Page 88 - J. C. Turner "History and Science of Knots"

78 History and Science of Knots

the other groups, the second the sum of those in the second position and so
on (see Fig. 5).
We can assume that the whole quipu was completed before the knots were
tied into it, because several quipus without any knot were found, and all the
knotted single cords that were found were obviously broken.
The Number System
The Incas used a base-ten positional system. Hence they had developed in-
dependently the same number system that we use today. The digits were
represented by clusters of one to nine single overhand knots, and the positions
were separated by spacing. The clusters closer to the main cord represented
the higher positions, while the unit position was close to the end. The digits
in the unit position were represented by special knots, namely by multiple
overhand knots whose number of turns indicated the digit (see Fig. 3). They
are referred to as `long knots'. As an overhand knot with only one turn is the
same as the simple overhand knot used for the other positions, a 1 in the unit
position was represented by a figure eight knot. Using different knots for the
unit position allowed the placing of several numbers on one cord without am-
biguity in where one number ends and the next one begins. Several numbers
on one cord were actually found on ancient specimens.
354

x
x
X
x
x
X x = single overhand knot
(- = multiple overhand knot
x 8 = figure eight knot

Fig. 6. Example of Numbers and Sum Recording

There are two ways to pull a long knot tight. Either hold the knot in one
hand and pull the end which in Fig. 3 points upward with the other hand;
then the belly of the knot stays straight. Or pull both ends, then the belly
will curl around the spine, and the windings that are counted to determine
which number the knot denotes are in fact the windings of the belly. Knots