WHEN PAUL DE MAN ASSERTED that history was composed of texts not events(2), he drew attention to the way in which a few moments out of trillions of possibilities are selected, ordered, and interpreted to explain the past or to map our location in the present. In the spirit of the PBS series Connections, one may weave far-flung links between, say, the printing press and the rocket or medieval monastic life and the contemporary electronic highway while remaining aware that the tale is an act of authorial magic that transforms caprice, luck, and intention alike into fluid narrative. Today, my son visited Saint-Peter's in the Vatican--he didn't climb up into the dome, but saw the Pieta. One day he or another writer may choose to remember this one afternoon as filled with disappointment (the unclimbed dome), pleasure (the Pieta) or new horizons (the Swiss Guards as a career choice). But however 1 July 1996 is chronicled, original events lurk behind and between the words.
In 1262 pope Urban IV set about erecting a church to his patron saint and a shrine to honor his birthplace in the city of Troyes, France. An aggregate of ephemeral 'events' including real estate purchases, stone carving, and arson went into the making of the structure which we can see to this day. This brief notice offers a preliminary explanation of one of the most important, yet unrecorded activities of the architectural process: the design of the building's plan. When I began my analysis of Saint-Urbain, I pursued a definitive description of the way the church must have been designed. What I have found instead is an architectural Rashomon. As in Kurosawa's cinematic masterpiece, the basic facts are clear: the plan is composed from a lucid scheme of squares, octagons, and rectilinear modules. It is in the way these geometric facts happened and how the figures fit together as a dynamic sequence that multiple possibilities of thought and action emerge. Not only rules of craft, a mason's training and skill, but also the intervention of the patron and the site shaped the performance of the design. Encoded into the 'text' of Saint- Urbain's plan and the shape of its spaces are the conception, the debates, the decisions, the meaning and the making of the church.
Beginning from the outside in
On a mild fall day in 1262, a master mason strides onto the cleared worksite with a parchment plan in hand. The church is a tight fit here in the middle of the city he tells his oldest apprentice. With the Grande Rue on the north side and the Rue Moyenne running along the south flank, I had to start the design from the practical consideration of available space. We've also had to watch it on the east since pope Urban appropriated some land from the good nuns of Notre-Dame-aux-Nonnains and I hear they are still not happy about this project. But I think I've been able to satisfy everyone: the church will not clog the two main city streets which will please the merchants, it sits nicely in the parcel of land the Pope's agents have purchased. The length and width of the church are based on squares, ad quadratum. It will be easy for us to lay out and will be quite beautiful We should have the first couple of steps done by lunch, so let's get to work...
A square (ABCD) is constructed using the available distance between the two city streets (approximately 37 meters per side). Rotating the diagonal of this square (AC,BD) establishes the length of the entire building ( 52.35 meters at AE and BH). A second 37-meter square (EFGH) is laid out from the end point of the diagonal (fig.l). These two overlapping squares fix the alignments of the west facade buttresses (EH), the eastern edges of the choir salients (AB), the inner faces of the lateral porch buttresses (AE,BH), as well as the axes of the eastern piers of the nave (CD) and the western piers of the choir (FG). The center of the plan can be found easily.
As the next logical step. the Saint-Urbain master inscribes a pair of squares (JKLM, NOPQ) within the first. In the choir, its 26.175 meter sides define the exterior surfaces of the diagonal walls of the main apse and lateral chapels (KJ,KL). These squares, turned forty-five degrees and aligned with the eastern and western limits of the site frame the body of the church. In short, the setting out of the exterior package of the papal shrine unfolds from the realities of its crowded urban location.
Urban IV, residing in Viterbo, follows the progress of his chapel with interest and growing satisfaction. A harmoniously proportioned edifice has been planned for the site of my father's humble shoemaker's shop in the heart of bustling Troyes and those formidable nuns of Notre-Dame have acquiesced to this worthy endeavor with remarkably little grumbling. Let my mason proceed with the internal details of the plan, the pontiff muses. Time to ask Thomas Aquinas's advice about the subjects of a glass program devoted to thc Corpus Christi and to see if he might also have time to compose an appropriate liturgy....
The overlapping squares JKLM and NOPQ, laid out as the second step of the operation, create a smaller square about the center of the plan (MROS: 15.33 meters per side). The inscribed square TUVW, with a side of around 10.85 meters comes close to the square of the crossing measured to the center of the piers (average 1O.58 meters)--the error is some 2.5%. Extending the lines of the crossing out to the great squares fixes the spatial corridors of the nave and transept.
Next, the diagonal of half the crossing square (XV) is rotated to form TY whose segments TU and UY (6.71 meters) are in a golden section relationship to one another. UY defines the approximate width of the aisle.
The crossing and aisle dimensions (as built: VU=10.58 x UY=6.54 meters) are used to construct a rectangle (bl). This golden section unit is repeated in each transept arm (b I, b4, their exterior porches (b3, b6), and the lateral choir chapels (b2, b5). Once the central vessel supports are designed, the intermediate aisle shafts will be placed on the axis of the arcade span.
Urban IV, residing in Viterbo, follows the progress of his chapel with interest and growing satisfaction. A harmoniously proportioned edifice has been planned for the site of my father's humble shoemaker's shop in the heart of bustling Troyes and those formidable nuns of Notre-Dame have acquiesced to this worthy endeavor with remarkably little grumbling. However, Urban is too busy worrying about Manfred's armies, finding French military aid, and the fall of the Latin emperor in Constantinople to give serious thought to planning details of Saint-Urbain. My nephew, Cardinal Ancher, assured me that I hired the best master mason in France, sighs the weary pontiff. I'll pray he creates an inspired building...
In this scenario the interior design of Saint-Urbain unfolds out of a sequence of inscribed squares (S3-S6). The fifth square (S5: 9.25 meters) in the series corresponds closely to the width between the buttresses of the central portal of the west porch. However, it is the sixth square (S6: 6.54 meters) that generates the interior spatial relationships. Set in the center of the plan, the diagonal from the midpoint of one side is rotated to establish a new line (TU) that is used as the dimension of the crossing square. Extending the lines of the crossing demarcates the width of the central vessel and the transept.
Once the crossing square is laid out, the aisle could be generated as in the mechanical version (see figs 4.5). Its width could also be determined by simply extending the side of the crossing ((TU or VW) by the distance of a side of S6 (6.54 meters). This alternative reveals an approach that is based to a greater degree on the repetition of a module.
The interior unfolds--the symbolic generator
Urban IV, residing in Viterbo, follows the progress of his chapel with interest and growing satisfaction. A harmoniously proportioned edifice has been planned for the site of my father's humble shoemaker's shop in the heart of bustling Troyes and those formidable nuns of Notre-Dame have acquiesced to this worthy endeavor with remarkably little grumbling. But now, muses the pontiff: the real act of architecture is at hand, one that will turn a mere pile of stone into a celestial structure. As my mason and I agreed, sitting squarely in the center of Saint-Urbain will be perfection...
At about 10.58 meters per side, the crossing square is almost exactly 36 Roman feet or .294 meters. Thirty-six is, of course, six squared which, if you know your Augustine, is the perfect number--both the sum and product of its factors. As he writes in The City of God:
'The works of Creation are described as being completed in six days, the same formula for a day being repeated six times. The reason for this is that six is the number of perfection... For six is the first number which is the sum of its parts, that is of its fractions, the sixth, the third and the half; for one, two and three added together make six...(T)he theory of number is not to be lightly regarded, since it is made quite clear, in many passages of the Holy Scriptures, how highly it is to be valued. It was not for nothing that it was said in praise of God, "You have ordered all things in measure, number and weight."'3
Lay this 36 foot square out at the center of the plan. Rotating the diagonal (XZ) from the midpoint of the east or west side of the crossing square will yield the aisle dimension. This is followed by the sequence described above at Figure 4.
Three explanations of the way in which the main features of Saint-Urbain's interior might have been generated (the apse geometry will be discussed below): each involves elementary manipulation of the same units. However, the apparently minor differences in the sequence of geometrical events reveals crucial differences in the conceptual orientation of the design.
In the first alternative, the 'mechanical' approach (figs. 3-4), the exterior and interior of the building, derived from a single sequence of rotated squares, are conceived as an intimately related continuum. Design advances first from the 'outside in,' followed by steps that unfold from the 'inside out.' The crossing is not the cradle out of which the plan emerges but rather the byproduct of the geometry of the exterior. While this method appears to be the least accurate of the three options, small deviations from the measurements of the extant building that occurred in laying out the great squares of the exterior would account for the dimensional inconsistencies.
The 'square sequence' (fig. 5) generates dimensions and spatial blocks from a single square (S6) by means of a consistent procedure, the rotation of diagonal lines to produce golden section relationships. Stephen Murray has proposed that the golden section ratio of main vessel to aisle dimensions encodes a diagram of heaven into the plan at Amiens Cathedral.(4) At Saint-Urbain, the method of generating the plan out from the crossing becomes a procedural expression of the subtly centralized character of its basilican plan. Located at the exact center of the plan with the nave and the choir balanced on either side and at the intersection of the four arms, the crossing is presented as the spatial focus of the church. This procedure, although extremely accurate in its relationship to the actual building, involves the most steps and an awkward transfer of key dimensions. While, to my mind, the square sequence does not offer a compelling design model, it does highlight the fact that Saint-Urbain's plan could be generated by a variety of methods. Further, as we shall see below, squares 5 and 6 were involved in the design of the apse and the west facade portals indicating that the rotational sequence may well have formed a geometrical subtheme in the generation of the plan. We assume that the master mason knew or discovered the most elegant, economical solutions to design the building's plan. This, however, must remain our own leap of faith.
Exterior and interior do not issue from a continuous geometric sequence in the 'symbolic generator' explanation (fig.6) although they are connected by golden section relationships. The plan unfolds from the center, the crossing, in a series of steps that operationally is identical to the 'mechanical version'. Setting the plan upon a symbolic foundation opens a door onto a further constellation of hypothetical historical tableaux.
First, the plan expresses implicitly the 'patron's share' in the conception of the church as it reveals explicitly the 'master mason's share' in devising geometrical operations that brought the design into architectural reality. Just as Suger's direction to 'harmonize the new with the old' may have set the design of twelfth century Saint-Denis in motion, Urban IV might have hoped aloud that his chapel's geometry would reflect that of other divinely inspired structures: the 36 Roman-foot dimension of the crossing, in addition to the square of six, is also one-fourth of 144, a dimension used, as in the Palatine Chapel at Aachen, as a signifier for the Celestial Jerusalem. Second, if the 36-foot crossing was deliberately chosen, then the pontiff himself and his mason may have had conversations that ranged over the streets of Troyes, craft rules of design, historical models for the project, and the theology of numbers. Time-consuming correspondence between Italy and Champagne or communication through agents and intermediaries seems far less plausible than a face-to-face interview in Viterbo. Third, the designer reasonably would work out the connection beween the two geometric systems-the outer envelope based on specific physical parameters, the interior developed from a dimension chosen, at least in part, because of its symbolic value-in sketches and drawings.
The 'symbolic generator' is a theoretical house of cards built of fictionalized conversations, imagined decisions, and plausible geometry. Nevertheless, in my opinion, it offers the most satisfying story of the design of Saint-Urbain, for it generates an architectural narrative that is active, complex, and human. As Simon Schama writes, 'In its original Greek sense the word " histona " meant an inquiry...But to have an inquiry, whether into the construction of a legend or the execution of a crime, is surely to require the telling of stories. And so the asking of questions and the relating of narratives need not, I think, be mutually exclusive forms of historical representation. And if in the end we must be satisfied with nothing more than broken lines of communication to the past...that perhaps is well enough to be going on with.'(5)
The Four Octagons
Figure 7
The series of rotating squares and golden section rectangles establish the proportions of the major spatial blocks and fix the locations of the mural envelope and interior supports. The second square in the sequence closely approximates the alignment of the polygonal walls of the apse and flanking lateral chapels (fig.2). The apse itself is designed around five sides of an octagon.
To find the geometric center of the apse, an arc whose radius is one-half the diagonal of the sixth square (4.63 meters) is swung eastward from the center to intersect with the centerline of the plan (fig.8). The octagon which defines the inner wall surface of the apse could be generated from a circle whose radius is 5.29 meters, that is, one-half of a side of the crossing square: the diagonal of the octagon, 10.58 meters, equals a side of the crossing. A subtle, but tangible geometrical connection is thus created between the center of the building and its liturgical sanctuary.
Remarkably, an identical geometry underlies the dispositior of the transept porches and the central portal of the west facade (fig.7). Transferred to the exterior of the transept, aligned with the north-south axis of the plan and the line of square one (AE or BH), the sides of the 'apse' octagon mark the inside faces or the buttress salients of the porch and its center locates the apex of the trumeau between the two doors. The placement of the slim free-standing porch columns is found by inscribing a square within the octagon. In the central portal of the west facade, the octagon, laid on the western line of the site (EH) and aligned with the east-west axis, appears to dictate the length of the west bay of the nave while its side fixes the interval between the free-standing porch columns.
Saint-Urbain's west, north. and south porches. as revealed by the geometry, are neither additive nor independent features of the plan. The placement of the octagons pulls the polygonal and projecting spaces on the cardinal axes in toward the interior: conversely, the apse and porches become coherent extensions of spaces which unfold outward like the petals of a flower. Geometrically tied to the crossing about which they orbit, the four octagons superimpose a cruciform figure on the basilican plan. The insistent centrality identifies Saint-Urbain not only as a shrine, a memoria to martyr saint and papal patron, but likely represents it as a shrine to the Corpus Christi. Devotion to the body of Jesus was a matter of intense personal interest to urban IV who promulgated the new feast of Corpus Christi in 1264 and the sacrifice of Christ forms the central theme of the stained glass program of the apse.
Like the main apse, the five-sided chapels which form the eastern termination of the aisles are based on a regular octagon (fig.8). Further, the circle that circumscribes the octagon bears the same geometrical relationship to the aisle as the apse to the central vessel: its radius (3.27 meters) is half the width ofthe aisle and the diagonal of the octagon (6.54 meters) equals the aisle width. The center can be found through a purely mechanical process by stretching the radius to the east-west axis line of the aisle from the intersection of line FG and south edge of block b2 (figs, 4,8)
The Saint-Urbain designer conceived the three portals of the west facade as exterior reflections (or anticipations) of the interior (fig.9). Again, geometry provided the connections as it also served as the vehicle for variety. As we have seen, square 5 in the rotational sequence and the side of the octagon set the width of the central portal and the spacing of its columns respectively. The ratio of the depth of the entry (2.48 meters) to the side of the octagon (4.05 meters) closely approximates a golden section.
The geometry of the deep lateral portals is considerably more complex, less transparent (fig.9). I have built the following solution on the assumption that the Saint-Urbain master, as he did throughout the design, locked these entries into the plan as a whole through the repetition of or geometric variation on other polygons and dimensions. First, the octagon of the lateral chapels is laid on the western line of the site (EH), the five sides determining the depth of the portal and wall. Second, a perpendicular line (de) equal to the side of the apse/ central portal octagon (4.05 meters) is constructed from the midpoint of the east side of the octagon. This line's end point (.225 meters east of EH) not only serves as the center for the construction of a series of geometric forms that compose the portal but also marks the flat face ot the facade salients. A square locates the inside surface of the lateral walls and the exterior plane of the doorway wall. At 5.70 meters per side, it was surely derived from square 5 (the central portal width) through the construction of a golden section (fg). Thus, the dimensions of the central and lateral portal openings maintain the relationship of the nave and aisle spaces. The distance between the side of the crossing square (10.58 meters) and square 5 (9.25 meters) yields the thickness of the west facade salients. Finally, from the same center a hexagon is laid out to position the angled walls of the portal. Anchored to the axes of the flanking buttress salients, the hexagon can be inscribed in a circle with a radius of 3.50 meters. By using the hexagon, the Saint-Urbain designer at once created polygonal entries that echoed the chapels to the east, yet achieved a subtle independence. This same love of rich formal diversity within a tightly woven framework will characterize his tracery compositions.
Several salient points emerge from the analysis of the plan of Saint-Urbain concerning the way in which the building was conceived and executed. The entire design started from the physical limitations of the building site. The master mason then used geometry as a tool to control the overall exterior dimensions. In the short, the body of the building did not unfold from a single key dimension or geometric figure, but was formulated as a whole unit whose internal dispositions were defined through subsequent steps. Once the envelope was set out, the way was open for meaningful patronal input.
At first inspection, Saint-Urbain appears as an unremarkable basilican plan whose three aisles terminate in polygonal apses similar to Saint-Lazare, Autun or Notre-Dame, Dijon. Only in mapping the geometry does the cruciform personality of the design emerge. The unusual combination of longitudinal and centralized plans suggests that Saint-Urbain embodied Urban IV's specific vision. We can well imagine this widely-traveled, highly educated pontiff, a man who 'after his dinner...was fond of making (learned men) sit round him and of listening to them discussing different questions,'(5) meeting with his master to describe buildings he had seen in France, in imperial Germany, in Rome, urging him to find the means to accommodate both the requirements of the liturgy and the symbolism of the Cross. He might have proposed the dimension of the crossing at the heart of the plan, one of the few distances that can be translated credibly into whole feet.
For his part, the architect doubtless used plan drawings to effect the precise integration of pragmatic constraints, patronal demands, and craft practice. Yet despite its semiotic and symbolic opulence, the design can be translated easily from parchment to building site for its setting out requires nothing more than the construction of squares, octagons, and hexagons and the rotation of diagonal lines. Space and structure were generated together: pier placement and wall thickness appear to be the by-product of the geometric matrix, not the result of an independent system.
Although I have offered three alternatives for the design of Saint-Urbain, in truth these solutions are not mutually exclusive. As we have seen, the 'symbolic generator' can be elaborated by means of the physical steps of the 'mechanical version' and the 'square sequence' appears to be a necessary prologue to the generation of the apse and west portals. Individually, each possibility offers us a perspective of the process by which one remarkable building of the thirteenth century was given form and meaning. Together, they tell us a human story by bringing us closer to the actions, words, and thoughts of thirteenth-century individuals. We can now hear more clearly that after-dinner conversation between Urban IV and his master mason on a fall evening in the papal residence in Viterbo.
I am so glad that you have arrived safely, my friend Although I know you must be weary after the long journey from Troyes, my enthusiasm for this project simply will not wait until morning.
Your Holiness, it is my honor to know your will for this chapel. Have you seen the portrait that I have prepared? Several houses remain to be demolished, but enough has been cleared to measure the length and breadth of the building. It works out that the edifice is 178 by 126 Roman feet so it just fits into a piece of land that is 8 perches long and 6 perches wide.
My agents, Jean and Thibault assure me that all of the houses will he purchased in the next months. Heaven knows I have given them enough money. Anyway, as you know from my letter of this past May, I am following the example of Saint Gregory who built a chapel, now called S. Gregorio Magno, at his villa on the Caelian hill in Rome. My recent predecessor, Gregory IX did likewise at Agnani and it seems to me a worthy undertaking. Because the church will have only twelve canons and a dean, it does not require numerous altars and chapels. In my many voyages through this world I have observed that churches of the glorious martyrs are built in the shape of squares or circles or crosses. I am especially interested in this idea of the cross for my church will not only honor saint Urban and the memory of my birthplace, but will also remind the faithful of the sacrifice of Christ and the sacrament of his body. When you go to Rome, Ancherus, my nephew who is the cardinal of Saint-Prassede, will show you S. Stefano Rotondo, a venerable and magnificent structure, which is both a circle and a cross. And last, so that these mute shapes will have meaning that elevates the soul, I would like the perfect number, six, to occupy a pre-eminent place in your plan. Now, of course, I am no master in the art of building, but I do hope that my ideas have merit.
Reverend father. I have no doubt that geometry will show me the way to transform our discussion into stone and glass. With compass and straight edge, I shall invent a plan worthy of your vision of a church that will resemble one of the chambers of the City of God.
1. The conclusions presented here concerning the design of Saint-Urbain in Troyes are the result of an NEH sponsored research grant undertaken in collaboration with Linda Neagley of Rice University and with the assistance of graduate students from the University of Michigan. the University of California, Berkeley, and Columbia University. Surveyed during the summer of 1992, Saint-Urbain, along with the fourteenth-century abbey of Saint- Ouen, Rouen and the fifteenth-century Saint-Maclou, Rouen which compose the broader parameters of our study, will offer the opportunity to compare the designs of three structures located in two distant cities, embracing a 250-year time span, serving distinct functions (shrine, monastic church, parish church), and representing strikingly different plan types. The geometric analysis was carried out at Mount Holyoke College using AutoCAD version 13. My thanks to Peter Zieja, project engineer, for his patient mentoring and good humor.
2. John Casey. In the same madhouse, review of Wendy Steiner, The Scandal of Pleasure, (Chicago, 1996) in The Times Literary Supplement, June 14, 1996: 9.
3. Saint Augustine, City of God, trans. Henry Bettenson, London, 1984: 465 (book xi, chapter 31).
4. Stephen Murray. The Cathedral of Notre-Dame of Amiens, Cambridge, 1996: 42-43.
5. Simon Schama Dead Certainties: unwarranted speculations. New York. 1991: 325-326.
6. Horace K. Mann, The Lives of the Popes in the Middle Ages, XV. 1929: 145.