Posts Tagged ‘babylonian labyrinth’

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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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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In the article by Richard Myers Shelton in Jeff Sawards Caerdroia 42 (March 2014)  there is the picture of a visceral drawing on a clay tablet which is older than those we have seen before (see related posts below).

Clay tablet with diagram

Clay tablet from Umma of Old Babylonian times, photo courtesy of the Louvre

The clay tablet with the visceral drawings was found in the old Sumerian city of Umma, the today’s Tell Jokha in Iraq. It dates from the time about 1900 – 1600 B.C. and you can now see it in the Louvre under the number AO 6033.
The photo can be found in the cuneiform digital library initiative of the University of California, Los Angeles, under the CDLI number P 386355.

Unfortunately, the tablet is damaged. Nevertheless, the missing lines can be reconstructed perfectly and then show the following plan:

The visceral drawing on tablet AO 6033

The visceral drawing on tablet AO 6033

The alignment reminds very strongly of the so-called Berlin labyrinth on the clay tablet VAT 744 at the Vorderasiatisches Museum of Berlin which is some hundred years younger.

The visceral drawing on tablet VAT 744

The visceral drawing on tablet VAT 744

Despite the resemblance the lines in the visceral drawing on tablet AO 6033 show a completely different labyrinth.
The path (Ariadne’s thread) inside the tablet ascertained from the boundary lines looks thus:

Ariadne's thread in the visceral drawing on AO 6033

Ariadne’s thread in the visceral drawing on AO 6033

Based on these lines I construct a geometrically exact figure consisting of arc elements. The midpoints of them can be arranged on a single line.

Ariadne's thread geometrically correct

Ariadne’s thread geometrically correct

After that I construct the boundary lines around the same midpoints and will obtain the complete labyrinth:

The labyrinth

The labyrinth

The alignment is completely different from the one of the Berlin labyrinth. In the middle there is a kind of a double spiral. Besides there are two turning points. The two sickle-shaped empty areas are remarkable.

Anyway we see an hitherto unknown walk-through labyrinth. Maybe even the oldest one proved so far? In any case, it is older than the example on the tablet of Pylos.

How should one name it? Referring to the proposals of Andreas maybe: The Babylonian Umma labyrinth.

Who would like to draw or build such a labyrinth as a walkable one? The following drawing offers the necessary information. The measurements are to be understood as units. So “1” can be: 1 cm, 10 cm, 60 cm, 1 metre, 1 yard, 1 foot, 2 feet, a step length, a stick and the like.

The layout drawing

The layout drawing

One best goes forward as follows: Fix a line, divide it into 16 parts, mark the mid points of the circles, then make the arcs with a string, wire, circle, tape or the like.  The radii are a multiple of the unity, so R2 means 2 times the unity etc.

The labyrinth can be drawn with compass and pencil on paper or can be scratched as a walkable labyrinth into the sand, strewn with sawdust or laid with stones or similar. The two accesses can be arranged by wish. It would make it easier to begin with the arcs above the line.

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While dealing with the Babylonian labyrinths in the detailed and excellent article of Richard Myers Shelton in Jeff Saward’s Caerdroia 42 (March 214) I also saw the following illustrations of sacrificed sheep’s guts. They are all different and served as patterns for extispicy.
They look similar to labyrinths, because they are depicted as one single uninterrupted line. Nevertheless, they have no center, rather two entrances/exits which mostly lie side by side. One could call them walk-through labyrinths or “prelabyrinthine”.

Clay tablets with diagrams of sheep's guts

Clay tablets with diagrams of sheep’s guts

To our today’s usual Western notion a labyrinth is a figure with one single path free of crossings leading to the centre and back again.

Does a relationship to “our” labyrinth exist in these intestinal loops or can they possibly be transformed into such?
This works, and as an example I choose the well recognizable drawing on the left clay tablet E 3384 (marked with a red cross).

Note from September 2017: Meanwhile I finished a drawing named E 3384 r_8 for the template.

Drawings from the clay tablet E 3384 recto

Drawings from the clay tablet E 3384 recto

Template for a visceral labyrinth

Template for a visceral Labyrinth

In it I determine the path sequence of the side by side lying intestinal loops and number them from the left to the right. The entrance lies in the middle and on the right side I leave the figure.

The layout of the visceral labyrinth

The layout of the visceral labyrinth

The pattern of the Labyrinth thus becomes visible. I read the order in which the single loops will be passed through: 5-6-9-2-3-8-7-4-1-10.

Using this path sequence I construct a closed, more round labyrinth in which the way ends in the centre.

Conversion of the path sequence into a closed round labyrinth

Conversion of the path sequence into a closed round labyrinth

I get a labyrinth with three turning points and nine circuits. Now this can still be reshaped by twisting and shifting the turning points. I can also choose a bigger middle and straighten the figure more centrally to the perpendicular bisectors of the sides.
Then it looks like this:

The visceral labyrinth in Knidos style

The visceral labyrinth in Knidos style

In front of us we have a new, hitherto unknown labyrinth. The path sequence is: 0-5-6-9-2-3-8-7-4-1-10. I walk directly into the internal area of the labyrinth and  I also go round the centre very quickly with 0-5-6-9. Then I walk outwardly and through the whole internal area with -2-3-8-7-4. From here I come to the outermost circuit once again and then with a big jump I arrive at the centre: -1-10. The alignment seems to be very dynamic and with a lot of movement. One should feel that when walking the labyrinth.

Who is the first to build such a labyrinth?

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Some time ago I already posted a walkable Babylonian visceral labyrinth (see related posts below).

Today I will present another one.

Babylonian Snail Shell Labyrinth

Babylonian Snail Shell Labyrinth

I have called it snail shell labyrinth because it reminds me of one. In addition to that I have also extended the entry area on the left a little bit wave-shaped.

It is a new type of labyrinth again: It has an unequivocal way through a labyrinth, not into a labyrinth. Therefore there are two entrances, no center to stay in or to return from.

I have written about the labyrinth and the origin quite detailed (see related posts below). The illustration on the clay tablet VAT 9560_5 of the Vorderasiatisches Museum Berlin forms the basis of the layout. Hewre we deal with a walkable implementation.

The following drawing shows the main elements.
At first one should fit the labyrinth into the available locality and determine the orientation. To achieve that one defines the points M3 and M5.

The main elements

The main elements

By use of triangular measurements from two points the other salient points are determined. One do not necessarily need to define the beginning and the end of each curve in advance. They lie on the (imaginary) lines between the main points or along the extension about these points.

If one puts on the semicircles in the right part first (in Blue) using M4 as midpoint, one has already created a large part of the arcs and can then add the other pieces.

As to the five curves around M3 one must pay attention that only the most internal two semicircles are continuous, the three external ones only reach up to the line determined by the points M3-M1-M6.

One could also form the entry area around M6 in a different way.

The exact measurements of the entire labyrinth are found in the layout drawing below.

The following layout drawing is a sort of prototype with the dimension of 1 m between  the axes which also corresponds to the distance from line to line. The remaining measurements arise from this definition and the shape of the labyrinth.

The construction is scaleable. This means, all other desired path widths can be derived from it.

If e.g., a path width of 60 cm is desired, one takes the factor 0.6. All other measurements of the drawing are calculated with this factor, i.e. the road length as well as the line length, the main dimensions, the radii, the oblique distances of the centres etc.

Layout drawing

Layout drawing

Two examples:

One labyrinth sprayed on the lawn in the garden of Gundula Thormaehlen Friedman in Bad Kreuznach.

One painted with chalk on the plaster of the parking area in front of our flat in Würzburg. The children of the surroundings had a lot of fun and were running it tirelessly.

By the way, one can also walk the labyrinth hand in hand. After the first round the partner starts in the upper entrance. In the meander of the middle one meets and changes the paths.

Here the layout drawing as a PDF file to watch/print/copy/save (for non- commercial uses only) …

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In the meantime, I could put on some walkable visceral labyrinths. As a walk through labyrinth without central middle it provides quite new experiences.

It is a new type of labyrinth: An unequivocal way through a labyrinth, not into a labyrinth.


Babylonian intestinal labyrinth

Babylonian intestinal labyrinth

As a name came to my mind also: Tapeworm labyrinth or intestinal labyrinth.

Because it is, however, only the geometrically exact transformation of the figure on the clay tablet VAT 744 of the Vorderasiatisches Museum Berlin, one could also maintain the name chosen by Ernst Friedrich Weidner in 1917 “Berlin Labyrinth”.

Quite unexpectedly has turned out that this special type is a “pair labyrinth”. Since one can go from the beginning side by side on different paths and meets only at one single place with a change of course.

While marking out the labyrinth I have also found out how one should proceed while putting on the labyrinth. The following drawings will explain this clearer.

At first the approximate middle is fixed in point M4 and following the main axis up to the point M5 (9.00 m).

The further salient points are fixed with triangulation measurement from 2 points.

This is here only the point B. With the distance M4-B (8.00 m) and the distance M5-B (5.67 m) point B is marked out.

The exact measurements for a prototype with 1 m dimension between axes are found in the layout drawing below.

Point A lies in the lengthening of the line from point B through M4 by 6.00 m.

Then one fixes the midpoints M1, M3 and M2 along this line. Maybe also the beginning or end points of the arcs with a distance of 1 m.

To this see Fig. 1.Fig. 1 and 2
Now it is best, to pull all eight semicircles in the right upper part.

The first four semicircles 1 – 4 have M1 as midpoint and are drawn with the radii 1 m, 2 m, 3 m, 4m.

The different arcs, midpoints and numbers are shown colourfully differently.

To this see Fig. 2.
Fig. 3 and 4

Around M2 there is only one semicircle (radius 1 m). This is at the same time the “secret” middle with the sickle-shaped left blank figure.

Around M3 there are three semicircles (with the radii 5 m, 6 m, 7 m). Here don’t let you confuse by the design of the curves. Since they begin or end together with other curves. Thus the sickle-shaped “fontanel” is also generated.

To this see Fig. 3.

Then around M4 one pulls six semicircles 1 – 6 (beginning with radius 1 m, further to radius 6 m) in the left lower part up to the sloping line.

The both curves 7 and 8 with the radii 7 m and 8 m are only drawn up to the vertical between M4 and M5.

To this see Fig. 4.
Fig. 5 and 6

Around M5 are the three quarter circles 1 – 3 to pull (radius 1 m to radius 3 m) for the input area.

To this see Fig. 5.

All lines (the boundary lines) of the labyrinth are to be seen in Fig. 6. The actual way through the labyrinth is the free area between these lines.

The following layout drawing is a sort of prototype with the dimension between axes of 1 m for the distance from line to line. This corresponds to a path width of 1 m. The remaining measurements arise from this definition and the design of the labyrinth.

The construction is scaleable. This means, all the other desired path widths can be derived from it.

The following photos show the labyrinth with a path width of 50 cm. All measurements were multiplied by the factor 0.5 to build them.

If e.g., a path width of 60 cm is wished, one takes the factor 0.6. All other measurements of the drawing are to be calculated with this factor, so also the path length, the line length, the main dimensions, the radii, the sloping distances of the midpoints etc.

Layout drawing

Layout drawing

Two examples for a path width of 50 cm:

The worldwide first labyrinth of this kind on grass in the garden of the co-founder of the TLS Gundula Thormaehlen Friedman in Bad Kreuznach (Germany).

The second one on the pavement of the parking place in front of our home in Würzburg (Germany).

Sprayed on grass

Sprayed on grass

Painted with chalk on pavement

Painted with chalk on pavement

Walking two by two: The test by our grandson and his girlfriend from the neighborhood.

Here the layout drawing as a PDF file to watch/print/copy/save (for non commercial uses only) …

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I have already written about the Babylonian visceral divination labyrinths and tried to prove their relationship with the labyrinth. They date to the Middle Babylonian and Neo-Babylonian time (ca. 1500 to 500 BC).

However, there are even older labyrinth representations from Old Babylonian time (ca. 2000  to 1700 BC) which look quite differently than the visceral labyrinths and which can probably be taken for the ancestors of the labyrinth.

The Swedish historian of Babylonian mathematics and cuneiform script expert Jöran Friberg has studied the Babylonian mathematical  tablets of the Norwegian Schøyen Collection in detail and has documented that in 2007. He calls the following figures labyrinths and tries to prove that.

In the journal Caerdroia 42 Richard Myers Shelton has written extensively on the subject of the Babylonian Labyrinths. Most of my information I got from him. Here it is a matter for me of founding in what the relationship with the labyrinth consists.

One must take therefore the following representations as the oldest labyrinths known so far.

Here a rectangular labyrinth labelled MS 3194 in the Schøyen Collection:

The rectangular labyrinth MS 3194

The rectangular labyrinth MS 3194, source: Schøyen Collection

We do not know anything about the purpose of this figure. It could have served quite philosophical or mathematical considerations.

In what does the relationship with the labyrinth exist now?

We must look at it more exactly. Richard Myers Shelton could reconstruct the lines on the clay tablet perfectly and therefore I can present a colored drawing of the entire figure.

The rectangular Babylonian labyrinth

The rectangular Babylonian labyrinth

The thin black lines limit the ways. These are the free space between the lines. There are two open entries to the rectangle. One entrance lies roughly in the middle of the left side, the other one opposite on the right. The way from the left is highlighted in ochre, from the right in green. In the middle they meet and change the direction. The one way is leading in, so to speak, and the other out.

There are no forks or dead ends. The whole, long and winding path must be accomplished. The entire rectangle is crossed.

The layout shows a certain, but not quite successful symmetry. The last laps round the center remind a double spiral. The other circuits are intertwined in the shape of meanders.

We have thus an unambiguous, doubtless and purposeful way through a closed figure, as we know it from a “true” labyrinth.

Then there is still a square labyrinth labelled MS 4515. Here the colored drawing:

The square Babylonian labyrinth

The square Babylonian labyrinth

Maybe it should represent a town? As we know that from other labyrinths. With gates, bastions, walls?

Amongst the Babylonian tablets is another one with geometrical illustrations. Jöran Friberg calls them mazes. They are quite sure not.

One could consider these lines as labyrinthine finger exercises. Some are difficulty to reconstruct. So, Friberg and Shelton come to different results.

There are two rows with four fields in which a rotationally symmetric closed path runs without beginning and end through four sectors. All areas are mostly touched, sometimes there are inaccessible places. One is reminded of the Roman sector labyrinths many centuries later.

The tablet MS 4516

The tablet MS 4516, source: Schøyen Collection

Here the drawings of two fields:
The first field on top left

The first field on top left

The fourth field on bottom left (reconstructed)

The fourth field on bottom left (reconstructed)

Clearly one recognises the meander, the symmetrical arrangement and the alignment of the paths between the black lines.

Much later similar representations on the silver coins of Knossos are found:

Swastika meander

Swastika meander on a coin, 431-350 BC / source: Hermann Kern, Labyrinthe, 1982, fig. 49 (German edition)

The right “ingredients” for a labyrinth, namely meander and spiral were already known in Old Babylonian times. The idea of a confusing, winding, nevertheless unequivocal way in a restricted space with rhythmical movement changes can have originated from there.

We can push back the time for the origin of the labyrinth some hundred years later to the time about 1800 BC. At first it was the idea of a walk through labyrinth. The further development happened in Middle to New-Babylonian times in the intestinal labyrinths with also two entries, yet unambiguous way.

Since 1200 BC we know the Cretan labyrinth with only one entry and the end of the path in the center. We could call this a way in labyrinth whereas the Babylonian labyrinth is a way through labyrinth.

Till this day have remained walk through labyrinths in the type of the  Baltic wheel and the Wunderkreis (wonder circle). We recognise them as real labyrinths, although they also have two entrances and do not end in the middle.

The Kaufbeuren Wunderkreis

The Kaufbeuren Wunderkreis

More information is to find about the Babylonian labyrinths in an excellent article by Richard Myers Shelton in Jeff Sawards Caerdroia 42 (March 2014), and in a new article from him in Caerdroia 44 (April 2015) about the Transylvanian Wunderkreis.

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