Tally Sticks

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.

Knotted Strings

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.

Like 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 toKnotted 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.

 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.

 

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An example of a tally stick that contained numerical symbols, rather than notches, are the Swiss water tallies. These tally sticks showed the amount of time that a particular farming family had water rights to on any given day.

 

 

 

 

This method could be used for more than one customer and in many more situations.  To differentiate between tally sticks, they would be marked with the owner’s mark, or signature.  With the use of an identifying mark, tally sticks could be used for more accounting type purposes.  Even until the 1800’s, tally sticks were in use for taxation purposes.  The illustration to the left is of a Russian ‘tax book’.  Each tally stick in the collection contains a family mark, or signature, the number of family members and the amount of tax to be paid.

 

For example, the number 3,643 would be represented on one of these strands as in the illustration to the left.

Another detail that has been added to these quipus is the use of three different types of knots.  The image aside shows these different knots.  First there was the single knot (illustrated as number 1), then the double or figure-of-eight knot (illustrated as number 2) and finally the slip knots, which could have from 2 to 9 loops (illustrated as number 3 with three loops). However, the double knot and slip knots were used only to represent the units in a representation.

 

 

Possibly a descendant if the quipu was the chimpu of the Bolivian and Peruvian Indians.  The chimpu was a very similar device to the quipu, however, in this case number were represented using more than one string.  The order of magnitude of a group of knots was not only determined by the relative position of the knots on the strings, but also by the number of strings the knots held together.  For example, the number 4,456 would be represented as illustrated to the left.