The Nazca Maze & Labyrinth Architecture
Lindsay Heyes
There is a pre-Colombian maze on the plains of Nazca, about 20 km northwest of that city, quite close to the pan-American highway in "darkest Peru". The world's leading expert on mazes, Hermann Kern, described it as a spiral-like figure in his book on the earth drawings there, later omitting it from his catalogue of mazes. Consequently Kern condemned the use of mazes by South American Indians as originating from late European influence.
Twelve metres across, it is the most fragile labyrinth in the world. A camper could obliterate it by pitching his tent there. It is thought to have originated between the 5th century BC and the 13th century AD. A wooden stake thought to have been used in forming the hundreds of patterns on the plain has been dated at 525 AD ±80 years.
How did a diligent and outstanding researcher like Kern come to miss proof of the existence of labyrinths in the pre-Colombian New World? We know that Kern left a number of mazes out of his catalogue because they were, in his opinion, "incorrectly drawn". The Nazca maze is still often mis-classified, treated as if it is outside the main-stream of labyrinth architecture. How can other researchers avoid falling into the same trap?
 The Nazca Labyrinth
Kern's view of the construction of Classical labyrinths followed Thordrup, Loewenstein and early work by Stjernström. Kern appreciated that the method of construction is algorithmic - the labyrinth is grown around what I like to call a "seed pattern", but although he recognised that labyrinths of different sizes could be made in the same way he did not investigate the algorithm in depth.
Many school parties visiting our Museum of Mazes use a kit we call the Magical Mathematical Maze Maker to build a maze in about ten minutes. All that is needed is a rope, brightly coloured markers for stones, half a dozen stakes, and someone who knows the secret. You do it like this:
Prepare the ground:
1	Knot a rope at exactly regular intervals (e.g. one megalithic yard), and tie two end knots together to make a loop. This is your clew of twine;
2	Place a stake in the ground at the intended point of destination, drop the loop over the stake and walk the extended rope around to check the available space, and decide on the number of rings you can fit into it.
Construct the Seed Pattern:
1	Place stakes to mark the corners of a polygon of at least three sides, such that: the perimeter of the polygon measures twice the radius of the intended maze; two of the corners and the destination point form a straight line; all the stakes coincide with knots in the rope as it is extended around the perimeter; the pattern is bilaterally symmetrical; and the stakes are at least two knots apart;
2	Use stones to form a star-like figure from the centre of the polygon to the mid-points between the corner-stakes, then sub-divide the resulting sections with arcs inside the bounds of the polygon centred on the stakes, such that the ends of the arcs coincide with knots in the rope extended around the perimeter (place these stones close together, or you get lost in the maze - really!);
3	Extend the rope around the perimeter of the seed pattern until you stand opposite the destination (seen across the centre of the star). Keep your hand on the knot which is destination-wards! It doesn't matter which way you go around the perimeter.
Prepare your Assistants:
1	Place a helper at each knot between you and the destination, facing the maze and with some stout types pulling a cart loaded with stones to their backs;
2	Explain that they will walk backwards, dropping stones UNDER the knots of the rope as you move it, until they reach the polygon's edge. They should not cross the rope, move any marker or stake that they think it is in the wrong place, nor work ahead of the rope. Stones are most economically placed about half a yard apart.
Grow your maze:
1	Holding the rope close to the ground and keeping it taught, walk away from the edge of the Seed Pattern, unwinding the rope from the edge of the polygon as your helpers place the stones, and then winding back towards the polygon as the rope bends around stakes at the corners of the Seed Pattern;
2	Stop when you get back to where you started at the edge of the Seed Pattern - you are at the entrance to the maze. Remove the stakes, replacing those at the corners with stones. Infill with some extra stones in the walls near any "free" ends;
3	Enjoy! Try skipping round it in a chain, making an escape route, then running as a chain - was this what people did before roundabouts at fairs?
 based on Maze Making Magic graphics, copyright L.Heyes 1993.
The Nazca labyrinth was constructed using a method similar to the above, using a regular pentagon as the basis for the Seed Pattern. It IS a classical labyrinth, but it didn't look that way to Kern. It is not formed around a cross, and this turns out to be quite common amongst ancient labyrinths: Cakra-vy_ha, as depicted in Indian temple carvings, is based on a triangle. Otfrid's maze, often cited as a precursor of the Mediaeval Christian Maze, is also of this type - it is a classical labyrinth distorted into the concentric style by stretching the point of the star. There are many examples in Kern, and some faint rock carvings, photographed as they are with sugar or chalk highlights, may have been misinterpreted if this was not understood by the photographer.
Such mazes have been often been treated as stylistic variants, but the consistent variance in Europe, India, North and South America is evidence that the parameters of the algorithm include variation of the polygon - it is not necessary to start building with a cross at the heart of the Seed Pattern, and the position of the destination can be shifted a unit at a time along the perimeter. Kern was not aware that these mazes could be built by a single algorithm, which begs the question "How many mazes of this type remain outside the catalogue?". The persistent support by some researchers for the contention that the internal structure of labyrinths is inextricably linked with the Compass Rose is perhaps less self-evident than self-fulfilling.
Identification of the Nazca Labyrinth is complicated by the fact that all the Nazca earth-drawings are paths made by brushing the oxidized surface of the ground away, exposing the lighter-coloured underlying material. Conventionally, walls are marked, although the Classical labyrinth at Somerton in Oxfordshire is like that on Nazca - the design you see is that of the paths. Kern's trained eye recognized many of these negative-image mazes, but where the underlying polygon was not a square he was at a disadvantage.
 The Nazca labyrinth, based on graphics copyright L. Heyes, 1993
The Nazca labyrinth is almost alone amongst the patterns on the plain in deviating from geometric perfection, yet the method of rope and stake construction is the very method by which the Nazca patterns were produced. A likely explanation is that interstitial stones at Nazca may have been removed (or perhaps essential elements of the Seed Pattern alone existed) with the path arcs then being estimated by the builder.
Comparison between the actual path and that obtained in simulation shows the entrance to have been deliberately widened to obtain additional path separation. In contrast, the precision of construction of the path at Somerton suggests that there it was cut directly from measurement along the rope.
The final pitfall in identifying the Nazca Labyrinth is the quick exit. Again this is not a unique feature of mazes, existing in Europe and made in the same way as in Nazca. The method was demonstrated by Stjernström at Labyrinth'91. Indeed the only part of the world where this method is not depicted is in India. The author's personal experience is of a taboo relating to this: Mahabharata infers that great power is conferred in knowing the route out of Cakra-vy_ha, which Krishna is said to have described as "a trap which even gods cannot penetrate". Indeed it is interesting to note that the labyrinth usually chosen to depict Cakra-vy_ha is one for which it is impossible to create a sealed escape route.
There can be no doubt that the Nazca Labyrinth occupies a very special place in the history of mazes: it proves a pre-Colombian existence of labyrinths in the New World. It shows that the more generalized algorithm for construction of classical labyrinths, including their escape routes, was in use there from the start. It demonstrates that there are still new labyrinths to see, if we but open our eyes. Its fragile nature reminds us of the need for positive measures to conserve labyrinths for posterity. It demonstrates the need for a system of classification of these labyrinths
This last point is perhaps the most important. A comprehensive system for classification of Classical Labyrinths has been proposed by Stjernström, one of the leading authorities on the topology of mazes. It can encompass the entire possible set of these patterns, infinite though it is. Had Kern used Stjernström's system it is my belief that he would have found the truth about the Nazca Labyrinth, and history (and herstory Sig) would have been written differently.
The final word: There IS only one true labyrinth. All the Classical Mazes we can see are sections in two-space of a multi-dimensional branched figure, a folded surface of infinite size and zero density.  Some parameters remain to be determined. All correspondence is welcome.
Lindsay Heyes, The Jubilee Maze and Museum of Mazes, Feb. 1993
Bibliography:
Kern, H.: Labyrinthe 2nd ed., Prestel, München, 1982.
Kern & Reiche: Peruanische Erdzeichen 2nd ed., Kunstraum Muenchen, München, 1975
Stjernström, B.: Dokumentation och Klassificering, Tyresö, 1982
Stjernström: Klassningsschema foer Klassisker Labyrinter, correspondence of 1991 possibly unpublished
Thordrup, J.: Fra Tranedans til Haekkelob. Af labyrinternes indviklede historie Iconographiske Post, Copenhagen, 1976
Hodges: An unpublished volume of correspondence with the author with regard to algorithmic construction, Cheltenham, 1989 to 1991
Heyes: How are Mazes Drawn? in Mazes and Mysteries exhibition at the Museum of Mazes, Symonds Yat, 1991
The author has also drawn on:
Bloomfield, Heyes, Branchett: "Mazing Mathematics" workshop at the Joint Conference of the Mathematics Society and the Association of Teachers of Mathematics, Nottingham University 1992
Heyes: "Maze Making Magic" maze-building workshops for schools at the Jubilee Maze and Museum of Mazes, (Symonds Yat (West), Herefordshire HR9 6DA, England, Tel: 0600-890360) 1992
Special thanks are due to: Bo Stjernström, Zeta Eastes, and Nigel Hodges
Author's Note:  Groups of 15 or more paying visitors booked to visit the Jubilee Maze can choose to have either a game of "Maze Man's Hat" or "Maze Making Magic". These services are provided at no extra charge, but are not available on Sundays nor during busy periods of school holidays.