In our minds, many of us think of buildings as solid, stationary, immovable and hence unmoving, the stuff of “still-life,” if we were to use a term from art. As we come into the open space and see the whole cathedral for the first time, we ought to take note of a few basic first impressions. First of all, of course, is its size and mass. While clearly the largest building around, it is not the heaviest. Recall Stallings Hall, our static shoebox that seems much heavier and immovable than Holy Name. Marquette, in many ways seems much more rooted to the ground. 
 
Part of the effect of Holy Name is that it is an “active” building, in the sense that the links between its various parts do not allow our eyes to rest for any long period on any single element.  The most basic movement is from earth to sky. Also note that the nave or main body of the church seem to be constructed in three successively narrow tiers, or stair-steps with the widest and heaviest on the bottom, the narrowest and the lightest on the top. The effect is a type of pyramid, or perhaps an angular ladder or staircase, drawing our line of sight inward and upward. Also notice how that movement is reinforced by the many “arrows” that all work together directing our gaze upward. Their concerted effort also gives the building a sense of unity as well as motion.
So let’s start at the bottom and read the building as our eyes travel the visual path that the builders have set for us. At the lowest level where the building touches the earth, there are the arches of the cloister. Their effect is to lighten the base of the building and to serve as pointers to the first major symbol on our visual journey to the top of the building.
The tops of the arches point to the white stone decorations which mark the first of the building’s three levels: solid stone squares, each with a quatrefoil or four leafed design in its middle.   The squares are even grouped in fours.  Now if “four” is the dominant theme of the first level, what exactly does four stand for, what is the book of the cathedral trying to say? Four, not just in medieval Christian thought, but universally is a number associated with earth and physical creation.
No matter how diverse in their understanding of the physical world, cultures almost inevitably ascribe four cardinal compass points or directions as well as four winds to their models of the world. Many cultures posit four central rivers if not in their creation stories then in their maps. No doubt part of this universal symbolism is rooted in some basic human observations about geometric relations. Squares by their nature seem bounded, that is finite, not infinite. Moreover four is a non-prime number; it is multiple  (2x2) and hence reducible into lesser parts. Like the physical world, it is multiple rather than singular or unified. And as Pythagarus noted, four points are the first level at which the world becomes manifest in the pyramid, which is the first solid form in geometry. The point by itself has no substance. Two points create a line, which is infinite. Three points define a likewise infinite plane. But add a fourth point over the triangularly defined plane and the first solid (3-dimensional), material object generated by plane geometry is created.
 
Now look at the second or middle level, which looks like a battlement on a medieval castle.  Here the squares of the first level have been elevated and transformed in an interesting way. What one has here is not a series of solid squares but rather a series of alternating squares. Certainly there are the solid forms of the battlements, but between each of those is an equally defined “empty” or “spiritual” square. The middle level might well be seen as the meeting ground, the dialectic arena where the material meets the spiritual.
  
The third level presents its own numeric code. While the lowest level was dominated by fours, the tracery, or lace-like stonework that borders the roof, is defined by threes. The square has become the triangle. The quatrefoil, or four-leafed figure, has metamorphosed into the trefoil, or three-leafed design. The stone hard solidity of the quatrefoils, which were cared in relief, has given way to the spiritual unsubstantiality, for the trefoils are carved out, hollow forms like the hollow “spiritual” squares of the second level. 
Three, of course is a number associated with spiritual or divine. In contrast to four, which could be broken down into its factors (2x2), three is prime, in a sense an indivisible unity. Yet the triangles generate another visual effect as well. Unlike static squares, triangles are dynamic in that they do not exist solely on one register. Looked at from one perspective, there exist a series of triangular forms which are wide at the base and which taper skyward to a point. Yet seen from another perspective, the set is comprised of triangles whose bases are at the top of the row and whose apexes point downward, back to the earth. The optical illusion here is an important one because it is the key to another level of symbolism in the text of the building.
So far we have seen that the building replicates the somewhat abstract relationship of the material to the spiritual. We might even go so far as to see the stair-step form as a type of Jacob’s ladder connecting earth and heaven.As such, it is a map of the medieval cosmos which is the union of top and bottom, two elements that are distinct and yet inseparable, since one cannot have a top without a bottom and vice versa. Jacob’s ladder is, in fact, carved on the face of Bath Abbey, where again the commerce between heaven and earth is dual directional, angels being represented as moving in both directions. 
God, the Father, at the top of the ladder with approaching angel, front tower of Bath Abbey
An angel ascendinging the ladder looks back at us in a dual motion that  emphasizes the connection between Heaven and Earth
 A descending angel. Notice the difference between the postures of  the ascending angel and this one. 
 
Where then is the place for Man in this creation? For medieval man, society, itself, was divinely ordained, a microcosm of cosmic order. And so, if there are indeed three levels to this edifice, implicit in them is the order and hierarchy of medieval society. At the bottom are the peasants, the workers and toilers of the earth, who are symbolized by the fours in the first level. (Parenthetically, the same quatrefoil design is repeated inside in the pews, the seats for the common, ordinary worshipers inside the church.  Above the peasants are situated the nobility who are represented by the castle battlement. Like the “invisible” squares that exist between the more physical ones of the battlement, the nobles are worldly men, men of four, but elevated. Situated above the nobility are the final estate, the clergy who are symbolized by the triangles and trefoils. The optical illusion, the dual direction of the triangles, represents the dual function of the clergy who, like Jacob’s angels, are to help bring the divine to earth (the downward pointing triangles) and to lead men to heaven (the upward pointing ones).

The building then is an active and, above all else, an ongoing dialogue between three and four. In that sense it is a portrait of the act of spiritual becoming. Nowhere is this more evident than in the tracery of the two rows of stained glass windows, which decorate the nave. The first row is situated immediately between the first and middle levels, between the fours of the peasantry and the battlements of the nobility. 
The pointed arches of the windows again serve as arrows directing our vision upward to the next level. Looking closely at the apex of the pointed arch, we can detect a replication of the quatrefoil theme. The figure, however, has started to mutate as it ascends the building. It has kept its essential form, but it has rotated becoming an “x,” possibly a Greek “chi” in its new orientation. Just below it are a host of variations on the quatrefoil theme. 

Now let us look at the widows that join the middle level of the battlement to the highest level of the clergy with its triangles and trefoils.  

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              Not surprisingly, the quatrefoil at the tracery’s apex has become further transmuted. Not having yet reached the top level of the triangles, the figure has remained a quatrefoil, but a very interesting transformation is taking place before our eyes. The quatrefoils no longer have the rounded leaves of the first level or of the lower windows. Instead, the leaves have begun to become elongated and quite pointed. In short, they are beginning to take on the form of the trefoil leaves. The windows, then, neither solid stone nor open air, capture the metamorphosis of the one into the other. And it’s a joining captured remarkably in the stone decoration that adorns the sides of vestibule on the lower west side of the nave.  
Here situated between the lowest and the highest levels, we find the squares of the lowest level, but they are formed by the joining of two equilateral triangles, each containing a trefoil, but not having reached the third level, the trefoils are solid, like the relief quatrefoils of the first level. Closer to the bottom than the top, they are heavenly forms made manifest and hence substantial in the material world. Visually, threes and four come together to form a complete unit which in keeping with medieval number symbolism may be read as either 7 (3+4), a number signifying the cosmos which is made up of spirit and matter or 10 (3+3+4) a number of completion and perfection. 
         Interestingly, while the figures on the side of the vestibule are square, the same joining of the triangles in the front forms not squares but rhombuses which point upward to the church’s tower, an area which we will see is a representation of the perfection ("tenness") of Heaven.

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