, an interesting experience that internalizes external artifact.

I don’t know what cognitive processes are going on in other people’s heads when they are calculating mentally, but for me, there exists a mental abacus in my mind, maybe due to heavy exposure to abacus training when I was little. That is to say, when I calculate, a vivid, three-dimensional image of abacus emerges in my head, with all the beads in their default positions. Then, I calculate by using a virtual hand to move the virtual beads according to the pithy formula and physical laws and then translate the final virtual beads position into numbers. The image can be enhanced by simultaneous actual hand movements. What is more strange is that sometimes, I even think my finger could feel the texture of the virtual beads—plastic, white, light-weighted, smooth, and cool like marble, attributes that may be associated with the forming of mental abacus and of which the specific neural circuits are retrieved by the emergence of mental abacus.

What is similar to the US Navy ships experiment by Hutchins is that, the cognitive processes required for a task are different from those processes actually used in the task, and just like the navigators who feel bearing as a direction in space relative to the position of their body instead of numbers [iv], this cross-modal representation is easy to go wrong. If the numbers are too long, then my mental abacus is easy to get fuzzy.

Nevertheless, I always wonder, what if I build a mental slide rule, can I calculate logarithmically?

4. Question

At last, I want to discuss a question. In his Cognitive Artifacts Chapter in Designing Interaction, Norman insisted that artifact could not change individual’s capacities. Rather, it just changes the nature of task performed by the person, in turn, extends the cognitive capacities of the whole system. I think, however, it contradicts with the co-evolution theory of language and brain in Terrence W. Deacon’s The Symbolic Species[v].

According to Cole, language is a cognitive artifact, just like hammers and tables[i]. Meanwhile, from his interdisciplinary study, Deacon stressed the importance of co-evolution of the human brain with language and symbolic cognition that then enabled human culture and technologies. This implied that artifacts do enhance individual’s capacities, both cognitively and physiologically—maybe through rewiring some vital neural circuits, otherwise, co-evolution would not have happened.


[i] Cole, Michael. 1996. “On Cognitive Artifacts.” In Cultural Psychology: A Once and Future Discipline. Cambridge, Massachusetts: Harvard University Press.

[ii] Norman, Donald A. 1991. “Cognitive Artifacts.” In Designing Interaction, 17–23. New York: Cambridge University Press.

[iii] Zhou, Raymond. 2014. “Honor the Past, Live in the Present.” China Daily, International Ed., January 4.

[iv] Hollan, James, Edwin Hutchins, and David Kirsh. 2000. “Distributed Cognition: Toward a New Foundation for Human-Computer Interaction Research.” ACM Transactions, Computer-Human Interaction 7 (2): 174–96.

[v] Deacon, Terrence William. 1997. The Symbolic Species: The Co-Evolution of Language and the Brain. 1st ed. New York: W.W. Norton.


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