PERSICA XIX, 2003 MATHEMATICS AND MEANING IN THE STRUCTURE AND COMPOSITION OF TIMURID MINIATURE PAINTING Sarah Chapman University of Edinburgh INTRODUCTION Even at first glance many Timurid miniature paintings reveal a strong sense of pattern and organization on which much of their overall dynamism depends. One can see the repetition of geometric shapes created by the figures, the very static and linear nature of much of the architecture, and the feeling of proportion and harmony in their composition. The obvious deliberation in their structure suggests that they may have been precisely planned and may even adhere to some kind of mathematical formula. The formal qualities of Persian miniature painting have been remarked on many times, and many techniques and conventions have been identified by scholars. Of particular rel- evance to this investigation are the studies of Guest,1 Zain,2 Adle,3 and Stchoukine.4 Guest identifies the importance of text panels in the calculation of important measurements and relationships within Persian painting, and discusses the repetition of certain measurements and distances as “a kind of counterpoint throughout the design.”5 Zain further investigates the relationship between text and painting, identifies certain formulaic tendencies in the building of Timurid compositions, and discusses the presence of a “hidden structural line” in many paintings which “guide” our experience as a viewer.6 Adle and Stchoukine both investigate the ‘mathematical’ nature of Persian painting in some detail: Adle finds, like Guest, the repetition of certain measurements and goes on to describe a modular system for the organization of hunting and sporting scenes especially. Stchoukine identifies different geometric types of composition, and investigates the presence of preconceived linear struc- tures behind apparently random and unstructured scenes.7 1 G.D. Guest, Shiraz painting in the sixteenth century (Washington, D.C., 1949). 2 D.H.B.M. Zain, Formal values in Timurid painting (Kuala Lumpur, 1989). 3 C. Adle, “Recherche sur le module et le trace correcteur dans la miniature orientale”, Le Monde Iranien et l’Islam 3(1975), 81-105. 4 I. Stchoukine, Les peintures des manuscrits Timurides (Paris, 1954). 5 Guest, Shiraz painting, 25. 6 Zain, Formal values, 13. 7 Stchoukine, Les peintures des manuscrits Timurides, 143-54. 34 SARAH CHAPMAN All these scholars are aware of the presence of a mathematical element in the pat- terned structure of Timurid painting and analyse this to some extent. However, their studies have tended to focus on the broader features of the compositions. A suspicion remains that the full complexity of the mathematics behind some of the very finest Timurid composi- tions, and its full significance, has yet to be discovered. The following study investigates the structure and organization of composition in Timurid painting in even greater detail, in an attempt to reveal the full extent of mathemati- cal conception, and to explore the possibility of an aesthetic meaning behind this math- ematical approach. The paintings analysed here include both architectural scenes and those with some landscape elements. The architectural scenes have been chosen specifically for their general appearance of formal patterning and strong linear structure, and the “semi- landscape” scenes because they include some of the characteristics of architectural scenes within a non-linear setting. It is obviously not possible to include all genres of painting within the scope of this study: hunting and sporting scenes, for example, fill a large part of the canon of Persian miniature paintings and seem to be based on a common conception of a diagonal grid, but they are too big a subject to tackle here. Furthermore, they tend to lack some of the elements, such as architectural features and static groupings, which most lend themselves to precise shapes, measurements and ratios. In order to appreciate the precision of the Persian painter and the intricacies and detail of the compositions, it is necessary to invest the same qualities in the analysis. The present study has involved precise measurements and prolonged scrutiny of the paintings. This detailed examination of the architectural scenes has revealed that a mathematical concep- tion is frequently fundamental to the whole painting. Often there is a considerable variation in the extent, complexity and possible significance of mathematical structuring, not only between different paintings but also between different areas of a single painting. While some paintings have a fairly rudimentary structure, in others the level of complexity and precision is astonishing. Often the painter has employed two layers of structure in the one painting, using different branches of mathematics: for example both geometry and algebra. The strong sense of visual structure which is so immediately apparent can turn out to be only the most basic level of organisation: there is another, far more complex structure which dominates the painting mathematically, but ‘invisibly’. This study makes use of illustrations selected from published works on Persian mini- ature painting. The references are supplied at the point where each painting is introduced. The findings presented below raise several questions. Did the Persian miniature painter employ a mathematical composition purely for its visual effect? Do the differences in struc- turing between architectural and landscape scenes have a metaphorical significance? The arcane nature of some of the mathematics, sometimes so hidden as to have no apparent visual meaning at all, leads to the further problem of the role of the contemporary Persian viewer: how much of the painter’s complex conception did he intend the viewer to perceive? A further investigation into the structural system which underlies landscape painting also sheds some light on the question of aesthetic meaning. The employment of mathemat- ics to structure the man-made and artificial scenes, and their absence in landscape areas indicates the association of mathematical control with the materialism of the transitory, human present, while uncontrolled space implies the freedom of the natural world. TIMURID MINIATURE PAINTING 35 THE PAINTINGS A painting which raises all these issues is ‘The Celebration of the Birth of Majnun’ (pl.1) from a Layla u Majnun of Amir Khusrauw Dihlavi (890-1/1485, Chester Beatty Library, MS 163, f. 104v).8 The overall effect in this painting is vivid and dynamic. This is due to several contrasts within and between the different structural aspects of the painting: for example, between the vertical and horizontal lines of the architecture and the repeated trian- gular pattern of the figures, but also between the generally static quality of these linear and geometric patterns and the animation of the individual figures themselves. The dramatic and compositional use of colour also contributes to the dynamism of the painting. It is the contrast between the lines of the building and the triangles of the figures that gives the painting its immediate structure: this is reinforced by the painter’s use of primary colours. The predominant colour in the architecture is blue, and a bright sky-blue is used to empha- sise the important shapes in the building and courtyard wall. In contrast to this blue, the painter uses red and yellow, the other two primary colours, to provide force and movement in the figures. As figs. 1a and b show respectively, red and yellow are plotted to draw the eye along the two triangular shapes. The contrast between the verticals of the building and the strong geometric shapes created by the figures provides an immediate visual structure: it allows the eye to receive the painting in terms of two separate compositional ideas. This is the visible structure of the painting; however there is another, more arcane plan which is not readily discernible at a glance and which governs the layout of the building and the placing of the boxes of text. This second structure is also mathematical. As fig. 2 shows, the vertical lines of the architecture in this painting define a highly complex, algebraic pattern of distances A and B. Even the text blocks are integrated into the picture by being a width of 2A and placed at a mathematically appropriate point in the painting: if each text were repeated again on either side they would fit exactly against the left margin of the painting and the end of the pink wall. The curtained gateway, which would appear to interrupt the ordered plan of the building, is in fact mathematically allied to it. The left-hand pole of the gateway is exactly at a distance of 2A from the right-hand margin. This upper part of the painting displays an extraordinary degree of mathematical coherence that, unless the viewer approaches the paint- ing armed with a ruler, is virtually invisible. It is not clear why the painter went to such lengths of precision and detail. The contradiction between the two layers of structure in this painting (first, the obvi- ous triangular and vertical shapes which knit the painting together visually, and secondly the ‘invisible’ mathematical calculations) is not the only puzzle of the painting’s composi- tion. Also curious is the discrepancy between the visual focus of the painting, and the focus of the subject matter, i.e. the baby, Majnun. The eye is drawn naturally towards the apex of the upper triangle of figures; however the baby, who is the cause of the celebrations taking place in the scene and who, one would assume, should be the focus of our attention, simply forms part of the right side of the triangle, and does not stand out at all. Even more curious, 8 E. Bahari, Bihzad. Master of Persian painting (London and New York, 1996), pl. 26. 36 SARAH CHAPMAN however, is the fact that the baby lies virtually in the centre of the painting (fig. 3). There- fore the visual focus is apparently unconnected with the baby, who is nevertheless virtually the mathematical centre of the painting.