# Listening to the Labyrinths

### 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.

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