Title page of book
Contents of book

This book's main objective is to propose a new general theory of the rhythmical structure of the Medieval labyrinth. This rhythmical aspect is essential, because it explains the whole phenomenon of the Medieval labyrinth. Some Medieval labyrinths embody a specific rhythmical structure which determines their whole design. Hence the notion of canonical or perfect labyrinth.

This theory makes it possible, for the first time, to "de-mythologize" the labyrinth, both in the interpretation of its meanings and in its practical use.

Robert Ferré and Craig Wright are two authors writing about the Medieval labyrinth. These two authors seem to be presently the only ones approaching directly and explicitly the rhythmical aspect of the labyrinth.

My own research has brought me to the rhythmical nature of the Medieval labyrinth in early 1999, which is now about six years ago. Since that time, I was more involved in completing the theory and exploring its consequences than in getting it ready for publication. Other researchers are now entering that field, therefore I must publish. My findings will permit to push one step further the rhythmical theory of the Medieval labyrinth, and to derive from that theory several unexpected historical and practical consequences.

This is a shorter version of the technical part of a book still in preparation, which I expect to publish soon.

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I want this book to be readable by itself, and accessible to anyone simply interested in the Medieval labyrinth. I have included some material of a more general interest, and some practical applications of the theory. In particular, collected at the end of the book, are suggestions for the practical use of the different labyrinths. There are also some notes about the symbolical-psychological meanings of the Medieval labyrinth.

More information is available on my internet site (www.labyreims.com). Yet more will be posted, now that this book is being published. The site should be referred to as a complement to the present book.

The more practical parts of the book can be read before the theoretical ones. I insist on the fact that one can use immediately the labyrinth drawings at the end of this book, even before reading the text part of the book. An intuitive process will bring an understanding of the rhythmical workings of the labyrinths.

This text has to be read in very close relation with the drawings collected at the end of the book. Few references are made from the text to these illustrations, because the reader should be continuously referring to them. I tried to provide descriptive titles and clear indications on the drawings, so that the retrieval should be quite easy.

One should read with pencil in hand. The notions involved are quite simple, but they have to be clearly visualized and understood, in order for the whole to make sense. Use a pencil that can be easily erased (soft lead and good-quality white plastic eraser).

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That short book is about the rhythmical structure of the Medieval labyrinth. As a consequence of that rhythmical approach, I have been able to develop the notion of canonical (or perfect) Medieval labyrinth and to derive 19 different such canonical labyrinths, including the Chartres and Reims labyrinths, and the recently discovered authentic design of the Sens labyrinth (which by then I did not know). The first edition corresponded to my results at the time.

Shortly after that, I read Pierre Rosenstiehl's article on the mathematics of the Medieval labyrinth: "How the Path of Jerusalem in Chartres separates Birds from Fishes" published in "M. C. Escher: Art and Science" (New York, 1986-1988). In this paper, the author pretends to demonstrate that the Chartres labyrinth design is the only possible form of the Medieval labyrinth. This paper still seems to have some credibility. Of course, I did not agree with this conclusion, since I knew 19 such labyrinths, of which 3 have even existed historically. I decided to write a response to that article: "The supposed uniqueness of the Chartres labyrinth". For that response, I had to improve my methodology and include a systematic research procedure. I then discovered (to my shame) that my previous method had left out one possible Canonical labyrinth, which brought the total to 20.

This addition of a new labyrinth to the original series made necessary a modification of the general numbering sequence. I decided to revise it completely, based on the "natural" order suggested by the mathematical method used in the new procedure. The order of the 6 families is not modified and remains principal. The order of the individual labyrinths inside some of the families had to be modified, and of course, the addition of the new labyrinth pushes down all those who follow it.

This new edition incorporates all these changes (in the method and in the numeration), and contains in particular the new labyrinth, the binary table of the possible keys, and some minor corrections.

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For the first time in Wright's and Ferré's books (2001), rhythm is explicitly being mentioned as an important aspect of the Medieval labyrinth's path structure. And for the first time, someone is interested in the Reims labyrinth for a different reason than its bastions, that is, for its rhythmical structure. Both Ferré and Wright consider the Reims labyrinth to be as representative of the rhythmical structure of the Medieval labyrinth as the Chartres labyrinth. They add to these two already well known labyrinths, a third one, from an 18th century drawing recently found by Wright and now identified as representing the authentic design of the Sens cathedral floor labyrinth.

The Sens labyrinth is so called because, like those of Chartres and Reims, it was part of the floor of the Sens cathedral. Like that of Reims, it was destroyed in the late 18th century. Only the Chartres labyrinth still exists. The Reims labyrinth is known by a drawing made before its destruction. The Sens labyrinth was, until recently, thought to be of a design with no particular rhythmical interest (Kern, No 289). The drawing discovered by Wright is extremely important, because it brings to light an hitherto unknown labyrinth design with obvious rhythmical properties similar to those of the Chartres and Reims labyrinths.

The general structure of the Medieval labyrinth

The Medieval labyrinth is built on a system of 12 concentric circles delimitating 11 lanes on which the path is established. The lanes are alternately of contrary direction, so that by crossing to the next lane, the path changes direction. 4 axes determine 4 quadrants; lane crossings are located along these axes.

The rhythmical analysis of the Medieval labyrinth

Wright and Ferré probably first had, as I did, an intuitive perception of the rhythm of the Medieval labyrinth. They then proceeded to verify that intuition through some kind of rhythmical analysis. Wright developed a notation system, Ferré used more graphical diagrams and charts. I developed both a notation system and a graphical way of representing the rhythmical sequences. I think my intuition was more physical/kinesthetic than theirs.

For his rhythmical analysis, Ferré uses, as I did, a circular version of the Reims labyrinth. Wright probably did, but does not say. The Reims labyrinth is octagonal and it has four bastions, which makes it quite difficult both to analyze by itself and to compare with the Chartres and Sens labyrinths. This circular version is similar to the manuscript versions: this is why I call it "script". Similarly, the Chartres labyrinth, in its "script" version, has no petals in the center, no rounded form to the crossings and no tooth motif around its perimeter. The new Sens drawing discovered by Wright is already in a "script" version (except for the rounded form of the crossings).

The names of Chartres, Sens and Reims are used here to designate the "script" version of these labyrinths, which is their "manuscript-style" version.

A first rhythmical analysis

Unless otherwise specified, the labyrinths are always assumed to be in their clockwise form, the entry being at the left of the main axis and facing down.

Wright and Ferré both note that the three labyrinths (Chartres, Sens and Reims) contain only half-circle and quarter-circle segments, and their graphical analysis, although quite different, are otherwise so advanced that both authors are within a single intuition of being able to construct this whole theory, that I still think to be the first to discover and publish.

Wright's rhythmical notation system (p. 67) is similar to the one that I have been using for several years.

Wright represents quarter-circle segments by "Q" and half-circle segments by "H". The Chartres labyrinth is noted thus:

QQHHQQHQHQHQQHQHQHQQHQHQHQQHHQQ

The Reims and Sens labyrinths are noted thus:

QQHQHQHQQHHQQHQHQHQQHHQQHQHQHQQ

In my own notation system I represent quarter-circle segments by a dot, half-circle segments by a hyphen, Chartres being noted thus:

..--..-.-.-..-.-.-..-.-.-..--..

Reims and Sens being noted thus:

..-.-.-..--..-.-.-..--..-.-.-..

In the rhythmical structure of the Medieval labyrinth, the radial parts of the path (the actual crossings through the partitions, forcing the change of lane and of direction), are not counted, even when they are longer, as happens along the main axis of all labyrinths. Wright is clear on this, but not Ferré.

Wright and Ferré acknowledge the fact that the general rhythmical pattern of these three labyrinths is reversible. This means that the path has the same rhythmical structure going in or out of the labyrinth: similar elements occupy similar positions in both sequences. The reversed (or backwards inverted) "score", in the musical sense of these words, is identical with the original one. Put differently, the "retrograde" reading gives the same result as the normal reading. For this to be possible, the rhythmical structure of the path has to be symmetrical: it has to have a center of symmetry. In Wright's notation, the center of symmetry is indicated by the bold "H".

A deeper rhythmical analysis

You will find my rhythmical analysis of the Chartres, Sens and Reims labyrinths at the end of the book (annex B). The cover page of the book shows the circuits (textured) and bridges (clear) of the Chartres labyrinth in its "floor" version.

This rhythmical structure of the Medieval labyrinth is its "raison d'être". The twelve concentric circles and eleven lanes, the 10 crossings (or more, depending on the way they are counted) and the 31 segments of the path, the partition into four quadrants, everything is entirely governed by the rhythm. No symbolic numbers, no so-called "christianization" by the superimposition of the cross, have to be used to "explain" its form.

Of course, symbolic meanings can be added (and, in fact, have been added) to the drawing afterwards, or even found in it as if already contained, but cannot be invoked to explain its internal structure, which is rhythmical. As an example, the ternary structure of the round three-step circuit may be considered as a symbol of the Trinity, but the symbolic value of the number three does not explain why that circuit is ternary: the reason is in the spatial arrangement of the alternately long and short steps around the circular course.

Regarding the so-called "christianization" of the labyrinth design by superimposing the cross motif on the so-called "pagan" (Cretan) labyrinth (Kern, p. 105-106): Roman labyrinths were always built on a quadrant structure. This type of labyrinths was spread all over the Roman Empire (including Blois and Lyon in France, from the third century) usually in the form of floor mosaics. Early medieval illustrators (ninth century and before), who "invented" the Medieval labyrinth, certainly knew that design, and will have incorporated in their own design its quadrant structure, for the rhythmical reasons already outlined, without any "christianizing" intention.

It may be interesting to note here that the 17-lane Saffron Walden turf labyrinth (Kern, No 306) is in fact a "super-Chartres" labyrinth with 5 spiral courses instead of 3. The same design occurs in other places (Kern, No 403, 470).

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The word canonical means following the rules. In the present context, it also means perfect. From what we just saw, it should be apparent that there exists a notion of the perfect Medieval labyrinth. It could be summarized thus: three circuits (with their 8 bridges) assembled in a reversible sequence. (An additional historical limitation, probably aesthetic in nature, is that the crossings along the main axis be no more than two level deep.) We presently know three such perfect or canonical labyrinths: Chartres, Reims and the newly discovered Sens. It seems that there existed no other. I have discovered that several more can be derived from that rhythmical structure, historically realized in those three labyrinths.

The general templates

My method is to consider the arrangement of the crossings along the axes (or, more precisely, "half-axes") of these labyrinths. In order to be able to formalize the analysis, the parts of the labyrinth have to be identified in some manner. The axes will be identified by letters. We start with the main axis, along which is the entry of the labyrinth: it will be called "A". We then go clockwise with the axes "B", "C" and "D", and terminate on the other side of the main axis with the letter "E" (the two sides of the main axis have to be distinguished, because the arrangement of the crossings is different on each side of this axis). The lanes are numbered 1 to 11 from the exterior to the interior. If necessary, the exterior and the center may be designated by 0 and 12 respectively.

The "ordinary" templates

All three perfect labyrinths have the same arrangement along the "C" axis. Along the "B" and "D" axes, Chartres and Sens have the same arrangement, whereas Reims has a different arrangement (this confirms that Chartres and Sens belong to the same family, and Reims to a different one). Other arrangements along these 3 axes are possible. These different arrangements will determine "templates" for different "families" of labyrinths: possibilities can easily be explored systematically.

Different arrangements are also possible along the main "A-E" axis: all three of our known perfect labyrinths have different arrangements along this axis. These arrangements determine the lane of entry and the order in which the different elements are visited. The arrangements along the main axis are like "keys" for different visiting sequences of the same template, resulting in different labyrinths. All the possible arrangements along the main axis can be explored systematically but each one will have to be tested empirically against each template.

If the general structure of the 3 circuits and 8 bridges is to be preserved, there has to be 3 crossings along the "B" and "D" axes and 4 along the "C" axis. This has to do with the spatial layout of the circuits and bridges on the 11 lanes, and, in particular, the number of times that the "C" axis has to be crossed between the two halves of the labyrinth (which is 3). Even though I have no formalized and explicit mathematical proof, this becomes self-evident after some time of practice of the labyrinth.

Since the arrangement along the "C" axis is the same for our three labyrinths (Chartres, Sens and Reims), let us start with this arrangement, and let us now look at the "B" and "D" axes. Because the rhythmical structure has to be reversible, these arrangements will have to be symmetrical to each other in the sequence of visit. The result on the drawing is that axis "D" looks similar to axis "B" (as if the result of a geometrical operation of translation). We already have two different arrangements of these axes: Chartres and Reims. Two more arrangements are possible: we shoud recognize in them the inverted Chartres and Reims arrangements. These two new arrangements are compatible with the current "C" axis arrangement (they don't create inaccessible portions of space, or islands). The real test will come later, when we start designing "keys", whether we can actually build functional labyrinths from these new templates.

The "meta" templates

In addition to the current "ordinary" arrangement along the "C" axis, others are possible. The disposition of the crossings along this axis has to be symmetrical in regard to lane 6, and has to allow the layout of the three circuits. Only one other arrangement respects these conditions, and it will allow two folded and one spiral round courses. Therefore the resulting templates will be related to the Reims labyrinth, not to the Chartres labyrinth. I propose to call these "meta-Reims". We can note immediately that the two folded circuits will be in an inverted position in comparison with the original Reims structure: they are laid sequentially on lanes 1, 3, 1 and 11, 9, 11 instead of 3, 1, 3 and 9, 11, 9.

Now for the "B" and "D" axes of the meta-Reims templates. The preliminary rule-of-thumb is that no island (closed portion of space) results from two crossings being placed face to face. There are only two possible arrangements, each one being the inverse of the other. Therefore, we get two meta-Reims templates: the meta-Reims and the inverted meta-Reims.

The six families of canonical labyrinths

We now have 6 theoretically possible templates, resulting in a possibility of 6 labyrinth families.

It should be said here that inverted templates do not produce mirror images of the same labyrinths, but really different labyrinths, because the "A-E" axis arrangements are not inverted with the inversion of the template: the entry is always on the left side of the axis. In fact, templates are inverted before doing the "A-E" axis arrangements. Real mirror images will be derived later, in a different context.

The keys and the actual labyrinths

We don't know yet if these templates will really be operational (except for the three already known labyrinths). Let us now proceed to examine the possible "keys" to these templates. Keys are formed by the arrangement of the crossings on both sides of the main axis. Because of the symmetrical structure of the path of the labyrinth, arrangements on either side of the "A-E" axis have to be symmetrical, which means: in mutually reverse order.

Let us now formalize the different arrangements possible along that axis, that is, the different "keys" possible. The default elementary structure of the key of a labyrinth is entirely formed of single level crossings along both sides of the main axis ("A-E"), like in the primitive labyrinth that I called "boustrophedon" (which has only that main axis and no secondary axes or quadrants). The building-up of the Medieval labyrinth calls for adding some second-level crossings, which will be nested inside extended first-level crossings. What has to be specified is the location of these second-level crossings.

The second-level crossings occupy two lanes and allow the passage from an even-number (clockwise) to an odd-numbered (counter-clockwise) lane. As a convention and because of the easier spatial referencing, we will reference these crossings to the lane nearest to the exterior of the labyrinth (which in this case is odd-numbered). Five locations are possible. This is easily represented on a five-column table, the columns being numbered 1, 3, 5, 7, 9, from the lanes where the crossings are located. The 32 lines of the table represent each of the 32 possible "key" structures or arrangements (2 at the fifth power).

Each of these possible structures then has to be tested against each of the 6 general "templates" aready described and resulting from the different possible arrangements of the three other axes. The method is empirical but relatively easy and rapid. The preliminary rule-of-thumb applied for the "B" and "D" axes will again be applied here: arrangements resulting in islands because of crossings facing other crossings on other axes are easily recognized and excluded. Other arrangements have to be tested by doing the complete path and counting the segments, which should be 31, to exclude larger and less visible islands.

The total number of theoretical possibilities is 192, of which only 20 produce functional labyrinths, which are indeed the 20 canonical labyrinths, of which 13 are built from the 4 "ordinary" templates and 7 from the 2 "meta" templates.

12 of these labyrinths are entered on lane 1, which may, to some people, seem unacceptable for aesthetic reasons (indeed, historically, this was never used on any labyrinth). These 12 labyrinths with entry on lane 1 are relatively less perfect but theoretically correct, and some people even prefer them. I decided to keep them.

If we remove from the list the labyrinths with entry on lane 1, we are left with 8 labyrinths which are aesthetically more perfect, among which are the three labyrinths having existed historically: those of Chartres, Sens and Reims. These 8 labyrinths are all derived from the 3 first families of the ordinary "C" axis arrangement.

The result of my research is in the accompanying table and drawings. The table C.3 describes all the possible canonical Medieval labyrinths. These are classified by families according to the general templates from which they are derived. They are described by referencing the crossings along each axis to the lanes on which they are located (crossings being on two lanes, they are referenced to the lane nearer to the exterior of the labyrinth, independently of their direction). The "D" and "E" axes are not mentioned on the table because they are the symmetricals of the "B" and "A" axes respectively and are easily derived. The illustrations of anned D show the 20 canonical labyrinths, with their identification, in their normal (clockwise, or right-handed) and mirror (counterclockwise, or left-handed) versions.

From all this it should be apparent that I knew the Sens labyrinth before seeing it in Ferré's and Wright's books. It is identified here as No 1. I had even designed an easy way to modify temporarily the Chartres path (No 3)on a large canvas labyrinth to reproduce that pattern, as well as another one identified here as No 2, with the entry on lane 1.

Wright's discovery of that drawing was no surprise to me. On the contrary, the previous Sens design made no sense to me because it was not canonical: it should have been, in view of the importance of the cathedrals and monasteries of Sens and Auxerre in the history of the Medieval labyrinth. Wright thinks that the labyrinth of the cathedral of Auxerre, also destroyed but not recorded, may have been of the same design. I agree, because it is in Auxerre that the authentic Sens design was found.

From a different point of view, designs of the Reims families would probably be associated with the Reims geographical area and medieval archdiocese, whereas labyrinths of the Chartres familes would be associated with the neighboring archdiocese which included Chartres and Auxerre (and Paris), Sens being the see of that archdiocese.

A later (ca. 1465) Medieval labyrinth (Kern, No 211) is built on the inverted Chartres template, but the "key" is not symmetrical, therefore the resulting labyrinth is not canonical. Furthermore, some crossings forming the "key" are three level deep. Nevertheless, it is interesting to find a historical occurrence of one of the templates that we just derived from our theoretical analysis.

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Part of the psychologic efficacity of the labyrinth comes from the kinesthetic effect of the movements along the rhythmical structure of the path. Different labyrinths have different rhythmical structures and will therefore have different kinesthetic effects. Furthermore, the same labyrinth can be traveled in different ways. Methods for using the labyrinths can now be designed to be more adapted to specific needs or objectives.

Different labyrinths

We have 20 different canonical labyrinths, with entry on different lanes, with different sequences of visit, with different forms of "circuits". All these labyrinths have a "right-hand" and "left-hand" version, that is, with the main direction of the path being clockwise or counterclockwise. All these different figures will induce completely different kinesthetic effects.

I have made some tests with these differences. Different people prefer different labyrinths. Different personal situations are better expressed or call for "nursing" and nurturing by different labyrinths.

Different practices

Apart from labyrinths being different among themselves, each labyrinth can be spatially orientated in different manners. The orientation of the labyrinth may be referenced to the person visiting it or to some external object or system (architectural, local, cosmic). The orientation of the person in relation with these external systems may also be considered.

Most of these suggestions are equally applicable to the small drawings of the labyrinth on a sheet of paper and to the large-scale "walkable" labyrinths painted on canvas or otherwise marked on the floor or on the ground.

The actual practice of visiting the small labyrinths should be done either with a finger or some non-marking instrument. After some training, it can be done simply with the eye movement. One should try changing hands or even fingers for the tracing movement.

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I don't want to discuss here the history of the symbolical and psychological meanings of the labyrinth. I just want to outline a practical method to access the psychological efficacity of the labyrinth.

The current approach to the practice of the Medieval labyrinth is to consider it either as a pilgrimage to Jerusalem, or as the journey of life directed towards Salvation or Enlightenment, of which the pilgrimage is also a figure.

My approach is that of role-playing. Forget any intrinsic meaning of the labyrinth itself. Picture yourself as some character walking the path of the labyrinth. Your imagination will completely rebuild your perception of the labyrinth according to the intention of the character whose role you are playing. Are you a pilgrim? The labyrinth is the road to Jerusalem (or any other pilgrimage destination). Are you Theseus? The labyrinth is the very dangerous prison of the Minotaur. Are you a warrior? The labyrinth is the approaches to the castle that you are either attacking or defending.

Are you a peasant tilling his field? The labyrinth is the field, the lane is the furrow that you plough, sow or harvest. For this role, the center of the labyrinth does not have the same importance as for the previous ones: the only important part is the furrow that you work upon, in patiently and humility; the center is nothing more than the place where you lift your plough and start walking back across the furrows and out of your field. This last example shows how wide can be the range of significations of the labyrinth and of its parts.

The act of role-playing gets its efficacity through the extensive realization of the details pertaining to the role, especially the corporeal attitudes and gestures, which are involuntarily but irresistibly reproduced, and which are directly and very deeply related to the personal meanings, both individual and collective.

The roles to be played can be found in one's personal life, but they can also be borrowed from mythology and archetypes, history, literature, cinema... and even the specifically religious contents of one's religion.

Different labyrinths, and different versions (clockwise or counterclockwise) and orientations of the same labyrinth will bring out different aspects or meanings of the role played.

Ferré, Robert: "Origin, Symbolism, and Design of the Chartres Labyrinth", 2001 (52 p., 5.5 x 8.5 in.). Available on the author's web site: (www.labyrinth-enterprises.com).

Kern, Hermann: "Through the Labyrinth, Designs and Meanings over 5,000 years", Munich-London-New York, Prestel, 2000 (Orig. German Ed. 1982, 1983, 1995) (400 p., 9.5 x 12 in.), ISBN (1982): 3-7913-0614-6, (2000) : 3-7913-2144-7.

Wright, Craig: "The maze and the Warrior: Symbols in Architecture, Theology, and Music", Boston, Harvard College, 2001 (365 p., 6 x 9 in.), ISBN: 0-674-00503-1.

Note on Kern's book

See my site: Kern

See my site: Author