The Origin of String Figures

We shall show that, given ready access to a loop of string and with sufficient time to experiment, the invention of string figures may well have arisen independently in different areas. In particular we shall demonstrate that the most widely distributed string figures are those most capable of independent invention.

Taking up a loop, a potential string figure artist holds a section between the fingers and ties a simple knot (figs 2 and 3): as if by magic, between the hands, an interesting shape appears (fig. 4). Was this the first string figure? We shall call it the Primordial Moon.

The Primordial Moon has two qualities required for a plausible initial discovery: it was formed without taking up the loop in a standard string figure opening, and without making use of standard string figure manipulations.

But perhaps the first string figure was Crow’s Foot, a string figure which is merely the Primordial Moon pulled into another shape. If the supporting loops of the Primordial Moon are hung on the fingers of the left hand, and if the bottom of the moon is pulled down with the right hand, Crow’s Foot (a figure that may be seen as having four toes) appears (fig. 5).

Crow’s Foot - whether or not seen as the foot of a bird - suggests the possibility of placing a second ‘foot’ at the other end of the loop. The single foot was mechanically constructed: can an alternative mechanical construction provide a symmetric figure with ‘feet’ at both ends?

It is possible, by laying Crow’s Foot on the ground, to study the way in which the foot is formed (fig. 6). The ‘foot’ is partly unravelled (fig. 7).

The other end of the long loop is similarly configured (fig. 8). Feet are then formed at both ends: the result is Crow’s Feet (fig. 9).

The above investigation suggests the following as a means of proceeding directly to Crow’s Feet without first constructing Crow’s Foot. First lay the loop on the ground as in fig. 10.

Pick up the points marked A and B; lay these as in fig. 8; pull them into the position of fig. 9; pick up the near loops with the thumbs; pick up the far loops with the little fingers; extend.

What appear to be deliberate attempts to create a pre-conceived Crow’s Feet string figure have been collected from Central Africa, Sierra Leone, China, Japan, India, Alaska, Peru, Tonga and Britain.

We use the Primordial Moon as an example to illustrate the accumulation of string figure techniques. Merely displaying the figure causes the moon to shrink in size (fig. 11).

A natural enough reaction is to insert fingers into the collapsed moon and enlarge it (fig. 12): releasing the inserted fingers recreates the Primordial Moon. An elementary operation revealed by this action is the releasing of a loop. Further, having obtained the position in fig. 12, an equally natural procedure is to attempt systematically to unravel the figure.

Viewing the figure from above (fig. 13) it is seen that the left thumb (L1) loop may be moved up through the little finger (L5) loop, then set back on the left thumb, giving fig. 14: to the set of revealed elementary operations may now be added the drawing of one loop through another. The loops on the thumbs may be further unravelled by means of a half-twist: giving a twist to a loop thus becomes part of the set of revealed operations.

The untwisting of the thumb loops towards the end of the last section has resulted in a 2-loop opening.

We now take the simple string figure techniques we discovered above and, applying them to the 2-loop Opening, we shall succeed in discovering the following string figure.

1. Form a 2-loop opening (e.g. insert little fingers into the loop; insert the right thumb into the left little finger loop from above and, rotating the left thumb towards you and up, pick up the near left little finger string; insert the left thumb into the right thumb loop from below; extend).
2. Using the other hand, draw each little finger loop up through the thumb loop, and return the loop to the little finger. (Note that the result is equivalent to giving the little finger loops a 360 degree twist towards you.)
3. Using the other hand, draw each thumb loop up through the little finger loop, and return the loop to the thumb. (Or more efficiently: each thumb enters the little loop from below; the index picks up the lower far thumb string; release thumb; thumb removes index loop from below.)
4. The 2-mesh net collapses unless a suitable method of extension is used. A variety of different techniques are used around the world to display the figure on the hands. Here is a simple means of displaying the 2-mesh Net: extend fully; use the right hand to grasp both the far left thumb string and the near left little finger string and pull the strings out a short distance to the right, but don’t extend; repeat on the other side, but don’t extend; hold 1 and 5 against 234 to prevent the strings slipping during the next action; extend gently. Alternatively, if the procedure just described doesn’t work for you, simply lay the figure down and, by spreading out the strings, reveal the 2-mesh Net.

Was this the construction by which the figure was first discovered? Not necessarily. But the final design is potentially lurking only a few moves away from the opening and, in spite of whatever random moves might be made by anyone experimenting with string figure operations, and no matter which particular route is taken to get there, the design can hardly avoid discovery.

The 2-Mesh Net, under a variety of names, has been collected from the Torres Straits, Australia and Africa, and also occurs as a transient figure in other string figures including the widespread Jacob’s Ladder.

Assuming a 2-loop opening has been discovered, a natural next step would be to experiment with 3, 4 or 5 loops. An advantage of 3 loops over 4 or 5 is that the sequence of manipulations tried out would be easier to remember. There are four ways (apart from the fingers used) of setting up three loops on each hand (figs 17 to 20).

The reason for the ubiquity of Opening A of fig. 17 is probably due to two factors: (1) it is more rapidly formed than that of fig. 19 or fig. 20, and (2) the possible tendency for a right-handed person to operate first with the right hand, picking up the left palmar string before the right. Estimates of the incidence of left-handedness ‘vary all the way from 1 percent to over 30 percent’ (Martin Gardner, The Ambidextrous Universe, 1982:72). Evolutionary sequences similar to that suggested here (loop, then Primordial Moon, then 2-loop Opening, then 3-loop Opening) could have led to independent discoveries of the ‘not very obvious’ Opening A.

We again make use of the simple string figure techniques discovered above but this time we apply them to Opening A. Experimentation leads us to the discovery of the following string figure.

String figure glossary

1. Opening A.
2. Remove the index loops from the index fingers, give each index loop a half turn towards you, then replace each loop on the index.
3. Pass each thumb loop up through the index loop and replace on the index. (To do this neatly, reach through the index loop with the middle and ring fingers, pinch the far thumb string between the tips of these two fingers, pull the thumb loop off the thumb and up through the index loop, then transfer the loop back to the thumb.)
4. Pass the little finger loop down through the index loop. (To do this neatly, pass each thumb through the index loop from below and with it remove the little finger loop, pull it down through the index loop and replace it on the little finger.)
5. Release the index fingers.

As with the 2-mesh Net, the Sun too is a design that is lurking only a few moves away from the opening.

The Sun, being so easily discoverable, will endlessly appear through experimentation. (The author, having set out to investigate the possibilities with a 3-loop opening using nothing but the simplest of loop operations, discovered the Sun, along with other interesting designs formed by obvious variations of steps 2-4 above, all within one minute of beginning the investigation.) The figure is the earliest to have been recorded (in Greece, 4th century AD) and is of world-wide occurrence, having been recorded in the Pacific islands of Tikopia and Tuvalu, in Australia, in South America and in Central Africa. Closely related string figures occur in other parts of the world.

1. Certain figures are so readily formed from the simplest of manipulations as to be capable of independent discovery.
2. The Primordial Moon is a plausible ‘first string figure’.
3. Crow’s Feet may have been inspired by the quickly derived Crow’s Foot.
4. The 2-mesh Net is discoverable in every string figure making culture with a liking for symmetrical figures.
5. The possibility of a simple and logical route of development such as loop, then Primordial Moon, then 2-loop Opening, then 3-loop Opening, suggests that it may not be that remarkable that Opening A has been found in use all over the world.
6. The Sun is another string figure discoverable in every culture which has an interest in developing symmetrical figures.