Transformational Geometry and the Central European Baroque Church

Abstract

The Central European Baroque church appears to be in endless conflict with itself: at once unified and chaotic, continuous and fragmented. Architects strove to unite architecture and the plastic arts merging into a symphonic whole, forming contrasting tectonic systems into composite and dissolving sharply-defined boundaries. A look at scientific/mathematical developments of the age helps place this in context: Desargues, Newton, Leibniz and Descartes all dealt with theories of synthesis and convergence. The effect of the new mathematical ideas was on architecture was a gradual transformation of space from pure, static and isolated to composite, dynamic and interpenetrating. Transformational operations were of utmost importance, including area, rotation, reflection, translation, coordinate transformation, Borrominian transformation, dilatation. A projective transformation is related to mapping, with a three-dimensional form projected onto a two-dimensional surface. In Baroque vaults a far-reaching potential of projective geometry as a form generator may be recognized.

The parts of a continuum, like a line, can only be individuated if distinguished by an indivisible boundary between them. Without such an indivisible divisor between the parts, the parts themselves would compenetrate one another; more than one part would be in the same place; and parts would no longer be individuated by their situs. They would in fact melt into the confusion of the indeterminate (Smith 1954: 53–54).

First published as: John Clagett , “Transformational Geometry and the Central European Baroque Church”, pp. 37–51 in Nexus I: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba, 1996.