As mentioned earlier,
primitive people had various ways in which they counted objects.
In many cases, the tools used to keep track of various objects
depended on the availability and ease of use of different
materials. For example, some cultures used collections of
shells while others used tally sticks. No matter what aid
was used for the counting process, the underlying concept was the
same. It was all about making a correspondence between the
objects of interest and the counting aids. What is
interesting about of this type of counting are the different
A very common form of
counting was by using the hand. The hand was an obvious
choice for the use of correspondence counting, or reckoning, as
it is an instantly accessible device. As noted
by Aristotle, the widespread use of counting to ten is not
the result of a calculated choice, but rather the anatomical accident
that most humans are born with ten fingers and ten toes. So
man learned to count using his fingers and perhaps at this stage,
without names for the numbers that he was counting. Nevertheless, this was an effective method of counting that is still used all over the world. Even in schools today, young children
are taught to count on their fingers.
Finger counting was such
an effective method that it was used by some people to count to
numbers greater than ten. For example, there exist certain
South African people that employ the use of three people to
count to numbers larger than one hundred. This is done by
the first person, beginning with the little finger on their left
hand, counting continuously until ten is reached. Then when
the first person reaches ten, the second person raises their left
little finger and the first person starts again. Each time
ten is reached, the second person raises a finger. Similarly,
when one hundred is reached the third person raises their left
little finger and the process continues until the desired number
is reached. Therefore, by using three people, the first
representing units, the second representing tens and the third
representing hundreds, these South African people were able to
count to numbers above one hundred.
Using the body as a counting tool, people
were able to communicate information between tribes. For example, a messenger could be sent to another tribe with the message that they wished to trade 20 baskets of food for 15 pearl necklaces, say. This could have been done by simply
indicating the point on his body that corresponded to the correct
number of objects.
Unfortunately, counting on any part of the
body was not permanent and in many cases permanent records needed
to be kept. So while body counting was extremely useful,
another method would be needed if any type of permanent record were to be
Another type of method of
keeping a record of the number of objects is by having a
collection of smaller objects that can be used to make a
one-to-one correspondence with the objects to be counted. This
method was briefly explained earlier with the example of the
shepherd, his sheep and a collection of pebbles. Keeping a record of the number of objects to be counted is as simple as placing one of the smaller objects in a pile for each of the objects to be counted. In this way, as explained earlier,
there is one smaller object for each of the counted objects.
Now if we were to come back and check our counted objects, all
that is required is to repeat this method. It can be quickly seen if there are any objects missing, as there would be some of the smaller objects left over.
A slight variation on the
example of the shepherd is the following. For each animal
let out of the enclosure, place one pebble in a collection. Then
at the end of the day, remove a pebble for each animal that
returns to the enclosure. This way you quickly see if you
have lost or gained any animals throughout the day.
Many primitive people in
varying ways used this method of keeping tally. Some
cultures used collections of shells, pearls, pebbles, elephant
teeth, sticks, or even coconuts to keep a tally. These were quite useful methods that were employed frequently by early people; however, in some cases it could be quite impractical. If the shepherd had a very large flock of sheep; it would not be very convenient to be carrying around a large, heavy bag of pebbles. So
from this we move to another method of keeping
a tally of objects.
Tally sticks are yet
another way of counting a group of objects. A tally stick consists of a piece of wood, bone or any object in which it is possible to cut small notches. Each notch in the tally stick
corresponds to an object being counted. Primitive man would have used this method of counting to make a record of anything of interest or importance, for example, the number of animals slain by a hunter. Tally sticks were a much more efficient way of keeping track of the number of objects being counted, as one needed to carry around only a small piece of wood or bone. The following picture illustrates some very primitive
tally sticks made from bone.
As tally sticks were an
extremely convenient way of keeping tally, they were still in use
much later in time. However, in some
cases, the tally sticks evolved to become more than just notches cut
into wood and had more varying uses. Not only
could they be used to count a group of objects, but they could
also be used to keep a record of debts or credits owed by a
person, the number of days, weeks, months or years gone by, or
even a mark of ownership.
Tally sticks could also be used to keep a record of credits.
For example, if a baker had given a number of loaves of bread to
a woman over a week and was to settle the account at the end of
the week, then a tally could be kept in the following way. The
baker would have one tally stick and the woman another. When
a loaf of bread was received, the tally sticks would be placed
together and notches would be cut in both, corresponding to the
number of loaves (in the presence of both parties). This
would continue during the week and at the end of the week the
account could be settled without argument. No dispute would
occur as the tally sticks would be placed together and compared.
If the baker tried to add notches it would be obvious and it
would be very difficult for the woman to remove any notches,
therefore there would be no dispute about the account.
We now move on to another
type of counting that involves the use of knotted strings. In
their simplest form, knotted number strings are much the same as
the simple tally sticks. That is, one knot in the string
has the same meaning as one notch in the tally stick. Counting
with the use of knotted strings has been found all over the
world. For example, Tibetan prayer-strings and the rosary
are both simple knotted number strings, which are used to
prescribe the number of religious exercises to be undertaken.
the tally sticks, the knotted number strings gradually evolved into a slightly
more complicated device. Combinations and different types of knots replaced
the simple single knot. Different types of knots carried
different values and the relative positions of the knots on the
string came to denote the order of magnitude of the number.
This can be seen clearly
in the case of the Peruvian quipu, a number string used by
the Incas to record, not only numbers, but also financial
transactions, laws and even history. The following is an
illustration of a Peruvian quipu.
Each string coming from
the main strand at the top contains knots which represent a
particular number. The knots have been grouped together
along the string in such a way that the higher orders of
magnitude are above lower orders of magnitude. That is,
higher orders of magnitude are closer to the main strand.
Knotted strings could be
used to record any number of things such as taxes, wages owed,
calculations and even the weights and types of bagged produce.
In Germany, millers had their own system of knots that were used to inform the bakers of the weight and type of flour in a bag. These knots were tied in the ends of the
strings that were used to seal the bags of flour. The following knots
were used to represent the weights of the bags of flour.
And these knots were used
to identify the types of flour in the bag.
A slight variation on the
knotted number strings is strings of beads. Strings of
beads can most commonly be found used for religious purposes, for
example Christian rosaries. Even
today, many religious persons such as
Muslims, Buddhists and Catholics use prayer beads to help in the
recitation of certain prayers. These strings of beads consist of
the correct number of small beads and in some cases larger or
coloured beads separate these smaller beads as markers. As
recitation begins one moves their fingers over each bead as the
prayers are said until no beads remain. Below we can see a
string of Muslim prayer beads.