THE PATTERNED IMAGINATION: A STUDY OF SELECTED WEST
AFRICAN TEXTILES IN MUSEUM COLLECTIONS WITH REGARD TO
THE MAGIC SQUARES REPRESENTED ON THEM
PATRICIA BENTLEY
A Thesis Submitted to the Faculty of Graduate Studies in Partial Fulfillment of the
Requirements for the Degree of Master of Arts
Graduate Program in Interdisciplinary Studies
York University
Toronto, Canada
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The Patterned Imagination examines certain visual repeat patterns in order to better understand their unique role in the production of cultural meanings. The specific focus of the study is on a constellation of patterns that emerge from magic squares, especially on West African textiles in an Islamic context. Magic squares are represented in patterns on many Islamic West African textiles as talismans with the power to effect protection and healing for the wearer. A pattern is also a blueprint, a guide for making something, and it is in this sense of the word that I contend the magic square acts as a
“pattern engine” in West African visual cultures.
The textiles examined are in the collections of the Textile Museum of Canada, the
British Museum, and the Metropolitan Museum of Art. The study analyzes how the meaning of their patterns has changed through their move from their originating space into an institutional space. V
Acknowledgements
Interdisciplinary Studies at York enabled me to pursue the aspects of mathematics, art, and cultural history that relate to the study of pattern. Throughout,
Jamie Scott perceptively encouraged and advised me in my project’s direction. I felt privileged to be a student in the program.
I also would like to acknowledge the support and guidance of the following individuals and extend to them my warmest thanks. My supervisory committee, Leslie
Korrick, Steve Bailey, and Margaret Sinclair, offered me valuable insights and suggestions as I chose my topic and began my research, and cogent editing as I wrote the chapters. When Professor Sinclair withdrew due to illness, Ruba Kana’an stepped in, providing the expert knowledge of Islamic art, and sensitivity to its place in the West
African milieu, that my project needed in its later stages. I am also very grateful to Mary
Leigh Morbey and Zulfikar Hirji for their help and advice. It has been an honour to work with all of them. Table of Contents
Copyright Page ...... ii
Certificate Page...... iii
Abstract ...... iv
Acknowledgements...... v
Table of Contents ...... vi
List of Figures...... vii
Chapter One, Introduction ...... 1
Chapter Two, Review of the Literature on Magic Squares in Muslim West African Visual
Cultures ...... 19
Chapter Three, Transformations of the Magic Square: The Shirt from Burkina Faso 41
Chapter Four, the Magic Square as a Pattern Engine ...... 69
Chapter Five, Conclusion ...... 98
Appendix A: Translation and Interpretation of the Shirt Front by Ruba Kana’a n ...... 108
Works Cited...... 116 List of Figures
Figure 1: A 3 x 3 magic square ...... 2
Figure 2: A 3 x 3 magic square, (left) consecutive numbers joined by lines and (right) even numbers coloured in ...... 21
Figure 3: (left) The continuous method of creating a 3 x 3 magic square; (right) a torus. 21
Figure 4: The gnomon, an L-shaped symbol ...... 25
Figure 5: Shirt (side with two squares), Village of Kiembara, Burkina Faso, Mossi, c.
1990, cotton, hand-spun, woven, sewn, and inscribed with Arabic writing and graphic symbols, gift of Victoria Henry, T91.0091 TMC...... 58
Figure 6: Shirt (side with one square), Village of Kiembara, Burkina Faso, Mossi, c.
1990, cotton, hand-spun, woven, sewn, and inscribed with Arabic writing and graphic symbols, gift of Victoria Henry, T91.0091 TMC...... 59
Figure 7: Pattern drawing of the shirt showing the continuous strips over the shoulders. 60
Figure 8: The Arabic text on the shirt translated into English, with arrows indicating the
order of the text. The panel with the squares can be read independently. Translated from
Arabic by Ruba Kana’an ...... 61
Figure 9: Talismanic shirt, fifteenth or early sixteenth century, India (north India or the
Deccan), ink, gold, and colors on stiffened cotton, purchase, Friends of Islamic Art Gifts,
1998.199 Metropolitan Museum of Art...... 62
Figure 10: (left) The 2 x 2 square on one side of the Burkina Faso shirt ...... 63
Figure 11: The translation of the 2 x 2 square in Figure 10 ...... 63 Figure 12: Tunic front (above) and back (below), Nigeria, Hausa, late nineteenth century, cotton, leather, paper, pigment, acquired from Captain Alfred Walter Francis Fuller,
A fl940,23.1 The British Museum ...... 64
Figure 13: Hunter’s shirt, Mali, c.1900, cotton, strip-woven and sewn, with attached leather-covered amulets, gift of Dr. Peter Herschman, T86.0071 TMC ...... 65
Figure 14: Hunter’s coat, Mali, 1960-70, cotton, woven and embellished with amulets and mirrors, museum purchase, T81.0112 TMC ...... 66
Figure 15: Tunic, Liberia, twentieth century, cotton, strip-woven, sewn, appliqued and embroidered, from the Opekar/Webster Collection, T94.3006 TMC ...... 67
Figure 16: Robe (shabka), Nigeria, Hausa, 1920-1929, cotton, silk, strip-woven, sewn, embroidered, needle lace, From the Opekar/Webster Collection, T94.3007 TMC ...... 68
Figure 17: Page from a Hausa Qur’an, Nigeria, nineteenth century.Web.
Leamingarabicweekly.com. Accessed 10 Nov 2010 ...... 68
Figure 18: The scenario of Gioseffo Zarlino (25)...... 74
Figure 19: The Klein Group represented by white and black values ...... 75
Figure 20: The Klein Group represented by even and odd values ...... 76
Figure 21: The Klein Group interpreted by Elkins and Krauss ...... 77
Figure 22: A 3 x 3 magic square, (left) consecutive numbers joined by lines; (centre) an interlaced ribbon linking consecutive numbers; (right) an embroidered knot on a Hausa robe, Nigeria, twentieth century, T94.32005 TMC ...... 78
Figure 23: A weaving draft for a two shaft loom ...... 80
Figure 24: A weaving draft for a three shaft loom ...... 81 Figure 25: Wrapper, Niger, Djerma, early twentieth century, cotton, strip-woven in supplementary weft technique and sewn, gift of Barbara Barde, T04.34.2 TMC ...... 93
Figure 26: Blanket (kaasa ), Mali, Fulani, 1950-70, wool, strip-woven in supplementary weft technique, sewn, gift of Madeleine Boucher Harvie, T04.7.3 TM C ...... 94
Figure 27: Girl’s wrapper (basiae), Mali, Bamana, twentieth century, cotton, strip-woven, painted and dyed with mud, museum purchase, T77.0005 TMC ...... 95
Figure 28: Wrapper, Burkina Faso, Mossi, twentieth century, cotton, commercially woven, sewn, tied resist-dyed, private collection...... 96
Figure 29: Gown, Liberia, 1860, cotton, strip-woven, sewn, embroidered, appliqued, donated by Henry Christy, Af2797 The British Museum ...... 97
Figure 30: Man’s robe, Nigeria, Hausa, twentieth century, cotton, strip-woven, sewn and embroidered with silk thread, from the Opekar/Webster Collection, T94.3002 TMC ...... 97 1
Chapter One, Introduction
“Pattern” is a word that is used to describe conceptual ordering principles about the ways things repeat. These principles may be represented in a wide variety of patterns: those that we see, those that we hear, those that we feel, and even those that we perform with body movements. The mind develops and operates pattern recognition systems to group objects of interest that are similar to one another and to distinguish objects that are different from one another (Grossberg 438; Reed 382). This ability is so basic to human cognition that no learning could take place without it. Kerstin Kraft writes, “Cognitive sciences state that pattern matching and pattern construction are required means of complexity reduction, a key function of human behaviour” (275).
She applies this statement to patterns on textiles, but it need not be limited; for example, patterns in sound also perform the function of complexity reduction.
According to musician Vijay Iyer, “Musical meter provides us with an attentive mechanism - a temporal template against which to process information in time, reducing demands on memory” (18). The fundamental relevance of patterns to human cognition is also articulated by Marcus Du Sautoy, who writes that a mathematician is, in essence, a pattern searcher (96). In the context of textile patterns, I adopt Dorothy
Washburn’s definition of pattern as “an arrangement of marks that repeats in systematic fashion” ( Embedded Symmetries 47). The marks repeat according to the principles of symmetry; Washburn and Crowe have shown these principles to be instrumental in expressing certain cultural beliefs through patterns on textiles and other artisanal objects ( Embedded Symmetries; Symmetries o f Culture; Symmetry Comes o f Age). 2
Given pattern’s importance for learning and understanding, I argue that it is a tool, not only for cognition, but also for meaning.
In this study I examine non-figurative repeat patterns in order to better understand their unique role in the production of cultural meanings. More specifically I am interested in a constellation of patterns that emerge from “magic squares,” especially patterns of checkerboards and knots that appear on West African textiles in an Islamic context. A magic square is an arrangement in a square array of “n” numbers in such a way that each row, each column and each main diagonal has the same sum
(Biggs 118). It is represented both explicitly and implicitly in patterns on many Islamic
West African textiles as a talisman with the power to effect protection and healing for the wearer. Figure 1 shows a 3 x 3 magic square, historically the original, and mathematically the smallest, form.
4 9 2
3 5 7
8 1 6
Figure 1: A 3 x 3 magic square.
From their origins in ancient China, the numeric arrays that are today known as magic squares were considered models of the perfection of the universe (Cammann
183; Schintz 9). This consideration led to their use in parts of the Islamic world as 3 components of talismans with the power to effect protection and healing for the wearer.
In the Encyclopaedia o f Islam, magic squares are called wafk al-a ’dad, “harmonious arrangement of the numbers” (Sesiano “Wafk”). In the medieval Islamic milieu of the ninth to the twelfth centuries CE, they came to be associated with talismans but not with the word sihr, or magic, which was not considered legitimate (Ibn Khaldun 179).
The “magic” in the name used for them here is attributed to their later association with
Arabic alchemical texts by European scholars (Sesiano “Quadratus Mirabilis” 201).
I will analyze a selection of West African textile objects that contain references to magic squares in order to trace the transformations of the magic square from an array of numbers into a metaphoric symbol for the universe’s perfection, then into a talisman for protection and healing developed from Islamic abjad letters, and then to textile patterns that keep the emotional charge of the talisman by referencing it.1 As mentioned earlier, my aim in this thesis is to deepen my understanding of patterns’ role in the production of cultural meanings; I plan to do this by using the patterned derivations of one motif - the magic square - represented on textiles in one region of the world -
West Africa - as a case study. Magic square-related patterns on Islamic West African textiles refer implicitly to magic squares as components of amulets, which imbue the textiles they are on with talismanic power. I will show how this power comes in part from textiles’ intimate contact with the body, and how it is obscured when the textiles become part of a museum’s collection.
1 Arabic abjad letters, used before the advent of Hindu numerals, are systems of assigning numbers to letters of the alphabet. 4
A pattern is also a blueprint, a guide for making something, and it is in this sense of the word that I contend the magic square acts as a pattern engine in West
African visual cultures. My notion of pattern engine is adapted from the idea of
“metapattem” in several disciplines, including anthropology, biology, and visual culture studies, and I will develop it fully in Chapter Four. However, I offer here a definition of metapattem from biologist Tyler Volk, who describes it as “a pattern so wide-flung that it appears throughout the spectrum of reality” (viii); he gives a biological example, taken from Gregory Bateson (as cited in Volk vii), of the arthropod pattern of claws with pincers. A metapattem, then, is a metaform that equips all successive generations of, say, arthropods with pincer claws. It is a pattern because it repeats, and in the biological realm it repeats not isometrically, with every copy exactly the same forever, but iteratively, with the pattern changing as a result of feedback that adapts and changes the pattern. Magic squares are recognized by many scholars as important motifs in West African textile patterns (Prussin; Aronson; Kreamer et al.), but their function as pattern engines in this context has not been fully explored. I will examine how this pattern-generating function works, how it is linked to magic squares’ use in talismans, and how its talismanic function has given the magic square the deep significance that led to its becoming a pattern engine in West African visual cultures.
To make a case for my contention, I will cite some of the meanings and functions attributed to magic squares; the squares can be examined from multiple points of view, as they are representations with a rich cultural, mathematical and art historical provenance. 5
My approach is taken primarily from visual culture studies, especially as it relates to recent theories linking the field to other senses than sight (Edwards, Gosden and Phillips; Edwards and Bhaumik). According to many of its scholars - notably WJT
Mitchell, Nicholas Mirzoeff and Mieke Bal - the study of visual culture takes as its object all the manifestations of a given culture, not solely its art, nor even solely its visual products (Mitchell 167). The objects of visual culture thus may include traditional art works like painting, material culture objects like West African textiles, or work in new media, for example film or digital media. The perspective of visual culture is taken by many scholars to be an interdisciplinary way of approaching the development of theories of knowledge, and so it closely mirrors and overlaps theories and practices of visual anthropology and material culture studies.
Looking at magic squares symbolism on a specific group of West African textiles through the lens of visual culture moves the perspective away from older notions contrasting “primitive” African cultures to “sophisticated” Islamic societies, as discussed by earlier Africanists (Trimingham; Lewis). The claim that an Islamic prohibition on representational art withered the decorative arts in West Africa, as voiced by J.S. Trimingham (199), is countered by Rene Bravmann, who believes
Trimingham has relegated art to a peripheral function in a society (36). Bravmann notes that the visual arts are central to the lives of Africans and that patterns used in West
African textiles reflect a centuries-long interaction of indigenous and Islamic systems of belief. In this study I consider a view in keeping with visual culture theory that posits, according to Mirzoeff, a transculture that is “always the hybrid product of 6 networks” (41). It is important to note here that even the term “hybrid” may imply the existence of a central, “pure” Islam and a “hybrid” Islam. I hold the opposite view, that the world religion of Islam is not a monolith but a diverse faith with many regional variations and reciprocities.
The sense of touch is of primary importance in the cognizance of textiles and is an important contributor to the efficacy of the magic square as a talisman. The sense of hearing also has a function in understanding repeat patterns, since both visual and auditory patterns operate by repetition. The patterns in this study are based on number relationships and are therefore particularly analogous to aural or musical structures. In
Muslim West Africa as in the rest of the Muslim world, the Arabic writing in a talisman derives its power and meaning from the Qur’an, which is considered the unmediated and originally spoken word of God (Bravmann 19; Dilley 189; Levtzion and Pouwels
493). Talismans containing magic squares are thus regarded by some researchers as
“supercharged prayers” (Canaan 129; Dols 87). In other words, the essentially oral nature of the Qur’an influences the way the amulets containing the magic squares are viewed by their makers and users, as the patterning of sound and the spoken word is recognized as akin to the visual pattern of the talisman.
What is pattern’s role in visual culture? An in-depth discussion of this question would involve an examination of multiple approaches to the science of human cognition and is beyond the scope of this study, but the importance of pattern recognition in human learning of any kind is beyond question according to Bal (24), and, in the context of musical learning, Ingrid Monson (38). Eilean Hooper-Greenhill 7 writes about learning in a museum setting, “Understanding happens, not by being fed information, or having an experience, but when new information or experience can be fitted into a pattern, when the patterned relationships between elements can be seen”
(117).
The scholarly literature on visual culture theory is vast, and only a selection of it
is discussed here. Material culture studies have important areas of overlap with topics that concern visual culture studies. In recent writing, especially by Fiona Candlin, Tim
Ingold and Bill Brown, approaches to visual culture and to material culture have overlapped and even joined in ways that are fruitful for this inquiry. The related disciplines of visual culture and visual anthropology have also been well-defined and discussed by scholars such as Mitchell (100), Mirzoeff (1), Christopher Pinney (85), and Elizabeth Edwards (4), whose call for the inclusion of other senses in any discussion of visual media is especially pertinent to the patterns and symbols in this
study.
In addition to visual culture theory, my approach uses the object-focused
analysis typical of material culture studies, informed as well by anthropology and
museology. I draw upon recent research in visual culture studies that positions
museums in relation to visual culture, highlighting the relationship between the seer and
the seen (Hooper-Greenhill 15), and the implication of all the senses in visual perception (Edwards and Bhaumik 3).Visual culture is discussed by various scholars as
a field (Bal 5), an inter-discipline (Ginzburg et al. 242), an “in-discipline” (Bryson et al.
542) and even a movement (Bal 6). Mary-Leigh Morbey argues for “transdisciplinary” 8 to describe “an expanded cultural field that can lead to new opportunities, often in the
‘terrain vague’ or conceptual space between disciplinary practices” (7). Because of its interdisciplinary structure (by any name), visual culture can act as a useful theoretical perspective for an investigation of magic squares, which have simultaneous mathematical, cultural and art historical manifestations.
Visual culture investigates the seer/seen exchange, positing that how something is perceived is as important as what is perceived, and that meaning is produced dialogically through the interaction between subjects and objects (Hooper-Greenhill
117). Two concepts emerge from this dialogic interaction: the first concept, embodied cognition, posits that perception, learning and understanding are tied not just to visual acts but to all the senses; thus, cognition is seen as “an act of the body that is constructed by its ‘situatedness’ in its environment” (Monson 38). The second, closely related concept is object agency, which states that objects have the power to effect change in their environments, not just reflect their environments. These two concepts are key to my contention that the magic square is a pattern engine and I will present my rationale for this contention in Chapter Four. Here, I will give a brief summary of their background. Gerald Edelman defines embodied cognition for cognitive science as the biological basis for cognition via reentrant loops in the brain which map new perceptions to known patterns of activity to make sense of phenomena and experiences
(85); Edelman argues that embodied cognition underlies the way human beings are able to navigate and make sense of their environment, “a dynamical and embodied approach
[that] proposes to explain intelligent behaviour as a result of the fine-grained 9 interactions between a neural system, the particular embodiment of an agent and the characteristics of an environment” (280). Edelman further clarifies the mechanics of these interactions as enabled by reentrant loops that continually and dynamically respond to conditions for both autonomic and consciously motivated functions. To paraphrase, cognition is iterative behaviour: the mind maps what it perceives to existing patterns held in memory and forms a response based on, but not strictly limited to, prior patterns. In the following passage, Edelman stresses the iterative nature of cognition:
The dynamic arrangements of the brain show the system property of memory:
previous changes alter successive changes in specified and special ways.
Nervous system behaviour is to some extent self-generated in loops; brain
activity leads to movement, which leads to further sensation and perception and
still further movement. The layers and the loops between them are the most
intricate of any object we know, and they are dynamic; they continually change.
(29)
Philosopher Hubert Dreyfus identifies embodied cognition as the defining factor in what makes us human, noting that “what distinguishes persons from machines, no matter how cleverly constructed, is not a detached, universal, immaterial soul but an involved, situated, material body” (236). Thus in Dreyfus’ view, the reason computers cannot think is not because they do not have a mind, but because they do not have a body (as discussed in Tilley 274).
The notion of embodied cognition is linked to the view of vision as an embodied sense, inseparable from other senses (Edwards, Gosden and Phillips; Edwards and 10
Bhaumik; Mitchell; Pinney). Judith Becker adapts this definition to the creation and perception of music by seeing it as a process of knowledge through intimate bodily involvement with the world (118). The implications of embodied cognition for music have also been explored by Monson and Iyer. For them, music is perceived and made
sense of through embodied cognition, and it possesses “perceptual agency” to profoundly and dynamically mould individuals and societies (Iyer 25; Monson 38). I use the term embodied cognition in this study to categorize ways of knowing and making in West Africa as evidenced by specific textiles.
I will argue in Chapter Four that patterns of cognition associated with healing
are embodied, through references to magic squares, specifically in the textiles under
study, and more generally in Muslim West African objects and practices with those
objects. In their embodied forms on West African objects, magic squares exemplify the
multi-sensorial nature of the seer/seen exchange. For example, when a magic square-
derived pattern appears on cloth in the context of West African healing practices such
as the Bamana incision rituals discussed in Chapter Four of this study, its meaning is
mediated by the tactility of the cloth (Brett-Smith “Cloth as Amulet”). When the square
is inscribed on a Qur’anic writing board along with other writing, the writing is washed
off and the liquid is drunk in a practice described as erasure, the meaning is actually
taken into the body, implicating taste and smell2 (El-Tom 416). In yet another example,
this time involving the use of audiotapes in religious practice, Dorothea Schulz extends
2 Erasure is a term given by Abdullahi Osman El-Tom to a ritual practice that he has observed among the Berti people of South Sudan. Qur’anic writing and graphemes are inscribed on a wooden writing board and the water used to wash them off is drunk for healing and protective purposes. See also Silverman for more information on this practice. 11
the notion of embodied cognition to include sound, describing sound/touch as a
“common pool of sensual mediation... grounded in the particular agentive capacity that
people throughout West Africa have conventionally attributed to aural experience and
the spoken word” (147). What all these examples have in common is the viewpoint that
people affect and are affected by material objects in fundamental ways.
The second key concept, object agency, derives from the view that the subject of
visual culture’s inquiries is neither physical artifacts and their provenances as in art
history or material culture, nor the study of people as in anthropology, but the study of
what happens in the space between objects and people or, as Hooper-Greenhill writes,
“To consider objects from the perspective of visual culture is to focus on the
relationship between the object and the subject - the seen and the seer” (108). Hooper-
Greenhill advances the concept of object agency as it operates in museum
environments, contending that museums themselves are constitutive of cultural attitudes
rather than just reflective of them, especially by controlling what is left out, ignored, or
hidden (13).
When Mitchell wrote that “all media are mixed media” (170), he was refuting a belief in the exclusivity of sight in visual culture studies. Mirzoeff, Constance Classen, and Bal concur with his statement. They owe a debt to Maurice Merleau-Ponty, who wrote many years earlier of the body as the ground of perception and of the
impossibility of separating its various senses in a particular perceptual event (222). The magic square-patterned textiles in my study are all meant to be worn on the body; therefore, Bal’s description of seeing as “profoundly impure” (8) can be applied as well 12 to these textiles, and their “impurity” with its accompanying complexity is what is lost when they are only seen and not touched, felt or smelled.
Along with Mitchell, Bal decries the focus on visuality in visual culture studies and offers strategies for opening the discourse up to other sense modalities. Her aim is to describe the object domain of visual studies, which she says is a result of framing, not only of the object, but of ways of looking at it (23). She draws her ideas about the relationship of museums to visual culture from Hooper-Greenhill, agreeing with
Hooper-Greenhill’s analysis of the role of the museum in “denaturalizing” the object
(Bal 14). However, Bal’s accusation of visual essentialism in other scholars seems inaccurate since, as I mentioned earlier, there is much consensus that the senses are intertwined in perceptual and cognitive acts. Her claim prompted a series of published rebuttals, in which several ideas key to my study emerged: Mitchell’s assertion that
“the experience of being seen is equal in importance to, and intertwined with, the process of seeing” (Bryson et al. 251) is closely tied to the notion that objects have agency of their own. In her response to Bal, Michael Ann Holly calls this agency a
“fundamental phenomenological conviction” (Bryson et al. 240). This notion of object agency is one I take up in more detail in Chapter Four, when, having examined the textiles, I analyze my findings and explain my contention that the magic square has influenced the formulation of their patterns by acting as a kind of pattern engine.
Three scholars of anthropology have made important contributions to the discourse about object agency: Alfred Gell calls objects “indexes” that, once made, can profoundly affect the interactions of individuals and societies. Gell suggests that 13 cultural and transcultural exchanges of objects enact a form of cognition that occurs in the space between objects, makers and users (Gell 232). Tim Ingold stresses that the forms of objects do not grow from disembodied designs, but emerge from the combined
interactions of people, materials, and environments (89). In addition, Jean-Pierre
Wamier notes that the lives of the makers and users of these objects are significantly changed by the practice of making and using them (465). The notion of agency that emerges from this selection of the research on visual culture is complex; on one hand we talk about the agency of the viewer in the seer/seen exchange, on another, the agency of the object. Neither, it seems, is passive in the dynamic process of interchange between subject and object.
The concept of object agency leads to my interpretation of magic squares as pattern engines. In an article called “What do pictures really want?” Mitchell describes how some images ‘“have legs,’...as if they had an intelligence and purposiveness of their own” (73). He discusses this concept further in Picture Theory, using the term metapictures to describe pictures about other pictures (35). In a similar vein, anthropologist Ira Jacknis refers to metaobjects, objects about other objects (5). Brown brings the concept of metaobject into tighter relevance for magic squares by explaining
its basis in computer science, where it “designates a base object that generates or manipulates other objects” (192). Brown further explains how a work of art can operate as a metaobject that “isn’t satisfied with just being an object and seems to insist instead on taking other objects or object cultures as its object of address” (192). Taking up
Brown’s perspective, I contend that Islamic amulets in West Africa can be regarded as 14 metaobjects because the magic squares within them act as metapattems, patterns about patterns, or even pattern engines, generating other patterns.
Chapter Four of my study will chart the magic square’s development from a numeric concept first to a metaphor for cosmic perfection, thence to an embodied representation on textiles or other material in West Africa. The study looks at both the square itself and the object the square or its related pattern is on, since the magic square gains its talismanic power through becoming visible and tangible. Furthermore, the study looks at the relationship between objects as well as the objects themselves. The fact that they communicate meaning has been amply proved by other scholars, especially Washburn and Prussin, but this study examines how these patterned textile objects communicate, and what they continue to communicate through their use. The textile objects are the primary sources of the study and this necessitates using the inductive methodology of material culture studies, looking first at what the objects can tell us about themselves. However, this approach is also closely related to what Bal refers to as “seriating” in her account of visual culture studies. The methodology of visual culture studies as defined by Bal involves the key activity of different kinds of analysis, and first among these is seriating, “a critical analysis of specific series and the grounds that bring the objects together” (21). Seriating will inform my evaluation of the textiles I have selected for examination.
I have embarked upon this study in order to better understand patterns’ unique role in the production of cultural meanings, through analysing the patterned derivations of one motif represented on textiles in one region of the world. This process of analysis, 15 as I will discuss further in Chapter Four, has led to my contention that magic squares function as pattern engines in the Islamic West African environment. To consider magic squares in this way reveals something about the nature of non-figurative, iterative pattern that sets it apart from that other category of image, the figurative representation. A figurative image has an indexical relationship to that which it represents, even if its meaning is obscure - for example, once one is aware that a circle refers to the moon, one can forever after see the moon in the circle - but a checkerboard pattern on cloth is related to the magic square in a less direct, more connotative way.
The original meaning of a magic square is not in its numbers, but in the relationships between its numbers. Grasping its meaning involves understanding its number relationships in a process similar to solving a puzzle or cracking a code; this quality has
led to its incarnation in popular mathematical recreations like Sudoku or Kenken.
Number relationships are present as well in a checkerboard pattern but they are of
opposites (for example, on/off, positive/negative, or foreground/background) - they can be expressed numerically as even/odd or 0/1. As Washburn suggests, non-figurative, repeat pattern is better than figurative image at encoding cultural information that is
about “relationships, not things” {Embedded Symmetries 54). In my study, I will adapt
Labelle Prussin’s argument that the checkerboard pattern in Muslim West African textiles encodes cultural information about the healing power of talismans through its matrix arrangement (96) to my hypothesis of the magic square as a pattern engine.
Two areas of focus will be addressed through a review of early and more recent research, to probe the significance of magic squares as they appear on textile objects in 16
Muslim West Africa. Each focus area is associated with a research question that will be addressed through the study. The focus areas are, first, the mathematical and cultural history of magic squares and second, magic squares’ operation in Islamic West African textile patterns.
The first focus area will be addressed through evaluations and comparisons of key works written about the history of magic squares. Chapter Two will offer a summary of the squares’ origins and development as important visual metaphors for universal order, with particular attention to their use in Islamic contexts, where they are relevant to both mathematical and cultural history. Here, the key question is, how does a concept transform into a pattern on textiles?
The second area of focus is the significance of magic squares in Islamic West
African art, specifically on textiles. In this context, they have been considered important decorative motifs by many researchers (Prussin; Aronson; Kreamer et al.;
Brett-Smith; Roberts et al.). The research question that arises is: why is the magic square given so much prominence in West African material culture? Chapter Two examines some of the key research in this area. Chapters Three and Four offer a detailed analysis of the textiles under study with this question in mind. The material study of the textiles themselves and conclusions that can be reached thereby forms the core of the present study and will lead to a discussion in Chapter Four of the metaphoric nature of the magic square and speculation about its function in West
African iconography as a pattern engine. I will conjecture, by analyzing the textile objects and referring to anthropological research in the field (Dilley; Hassan) that 17 magic square-related patterns are consciously embodied in West African textiles for their talismanic power by both makers and users. It goes against the conventional view of a Western separation of mind and body to claim the ability of this drawing of a grid filled with numbers to move in opposite directions simultaneously, manifesting as both an abstract concept and a vividly, intimately embodied talisman that is seen, worn, felt, tasted, and even heard. However, my discussion in Chapter Four will claim this for the magic square and its constellation of related patterns on West African textiles.
The qualifier “magic” in magic squares needs clarification since magic has many meanings in contemporary usage. As I embark upon a review of writing on magic squares in the context of West African textiles, I find that I am entering a space in which there is profound disagreement about the notion of magic. On one hand, some writers on Islam (Canaan; Dols; Asatrian) attempt to find a possible place for magic, defined by Constant Hames as “ensemble d’idees et d’actions qui modifient le cours naturel des evenements, ‘a set of ideas and actions which change the natural course of events’” (7). On the other hand, contemporary Western thinking denies the existence of magic, pitting it against rationality (Becker 90; Golding 225). Finally, the conventional view of West African societies is that they embrace and perform magic in a myriad of
forms, including the enactment of spectacular masquerading ceremonies (Visona). This background of conflicting views on the “magic” in magic squares will inform my review of the research in Chapter Two. In my mind the word refers firstly to the magic
square’s mathematical and gamelike function - the fact that all directions in the grid add up to the same sum is called “magic” as in a particularly elegant magic trick - and 18 secondly to an alternate system of rationality with its own internal logic that has deeply informed art practices of many different kinds, worldwide. It is to me an essential and fascinating part of the way humans interact with their environments and make meaning in their lives.
The terms “amulet” and “talisman” have similar meanings and are used interchangeably in the literature and in this study. Their usual names are jadwal, the
Arabic term for table, or khatim, the term for seal, from which the West African Fulbe word hatumere is formed (Prussin 74). This study will use “amulet” to refer specifically to any small, self-contained item featuring or containing talismanic designs; for example, the packets sewn to the Burkina Faso shirt in Figures 5 and 6 are referred to as amulets.
This study of patterns on West African textiles cannot be definitive or conclusive: its author has not gone to West Africa, nor communicated directly with any of the makers of the textiles. Indeed, the individual makers are almost all unknown.
Other limitations include my inability to read any languages other than English and limited French, and my lack of proficiency in higher mathematics. In other words, I come to the study as neither a mathematician, nor an expert in Islamic art, nor an anthropologist, to investigate a topic that has elements of all three in its history. The study is intended to raise particular possibilities for further interdisciplinary research, in more breadth than is possible here, into the deep vein of magic squares-related representation that threads through West African textiles, informing their meaning even as they are moved into the decontextualizing environment of a museum. 19
Chapter Two, Review of the Literature on Magic Squares in Muslim West African
Visual Cultures
Magic squares have a mention in many histories; it could be argued that their trajectory - from numeric models of the universe in ancient China to mathematical recreations played on the subway in forms like Sudoku and Kenken (Boyer 37) - reflects some of the conflicting attitudes to magic and its function in human societies that I discussed in Chapter One. It is my aim to address a specific part of this trajectory by examining certain textiles to discover what they can tell us about magic square- influenced patterns in a particular time, place, and cultural context. Therefore, as a historical background, this chapter reviews a selection of literature on magic squares to illuminate the reasons why they are such powerful pattern creators in Islamic West
Africa. I will examine, firstly, research about magic squares’ mathematical and sociocultural history and secondly, their agency in the Muslim West African environment as references to talismans.
In order to move to a consideration of the literature on magic squares symbolism in West African textile patterns, it is necessary to first step back from my main topic and start with a review of the origins and the mathematical properties of magic squares. Both of these perspectives are relevant to the questions being asked in this study, of where its power originates, and of how the magic square has become important to West African textile patterns. My investigation of both these questions must begin in the early history and functions of the squares. The sources found to accomplish this aim include works by
W.C. Andrews, Frank Swetz, and Clifford Pickover; these works are not scholarly in 20 nature but are written for a broader audience. They focus on the squares’ mathematical history and their complexity as puzzles, while dealing simplistically with their religious or cultural meanings. Journal articles by N.L. Biggs and Schlyer Camman take a more scholarly perspective, but all the aforementioned authors essentially relay the same historical information and descriptions of magic squares’ mathematical workings. Biggs introduces the squares as the most ancient examples of combinatorial mathematics (127) while Camman’s focus is more on their significance in religious history (199). Andrews,
Swetz, and Pickover approach the squares as mathematical recreations, “mere” intellectual playthings (Andrews vii). They describe the weird and fascinating mathematical gymnastics of the squares in order to explain them to a reader who is primarily interested in them as puzzles and brain-teasers.
Swetz and Pickover specify different ways that the magic square can be visualized as the basis for graphical representations: by tracing a path from one consecutive number to the next as shown in Figure 2, left; or by colouring in certain cells, for example cells containing even numbers, as in Figure 2, right. These are demonstrations of the simplest methods for turning the matrix of numbers into a graphic motif; the motif, which becomes more complex as the matrix increases in number, can then form the basis for geometric patterns (Swetz 142; Pickover 262). Swetz indicates that mathematicians continue to be interested in discovering more of magic squares’ properties, especially as they resemble matrices, which are mathematical structures made of vectors (127). 21
4.
1 * 7 ^, ' f/ - i ^ / \ i ' ' r 6
Figure 2: A 3 x 3 magic square, (left) consecutive numbers joined by lines and (right)
even numbers coloured in.
Andrews, Swetz and Pickover go into considerable detail about the mathematically complex operations that are possible for the squares through their relation to number theory, algebra and group theory, but give little attention to the squares’ philosophical or cultural meanings; any description of these aspects is brief and basic.
None of these aforementioned authors is concerned with the passage of magic squares into West Africa, or onto textiles.
4 19 12 3 8
Figure 3: (left) The continuous method of creating a 3 x 3 magic square; (right) a torus. 22
Camman offers a description of the continuous method of construction, naming its
Muslim inventor as anonymous,3 but Vladimir Karpenko cites its origin in the encyclopaedic writings of the Ikhwan al-Safa, the Brethren of Purity4 who lived in Basra,
Iraq in the tenth century (“Two Thousand Years” 150). The method involves visualizing the square as wrapped around a vertical cylinder so the cells adjoin, while simultaneously
imagining it wrapping in the horizontal direction, as if the two-dimensional square were a three-dimensional torus (Figure 3, right). The numbers are added to the cells one by one according to a consistent rule; in Figure 3 left, the rule is to move one square down and one square to the left. For example, the position for the number two drops it below the
square, so the “next” cell is at the top, and so on until the square is completed. The continuous method is similar to a base number system that does not use zero: in a base number system, for example binary (base-2) or decimal (base-10) any calculations are done with only these numbers. They are used in combinations to express numbers larger
than their limit. In the 3 x 3 magic square there are only nine positions so all the numbers must fit within them. I will discuss this point with reference to weaving drafts and
checkerboard patterns in Chapter Four. Camman suggests that the spiral action of the
continuous method accounts for the squares being seen as active symbols of life renewing
itself around a divine source symbolized by the middle number and this leads to a belief
in their power as talismans able to influence actual events (197). This method has
important implications for the transformation of the squares into patterns on West African
3 Camman traces the appearance of the continuous method to two thirteenth century Persian manuscripts, one at Princeton University Library and the other at the British Museum (196).
4 See Y. Marquet for information on the Ikhwan al-Safa. 23 textiles; intriguingly, it is identical to the method for graphing a weaving draft. I will discuss these implications in Chapter Four.
Having determined some of their basic mathematic functions, I now can turn to a consideration of the literature on magic squares that discusses their historic background and their religious and cultural relevance to Islam. This will then lead us to an examination of the research on their talismanic functions when they move into Muslim
West Africa.
Magic squares functioned for ancient Chinese, Persian and Indian belief systems as numeric models of the ordering of the universe (Cammann 183; Swetz 19). This is also a Pythagorean notion; for the ancient Greek philosopher and mathematician Pythagoras, the harmony of the universe was fundamentally arithmetical (Stapleton and W. 31).
Camman writes that the 3 x 3 magic square originated in ancient China earlier than 1025
BCE and was regarded as a powerful model referencing the sacred (185). Alfred Schintz notes its use in the floor plan of the Ming Tang, an ancient hall of audience in the
Emperor’s palace (71). Other authors writing about the history of magic squares share
Camman’s view that they moved with the Islamic conquest of India in the seventh century into Persia and westward (Biggs 117; Pickover 8), but H.E. Stapleton contends that the squares were known to philosophers in Hellenistic Greece, and even much earlier in ancient Iran through their association with alchemy, an ancient science that is concerned with discovering and manipulating the fundamental properties of materials
(18). In fact Stapleton and Schintz argue there is evidence that they were carried east to
China in the second millennium BCE by Iranian or Bactrian emissaries to Emperor Wu’s 24 court and then were carried back west by Muslims in the seventh century. Gerhard
Endress describes the scientific and philosophical knowledge that came into Islamic thought as “neither pagan nor Christian nor Islamic but universal” (123) and situates mathematics within this knowledge as occupying the space between “the eternal intelligibles and the corruptible sensibles” (130).
The first mention of a magic square by a Muslim author is attributed to the famous ninth century Persian scientist Jabir Ibn Hayyan, who was possibly a composite of many authors (Biggs 119; Stapleton 2). In the following passage Syed Nomanul Haq describes Hayyan’s neo-Platonic Science of Balance:
In the natural world, to give merely an outline of Jabir’s doctrine, all bodies
contained the four qualities in a specific, immutable, and noble proportion which
was governed by the Supreme Principle. This proportion was 1:3:5:8 whose sum
17 was the foundation of the entire Science of Balance ... The alchemist who has
mastered the Science discovers through this proportion the quantitative structure
of all things. He is then able to change anything into any other by creating in it a
new configuration of qualities. (Haq and ibn Hayyan 67)
According to Haq and Stapleton, the 3 x 3 magic square embodied the numbers
1:3:5:8, with their sum of 17, through the application of a gnomon, (Figure 4), a geometric symbol used by the Pythagoreans to isolate numbers in the square5 (Stapleton
“The Gnomon” 9; Haq and ibn Hayyan 206).
5 Stapleton argues for the significance of the gnomon in Pythagorean number mysticism as a reference to the Babylonian temple form ofziggurat, its steps in turn representing the movement of the planets (“The Gnomon.”9). 25
4 9 2
3 5 7
8 1 6
Figure 4: The gnomon, an L-shaped symbol.
Thus, the magic square was important in Hayyan’s alchemy as a coded reference to the Supreme Principle that would be recognized by all initiates in the discipline. The talismanic function is key to its agency and, I would suggest, is rooted in this alchemical interpretation of its numerical relationships.
In Magic and Divination in Early Islam, Emily Savage-Smith laments the predominant focus on mathematics and puzzles in the existing writing on magic squares
(xiv). This criticism can be fairly levelled at Swetz, Andrews and Pickover, who do not address the cultural or magical significance of the squares in any depth. Savage-Smith’s edited volume provides a primer on the function of magic squares in the medieval period of Islam from the ninth to the twelfth centuries, when they developed their significance to neo-Platonic and neo-Pythagorean thought and alchemy through the writings of Hayyan, the Brethren of Purity and Ahmad al-Buni.6 In this volume, Michael Dols addresses the general unease with the concept of magic in Western thought and differentiates between the Western opposition of magic to rationality and the concept of “supercharged prayers”
6 See Vladimir Karpenko for the relation of al-Buni and his work, theShams al-Ma ’arif to magic squares (“Between Magic and Science” 124). For more information on al-Buni and theShams al-Ma ’arif see A. Dietrich. (87) that are potentized by phrases from the Qur’an, the ninety-nine names of God taken from the Qur’an, and magic squares.7 Dols also writes that the “prayers” are potentized by physical contact with their makers’ and their users’ bodies, and at times with their sweat, spit and semen (86). This activation of the talisman’s power through its embodiment is relevant to my contention that the squares’ instantiation in textiles to be worn against the skin is a key factor in their ability to act as pattern engines for West
African cultural forms. It is important to note the central role of calligraphy, especially writing in Arabic from the Qur’an, in the development of amulets containing the
“supercharged prayers.” Savage-Smith agrees with Dols and emphasizes that Islamic amulets are supplications to God rather than invocations to demonic forces, or constituents of magical ceremonies (133).
Savage-Smith, Dols, and Tewfik Canaan all agree that amulets, and the use of magic squares within them, are prayers appealing to a divine power for protection or for agency of some kind. Canaan’s study in particular, originally written in 1937, is a seminal study of talismans in the history of Islamic thought. His explanation of abjad letters 8 and of the ninety-nine names/attributes of God Q and how both are related to magic squares is essential to an understanding of the squares’ impact in the West African milieu
(91). These scholars argue for the legitimacy of magic as “a form of rationality with its
7 For more information on the ninety-nine names of God, see L. Gardet.
8 In the abjad alphabet, letters have numeric values. The 3 x 3 square was known asbuduh because the comers of the square contained the letters b, u, d, and h. For an explanation ofabjad letters see Venetia Porter (187).
9 According to Canaan, the preponderance of the ninety-nine names of God in talismanic “supercharged prayers” was based on a belief that God would answer if He was called by one of them (136). 27 own set of assumptions, based upon a process of analogy rather than proven causes and effects” (Savage-Smith xiii).
There are other, widely divergent theories about the cultural meanings of symbols and patterns in non-figurative Islamic art, including those that refer to magic squares. In
Enfoldment and Infinity: An Islamic Genealogy of New Media Laura Art, Marks groups these theories into four approaches, which she terms positivist, universalist, theoretical, and phenomenological (28). I will use her categories in the following review of theories for interpreting aniconic, geometric Islamic art. First, the “positivist” camp includes such scholars of Islamic art as W.K. Chorbachi (760), Richard Ettinghausen (18), Oleg Grabar
(32), and Sheila Blair (172), who resist attributing meaning to such symbols and patterns as the magic squares, on the grounds that they should be seen in the strictly geometric terms of their construction and this is all that can reasonably be assumed to have been in the minds of the artisans that used them in their work; in other words, to their makers they are decorative and nothing more. Ettinghausen suggests that, while there may be religious connotations to particular motifs in Islamic ornament, these are too vague to be taken seriously (18). Marks opposes this approach on the grounds that it drains Islamic patterns of any possible significance beyond pure decoration by refusing speculation about them (Marks 28). I will reconsider this view in more detail in Chapter Five when I discuss counter arguments to my conclusions.
In the second camp, and again according to Marks’ categorization, “universalist” scholars like Seyyed Hossein Nasr and Keith Critchlow err in the other direction, attributing universal spiritual significance to geometric patterns in Islamic art. Nasr’s 28
notion of the Unity of Being, a mystical principle attributed to Ibn Arabi, claims that the
harmonious division of a circle underlies all geometric Islamic art.10 This attempt to make
all geometric operations spring from one origin (188) is refuted by Chorbachi, who
argues, correctly in my view, that there are seventeen groups of distinct two-dimensional patterns and that it is a scientific fallacy to reduce them all to the divisions of a circle
(759). Here, the error seems to spring from an eagerness to explain mathematical forms -
for example, the symmetry groups that govern isometric patterns - in terms of theological
and mystical interpretations. Critchlow takes the opposite view to Pickover, who reduces
the squares to recreations, by extolling the science of numbers as the root of all sciences
and the highest form of knowledge, as expressed in magic squares (42). Critchlow’s
diagrams (examples are shown in Figure 2) are helpful in understanding how numerical
relationships can be represented graphically by colouring in different areas. However,
Mark’s contention is that the “universalist” approach is reductionist and ahistorical, and
does not take cultural contexts into account (Marks 28). Yasser Tabbaa also assigns
profound meaning to geometric form in his interpretation of muqarnas domes as
representations of a universe that is being constantly changed by the will of God, but he
cautions that the “high symbolic charge” associated with the form tends to be debased
into mere decoration over time (61).
Thirdly, Marks lists the theoretical approach, followed by such scholars as Gulru
Necipoglu, Valerie Gonzalez, and Carol Bier, and argues that this approach offers new
and valuable ideas about what the significance of geometric patterns might have been,
10 For information on the Unity of Being principle see W. C. Chittick. 29 given the environment in which they developed. In her analysis of the sixteenth century
Timurid Topkapi scroll, Necipoglu posits that its complex geometric patterns formed part of the consciously applied design repertoire of master craftsmen in that period (457). Bier maintains, in agreement with Chorbachi’s relating of Islamic geometric pattern to mathematical ideas (260), that Islamic geometric patterns developed in the medieval period as neither strictly decorative nor universally spiritual representations, but as expressions of the heightened interest at the time in the mathematics of space and form
(262). Bier’s approach is neither simplistic in the direction of the “positivists,” under interpreting the patterns by refusing to admit of any deeper meaning for them than the purely decorative; nor all-inclusive and reductionist, forcing every pattern to conform to one spiritual system, the “Unity of Being,” thereby over-interpreting the significance of the patterns. Bier’s perspective on Critchlow’s transcendentalist theories of the meaning in Islamic geometric patterns is more positive than Chorbachi’s or Ettinghausen’s; she sees him as framing a “spiritual quest on the part of the patternmakers” (259). With this statement she enters the debate among scholars of Islamic art that concerns intentionality.
Necipoglu and Bier argue that something of the philosophical meanings of the patterns may have been known to the designers and artisans who devised and made them. George
Saliba, in disagreement with Necipoglu and in concert with Grabar and Chorbachi, denies that there is any historical evidence of written communication between philosophers who devised religious symbolism and the medieval artisans who actually carved the stones, painted the ceramics or wove the cloth that contained the so-called symbolic 30 ornamentation (637). I will draw upon this research in Chapter Four for a discussion of intentionality in relation to West African textile patterning.
Finally, Marks aligns her own perspective on geometric Islamic art with the fourth approach that she terms “phenomenological.” Marks adapts this approach from
Merleau-Ponty’s notion of the phenomenology of perception (229), calling it “existential phenomenology, which sees one’s own experience, sensory and mental, as a basis for analysis, but does not assume this experience can be generalized” (28). Notions of embodied cognition and object agency - as interpreted by the visual culture scholars discussed in Chapter One of this thesis - are firmly rooted in Merleau-Ponty’s earlier theories of the body as the ground of all perceptual acts (Tilley 34).
Marks sets out to reveal the relation of contemporary computer-based art to medieval Islamic art, which she calls “logical depth,” a term she borrows from computer theory. In mathematical physics, a logically “deep” object is one that requires a lengthy
calculation (Bennett 3). Marks applies the term to made objects; she argues that
everything constituting an object, all its histories, even including those histories that have been discarded, is still present, mediating its effect and contributing to its agency (23).
According to this view, the manifested object that we perceive is imbued with and
informed by all the encoded calculations, religious symbology, and mechanical
operations that went into its production. Marks views logical depth as a way to understand the hidden layers of meaning informing the genealogies of the art forms she
studies, “to plumb their logical depth, unfold what is enfolded, touch on the batin
concealed by the zahir, and pursue the social and historical connections hinted at by their aura”11 (24). Marks also notes that batin and zahir have particular embodied references in
Islamic writing - batin, the enfolded or hidden, has a conceptual correspondence to the womb while zahir, the unfolded or visible, corresponds to the chest - that their Greek antecedents, manifest and latent, do not (15). I will return to a consideration of logical depth, batin, and zahir in Chapter Four.
One notable point I want to make about the research so far before we move into
West African textile patterns is that it focuses mainly on the medieval period of the ninth to the twelfth centuries; this is also the period when magic squares were brought to West
Africa, especially via amulets, and came to strongly influence the West African design gestalt in the ensuing centuries up to the present day, as we will see in the following section.
We turn now to the body of research that deals with the transformations of the magic square into textile patterns in the West African social, religious and cultural environment. Many resources exist that offer scholarly examinations of the manufacture and customary use of textiles in West Africa. The entire oeuvre of African Arts magazine, published by the University of California at Los Angeles (UCLA) since 1970, provides an example. Equally, much writing has been done on Islamic influences in West Africa, but with very little attention to patterns on textiles. Therefore, relatively little literature has been found that looks with any depth at textile patterns, in West Africa, in the context of Islamic art and culture. Bravmann and Nehemia Levitzion have written on the subject of Islamic art and culture in Africa but give scant attention to textile patterns; however,
11 The Isma’ili branch of Shia Islam has terms for the manifest and hidden aspects o f the faith: zahir describes exoteric religious life, andbatin, mystical or esoteric realities (Poonawala). 32 their writing is important for establishing the Islamic context within which magic squares and the patterns that refer to them are represented on textiles. Monica Blackmun Visona’s work on the history of art in Africa also touches upon the significance of textile patterns and Islam but is concerned more with sculpture and architecture.
Most research on West African textiles found for the purposes of this study have mentioned Islamic influences on textile patterns only briefly, giving the impression that these influences are negligible or marginally relevant to their production and use (Picton,
Rubin, Gilfoy, Perani). However, there is a body of research that has given in-depth careful attention to magic square-related patterns on textiles. In the following section, I will discuss four scholars who have made significant contributions: Labelle Prussin,
Sarah Brett-Smith, Christine Kreamer, and Ousmane Kane.
Recent publications have addressed the dearth of attention in the research to the influence of Islamic calligraphy on the West African cultural environment, lamented by
Arnold Rubin. He notes that the lack of focus on Africa’s role in extensive trade networks from ancient times feeds into the “darkest Africa” syndrome (67). This lacuna began to be filled with the publication of Hatumere: Islamic Design in West Africa. In this influential work on Islamic influences in the West African built environment, Prussin examines the pervasive presence of Islamic aesthetics that reflect belief systems in that region. She draws on research by earlier scholars like Bravmann, who argued in favour of the synergy of Muslim and indigenous West African art and culture (Bravmann 1), but takes the argument much further, in an attempt to fit every visual representation she discusses into her theory that the West African talismans containing magic squares (the 33
“hatumere ” of the title) dominate the history, ancient and recent, of West African visual culture. She argues for a unity of symbolism across a diversity of two-dimensional forms where the same patterns appear in different variations, and offers the rationale that religious clerics often make secular objects for their communities. For example, leatherworkers who make Qur’an covers also make sandals, riding boots, and also the amulet covers such as those on some of the textiles in my study (52). Salah Hassan offers another instance of this crossover of professions in his ethnography of the Hausa in
Nigeria, writing that malams (Muslim clerics) often do cap and gown embroidery to supplement their incomes (101).
Prussin agrees with Camman’s argument that the continuous construction method invented for magic squares by the Ikhwan al-Safa contributed to their talismanic value as
“symbolic representations of Life in a process of endless flux, constantly being renewed through contact with a divine source at the center of the cosmos” (Cammann 199).
Prussin offers a further argument for the transformation of the square into a talisman and thence into patterns like woven checkerboards and embroidered knots that reference talismans: while the “conceptual baggage brought by the early Muslim trader was embodied in the written word” (73), the majority of West African residents have traditionally been non-literate (73). Therefore, Prussin argues, over centuries the magic square, a “number-grapheme of Arabic” (75), was simplified and reduced to a graphic motif that referred back to it; in her view, “the pattern becomes a surrogate for the emotional charge associated with the sacred script” (78). Prussin’s analysis, while perhaps too all-encompassing, provides a valuable background of viewpoints on magic 34 squares in West African visual culture that I will build on in my examination of textile patterns with magic square representations.
Pmssin’s theories, especially her architectural claims, have been accused of reductionism by F.W. Schwerdtfeger (152). He contributes to the debate about intentionality by relating a conversation he had with a Hausa builder in Nigeria, during which the builder acknowledged familiarity with magic squares but denied he ever used them as models in building design and construction. Rather than accepting the magic square as the root of all design in the West African built environment, as Prussin seems to do, Schwerdtfeger argues for a design methodology based more on similar design problems leading to similar solutions, whether in West or North Africa or indeed anywhere. This argument is sound with regard to textile design as well - it must be said that a checkerboard structure is very common in textile design - but in my view this commonality can cohabit with a deeper symbolic meaning for a checkerboard pattern in a specific environment. Schwerdtfeger also disagrees with some of Prussin’s dates for West
African buildings and, significantly for this study, contests the provenance of a robe she attributes to Timbuktu (Prussin 146). A similar robe (Figure 16) in the collection of the
Textile Museum of Canada (hereafter referred to as TMC) is one of the objects examined in Chapter Three.
Prussin’s study ranges geographically over all of West Africa and temporally from the eighth century to the present day. Two other ethnographies have a much tighter focus: Roy Dilley looks at the conflict between orthodox and locally inflected Islamic practices in mid-1990’s Senegal, from the results of his field work there. Salah Hassan 35 concentrates on the interconnections among art, literacy, magic, and healing among the
Hausa in historic and contemporary Northern Nigeria. Both authors emphasize the importance of Arabic calligraphy in the formulation of Islamic amulets, as well as the close connection between the spoken and the written word in Islam through the Qur’an, which is considered the revealed word of God (Dilley 188). Dilley argues strongly for the syncretism of Islamic and indigenous West African social and artistic practices over centuries; in this he is in agreement with Hassan as well as with Prussin, Bravmann, and
Levtzion. Hassan concurs with Prussin’s view that Islamic magic square construction is especially relevant to a number of design constructs in West Africa, but he also notes:
The rich heritage of Arabic literacy . . . has been adopted by the Hausa. This
heritage is not only Islamic but also Jewish, Christian, or Greek . . . this may lead
to a reconsideration of the issues of syncretism and the so-called pre-Islamic
survivals in Afro-Islamic cultures. (230)
The relevance here to my study of magic square-influenced textile patterns is that, following Prussin’s, Dilley’s and Hassan’s views about the made environment in West
Africa, one can extend their arguments to surmise that these textile patterns were produced over centuries in a context of making that is diverse and changing, not one that is divided into a pre-Islamic time (non-literate, primitive) and an Islamic time (literate, sophisticated). Alain Epelboin contributes another perspective to this view of the textiles’ diversity in his study of talismanic shirts retrieved from the garbage dump in Cap Vert,
Senegal; he writes, “des objects islamiques sont integres dans les rituels d’un feticheur 36 parfaitment paien. ‘Islamic objects are integrated into the rituals of a completely pagan practice’” (Epelboin, Hames and Raggi 149).
Dilley makes an important point about the role of touch in the fabrication and use of amulets: he describes an amulet maker singing as she makes one, and spitting her saliva “to carry the power of her words into the clay” (70). Dorothea Schulz makes a related observation about the use of touch and hearing in religious practices, but this time it is in the Mali of 1999, where audio tapes are used for listening to a sermon. These tapes are kissed and fondled, leading Schulz to compare them to ‘“works’ fabricated by
Muslim experts in the esoteric sciences” (149).
Earlier scholars mentioned that the magic square’s ubiquitous presence in West
African amulets has resulted in the creation of symbols and patterns that refer to it on many types of textiles; however, these mentions have generally been very brief. In a footnote, Arnold Rubin includes a reference to magic square patterns on Asante adinkra cloths, Yoruba starch-resist adire cloth, and Bamana bokalanfini, which had not previously been thought to contain any Islamic symbolism (91). Judith Perani and Brett-
Smith also mention the possibility of Islamic influences in the stamped patterns of adinkra cloths (Brett-Smith “Cloth as Amulet” 75; Perani 81). Claude Ardouin is beginning to conduct new research on references to magic squares in patterns on Fulani wool blankets (khasa) from the Niger River region (Ardouin). While these blankets are produced exclusively by Muslim people, their patterns have not been considered Islamic in past writing about them. 37
Brett-Smith’s work on symbolic patterns in Bamana mud cloths, worn by girls undergoing excision in Mali, is an example of the matrix pattern, “a large square divided into a matrix of smaller squares” (“Cloth as Amulet” 70), being adapted to a new, specific function. Brett-Smith conjectures that the magic square is the basis for the patterns on the kind of bokalanfini termed basiae cloths (“Cloth as Amulet” 75); here it is utilized to imbue the cloth with the power to protect the initiate from the primal power - nyama - that is released in the excision ceremony. As the cloth soaks up the bodily fluids that result from the operation, it also holds and contains the nyama, keeping the girl and her community safe from its dangers. One of the objects examined in Chapter Four of this study is a Bamana wrapper that has the grid arrangement and the “M” markings characteristic of an excision cloth (Figure 27). Brett-Smith also provides a perspective on the significance of talismanic shirts like the one pictured in Figures 5 and 6: by virtue of the Qur’anic writing and magic squares on its surface, the shirt becomes an embodied rendition of the power of protective speech (“Speech Made Visible” 140).
Brett-Smith contributed a chapter on Bamana mud cloth to the catalogue for a
2007 Smithsonian Museum exhibition, Inscribing Meaning (Kreamer et al.), which examines African writing systems’ impact on both historic and contemporary African art.
Arabic calligraphy, notable among these writing systems, has influenced the art and architecture of West Africa since the ninth century, as Prussin has documented. Christine
Mullen Kreamer (19), Mary Nooter Roberts (91), and Raymond Silverman (119) reiterate
Canaan and Dols’ description of amulets as prayers that materialize the connection between oral and written communication. Roberts makes the important point that in West 38
Africa the idea of the magic square has become more significant than its form or its formulae (62). This means that the transformation of the magic square from mathematical concept to textile pattern is complete; therefore, it no longer matters if the numbers are correctly written in the cells. Geert Mommersteeg makes the same point, that while mathematically speaking the square is not magical if it does not have the magic constant
(each row, column and diagonal adds up to the same number, fifteen in the 3 x 3 square), in the context of talismanic use it can still be effective (506). In his examination of the
West African practice of using water that has washed talismanic writing off a Qur’anic writing board as a potion, Silverman indicates another transformation of the magic square that moves it from an inscription whose power originated in the spoken word to an embodiment of it in ink and finally to an internal medicine that acts upon the body from within (120).
The collection of chapters in Inscribing Meaning, along with Prussin’s Hatumere, has inspired and formed the basis of my research for the present study. As mentioned earlier, the word “magic” can be contentious, to the point that the Inscribing Meaning curators/writers refer to magic squares throughout their catalogue as “mystical” squares
(Kreamer et al.). I find it puzzling that the many insightful references to magic squares in the work rename them as “mystical” squares, rejecting their established English name.
The term “magic” connotes agency, while “mystical” is a more neutral term that does not.
As I have discussed, my view of magic squares’ ability to generate a constellation of patterns derives from its agency. Therefore, for me, “magic” is a good modifier for magic squares. However, I do not disagree with the application of the term “mystical” since it 39 may reflect the authors’ wish to reference the importance of the term “mystical” within
Islam.
Kane’s recent article offering his analysis of a Senegalese talismanic textile at the
Art Institute of Chicago makes several observations that are helpful to my study. His stated purpose, in agreement with Dilley, is to prove the continuing interaction of Islamic and pre-Islamic beliefs (Kane 157) as opposed to an earlier model of antecedents or of outright conflict (Trimingham 88). With Dilley (151) and Mommersteeg (502), he situates talisman making in West Africa historically before the advent of Islam. His related assertion that Islamic symbolism in talismans has long had an influence in non-
Islamic communities (143) helps explain the pervasiveness of this symbolism in the textiles I analyse for this study, some of which are not associated directly with Islam. In particular, he theorizes about the ubiquity of the checkerboard pattern in West African textiles, writing that on the one hand it is often used to embellish Arabic calligraphy, so can have a decorative purpose, but on the other, it is linked to “an established tradition in
West Africa, which equates the aesthetics of graphic design with magical efficacy” (155).
Kane follows Hames’ designation of a “talismanic” or “vernacular” approach to the
Qur’an, which sees it as different from the liturgical Qur’an because it is operationalized for talismanic purposes (145). His description of how it is made operational, by taking a
Qur’anic verse out of context and repeating it, is important to my examination of the
Burkina Faso shirt (Figures 5 and 6) in Chapter Three. Finally, Kane’s method of starting with a physical description of the textile, thereby establishing what it can tell us, then moving on to comparisons with other objects and to “a framework of reasonable guesses 40 based on studies of the symbolism and technology of talisman manufacture” (142), is one
I will adapt to my examination of the objects under inquiry in Chapter Three.
Having detailed the range of positions on the significance of magic squares, from
“mere” mathematical playthings all the way up to being “a significant part - if not the most significant one - of the patterns of several important (socially, culturally) designs”
(Ardouin), I will take up some of these positions in the following chapters in order to demonstrate and interpret the transformations of the magic square across several West
African textile examples, from explicit writing to repetitive patterning. 41
Chapter Three, Transformations of the Magic Square: The Shirt from Burkina Faso
Cloth has an ancient history in West Africa and some distinctive characteristics that link it to the region. It is traditionally made of a unique species of cotton native to
West Africa whose cultivation may have begun well before 1 BCE (Gilfoy 15). Hand- spun cotton yams are woven into strips on narrow looms that are operated predominantly by men; the strips are then sewn together to make a larger cloth
(Gumpert 13). Variations of this cloth cover peoples’ bodies from birth to death, as wrappers, blankets, turbans, or shaped garments like trousers. By its very physicality, cloth protects the body from cold, heat, sun, insects, and other vagaries of nature.
But cloth is protective - and powerful - in another way in West Africa. Patterns and motifs with talismanic meanings are painted, printed or embroidered on its surface or woven in its structure. As we have seen, foremost among these motifs is the magic square. In this chapter I will examine a selection of textiles and evaluate the
significance of their patterns from a West African visual and material perspective. I will begin with an examination of a shirt from Burkina Faso (Figures 5 and 6) and then will compare it to garments that have amulets sewn to their surfaces, as well as those that reference the magic square and the amulets through their patterns and motifs.
I begin with the shirt from Burkina Faso because it is central to my study in many ways: it is a garment as well as a written document that makes an explicit connection to the Qur’an, the ninety-nine names of God, and magic squares. All of the other textiles in the study are garments as well, with the exception of one blanket
(Figure 26). Therefore, they share the characteristic of intimacy with the body of the 42
wearer or user. They also share a relationship to the iconography of magic squares, whether explicitly by means of their inscriptions or implicitly by means of their patterns.
Like all textile objects that have been made by hand for personal and
community use, the Burkina Faso shirt contains a wealth of information about its
origins, its use and its environment - in other words, its life. Some of this information
can be gleaned from a close examination of the textile itself, but the rest must be
composed of Kane’s “reasonable guesses based on studies of... symbolism and
technology” (142). Examining the shirt as it is now at the TMC, it can give us much
information about itself: first, that it is constructed of coarse tan coloured cotton yams, which appear to have been hand-spun and then hand-woven in 10 cm wide strips. The
strips were cut and hand- and machine-sewn together in order to make a tunic-like
garment: two strips at the centre front and two strips at the centre back, then two strips
on each side going over the shoulders to join the front to the back. To give the garment
some shaping, more strips were added at the sides below the armholes, forming side panels. Four small amulet packets of yellow cotton are sewn to the shirt; based on the way it is folded now, it appears there are three on one side and one on the other. Figure
7 shows a drawing of the garment as if the side seams were undone and it was spread
flat on the table. This drawing reveals the strip-woven construction and shows the
strategic placement of the amulet packets to frame the head of the wearer.
So far, the shirt tells us that everything about it is made by hand, which makes it
an intensely personal, intensely particular textile object. The cotton itself may have 43 been grown locally, and its tan colour likely conies from a natural dyestuff such as chestnut hulls (Epelboin, Hames and Raggi 148). Epelboin, writing about talismanic shirts found in Senegal, notes that shirts made of hand-spun and hand-woven cotton are much rarer than those of industrially woven cotton, but that hand-woven cloth carries associations with ancient local traditions. Epelboin further notes:
On peut aller plus loin en remarquant T omnipresence du coton [grains, racines,
fil, tissu] dans les amulettes et objets magiques afficaines, affecte de vertus
therapeutiques ou preventives. Le fil de coton, fabrique traditionellement par les
femmes, est un ingredient omnipresent dans les amulettes, servant en minima de
bobinage du talisman. One can go even further, noticing the prevalence of
cotton [seeds, roots, thread, cloth] in African amulets and magic objects, which
are assigned preventative or therapeutic powers. Cotton thread, traditionally
spun by women, is always present in the amulets - at least in the binding of the
talisman. (Epelboin, Hames and Raggi 149)
The panels of the shirt were primed in rectangular blocks with some kind of liquid sizing, to help the surface accept the Arabic writing in ink that was then inscribed on the blocks. Was this done before or after the shirt was assembled? The evidence points in different directions: one section of writing that goes over one shoulder, starting on one side and continuing on the other, suggests that it may have been possible to apply some of the writing to the strips, like writing on a scroll, before the strips were assembled into the garment. However, the blocks on the side panels are somewhat tapered to accommodate the shaping of these panels, and some of the 44 individual written sections overlap the seams. These features tell us that the shirt was sewn together and then sized and inscribed. The overall effect is of a garment that is entirely private, made not for show, not for sale, and not for public consumption.
Textiles are structured by repeat patterns of interlacement such as weaving or knitting, and are often decorated with patterns, usually depicting graphic or geometric abstractions of the flora or fauna of their place of origin. The meaning of these patterns can be obscure or even entirely unknown to the contemporary viewer. However, this is not the case for this shirt, for the writing on its surface can be read like a document. In a recent study, Ruba Kana’an has examined the shirt and prepared a translation and interpretation of the inscriptions. According to Kana’an, all the writing is Qura’nic in nature (derived from the Qur’an or taken from different parts of it) with a limited number of direct quotations of Qur’anic verses (Kana’an). It is important to reiterate here that the text of the Qur’an itself is seen by Muslims to have talismanic significance. Twenty of the twenty eight primed blocks contain recitations of the ninety-nine names or attributes of God derived from the Qur’an. The remainder of the written sections contain prayers, sayings, and blessings, as well as three gridded squares. One side of the garment holds a 7 x 7 square and a 2 x 2 square; the former is filled with enigmatic symbols and the latter has circles containing symbols on each of the vertices and Arabic writing in the cells. The 2 x 2 square is repeated, with some changes, on the other side of the shirt. Figure 8 shows Kana’an’s translation of the side of the shirt with two squares. The arrows indicate the order of the inscription of the ninety-nine names of God; the strip that holds the squares can be read independently of 45 the other blocks. In this strip, the middle block contains the first nine lines of the
Qur’an, followed by “God will protect you from people” (Qur'an 5:67) repeated four times. Kana’an’s full translation is in Appendix 1.
The shirt can give us more information about itself, especially if we continue to compare it to similar garments and to the current scholarly research and studies of talismanic garments in West Africa. According to Kane’s research, the writer would certainly have been a Muslim cleric (143). It is unknown whether the writer also made the shirt, although this could have been the case; in West Africa, Muslim clerics are known to supplement their incomes with textile work.
What can we learn about the shirt’s original function? Its small size tells us it was made to be worn by a small person, probably a boy. The TMC record, written when the shirt was acquired, tells us that the donor acquired it in Burkina Faso in the 1970s from a local vendor. She wrote that it was possibly used in puberty rites for a Muslim boy (Textile Museum of Canada “T91.0091”). This conjecture led to the shirt being called an “initiation shirt” in the TMC’s public database, but this may not have been its function. The repetition of the line “God will protect you from people” in one block suggests a protective role for the shirt, possibly in war or conflict. Epelboin writes that this line is found on each of the five talismanic shirts in his study, although they differ greatly otherwise in design and inscriptions (170). Furthermore, the verse from the
Qur’an written directly under the 2 x 2 square (see Figure 8) specifically refers to protection from a fire for war (Kana’an). 46
It is also not certain that the shirt was made to be used by Muslims. Talismanic objects are found in many societies in West Africa that are not predominantly Muslim; the Yoruba in Nigeria and the Asante in Ghana are two examples. Kane writes about a
Senegalese talismanic textile:
Potential users of the original may or may not have been Muslim since many
West Africans irrespective of their faith and religion have used talismans over
the centuries ... The production and consumption of talismans is a field in
which a kind of ecumenicalism is most evident. (143)
Islam was brought to West Africa as early as the eighth century by Muslim traders engaged in the cross-Saharan trade of such vital commodities as gold and salt; it has been a major factor ever since, not only in the religious life of the region but in its ongoing development of political and socio-cultural forms. An in-depth reading of this history is beyond the scope of this study, but it is pertinent to reiterate here the view I presented in Chapter One, in agreement with Bravmann (490), that over the centuries
Islamic and indigenous African religious and healing practices have deeply influenced each other. Hassan writes that any attempt to divide West African practices between
Islamic and pre-Islamic beliefs “tends to reduce a very creative and complex process of cultural interaction between an intrusive religion and an indigenous culture to a simple polarity between a ‘true’ Islam and its ‘popular’ deviation” (230).
We now turn to the grid layout of the shirt’s inscriptions. Why are the written segments divided into a number of rectangular blocks, each having been prepared separately with sizing? A possible answer is suggested by another shirt that is in the 47 collection of the Metropolitan Museum of Art in New York (Figure 9). It is from India and has been dated to the fifteenth or early sixteenth century. Like the Burkina Faso shirt, it is made of cotton, with writing and graphic elements inked onto its surface, but its cotton foundation is much more finely spun and woven, and the writing is infinitesimally tiny. In fact, according to the Metropolitan Museum’s object record a full copy of the Qur’an is written on it, bordered by the ninety-nine names of God in large red script (Metropolitan Museum of Art). The writing, mostly black except for chapter headings in red, is divided into blocks by a square grid, although the blocks do not correspond exactly to the chapter divisions of the Qur’an within them. That is, the writing conforms to the grid, not the grid to the writing. An Indian talismanic shirt in the online collection database of the National Museum of Scotland dated to the fifteenth century is similarly divided (National Museum of Scotland), as is a fourteenth century
Turkish shirt in the online collection database of the Museum of Turkish and Islamic
Arts, Istanbul (Museum With No Frontiers). While it is impossible to answer my question by drawing a direct parallel between the Burkina Faso shirt and the other talismanic shirts, especially because of their different places of origin, it is noteworthy that all of them, although separated by large spans of time and space, and notwithstanding their other differences, have their surfaces divided into grids to receive the writing. In the Burkina Faso shirt as well, the writing conforms to the grid, as if the grid were created first and the script written into it. The picture plane of the shirt has been, to use Prussin’s term, “geometrized” (95), treated not as a whole, but as a coordinated series of cells. Do these cells possibly reference the separate pieces of 48 parchment or paper that are the most common substrate for the inscriptions? I suggest that they do, and that this is one of the multiple layers of meaning in the grid layout, which also references the matrix arrangement of the magic square. I will continue my discussion of multiple layers of meaning in Chapter Four.
Let us now look more closely at the four amulets of yellow cotton sewn to the
Burkina Faso shirt. In the TMC record there is a handwritten note that says, “Each pouch contains fold (sic) pieces of paper inscribed with text from Koran, astrological or mystical source. One pouch contains needle and paper” (Textile Museum of Canada
“T91.0091”). It is current museum policy never to alter the condition of an object so opening the amulets is impossible, but we can conjecture from this note that at least one of them was once opened. The typical contents of an Islamic amulet are described by
Raymond Silverman in the following passage:
The message found inside most amulets comprise two parts, referred to in
Arabic as da ’wa and jadwal. The message is written on a piece of paper or other
surfaces. The da ’wa, usually beginning with the bismallah (a phrase that
precludes all important acts, “In the name of God, the Compassionate, the
Merciful”), is followed by a portion of the Qur’an. This is sometimes followed
by any of the ninety-nine names for God, the names of the angels, single letters
or combinations of letters that have numeric value. The jadwal may be in the
form of a magic square or some other geometric design. The inscribed piece of
paper is most often carefully folded, wrapped with string or thread and then
sewn into a leather (or sometimes metal) envelope. (121) 49
The sewing of the amulet packets to the shirt is a unique feature of Muslim
African talismanic shirts that distinguishes them from Ottoman and Moghul shirts - the latter feature only inscriptions and graphics written directly on their surfaces (Epelboin,
Hames and Raggi 161).
Next I want to look more narrowly at the three pictorial blocks containing matrices with symbols and letters. There is a 2 x 2 matrix on each side plus a 7 x 7 matrix on one side. Figure 10 shows the squares on the front. Considering first the 7 x 7 square, we can see that each cell has one or more symbols written in it. These enigmatic symbols resemble a group of seven signs variously known as the Signs of Solomon or
Solomon’s Seal. They were described by the medieval writer Ahmad al-Buni (d. 1225) as a way of representing the Ineffable Name of God. Al-Buni’s major work, the Shams al-Ma ’arif, has not yet been translated into English, but interpretations by Savage-
Smith and Porter emphasize the significance of the signs for talismanic practices
(Porter 189; Savage-Smith and Maddison 60).
Since the focus of this study is magic squares as pattern generators on Muslim
West African textiles, the 2 x 2 squares that are written on the Burkina Faso shirt are of particular interest. Figure 11 shows Kana’an’s translation of the square on the side that is identified in the TMC record as the back. The triangles contain the names of the prophets. If the circles over the intersections are perceived as forming a 3 x 3 matrix, these two drawings can be considered a reference to a 3 x 3 magic square. The symbols in the circles remain unintelligible at this time, except for the word representing the name of Allah written in the central circle. According to Kana’an’s interpretation, the 50 main lines of the square are constructed of the lines of the Qur’anic verse, Sura al-
Ikhlas (Qur'an 112). Kana’an believes the front and back are misidentified in the TMC record: the side bearing two squares as opposed to one plus the name of Allah has to be the front of the shirt.
My examination of the Burkina Faso shirt thus leads me to conclude that the shirt itself is a talisman, made to enfold its wearer in protection by means of the cotton material, the hand-made construction and the talismanic writing it holds. Multiple levels of reading and understanding operate on the Burkina Faso shirt: first, the writing can be read by viewers who understand Arabic. Second, it can also be “read” as a talisman by someone who understands the significance of the ninety-nine names and the squares that encode this information. Finally, the Arabic writing itself can be
enough to signal the presence of talismanic meaning and thus it is not necessary to read
it for comprehension, as for example when Arabic inscriptions are placed on buildings
in places where they cannot be read from the ground (Grabar 19).
Now I will compare the shirt’s iconography to that of other garments to note how they also reference the magic square. A Nigerian tunic in the collection of the
British Museum (Figure 12) is similar to the Burkina Faso shirt in that Arabic script is written on it and amulet packets are sewn to it. The surface of the shirt is covered with writing and signs, with a large geometric symbol on the centre back containing four magic squares. On this tunic the leather packets are sewn on the inside. David
Heathcote lists the three necessary steps for the creation of this kind of garment. These methods are, first, the attachment of charm material to a garment; second, the soaking 51 of an article of clothing in water that has been used to wash prescribed Qur’anic phrases from a writing board; and third, the inscription of characters on to the surface of the garment so that they are clearly visible (621).
The tunic in Figure 12 appeared in the 2008 exhibition and catalogue at the
Metropolitan Museum of Art, The Essential Art o f African Textiles: Design without End
(LaGamma and Giuntini 56). The same tunic is used by Prussin to illustrate her thesis of “design transformation” (90) that I introduced in Chapter Two. Prussin conjectures that there is a process of transformation by which script becomes pattern. In this process, Islamic forms of writing combine with indigenous West African materials and techniques to produce a pattern system that is widely recognized, fabricated and used by many communities in West Africa. Since Islam began to penetrate West Africa as a major religious and cultural force in the eighth century, this process can be understood to have been at work from the earliest days of that contact.
The location of the leather-wrapped amulets inside the Nigerian tunic is indicative of their secret aspect. The talismanic meaning that was represented on the outside of the Burkina Faso shirt by the writing and the squares, and that was also hidden inside its four amulet packets, is here further hidden by placing the amulets on the interior of the tunic. Both garments feature talismans that are observable (by being written on the surface) and talismans that are hidden (by being concealed within packets). It is noteworthy that there are multiple layers of talismans, and of the concealment of talismans, in shirts such as these, which are themselves worn under other clothing. The fact that the writing is in Arabic offers an additional layer of 52
concealment. Colleen Kriger suggests a rationale for this secrecy; she notes in reference to an embroidered Hausa robe, “If the imagery functions as a protective device, the
embroidery need not be read, but needs only to exist and to be worn. The imagery is not primarily for visible display, but directs itself toward superhuman powers” (194). The
layers of concealment present in the tunic are paradoxical since some talismans are written on the outside of the tunic while others are hidden on the inside.
Two other garments, identified with hunting (Figures 13 and 14), have amulets
sewn to their surfaces. The dangers of hunting in the West African bush are prime motivations for the use of amulets on hunters’ ritual garments such as these
(McNaughton 57). The hunter’s shirt (Figure 13) holds no writing, but six leather-
covered amulets are sewn to the back, and eight to the front. These bear a resemblance
to leather Qur’an covers; according to Hassan, in Nigeria the same leatherworkers make both (8). In contrast to the simplicity of the hunter’s shirt, the hunter’s coat (Figure 14)
is densely covered with different kinds of amulets. The TMC record for the coat,
written in 1981 when it was purchased, adds to the layers of meaning that can be read
from its striking appearance. One of the record writers describes it as “the single most
frightening piece of cloth we’ve got in the place” (Textile Museum of Canada
“T81.0112”). A leather case was opened at the time of writing and was found to contain
“pieces of Qur’an, blood, needle,” adding to the horrific effect (a later amendment
noted that the blood was “probably rust”).
In this record entry we read an interpretation of the coat as the embodiment of
Western notions of magic - exotic and “dark” - and of Africa as a place of that kind of 53 magic. I hope to counter this view, offering instead an interpretation of the coat that places it within a taxonomy of talismanic garments composed of Islamic elements (the leather amulets containing Qur’anic writing) and West African ones (the handmade cotton foundation and the amulets made of animal horns). Dilley writes that, paradoxically, “the sources of power and potency to effect transformations are found in or associated with the wild, the bush” (79). In other words, the dynamic interplay of
Islamic and West African practices is embodied in garments like the hunter’s coat, where Islamic talismans join others - such as cowrie shells, horns, and hooves - to overlay a garment in which both systems of belief unite to harness the power of the wild while protecting the wearer from it.
The pieces of twisted cotton string attached to the coat are amulets as well. In
West Africa, knots are used as amulets: the maker chants an incantation as he ties the knot and it is thus considered to hold the power of the incantation (Imperato 89).This is the most likely significance of the strings covering the hunter’s coat in Figure 14.12
Brett-Smith draws an analogy between the tied amulets and Islamic script in the following passage:
Each knot in every tafo (twist of cotton) represents the concentrated power of a
klissi (incantation) which has entered the cotton through the spit and saliva with
which the maker saturates every twist as he ties it, simultaneously muttering the
proper incantation . .. Here, under the influence of Islam, the knotted cotton
threads of the animist’s shirt have been transformed into elegant, linear letters. It
12 Ibn Khaldun cites the Qur’an 113.4, “and I take refuge in God from the evil of those who blow into knots” as a way o f cautioning against sorcery. (168) 54
is this type of Arabic derived inscription that which provides the realization that
klissiw, their power, and indeed even generalized knowledge about society can
be embodied in two-dimensional geometric form. (“Speech Made Visible” 140)
The mirrors on this coat are enigmatic to the present writer; there is no doubt that they add to the talismanic power of this garment in some way. They are round in shape on the front of the garment and square on the back. Further research is needed to find their definitive meaning; a direction is suggested by Savage-Smith, who notes, “it is possible that the dark polished surfaces of the thirteenth century mirrors, as well as the Safavid or Mughal examples, were used on occasion for some form of magic or divination employing reflective surfaces” (125).
My study of the magic square’s transformation from a signifier for Islamic meaning to a pattern on cloth now turns to two garments that contain no writing and no amulet packets, but nevertheless allude to sacred writing by means of embroidered shapes. Once again I begin with an example from Prussin, who refers to a tunic from the republic of Benin to illustrate the transformation of explicit scripts, matrices and signs into embroidered designs (91). For Prussin the designs communicate the magic power of the amulet by their shapes alone, without text. Here, the shape is enough of a signifier to carry the meaning.
A similar tunic in the TMC’s collection (Figure 15) is covered with embroidered motifs that refer in the same way to the shapes of the leather packets on the hunter’s shirt. The resonances here are many: in one motif, the checkerboard designs evoke a magic square, as if a talismanic packet was opened up and we were able to see within. 55
In another, appliqued triangles, themselves symbolic of protective amulets in West
Africa, combine with rectangular shapes to suggest amulet packets like the ones on the hunter’s shirt and the hunter’s coat. The power of the talisman to protect the wearer is here, inherent in the shapes of the motifs and their patterned arrangement.
The second garment in this group, pictured in Figure 16, is embroidered with circular motifs that are connected by an underlying grid. This robe, woven of cotton and embroidered with indigenous silk, is designed in the traditional style of big robes worn by elite Hausa men in Northern Nigeria. The circles recall those of the magic square on the Burkina Faso shirt, but even more directly they resemble the grids on the talismanic shirts from India (Figure 9) and Turkey, where every vertex is marked by a small circle.
Heathcote writes in reference to a virtually identical robe:
Its overall decorative scheme bears a striking resemblance to that on a Muslim,
15th c talismanic undershirt from India on which prayers and chapters from the
Qur’an, and the Muslim profession of faith, are inscribed. The calligraphy has
been carried out within a design of squares and circles resembling the layout on
certain West African charm papers as well as that on the shabka ...
Furthermore, although the shabka in the exhibition is devoid of writing, it
nevertheless bears, within many of its circular, embroidered motifs, linear
configurations for which one can find matching parallels in Hausa versions of
the Qur’an. This, together with other aspects of embroidery in Nigeria, indicates
that there is scope for further investigation. (40) 56
A page from a Hausa Qur’an is pictured in Figure 17, showing the circular motifs mentioned by Heathcote. In her discussion of a similar robe, Prussin reiterates the closeness of embroidery patterns in West Africa to the geometric designs found in liturgical texts like this one (146).
What have we learned from this examination of the Burkina Faso shirt and its comparison to other garments? I have argued in this chapter that the shirt itself is a talisman, and, I would add, one with a complex nature: its differences from other
Islamic talismanic shirts include the coarse, hand-spun cotton, the strip-woven construction, the cut - West African talismanic shirts, unlike other examples, all lack sleeves (Epelboin, Hames and Raggi 161) - and the presence of amulet packets sewn to the front and back. Its similarities to other talismanic shirts include the inscriptions taken from the Qur’an and the magic squares. The complexity increases when we evaluate the presence of the magic squares on this shirt. Of all the garments examined for this study, the shirt from Burkina Faso carries the most explicit reference to the magic square, a visual reference to the perfect numeric order of the universe, which, in
Islamic belief, is the perfection of God. The square’s instantiation on the shirt is paradoxical because it is both a physical manifestation and a metaphysical sign - it seems to point in two directions at once. One direction refers inward, to its inception as the numeric concept that is the source of the magic square; these are its hidden meanings, corresponding to the Islamic philosophical notion of batin, or hidden, knowledge. The other direction points outward, towards its embodiment in patterns like the ubiquitous checkerboard, in a correspondence to zahir, or public, knowledge 57
(Poonawala). But the directions seem to cross and contradict each other: the talisman in its most explicit form - Arabic letters and graphic signs - is at its most conceptual, while in its most encoded form - where nothing but the grid is the referent - it is at its most embodied in woven, worn cloth. It is this paradoxical transformation that I pursue further in Chapter Four, by examining the magic square’s operation as a visual metaphor and, consequently, a pattern engine, in the Muslim West African environment. 58
Figure 5: Shirt (side with two squares), Village of Kiembara, Burkina Faso, Mossi, c.
1990, cotton, hand-spun, woven, sewn, and inscribed with Arabic writing and graphic
symbols, gift of Victoria Henry, T91.0091 TMC. 59
Figure 6: Shirt (side with one square), Village of Kiembara, Burkina Faso, Mossi, c.
1990, cotton, hand-spun, woven, sewn, and inscribed with Arabic writing and graphic
symbols, gift of Victoria Henry, T91.0091 TMC. 60
Figure 7: Pattern drawing of the shirt showing the continuous strips over the shoulders. 61
i ti>i
Figure 8: The Arabic text on the shirt translated into English, with arrows indicating the order of the text. The panel with the squares can be read independently. Translated from
Arabic by Ruba Kana’an. Figure 9: Talismanic shirt, fifteenth or early sixteenth century, India (north India or the
Deccan), ink, gold, and colors on stiffened cotton, purchase, Friends of Islamic Art Gifts,
1998.199 Metropolitan Museum of Art. Figure 10: (left) The 2 x 2 square on one side of the Burkina Faso shirt;
(right) the 7 x 7 square on the same side.
Adam
M 8U O f
Moses
Figure 11: The translation of the 2 x 2 square in Figure 10. Figure 12: Tunic front (above) and back (below), Nigeria, Hausa, late nineteenth century,
cotton, leather, paper, pigment, acquired from Captain Alfred Walter Francis Fuller,
Afl940,23.1 The British Museum. 65
Figure 13: Hunter’s shirt, Mali, c.1900, cotton, strip-woven and sewn, with attached
leather-covered amulets, gift of Dr. Peter Herschman, T86.0071 TMC. Figure 14: Hunter’s coat, Mali, 1960-70, cotton, woven and embellished with amulets
and mirrors, museum purchase, T81.0112 TMC. 67
Figure 15: Tunic, Liberia, twentieth century, cotton, strip-woven, sewn, appliqued and
embroidered, from the Opekar/Webster Collection, T94.3006 TMC. Figure 16: Robe (shabka), Nigeria, Hausa, 1920-1929, cotton, silk, strip-woven, sewn,
embroidered, needle lace, From the Opekar/Webster Collection, T94.3007 TMC.
Figure 17: Page from a Hausa Qur’an, Nigeria, nineteenth century.Web.
Leamingarabicweekly.com. Accessed 10 Nov 2010. 69
Chapter Four, the Magic Square as a Pattern Engine
In Chapter Three I examined a collection of West African garments, using the inductive approach typical of material culture studies. From the examination, and aided by studies of the technology and symbolism of talisman manufacture in Africa, I began to form conjectures about the stages of the magic square’s transformations. The garments hold the visible evidence of the magic square’s path of transformation into patterns, but they also have symbolic meaning in and of themselves, as cultural instantiations of ideas and beliefs in West Africa. The ideas and beliefs are represented in these garments in more or less encoded form as actual writing, as amulets that contain writing, or as shapes that reference the object that contains the writing, for example an amulet (Figure 15) or a Hausa manuscript (Figure 17). The textiles that I will examine in this chapter refer to the magic square in progressively more coded ways, moving the reference further from its source in a grid of numbers, letters and signs. It is important to note here that all these stages of the transformations can exist simultaneously; for example, the shirt (Figures 5 and 6) and the checkerboard wrapper
(Figure 28) come from the same place - Burkina Faso, and the same time period - the mid-twentieth century.
Before looking at more textile examples, I go back to the conceptual notion of
“magic square” in order to trace the transformations of the magic square from a purely mental calculation without form or shape to a “figural concept,” then to a visual metaphor, and finally to a pattern engine in the West African visual environment. I argue that the grid configuration of the magic square shares some striking qualities with 70 the structure of woven cloth, and that this is a significant factor in the magic square’s multiple layers of meaning. I will develop my argument by examining a group of textiles that show the magic square’s agency as a pattern engine for West African textile patterns. This agency is deeply rooted in the religious, artistic, and sociocultural histories of the region; therefore, my investigation calls for an interdisciplinary approach that is grounded in a view of pattern as part of the ontology of human cognition.
The concept of metaphor is fundamental to my plan to trace the magic square’s transformation into embodied forms. George Lakoff and Mark Johnson posit this definition: “The essence of metaphor is understanding and experiencing one kind of thing in terms of another” (5). To use Lakoff and Johnson’s terminology, “Reality is a
Numeric Proportion” or, “The World is Made of Numbers.”131 advance the view that the power of the metaphor of numeric right proportion has contributed to making the magic square a key component in the practices of healing that have pervaded West
African societies for centuries, and that, according to Ousmane Kane, continue to proliferate there and elsewhere (158).
As mentioned earlier, before it can become a metaphor the magic square first exists purely as a mental calculation: a set of additive relationships between numbers.
When it is then mentally pictured as a grid with numbers in the cells, it becomes a combination of a mathematical concept and an image. Ephraim Fishbein calls mental
13 The concept of the phenomenal world being based on numeric proportions comes from Pythagoras and other ancient Greek philosophers but these two phrases are meant to express it in the style Lakoff and Johnson use inMetaphors We Live By, where every word is capitalized. 71 figures in geometry “figural concepts, images intrinsically controlled by concepts”
(160). A figural concept is a mental visualization of a calculation - for example the additive operation in a magic square - that gives it spatial properties like directionality, position and shape. Specifically, a calculation is pictured in the mind as having a geometric shape. The magic square can be viewed this way, as a figural concept that possesses the qualities of both concept (ideality and abstractness) and image (shape and position). By the mental formulation that gives it a grid format, the purely numeric concept of the magic square thus becomes a figural concept with the shape of a square, directions like up, down, and across, an inside, and an outside. We are still talking about a mental form, manipulated by the reasoning process, but this stage is an intermediate one that can lead to the magic square’s manifestation as a visual metaphor.
It is the first transformation of the magic square, which enables it, I would argue, to ultimately transform into the checkerboards and knots of textile patterns. This figural concept stage is a vitally important one, not only for mathematicians, but also for textile makers and other artisans, who often expertly formulate and retain the patterns they produce solely as models in their minds (Adams 36).
Once the grid of numbers is represented on a surface, whether it is written with pencil on paper, or applied with ink on cloth, it can be viewed as a visual metaphor; this is the second transformation of the magic square, and the one that appears on the shirt from Burkina Faso (Figures 5 and 6). At this stage I suggest that the magic square is also a mathematical metaphor: its meaning resides in and is tied to its numerical relationships. As I have discussed, the magic square was viewed by ancient Chinese 72 and medieval Islamic philosophers as a model of the harmonic order of the universe.
The idea that “The World is Made of Numbers” can be traced back at least to Hellenic number mysticism, especially to Pythagoras (fourth century BCE) who believed that the essence of all being was number (Endress 124). In medieval Asia the magic square was thus considered to have considerable power, and knowledge about its construction and operation were kept secret (Cammann 185). The medieval scientist Jabir ibn Hayyan wrote about its number relationships as expressive of the Supreme Principle that underlies the working of the universe and therefore fundamental to the science of alchemy (Haq and ibn Hayyan 67). The Ikhwan al-Safa (Brethren of Purity), who lived in Basra in the late tenth century, wrote treatises that hypothesized the meaning of magic squares, as Bier writes, from the perspectives of “algebra and geometry, ethics,
Aristotelian logic, physical and corporeal questions, the intellect, and ways of knowing
God . . . Disciplinary boundaries as we know them today were fluid or non-existent”
(269). Likewise, Marks notes in her discussion of the congruity between medieval
Islamic and new media art forms, especially computer-generated art, that “for the neo-
Pythagorean Brethren, music and magic squares focused cosmic forces into crystalline forms with cosmic powers ... Software that works through condensed images, such as contemporary musical and image programs like MAX-MSP, has a direct lineage in the
Brethrens’ magic squares, equations of a symbolic source code to the operations of the universe” (164). This statement, which is fundamental to Marks’ thesis of concordance between medieval Islamic art and new media art, brings musical and visual forms together through the mathematical metaphor that unites them: “The World is Made of 73
Numbers.” At the stages of figural concept and visual metaphor the magic square is not a pattern - the numbers do not repeat - but it holds pattern potentialities, as can be seen in Figure 2. Likewise, the magic square is not a symbol, but an array of symbols whose significance is in their numerical relationships.
The magic square is not the only model of universal numeric proportion; others have been formulated as well. I would like to touch upon two of them for comparison, one from the European Renaissance and another from Western thought in the twentieth century. Both model the metaphor that “The World is Made of Numbers,” and both bear similarities to and differences from the magic square.
Pythagorean and Platonic belief in numbers as the essence of being, besides being influential for mathematics and philosophy, was also reflected in ideas about music, and led to theories of consonance that work on the assumption that there is a harmonic order and that it can be expressed by a visual diagram. In 1558, Gioseffo
Zarlino, a Renaissance scholar and musician, expounded his theory of the senario, shown in Figure 18 (Da Col 42). The senario has a particular resonance with the magic square, since they were both responses to Platonic and Pythagorean modes of thought.
Medieval Islam and the European Renaissance share common roots in late antiquity
(Blair and Bloom 171). The senario maps consonances - the intervals between notes that, when sounded together, produce a pleasing sound - as proportions depicted by overlapping circles. 74
Figure 18: The scenario of Gioseffo Zarlino (25).
The metaphysical problem that confronted theorists of the Renaissance arose from the question of why the consonances were heard as harmonic, therefore pleasing and even beautiful, and the dissonances were not. Zarlino based his theory of the consonances on the number six, the numero senario. In the introduction to the translation of Part Three of Zerlino’s Le Istitutioni Harmoniche, Guy Marco and Claude
Palisco explain the significance of the number six in terms of Zarlino’s belief that music, as the harmonizing agent of the universe, maintained the harmony of the soul and the body (Zarlino xv). The senario, a diagram in keeping with Platonically inspired number mysticism, was a model of the harmonics of both the world outside and the world within. Thus, in the scientific climate of the Renaissance, the scenario was a diagram of the elemental harmonic order of the world based on numbers that not only pictured reality but actually constituted it in its interaction with the human soul. As 75 science historian H. Floris Cohen puts it, “Harmony is not something given from outside; rather harmony is an activity of the soul” (357). One generation later, Johannes
Kepler posited a geometric model of the consonances based on the divisions of a circle, and, like Zarlino, explained their beauty in terms of the mathematical proportions that guided God in creating the Universe and that are reflected in the soul (Cohen 356).
The next model I wish to discuss arose in the late nineteenth century, in a radically different intellectual climate than that of either medieval Islam or the
European Renaissance. In the mathematics of group theory, a 2 x 2 square is known as the Klein Group, after Felix Klein, who instituted the system of transformational geometry in 1872 (Millman 338).The Klein Group can be depicted in several ways;
Figure 19 shows it represented by white versus black.
Figure 19: The Klein Group represented by white and black values.
As its name implies, the Klein Group is one of the simplest expressions in
Group Theory, an important theory of symmetry operations in geometry (Du Sautoy
230). M. A. Armstrong likens it to the group of plane symmetries in a checkerboard,
identifying its isometries as translation (no change), reflection (across the diagonal), 76 and rotation (around the centre) (53). In the additive table in Figure 20, black is represented by even numeric values (E) and white is represented by odd numeric values
(O). The values within the cells are considered as additive expressions of the top row and the left column, both outside the cells. In other words, even + even = even; even + odd = odd; odd + even = odd; and odd + odd = even. This exact configuration is also seen in Figure 23 as a draft for weaving cloth on a two shaft loom.
O
0
Figure 20: The Klein Group represented by even and odd values.
Art historian James Elkins offers a further interpretation of the Klein Group as
“a square that posits the sum total of logical possibilities in any closed conceptual system, whether it is religious beliefs or linguistic categories” (Elkins 103). Figure 21 shows a diagram of his interpretation. Elkins uses the Klein Group as a diagram of the figure/ground relationship in pictures. He has adapted this approach from Rosalind
Krauss, who theorizes the Klein Group 2 x 2 square as a metaphor for Modernism, a twentieth century aesthetic system she presents as closed, repressive and finite (Krauss
353). According to Krauss, the advantage of picturing the square as a metaphor for 77
Modernism is that, as a topology rather than a chronology, it clearly reveals a cognitive system that is closed, and how it is closed.
figureground
not ground not figure
Figure 21: The Klein Group interpreted by Elkins and Krauss.
I suggest there are similarities between the Klein Group as a metaphor for the cognitive process (as it was used in Structuralism and adapted by Krauss and Elkins) and the magic square as a model of the universe. They both operate as knowledge systems based on number relationships that influence the beliefs in their societies about how reality is constructed. Both the magic square and the Klein Group offer models that purport to represent the fundamental nature of “reality.” In the versions shown here, the Klein Group, like the checkerboard, graphically depicts oppositions of either
/or, off/on, or black/white. It represents a worldview that states, according to Michael
Lane, “All patterns of human social behaviour are codes, with the characteristics of languages. Relations can be reduced to binary oppositions” (Lane 18). In contrast, magic squares are not based on binary oppositions; in fact, a 2 x 2 magic square is 78 arithmetically impossible.14 Beyond this, there is a key aspect of the magic square that differs from both the scenario’s balance and harmony and the Klein Group’s rigid dichotomy, and that is the rotational action of the continuous method used to construct the magic square mentioned in Chapter Two. Figure 3 shows how the consecutive numbers loop from bottom to top and from right to left as they fill the 3 x 3 grid. The drawing on the left in Figure 22 traces the path of a line drawn from one consecutive number to the next and the one in the centre depicts the knot motif formed by a ribbon tracing the same path and following an over-one, under-one rule. An embroidered knot motif on a Hausa robe is shown on the right for comparison. Figure 3 and the illustrations in Figure 22 all possess rotational symmetry around a centre; those in
Figure 22, centre and right, add interlacement to the rotational action. The continuous method used to construct the magic square thus mirrors the spiral action of spinning and interlacing to produce that most embodied of mathematical forms: cloth.
Figure 22: A 3 x 3 magic square, (left) consecutive numbers joined by lines; (centre) an
interlaced ribbon linking consecutive numbers; (right) an embroidered knot on a Hausa
robe, Nigeria, twentieth century, T94.32005 TMC.
14 For a mathematical proof that a 2 x 2 magic square is impossible, see Swetz (120). 79
I propose that this similarity between the rotational action of the magic square and the spiral actions of spinning yam and interlacing that yam to make cloth are deeply significant for the transformation of the magic square into patterns, especially those that are interlaced (I include embroidery in this category), rather than simply drawn or printed, on cloth in West Africa.
There is an important metaphoric significance to weaving in many cultures.
Some of the most cogent research and writing on symbolic meanings in textile patterns has been done by Mary Frame on ancient Andean cloth. She cites the checkerboard pattern in that context as a metaphor for the balanced plain weave that is the fundamental structure of woven cloth (123). Taking up Frame’s notions of metaphor in cloth form, I contend, with Prussin, Gilfoy, and LaGamma, that the magic square is referenced in West African weaving by the checkerboard pattern. To develop my contention I will analyse two weaving drafts to show their visual and structural concordances with the magic square. Textile weavers use variations of these as written guides, or, alternately, as figural concepts that allow them to visualize the cloth’s structure as they weave it.
The diagram in Figure 23 provides the instructions for weaving cloth on a two shaft loom, the simplest loom for weaving cloth. The threading of the warp threads on shafts one and two is across the top, the scheme for tying the shafts to the foot pedals is in the grey block at the upper right edge, and the order in which the pedals are pushed is in the column on the right. The central grid represents the cloth. A two shaft loom 80 operates on opposites, like a checkerboard. Thus, the checkerboard pattern is a visual metaphor for the basic tabby construction of woven cloth.
Figure 23: A weaving draft for a two shaft loom
There is a further connection to magic squares in weaving drafts, one that shows how weavers visualize the figural concept of a base numbering system in order to plan and execute their weaving. The continuous method of constructing the magic square
that was shown in Figure 3 mirrors the numeric operation of a weaving draft for a loom with three shafts or more. The diagram in Figure 24 provides the instructions for weaving cloth on a three shaft loom: the threading of the warp threads on shafts one to
three is across the top, the scheme for tying the shafts to the foot pedals is in the grey block at the upper right edge, and the order in which the pedals are pushed is in the
column on the right. The central grid with no numbers represents the cloth. Note the
continuous method of numbering the cells: where there is no fourth position, three is 81 followed by one. This is a base-three numbering system, where mathematical calculations are limited to three numbers.
Figure 24: A weaving draft for a three shaft loom.
As in the Klein Group diagram as odd and even values in Figure 20, a value in the rows running along the top (the threading) combines with a value in the columns running along the left side (the pedaling) to produce a value in the central grid, which represents the cloth. Basically, the command is to a weft thread to go under or over a warp thread. The continuous method of positioning the numbers in the threading and the pedaling of a weaving draft for three or more shafts is exactly like the continuous method of constructing a 3 x 3 magic square. In the magic square, there are nine numbers available for nine positions in the square. In the weaving draft, there are three numbers available for the nine positions. In both cases, when the order of construction 82 puts the next number outside the grid, it must find its position by looping around, as if the two-dimensional grid were a three-dimensional torus.
I do not suggest that West African makers consciously manipulate the magic square’s symbolism into patterns like checkerboards and knots; rather I believe that its intrinsic similarity to the way cloth is constructed is a feature that facilitates the adaptation of the symbolism to cloth technologies. The question of intentionality - how much of the symbolic meaning is in a maker’s consciousness when she or he instantiates a pattern in a textile - leads us to consider the larger question of the patterns of cognition that are related to making.
I posit that intentionality is key to the transformation of the magic square into a pattern engine. The pattern engine, after all, does not exist “out there.” It exists in minds as a shared form, held in common by the minds in a society, trans-generationally.
As Frame suggests, pattern is a mode of cognition in the mind of the maker (113).
These “patterns of cognition” are not arbitrary, but culturally specific. Furthermore, makers are not automatons. Something of the template, or pattern as blueprint, has to operate somewhere in the maker’s cognition. It is a shared template. Visual metaphors like the checkerboard and the interlace act as cognitive clues that people - textile makers, amulet makers, and textile and amulet wearers, use to make cloth, but also to make sense of their cultural context. On the other hand, different levels of understanding exist: the conceptualization of a matrix form’s meaning is vastly different for a Jabir Ibn Hayyan than for a cleric who writes a jadwal on a piece of paper while making an amulet, or for an artisan who embroiders a knot or checkerboard 83 motif on a robe. On the Jabirean level the code is understood completely - Hayyan even writes the code - while on the cleric level it is used with some understanding, and on the artisan level the understanding is diluted in various degrees. As mentioned in
Chapter Three, in some instances the cleric and the artisan are the same person: Hassan points out that in Nigeria malams (Hausa Muslim clerics) who make amulets are also skilled in embroidery and cap making, and often use these skills to augment their incomes (101).
The garments that I examined in Chapter Three contain direct written or iconographic references to magic squares’ talismanic function. I will now examine textiles with two kinds of patterns, matrices and interlaces, which act as referents in more coded, less obvious ways. Matrix patterns are rectangular arrays of symbols.
Checkerboards are types of matrix patterns whose cells may contain symbols but commonly are differentiated by colour alone. Interlace patterns are typically composed of narrow bands or cords that appear to cross each other, turning in different directions.
Both pattern types are present in the design of the Burkina Faso shirt: the writing is applied in the form of a matrix, and it follows an interlaced path in both the order of the blocks, indicated in Figure 8 by the arrow, and even in the names themselves, which cross back and forth in a series of alternations, for example in block four, “The
Withholder. The Expander. The Abaser. The Exalter. The Bestower of Honour. The
Humiliator.”15
15 See Appendix A for the complete translation of the writing on the shirt. 84
In the next three textiles, we are looking at the matrix arrangements of the designs to find the reference to the magic square. The “geometrization of space” expounded by Prussin in her hypothesis of the magic square as a design gestalt in West
Africa (96) is depicted in the first textile in this group, a Djerma wrapper from Niger
(Figure 25). Lisa Aronson notes the significance of the patterning on this wrapper, asserting its reference to magic squares in talismans through both its pattern of alternating blocks and its concentration of design in the centre, which she likens to the importance of the central number in a 3 x 3 magic square (1).
A woollen blanket, called a kaasa, the second textile in the group (Figure 26), is wrapped around the body as protection against the cold weather and the mosquitos of the Niger River region. Dr. Claude Ardouin of the British Museum is researching the
Islamic iconography of these blankets from the perspective of their function as power objects; he writes “the Islamic motifs - particularly the magic square - form a significant part - if not the most significant one - of the patterns of several important
(socially, culturally) designs . . . That aspect is one of the major features that remain unexplored by research on textiles” (1).
Other researchers (Rubin; Heathcote) concur with Dr. Ardouin’s assertion of the significance of magic square iconography in West Africa, extending it to include textiles that, like the kaasa, have not been previously thought to contain Islamic symbolism; for example, the adinkra of the Asante in Ghana, the adire of the Yoruba in
Nigeria, or the basiae of the Bamana people in Mali could be studied further from the perspective of Islamic symbolism. As mentioned in Chapter Two, Brett-Smith has done 85 in-depth research on the basiae and notes the relation of its iconography to the pervasive West African magic square patterns. Figure 27 shows a mud cloth, the third and final textile in the group, which has the basiae motifs she mentions.
This wrapper is made of hand-spun and strip-woven cotton, and it is painted with mud dyes that have been painstakingly applied to form a dark background for patterns that are first sketched on the surface of the cloth. That is, instead of the dots on the lower border, for instance, being painted with light paint on a dark background, the mud is painted around the dots, which are left the pale colour of the cloth. According to
Brett-Smith, the matrix arrangement references the talismanic power of magic squares, adding to the cloth’s power to protect the female wearer during the dangerous and traumatic ritual of excision; she writes, “we can see the basiae and its grid-like armature as an amulet writ large across the female body at the most vulnerable points in a woman’s life cycle” (“Cloth as Amulet” 72). As I noted in my discussion of the hunter’s coat, the bush is conceptualized as both dangerous - here it takes the form of nyama, primordial energy - and a source of power to be harnessed through the talismanic functions of the cloth (Brett-Smith “Symbolic Blood” 27).
There are two garments in this group that represent the many variations of the checkerboard pattern. As I stated in Chapter Two, the checkerboard pattern is widely used for textiles, especially in patterned structures for weaving. The technology of the loom lends itself to this type of patterning through the use of contrasting colours of yams. Weavers all over the world apply these contrasts in both warp yams (the set of threads that are held longitudinally in tension on a loom) and weft yams (the threads 86 that are woven individually into the warp). Especially in West Africa, where cloth is
traditionally woven in narrow strips that are sewn together to make wider cloth, the pattern can be accomplished through weaving blocks of yams in different colours and
then alternating them when the strips are joined. A Liberian gown in the British
Museum’s collection (Figure 29) shows the pattern of alternating light and dark blocks; the cloth is woven so the interchanging dark blue and white weft yams completely
cover the warp, resulting in a purely contrasting checkerboard pattern. Some blocks
feature inlaid motifs (additional wefts are inserted by finger manipulation to add more varieties of colour and pattern to the cloth). The strip-woven structure is so thoroughly associated with the patterning of cloth in West Africa that it is often mimicked in wide-
loomed cloth: for example, a wrapper from Burkina Faso (Figure 28) is not only resist- patterned in a checkerboard pattern by tie-dying, but the pattern is accomplished in commercially woven cloth that is cut into narrow strips then joined.
The checkerboard has an iconographic meaning beyond its structural use: it is a coded reference on West African textiles to the magic square (Prussin 96; Gilfoy 45;
LaGamma and Giuntini 72). The checkerboard pattern does not use script to refer to the magic square’s talismanic function as does the Burkina Faso shirt (Figure 6). Nor does it feature symbols that point to amulets, as in the Liberian tunic (Figure 15) or Qur’an covers, as in the hunter’s shirt (Figure 13). Here, the reference is solely to the matrix configuration of the magic square. I view the checkerboard as the pattern that is the furthest from its referent, and therefore the most veiled: only the grid conveys the meaning. 87
The final garment examined for this study is called a rigan giwa (robe of the elephant) (Figure 30). According to Heathcote and Kriger among other scholars of
African textiles, it is a type of robe made, like the shabka in Figure 16, for Muslim
Hausa elite men in Northern Nigeria. This robe features embroidered motifs that signify good fortune and victory in war (Kriger 52). Three of the motifs refer to magic square symbolism: the checkerboard in the circle, the knot on the lower left of the robe, and the two long thin shapes below the neck opening.
Interlace or knot imagery is a common motif in ancient and historic decorative vocabularies, including those used by Hebrew and Celtic visual systems, and it also has significance for the geometric repeat patterns of Islamic art. Gulru Necipoglu asserts that the distinctive form of geometric design found in the fifteenth century Timurid dynasty Topkapi Scroll, based on repeating star and polygon patterns, was known to architects and builders as girih, the word for knot in Persian. She explains:
The term refers to the nodal points or vertices of the weblike geometric grid
systems or construction lines used in generating variegated pattern for
architectural plans and decorative revetments in two and three dimensions (each
“knot” centre where a number of construction lines intersects has an n-fold
rotational symmetry). (9)
I view the robe in Figure 30 as representing versions of magic square-related motifs and patterns in various stages of transformation. The imagery on this robe and on others of its type has multiple overlapping meanings, both indigenous and Islamic and the two combined, and this makes it difficult to separate and categorize the 88 meanings, which were not necessarily separated for their makers and their wearers. The checkerboard in the circle represents a 3 x 3 magic square. But on a similar robe, Kriger also identifies a knot as a 3 x 3 magic square, one that has been “transformed into a crossed lozenge or interlace form” (78). Figure 22 pictures this transformation of the magic square. Here, a magic square is visualized as a knot or interlaced motif by picturing the two-dimensional form of a line as a three-dimensional ribbon that crosses over and under itself as it travels past each number.
Kriger goes on to link interlace forms in the region with the representation of lizards, and argues for an appreciation of the many layers of meaning inherent in these forms (79). Finally, the long thin shapes below the neck opening are known as “two knives” (Kriger 52) and there are, again, many possible interpretations of them. One that includes magic squares is put forth by Prussin, who argues that the knives developed as a reference to a talismanic geometric pattern like the one on the back of the tunic in Figure 12 (Prussin 93). Overall, Kriger argues that the rigan giwa should be viewed as “a fusion of Islamic charm gowns associated with literate (Sufi) traditions and the robes of honour and nobility which have tended to be seen as political and diplomatic statements” (193).
Talismans and encoded patterns have traveled widely in West Africa, and appear in many forms even on the textiles of non-Islamic societies. Therefore their influence is widespread and not confined solely to Muslim contexts. Epelboin notes in reference to the talismanic shirts from Senegal: 89
Au-dela du contenu, Tapparence de l’objet, son mode de portage, voire
d’exhibition, constituent un metalanguage non verbal transcultural. Above and
beyond the object itself; the appearance of the object, the way it is carried, the
way it is shown, amount to a transcultural non-verbal meta-language. (Epelboin,
Hames and Raggi 150)
As I have stated, the patterns of checkerboards and knots on textiles and other objects of material culture are coded references to the magic square, retaining the emotional charge of its talismanic function. However, checkerboards, knots, and interlace designs are hybrid motifs that can possess multiple meanings: for example,
Kriger talks about interlace designs as symbolic of serpents in Hausa iconography, as well as being symbolic of magic squares (190) and Westermarck traces the symbolism in Morocco of the number five in amulets as shorthand for the hand’s five fingers, held up, to protect against the evil eye (213). There is a layering of meanings in the West
African textiles selected for this study. This layering can be explained as the laying down of influences, beliefs and habitual ways of doing things by countless individuals through many centuries of history. Becker offers a definition of “culture” that expresses the trans-generational yet deeply embodied layering of meanings in the interaction between individuals and material culture objects (130). Multiple layers of meaning in these textiles can also be explained by Marks’ notion of logical depth, introduced in
Chapter Two as an index of all the histories that went into the making of an object. I would extend the notion of logical depth to include as well all the ways in which an object has been used after it was made. Changing contexts and attitudes and even use 90 and repeated handling leaves physical evidence of the intense emotional charge in certain objects, contributing in turn to the creation of that emotional charge. For example, discussing a stone altarpiece in a cathedral, Edwards describes how its surface is worn away by the kisses of supplicants (Edwards, Gosden and Phillips 10). Logical depth also implies some of the accrued layers being hidden or less obvious than others.
This encourages coded references, which nonetheless condense some of the protective power of the amulet into a pattern or motif that refers to it.
It is this all-important quality of the magic square - the fact that it is used as part of a talisman embodied in material objects with many accrued layers of meaning, some of them secret - that causes it to “have legs” (Mitchell 73), to lose its specific mathematical meaning and to be referred to in coded references through textile patterns like checkerboards. If the first transformation of the magic square is its formulation in the mind as a figural concept, and the second is its manifestation on a surface, enabling it to be represented as a visual metaphor, the third is its transformation into patterns.
The matrix form is the marker and whether there are numbers or not becomes unimportant. The knot and the checkerboard pattern thus become metaphors for the talismanic function of the magic square.
Here I would like to again take up the notion of object agency and relate it to the action of the magic square as a pattern engine. Object agency describes the interaction between objects and their makers and users; the way certain objects are perceived and used determines how they are developed and changed over time, and how this activity 91 has real and often profound effects on their makers and users. In other words, we make the object, the object makes us, and together we make a world.
How can an object help to make a world? In his writing about the talismanic shirts retrieved from the garbage dump off Cap Vert, Senegal, Epelboin theorizes about object agency in the following passage:
L’objet talismanique, une fois qu’il echappe au controle de son fabricant...prend
vie, est charge de sens, de pouvoirs autonomes, au gre des evenements, dont il
est devenu acteur. Objet traditionnel fort, charge d’une memoire de terroirs,
d’evenements, de personnes humaines et non humaines, s’il est associe a des
reussites, il devient un complement indispensable de la personne. Once the
talismanic object is beyond the control of its maker, it takes on its own meaning,
with its own powers; it becomes an actor in new contexts. As a powerful
transitional object — full of memory, of terroir, of events past, of beings both
human and non-human - once it is associated with success, the object becomes
an indispensable part of the owner’s life. (Epelboin, Hames and Raggi 150)
Obviously, inanimate objects are not capable of acting, so Epelboin’s claim that a Senegalese talisman becomes an actor is itself a metaphor that describes the agency of the talisman (Epelboin, Hames and Raggi 150). I suggest that the answer to this question lies in the way the human mind makes meaning, through the process known as embodied cognition. The dynamical view of consciousness as emergent, constructed, and phenomenological in relation to music (Monson 48) is also a useful view of the agency that the magic square exhibits in its function as a pattern engine. Because the 92 magic square starts off as numbers, it is always held to represent, not things, but the code behind things - the batin that is concealed by the zdhir (Marks 24). It represents, not reality, but the process by which we create reality, in our minds, through Edelman’s reentrant loops (29). Because of this, nonfigurative, iterative patterns, as I noted in
Chapter One, are better than figurative images at picturing relationships, not things. The patterns I have been discussing in my study, viewed in this light, structurally express the relationships in the magic square that have made it a powerful healing talisman for
Muslim West African societies. 93
Figure 25: Wrapper, Niger, Djerma, early twentieth century, cotton, strip-woven in
supplementary weft technique and sewn, gift of Barbara Barde, T04.34.2 TMC. Figure 26: Blanket (kaasa ), Mali, Fulani, 1950-70, wool, strip-woven in supplementary
weft technique, sewn, gift of Madeleine Boucher Harvie, T04.7.3 TMC. 95
Figure 27: Girl’s wrapper (basiae), Mali, Bamana, twentieth century, cotton, strip-woven,
painted and dyed with mud, museum purchase, T77.0005 TMC. Figure 28: Wrapper, Burkina Faso, Mossi, twentieth century, cotton, commercially
woven, sewn, tied resist-dyed, private collection. 97
i1111r- v * ■ 11is m i l l v i j j . 1 . ® . 11111 r J / J ■ 1111 m 1 1 1 ■ i . i . i . i . 1111 I n i i i m i 11 • > . < ■ 1 1 1 1 11 I 11 I I III! I I J I | | I | |
Figure 29: Gown, Liberia, 1860, cotton, strip-woven, sewn, embroidered, appliqued,
donated by Henry Christy, Af2797 The British Museum. k
L-/J
m
t %
Figure 30: Man’s robe, Nigeria, Hausa, twentieth century, cotton, strip-woven, sewn and
embroidered with silk thread, from the Opekar/Webster Collection, T94.3002 TMC. 98
Chapter Five, Conclusion
My whole argument in this thesis can perhaps be boiled down to this statement: patterns have meanings for the societies that produced them. These meanings are experienced in myriad ways but they can be rediscovered outside their originating contexts through a diversity of approaches including that of historical research. For example, writing about ancient Andean textiles, Mary Frame has shown that their patterns explicitly refer to a “geometrization” of space that recalls Prussin’s use of the term for West African textile patterns. For Frame, the checkerboard pattern found on
Andean textiles represents balanced plain weave, the diamond grid represents braided structures (“Beyond the Image” 123), and patterns of birds in flight, intertwining serpents, or simply Z or S shapes symbolize the helical rotation in space of twisted and spun yam (“Motion Pictures” 167). Another researcher, Peter Roe, calls the wealth of meaning inherent yet hidden in ancient geometric Antillean ceramic patterns “the ghost in the machine” (98).
What I have argued throughout this study is that the magic square’s agency as a pattern engine derives from four accumulative qualities: first, it models the harmonics of universal order which are numeric relationships - not things - that exist in the mind prior to their representation in a seen diagram or a heard sound. We have seen that this notion of the numeric basis of reality has been represented by the magic square in geographic regions from China to Europe and across time periods ranging from ancient
Greece and Babylon to Medieval Persia and Renaissance Italy. Second, as it manifests in West Africa in the Islamic version, the magic square has an inherently dynamic, 99 spiral action, so it represents something that is in a constantly interacting and iterating relationship with its environment, giving it a generative agency. We have noted how this rotational symmetry is closely related to the actions characteristic of spinning yam and weaving cloth. Third, the power to so cogently represent relationships and dynamic actions leads to the magic square’s inclusion in talismans that are widely considered capable of influencing the course of events. We have seen how these talismans are used in the Islamic world, including in West Africa, as “supercharged prayers” for protection and healing and how they gain in efficacy through being worn close to the body (Dols
86). Fourth, the generative agency of the magic square, the “pattern engine,” is encoded in nonfigurative, iterative textile patterns like checkerboards that have lost its specific mathematical operations but retain its emotional charge. This quality also comes from its origin in Qur’anic writing in Arabic whose presence alone, as mentioned in Chapter
Three, is enough to signal the talismanic meaning. To paraphrase Kriger’s comment in reference to the Hausa robe, it does not have to be read, it only has to be known to be there (194).
In this study, I have hypothesized the magic square’s agency as a pattern engine in West African material culture through the analysis of selected garments in museum
collections. In Chapter One I maintained that the magic square-inspired textile patterns
in this study belong to a wider domain of non-figurative, iterative patterns seen on objects of material culture all over the world. This domain’s ubiquity and multiplicity
of expression make it impossible to address here in any detail, but I would reiterate that these non-figurative patterns differ from figurative images in their ability to connote, 100 rather than directly represent, cultural relationships. Further, the patterns I have discussed that are derived from the magic square are possibly unique among non- figurative patterns in their lack of reference to anything other than number relationships. Many symbols used in patterns on cloth and other objects appear entirely non-figurative but if traced back far enough, each originated in a plant, an animal, or a human figure.16 In contrast, the checkerboard pattern in Muslim West African textiles encodes cultural information about the healing power of talismans solely through the matrix array of the magic square.
Chapter Three deals with the visual symbol of the magic square: through closely examining a shirt from Burkina Faso that has writing and squares inscribed on its surface and comparing it to other garments, I showed that that the square on the shirt paradoxically is at its most embodied when it is in its most explicit, written form. I also conjectured that the use of the magic square in talismans is the source of its ability to influence the generation of visual patterns in textiles. Chapter Four deals with metaphor and pattern engine: I traced the transformations of the magic square from a numeric concept to a pattern on cloth and compared it as a model of harmonic proportion to other models.171 also argued in favour of a metaphoric relationship between magic
16 The ram’s horn of Central Asia, the goddess o f Eastern Europe, the Indianboteh that became the European paisley, and the dragon on Caucasian carpets are examples of naturalistic imagery that transformed over time into non-figurative patterns on textiles, ceramics, and jewellery.
17 Two other models of note are related to those examined in this study: one formulated by Peter Roe in reference to the patterns on ancient Antillean ceramics has axes of positive perception, negative perception, positive execution, and negative (resist) execution (106). The other model comes from analytic psychology and graphs the relationship between the conscious and unconscious minds of analyst and analysant in the analytic relationship (Meier 281). Both authors state that these models represent all the variations possible in their respective subjects. Furthermore, both models, like the Klein Group, are based on a square and have four axes. 101 square symbolism and weaving through the matrix arrangements of checkerboard patterns, and the interlaced arrangements of knot patterns. Moreover, I theorized that the weaving metaphor, as conceptualized by the understanding of the makers and users, enables the agency of the pattern engine - that the embodied making, wearing, and using of the garments is key to the production of their multiple layers of meaning in
West African societies.
This final chapter brings together the study of the garments with the notions of metaphor and pattern engine I brought forward in Chapter Four to examine the final transformation of the magic square. If its third transformation is into patterns on textiles that reference it, the fourth transformation occurs when those textiles are taken from their original environment, where their talismanic meaning is received with various levels of understanding by their makers and users, and moved into an institutional space, whether physical (museum) or virtual (photo, cinema or Web-based representation or academic discourse). As a result of this move, the role of other senses than sight is invariably diminished as the textile is no longer worn, handled, or smelled.
Detaching it from its originating context can cause it to lose its original, purpose-built agency. Furthermore, since humans need to use their senses in order to make meaning - as the theory of embodied cognition tells us - the reduction of the viewers’ sensory apparatus to sight alone results in a loss of understanding. Any object loses agency via this transformation but I would argue that the loss is especially marked for textiles, which are generally considered less important than other media in the Western art canon. 102
Embodied cognition, a model of consciousness that defines perceiving, learning and knowing as situated in an interaction between the body and its environment, has been proposed by neuroscientists (Edelman and Tononi 274) and adapted by contemporary theorists of visual and material culture (Edwards, Gosden and Phillips;
Edwards and Bhaumik; Mitchell; Pinney) who use it to interpret the perception and understanding of art. As discussed in the previous chapters, it is closely tied to object agency - the notion that objects not only reflect, but can constitute and change cultural paradigms - and to logical depth - the hidden history composed of everything that went into an object’s making and using, even those elements that were rejected. These three concepts, separately and in combination, are active in the institutions where the textiles in the study now reside. If humans perceive and make meaning through embodied cognition, we are disadvantaged by the removal of other senses than sight in museum displays, where textiles are often encased in glass or Plexiglas in dim light. If a textile in a museum collection has a new kind of agency as a museum object, this agency can be used selectively as the institution uses the object to deliver the narrative it prefers.
And a textile’s logical depth, the sum of all its histories of construction and of reception, can be used selectively as well. An example of this rerouting of narrative is in Chapter Three, where the hunter’s coat (Figure 14) is described as “the single most frightening piece of cloth we’ve got in the place” (Textile Museum of Canada
“T81.0112”).
The decontextualizing tendency that occurs from this final transformation of the magic square/pattern engine can be countered by means of various interpretive 103 strategies. A more detailed examination of these strategies in museum contexts is beyond the scope of this study, but it is important to note here some of the recent research that has been done by scholars of museology. Viv Golding suggests including physical engagements with replica objects in exhibitions (224), while Fiona Candlin evaluates multi-sensory experiences that involve active play (167). Sandra Dudley describes artistic interventions, where contemporary art is juxtaposed to historic objects to aid in visitors’ understanding of each form (13). Each of these approaches is based on a model of embodied cognition that follows Edelman’s theory, positing the biological basis of cognition and thus the need for interpretive strategies to activate all of the senses in the perception and comprehension of museum displays. I suggest that their use in a contemporary museum practice that allows for multi-sensory engagement mitigates in favour of the positive effect that museums can have in fostering greater knowledge and deeper understanding of objects like the textiles in this study. The more textiles like these are displayed and contextualized in exhibitions, the more questions are asked about them and new research stimulated.
I return now to my main topic in order to re-examine some counter-arguments to my hypothesis that the magic square operates as a pattern engine. In Chapter Two I mentioned Grabar, Saliba, and Chorbaichi among scholars named by Marks in her book, Enfoldment and Infinity. It is pertinent to revisit their position that there is no evidence that geometric patterns had any meaning beyond beautification for the medieval Muslim architects and artisans that made them, in light of the opposing case I have made for the magic square as a pattern engine. In particular, Grabar’s statement 104 that there is not “a single instance justifying the view that the Muslim community, the ummah, as opposed to individual thinkers, understood mathematical forms as symbolizing or illustrating a Muslim cosmology” (267) seems too narrow as it does not allow for the many levels of understanding with which magic square symbolism is received in Muslim West African societies. These many levels of understanding, as I stated in Chapter Four, are based on an assumption that patterns on textiles are not merely decorative but have meaning for their makers and users. This assumption in turn depends on the patterns’ agency, through their embodiment on textiles, as active influences in their societies. It also depends on the patterns’ logical depth, which invests them with complex histories and layered meanings that travel with them, even if some of these histories and meanings are in hidden or coded form.
Another counter-argument would involve the question of linearity in the transformations of the magic square that I have discussed. I stated in Chapter Four that there is no progression in time from the magic square’s use as a component of talismans in West Africa to the appearance of textile patterns referring to it, since both these forms co-exist at the same time and place. But it is also possible to assume that there is a cultural progression from the “sophisticated” and secret use of the magic square as a talisman to its representation in geometric patterns on “primitive” textiles. I hold the opposing view to this assumption, believing that textile making of the kind that is seen in the garments selected for this study are examples of complex and highly developed thinking involving pattern recognition with differentiation of figure and ground and advanced levels of hand-eye coordination and dexterity. 105
I make the case that patterns have meanings for the societies that produced them
as a general one which is applicable to many systems of patterning in visual art, but I
clearly can only support it in the context of this study of magic squares. Can my
argument be applied more broadly to meaning in Islamic patterned art, beyond
talismanic shirts and ornaments? More research can be done in the future to investigate
the assertion for other pattern systems. The two Hausa robes in Figures 16 and 30, for
example, would benefit from the kind of focused, detailed analysis that has been given here to the Burkina Faso shirt (Figures 5 and 6). The shirt itself has not yet revealed all
of its secrets: more research could be done on the symbols within the squares inscribed
on its surface, which remain enigmatic. Another direction for future research lies in the
further investigation of patterns of cognition that are related to making. Ingold
contributes some valuable insights in this area by analyzing the phenomenological
process of weaving as done by both humans and by weaver birds (353). It would be productive to examine, not another specific region of the world as was done in this
study, but an object typology that is common to many regions. For example, baskets are
fundamental objects in the material cultures of many societies. They are built of
patterned structures and often have patterns as embellishments. Basket making
techniques are rudimentary - no machine can make them, so they are always made by
hand manipulations - and their materials tend to be relatively unprocessed. The process
of interlacement could be examined as a cognition pattern by focusing on choices made
by basket weavers such as figure/ground, inner/outer surface, and the shaping of edges,
and the differentiations in perception and action these choices necessitate. This future 106 study would necessitate an interdisciplinary approach that is taken from the disciplines of material and visual culture, as well as touching upon mathematics, psychology, and cognitive science.
Another aspect of pattern that could productively be explored is suggested by
Grabar, who characterizes the ludic aspect of pattern as “the game of covering space, that is to say a desired activity with rules but without certainty about outcome” (152).
The history of the magic square has a connection to this aspect, as the origin of the continuous method of construction is believed by Camman to be related to the “knight’s
move” in chess (97). And in the textile domain, the process of interlacement itself can be viewed as a kind of puzzle involving a series of strategies that lead to a win state, in
this case a well-designed and fabricated object.
Finally, a provocative question could be asked about the magic square, both in
its ancient, original form and as part of talismans in West Africa. If, as Kreamer
suggests, verses from the Qur’an sewn into a garment not only represent the perfection
and protective power of God, but literally constitute it, “collapsing entirely the
interpretive space between word and meaning” (19), does the magic square in a
talismanic context also collapse the space between image and meaning when it is used
as a supercharged prayer, making it, not as much a metaphor for that perfection, as an
actual embodiment of it? This possibility suggests a line of inquiry that interrogates and
problematizes the essential nature of patterned representation from the perspectives of
visual and material culture. 107
Pattern as a field of scholarship is vast, and truly interdisciplinary. As has been demonstrated here, it is an important factor in many branches of mathematics - group theory and transformational geometry are two examples - and of science, including biology and neuroscience. In the arts, pattern is a key principle of design, essential to the performing and visual arts. Finally, patterns of behaviour are deeply implicated in the ways human beings form and maintain communities and customs. The field of pattern thus must reside in a space between disciplines, not belonging entirely to mathematics, or art, or anthropology, and yet drawing from all of these. It is hoped that this inquiry into the magic square as a pattern engine in West African textile patterns contributes to that scholarship, and that it provokes further questions and research, and new insights. 108
Appendix A: Translation and Interpretation of the Shirt Front by Ruba Kana’an
Block 1
In the name of God The Compassionate. The Merciful.
God. The Compassionate. The Merciful. The King.
The Holy. The Peace. The Giver of Security.
The Protector. The Mighty. The Compeller.
The Majestic. The Creator. The Maker. The Fashioner.
The Forgiver. The Subduer. The Bestower.
The Provider. The Opener. The All-Knowing.
The Withholder. The Expander. The Abaser.
The Exalter. The Bestower of Honour. The Humiliator. The All-Hearing.
The All-Seeing. The Judge. The Just. The [sic]
The Gentle. The All-Aware. The Forebearing.
The Magnificent. The Forgiving. The Appreciative.
The Most High. The Great. The Preserver.
The Sustainer. The Reckoner.
Block 2
(under the 7 x 7 square)
The Sublime. The Generous.
Block 3
The Watchful. The Responsive. The All-Embracing.
The Wise. The Loving. The Most Glorious. 109
The Resurrector. The Witness. The Truth. The Disposer of Affairs.
The Most Strong. The Firm.18 The Praiseworthy. The Counter.
The Originator. The Restorer of Life. The Giver of Life. The Causer of Death.
The Ever Living. The Self-Existing Subsisting. The Noble. The Finder.19
The Unique.20 The Eternal. The Able.
The Powerful. The Expediter. The Delayer.
The ruler.21 The Last. The Manifest. The Hidden.
The Friend. The Supreme One. The Source of Goodness. The Ever Relenting.
The Avenger. The Pardoner. The All Pitying.
The owner of all Sovereignty. The Lord of Majesty and Bounty.
Block 4
God. The Compassionate.
The Merciful. The King.
The Holy. The Peace.
The Giver of Security. The Protector.
The Mighty. The Compeller.
The Majestic. The Creator.
The Maker. The Fashioner.
The Forgiver. The Subduer.
18 [The Protector] is missing 19 The order of the last two names is reversed 20 [The One] is missing 21 Should be al- awwal (The First) 110
The Bestower. The Provider.
Block 5:
The Opener. The All-Knowing.
The Withholder. The Expander.
The Abaser. The Exalter.
The Bestower of Honour. The Humiliator.
The All-Hearing. The All-Seeing.
The Judge. The Just.
The Gentle. The All-A ware.
The Forebearing. The Magnificent.
The Forgiving. The Appreciative.
The Most High.22 The Preserver.
The Sustainer. The Reckoner.
The Sublime. The Generous.
The Watchful.
Block 6
Ln 1-3: the same formula repeated three times (4 words)
The Responsive. The All-Embracing. The Wise.
The Loving. The Most Glorious. The Resurrector.
The Witness. The Truth. The Disposer of Affairs.
The Most Strong. The Firm.23 The Praiseworthy.
22 [The Great] is missing Ill
The Counter.24 The Restorer of Life. The Giver of Life.
The Causer of Death. The Ever Living. The Self-Existing Subsisting.
The Noble. The Finder.25 The Unique.26
The Eternal. The Able. The Powerful.
The Expediter. The Delayer. The First.
The Last. The Manifest. The Hidden.
The Protecting Friend. The Supreme One. The Source of Goodness.
The Ever Relenting. The Avenger.
Block 7
The Pardoner. The All Pitying.
The owner of all Sovereignty.
The Lord of Majesty and
Bounty. The Equitable.
The Gatherer. The Self Sufficient.
The Enricher. The Preventer.
The Distresser. The Propitious.
The Guide. The Incomparable.
The Everlasting. The Inheritor of All.
The Guide.
The Patient.
23 [The Protector] is missing 24 [The Originator] is missing 25 Usually [The Finder. The Noble] 26 [The One] is missing 27 [The Light] is missing [same as 4-word formula in block 1. Also in three times, one word per sideways: May God bestow prayer on our Prophet Muhammad and on
His family and friends and grant them peace.
Block 8
God. The Compassionate. The Merciful.
The King. The Holy.
The Peace. The Giver of Security.
The Protector. The Mighty.
The Compeller. The Majestic. The Creator.
The Maker. The Fashioner. The Forgiver.
The Subduer. The Bestower. The Provider.
The Opener. The All-Knowing. The Withholder.28
The Exalter. The Bestower of Honour. The Humiliator.
The All-Hearing. The All-Seeing. The Judge.
The Just. The Gentle. The All-A ware.
The Forebearing. The Magnificent.
Block 9
The Forgiving. The Appreciative. The Most High.
[.]29 The Preserver. The Sustainer. The Reckoner.
The Sublime. The Generous. The Watchful.
The Responsive. The All-Embracing. The Wise.
28 [The Expander. The Abaser.] is missing 29 [The Great] is missing 113
The Loving. The Most Glorious. The Resurrector. The Witness.
The Truth. The Disposer of Affairs. The Most Strong. The Firm.
The Protector. The Praiseworthy. The Counter.
The Originator. The Restorer of Life. The Giver of Life.
The Causer of Death. The Ever Living. The Self-Existing Subsisting.
The Noble. The Finder. The Unique.
The One.30 The Eternal.
Block 10
The Able. The Powerful.
The Expediter. The Delayer. The First.
The Last. The Manifest. The Hidden.
The Protecting Friend. The Supreme One. The Source of Goodness.
The Ever Relenting. The Avenger. The Pardoner.
The All Pitying. The owner of all Sovereignty.
The Lord of Majesty and Bounty. [The Eq]
The Equitable. The Gatherer. The Self Sufficient.
The Enricher. The Preventer. The Distresser.
The Propitious. The Light. The Guide.
Block 11
The Incomparable.
The Everlasting.
30 [The One] is missing. 114
The Inheritor of All.
The Guide.
The Patient.
And say
And say Oh God! Giver of Sovereignty
Unto whom Thou wilt,
In Thy hand is the good. Lo! Thou art
Able to do all things.31
May God bestow prayer on [Prophet] our Prophet Muhammad and on
Muhammad’s family and grant him peace.
Block between the two squares
In the name of God The Compassionate. The Merciful
Praise be to God, Lord of the Worlds
The Beneficient, the Merciful, Owner
Of the day of Judgement. You alone we worship
You alone we ask for help
Show us the straight path
The path of those whom you have favoured
Not those who earned your anger
31 Q 3: 26 The verse has various mistakes and missing words “Oh God! [Owner] of Sovereignty unto whom Thou wilt, [and Thou withdrawest sovereignty from whom Thou wilt. Thou exaltest whom Thou wilt and Thou abasest whom Thou wilt.] In Thy hand is the good. Lo! Thou art Able to do all things.” 115
Nor those who go astray32
Amen. God will protect you from people33
God will protect you from people
God will protect you from people
God will protect you from people
May God bless our Lord Muhammad and give him salvation.
Under the 2 x 2 square
Note: a two-line Q: 5: 64
“Whenever they light a fire for war, God extinguishes it.”
32 Lines from 1-9 is the opening verse of the Qur’an 33 Q 5:67 116
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