The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry

Peregrinations: Journal of Medieval Art and Architecture, Dec 2015

By Nelly Shafik Ramzy, Published on 01/01/15

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The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry

Art and Architecture The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry Nelly Shafik Ramzy Recommended Citation Part of the Ancient; Medieval; Renaissance and Baroque Art and Architecture Commons The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry 1. Introduction When performing geometrical analysis of historical buildings, it is important to keep in mind what were the intentions of the originators, even though these intentions have likely changed many times as the master masons changed. For the medieval builders, geometry in design was a tool used to structure ideas and aesthetic impulses or perhaps to incorporate into this work a meaningful system of symbols; it was the internal logic of the building that mattered more than achieving beauty or following the correct canonical models as was the case in Renaissance era.1 Geometry was used in Gothic architecture as visual tools for contemplating the mathematical nature of the Universe, which was directly linked to the Divine, the architect of the Universe as illustrated in the famous painting of God the Geometer (Austrian National Library, Codex Vindobonensis 2554). To seek these principles would thus be worshipping God. The 1390s- Constitutions of Masonry or The Regius Poem opens with: "Here begin the Constitutions of the art of Geometry according to Euclid."2 Regardless of the accuracy of this document, the medieval masons clearly understood that the science of Geometry that they used was received from its inventor: Euclid. The medieval geometry of Euclid had nothing to do with the geometry that is taught in schools today; no knowledge of mathematics or theoretical geometry of any kind was required for the construction process of medieval edifices. Using only a compass and a straight-edge,3 Gothic masons created myriad lace-like designs, making stone hang in the air and glass seem to chant. In a similar manner, although they did not know the recently discovered principles of Fractal geometry, Gothic artists created a style that was based on the geometry of Nature, which contains myriad of fractal patterns. Architectural theorists Nikos Salingaros and Christopher Alexander believe that buildings must convey languages, among them are pattern language and form language; the former is the basic system for the design of any space, while the latter is what makes the former unique and beautiful; patterns are general and consistent throughout certain style, while forms are local and changeable from one building to another.4 Applying this to Gothic architecture, one may say that its general features, like pointed arches or high spires, are pattern language, while the specific design of each building and how these patterns came together is the form language. Salingaros also writes that, with the elimination of the ornaments and details within the range of scales -5mm to 2m or thereabouts- which corresponds to human scale, the dialogue between architecture and human beings is also removed.5 Based on this, the paper assumes that the Gothic cathedral, with its unlimited scale, yet very detailed structure, was an externalization of a dual language that was meant to address human cognition through its details, while addressing the eye of the Divine through the overall structure, using what was thought to be the divine language of the Universe. It discusses the hypothesis that geometry was used in the Gothic style to reproduce forms and patterns that reflect this dual language. In doing so, master masons distinguished between the abstract overall proportional lines of plans and elevations (form language), and the organic ornamental patterns on walls, ceiling, openings, and pavements (pattern language). It is suggested here that Euclidian geometry was employed for the, usually invisible, proportional or working lines of the 3 Lon Shelby, Gothic Design Techniques, 1977 : 82–83. 4 Nikos Salingaros, Twelve Lectures on Architecture, 2010: 26. 5 Nikos Salingaros, Architecture, Patterns, and Mathematics, 1999: 61-72. former, which are perceived only by the designer himself or by analytical view of the drawings with a mesh of imaginary lines; while Fractal Geometry, was used for the visible details of the latter, at which the worshipers can gaze and wonder about and may establish a "visual dialogue"; the former is to address the eye of the Divine, while the latter is to address the earthly eye of humans. This paper will test this hypothesis by finding the actual logic and context (proportional lines, decorating pattern, invisible line, visible details, etc), with which these two types of geometry were used in Gothic buildings, locating the settings (in structural elements, in plans, in decoration elements, …etc.), in which they functioned in these buildings. It also aims to find the b (...truncated)


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Nelly Shafik Ramzy. The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry, Peregrinations: Journal of Medieval Art and Architecture, 2015, pp. 135-172, Volume 5, Issue 2,