Another Geometry

      People who see symbols everywhere are quite tiresome; those who deny their presence and role on principle often fall into an excess that may be just as dangerous.

Matila C. Ghyka

Let’s turn our attention to the labyrinths in cathedrals. Some are very famous, such as those in Chartres and Reims. They stand at the center of the naves and all represent a single path that inevitably leads from the periphery to their center. They were sometimes called the “League of Jerusalem.” Penitents unable to undertake pilgrimages could thus complete this mystical journey without having to fear the hardships of a trip to the Holy Land or the cruelty of the infidels.

But that is not their sole purpose; these motifs predate the Crusades, the Gothic period, and Christianity itself. Indeed, from Sweden to Galicia, from England to Greece, numerous prehistoric labyrinths attest to the antiquity of the concept.

It is generally accepted that these designs are linked to the Hellenic legend of the myth of Icarus. This Athenian represents the ancient archetype of the initiated Architect. In any case, he is the master builder of the mythical labyrinth to which he gave his name. In this sense, we can safely draw a parallel between this figure and the legend of Hiram, King Solomon’s master architect, who features in Masonic rituals and the guilds of stonemasons.

But Daedalus’s labyrinth, reputed to be impenetrable, featured multiple forks and dead ends. Theseus was only able to find his way out with the help of a thread that has remained famous. Associating him with medieval labyrinths—which, for their part, offer only a single path—might seem questionable were it not for the fact that the labyrinth at Chartres featured an image of Theseus and the Minotaur at its center.

 

Fig. 1 - Ariadne, Theseus, and the Minotaur (Master of Cassoni Campana) - D.P.

In fact, the labyrinth appears to be a graphic stylization of the maze, more closely associated with the architect than with the labyrinth itself. This explains why the names of master builders or bishops were inscribed on epigraphs at the center of these labyrinths, as in Reims or Amiens (fig. 2).
These features may indicate an ancient lineage, providing assurance that the building was constructed according to the rules by a skilled builder.
It is therefore understandable that the church relentlessly sought to destroy these initiatory labyrinths, which were seen as an ostentatious expression of blasphemous paganism.
 

Fig. 2 - Center of the Amiens labyrinth - Credit: Codex - CC-BY-SA

In any case, the extreme variety of their structures and the freedom governing their layout seem to rule out the idea of a direct link to the guiding lines. Admittedly, the labyrinth adopts the structural module of the building that serves as its setting and harmoniously aligns with the geometry of the whole. Yet I have been unable to establish any direct correlation from a structural standpoint.

On a psychological level, however, the situation is different. Labyrinths are uniquely capable of evoking numerous resonances in the mind of the penitent who walks through them. Psychomental states oscillate to the rhythm of the meandering paths dictated by the paving, and it is almost with surprise that one reaches the center of the circuit, still and vibrant. This catharsis, this act of purification, is a form of spiritual alchemy that allows one to accompany mystical introspection with a sacred physical dance.

  

Fig. 3 - Saint-Quentin Labyrinth - Credit: Vincent Zénon Rigaud - http://vincentzenon.com

Apart from Chartres Cathedral and the Basilica of Saint-Quentin (Fig. 3), few sanctuaries have been fortunate enough to preserve their labyrinths. As early as the 17th _^century, Canon Souchet railed against this “foolish pastime, in which those with little to do waste their time circling and running.” A century later, the canons of Reims had their labyrinth destroyed in 1779. The one in Arras did not survive the Revolution, while the year 1825 saw the end of the labyrinth in Amiens.

The pretext often cited for ordering these demolitions was the noise made by children who enjoyed playing in them, as if they were mere hopscotch courts. This did little to mask the hatred of Gothic architecture expressed by the canons of that era.

 

Ordinary hopscotch - Everyday hopscotch - Cathedral

Setting aside historical reality, this parallel between labyrinths and hopscotch is by no means merely a rhetorical device. Offering a single path that leads us to a mystical center eloquently named “Paradise,” the circular hopscotch game is reminiscent of the Gothic labyrinth or the game of the goose. In the same vein, “seated” hopscotch games seem to be a direct representation of a geometric pattern or progression.

It is fascinating to see the resemblance between the so-called “9-piece” hopscotch and the figure known as the “triple enclosure,” which itself mirrors the Gothic regulatory layout. It is therefore worth further exploring the origin of this symbol.

The etymology of “marelle” is controversial. The most common theory links the term to the Old French “mérelle, méreaux,” meaning a token or a disc. Others believe it derives from the fusion of the Latin “mereo,” meaning “to be worthy of something,” and “meritum,” which roughly translates to “reward.” A new theory seeks to link both “méreaux” and “marelle” to the Pre-Roman word “Marr,” meaning “stone.”
However, the etymology linking “marelle” to the Greek “meros” is the most compelling. “Meros” conveys the idea of parts, measurement, and distribution—concepts perfectly expressed by the geometric grid of a hopscotch game.

The pattern is variously called a triple enclosure, a labyrinth, a magic square, the game of the mill, or hopscotch. Its origin is lost in the mists of time. Examples can be found in Egypt, at Troy more than 5,000 years ago, in the Indus Valley, and in Ireland during the Bronze Age. In France, they can be seen on the walls of castles, churches, and commanderies, as well as on paving stones, in caves, and in a wide variety of other locations. However, the random nature of these arrangements makes it impossible to establish any correlation.

There are only a few examples of Neolithic triple enclosures in France. I will note primarily the hopscotch known as the “Pierre aux Chevaux” in the Vosges and the “Pierre de La Turbale” in Loire-Atlantique. Until recently, people still referred to the one discovered in 1800 at Suève in the Loir-et-Cher, a stone described as “druidic” at the time. But the latest research has set the record straight. While the stone is ancient, the origin of the engraving is indisputably medieval. Proof, if any were needed, is that the construction that guided its layout and positioning demonstrates a definite knowledge of geometry. This observation identifies it as the work of a stonemason versed in the intricacies of line work.

The connection between the triple enclosure and the labyrinth mentioned earlier may seem surprising. But everything becomes clear when one studies the layout of the religious site at Uruk in Mesopotamia. One can clearly see (Fig. 5) a triple enclosure, each polygon of which features an opening. The whole forms a sort of simplified labyrinth.

 
Fig. 5 - Site of Uruk (Mesopotamia)

What happened in Uruk is what happened in the West millennia later: “The labyrinth takes the form of a game (notably the Game of the Goose). [...] Finally, in its ultimate form, the labyrinth [becomes] the game of hopscotch.” Once again, the symbols intersect and refer back to one another. In this example, the connection between the triple enclosure and architecture is evident.
What remains is the esoteric meaning of the layout. In light of the *Liber chronicarum*, also known as the “Universal Chronicle” or the “Nuremberg Chronicle,” we can understand that it represented a biblical architectural archetype: the heavenly Jerusalem (fig. 6). This drawing schematizes the prophetic vision of the Heavenly Jerusalem given by Ezekiel.

Fig. 6 - Folio LXVI of the *Liber chronicarum* (1493) - D.P.

The same illustration also appears in the *Postilla in Bibliam* by Nicolas de Lyres (1270–1349). These plates simply interpret the ancient image of the heavenly Jerusalem (Fig. 7), which can be found in the miniatures illustrating the Apocalypse of Beatus of Liébana or in those of the Apocalypse of Saint-Sever (11th century). It should be noted that the origin of this representation likely predates the ^9th century.
However, the drawing conceals a secret: a triple wall. At first glance, the eye does not perceive this outline. Following the rules of traditional symbolism, the artist deliberately concealed it from the uninitiated.

Look at Figure 8. Each side of the miniature is bounded by lines which, if extended, intersect, forming the three walls. It thus appears that, from the very beginning, the esoteric symbolism of the triple enclosure was present in the iconography of the Heavenly Jerusalem. 

 
Fig. 7 - Beatus of Liébana, (1047) - D.P.

 
Fig. 8 - The Hidden Triple Enclosure

In summary, I conclude that the triple enclosure can be related to a regulatory layout, a geometric progression, while also symbolizing the Heavenly Jerusalem. It is a secret, concealed pattern, which explains its rarity—or even its near-absence—from the ornamental landscape of churches and cathedrals. It was reserved for a small circle of initiates.

It should be noted that Freemasonry has never directly claimed this symbol as its own. Some Masonic orders are said to use it as an allusion to their rituals, to the symbolic layout of the Temple, and to the representation of the three main degrees of initiation. René Guénon confirms this last point, but I lack reliable information to elaborate further. In any case, the connection to architecture is very tenuous here.

Fig. 9 - Detail of the floor of Amiens Cathedral.

There remains a frequently advanced hypothesis, one that associates the triple enclosure with the Celtic cross. Indeed, in Celtic studies circles, the triple enclosure is called the “druidic square.” Consequently, it is only natural to associate the circles of the cross—Keugant, Abred, and Gwenwed—with each of the enclosures. This is interesting. Unfortunately, no direct historical source can support this theory. However, we cannot simply dismiss it with a shrug. In the realm of symbols, surprises abound.

The Celtic cross, which unquestionably draws on Druidic symbolism, hides innocently behind the cross of the one true religion. Thus, it is entirely conceivable that a later syncretism allowed for the fusion of the Celtic cross with the symbolism of the Celestial Jerusalem. Note that, in the same way, the triple enclosure is hidden at the center of the cathedral, within the Latin cross. As for the so-called “ordinary” or “daily” hopscotch games, they seem directly inspired by the floor plans of Christian churches.

Thus far, hopscotch games have concealed an operative and symbolic meaning. We must therefore ask whether they might not constitute a sort of instruction manual, a guide to cathedrals. Here we are dealing with something akin to a “cabin slang” or a Gothic art of Kabbalah, which François Villon would not refute. First and foremost, we must determine the rules and identify correlations. Note that the hopscotch pattern traces a path progressing from the outside toward the inside. Subsequently, a circular movement takes place, culminating in the final stage, that of the “Moon” or “Paradise.”

If we accept the parallel between this game and a church plan, the initiate enters through the western portal and walks up the nave. Upon reaching the transept crossing—which in a standard hopscotch game is sometimes called the “table”—the initiate follows the ambulatory in the direction indicated by the sequence of the days of the week. That is, counterclockwise. This counterclockwise rotation corresponds to the Earth’s rotation, as each day is ruled by a planet. Thus, Sunday corresponds to the Sun, Monday to the Moon, Tuesday to Mars, Wednesday to Mercury, Thursday to Jupiter, Friday to Venus, and Saturday to Saturn.

According to the rules, the player then enters Paradise. Along with the “resting place,” this is the only spot where hopping on one foot is no longer mandatory and where both feet may be placed on the ground simultaneously. We can therefore agree that hopping on one foot represents walking, and the resting place or Paradise represents the places where one must gather one’s thoughts and meditate with both feet firmly on the ground, in contact with the earth’s energy.

It is thus a true labyrinth that the initiate must traverse within the sanctuary to draw its benefits. This concept of a mystical journey was not unknown to Henry Vincenot, who offered another version of it and called it “the little labyrinth”:
“They walked the entire length of the central nave, walked back down it solemnly, took the north aisle and walked up it, passed in front of the choir, where they prostrated themselves on their knees, walked down the south aisle, walked up the central nave once more, very slowly, and stopped at the crossing of the transept, their eyes raised toward the back of the apse for a long moment .”

I will compare this “little labyrinth” to the path of the Tables of the Grail (see Les cathédrales retracées, p. 163): “The tables here are mystical and symbolic crucibles, receptacles bearing the Grail. Anyone who wishes to find this Grail must seek it on the three tables. In fact, the layout of a Gothic cathedral immediately reveals them in the form of a rectangular nave, a square transept, and a circular choir.
Whoever enters through the nave walks against the flow of the telluric current, becoming imbued with it. Spotting the light from the choir, they move forward, dancing through the labyrinth, and once purified, take their place on the transept’s cross—a table where the light of the rose windows reveals to them the axis of the world (axis mundi). The spirit gains two additional directions.
If it is worthy of taking a seat at the round table, it will turn away from the profane world, facing the current to better absorb it. The spirit will become circular, transcending directions.
The alchemical work is complete; the spirit of the world (spiritus mundi) has done its work. The initiate, the knight, has finished his quest; he has found the Grail. ”

It would be risky to draw further lessons from this timeless game, although other variations of hopscotch are arranged in a single spiral, evoking the labyrinth and the Game of the Goose. The latter, whose 42nd square is, as if by chance, called “labyrinth,” brings us back to the “goose’s foot” of the Cagots. The circle is complete… (read the first chapters of the book).

Now is the time to introduce you to the Visigothic church in the province of Lugo, in Galicia. It perfectly illustrates this point. It is the church’s western portal—more specifically, its tympanum—that will capture our attention (Fig. 10).

Fig. 10 – San Fiz de Cangas (Porch) – credit: Jaume – CC-BY-SA

At its summit, we can see a Greek cross (with arms of equal length) flanked by a moon on the left and a sun on the right. These figures dominate a composition consisting of a simple seated marelle and a triple enclosure.

We are in Celtic lands, crisscrossed by the pilgrim’s labyrinth leading to Compostela. Along these sacred paths, Romans, Visigoths, Carolingians, monks, journeymen, and other Cagots met, worked together, and shared their techniques. These petroglyphs remain as a testament to this secret history of people, religions, and knowledge at every stage of the journey.

N.B. You have reached the end of the excerpts from the book. However, this site offers neither an introduction nor a conclusion. To do so would require reproducing the entire text and discussing the evolution of the cathedral concept over the centuries, as well as the various issues it raises—such as orientation, financing, symbolism, and so on.

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