Discussion

These two gentlemen are labyrinth makers (designers and builders), consultants and researchers. Robert is among the best-known and most respected persons in the Labyrinth world. I am honored by their interest in my work. I thank them very heartily for sharing their ideas with me and with my visitors.

Mr Phillips (Tony) is professor of mathematics and a long-time labyrinth topologist.

Mr Saward (Jeff) publishes "Caerdroia", the international journal of mazes and labyrinths. In Robert Ferré's words, "he is the undisputed foremost labyrinth expert in the world. No one even comes close. Since this information wasn't really available in previous times, Jeff is probably the greatest labyrinth expert of all times".

- Robert Ferré (Labyrinth Enterprises, USA),
- Willem Kuipers (Willem Kuipers Labyrinths, Netherlands),
- Tony Phillips (State Univ. of NY, Stony Brooks, Math Dept).
- Jeff Saward (Labyrinthos, Britain).

This is posted here with their permission.

Robert: here is a longer response to your comments.

from Robert :

Updating the links on my website led me to your site again. I've enjoyed reading your comments.

I had never considered the influence of the Roman labyrinth on the development of the medieval one, as you suggest. Interesting. The basic shape, however, a circle with a cross in it, is much more ancient than the four-part Roman labyrinths. It is the alchemical symbol for earth. Since four is the number of the earth and physicality, I like the symbolism of the physical world surrounded by the infinite one (the circle). We wouldn't be qualified to enter into perfect, however, so the circle is opened to allow an entrance path. Lots of good meaning there.

from JH :

Of course this symbol is older, but I think the rhythmical intention of the medieval labyrinth designer brought the division of the labyrinth into four quadrants, and that idea must have been suggested by the already existing quadrant structure of the Roman labyrinth.

Then of course they may have recognized and welcomed the alchemical symbol and the cross pattern, but only afterwards, as some kind of happy coincidence.

from Robert :

The design for the St-michael's labyrinth seems to me to share more with Chartres than Reims, except that the Reims pattern has that long single line between the entrance and the center (which you have made into a double line). But since it requires moving the location of the labryses one path to the right, it seems that the Reims origins are not precise. In my view, counting from the inside outward, you have incorporated paths 2-6 of the left side of the Chartres pattern, and paths 6-10 on the right side. All of this with some variation is due to the elimination of partial labryses. The top remains as with both Reims and Chartres. The canon is there, which is good.

from JH :

In my page "The St-Michal's labyrinth "extracted" from the Reims labyrinth" (from the "St-michael's" page), I show that the St-Michael's design is directly "extracted" from Reims, being the 4th to 8th lanes or tracks, and then inverted into mirror-image.

Structural differences between Chartres and Reims are discussed in my book.

from Robert :

I have never really liked designs with entries into the outermost path, or entries into the center from the innermost path. This just doesn't seem balanced, as if one just falls into and out of the labyrinth. However, in the scale you are using, with hedges, it seems a bit more workable.

from JH :

I discuss that in the book. I also think it is mainly an aesthetic issue.

from Robert :

The thought that Heiric of Auxerre had doors in mind is something I would never had considered. We actually have a hedge maze at the Missouri Botanical Garden that replaces some of the walls with gates so that the workers can go into the center without having to walk the whole labyrinth. They aren't meant to change the pattern, however. Perhaps one could build a labyrinth in which the walker had a choice to push a button and control which way the door goes. Alternatively, I have thought of designs that have color-coded paths, so that the paths can intersect without creating a multiple choice, as you stay on your color. The next time you reach the same intersection, you would be following a different color.

from JH :

This of course is somewhat speculative (that Heiric, or the next draftsman who added them, had in mind some kind of doors), but I like the idea, and I myself went through that stage in trying to derive other labyrinth designs.

The use of colors is interesting in identifying a particular path determined by a particular position of the "doors".

from Robert :

If the Chartres pattern really did get a lot of attention in Auxerre, then why is the Sens labyrinth (or more precisely, the three Sens labyrinth patterns) of the Chartres type? I don't like what Craig Wright (bibliography) says about Chartres Cathedral. He makes some grave errors. But he did some great research, including unearthing a drawing of the Sens labyrinth. What a coup! But it has no rhythm or canon.

from JH :

You will see in the book that the new Sens labyrinth design discovered by Wright has the same "template" pattern as Chartres, whereas that of Reims is different. It has indeed a good rhythm and it is canonical, which, for me, confirms that this is the authentic design. Sens, Auxerre and Chartres were of the same archdiocese (Sens), whereas Reims was not.

from Robert :

In your comments on the medieval labyrinth you say that in France, around 1200, they were first moved from the manuscript to the floor. Of course Lucca is a wall (finger) labyrinth. There were some small floor labyrinths in Italy in the 12th century, but they were not large enough to walk and were covered with furniture, so as to make walking impossible. Perhaps, then, we can't really put them in the same category.

from JH :

You are right in mentioning that I should be more precise and say clearly that I mean large floor labyrinths, which are in their own category. I have addded a precision to my text.

Robert Ferré drew my attention to your interesting site. We are friends and have had many discussions on the peculiarities of designing labyrinths. In 2000 I published in Caerdroia 31, the journal of Mazes & Labyrinths edited by Jeff Saward, an article called 'Cadence characterizes labyrinths'. Robert's explanation in his book was partly inspired by my concept and graphical representations of the cadence of labyrinths. So, strictly speaking, Robert wasn't the first to mathematically formalize the rhythmical point of view.

Since you make visible in your site that you like careful research and reasoning, I felt free to draw your attention to this concept of cadence. Maybe it can add to your existing work.

I thank Robert for drawing your attention to my site.

I sure am interested in the notion of cadence which refers to a very specific event in music, both rhythmically or harmonically, and, I think, can be applied to the rhythmical structure of the medieval labyrinth.

But I must confess that my rhythmical approach is not (yet) that specific. It is on a more general kinesthetic level, not specifically musical.

I think the notion of cadence will be useful in the detailed analysis of a given labyrinth's rhythmical structure.

I also think (and these thoughts are more like improvisations) that even non-canonical labyrinths, with poor rhythmical structure, nevertheless will exhibit cadences, which make their interest (even limited, compared to the canonical-perfect ones).

I have used the cadence more as a rhythmic expression than as a musical one. The funny thing with 'non-canonical' labyrinths is that one can graphically see that the rhythm of the walk is truncated somewhere, or that it is a non-intriguing one.

I welcome your comments on the cadence concept and I am curious how you have come to your rhythm form.

I have been reading Willem's text (Caerdroia article)
More on that later (I am presently unable to open the illustrations)

I had read Tony Philips article quite some time ago, but my interest is more specifically the medieval labyrinth, which has a more complex rhythmical structure.

I have read (and commented at length in a 26-page review) a master's thesis by Vanessa Compton, a Canadian in Toronto who studied the labyrinth from a mathematical viewpoint. I met her at a lecture I gave on sacred geometry. In my remarks I said that the 13-pointed star theory isn't the basis of the Chartres labyrinth for a number of reasons, one of them being that you can't draw a 13-pointed star with just a compass and straight edge. She came up later and said that it could be done. In fact, she had several such proofs in her thesis. But none of them were practical in such a way that could pertain to Chartres Cathedral.

She also studied the work of Pierre Rosensteil, a French mathematician who made a formula for the cadence and rhythm of labyrinths. If you walked one segment of path it would be A, and the corresponding retun path would be A-prime. However, between the two would be other segments (B and C and D and their primes, etc.) In the end, he had a formula which, presumably, described the whole labyrinth. It was an exercise far beyond my capability. (Willem, you would likely understand it.) It was just a mathematical analysis, however, and showed no appreciation for what the labyrinth is.

The most lasting thing that I received from that whole interaction was a drawing by Rosensteil using the principle that to solve a maze you always keep your left hand on the wall. He made a three-dimensional drawing of a maze with walls and multiple choices with regards to paths and intersections. However, if you always stayed to your left, not only did you solve the maze, but the path pattern that you walked was exactly the path pattern of the Chartres labyrinth. It was a visual portrayal of my previous statement (appreciated by both of you) that the labyrinth represents the solution to the maze. The solution is unicursal, not the pattern.

My first glance at the labyreims website shows me that it is amazing how rich the form is, since there are so many ways to look at it. The regularity of the pattern shows very different in the rhythm way, compared to my cadence way. A thought that enters my mind, as it did when I was thinking about the cadence: if you have four quadrants, and you want to get from left-under to right-under, this 'ternary pattern' is the most efficient way to do that in a labyrinthine fashion. In the same vein, you have to do it thrice to be able to start left-under and enter the center from right-under.

The alternation of long and short reminds me also of a specific meditative walk, some people (Tibetans?) fancy: two steps forward, one step back. From that perspective, apart from the initial and final movements, one can think of the Chartres walk as a meditative form of walking clockwise, anticlockwise and clockwise to get to the center. Given the Chartres pattern, where the general pattern is: get inward, move slowly outward and then enter the center, this meditation gets more and more 'exciting' as the 'steps' get larger until the solution in the center offers itself.

I'll have to take a closer look to the canonical varieties, and maybe will wait till the book with the illustrations ease the study of the concept.

I'm not sure whether I could feel ever confident about an ultimate reason why the pattern of an e.g. Chartres labyrinth is thus or thus. In my article I conclude that Chartres is the most symmetric and efficient way to make a non-trivial pattern in a 11-circuit, 4 quadrant form. But I don't know why they wanted 11 or 4, although sacred geometry stories are plausible to me. I could agree with the statement that a truly good pattern unites manifold purposes and aspects. The pattern welcomes all faiths. In my presentation at the Atlanta gathering of TLS (The Labyrinth Society) I talked about the energetic properties of the cadence. There is still a lot to be discovered about the possible experiences - and its causes - while walking or even viewing a well designed labyrinth. Lately I'm riding them on a horse, which is again a wonderful experience.

That is an interesting story about Vanessa's thesis and the work of Rosensteil. I hope to hear someday more about it.

I have however a comment to make regarding the old 'Hand on Wall' method in mazes. This applies only to mazes that are 'coherent', that is, that all walls are connected in some way to the outer perimeter. If the designer makes 'islands' that are not connected, you will never get to the center. I read in a small book by Martineau that Hampton Court was the first maze to have islands, but the trick still works there, because the center is connected to the outer perimeter, I suppose. However, newer labyrinths are not solvable by the hand on the wall either left or right.

Willem: I finally could get to your article in PDF

Now, I see!

1. The Chartres 5-circuit labyrinth is the same I called "St-Michael's" on my site, because I used it for the St-Michael's project and because I was not aware of any previous existence of it. I made some original modifications, in particular 2 partition systems and direct shortcut.

But, as I discovered afterwards and as I show on my site, the basic design is already contained in the Reims labyrinth, lanes 4-8. In the case you submit, it is left as is, and entered from lane 5. In my case, it is mirror-image inverted and entered from lane 1.

I think (in fact I am quite certain) that this is the only 5-lane labyrinth possible with the perfect rhythm-cadence. That is why I was using it at St-Michael's.

2. All the canonical labyrinths that I derived should conform to your cadence pattern. I find it interesting that our two methods, being quite different, arrive at the same results.

Something I forgot to say, that may facilitate the reading of my essay:

The 5-lane "Chartres" labyrinth (which was the basis for my "St-Michael's) contains in fact all the elements of my rhythmical theory:

- The 3-step spiral course,
- 2 long and 2 short "bridges" to fill the remaining space but which also are part of the general rhythm.

This should help you visualize the whole thing.

Here are two 5-circuit labyrinth patterns that we use.

The first one is meant to be like the five inner circuits of Chartres.

Our "Heart of Chartres" pattern represents the first five inner circuits of the Chartres pattern on the left side, with a reflection of the same five patterns on the right side (just reversing it). We've been using this for years. That is the second pattern shown. I don't like the entrance into the center to be from the innermost path, but I have broken my own rute. I could have used the first design shown here, but I thought the two long entrances were too dominant in the appearance. For our Heart of Chartres we make a very stylized center, entering through one of the six petals, and also some pointed little lunation-like decorations around the perimeter. Unlike the Chartres pattern, the labryses on each side are in the same location, making it appear very symetrical. This was definitely a commercial compromise for people who wanted a small (12 feet in diameter) labyrinth that was somewhat Chartres-like. The Heart of Chartres can be seen on our website at: www,labyrinth-enterprises.com/personal.html

I have received the rhythm book friday and have only briefly studied the many illustrations. It has become clear to me, that I can understand the theory much better with the illustrations at hand. It is good that you included these rectangular spread diagrams. I had already thought that that might also be helpful to understand the differences.

It struck me that I have followed similar lines of thought for the classical (Cretan) labyrinth, that Jacques has done for the Chartres and Reims. Puzzle out all possible cadences, in my case out of sheer curiosity and fascination with the theoretical framework that I had unraveled. For you Jacques, this has meant much more work to say the least, due to the 11 circuits and four quadrants, compared to the 7 circuits of the Classical form.

I can imagine that different rhythms mean different things to different people. That concept is in a way still intriguing to me. But there is a warning to be made: two and a half years ago, I spoke with people who are experts in energy work, but were basically not very familiar with the labyrinth. I showed them some of my designs and the original ones. I had made designs to fit in with the place where I built the labyrinths. And those places were of course connected with the people who lived there. The energy workers said that it could very well be that my designs were fitting for the people who owned the location, but that they were not "foolproof" for all possible people who might visit there. While the classical design is so well balanced that no harm can come of it if you enter it in a somewhat deranged state of mind, that is not guaranteed with some of the other designs. So, yes, different designs can have different effects (and some designs may have negligible effects other than being dull or boring).

That was for me one of the reasons to lay off the further investigation of the various variations. I had proven in a coherent manner that they existed, and I found that many of the variations were esthetically not very convincing. As Robert mentioned, e.g. the variations where you enter the labyrinth via the outer circuit and enter the center via the inner circuit. So I felt satisfied with the conclusion that the original Chartres and the original Cretan were the most elegant, regular, harmonical or whatever.

Something like: I have my collection complete, I have filed it, problem solved, next curious phenomenon please.

Just received the book (Dominique Naert's - Reims labyrinth) this morning (bibliography). I will read it and report soon (I remember you told me you were trying to read it but French was difficult for you).

I am going through some of our past mails and trying to get back to our discussions.

1.

I just read Willem's note on islands in labyrinths (mazes) which will render inoperant the "hand on wall" method.

An island will not keep you from making it to the center and back to the exterior unless the center is inside an island. You will just walk past the island as if it was any small dot in the center of the lane, and come back walking along the other side of the island without touching it with your hand.

Of course, if the center is inside an island, you will just walk past it and go on along the wall until you are back outside.

2.

I remember a comment of Willem's about friends of his, experts in energy, who can evaluate a given labyrinth design.

I am quite interested, and somewhat skeptical, I should say, about the use of radiesthesy in relation with labyrinths. From what I know about radiesthesy, the twigs and pendulum are just means of rendering perceptible minute muscular reactions provoked by the subject's sensitivity to phenomena otherwise imperceptible.

Finding water is an example where I am not skeptical, because the subject does not know or expect he will find something. He is just receptive.

Testing a labyrinth that you see with your eyes is something else: previous to feeling the energy, there is the knowledge that you are in presence of a labyrinth and that you should expect to find some energy there. Then how can you distinguish between the energy that you expect to find and may involuntary feel, and any real energy that you should be able to feel without seeing the labyrinth or even without knowing that you are in the presence of a labyrinth?

My comment applies to both large physical labyrinths and small labyrinths drawn on paper.

I would like your views on that question because that aspect of labyrinth exploration is very present in the literature, especially on Sig Lonegren's site.

I think any energy present in the labyrinth is projected in the image I make of it for myself and it may indeed be extremely powerful, but it exists through my perception of the image

With the exception, that I aknowledge, of preexisting telluric forces at the place where a physical labyrinth has been located, precisely because of those forces.

But then again, finding and measuring those forces in the labyrinth should be done without the subject knowing he is in a labyrinth or in any place where he might expect to find that kind of energy or force As in a cathedral, for example, which is a case often mentioned.

3.

Related to the same comment, Willem wrote about the possibly inferior quality and even negative efficacity of some new designs, these qualities and efficacities being possible to evaluate through energy measure by people sensitive to it.

My point in deriving new designs was completely independent from any "quality" or goodness property of those designs but only a theoretical "curiosity" about the very fact that the method did yield new designs that could be considered "canonical", from a geometrical and graphical point of vue, because of their rhythmical properties, on the same level as Chartres, Reims, and the new Sens labyrinths.

The question of their practical quality and efficacity is completely different, and borders on aesthetic preferences. A friend here found that he preferred the Sens labyrinth over all the other canonical that I had derived, even before I (or he) knew it had existed historically. I indeed think that the Sens labyrinth may be superior to the Chartres one in terms of ease and pleasure of use.

4.

While being extremely pleased and excited by our discussions, I was expecting both of you to give me some strong reactions about my somewhat pretentious assumptions to explaining both the structure of the medieval labyrinth, and the whole phenomenon of its specific history as a graphic motif, with the rhythmical theory.

I have been told by other people here that reading my essay is somewhat difficult for lack of detailed (and lenghty) explanations. I sure hope this is not the case for both of you who are already quite familiar with that kind of speculations about the labyrinth.

But my point in writing this essay was precisely to be brief and technical. Maybe I overdid it?

I sat down and read most of your book just after receiving it. I remember that it brought up a number of responses. Then I put it down and it got buried. I hope to get back to it soon and share those feelings with you.

I read most of Dominique Naert's book on the Reims cathedral labyrinth (bibliography) that you sent me, Robert (thank you again!).

I find myself about in the same situation as with Patrick Conty's book (bibliography):
I don't see the point they want to make:
As if I couldn't understand what I read and make sense of it.

Most of the book deals with the history and geometry of the cathedral and the inscriptions on the labyrinth.

Only 10 pages of the book (p. 78-87) deal with the labyrinth itself.

At the beginning of that section there is a demonstration of a procedure to construct a circle having the same area as a given square (I will send to both of you that demonstration by FAX).

Just by looking at the drawing, which seems to reflect correctly the explanations of the text, it is very obvious that the square and the circle resulting from that procedure are not of the same area (I have hatched a section of the circle outside the square, and a section of the square outside the circle, which should obviously be equal, but are obviously not).

Then he goes on with an unproven method for constructing the labyrinth itself deducing all the dimensions (octagonal bastions, width of the lanes, etc.) from a very complicated geometrical diagram with inverted pentagons and rotated squares and parallel lines spaced by a given number of widths of the lane.

We have to remember that we don't know the dimensions and proportions, and even the alignment of the bastion lines with the main labyrinth lines, as you (Robert) have said in your Chartres book (bibliography) which forces us to re-draw the whole labyrinth refferring to some sort of regular geometry (which has to be hypothetical, since we don't know the original floor labyrinth).

Jacques Cellier's drawing, which seems to be the best we have if not the only one, cannot and does not pretend to be accurate as to the dimensions and proportions of the components of the labyrinth.

So that Naert's reconstruction is completely imaginary and un-verifiable.

Then, what does his speculations amount to?

And if his speculations on the cathedral itself are of the same quality, what value is his book?

I have the same general feeling with Conty's book, which seems to me to be some kind of meditation on the very general and abstract (and un-verifiable) correspondences between the labyrinth as a graphic motif, the labyrinth as a mythological motif, the knot (3-D and 4-D!), the string-figure game (cat's cradle), the supposed topological structure of myths and other things that I forget.

As in Naert's book, I found nothing in Conty's book with any direct relevance to the actual geometry of the labyrinth. The illustrations are nice but the title is at best very misleading.

So the problem wasn't my limited French! That's good.

I agree that everything we know about the labyrinth is speculation. How often do people report that the labyrinth was a substitute for pilgrimage to the Holy Land? There's no record of that. Lauren Artress in her book (bibliography) says that seven cathedrals were designated as substitute pilgrimage sites. I have asked her for verification, but none has ever been given. I think she got the number seven from something Sig Lonegren wrote (bibliography), perhaps that seven cathedrals had floor labyrinths. But the rest was hypothesis.

With regards to the Reims geometries, I think that a complicated solution is unlikely. From John James' studies of Chartres, I believe that the geometries were basic, including root rectangles, vesicas, hexagons, and a few other basic constructions. Incidentally, John James has begun a website that I think will be very interesting (www.johnjames.com.au).

I value the fact that you did not see Conty's point:
This means that I am not the only one not to understand, and that maybe there is not much to be understood.

I just found yesterday a reference to John James' site, but have not yet had time to go visit it.

I like his theory about the sequence of construction of the Chartres cathedral by horizontal layers instead of vertical sections; I think it is obvious once understood but has not yet been well accepted.

I have his "Chartres - the masons who built a legend" (1982) in French translation (1990) (bibliography).

James uses the word "canonical" in regard to the Chartres labyrinth, meaning something like "original" or "representative" or "typical":

"its design is canonical, since there exist numerous examples in medieval churches,
and all those dating from the same period correspond exactly to the same design"
(my English translation from the French translation).

This is quite vague and maybe misleading, and considering Reims and Sens, downright false (my excuses to John James: this does not diminish the very high respect I have for his work).

And "canonical" does not mean that, but "according to the rules".