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In my last post I have shown the sequence of segments in labyrinths with multiple arms. This is unambigous. But as a disadvantage it does not indicate directly which circuit is encountered by the pathway.
Now it is also possible to keep the partition in segments but only number the circuits. This allows to indicate directly in the sequence of segments, which circuit is visited by the pathway. Thus the same number may repeatedly occur in this sequence. This works well in many cases but may also leed to problems. In the labyrinth I had shown in my last post the problem does not occur. Therefore I will illustrate it here with an other example. For this I chose the labyrinth by Valturius as this is a small, understandable example (Fig. 1).
This labyrinth from a military manuscript by Robertus Valturius of the 15th century has three arms and four circuits. (Please note, that the arms are not proportionally distributed. This, however, has no influence here. I therefore use a proportional distribution for reasons of simplicity.)
Figure 2 shows in the left image the partition and numbering by segments I had already used in my last post. The right Image shows the same partition of segments although numbered by circuits only. As the labyrinth has four circuits, there are 12 segments.
The labyrinth by Valturius is alternating. However there exists a non-alternating labyrinth with the same level sequence. And this brings us back to the problem.
Figure 3 shows the alternating labyrinth by Valturius (left image) and the non-alternating variation (right image). They show two different courses of the pathway. These are also correctly represented by the two different sequences of segments. Both sequences of segments are similar for the first 9 segments: 1 4 7 8 5 2 3 6 9 … The sequences of the three last segments, however, are different. In the labyrinth by Valturius the sequence continues with segments ……… 12 11 10. On the other hand, the sequence of segments in the non-alternating variation is ……… 10 11 12.
If, however, we number the segments by circuits, we lose the uniqueness.
Figure 4 shows the same labyrinths as fig. 3. But with their segments numbered by circuits. Both variants have the same sequence of segments 1 2 3 3 2 1 1 2 3 4 4 4. So here we can always identify in the sequence of segments, which circuit is encountered by the pathway. However, for the same sequence of segments there may exist multiple (in this case two) different courses of the pathway. The same problem occured already in the level sequence of one-arm labyrinths.
There is now a new labyrinth at this extraordinary and historically significant place.
In the church Mariä Schutz a labyrinth was built during the three-year period of renovation and rebuilding on the area of the Vogelsburg.
Father Bernhard Stühler, hospital chaplain of the Juliusspital, initiated it. Architect Stephan Tittl from the office SequenzSieben Würzburg made the architectural design of the church and delivered the layout. During the inauguration of the project turned out, that Sr. Hedwig Mayer, prioress of the Augustinusschwestern on the Vogelsburg, always had wished a labyrinth.
It’s a newly created sector labyrinth with 5 circuits. In the middle is a bowl-shaped pitch circle to divert the direction. The dividing bars form a cross and are arranged symmetrically.
The diameter amounts to 6 m, the middle to 2 m. The ways are 34 cm wide and are marked by a 6 cm wide brass sheet on the terrazzo floor. The way into the center amounts to about 64 m.
One enters the church from the south over an outside stair. On the left hand of the entrance is the labyrinth which is aligned to the west and the east. You enter it from the west, arriving the center, one looks to the east in the direction of the altar and leaves it also again in this direction.
The Oberpflegeamtsdirektor (Chief Administrative Officer) Walter Herbert of the Juliusspitalstiftung (foundation Juliusspital) said on occasion of the inauguration of the altar in May, 2016 to the interior design of the church:
With the elected interior design and with the labyrinth in the ground we would like to offer to every visitor of the Vogelsburg the possibility to find the way to one’s own center, to get back to basics and to find the possibility of steering towards God in the church space.
As Andreas proposed in his last article we can number the 20 segments for the 5 circuits in this 4-armed labyrinth. The sequence of segments can be derived from it for the pathways. Some segments form a connected section which runs through several quadrants. These segments can be marked by brackets. The sequence of segments then looks as follow: 9-5-(1-2-3-4)-8-12-(16-15)-11-(7-6)-10-(14-13) – (17-18-19-20)-21. I write the result a little bit differently than Andreas and still add the center at the end. Inside this labyrinth we have as a specific feature two segments which enclose the full length of a circuit.
Further Links (in German)
In one-arm labyrinths, each circuit is represented by one number. Therefore it is possible to capture even quite large labyrinths appropriately with the level sequence. In labyrinths with multiple arms, the pathway may repeatedly encounter the same circuit. Various possibilities exist to take account of this in the level sequence. For this, according to the number of arms, the circuits have to be further partitioned to segments. Here I will show a method in which all segments are numbered through.
For this I use an example of a labyrinth that has repeatedly been presented on this blog. It has 3 arms and 3 circuits.
First, each circuit is partitioned to three segments. One segment corresponds with a unit of the pathway between two arms. Next, the segments have to be numbered through. This can be done in different ways. Here I number them from the outside to the inside and one circuit after each other.
Now we can track the course of the pathway through the various segments. This results in the sequence of segments encountered by the pathway. In labyrinths with multiple arms the level sequence thus extends to a sequence of segments.
The sequence of segments of this labyrinth is 7 4 1 2 5 8 9 6 3. The length of this sequence of numbers is a result of the number of circuits multiplied with the number of arms. Thus, for a labyrinth with 3 circuits and 3 arms, 9 numbers are required. Whereas in a one-arm labyrinth with 3 circuits only 3 numbers are needed.
However, besides the numbers no other information is needed. The sequence of segments itself determines where the pathway makes a turn or traverses an axis. In one-arm labyrinths this had to be indicated additionally by use of separators.
Finally, I got around to visiting this unusual labyrinth from granite ashlars in the Fichtelgebirge.
You may reach it over the street from Kleinschloppen to Kirchenlamitz. There is a parking place opposite the restaurant Waldschmiede in the district Buchholz and directly behind it lies the labyrinth.
Willi Seiler from Wunsiedel, a former professional schoolteacher in the technical school for stone processing in Wunsiedel had the idea of the labyrinth. The construction works were carried out after the plans of architect Peter Kuchenreuther from Marktredwitz in 2009.
The labyrinth is from type Roman sector labyrinth with a meander in every quadrant and has 5 circuits. It is put on squarely and has the dimensions 34 x 34 m. The middle is a square of 6 m sides length with a 5-m-high obelisk, where Hermann Kern’s famous words: “In the labyrinth you will not get lost. In the labyrinth you will find yourself. In the labyrinth you will not meet the Minotaurus. In the labyrinth you will meet yourself.” are chiseled.
The ways and the granite bolders are each about 1.20 m wide. The higher ashlars in the middle and around are about 1.20 m high, the smaller ones inside from 60 to 80 cm. In every quadrant there is a small loophole to leave the way which amounts to 400 m after all. The middle contains the obelisk, some wooden benches and the ground is covered with a paved labyrinth showing the paths enlargedin black stones as it were a negative of the “big” labyrinth.
The middle enlarged:
Behind the labyrinth a small hill is raised from which one can overlook the whole area. Several boards of information to the geology, fauna, granite quarrying in the Fichtelgebirge among other things as well as to the idea of the labyrinth are put up on the site.
Service station for spirit and soul
Labyrinths still are in the world since millenniums in the most different forms. After Ancient Greek myth the first labyrinth was built by Dädalos for king Minos on Crete as a prison for the Minotauros. In the antiquity it is often shown as a square built by windings of meanders. The Christians pervaded this ancient motive with new sense. In many old churches labyrinths drawn on the ground with black and white stones show with their unpredictable bends the human life with all its scrutinies, delays and complications, while in the middle, the aim, waits heavenly Jerusalem.
The labyrinth is always purposeful and not a maze, how frequently is falsely presumed.
„The construction plan of the labyrinth is conceivably simple. It has an entrance and a way which leads in numerous bends to a middle. One can go through it fast without having found out something. Then the way through the labyrinth is not more than just a leisure activity or a sportive act. Who crosses, however, the way with a spiritual feeling, who embarks on a journey consciously and with alert soul, will attain a place of self-encounter and self-discovery.“ Uwe Wolff
In an earlier post „Type or Style / 6“ (see related posts, below) I had already mentioned the level sequence. And I had stated two reasons for why I do not use it for naming types of labyrinths.
- Among the one-arm labyrinths only in alternating labyrinths there exists exactly one type of labyrinth for each level sequence. If we also consider non-alternating labyrinths, in which the pathway traverses the axis, there can exist multiple courses of the pathway for the same level sequence.
- In labyrinths with multiple arms the level sequence may rapidly increase to a length and complexity that is difficult to memorize.
Here I want to address the first issue further. I do this because there is a very simple solution for it. In one-arm labyrinths every circuit is represented by one number. In real practice only few of the larger labyrinths will have more than 15 – 17 circuits. Most one-arm labyrinths have a markedly smaller size. Therefore these labyrinths could be quite simply be named with their level sequence. But there remains the problem with the ambiguity. Erwin had elaborated on it in his post “The Classical 7 Circuit Labyrinth with Crossed Axis“ (see related posts, below). I will illustrate it here and use some figures of Erwin’s post.
In Figure 1 three labyrinths with the level sequence 3 2 1 4 7 6 5 are shown. The first image shows the alternating Cretan type, the second and third images show non-alternating labyrinths with the same level sequence. In the second image, the pathway traverses the axis when changing from the 1st to the 4th circuit. In the third image it traverses the axis from the 4th to the 7th circuit. (There is an other labyrinth with the pathway traversing the axis twice, first from the 1st to the 4th and second from the 4th to the 7th circuit). We thus are here presented with the only one alternating and several non-alternating types of labyrinths with the same level sequence.
Now there is a simple solution, to take account of this in the level sequence. For this it has to be considered, that the single numbers (not numerals) of the level sequence are separated. This separation can be obtained in different ways, using blanks, commas, semicolons etc. These separators, however, can also be used to indicate how the path will continue on the next level. Therefore we could e.g. define: if the path changes direction from the former to the next circuit, we will separate the numbers with a vertical slash. If, on the other hand, the path continues in the same direction and thus traverses the axis, we separate with a hyphen. This enables us to specify the level sequence so that it is unique also in non-alternating labyrinths. I show this in figure 2 using the images from figure 1.
Here we see for each labyrinth the unique level sequence with separators. The sequence of numbers is the same 3 2 1 4 7 6 5 in all three labyrinths. However, whereas in the alternating Cretan type all numbers are separated by slashes (as the path always changes direction when progressing from one circuit to an other), the level sequence in the second labyrinth is written with a hyphen between 1 and 4, and the level sequence in the third image with a hyphen between 4 and 7.
Indeed, the notation can be even simplified by separating with blanks and using hyphens only to indicate where the pathway traverses the axis. The level sequences would then be written as follows:
for the 1st image: 3 2 1 4 7 6 5
for the 2nd. image: 3 2 1-4 7 6 5
for the 3rd image: 3 2 1 4-7 6 5
What matters is that in the level sequence it is indicated where the path traverses the axis. With this specification it is now possible to give a unique level sequence to each course of the pathway and thus a unique name to each alternating and non-alternating type of labyrinth.
This way to walk a labyrinth is known as the Appleton for the Classical labyrinth (read more in Further Links at the bottom of this post). Thereby one can go in pairs in the same direction on lanes next to each other. However, one person goes into the labyrinth and the other outwards. This also functions in groups. However, this is only possible on certain lanes, not on all.
In the Baltic wheel this is quite different. There it is possible on all lanes from the beginning to the end. For there are two ways: One long way to walk in or out, a second short way to do the same.
The blue ball wants to get into the center of the labyrinth and takes the long way in. The yellow ball takes the short way directly into the center, from where it wants to take the long way out.
They stand side by side and walk off together in the same direction. It is also possible that others join them and form a long queue, since there is enough place.
Arriving at the second turning point there is a special moment: They meet each other and their lanes cross.
But they don’t change direction. They continue their way.
They have both nearly achieved their aim: The blue ball has arrived at the center. The yellow ball approaches the end of its way.
The blue ball can take the short way out. The yellow ball has arrived the exit. Both have exchanged their places.
The end is the beginning and the beginning is the end.