Page 82 - J. C. Turner "History and Science of Knots"

72 History and Science of Knots
`One knot-one object' Systems

In the most simple systems which use knots to denote numbers, one knot,
for example a simple overhand knot, corresponds to one object. To denote
the number `two', two knots are tied next to each other, and so on. One of
the most widely known examples where this system is used is the mariner's
logline, a device for measuring the speed of a ship. It consists of a rope with
a piece of wood, called the chip, tied to its end. The chip is thrown overboard
and stays more or less stationary in the water. As the ship moves ahead, the
rope runs out astern. It is divided into lengths of 15 m, marked by pieces of
string which are inserted between the strands of the rope. The strings carry
as many overhand knots as there are lengths between the string and the chip.
The number of lengths that run out astern in 28 seconds is the speed of the
ship in nautical miles an hour, or `knots' (see [9], p. 14).
Another example is the rosary of the Greek Orthodox monks of Mount
Athos, where knots instead of beads are used in order to count the prayers
([9], p. 14). There are many more examples, as this simple system has been
invented many times independently.

The Zuni System
The Zuni of New Mexico used a base-ten positional system, which allowed
them to denote high numbers without tying many knots. It worked much like
the Roman system. There were distinct knots for one, five, and ten. Two
`one'- knots meant `two', three 'one'-knots `three'. A 'one'-knot above a 'five'-
knot had to be subtracted, hence both together meant `four'. If the 'one'-knot
was under the `five'-knot, it had to be added, giving `six' (see Fig. 1, and [7]).

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IV VI IX XI

Fig. 1. Zuni Knots (adapted from [7], p. 301)