Examples of Design Transformation (1): Delicately decorated seventeenth century Kongo baskets   Paulus Gerdes Mozambican Ethnomathematics Research Centre, C.P. 915, Maputo, Mozambique pgerdes@virconn.com In several European museums several 17th century Kongo baskets are kept from the Lower Congo area along the border of today’s Angola and Congo (Zaire). A basket woven with much precision around a calabash is kept at the Ulmer Museum (Ulm, Germany). Its height is 52 cm (see photograph in Falgayrettes-Leveau, p. 266). A twill-plaited container is kept at the Linden-Museum (Stuttgart, Germany). Its diameter is 29 cm (see photograph in Falgayrettes-Leveau, p. 273). Two other baskets and the painting "Black woman with child" of Albert Eckhout of 1641 displaying a delicately plaited basket are kept at the National Museum (Kopenhagen, Denmark) (see photograph in Falgayrettes-Leveau, p. 270, 271). Another one is displayed in Sentance, p. 111. In all these 17th century baskets, designs may be observed that resulted from a thoughtful design transformation, as will be shown. Basket container with lid The wall of the basket container kept at the Linden-Museum (Falgayrettes-Leveau, p. 273) is decorated with two alternating design motifs, presented in Figures 1 and 2. The first design motif The first design motif seems to be an elaborate representation of a widespread symbol (Figure 3), called ‘imbolo’, meaning knot, by the Bushongo / Kuba (Torday, p. 101). Emil Torday (1925) formulated the hypothesis that the ‘imbolo’ symbol may have its conceptual origin in the start structure of the normal over-one-under-one plaiting, as the diagram in Figure 4 sketches. The dominant twill of the motif in Figure 1 is the over-three-under-three weaving (3/3), interrupted by normal plaiting (1/1). The large 1/1 plaited hooks have a weaving width of three units. Maybe they were invented as a substitution of 3/3 hooks turning them more visible and more beautiful. Figure 5 displays the hypothetical weaving design from which our motif may have been derived. On their turn, the five plaited centres that form a square together with the square’s centre may have been derived from 3/3 woven centres (Figure 6). In Figure 6 we can see that the weaving structure still materialises the ‘imbolo’ symbol. What may be the weaving structure from which Figure 6 was derived to be able to realise the ‘imbolo’ symbol? Like the ‘imbolo’ symbol, the visual image of the woven materialisation of the symbol (Figure 1) and of the weaving structures in Figures 5 and 6 display a fourfold rotational symmetry. The rotational symmetry may have resulted from deliberately breaking double bilateral symmetry. In other words, the weaving structure in Figure 6 may have resulted from the transformation of the weaving structure in Figure 7. In Figure 7 the ‘imbolo’ symbol is still recognisable, but it obliterates the over-one-under-one plaiting structure of the symbol itself. The weaving structure in Figure 6 seems to be a thoughtfully constructed adaptation of the weaving structure in Figure 7 in order to turn the original plaiting structure of the ‘imbolo’ symbol evident. The weaving structure in Figure 7 may have been carefully constructed in a reflection about the regular toothed-square weaving structure in Figure 8 in an attempt to isolate the basic shape of the ‘imbolo’ symbol. The second design motif The second design motif (Figure 2) may be analysed in the same vein as the first one. It may have been derived from the same regular toothed square weaving structure in Figure 8 by selecting a bilaterally symmetrical part with seven local centres (Figure 9). The regular structure might have been broken by a staggered, closed polygonal woven line, which embraces all the seven centres (Figure 10). Figure 11 shows this closed polygonal line separately. Its inventor constructed it carefully in order to guarantee that all the seven centres would be ‘embraced’ by it. The diagram in Figure 12a displays schematically the closed polygonal line around the seven local centres. In Figure 12b and c two possible alternatives for the construction of such a closed polygonal line are presented. Substitution of the closed polygonal line with a weaving width of 3 units (Figure 10) with 1/1 plaiting leads to the second design motif in Figure 2. The two design motifs (Figures 1 and 2) are bordered by another regular toothed square weaving structure (Figure 13). Basket woven around a calabash The lowest level of the basket plaited around a calabash, kept at the Ulmer Museum (Falgayrettes-Leveau, p. 266) is decorated with two alternating design motifs, presented in Figures 14 and 15, once more bordered by the regular toothed square weaving structure in Figure 13. The third design motif The design motif in Figure 14, similar to the mathematical infinity symbol, seems to be a woven embodiment of a symbol called ‘bashungu’ (the spirits) by the Kuba (Torday, p. 101). It displays a twofold rotational symmetry. The woven design motif may have once more its conceptual origin in the inventor’s recognising the symbol on a mat with a regular toothed square weaving structure. The recognition and re-conceptualisation lead successively to the woven designs in Figures 16 and 17 and than to its final transformation into the design motif of Figure 14. The fourth design motif The design motif in Figure 15 displays also a twofold rotational symmetry. A closed polygonal line (Figure 18) embraces eight local centres. The design motif seems to derive from the deliberate transformation of another regular toothed square pattern (Figure 19) by first isolating eight toothed squares (Figure 20) and then imagining and weaving a closed polygonal line around these eight local centres. Several closed polygonal lines are possible (Figure 21 presents an alternative). The inventor opted for a symmetrical solution (Figure 18). But there are various symmetrical solutions (Figure 22 presents an alternative symmetrical solution). Might there have existed a special reason why the inventor selected the special symmetrical solution in Figure 18? The middle and top parts of the decorated calabash may give us a clue. They seem to represent plaited bands. The particular way in which the over-and-under plaiting is represented leads me to suppose that the design motif corresponds to a small plaited mat. Figure 23 displays the possible evolution of a small plaited mat design into the symmetrical polygonal design motif. The plaited mat design in Figure 24 is well known from the central African cultural area. Among the Kuba it is called ‘namba’, the bowels (Torday, p. 101). As a pictogram among the Ngangela it represents friendship (Pearson, p. 157). A particularity of the small plaited mat is that it is made out of only one strand. This oneness seems to be reflected in the oneness of the constructed polygonal line: only one polygonal embraces all the eight local centres. It may be concluded that the inventor of the design motif in Figure 15 wanted to represent a cultural important symbol and was able to invent a woven expression for it that incorporated both the oneness and symmetry.       Figure 1   Figure 2   Figure 3     (a)   (b) Figure 4   Figure 5   Figure 6   Figure 7   Figure 8   Figure 9   Figure 10   Figure 11     (a)   (b)   (c) Figure 12   Figure 13   Figure 14   Figure 15   Figure 16   Figure 17   Figure 18   Figure 19   Figure 20   Figure 21   Figure 22   Figure 23   Figure 24   References Falgayrettes-Leveau, Chistiane (Ed.) (1997), Réceptacles, Musée Dapper, Paris Pearson, Emil (1977), People of the Aurora, Author’s edition, Seal Beach CA Sentance, Bryan (2000), Art of the basket, Traditional basketry from around the world, Thames & Hudson, London Torday, Emil (1925), On the Trail of the Bushongo, (reproduction) Negro University Press, New York, 1969     CONTENTS