The only abacus most of us have ever seen is the plastic toy with colored
beads hanging on a baby's playpen or crib. We push the beads back and forth,
cooing to the baby, and scarcely imagine that for centuries the abacus
was our primary medium of calculation. Though superseded long ago by written
notation with Arabic numerals and, more recently, by the ubiquitous pocket
calculator, the abacus had a long and illustrious career in the evolution
of computing. Indeed, electronic calculators and digital computers would
not have been possible without their humble ancestor. But the role of the
abacus in the development of sophisticated computing tools is only its
most obvious cultural legacy. There are other more subtle ways in which
the abacus has touched societies throughout the ages.
In this paper, I explore some of the ramifications of the abacus which
still reverberate in contemporary culture. First, I will discuss several
characteristics of the physical form of the abacus which have political,
social, and economic implications. Second, I will consider certain features
of the symbolic form in which information is coded on the abacus, features
which have intellectual, emotional, and epistemological implications.
Let's start with the physical form of the abacus. Though there have been
various incarnations at different times and in different places, all forms
of the abacus share a common operating principle, which is this. Small,
identical units called counters are assigned numerical value based on their
position or arrangement, and calculations are performed by physically manipulating
the counters. The counters might be pebbles, shells, metal pieces or beads;
they might be arranged on sand, boards, cloths or tables, or they might
be attached to rods or wires in a frame (Kojima 1954, pp. 22-25;
Menninger 1969, pp. 299-303,307-315; Moon 1971,
pp.
21-24, 30-32). The different physical versions of this
general abacus principle can be divided into two basic types. I call the
first type the closed or bead abacus, and the second type, the open or
line abacus.
The closed or bead abacus is one in which the set of counters is limited
because the counters are fixed or bound in a frame. All the components
are integrated into a compact, self-contained unit. It is the bead abacus
with which we are most familiar since this is the type which survives even
today. The advantages of the bead abacus are that it is small, light, portable,
inexpensive, and simple to operate, making it especially suitable for use
by average individuals (Kojima 1954, pp. 18-19; Menninger
1969, p. 313). The disadvantage of the bead abacus is that
it has a predetermined, finite number of counters and locations to place
them. Therefore, it works best for rudimentary calculations like addition
and subtraction (Kojima 1954, p. 19; Menninger 1969, p.
306). The bead abacus is still used in the Orient for business and
education, but in the West it is generally seen merely as a toy.
An open or line abacus, on the other hand, has two separate components:
the surface on which counters are placed and the loose, unattached counters
which are stored separately. Lines or grooves on the abacus surface indicate
the potential locations for placing counters. The advantage of the line
abacus is that it has a theoretically unlimited stock of counters as well
as extra space in which to lay them out (Moon 1971,
p. 30).
This results in greater flexibility and scope: more numbers can be represented
simultaneously, thus allowing more complex calculations to be performed
(Menninger 1969, pp. 350-351). But some variants of the line
abacus have a disadvantage: lack of portability. While modest counting
boards and small bags of counters can be carted around with relative ease,
massive tables with drawers full of counters certainly cannot. There is
another disadvantage to elaborate forms of the line abacus, such as counting
tables with multiple sets of embossed metal counters. They require certain
investments: in materials and workmanship, in the space needed to house
the apparatus, and in the number of people and the amount of time involved
in abacus production, training, operation, and maintenance. Investments
such as these make the line abacus especially compatible with commercial
organizations and bureaucratic institutions, and far less suited to individual
users. Nowadays, however, the line abacus is no longer in use. It was never
popular in the Orient, and though it reigned supreme in the West from the
Middle Ages until the end of the 16th century, it was eclipsed altogether
by the written calculations with which it coexisted for a time (Menninger
1969,
pp. 340-367, 375-388; Moon 1971, p.
24).
Whether closed or open, bead-based or line-based, the physical form of
the abacus has political implications. The abacus appeals to our sense
of sight, but more importantly, it appeals to our sense of touch. The abacus
is a manual tool with which people literally handle numbers, and this concept
of manipulation should not be underestimated (Bolter 1984, p. 235).
Lurking beneath the physical form of the abacus is the idea that the ability
to touch and manipulate information brings control over it. And control
over information means power, as the alphabet, the printing press, and
electronic technologies also demonstrate. By furthering our ability to
manipulate numbers in particular, the abacus stimulates our desire to manipulate
information in general, in both cases to achieve power.
But the bead abacus and the line abacus bestow political power on opposite
ends of the spectrum: to individuals, on the one hand, and to institutions,
on the other. The bead abacus is highly suited to the individual due to
its simple composition, easy operation, and wonderful portability. Because
of this, the bead abacus is quite democratic, a tool for the masses, for
the poor as well as the rich, for the illiterate peasant as well as the
itinerant merchant. The line abacus, however, is not. The investments demanded
by the elaborate counting tables of post-Renaissance Europe were well beyond
the scope of average individuals, and could only be managed by wealthy
aristocrats or by institutions. In fact, the close association between
the line abacus and bureaucracy is revealed in the etymology of the very
term "bureaucracy." The French word "bureau" first meant the cloth for
covering a counting table, then the table itself, then the room in which
the table was kept, and finally, the office and staff that ran the whole
counting house (Menninger 1969, pp. 346-347). This notion
of large abacus-based organizations devoted to calculation is also reflected
in our modern words "bank," "banker" and "banking," which come from the
German "Rechenbank" meaning reckoning board or table (Menninger 1969, p.
349). The line abacus favored the institution over the individual
for a long time. Nevertheless, there remained an undercurrent of computing
by private individuals. This tension between corporate computing and personal
computing is still alive today, though the advent of affordable microcomputers
will surely help even the score.
No matter who uses what kind of abacus, the issue of skill inevitably arises,
and it is here that the physical form of the abacus has social implications.
While the abacus extends our ability to perform complex calculations more
quickly and more accurately than we could without it, it does not calculate
automatically. The effectiveness of the abacus depends entirely on the
mental and manual skills of its human operator. And these skills are considerable,
involving a command of the basic mental arithmetic on which the abacus
relies, as well as practice to master its fundamental operating principles
and to acquire manual dexterity (Kojima 1954, pp. 19, 21;
Menninger 1969, pp. 308-309). In short, an abacus is no good
at all without someone who knows how to use it. This is why proficient
abacus operators are often held in high esteem, with abacus expertise conferring
social prestige.
The abacus, then, advances the view that computation, indeed all manipulation
of information, demands specialized training and practical experience.
As the first manual tool for computing to require a trained operator, the
abacus contributed to the drive towards professional specialization also
heralded by orators, scribes, and printers. Without the prior example of
the skilled abacus operator, perhaps there would be no accountants or computer
programmers today. The abacus shows us that calculating machines do not
work by themselves: someone must judge which numbers to combine and how,
and what to do with the results. One might say that the abacus supplied
an early hint of the maxim, "Garbage in, garbage out." In other words,
sheer possession of a technology alone does not guarantee its effective
use, because human competence is not built into the technology itself.
The abacus clearly illustrates that human participation is intrinsic to
computing. Despite all attempts to automate processing in order to reduce
both labor and error, the need for humans to program, operate, and supervise
computers endures up to the present.
The physical form of the abacus also has economic implications associated
with quantity and time. Since the abacus made possible a greater volume
of calculations, and since these calculations were fundamentally ephemeral,
people increasingly needed to keep records. There simply was a lot more
information to save, and the abacus couldn't save any of it (Kojima 1954,
p.
19). Two essential ingredients of our economic system, bookkeeping
in particular and recordkeeping in general, are ideas promoted by the abacus.
The abacus urges us to save numbers and calculations for future reference,
a suggestion which was taken up by its many successors. In written place-value
notation, in the 18th-century calculating machines of Charles Babbage and
Georg Scheutz, and in early 20th-century punch-card and paper-tape calculators,
we see evidence of our desire to combine calculation and recording in a
single technology (Aiken 1975, p. 192; Aiken and Hopper 1975,
p.
200; Bolter 1984, p. 161; Hyman 1982; Merzbach 1977).
Present-day computer networks with gigantic storage devices are the culmination
of this quest. If the abacus had not so blatantly emphasized the need for
storing information as well as manipulating it, perhaps the two functions
of calculating and recording would have remained independent until now.
These, then, are some of the political, social, and economic implications
of the physical form of the abacus. But even more provocative are certain
cultural ramifications of its symbolic form. The symbolic form in which
information is coded on the abacus has intellectual, emotional, and epistemological
implications.
On the intellectual level, the abacus teaches us to code information by
assigning meaning to elements exclusively on the basis of their position.
The abacus thus embodies the notion that infinitely large and infinitely
many numbers can be represented in a place-value system with a limited
array of counters. The counters and columns of the abacus are echoed today
by the binary word, made up of linear sequences of zeros and ones. The
binary word, which is a landmark intellectual development and the key to
digital computing, is undoubtedly a descendant of the abacus.
Modern digital computers use electronic technology to mimic the abacus.
The counters with which they represent all of their data are pulses of
electric current, with two extremely simple values -- on or off. Like the
counters of an abacus, these same values are used over and over again to
form binary words ad infinitum, exemplifying a truly conserving and recycling
mentality (Bolter 1984, pp. 226-227). Nonetheless, we pay
a price for such efficiency. Binary code is so abstract a medium that most
people require intervening layers of more comprehensible symbols to insulate
them from the starkness of digitally-coded information. This kind of symbolic
insulation is provided by computer languages such as Assembler, Fortran,
or Pascal, and also by the software applications programmed in these languages
(Bolter 1984, pp. 124-150). But artificial languages have
radically different properties than natural languages, and we are still
trying desperately to improve the interface between the two. Meanwhile,
our intellectual craving to communicate with the technologies we create
remains unsatisfied. This continues a trend initiated by the abacus, that
is, close interaction between humans and their calculating machines.
The symbolic form of the abacus also has emotional implications. They stem
from the fact that the abacus makes numbers tangible: it transforms them
into concrete entities that can be touched and felt. In short, the abacus
reifies numbers, and this leads in two opposite directions. On the one
hand, the abacus trivializes numbers; on the other, it elevates their status
in our eyes. Though at first glance these effects may seem incompatible
or contradictory, they are actually interrelated.
Many ancient civilizations traditionally revered numbers: numbers were
held in awe and were often linked to magic and religion. But once the abacus
put numbers under our thumbs on a daily basis, they began to lose their
aura of mystery. We lost our reverence and respect for their special abstract
qualities. We started to take numbers for granted and to think of them
as lowly servants to do our bidding. In the process, we also surrendered
some of our wonder, our sense of the infinite, of the inconceivable.
However, at the same time, we started to attribute great value to numbers,
perhaps because they became so useful. Although much of their power has
been transferred to the people and machines that manipulate them, we continue
to impart mystical properties to numbers. This might explain why many Westerners
think that everything can be understood in terms of numbers, venerating
statistics in particular and quantification in general. Lest we forget
that numbers mean nothing without human interpretation, the abacus stands
ready to remind us that numbers are, in fact, subordinate to the humans
who control them and subject to the quality of their interpretations.
There is one more point I would like to make, and it concerns the epistemological
implications of the symbolic form of the abacus. Just as writing can be
said to contain speech, and printing to contain writing, the abacus contains
numbers. By reducing numbers to ordered arrangements of identical elements,
the abacus is able to represent the entire numerical universe. This concept
of representing things through place-value coding encouraged two further
developments. First, it seems fair to suggest that the development of Morse
code relied at least in part on the example furnished by the abacus. By
using a place-value system with three simple values -- short, long, and
neither (that is, dots, dashes, and silence) -- Morse code can represent
almost all verbal discourse, a noteworthy accomplishment.
Second, and much more significant, is the development of binary computer
code. Binary code strips the set of coding elements down to the bare minimum,
absolutely the simplest imaginable: a single bead or no bead, presence
or absence, something or nothing, one or zero. With this binary technique,
digital computers are now on the verge of representing more of reality
than we ever dreamed. By this I mean that modern computers are capable
of condensing all kinds of information into digital code, not just numbers
(like the abacus) and language (like writing, printing, and Morse code),
but even images (like photography, film, and video), as well as sound (like
speech and music).
This capacity to express practically anything and everything in binary
digits, in electronic "super-beads" so to speak, is only beginning to be
explored. Proponents of what is often called "virtual reality" believe
that someday computers will use binary code to approximate and even duplicate
entire chunks of reality, including human thought and behavior. Perhaps
we will come to know our world and ourselves through simulation rather
than through direct participation, through symbol systems instead of actual
experience. It remains to be seen where this path will lead and what kinds
of cultural effects will follow. But whatever the outcome, the journey
will have begun with the humble abacus, ancestor of such extraordinary
possibilities.
References
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Randell (Ed.), The Origins of Digital Computers: Selected
Papers, pp. 191-197. New York: Springer-Verlag.
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Aiken, Howard and Hopper, Grace M. (1975). "The Automatic Sequence Controlled
Calculator
-- I." In Brian Randell (Ed.), The Origins
of Digital Computers: Selected Papers, pp. 199-206. New
York: Springer-Verlag.
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Bolter, J. David. (1984). Turing's Man: Western Culture in the Computer
Age. Chapel Hill: The University of North Carolina
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Hyman, Anthony. (1982). Charles Babbage: Pioneer of the Computer.
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Kojima, Takashi. (1954). The Japanese Abacus: Its Use and
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Moon, Parry. 1971. The Abacus: Its History;
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