Crossing Labyrinths

Most of all labyrinths we know are alternating labyrinths. In these, the pathway does not traverse the main axis. Every time it arrives at the end of a circuit it changes direction and skips to another circuit. 

However, there exist some few labyrinths with the pathway crossing the main axis. This means, it does not change direction but only skips to an other circuit whilst following a piece along the axis. Up to now I simply have termed these „non-alternating“ labyrinths, since „alternating“ can be considered the rule. If we don’t want to term the property negatively („non-alternating“), we could also use terms such as „traversing“ or „crossing“. From now on, I will use the term „crossing labyrinths“ for such labyrinths. 

Whether a labyrinth is alternating or crossing, this refers to its main axis only. That is the axis where the entrance to the labyrinth and also the access to the center are situated. In labyrinths with one axis, there is only the main axis. Labyrinths with multiple axes, have also side-axes in addition to the main axis. Note that the pathway always must traverse the side axes. Otherwise, no side axes could be designed. 

Among the 87 types of labyrinths in my catalogue of historical labyrinths (see: further links, below), 10 are crossing, the others alternating. Here, I will show the three crossing labyrinths with one axis once more. All three have already been presented on this blog. 

The most remarkable crossing labyrinth is the labyrinth of St. Gallen. 

Figure 1. Labyrinth of St. Gallen

It has been repeatedly confused on this blog with the alternating labyrinth with 6 circuits and the same sequence of circuits, of which no historcal example is known (related posts 1 and 2).

Another very beautiful crossing labyrinth is the one by Al Qazwini (related posts 3). 

Figure 2. Labyrinth by Al Qazwini

The third crossing labyrinth with one axis is Folio 53r by Sigmund Gossembrot (related posts 4).

Figure 3. Labyrinth Gossembrot Folio 53r

All three are interesting crossing labyrinths, in which the pathway does not enter on the first circuit nor reach the center from the last circuit. In St. Gallen and Qazwini it traverses on the full distance of the axis, in Gossembrot 53r only one part of the axis (from the 6^th to the 9^th circuit).

Related Posts:

1. How to Turn a Meander into a Labyrinth
2. Listening to the Labyrinths
3. The Labyrinth by Al Qazvini
4. Sigmund Gossembrot / 5

Further links:

• https://labyrinth-muster.ch/MHL/mhl.html

The Labyrinth on the Silver Coins of Knossos, Part 3

There are now digital coin collections in which I have found more coins with labyrinth representations. This is primarily the network of University coin collections in Germany (link below).

In the common portal of the NUMiD group (also link below) I have now found ten coins with the search term: Labyrinth Knossos, of which I would like to show here 5 pieces with the labyrinth of the reverse side.

All of these works and their content are licensed under a Creative Commons Attribution – Non-Commercial – Distribution Alike 3.0 Germany License.

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There are two coins in the coin cabinet of the Würzburg University.

One with the object number ID373 shows the head of Hera on the obverse side, and the 7 circuit labyrinth on the reverse side.

The 7 circuit labyrinth

The second coin with the object number ID375 shows the head of Apollo on the obverse side, and a male figure sitting on a labyrinth on the reverse side. This has 5 circuits and should be one of the “faulty” silver coins from Knossos.

The “faulty” labyrinth

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I also found two coins at the Erlangen University.

One with the object number ID134 shows the head of Hera on the obverse side, and the labyrinth of the Minotaur on the reverse side.

The 7 circuit labyrinth

The other with the object number ID135 shows the head of Zeus on the obverse side, and the labyrinth of the Minotaur on the reverse side.

The 7 circuit labyrinth

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Then there is the Münster University with one coin. It has the object number ID1316, and shows on the obverse side Zeus as a bull with Europa sitting on his back. The reverse side shows the labyrinth of the Minotaur, which is unfortunately a bit difficult to recognize.

The 7 circuit labyrinth

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In the digital coin cabinet of the Academic Art Museum of the Bonn University I found another coin from Knossos under the inventory number G.34.07.

It shows the head of Zeus on the front and a square labyrinth on the back.

The 7 circuit labyrinth

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I strongly recommend visiting the digital coin collections: For additional information and to view coins not shown here.

Further Links

• The Digital Coin Cabinet of Würzburg University
• Digital Coin Cabinet of the NUMiD collections
• Netzwerk universitärer Münzsammlungen in Deutschland (in German only)

• Related Posts

• The Labyrinth on the Silver Coins of Knossos, Part 1
• The Labyrinth on the Silver Coins of Knossos, Part 2
  

Pseudo Single Barrier

As was the case with double-barriers, we can also distinguish real from pseudo single-barriers (see: related posts, below). Here I want to show this first with the examples of two non-labyrinthine figures. I start with the figure „Luan“ (fig. 1).

Figure 1. Figure “Luan” 

^{Source: Kern, fig 604, p. 285}

This is a recent sand drawing of the Stone Age culture on Melanesian island Malekula (Vanatu). Kern writes, that this figure is not a labyrinth and cannot not even with any sound justification be considered misinterpreted labyrinth (Kern, p. 285). It is made-up of a uninterrupted line without entrance or center. However, it has 4 axes and 5 circuits. 

In fig. 2, left image, I show a simpler version of it with only 3 circuits. This better illustrates the principle of its design. This figure clearly can be read as an uninterrupted Ariadne’s Thread, and therefore I have drawn it in red. Of course, we can also add the representation with the walls delimiting the pathway (right image, blue). As can be seen, this figure has a certain similarity with a labyrinth. The axes are formed by the same turns of the pathway that typically appear in the labyrinth of Chartres and many other types of labyrinths. 

Figure 2. Figure “Luan”, Reduced to 3 Circuits

In figure 3, I have redrawn the figure from fig. 2 and reduced it to 2 axes. The left (red) image shows the representation with the Ariadne’s Thread, the right (blue) shows the representation with the walls delimiting the pathway. Still, the Ariadne’s Thread is a uninterrupted line without entrance or center. Here we can see the special course of the pathway at the side axis. The two turns of the path are shifted one circuit against each other. In between, an axial piece of the pathway is inserted where the path changes from the first to the third circuit without changing direction. Analogically with the double barriers we can term these courses single barriers. The course of the pathway in figure 2 is a real, the one in fig. 4 a pseudo single barrier (see related posts, below). 

Figure 3. Redrawing with 2 Axes and Pseudo Single Barriers 

This figure can easily be transformed to a labyrinth with 2 axes and 3 circuits, as shown in fig. 4. The left (red) image shows the representation of the labyrinth with the Ariadne’s Thread, the right (blue) shows the representation with the walls delimiting the pathway. 

Figure 4. Labyrinth with 2 Axes and 3 Circuits

As far as I know, the pseudo single-barrier has appeared in two historical labyrinths (fig. 5). The left image shows the pavement labyrinth in Ely Cathedral with 5 axes and 5 circuits. The pseudo single-barrier is situated at the second axis where the path changes from the fourth to the second circuit without changing direction. The right image shows the third out of 8 labyrinth drafts by the clergyman Dom Nicolas Rély. This labyrinth, that I called Rély 3, has 9 axes and 5 circuits. The axes are designed as real (axes 1, 2, 4, 6, 8) and pseudo (axes 3, 5, 7) single-barriers.

Figure 5. Historical Labyrinths with Pseudo Single Barriers

^{Sources: Ely – Saward, p. 115; Rély 3 – Kern, fig. 457a, p. 241.}

References:

• Kern H. Through the Labyrinth: Designs and Meanings over 5000 years. London: Prestel 2000. 
• Saward J. Labyrinths & Mazes: The Definitive Guide to Ancient & Modern Traditions. London: Gaia 2003.

Related Post:

• The Labyrinths with 3 Pseudo Double-barriers, 4 Arms, and 5 Circuits

How to repair the Mistakes in Historical Scandinavian Labyrinths, Part 5

All that remains now are the last two enigmatic Icelandic labyrinths.
These are the drawings of two identical labyrinths from the National Museum of Reykjavik, NMI 3135 (Fig. 6) and NMI 5628 (Fig. 7) in the guest post by Richard Myers Shelton.

First I bring them into the geometrically correct form I am used to here.

NMI 3135

NMI 5628

The labyrinths look very similar. One is simply the other, each mirrored, so they are identical.

Both have 11 circuits and a larger center, but it is not possible to reach it. And there are only dead ends, but not all of them can be reached either. There is a branching for this, similar to the Wunderkreis.
The way via circuit 8 leads to 10 and ends here. The way via circuit 6 leads via 2 and 4 to 3 and ends there. I do not reach the end of 4 and 9 at all. The center can only be reached if I would make a hook directly after entering the labyrinth.

The thicker black lines (= the stone settings) form the uninterrupted line, Ariadne’s thread. But without any beginning or end, different from the Dritvík labyrinth. Presumably, the purpose of these labyrinths lies in the stone settings and not in the path between the lines, as we know it otherwise from all other labyrinths from this time and in this region?
But which one should it be? A prison for the spirits or trolls? A gateway to the underworld or the otherworld? A monument to a guardian spirit? For rituals or for magic?

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Now my explanation: None of the above. Only the attempt to make once another labyrinth. One with 11 circuits, which are numerous in this region. Most of them are based on the extended seed pattern. But mathematically, there are over 1000 possibilities for an 11 circuit labyrinth, as Tony Phillips has calculated.

The sequence of circuits must always consist of a series of even and odd digits. And the entrance to the labyrinth must be on an odd circuit.
In addition, the four dead ends must be replaced. A boundary line may end here in each case, but not a path. So they become turning points.

Now my two suggestions for how the labyrinths could be redesigned:

11 circuit Classical labyrinth 7_5

First I drew an 11 circuit labyrinth according to the extended seed pattern with the cross, four double angles and four points (not shown here). I then numbered the circuits from the outside to the inside and then derived the sequence of circuits: 0-5-2-3-4-1-6-11-8-9-10-7-12. I read this backwards and thus got the sequence of circuits for the transposed labyrinth, namely: 0-7-10-9-8-11-6-1-4-3-2-5-12. With this again, I constructed the Knidos style labyrinth shown here. By the way, the complementary one looks exactly like this, because the basic labyrinth according to the seed pattern is self-dual.
So here, from the entrance, I first go to the 7th circuit and from the 5th circuit, I enter the center.
So we would have a complementary 11 circuit labyrinth in front of us, just like it was the attempt in the 15 circuit Borgo labyrinth.

The second proposal can be developed from a shifted seed pattern:

11 circuit Classical labyrinth 7_9

For this I take a cross, draw one angle at the top of each side and three angles at the bottom of each side. The points come again into the four corners (not shown here). The level sequence is then: 0-7-2-5-4-3-6-1-8-11-9-12. From this I construct the labyrinth shown here in the Knidos style.
The three other relatives of this labyrinth I get then with the methods described in detail in this blog by Andreas by counting backwards and supplementing the circuit sequences. This would give us again three additional new suggestions

However, since there are over 1000 other theoretical possibilities, we ultimately do not know what the authors of the Icelandic labyrinths had in mind and what ideas guided them.

Related Post

• The “Mistakes” in Historical Scandinavian Labyrinths