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The Two One-arm Labyrinths

Among the nine drawings by Gossembrot are also two one-arm labyrinths (see related posts, below).

The labyrinth on fol. 53 r has 9 circuits (fig. 1). In the center is written: inducens et educens, leading in and leading out. The design of the axis with it’s rhombus shape is eye-catching.
This almost looks a bit like an anticipation of the Knidos style… Furthermore, this is a non-alternating labyrinth. The pathway traverses the axis when changing from the 6th to the 9th circuit. I have highlighted this position in the labyrinth with two dashed red lines. To these correspond the dashed lines in the pattern. This pattern appears for the first time in the labyrinth by Gossembrot. Therefore it is a type of it’s own. I refer to it as type Gossembrot 53 r.

Figure 1. The Labyrinth on Folio 53 r

The labyrinth on fol. 54 v has 11 circuits and is designed in the concentric style (fig. 2). This type of labyrinth is also referred to as the scaled-up basic type or scaled-up classical / Cretan type of labyrinth. This, because the seed pattern in the classical style consists of a central cross with two nested angles and a coaxial bullet point between each two arms of the cross. The seed pattern of the basic type is made-up of a central cross with one angle and bullet point between each two arms of the cross.

Figure 2. The Labyrinth on Folio 54 v

There exist several historical examples of this type of labyrinth. The two earliest examples (fig. 3) are frescos in the church of Hesselager, Fünen, Denmark and in the church of Sibbo, Finnland (see literature, below).

Figure 3. Earliest Historical Examples (15 th Century)

Both were dated from the 15 th century without any further precision. Also, Gossembrot 54 v dates from the 15 th century (1480). Therefore, based on the dating, it is not possible to certainly identify the earliest preserved example of this type of labyrinth. So it is even conceivable, that the drawing by Gossembrot is earliest and thus Gossembrot was also the originator of this type of labyrinth.

Literature
Kern H. Through the Labyrinth – Designs and Meanings over 5000 Years. München, London, New York: Prestel 2000. P. 280, fig. 593; p. 281, fig. 601.

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The Four Labyrinths with 4 Arms und 8 Circuits

Four drawings by Gossembrot show labyrinths with 4 arms and 8 circuits. Among these, two each are on a circular and rectangular layout. Figure 1 shows these four figures compared. Figures a (circular) and c (rectangular) have the same course of the pathway (=). This is also true in figures b (circular) and d (rectangular). The two circular figures (a, b) as well as the two rectangular (c, d) have different courses of the path (≠).

Figure 1. The Four Designs Compared

All four figures bear inscriptions in their centers.

Figure a (fol. 51 v): „Laborintus inducens et educens“ – labyrinth leading in and leading out


Figure b (fol. 52 r): „Laborintus tamen educens nunquam intus perveniens fines“ – labyrinth leading out but nowhere arriving at the center

Figure c (fol. 52 v below): „Ibi introis et exis“ – here you enter and exit.

Figure d (fol. 52 v above): „Der Irrgang clausus est et numquam introibis“ the maze is closed and nowhere you enter.

From this we can see, that Gossembrot was engaged with the difference between labyrinth and maze. Figure 2 shows, using the lower, rectangular images, that the design of the side-arms in all four images is the same (areas within blue frames). The figures on the right side only differ with respect to the design of the main axis from those on the left side (areas within red frames). This becomes also clear from the patterns shown at the bottom of fig. 2. The left figures are labyrinths, the right figures are a special form of a simple maze. The pathway enters on the 6th circuit and there it branches. One branch continues to the first side-arm. There it turns to the 7th circuit, makes a full circuit and thereby traverses the main axis. It again turns at the first side-arm, leads back through the outer circuits 6 – 1 and arrives back in the other branch of the bifurcation. The innermost 8th circuit is completely isolated from the rest of the course of the pathway. It begins in a dead-end, does one round and ends in the center.

Figure 2. Labyrinth and Maze

So it seems, Gossembrot had derived a maze from the labyrinth. As a matter of fact, there exists a second historical labyrinth with the same pattern. This is sourced in a autograph (1456/63) of the Nuremberg physician and humanist Hartmann Schedel (see literature, below). The labyrinth drawn freehand was affixed to one of the last blank pages of the autograph. This autograph is accessible online in the same digital library as the manuscript by Gossembrot (further links, below). The original drawing of the labyrinth is oriented with the entrance to the left side. In fig. 3, for a better comparability, I have rotated it with the entrance to the bottom.

Figure 3. Type Schedel

Based on the earlier date (1456/63) of the publication by Schedel, I have named this type of labyrinth with „type Schedel“. Gossembrot was friends with Hermann Schedel, the uncle of Hartmann. The manuscript by Gossembrot dates from 1480. Having stated this, it has also to be considered that the labyrinth drawing of the Schedel autograph was affixed. Therefore it could also have been added later. Thus, it is well concievable that the drawings by Gossembrot were earlier and thus Gossembrot could have been the originator of this type of labyrinth.

Literature

  • Kern H. Through the Labyrinth: Designs and Meanings over 5000 years. London: Prestel 2000, p. 126, fig. 216.

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The Labyrinth on Folio 53 v

Originally I had intended to show the design on folio 53 v already in my previous post (see related posts, below). It can be seen as a mistaken attempt to the labyrinth on fol. 51 r. But then I took a closer look at it. And the result has prompted me to dedicate a separate post to this design. Fig. 1 shows the design on fol. 53 v.

Figure 1. Labyrinth on folio 53 v

The design on fol. 53 v was rejected, crossed out and overwritten with text. It is clearly recognizable a five-arm labyrinth with 7 circuits. Also the design of the side-arms is very similar as in the labyrinth on fol. 51 r.
As the labyrinth on fol. 51 r, also this labyrinth rotates anti-clockwise. In fig. 2 I have mirrored it, inscribed the Ariadne’s Thread and in parallel presented the pattern. The Ariadne’s Thread traverses the lines of the labyrinth in two places. These are marked with blue circles. I have assumed that these were still provisional auxiliary lines that would have been removed if the final version of this labyrinth had been completed.

Figure 2. Ariadne’s Thread and Pattern

The result is surprising. Segment 4 is not filled out by the pathway. The path on the innermost and the two outer circuits passes this segment and marks only the left side of the third and the right side of the fourth side-arm. In addition the main axis includes one superfluous axial piece of the path. The pathway leads into the center, and a second piece of the path in the center of the main axis leads from the center into a dead-end.

This design can be easily corrected such that there results a four-arm unicursal labyrinth as shown in fig. 3.

Figure 3. Corrections

In order to achieve this, each of the two pairs of walls delimiting the pathway drawn in blue must be shifted against another until they come to lie one above the other. This results in the extinction of the fourth segment and of the central piece of the pathway with the dead-end on the main axis.

Figure 4 shows the new pattern and the four-arm labyrinth derived from it.

Figure 4. The Labyrinth Hidden in the Draft on Fol. 53 v

So, in the rejected five-arm design, a four-arm labyrinth is contained or hidden. The course of the pathway of this follows about the same principle as in the labyrinth on fol. 51 r. I am not aware of any existing labyrinth of this type.

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The Labyrinth on Folio 51 r

In the previous post I have presented the nine labyrinth designs by Gossembrot and gave references to the sources (see below: related posts 1). The first labyrinth on folio 51 r undoubtedly is the most important of all. It is the earliest preserved example of a five-arm labyrinth at all. Furthermore, it’s course of the pathway is unprecedented and deviates from every previous type of labyrinth. Here I will show the course of the pathway and it’s special features stage by stage. For this, I use the Ariadne’s Thread inscribed into the labyrinth and in parallel the pattern. This is the same approach I had applied with the labyrinth by Al Qazvini (related posts 2). As a baseline I always use a labyrinth with the entrance on bottom and in clockwise rotational direction. Gossembrot labyrinth fol. 51 r, however, rotates anti-clockwise. Therfore, in figure 1, I first mirror the labyrinth horizontally.

Figure 1. Labyrinth on Folio 51 r (left), horizontally mirrored (right)

The image on left shows the original labyrinth of fol. 51 r, the right image shows the same labyrinth mirrored. Mirroring does not affect the course of the pathway with the exception of the pathway traversing in the opposite direction.

Fig. 2 shows the first stage of the course when it enters the labyrinth. This is nothing special. The path fills the space left over by the pattern and continues to the innermost circuit as directly as possible.

Figure 2. Way into the Labyrinth

This circuit is then traversed in a forward direction through all five segments, as can be seen in fig. 3. This is also nothing special either.

Figure 3. Forward Direction on the 7th Circuit Through all Segments

The special characteristic of the course of the path starts after it has turned at the end of the fifth segment. Then it proceeds to a movement in backward direction, following a line that alternates between forming a curve wrapping and being wrapped and also marking the axes. This process continues to the first side-arm (fig 4).

Figure 4. Backward Direction Onset of Special Course

At this point the former course is interrupted. Again the path marks the axis (first side-arm), but then continues as a meander through segment 2, as shown in fig. 5.

Figure 5. Backward Direction, Interruption, Insertion of Meander

From there the original course is resumed. Still in a backward direction, the pathway fills the rest of segment 2 and segment 1 and finally turns from the 2nd to the 1st circuit (fig. 6).

Figure 6. Backward Direction, Resumption of Special Course

From here now it continues again in forward direction and takes it’s course through all segments until it reaches the opposite side of the main axis. In passing, it fills the inner space it had left over on its course in backward direction in segments 3 and 4 (fig. 7).

Figure 7. Forward Direction Through all Segments

From there it reaches the center after having filled the space left over in segment 5 (fig. 8).

Figure 8. Completion, Reaching the Center

This course of the pathway, like in some sector labyrinths, results in symmetric pairs of nested turns of the pathway at each side-arm. Unlike in sector labyrinths, however, the pathway does not complete one sector after another, but traverses through all sectors in each direction. First in forward direction on the innermost circuit, then in backward direction modulating through circuits 6 to 2, and finally again in forward direction on circuits 1, 4, and 5.

Related Posts:

  1. Sigmund Gossembrot / 1
  2. The Labyrinth by Al Qazvini

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Labyrinth Designs – Overview

Sigmund Gossembrot the Elder, humanist and mayor of Augsburg, had compiled a miscellany around 1480 (siehe below: literature 1). Into a text in Latin on the seven arts were included nine labyrinth drawings, all executed in brown ink on paper (Kern, p. 139 / 140, see literature 2). This manuscript is accessible online in an unprecedented quality (see below: further links 1) and is licensed under a Creative Commons Attribution – NonCommercial – ShareAlike 4.0 International License (see below: further links 2).

The following figures have been obtained by copying and cropping the image files of the Münchener DigitalisierungsZentrum, Digitale Bibliothek. They can be found on sheets, folios (fol.) 51-54, each on the front-side r (= recto) and back side v (= verso). Here I first want to present a global overview. The links on the captions’ references to the folios directly lead to the corresponding pages of the online edition of the manuscript. Here you will be linked directly to a preview with miniatures of the pages. From there you can zoom in the pages or browse the manuscript. I strongly recommend to take a look at the manuscript, that is worth it!

Fig. 1 shows a five-arm labyrinth with seven circuits and a central pentagram.

Figure 1. Labyrinth on Fol. 51 r

 

Fig. 2 shows a circular, four-arm labyrinth with eight circuits.

Figure 2. Labyrinth on Fol. 51 v

In fig. 3 another circular, four-arm labyrinth with eight circuits and a somewhat differing course of the pathway is depicted.

Figure 3. Labyrinth on Fol. 52 r

Fig. 4 shows the upper, fig. 5 the lower of two square form labyrinths each with four arms and eight circuits. The uppper has the same course of the pathway as the labyrinth in fig. 3, the lower the same as the one in fig. 2.

Figure 4. Labyrinth on Fol. 52 v oben

 

Figure 5. Labyrinth on Fol. 52 v unten

In fig. 6 we see a circular one-arm labyrinth with nine circuits.

Figure 6. Labyrinth on Fol. 53 r

Fig. 7 shows an incomplete labyrinth that was crossed out with recognizably five arms and seven circuits.

Figure 7. Labyrinth on Fol. 53 v

In fig. 8 a complex labyrinth with 12 circuits can be found.

Figure 8. Labyrinth on Fol. 54 r

Finally, fig. 9 shows a circular one-arm labyrinth with 11 circuits.

Figure 9. Labyrinth on Fol. 54 v

Some of these labyrinth designs include types of labyrinths of their own, others are of existing types, some of which with unchanged course of the path, whereas in others the course of the path was modified to a multicursal maze. I will come back to this more in detail in the next posts.

Literature

  1. Gossembrot, Sigismundus: Sigismundi Gossembrot Augustani liber adversariorum, 15. Jh. München, Bayerische Staatsbibliothek, Clm 3941.
  2. Kern, Hermann: Through the Labyrinth: Designs and Meanings over 5000 years. London: Prestel 2000.

Further Links

  1. Gossembrot, Sigismundus: Sigismundi Gossembrot Augustani liber adversariorum
  2. Terms of Use

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In Greek mythology, the labyrinth is the place where the Minotaur is hidden and imprisoned. It is therefore not necessarily a real place.
The labyrinth, as we know it today, is highly inappropriate. Because it has an entrance, a clear path and an accessible center.
Thus, on the silver coins from Knossos we also find very different interpretations of the labyrinth. There are meanders and other symbolic representations.
I want to pick out a motif today and take a closer look at it.

I found two examples with the same motif. One on a coin from the Coin Cabinet of Berlin:

Minotaur 420-380 BC

Minotaur 420-380 BC: Coin Cabinet of the Staatliche Museen zu Berlin, object 18218282 obverse

Labyrinth 420-380 BC.

Labyrinth 420-380 BC: Coin Cabinet of the Staatliche Museen zu Berlin, object 18218282 reverse

And one on a coin from the British Museum in London:

Square area meander 500-431 BC

Square area meander 500-431 BC / source: Hermann Kern, Labyrinthe (German edition), 1982, fig. 43

They both represent the same thing. Although the “Berlin” coin seems to be more exact, it contains small errors in two places in the upper area. Two vertical lines collide, where a gap should actually be. This area is more accurately represented on the “London” coin, although the lines there are harder to see.

I made a “final drawing” that shows what the coin maker wanted to show. You can see lines that follow a certain pattern. They are symmetrical, repeating themselves and showing an intricate “path system”. The drawn red thread shows that.
There are four nested paths without beginning and end, but also without entrance. This is not “our” labyrinth but better suited as a prison. The Minotaur would not come out that fast.

The revised area meander

The revised area meander

This could be a hint of the Roman sector labyrinth hundreds of years later.

But it also shows a certain relationship to the Babylonian labyrinth, hundreds of years older and developed in a different culture (see the labyrinthine finger exercises in the post about the Babylonian labyrinth).

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Sector Labyrinths

At the end I will also transform a sector labyrinth into the MiM-style. What is special in sector labyrinths is, that the pathway always completes a sector first, before it changes to the next. As a consequence of this, the pathway only traverses each side-arm once. Thus it seems, that sector labyrinths may be easier transformed into the MiM-style than other labyrinths with multiple arms. I will use as an example a smaller labyrinth with four arms and five circuits. There exist several labyrinth examples of this type. I have named it after the earliest known historical example, the polychrome mosaic labyrinth that is part of a larger mosaic from Avenches, canton Vaud in Switzerland.

Figure 1. Sector Labyrinth (Mosaic) of Avenches

Figure 1 shows the original of this labyrinth (source: Kern 2000: fig 120, p 88). It is one of the rarer labyrinths that rotate anti-clockwise. On each side of the side-arms it has two nested turns of the pathway and 3 nested turns on each side of the main axis. The pattern corresponds with four double-spiral-like meanders arranged one after another – Erwin’s type 6 meanders (see related posts 2). When traversing from one to the next sector the pathway comes on the outermost circuit to a side-arm, traverses this on full length from outside to inside and continues on the innermost circuit in the next sector.

In order to bring this labyrinth into the MiM-style, first the origninal was mentally rotated so that the entrance is at bottom and horizontally mirrored. By this it presents itself in the basic form, I always use for reasons of comparability. Fig. 2 shows the MiM-auxiliary figure.

Figure 2. Auxiliary Figure

This has 42 spokes and 11 rings what makes it significantly smaller than the ones for the Chartres, Reims, or Auxerre type labyrinths. The number of spokes is determined by the 12 ends of the seed pattern of the main axis and the 10 ends of each seed pattern of a side-arm.

In fig. 3 the auxiliary figure together with the complete seed pattern including the pieces of the path that traverse the axes is shown and the number of rings needed is explained. For this the same color code as in the previous post (related posts 1) was used.

Figure 3. Auxiliary Figure, Seed Pattern and Number of Rings

As here the angles between the spokes are sufficiently wide, it is possible to use all rings of the auxiliary figure for the design of the labyrinth. We thus need no (green) ring to enlarge the center. Only one (red) ring is needed for the pieces of the path that traverse the axes – more precisely: for the inner wall delimiting them –, four (blue) rings are needed for the three nested turns of the seed pattern of the main axis, one ring (grey) for the center, and five rings (white) for the circuits, adding up to a total of 11 rings.

Fig. 4 finally shows the labyrinth of the Avenches type in the MiM-style.

Figure 4. Labyrinth of the Avenches Type in the MiM-Style

The figure is significantly smaller and easier understandable than the labyrinths with multiple arms previously shown in the MiM-style. Overall it seems well balanced, but also contains a stronger moment of a clockwise rotation that is generated by the three asymmetric pieces of the pathway and of the inner walls delimiting these on the innermost auxiliary circle.

Related posts

  1. How to Draw a MiM-Labyrinth / 14
  2. How to Find the True Meander for a Labyrinth

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