Building Chartres Cathedral - a laboratory with Templates, String, and Geometry

"The construction of the Gothic cathedrals, such as Chartres, poses a number of questions. As a consequence of their presuppositions about distinctions between science and technology and the nature of theory and practice, many authors answer these questions in a way that makes the process seem mysterious and radically different from "modern" construction and design. What are the facts?

Over one and a half centuries, a population of 2.5 million people built 50 major religious buildings, 3,500 churches, numerous abbeys and retreats, military works, palaces, and houses. But not only were the Gothic cathedrals huge, complex, and ubiquitous, they were structurally radical and innovative, combining great height with thin walls and huge windows. (...) The question "How were they built?" is not a simple technical matter but complex and multifaceted, with political, social, religious, geometrical, economic, aesthetic, organizational, communicational, educational, and constructional aspects. (...)

The construction of the cathedrals can be demystified if the Gothic cathedrals are conceived as sites of experimental practice: literally as laboratories. (...) Laboratory-based procedures for the transformation of nature into accounts can be generally described as manipulable system. A key element in the creation of a manipulable system with respect to the construction of the Gothic cathedrals is the template. 

A template is a pattern or mold, usually outlined on a thin piece of wood, that a stonemason uses to cut a stone to a particular shape. This small item of representational technology has much of the power of a scientific theory; it manifests the integration of science and technology and theory and practice, and it is a solution to the central problem of how knowledge was transmitted. It was the use of templates, along with constructional geometry and a relatively small range of simple tools -compasses, straightedge, and string- that, in an experimental context, enabled the construction of extremely high, radically innovative buildings without a common system of measurement and, in the early Gothic period, perhaps without drawn plans and without continuity of architects or design. In the later part of the cathedral-building period (after 1225, TN), the use of plans became commonplace, and the role of master mason changed to that of architect. (...)

Chartres’s style cannot be explained as the result of a coherent Gothic aesthetic or even in terms of gradual transition from Romanesque to Gothic. Altogether there were nine different contractors or master masons who took between 25 and 30 years to build the cathedral in 30 distinct campaigns. There were 13 major design and structural changes in that 30-year period, but there was no overall designer, just a succession of builders. Chartres was the ad hoc accumulation of the work of many men. (...)

The achievement of the order of complexity and structural innovation involved in the construction of the cathedrals required a high degree of precision in the production of the stones and larger numbers of workers as well as types of workers. These factors create organizational difficulties that turn crucially on a fundamental problem: communication. Knowledge and instructions had to move among many participants. (...) In addition, knowledge had to be transmitted between sites and across successive generations of masons. (...) The building of all the churches and cathedrals in the Paris basin in this period tended to be conducted in short campaigns. (...) The erection of scaffolding, centering, and roofs made for delays in the cutting and laying of stone. The cycle of fund-raising through donation and tithing followed by expenditure also made financing a discontinuous process. (...)

In addition to the power to organize large numbers of workers, templates have the power to allow for great exactness of stone cutting and enabled a stable, enduring, and coherent structure, despite a discontinuous process and radical design and structural changes.

In the absence of rules for construction derived from structural laws, problems could be resolved by practical geometry using compasses, a straightedge, ruler, and string. The kind of structural knowledge that is passed on from master to apprentice related sizes to spaces and heights by ratios, such as half the number of feet in a span expressed in inches plus one inch will give the depth of a hardwood joist. These rules of thumb were stated as, and learned as, ratios. (...) The sort of geometry that is required is not that of Euclid; rather, it is a set of rules for deriving ratios and proportions through the division of squares and circles using compasses (...) Essentially, (this "constructive geometry", TN) enables a dimensionless analysis precluding the need for a common measure. (...)

It seems highly likely that the development of the theoretical laws of structural mechanics had its beginnings in the very process of their application, in building the cathedrals and schools in which scholars, monks, and masons were trained. (...)"

This blog quotes extensively partly rearranged sections from The Ad Hoc Collective Work of Building Gothic Cathedrals with Templates, String, and Geometry by David Turnbull, published in Science, Technology & Human Values · July 1993, source academia.edu; illustration shows a 13th century drawing of a treadwheel crane, source Wikiwand, Public Domain.

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