THE PRINCIPLE OF HOPE

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The church masons' guilds or architectural utopia in actual construction
Painting and writing can prepare the house, and overplay it too. Only the effort of building, the actual constructive effort, causes us to be inventive in a durable way. Ce
qu'il n'est pas formé n'existe pas,* and not just Being but also the utopian substance grows with formation, if it is a shaping one. This is all the more unencumbered as
the dream in the case of major actual construction, instead of vanishing in the face of technology, uses it for its advancement. The intention of the old church masons'
guilds also becomes important for this, which again means the image of the building which guided them as a perfect image in the work itself. The Gothic church masons'
guilds worked, as the Egyptian ones did long before, according to certain secret ‘rules’. Of course, as far as the canonical essence in the church masons' guilds is
concerned, we must distinguish between their secretiveness and the secrets they actually believed in. Undoubtedly a lot of mere tricks or dodges were also kept
concealed; thus they looked strange without being so. Likewise much of this kind of code, and of mere trademark, is to be found in the professional masonic symbols,
and also in the so­called basic figure used by the masons' guilds. The masonic symbols were granted to individual journeymen and, alongside any other meaning they
may have had, served to sign a work. The basic figure on the other hand, also called the ‘just basis of stonemasonry’, served among other things as a model to resolve
in practice to some extent proportions which arose and were incommensurable at that time, such as those which led to the irrational numbers √2 or √3. These ratios
already appeared in the diagonal bisection of a regular triangle or in boring a cube at an angle along its body­diagonal (the edge and body­diagonal of a cube have the
ratio 1:√3); but such irrationalities were a sealed book even to the theoretical mathematics of the Middle Ages, which was stagnant anyway. Thus the ‘just basis of
stonemasonry’, alongside other things which it signified as well, overcame this with a certain professional practicality. Which consequently, in a description hedged by
clauses, was to remain a trade secret and in this respect by no means contained ‘rules’ of a canonical architectural perfection. The late Middle Ages even imparted a
good deal of practical masonic mathematics in print; as in the ‘Büchlein von der Fialen Gerechtigkeit’, a collection of mechanical formulae. But of course: apart from this
kept or betrayed trade secret the Gothic masonic guilds explicitly
* ‘What has not been formed does not exist.’