Mandala and fractal thinking in Southeast Asia and the Pacific

The term "mandala" is often used in scholarly literature to describe the polities, the temple architecture and other aspects of Southeast Asian culture.  The same word could be extended into the cultures of the Pacific where both mandala and fractal types of thinking also prevail.

A mandala again, in this analysis, is a way of viewing or representing the cosmos, or a part of the cosmos seen as the whole in microcosm.  The term fractal refers to a geometric shape that can be broken into fragments that are copies or approximations of the whole.  In sociology and ethnology, the term fractal applies to ways of visualizing the cosmos as consisting of parts that are smaller copies or approximations of the whole -- the macrocosm.

Indeed, in Southeast Asia and Oceania, one can view the entire culture from polities and family relationships to iconography and orality through the prism of the mandala and the fractal. Such concepts are defining in identifying what is indigenous in these regions.


Fractal Cosmos, Fractal Person, Distributed Person

Thomas Reuter in Sharing the Earth, Dividing the Land: Land and Territory in the Austronesian World describes Austronesian society using indigenous metaphors that relate the self and the community to trees and other plants.

Botanic metaphors are among the most commonly used metaphors for social relationships in the Austronesian world. The source ancestor of a clan or founding clan of a village, for example, may be referred to as the ‘trunk’ or ‘root’ and his descendant or newcomer clients as the ‘leaves’ or ‘tips’ of the same tree. Similarly in a topogeny, the place of origin is usually the ritual centre or ‘trunk’ of the domain, to which a path of origin is ceremonially traced back along one or several ‘branch’ villages, beginning from the newest settlements or ‘tips’. The people who reside at, or in some other way can lay claim to, the origin site tend to maintain a position of ritual precedence or of political authority in the domain, but rarely both. Botanic metaphors generally suggest a segmentary process of spatial expansion due to organic growth from within, but can and are applied also within local societies featuring a population with multiple origins

....an underlying Austronesian territorial concept that envisages a shared social identity based on a specific ‘foundation event’. Many Gumai villages in the South Sumatran highlands are thought to have been established by, and thus trace their ‘origin’ to, a single ancestor, the puyang Ketunggalan Dusun. Villages contained a small ancestor house (lunjuk or rumah puyang) for the spirits of the founding ancestors, where rituals would be held to commemorate the village origins. The morpheme pu in puyang could be a reflex of puqun, which is a Proto-Malayo-Polynesian reconstruction meaning ‘tree’, ‘trunk’, ‘base’ or ‘source’. Villages are inhabited by the descendants of the puyang and their affines. The population is divided into origin groups called jungkuk which are ranked in order of precedence based on birth order and ritual seniority.

The idea of the "trunk" and the "tip" takes on fractal dimensions as Mark S. Mosko points out in "The Fractal Yam: Botanical Imagery and Human Agency in the Trobriands":

As Jim Fox and his collaborators on the Comparative Austronesian Project have amply demonstrated, the arboreal idiom of ‘base’, ‘branch’ and ‘tip’ animates the origin structures of precedence of many if not most societies of the Austronesian world...Based on recent ethnographic enquires at Omarakana, the site of Malinowski’s original fieldwork, this paper argues that the sequential recursiveness of base-branch-tip across North Kiriwinan contexts is fractally structured – borrowing a notion from chaos theory. The production of every ‘tip’, in other words, becomes the condition or ‘base’ of further base-branch-tip transformation, and so on.

The generation of self-similarity at every new tip applies quite broadly not only to Austronesian society, but also to the other non-Austronesian societies in the region.

In Kapampangan culture, the trunk or source is known as pun, which can also mean the chief or leader, who in ancient times was likely a "fractal chief."  One's relatives or siblings can be known as capsi from the word apsi "small branches."  Bergano defines capsi as "el un hermano, o pariente porque vienen de un tronco."  The "tronco" or 'trunk" here again is the pun.

The most ancient ruler was likely the clan leader, or pun, who like the latter chiefs, kings and emperors was seen as a personification of the community, kingdom or world, and like the original Cosmic Being was expected to "distribute" him or herself, at least ritually, to his or her followers.

According to Bergano, the opposite of pun is sepu -- a word referring among other things to the tip of a leaf.  The word sepu can also mean "history" as in one's clan history, the history of a village or nation, or history in general.  From this word, Bergano mentions the derived form casesepuan "ultimisimo de la historia" (the last part of  history), which might also be related to one of his definitions for the word suku as "the end of time."

The Rurutu deity Tangaroa or A'a represents the "Fractal Person" at the cosmic level -- the pantheistic concept of the cosmos as a person or other microcosmic form that generates similar smaller forms in the "creation" of the cosmos.  In the sculpture above, A'a generates other deities and humans as his eyes, nose, knees, etc. (Source: http://detoursdesmondes.typepad.com/dtours_des_mondes/anthropologie_de_lart/)



The depiction of fractal thinking appears quite early in this region.  For example, the Lapita motif below, dated to about 1000 BCE, shows "face" motifs that are believed to have been widely used by the Lapita culture.


Source: http://picasaweb.google.com/JTeddyT/LapitaFace?authkey=Gv1sRgCMfAr6DEpafBVg&feat=flashslideshow#5221186924082589314

The image above shows both larger and smaller face motifs as demonstrated below.

You can also rotate the image 180 degrees to double many of the face images.  Note that the highly stylized face motif that borders this "mandala" creates many face images. Click on image for larger view.

The image to the left is taken from Art and Agency showing Marquesan tattoos with "hand faces."

From Art and Agency, tattoos and mask showing mata hoata "faces," and ipu "eyes."

Mata hoata faces on leg, from the Marquesas. For more images, see: http://www.flickr.com/photos/runningafterantelope/sets/72157608481767555/

Variations of the etua motif (squatting figure motif, etua = deity, deified ancestor) from the Marquesas showing the number of ways the local artists could represent the "Distributed Person."

Fractal tortoise


Knots, knotted cords and carvings with knots are also used to portray the interconnected objects/persons in the family, community or world.  Some examples are the Malangan sculptures of New Ireland and the to'o knots of Tahiti. 

The Malanggan sculpture from New Ireland with carved knots represents the distributed or fractal self.  During death ceremonies, the breaking up and distributing of the carving is essential in passing on the land of the deceased to the involved parties. A bird is carved at the top of the sculpture. (Source: http://detoursdesmondes.typepad.com/dtours_des_mondes/anthropologie_de_lart/)

In Masantol, Pampanga, the myth of Mangatia or Mangetchay describes the Creator as a net-maker, which is the meaning of "mangatia," and the cosmos is described as a great interwoven net.  The image of a net stresses the interconnection of all things.


Imagining the world as mountain, tree

Earlier in this blog, I have described how the concept of the cosmos as a mountain was quite widespread in this region, if not throughout the world.

The depiction of this world mountain may come very early in this region depending on how one interprets symbols like concentric circles, triangles, spirals, etc. that appear in the very early Neolithic phase.

During the megalithic period, we see the rise of many types of terraced structures that in latter times where widely viewed throughout the SEA-Oceania region as representing mountains, and in many cases the World Mountain.

The megalithic period dates to around 3000 BCE from the Peinan Culture in Taiwan, with the specific evidence of terracing dating to about 2000 BCE from sites like Gio-Linh in Vietnam.  Megalithic monuments in Island Southeast Asia associated with Neolithic culture also show evidence of terracing that increases during the Bronze Age.


Many of the well-known Hindu-Buddhist temples in Southeast Asia are actually built over older pre-Hindu-Buddhist structures.  For example, Borobudur in Java is built over an indigenous Javanese pyramid with three great stone terraces.  Pre-Hindu-Buddhist terraced pyramids and platforms used for burial and ritual are found all over Java.

The use of terracing for both practical and ritual purposes is widely found during the Neolithic and Bronze Age periods in Southeast Asia.  Such forms also extend out into the Pacific where we find marae, the often cruciform-shaped paepae and similar platforms.  On some small islands of the Pacific there are hundreds or even thousands of these stone platforms.

At some point, it may be that the terraced mountainside became associated with depictions of the World Mountain. 




A house built on a terraced paepae in Hakaui, Nuku Hiva. (Source: http://www.insidemystery.org/hakaui-1971/arrival.html)



A massive paepae on Nuku Hiva. (Source: http://www.insidemystery.org/hakaui-1971/arrival.html)



The building plan of Borobudur in Java from overhead showing the cruciform staircases leading from the four directions to the apex or summit of this stone mountain-pyramid.  The slightly cruciform lower terraces lead to the circular terraces near the summit. (Source: http://commons.wikimedia.org/wiki/File:Borobudur_Mandala.svg)


The top of this Dongson bronze drum (northern Vietnam) might be a representation of a mandala with concentric circles showing depictions of the world.  Click on image for larger view. (Source: http://www.asianart.com/asianartresource/d10479.html)


The Borobudur stupa from Java has often been described as a mandala in stone. Although a Buddhist monument, Borobudur possesses characteristics of Southeast Asian temple architecture including the terraced pyramid form and the use of a cruciform building plan that were evident in pre-Hindu-Buddhist structures.

On many Tibetan cloth mandalas (thangkas), we see depictions of  "palaces" from an overhead view with the "gates" and other features that need to be displayed shown in a "flattened" out manner.



Kalachakra Mandala depicting palace as seen from above with gate towers flattened out. There are three concentric levels of terraces with the gates leading to the apex of the palace.  Click here for larger image.




The cruciform staircases at the four quadrants of Borobudur lead through gates with foilage-spewing carvings of Kala, the demon of time. The word "kalacakra" means cycle of time, and we can note also the gates of the palace in the Kalacakra Mandala.  (Source: http://commons.wikimedia.org/wiki/Category:Borobudur_entrances_and_stairs)




Borobudur gate with Kala at the top "devouring" the worshipper as they climb through the galleries to reach the stupa at the top.  The galleries at the bottom depict everyday life from the Jataka tales, and as one moves higher we see reliefs of the journey to become a boddhisattva.  The topmost terraces contain Buddhas, and thus, the mandala represents a movement in time toward ultimate enlightenment and Nirvana, which is possibly symbolized by the empty stupa at the apex. The Kalacakra Deity is the pantheistic source (Adibuddha) -- the Fractal Self -- in Kalacakra Buddhism and is seen as a personification of time, a belief that also is found in indigenous systems of Southeast Asia. (Source: http://commons.wikimedia.org/wiki/Category:Borobudur_entrances_and_stairs)


Click on image for full size. (Source: http://www.jps.auckland.ac.nz/document/Volume_48_1939/Volume_48,_No._189/The_Tuamotuan_creation_charts_by_Paiore,_by_Kenneth_P._Emory,_p_1-29/p1?action=null#)



In the image above, "creation" is shown as a stepwise process through time and space represented in the form of a concentric mandala. Click on image for larger view. 

(Source: http://www.jps.auckland.ac.nz/document/Volume_48_1939/Volume_48,_No._189/The_Tuamotuan_creation_charts_by_Paiore,_by_Kenneth_P._Emory,_p_1-29/p1?action=null#)


The Cosmic Person or Fractal Person that represents the cosmos can be a human, an animal like a dog, lizard or whale, a tree, or an "inanimate" object like a mountain since all these entities were viewed as fractal copies and parts of the greater Cosmic Being.


Regards,
Paul Kekai Manansala
Sacramento

References

Chiu, Scarlett, Detailed analysis of Lapita Face Motifs: Case Studies from Reef/Santa Cruz Lapita Sites
and New Caledonia Lapita Site 13A, http://epress.anu.edu.au/terra_australis/ta26/pdf/ch15.pdf, 2007.

Gell, Alfred. Art and Agency: An Anthropological Theory. Oxford: Clarendon, 1998.

Mosko, Mark S. 2009. "The Fractal Yam: Botanical Imagery and Human Agency in the Trobriands". The Journal of the Royal Anthropological Institute. 15, no. 4: 679-700.

Reuter, Thomas Anton. Sharing the Earth, Dividing the Land: Land and Territory in the Austronesian World. Canberra: ANU E Press, 2006, 25.

Schellinger, Paul E., and Robert M. Salkin. Illustrated Encyclopedia of Historic Places: Asia and Oceania. New Delhi: Aryan Books International, 1997, 147.

Smith, Ralph Bernard, and William Watson. Early South East Asia: Essays in Archaeology, History and Historical Geography : [Papers ... Submitted to a Colloquy on Early South East Asia Held at the School of Oriental and African Studies, London, in September 1973]. New York: Oxford U.P., 1979, 180.

Mandalas, Wheel Windows and Rose Windows

Following up on my posts on the evidence of "Tantric" eastern influences in Romanesque Europe, one very interesting element that pops up in Romanesque churches is the wheel window.

The wheel window generally adorns the west fronts of these churches staring in about the 12th century.  The subsequent rose window is widely believed to have been derived from the wheel window.  Most scholars see the wheel window as a development of the earlier Roman oculi, a circular opening in structures for ventilation and lighting.

However, most do admit that the designs of the wheel and rose window may indicate foreign influences. For example, some have suggested that the designs may have come from the six-petaled rosettes of the Khirbat al-Mafjar in Jordan.

A stronger argument exists, I think, linking the wheel window with the dharma cakra (wheel of law), and the initial rose window designs with the mandala.  These cultural elements could have been brought over, again, by the Sayabiga and related peoples.

Firstly, many of the earliest wheel windows have eight "spokes" as in these examples from 12th century Norman England:


Patrixbourne


Barfreston 



Castle Hedingham


(Source for photos:  Mary Berg at the Kent Archaeology Page)


The dharma cakra appears very early in Indian art, for example, in the Asokan architecture, but the spoke number can vary.  By the late ancient period though, the eight-spoked dharma chakra becomes well-established and it is the classical type used in Tibetan Buddhism.  At churches with eight-spoked wheel windows, we often see that many motifs also occur in groups of eight.

Another noteworthy similarity found in many early wheel windows is the use of the column motif for the "spokes."  In the Barfreston and Patrixbourne examples above, these column-spokes form a likeness of a trefoil arch between each spoke.

A traditional widespread form of the dharma chakra displays trefoil-like "knobs" that appear to protrude from each "spoke" through the "rim" of the dharma wheel as in the examples below:


 A dharmacakra on the flag of Sikkim.  Note the trefoil-like knob at each quadrant. (Source: Wikipedia)


A dharma cakra manufactured in Xining, China with large trefoil designs, one for each spoke. (Source: Wikipedia)


Another similarity is that the "rim" in both the dharma chakra and the window wheel is wide and often very ornately decorated, for example, with vegetative motifs.

A very striking comparison can be made between the wheel window of Barfrestron and the dharma cakras found on the Sun Temple of Konark, eastern India, which dates to the 13th century.  In both cases, the rims are decorated with the respective bestiaries of each culture.

Bestiary on rim of Barfreston wheel window includes griffins, winged lions, harpies, crabs and other creatures both real and fabulous. (Source: http://www.green-man-of-cercles.org/articles/bestiary_arches.pdf)

Rim of dharma wheel at Sun Temple of Konarak has elephants, swans, deer, deities, mythical creatures and sensuous couples displayed in a circular vine motif.


Rose windows

The early rose windows were obviously similar to the wheel windows that came before.  For example, the following window from the cathedral at Chartres dating to the late 12th century is sometimes called a rose window and sometimes a wheel window.



Wheel window at Chartres Cathedral (Source:  http://www.sacred-destinations.com/france/chartres-cathedral-photos/)


Here there are twelve column-like spokes in the central figure creating arch-like "petals."  The design is very much like the mandalas of Tibet.

While Tibetan tradition states that mandalas were originally taught by the Buddha, the first mandalas to appear on murals date from about the 10th century.  By the 11th century, highly-sophisticated textile mandalas were made.  While the word "mandala" can refer to any circular type of design, but in Tibetan art it generally referred to a representation of the cosmos that was concentric in nature.

The concentric design of mandalas often resulted in fractal patterns. For example, many Buddhist mandalas  display the fractal plane known as the Sierpinski Carpet.  Even a simple design of concentric circles is fractal in a way -- the outer circle surrounds a circle that in turn surrounds a circle surrounding a circle.

More complex fractal patterns can include, for example, a circle of Buddhas encircled by smaller circles of Buddhas.



The Mandala of the Six Cakravartins dates at least to the 11th-12th century Vajravali text, although it is based on an earlier prototype.  The mandala above was created in the 19th century.  In this mandala, a Cakravartin, or World Emperor, is enclosed in a circle surrounded by eight deities in lotus petal-like containers. The lotus is encircled and placed in a square with cruciform "gates."  Five other Cakravartins in similar presentation surround the central figure. (Source:  http://en.wikipedia.org/wiki/File:Mandala_of_the_Six_Chakravartins.JPG)




A 14th century Vajravarahi Awakening Mandala shows a central eight-petaled lotus or rosette with deity figures surrounded by smaller six-petaled lotuses. (Source: http://www.asianart.com/mandalas/page14.html)


In the wheel window of Chartres Cathedral the central lotus or rose-like figure has twelve "petals" and has a rosette-like figure at its center with twelve apses.  The rose is surrounded by smaller circles with eight apses.

These figures with the apses may possibly be related to the description giving in Titurel during the 13th century of the Grail Temple:




Grail Temple plan after Ringbom (A. A. Barb, 1956: 34) following descriptions in Titurel. 


In the following sand painting of a Mandala Palace, the outermost lotus figure has 22 petals, which can be compared to the 22 apses of Titurel's Grail Temple.  The number 22 in Tibetan Buddhism can represent the 22 deities of the Kalacakra Deity's Palace, the 22 Bodhisattvas, etc.



Source: http://buddhistsymbols.info/wp-content/uploads/2008/07/mandala.jpg


  
Architectural changes during the Romanesque period

Changes in design and orientation are also supportive of the idea of eastern influences in line with those already described in this and previous posts.

For example, we see the rise of cruciform churches during this period.  The new architecture is generally seen as a fusion of the Visigothic cruciform church and Mozarabic design elements.  However, one interesting feature is the idea of the church representing Paradise -- something that is carried on into the Gothic period.

The churches now have gates or portals that can be viewed as entrances into a representation of either the divine or the terrestrial paradise.  One interpretation of the trees, vegetation and rivers represented in Romanesque and Gothic churches is that they are intended to represent the Garden of Eden. The palm tree, in particular, is represented as the Tree of Paradise.  In a similar sense, the terraced pyramid temple of Southeast Asia, which also had a cruciform building plan, represented the cosmic mountain, the axis mundi.

Additionally, during this period the churches began to be pointed in an eastward direction.  The high altar was placed at the "top" of the cross in the easternmost part of the church.  However, the churches were not oriented directly at the rising Sun during the equinoxes.  They usually diverged from a few degrees to 15 or more degrees from true East.  Previously Christian churches had no particular orientation and could be facing in any direction.

Now the great majority of temples in South and Southeast Asia traditionally had the same orientation -- toward the East but rarely toward true East.

Various explanations have been given for the orientation of Romanesque churches including the idea that they faced the Sun on first day of building or on the patron saint's day.  Some have also suggested that compasses were used for orientation and that they were thrown off by magnetic declination.

One possibility that could be tested is whether the churches or a subset of them were oriented toward a fixed geographical location like the mosque was oriented toward Mecca.  Giving the paradisaical themes of Romanesque churches, they may, for example, have been pointed toward the perceived location of the Garden of Eden in the East.  If this were the case, then we should see that the churches tend to face more southward as the church's location is more eastward in longitude and northward in latitude.

Regards,
Paul Kekai Manansala
Sacramento

References

Abrahamsen, Niels. Orientation of Romanesque Churches and Magnetic Declination in the 12th Century in Denmark. GeoSkrifter, 23. Aarhus: Geologisk Institut Aarhus Universitet, 1985.

Brunius, Teddy. "Old nordic churches and the points of compass" Konsthistorisk Tidskrift/Journal of Art History 66.4 (1997). 03 May. 2010.

Cowen, Painton.  The Rose Window, London and New York, 2005

Grabar, Oleg. Constructing the Study of Islamic Art 2 Islamic Visual Culture, 1100 - 1800. Aldershot [u.a.]: Ashgate Variorum, 2006, 387.

Graham, Robert Maxtone. The Sculptures at the Church of St Nicholas, Barfreston, http://www.green-man-of-cercles.org/articles/bestiary_arches.pdf, 2008.

Hoare, Peter G., Caroline S Sweet, "The orientation of early medieval churches in England," Journal of Historical Geography, Volume 26, Issue 2, April 2000. 

Hughes, Robert. Heaven and Hell in Western Art. London: Weidenfeld and Nicolson, 1968.


Kubach, Hans Erich. Romanesque Architecture. History of world architecture. New York: Abrams, 1975.