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Posts Tagged ‘walk through labyrinth’

Here it is about the decoding of the circuit sequences of the row-shaped 21 visceral labyrinths shown in the last article on this subject (see related posts below).

The question is: Can I generate one-arm alternating labyrinths with one center in the middle from them? That means no walk-through labyrinths where the also unequivocal path passes through, but is ending at an aim in the middle.
Maybe one could call them “walk-in labyrinths” contrary  to the “walk-through labyrinths”?

The short answer: Yes, it is possible. And the result are 21 new, up to now unknown labyrinths.

The circuit sequence for the walk-through labyrinth can be converted into one for a walk- in labyrinth by leaving out the last “0” which stands for “outside”. The highest number stands for the center. If it is not at the last place in the circuit sequence, one must add one more number.
This “trick” is necessary only for two labyrinths and then leads to labyrinths with even circuits (VAT 984_6 and VAN 9447_7).

The gallery shows all the 21 labyrinths in concentric style with a greater center.

Look at the single picture in a bigger version by clicking on it:

 

All labyrinths are different. Not one has appeared up to now somewhere. They have between 9 and 16 circuits, the most 11 circuits. They show between 3 and 6 turning points.

In these constellations there are purely mathematically seen 134871 variations of interesting labyrinths, as proves Tony Phillips, professor of mathematics.

There are still a lot of possibilities to find new labyrinths or to invent them.

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Further Link
The website of Tony Phillips

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Or more precisely: The circuit sequence of the the row-shaped visceral labyrinths. Amongst the up to now known 27 visceral labyrinths there are 21 row-shaped visceral walk-through labyrinths.  The circuit sequence may serve as a distinguishing feature. Here I would like to show the sequences of all 21 specimens.

Look at the single picture in a bigger version by clicking on them:

The method is to number the vertical loops in series from left to right. The shifting elements do not receive a number. Besides, “0” stands for outside. The transverse loops in E 3384 r_4 and E 3384 r_5 are numbered the same way. A special specimen is E 3384 v_4. Here some loops are “evacuated”. However, also there a useful circuit sequence can be found.

All labyrinths are different. No one is like the other. That alone is remarkable. So they do not follow an uniform pattern.

A first look at the circuit sequences shows that they resemble very much the circuit sequences of the one-arm alternating classical labyrinths. That means: The first digit after 0 is always an odd number. Then even and odd numbers are following alternating.

One of the next articles will deal with the decoding of the circuit sequences.

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Or differently asked: Can I transform a classical labyrinth into a Babylonian visceral labyrinth?

Therefore we should first see the differences; and then the interlinking components.

As an example I start with the best known classical labyrinth: The 7 circuit Cretan labyrinth.

The 7 circuit labyrinth

The 7 circuit Classical labyrinth, on the right the complementary to it

It has a center and an entrance. There is only one way in. In the middle I am at the aim and at the end of the way. To leave I must turn and take the same way in reverse order.

Among the Babylonian visceral labyrinths one can distinguish two main groups. One are more round and devoured into each other, while in others the loops are arranged row-shaped.

Here as an example the labyrinth E3384_r8 on a clay tablet from Tell Barri (Syria) (for more, please see related posts below).

A Babylonisn visceral labyrinth

A Babylonian visceral labyrinth with 10 circuits and two entries

In the visceral labyrinth I have two entries and no real center. Nevertheless, the way leads through all of the loops to the other access. It is a walk-through labyrinth.

The circuits here are numbered from the left to the right, while in the classical labyrinths they are numbered from the outside inwards. “0” stands for the outside, in the classical labyrinth the last figure for the center.

Every labyrinth is designated by a row of numbers, the circuit sequence or the path sequence. This is the order in which the circuits will be run one by one.

The connecting element therefore is the circuit sequence. Hence, we must construct “row-shaped” walk-through labyrinths from the circuit sequence of the classical labyrinths.

At first we take the 7 circuit labyrinth as shown above. We use the circuit sequence and connect the circuits arranged in row accordingly. The second “0” indicates the walk-through labyrinth.
Then this looks as follows:

Das 7-gängige Labyrinth als Eingeweidelabyrinth

The 7 circuit classical labyrinth as visceral labyrinth, on the right the complementary

We make this still for some more classical labyrinths.

Das 3-gängige Labyrinth

The 3 crcuit labyrinth, on the left the original, on the right the complementary to it

The original is developed from the meander and is also called Knossos labyrinth. The right one is developed from the “emaciated” seed pattern. However, is at the same time complementary to the Knossos labyrinth. Under the walk-in labyrinths the visceral walk-through labyrinths.


A 5 circuit labyrinth:

Das 5-gängige Labyrinth

A 5 circuit labyrinth, on the right the complementary

There are still other 5 circuit labyrinths with an other circuit sequence. But, in principle, the process is the same one.

The shown examples were all self-dual labyrinths.


Now we take a 9 circuit labyrinth. There are more variations:

Das 9-gängige Labyrinth

A 9 circuit labyrinth in four variations

And here the corresponding visceral labyrinths:

Die Eingeweidelabyrinthe

The visceral labyrinths


Here the 11 circuit labyrinth with the corresponding visceral labyrinths:

Das 11-gängige Labyrinth

The 11 circuit labyrinth and its complementary

This one is self-dual again. Therefore there is only one complementary version to it.


Here the 15 circuit labyrinth:

Das 15-gängige Labyrinth

The 15 circuit labyrinth and its complementary

This is also self-dual.

If we compare these newly derived visceral labyrinths to the up to now known historical Babylonian visceral labyrinths, we can ascertain no correspondence. Maybe a clay tablet with an identical labyrinth appears somewhere and sometime?

So far we know about 21 Babylonian visceral labyrinths as row-shaped examples in most different variations.

For comparison I recommend the following article with the overview.

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We take a 7-circuit classical labyrinth and number the single circuits from the outside inwards. “0” stands for the outside, “8” denotes the center. I take this two numbers into the circuit sequence, although they are no circuits. As start and end point they help to better understand the structure of the labyrinth.

Ariadne's thread in the 7-circuit labyrinth

Ariadne’s thread in the 7-circuit labyrinth

The circuit sequence is: 0-3-2-1-4-7-6-5-8

Everybody which already has “trampled” Ariadne’s thread (the path) in the snow knows this: Suddenly there is no more place in the middle, and one simply goes out. And already one has created a walk-through labyrinth. This is possible in nearly all labyrinths.

Then maybe it looks like this:

Ariadne's thread in a walk-through labyrinth

Ariadne’s thread in a walk-through labyrinth

If one wants a more compact labyrinth, one must change the shape. The internal circuits become, in the end, a double spiral. We can make either two separate ways or join them. So we will get a bifurcation.

Just about:

The 7-circuit walk-through labyrinth

The 7-circuit walk-through labyrinth

We will get the following circuit sequence if we take the left way or the fork to the left:
0-3-2-1-4-7-6-5-0

Now we take first the right way or the fork to the right, then the circuit sequence will be:
0-5-6-7-4-1-2-3-0

Because the two rows are written among each other, they simply can be add up together (without the first and the last digit):
8-8-8-8-8-8-8

This means: If I go to the left, I am in the original labyrinth, if I go to the right, I cross the complementary one.

The complementary labyrinth of the 7-circuit labyrinth

The complementary labyrinth of the 7-circuit labyrinth

It has the circuit sequence 0-5-6-7-4-1-2-3-8.

Or said in other terms: The walk-through labyrinth contains two different labyrinths, the original one and the complementary one.

The 7-circuit labyrinth is self-dual. Therefore I only get two different labyrinths through rotation and mirroring as Andreas has described in detail in his preceding posts.

How does the walk-through labyrinth look if I choose a non self-dual labyrinth?

I take this 9-circuit labyrinth as an example:

A 9-circuit labyrinth

A 9-circuit labyrinth

Here the boundary lines are shown.
On the top left we see the original labyrinth, on the right side is the dual to it.
On the bottom left we see the complementary to the original (on top), on the right side is the dual to it.
However, this dual one is also the complementary to the dual on top.

The first 9-circuit walk-through labyrinth

The first 9-circuit walk-through labyrinth

The first walk-through labyrinth shows the same way as in the original labyrinth if I go to the left. If I go to the right, surprisingly the way is the same as in the complementary labyrinth of the dual one.

And the second one?

The second 9-circuit walk-through labyrinth

The second 9-circuit walk-through labyrinth

The left way corresponds to the dual labyrinth of the original. The right way, however, to the complementary labyrinth of the original.

Now we look again at a self-dual labyrinth, an 11-circuit labyrinth which was developed from the enlarged seed pattern.

An 11-circuit labyrinth in Knidos style

An 11-circuit labyrinth in Knidos style

The left one is the original labyrinth with the circuit sequence:
0-5-2-3-4-1-6-11-8-9-10-7-12

The right one shows the complementary one with the circuit sequence:
0-7-10-9-8-11-6-1-4-3-2-5-12

The test by addition (without the first and the last digit):
12-12-12-12-12-12-12-12-12-12-12

Once more we construct the matching walk-through labyrinth:

The 11-circuit walk-through labyrinth

The 11-circuit walk-through labyrinth

Again we see the original and the complementary labyrinth combined in one figure. If we read the sequences of circuits forwards and backwards we also see that both labyrinths are mirror-symmetric. This also applies to the previous walk-through labyrinths.

Now this are of all labyrinth-theoretical considerations. However, has there been such a labyrinth already as a historical labyrinth? By now I never met a 7- or 9-circuit labyrinth, but already an 11-circuit walk-through labyrinth when I explored the Babylons on the Solovetsky Islands (see related posts below). Besides, I have also considered how these labyrinths have probably originated. Certainly not from the precalled theoretical considerations, but rather from a “mutation” of the 11-circuit Troy Towns in the Scandinavian countrys. And connected through that with another view of the labyrinth in this culture.

There is an especially beautiful specimen of a 15-circuit Troy Town under a lighthouse on the Swedish island Rödkallen in the Gulf of Bothnia.

A 15-circuit Troy Town on the island Rödkallen

A 15-circuit Troy Town on the island Rödkallen, photo courtesy of Swedish Lapland.com, © Göran Wallin

It has an open middle and the bifurcation for the choice of the way. This article by Göran Wallin on the website Swedish Lapland.com reports more on Swedish labyrinths.

For me quite a special quality appears in these labyrinths, even if there is joined a change of paradigm.

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The Babylonian visceral labyrinths have found entrance in the modern medicine. In quite an unusual way. A labyrinth-like chip serves for the diagnosis of cancer cells in the blood. The labyrinthine arrangement of the fluid channels shows up to be an effective tool to isolate circulating cancer cells in the blood. That means that the curvature and the tortuous route in the labyrinth is especially useful.

Labyrinth-Chip

Labyrinth-Chip, Photo courtesy of the University of Michigan, © Joseph XU, Michigan Engineering Communications & Marketing

What kind of labyrinth is this now?
At first sight it reminds of a medieval labyrinth, as it is the famous Chartres labyrinth. It has ten circuits in three sectors, in one these are eight. They will not be traversed one after the other, but reciprocally. And then it has two accesses: An entrance and an exit. It is a walk-through  labyrinth as we know that of the Babylonian labyrinths. Hence, we have an own, new type. And we see the pathway in the labyrinth, Ariadne’s thread. This reminds us of the Greek myth of the Minotaur, which is to be combated like cancer here.
If the Babylonian visceral labyrinths served for the divination, here the labyrinth serves the medicine.
This reminds me of “Ancient Myths & Modern Uses“, the book about labyrinths of Sig Lonegren.

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I have written quite in detail about the Babylonian labyrinths. For that I refer to the Related Posts below. Now here it should be a summary.

I have taken most information from the detailed and excellent article of Richard Myers Shelton in Jeff Sawards Caerdroia 42 (March 2014) to which I would also like to point here once again.

The findings are in the most different collections and museums worldwide. I use the catalogue number to describe the various clay tablets.

The oldest specimens in angular shape dates back to Old Babylonian times about 2000 – 1700 BC and are to find in the Norwegian Schøyen Collection.

The Rectangular Babylonian Labyrinth MS 3194

The Rectangular Babylonian Labyrinth MS 3194

The Square Babylonian Labyrinth MS 4515

The Square Babylonian Labyrinth MS 4515

Then follows the different more round visceral labyrinths from the Middle Babylonian to the Neo-Babylonian times about 1500 – 500 BC. They are to be found in the Vorderasiatisches Museum Berlin (VAN… and VAT… numbers), in the Louvre (AO 6033), in the Rijksmuseum van Oudheden Leiden (Leiden labyrinth) or come from Tell Barri in Syria (E 3384).

I have numbered the tablets with more figures from the left on top to the right below and present the well visible ones (21 pieces) in a bigger tracing. Some figures are unrecognisable or destroyed. All together we have 48 illustrations.

Then there are another 6 single specimens. They follow here:

Visceral Labyrinths

Visceral Labyrinths

Here the 21 bigger tracings of the well recognisable specimens:

The Visceral Labyrinth on VAT 984

The Visceral Labyrinth on VAT 984

The Visceral Labyrinths on VAN 9447

The Visceral Labyrinths on VAN 9447

The Visceral Labyrinths on E 3384 recto

The Visceral Labyrinths on E 3384 recto

The Visceral Labyrinths on E 3384 verso

The Visceral Labyrinths on E 3384 verso

So we have a total of 56 Babylonian labyrinths, 29 of which are clearly recognisable.

It is common to all 29 diagrams that they show an unequivocal way which is completely to cover. There are no forks or dead ends like it would be in a real maze.

All 29 specimens have a different layout or ground plan and therefore no common pattern.

Everyone (except VAT 9560_4) has two entrances. On the angular labyrinths they are lying in the middle of the opposite sides. On the remaining, mostly rounded specimens they are situated side by side or are displaced.

The Leiden Labyrinth is simply a double spiral. An other special feature is the visceral labyrinth VAT 9560_4. It has only one entrance and a spiral-shaped centre, just as we have that in the Indian labyrinth. It shows perfectly a labyrinth.

The Mesopotamian divination labyrinth could also have a closed middle (and therefore only one entrance) and the loops run in simple serpentines.

The remaining 24 specimens have all a much more complicated alignment with intertwined bends and loops.

The 27 unreadable specimens are presumably structured alike. And maybe there are still more clay tablets awaiting discovery?

We know nothing about the meaning of the angular specimens. The remaining 27 more rounded specimens are visceral labyrinths.

The visceral labyrinths show the intestines of sacrificial animals as a pattern for diviners, describing how to interprete them for oracular purposes in the extispicy. From there it is also to be understood that they should look very different. This explains her big variety. And also again her resemblance. They represent rather an own style than an own type.

The Babylonian labyrinths come from an own time period, from another cultural sphere and follow a different paradigm than the usual Western notion of the labyrinth. They are above all walk-through labyrinths. However, in our tradition we also know walk-through labyrinths, especially the Wunderkreis.

A Wunderkreis in Babylonian style

A Wunderkreis in Babylonian style: The logo for the gathering of the Labyrinth Society TLS in 2017), design and © Lisa Moriarty

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And vice versa: How to make a Wunderkreis from a Babylonian visceral labyrinth.

That’s possible, at least with the Babylonian Umma Labyrinth.

The essentials of a labyrinth ly in the course of the pathway expressed by the level sequence, not the external form or layout. More exactly Andreas calls this the pattern.

The Babylonian Umma Labyrinth

The Babylonian Umma Labyrinth

The Umma labyrinth has two turning points surrounded by two circuits each and a meander in the middle. The two entries ly outside. There is only one, unequivocal way through the labyrinth.

The Wunderkreis has a double spiral in the centre and two other turning points with arbitrarily many circuits. Besides, a side has a circuit more than the other. The entries are in the middle section.

A large Wunderkreis

A large Wunderkreis

In order to indicate the single developing steps I first transform a “completely developed” Wunderkreis into the smallest possible version.

It looks thus: A meander in the middle and two other turning points with a total of three circuits as to be seen in the labyrinth type Knossos.

The smallest Wunderkreis

The smallest Wunderkreis

To be able to compare this small Wunderkreis to the Umma labyrinth, I lay all centres (at the same time the ends of the boundary lines or the turning points) on a single line. Just as if I folded the triangle built from the turning points.

The compressed Wunderkreis

The compressed Wunderkreis

Both entries are here in the middle section, in the Umma labyrinth they are outside and side by side. Besides, there is one more circuit on the left side. Now I add one circuit to the figure and the entry will change to the outer side on the right as well.

One more circuit

One more circuit

I now turn the second entry to the left side. As a result, the two entries  point in different directions.

The two entries outside

The two entries outside

Hence, I turn the right entry completely to the outer side on the left beside the left entry. As I do that geometrically correct, two empty areas appear.

The two entries side by side

The two entries side by side

Now I extend both entry paths by a quarter rotation upwards and turn the whole figure to the right by some degrees . Thus I receive the complete Umma labyrinth.

The Babylonian Umma Labyrinth

The Babylonian Umma Labyrinth

If I want to develop the Wunderkreis from the Umma labyrinth, I must leave out some circuits, turn the whole figure and finally raise the middle part.

The nucleus

The nucleus

The supplements made in the preceding steps are emphasised in colour. The nucleus of the visceral labyrinth contains the Wunderkreis.

Surely the Wunderkreis as we know it nowadays was not developed in this way. There are no historical documents to prove that. However, in my opinion the relationship of both labyrinth figures can be proved thereby. They are not simply spirals or meanders. These elements are rather included and connected in a “labyrinthine” way.

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