A Symmetry Analysis of Design Structure: 1,000 Years of Continuity and Change in Puebloan Ceramic Design

This paper postulates that cultural entities with long term structural integrity are characterized by symmetrical relationships between and among the constituent sectors of society. We demonstrate how such social relationships are embedded in the symmetrical arrangements of motifs in geometric design. We test this premise with an analysis of 1000 years of ceramic design from the northern American Southwest, AD 600-1600, with a description of the continuities and changes in the plane pattern symmetries that structure design. Two major points of change in symmetry use at c. AD 900 and AD 1300 correlate with changes in settlement type from pithouses to unit pueblos and from unit pueblos to multi-storied plaza oriented pueblos that accompanied adjustments to changes in environmental conditions. We propose that in the American Southwest the predominant use of bifold symmetry is a structural metaphor for the reciprocal social relationships basic to the organization of small puebloan agricultural communities and that the changes in these symmetries reflect the changing integration of the household into an increasingly complex social system. This interpretation of the meaning of design structure is derived from cosmological principles embedded in 20th century ritual songs of the Hopi, descendents of the prehistoric puebloans, as well as depicted in images in their 15th century kiva wall murals. We present this interpretation of the sequence of pueblo development in the American Southwest in terms of the changing symmetrical nature of the social relationships that integrated the agricultural communities as an example of the insights possible with this new approach to design analysis.