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 Though superseded long ago by written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.
I would like to explore with you today 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 intellectual
implications of the symbolic form of the abacus.
Let's start with physical form. 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, on boards, on cloths or on tables, or they might be
attached to rods or wires in a frame. 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. 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. The bead abacus is still used nowadays in the East 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. This results in greater flexibility
and scope: more numbers can be represented simultaneously, thus allowing
more complex calculations to be performed. 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: 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 East, and though it reigned supreme in the West from the
Middle Ages until the 16th century, it was eclipsed altogether by the written
calculations with which it coexisted for a time.
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. 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. 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. 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. In short, an abacus is no good at all
without someone who knows how to use it. This is why proficient abacus
operators have often been 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 and supervise computers
continues 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. 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.
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 there are also some provocative
implications stemming from the symbolic form in which information is coded
on the abacus, and these implications are intellectual.
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. Whenever 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 human interpretation.
The last idea I would like to discuss also concerns the symbolic form of
the abacus. The abacus teaches us to code information by assigning meaning
to elements exclusively on the basis of their position. 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 intellectual 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 (as in photography, film, and video), as well as sound
(as in 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 change will follow. But whatever the outcome, the journey will
have begun with the humble abacus, ancient ancestor of such extraordinary
possibilities. Thank you.
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