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On my own behalf

Welcome to the Labyrinth

The topic of this blog is the labyrinth. Under nearly all aspects, I would like to arouse your interest on the fascinating lines and the meaning of this old object. Being an old surveyor I put my focus on the geometrical shape.
A new post should be published about twice a month. Meanwhile I am accompanied by Andreas Frei as coauthor.

Contents

In a blog the single posts (articles) are disposed in reverse order: the latest posts first, the older ones following. The display of the content is thus different from a website where it is always permanent.

Anyone who is looking for something special about labyrinths or just wants to know what he could find on this blog, maybe would like to have an overview.

I can provide this now and offer it as an own page titled Contents.

The register with the table of Contents is on top of the blog above the header image next to About us.

For a better view

For a better view

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World Labyrinth Day 2019

Again you are invited from The Labyrinth Society to celebrate the World Labyrinth Day:

Celebrate the 11th Annual World Labyrinth Day on May 4, 2019 and join over 5,000 people taking steps for peace, ‘Walking as One at 1’ in the afternoon. Last year there were participants in over 35 countries.

Flyer TLS

A small, but global Wunderkreis on the flyer of the TLS

Most nicely it would be if everybody which is able would walk a labyrinth. But it is also possible, as a substitute to trace a finger labyrinth, to make a labyrinth meditation or to be active labyrinthine in some way.

More here:

If you are looking for a labyrinth near you, maybe you will find one here:

Find our Typology Confirmed

In chapter 3 of his book, Herman Wind (see below: Literature 1) aims at introducing a new categorization of labyrinths. For this purpose he has used images of labyrinths primarily from Kern (Literature 2) and also from some other sources. Wind has abstracted the sequences of circuits from the ground plans of the individual labyrinths. In the labyrinth library, table 3.2.1 A-F on pages 73-78 of his book, entries of 235 labyrinths can be found. Each line represents one labyrinth with a reference to figure, location, date when recorded and sequence of circuits. Labyrinths with the same sequences of circuits were arranged subsequently. By this, Wind has attributed similar labyrinths to the same groups, divergent labyrinths to different groups and thus created a typology. However, he does not term his groups „types“ but „families“ instead. These families have not been given different names and are also not always clearly distinguished one from another. Therefore in the labyrinth library, the reader himself must draw parentheses around the lines with the same sequences of numbers in order to identify the families.

In the book, five examples of the use of the labyrinth library are presented. Let us have a look at the first example (p. 81). This shows examples of labyrinths that were attributed to the same family as the labyrinth of Ravenna.

Figure 1. Labyrinths Attributed to the Same Family as Ravenna

Examples A „Filarete“, C „Ravenna“, and F l(eft) „Watts 7 circuits“ all have the same sequence of circuits. Example B „Hill“ was equally attributed to this family, even though it is completely different. It can be seen at first sight, that this labyrinth does not belong to this family. This is a faulty drawing of a labyrinth of the Saffron Walden type. It seems, there has been some mistake in the attribution of the labyrinth in the labyrinth library. Interestingly, neither the author nor the editor have noticed this. Although they have noticed the difference in the much more resembling example F r(ight) „Watts 11 circuits“, but only stated a certain similarity with the family of Ravenna. This is just what can be seen in a direct comparison of both images F l and F r.

The way Wind uses the sequence of circuits causes two problems:

First: This sequence of circuits is unique only in alternating one-arm labyrinths. If we consider also non-alternating labyrinths, examples with different courses of the pathway may have the same sequence of circuits (fig. 2).

Figure 2. Labyrinths with the Sequence of Circuits 7 4 5 6 1 2 3 0

So, Wind attributes the two non-alternating labyrinths (a) St. Gallen and (b) Syrian Grammar to the same family. This is correct. Should he find an alternating labyrinth of the shape (c), however, he would have to attribute this to the same family, although it has a clearly different course of the pathway. This because it’s sequence of circuits is 7 4 5 6 1 2 3 0, just the same as in examples (a) and (b). (For other examples with ambiguous sequences of circuits see related posts 1, 2).

Second: Wind’s sequences of circuits for the labyrinths with multiple arms are incomplete. They only indicate which circuits are covered at all but provide no information on how long the respective pieces of the pathway are. Such sequences of circuits are not even unique in alternating labyrinths. As Jacques Hébert explains, the sequence of circuits in labyrinths with multiple arms must take into account the division into segments and the resulting variation in length of path segments (Literature 3). This can be done in different ways.

Figure 3. Sequences of Circuits of the Wayland’s House Labyrinth

Figure 3 shows one of the possibilities using a pure sequence of numbers with the example of the Wayland’s House 1 labyrinth. The sequence of circuits of this labyrinth according to Wind (lower row W:) has 21 numbers. If we consider also the length of the path segments following Hébert (upper row H:) the sequence has 30 numbers. From Wind’s sequence of circuits the labyrinth cannot be restored without an image of it or only after multiple attempts. From Hébert’s sequence of circuits it can be restored without difficulty.

That there may exist alternating labyrinths with different courses of the pathway for the same incomplete sequence of circuits is shown in fig. 4.

Figure 4. Labyrinths with Different Courses of the Path and the Same Incomplete Sequence of Circuits

The two labyrinths shown have different courses of the pathway. This is represented in the complete sequence of circuits (upper lines). In the incomplete sequence of circuits (lower lines), however, the difference has disappeared. It is the same for both labyrinths.

Conclusion

The categorization by Wind is not new. We have done this already (Literature 4). We have used about the same material, have attributed similar labyrinths to the same groups and divergent labyrinths to different groups and refer to this as a typology (related posts 3, 4, 5). We also obtain more or less the same results (further links). Thus, the categorization by Wind confirms our typology to a great extent. As the criterion for similar or divergent, we use the course of the pathway. However, we don’t describe this with the sequence of circuits but with the pattern. This allows us a unique and complete representation of the course of the pathway and an unambigous attribution of the labyrinth examples to types of labyrinths.

Literature

  1. Listening to the Labyrinths, by Herman G. Wind, editor Jeff Saward. F&N Eigen Beheer, Castricum, Netherlands, 2017.
  2. Kern H. Through the Labyrinth: Designs and Meanings over 5000 years. London: Prestel 2000.
  3. Hébert J. A Mathematical Notation for Medieval Labyrinths. Caerdroia 34 (2004), p. 37-43.
  4. Frei A. A Catalogue of Historical Labyrinth Patterns. Caerdroia 39 (2009), P. 37-47.

Related Posts

  1. Circuits and Segments
  2. The Level Sequence in One-arm Labyrinths
  3. Type or Style / 6
  4. Type or Style / 5
  5. Type or Style / 1

Further Links

Katalog der Muster historischer Labyrinthe

In 2017, a commemorative coin dedicated to the Minoan civilization was issued by the Mint of the Central Bank of Greece.
This earliest civilization in Europe can be traced back to the years around 2600 BC. The Minoan civilization got its name from the famous King Minos. The story goes that, with the help of the god of the seas, Poseidon, and a white bull, he came to power and thus gained fame and reverence among his people.

The 50-euro gold coin from 2017 was issued with an edition of 1500 pieces and minted in real gold (999.9 / 1000) in the highest collector quality “polished plate”.

Here is the value side:

Value side: Hellenic Democracy 50 Euro

Value side: Hellenic Democracy 50 Euro

And here the picture side:

Picture side: Minoan Civilization 2017

Picture side: Minoan Civilization 2017

Two nested cross meanders can be seen in a large square around 5 smaller squares.
Here is the structure in a black and white tracing:

Draw up of the picture side

Draw up of the picture side

The black lines form two closed line systems without beginning and end. The white lines have branches and dead-ends, also without access. This is reminiscent of a similar representation on the silver coins of Knossos, which are well over 2000 years older (see related posts below).

Should the representation again symbolize the labyrinth of the Minotaur?

Related Posts

Type and Style

In my post Type or Style / 4 from August 2015, I have discussed the typology of the website Begehbare Labyrinthe (related posts 4). In the meantime, this typology has been completely revised (additional links). The new typology adopts our principles relating to type (related posts 3) and style (related posts 2). Furthermore it combines type and style. All walkable labyrinths were now attributed to types according to their course of the pathway. Labyrinths with the same course of the pathway (pattern, sequence of circuit) are of the same type. These types were then further divided into groups according to the style. Also the naming of the types has been reworked.

This whole thing can be well explained using the basic type. „Basic type“ is the new name of the type that formerly or elsewhere has been termed „classical“ or „Cretan“ type of labyrinth. This type has one axis, seven circuits and the pattern shown in fig. 1.

Figure 1. Pattern Basic Type

Figure 1 shows the pattern in pure form on left, and on right with an aid how to read it. It is read from top left to bottom right (related posts 5). To this corresponds the course of the path in it’s sequence of circuits 3 2 1 4 7 6 5 (related posts 1). By this, the type is accurately described. It is the most frequent type of labyrinth worldwide. And also in the typology of Begehbare Labyrinthe it is by far the most frequent type. Means that of the currently included 305 walkable labyrinths, 133 are of the basic type. These are designed in various styles:

  • „triangle“ (1 example)
  • „rectangle“ (1 example)
  • „classic“ (97 examples)
  • „Knidos“ (15 examples)
  • „concentric“ (15 examples)
  • „Man-in-the-Maze“ (1 example)
  • „other“ (3 examples).

Each type of a labyrinth in each of its styles is depicted with a figure of one corresponding labyrinth example. Figure 2 shows as an example the section representing the basic type in the classical style with its 97 examples.

Figure 2. Section Basic Type in Classical Style

If you move the cursor over the image of the labyrinth, the pattern is overlaid. At the side of the image all attributed walkable labyrinths are listed. Moving the cursor over a name makes an image of the corresponding labyrinth fade in. A click into a link brings you to the page with the full entry of the corresponding labyrinth. This often includes a comprehensive image of the whole labyrinth, and an extensive description of it including type, style, number of circuits, number of axes, size and measurements, materials and other information.

At present, the typology includes about 60 different types and some 10 styles. However, not every type is represented in each style. Despite this, the typology at the moment contains 92 groups composed of types and styles, what is more than the 60 pure types, that are based exclusively on the course of the pathway. These groups cover all walkable labyrinths listed in the website. However, from time to time, new labyrinth examples are added and therefore also the number of types and styles may increase further.

The full list of the types of labyrinths is ordered in increasing order first by the number of axes, then by the number of circuits. So, first all one-arm types of labyrinths are listed, and these in ascending order by the number of circuits from the smallest with 3 circuits to the largest with 11 circuits. Next follow the types with 2, 3, 4, 5, 6 und 8 arms, each again in ascending order by the number of circuits.

This new typology is now systematic, consistent, clearly reproducable, and completely covers the listed walkable labrinths. Furthermore it can be easily extended if labyrinth examples in new types or styles are added to the list.

Related Posts:

  1. The Level Sequence in One-arm Labyrinths
  2. Type or Style / 7
  3. Type or Style / 6
  4. Type or Style / 4
  5. How to Read the Pattern

Additional Links:

  1. Typology Begehbare Labyrinthe

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).

Related Posts

Further Link

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

The silver coins of Knossos are quoted again and again when we talk about the labyrinth. They can be found in the major museums of the world.

Last year I was able to see and photograph one of them on a trip to Vienna in the Coin Cabinet of the Kunsthistorisches Museum.

Kinsthistorisches Museum Wien

Kinsthistorisches Museum Wien

The book “Labyrinths” by Hermann Kern shows illustrations of 20 coins from the British Museum in London.

Meanwhile there is a digital interactive catalog of the Coin Cabinet of the Staatliche Museen zu Berlinn, where you can access more than 34,000 coins.

With the search term “Labyrinth Knossos” I found 22, which I can show here under the following license.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Germany License.

The coins cover a period of 425 BC until 12 BC. Shown is mostly the reverse of the coin.

For the interpretation of the representations I have found some interesting information in the description that I quote here (translated from German):

The Cretan town of Knossos has been closely linked to the myth of the Minotaur since antiquity. His mythical dwelling, the labyrinth, was one of the city’s landmarks. However, the depiction of the labyrinth on the Knossos coins came in very different ways, since a real non-existing place had to be shown. The labyrinth is always pictured in supervision, but with different outer shapes and structuring. Only in supervision, the labyrinth can be detected as such.

I highly recommend visiting the digital catalog. There are to find many additional details about the coins. In particular, there is the possibility to look at both sides and to retrieve further information.

Related Posts

Further Links

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