 Today, we're going to continue talking about Gothic architecture. There's lots to talk about because Gothic architecture is not simply a local phenomenon in France, but it's an international style. We have Gothic architecture happening all over Europe. Today, we're going to focus our attention on Gothic architecture in the region around Paris, which is called the Île de Fonds. I have this map up here just to show you the difference geographically in where we find large clusters of Romanesque architecture and where we find large clusters of Gothic architecture. The little red dots represent major Romanesque sites. Here's Cluny, that huge monastery that really organized commerce, trade, and the economy in France and in much of Europe throughout the Romanesque period. And here's Paris up here in blue. The area around Paris called the Île de Fonds is the area where Gothic architecture tends to cluster. These little crosses are Google Maps representation of where a Gothic site is. And you can see almost nothing down here in the area around Cluny and tons and tons of stuff in the area around Paris. And these are some of the specific sites, some of which we looked at last time and some of which we're going to look at today. Paris, once again, famous. Here's Saint-Denis, where we had our first Gothic church. I don't know why it's not on the map, but right about here we have Laurent, which we also looked at. So we've looked at these three Gothic churches. And on this map, we have locations for a couple more. Ah-ha. I love to say these. Ah-ha. Ah-myah. And Beauvais, which we'll look at today. And those really represent the high point of Gothic architecture. And when I say high point of Gothic architecture, we could go back to the discussion we had when we talked about Greek temples. We were quoting Le Corbusier, who says, the architect should proceed as the engineer. The type should be identified. The question should be asked. And once the question is asked in a clear enough way, then subsequent generations of architects can work on perfecting the type. And if you want to take that analogy to Gothic architecture, it works very well. You could say, what are the questions that are asked? And certainly one question is, how can the structure be dematerialized? Another question is, how can verticality be achieved? Another question is, how can structure become expressive of an architectural ornament, et cetera? And you will find iterations of these things happening again and again. So here's our friend, Party Skeleton. I always like to say hi to Party Skeleton every morning. And what is the point of Party Skeleton? Who can tell me what the idea of this slide is with the skeleton? OK, it shows the structural part of the building. Be more specific. What is the structural part of the building? OK, we have flying buttresses. Over here, we have them looking like buttresses. Over here, we have them looking like Party Skeleton. OK, somebody add to that. Yeah, it shows the verticality of the building. Good, and the verticality of the building, to a large extent, is achieved through the flying buttresses. What else is going on here? Yes? It shows how the weight's distributed. We have a load coming down. And instead of just having giant, massive buttresses holding up the loads coming down from the vault, we have a skeletal system, hence Party Skeleton, by the way. We have a system of ribs. We have a system of linear elements that begin to translate all those loads to points. And the benefit of that is the wall can go away. You can have this kind of skeletal cage, like Party Skeleton has no meat on his bones, but he still stands up in the same way Gothic architecture has really no wall to speak of. It's all done in this rib fashion. We used the word attenuated last time, which means stretched or lengthened. So attenuation is another nice word to use or to think about using when you talk about Gothic architecture. It's the idea that there might be something familiar, I don't know, like a vaulted structure. Let's say a Roman vaulted structure. Then you stretch it, like Raggedy Ann and Andy are stretching their taffy. Or I think this one looks particularly Gothic, doesn't it? This is somebody's sad little shoe with goo coming off of it. It looks exactly like this section through a Gothic cathedral, because this massive solid has been pulled into a tensile mode and it becomes arcuated and thin. If we take the zeitgeist argument of Heinrich Wöschlen that we discussed earlier, which I will succinctly summarize as Gothic people like things pointy, it's worth looking for a moment at what the representation of a human figure would look like. And this is an illustrated manuscript from the 14th century. The same notion of attenuation that we saw here with the gummy shoe is more or less also going on here. We have these people who have the proportions of a Barbie doll. That is to say, not proportions found in nature. Tiny little pinheads and incredibly lengthened bodies. And by the way, observe their footwear, pointy. We spoke last time about the emergence of Gothic architecture in the Church of Saint-Denis. This shift toward a different kind of architecture was provoked at Saint-Denis by some of the theories of Abbe-Souget, the head of the monastic order at Saint-Denis, who was really trying to find a way to symbolize God. And what did Abbe-Souget come up with? How do you represent the presence of God architecturally? Yes, light. Yeah, Souget felt nothing that you make as an image could represent God. And in fact, there were even biblical prescriptions against graven images. But somehow, if you could create a powerful feeling of light, that would be a way to express the presence of God, the emanations of power from God, and to make it palpable. And so you look at the Romanesque envelope of Saint-Denis, which is very much about the wall, very much about little punch windows perforating this continuous membrane, heavy membrane. And wow, look what happens in the Gothic transformation of that building. It's as if everything has become skeletal, like party skeleton. I think this is pretty instructive. If you just look at the play between these little columns over here, in a sense, the Gothic column is even more massive than, or let's say the Gothic pier because these aren't single columns, they're pier bundles, is even more massive than the Romanesque one. But notice how the Gothic pier is rotated so that your perception of it would be the thinnest part and then it folds back. So it's here in the Romanesque instance of Saint-Denis, the geometry of the piers reiterates the geometry of the nave. Here in the Gothic version, it's rotated at 45 degrees and appears even more slender. Also, I think what's really interesting is what happens to the mass of the wall. And you can see that pretty clearly here, where the wall buttresses are perpendicular to the enclosing membrane of the building. And it's almost the same kind of rotation that we saw with the piers, only even more dramatic. It's as if wall, which here is parallel to the nave and enclosing the nave, swings out and opens up space in between the pieces of pier. So you have really as much wall as you had in the Romanesque version. It's just that the wall is perpendicular. And when the wall is perpendicular, you then have the opportunity to inundate the space with a light, to inundate the space with this presence of God expressed through colored light coming through the windows. In both of these plans, the Romanesque plan and in the Gothic plan, you can see where the westward comes down. And how do we know where the westward is coming down? How can we tell where the towers are? Yes. Go ahead. Absolutely, the walls are really thick. The walls are really thick because they're supporting massive towers. So here you see the westward and the heavy towers. Here also you see the westward and the heavy towers. Look what happens to the chevet or the apps with its radial form. The Romanesque is closed. By the time we get to the Gothic condition, once again, you have really no wall at all. You just have open spaces between structural elements. It's really quite amazing. If Romanesque architecture had to do with punched windows in a wall, when the wall goes away, the window is simply the space between structure. And you get an altogether different effect. This is what Saint-Denis would look like. And I have to say, this is fake Saint-Denis. And it's the real Saint-Denis. But it's a Saint-Denis that has been elaborated over time. So if you look at the size of a clearer story here, that's not original to Abbey-Souget's church. That's something that got added. Last time, we also looked at another early Gothic church. And that was the Church of Laon, the Cathedral of Laon, which has the extraordinary ornamental program of cows, lots of cows, which I just adore. But you can see that the type of facade that's been suggested in Saint-Denis becomes clarified in Laon. And by clarified, I mean it's more systematic. And it's also more plastic. Let me go back to Saint-Denis. Here at Saint-Denis, we have these buttresses that begin to make three-dimensional, the surface of the facade. But the horizontal elements are really pushed back behind that. And you still read an architecture that's essentially a wall architecture. Little rose window gets punched in. A couple of pointed windows get punched in. But they become elements in the wall. The wall itself doesn't become completely activated. Already here just a few years later, by the time we get into Laon, it's almost as if the wall has become a weave-in. The wall has become this weaving together of horizontal and vertical elements. And if you had to say, where's the surface of the wall, you would be hard put to do that because the wall presents itself as having so many different surfaces. The wall is so much a kind of exploration of the thickness and depth, the plasticity of the wall surface. And some of that stuff gets, I think, exaggerated and amplified even by the way the towers are positioned. We noticed when we looked at the piers at Saint-Denis that they were rotated. So that they were at 45 degrees with respect to the nave. Here the towers are rotated so that the cows are at 45 degrees. And that just, it's kind of like architectural contrapasto. I mean, it kind of forces you to explore the other side of the building because you get this oblique view of the element that you're admiring. The plan of Laon is strange. We don't have a rounded apps here. It's one of these transitional works but they don't exactly know what they're supposed to do. But probably the most indicative element in Laon, in terms of representing this period of early in an untampered with way, Saint-Denis was tampered with in later centuries, is the nave wall. And when we looked at the nave wall, we saw something that is incredibly clear in its articulation, where it's a four-part division. We have this arcade at the bottom. We have this gallery or tribune up here. We have this little triforium here and then clear story windows. And it's so clear that you just have to love it. You can read it. You can read the articulation of parts of the hole really, really easily. But it also enforces a rather diminished height for the clear story. And finding ways to bring more light in is one of the ambitions. Back to the whole Corbusian question, you define the problem you want to solve. And like an engineer, you tackle it and you finally perfect it. So Laurent and Saint-Denis posed the problem of the Gothic and subsequent churches begin to refine it. For example, Notre Dame in Paris, which is also an early church, 1163, already takes the idea of the facade that we saw roughly stated in Saint-Denis and elaborated in Laurent. And I really think this is the most perfect Gothic facade. And maybe I think that because it's so reined in. It doesn't try to do things that take it away from the volumetrics of the church by adding porches or adding finials. It seems to be an architectural expression that's gained through subtraction rather than addition. So you look at the wall. And it's a wall of great plasticity. But it's plasticity through carving rather than adding. So this elaborate portal on the west work is scooped into the wall of the church. The elaborate rose window that spans between two structural ways is scooped into the church and so forth. So it really is a kind of perfect geometrical construct. But it's not simply a perfect geometrical construct because Gothic architecture is not really designed for your aesthetic appreciation. When Gothic cathedrals were being built, people didn't say, I want this one to be really pretty. Or I want people to come and say, this is darling. I'm going to have my picture taken here. Rather, Gothic cathedrals had to mean something. And one way they meant something was simply, let's say, visceral. And by visceral, I mean you get this gut feeling. It's not in your brain at all. It's in your body. When you walk into a Gothic cathedral, it's maybe 25 degrees cooler than it is outside because this building is like a cave. So your whole body transforms its sensory perceptions just by the quality of light and the quality of temperature. Then you look up and you see these vaults that don't seem to be supported by much. You kind of feel deranged and dazzled. And if you're a little peasant coming in from your mud hut and you walk into something that has these giant, soaring vaults, you would be truly of the opinion that only a miracle could make those things stand up. And the spatial qualities of the Gothic cathedral alone would clarify your faith. But also, in case you don't get all that, there's an elaborate sculptural program going on in these Gothic facades that will show you very explicitly scenes like The Last Judgment, where you know what kind of tortures will happen if you are a sinner, enthronement of Christ, or scenes like Adam and Eve. You can walk around a church looking at all the different sculptural elements, and you can get a pretty good instruction of the Bible. And you know these stories because you heard them in sermons, but you certainly never would have read them. On another level again, the form of the church encodes these complex meanings. Here's the facade of Notre Dame, which I say is darling and I want to be photographed near it. But it's also this map of a kind of scholastic order. We mentioned Thomas Aquinas on an earlier occasion. Here's his name down here. And he was a great scholastic philosopher who sought to find ways of really organizing and giving a kind of mathematical form to the cosmos. And in his categorizations and subcategorizations of elements, you can find a fairly strong correspondence in the way something like a Gothic cathedral is laid out. It is almost like a matrix. It is almost like a grid with different relationships that can be read in different ways across it. There are also other kinds of numbers going on here. Like when Notre Dame is being constructed, how big do you make it? Why do you make it that way? And part of it had to do with this desire to make visible on Earth certain things that are described in the Bible, like the Temple of Solomon. There are these complex measurements that recall those kinds of elements as well. So now let's move into a period that we didn't look at last time. It's really the High Gothic. It's the period when these ideas that are initiated and roughly sketched out in the early Gothic churches go farther and farther and farther. And you can probably see ways in which that transformation happens by looking at this slide, which shows you various nave walls. Laos, my favorite of all the Gothic cathedrals. I like Laos and the Vest because I'm so humble. Kind of short, turns out. Notre Dame, much bigger. Chartres, which we'll look at soon. Bigger again. Rhin, huge. Uh-uh, Amiens, even bigger. So on one level, the sheer verticality of these buildings, because they're drawn at the same scale here, is increasing in a rapid way. These churches are only a decade or so apart. They're not spread out by large periods of time. But in addition to the verticality of the building increasing, the wall is also becoming radically dematerialized. If you look at the condition of Laos with its four-part division of the nave and its relatively small, clear story windows, by the time you get to Notre Dame, there is a lot less mass. And the clear story windows are maybe twice as big. By the time you get to Chartres, the clearer story is almost as big as the arcade. The ability of the wall to simply become lantern-like and let light pour through the windows is increasing rapidly. And here, when we come to Amiens, it's kind of a miracle that the thing stands up at all. You have these spindly little columns and no wall, no wall, just nothing. And here again, here are a series of sections. Now we're just looking at Chartres and Amiens. Here you can see this kind of rush toward dematerialization that happens progressively from one church to the next. Compared to Amiens, Chartres looks clunky. We have these thick old buttresses. Look at that, pathetic. Look at Amiens. They doubled the buttresses. They made them thinner. This really looks like gum on the shoe, more than architecture to me. You might ask, how do you build these things? How do you finance these cathedrals? When we looked at the map of the Île de France, which is the name of this area surrounding Paris, we saw that there were a lot of these cathedrals being built more or less at the same time. And it's unbelievable. Where do you get the labor? Where do you get the materials? Where do you get the wealth to do it? And there was an increasing rise of the merchant class during the Gothic period. People believed that if they donated to these architectural campaigns, they could get indulgences and shorten their time in purgatory. And particularly in the case of Chartres, given to believe that laboring on the church would also buy them an indulgence. And so you're thinking, OK, I understand that the masons can labor in a profitable way on the church. But what about the lords and the ladies and the people with their pointy shoes? What do they do? And so at Chartres, one way materials were brought to the construction site was something called the cult of the carts. And the cult of the carts involved people, little princesses, little duchesses, little gentle people, strapping themselves to carts or strapping themselves to little sledges, pulling up chunks of stone, and walking up the hill like mules. So that was a way that materials came to Chartres. And Chartres was constructed in a ridiculously short period of time. We see here that the entire project of Chartres took about 25, 26 years, which is one of the fastest building campaigns of any church. St. John the Divine, for example, in New York City has been under construction for 100 years. And that's in New York City. The Sagrada Familia in Barcelona has been under construction for about 120 years. And that's in Spain. And these are people who have things like, I don't know, cranes and jackhammers and all kinds of technological devices to help them build the thing faster. But Chartres got finished in 26 years, which is unbelievable. Great-looking church, by the way. Here it is. And you might also wonder, well, why does it have lopsided towers? I would say that 26 years, it's enough time to get two ideas about towers going. Another reason that the towers are so different is that the present cathedral wasn't the first cathedral on the site. In fact, there had been an earlier Romanesque cathedral that was damaged by fire in 1194. And when a sacred relic of the Virgin was found in the ashes of the fire after they thought it had been destroyed, decided to redouble their efforts and construct a bigger cathedral. The South Tower, as we see it here, incorporates parts of the earlier Romanesque church while the North Tower is a more fully explored expression of the Gothic. Plus, there was nothing particularly necessary about symmetry. It wasn't as though they were striving to make these churches symmetrical. They were striving to represent very specific things. When Gothic churches get improved upon, it usually has to do with the fact that 19th century people knocked down the irregular tower and put up a matching tower. Because the 19th century thought that was the only way to go. Silly 19th century. 19th century was schooled in classical thought, schooled in the Ecole des Beaux-Arts, Desire for Symmetry and Balance. And so they tried to make Gothic cathedrals more perfect. So here's Schacht. It really operates at a geological scale. It is so much larger than anything around it. You can see it from five miles away. And people must have as a kind of pilgrimage destination that they strove to arrive at. And here is the plan of Schacht. You can see, unlike some of the other Gothic churches we looked at, like Notre-Dame and Saint-Denis, the transept here is more pronounced. We also have a elaborated chevet where radiating chapels begin to pop out. And here's the section. And it's got this characteristic section of almost like the wagon wheel thing coming on and through here. And the increasingly dematerialized nave with a strategy of making the clear-storey window, not singular but compound, that we have this method, it's called bifiori, puts the tracery together so that you get little, little inside of big with a little flower on the top. And that adds an interesting rhythm. It adds a kind of secondary bounce to the rhythm. And here's the effect of that increased space of the clear-storey window. It's a very different quality of light. It's a very different quality of building envelope than anything that we saw in the earlier churches. There's also a transformation in the vaulting here. At long, for example, we had six-part vaulting so that you had six different ribs coming together. And here we have four-part vaulting, which is a kind of tighter rhythm. Here's one of the things that I think is kind of interesting. These are buttresses, of course. And we know that on top of the buttresses, you wanna put mass to make them more effective in resisting the thrusts. But look at how this little buttress is terminated. It's not terminated by a little gothic guy, but it's terminated by a little classical guy. There's this little temple there. So all the little buttresses at Shaw have little temples on them. Adorable. The sculptural program of the door jams at Shaw is considered to be one of the most amazing of all the gothic cathedrals. Really high-quality work, really elaborate symbolism. And the kind of arrangement of things in geometrical structure that we saw on the facades also happens here, where there are various hierarchies of people and symbols and saints ranged out radially from the centerpiece. And just look at some of the carving. Really? Okay. And here's another place where saints are insinuated into the pier bundle. Once again, stretched, attenuated. Rhin cathedral really is much more perfect than Shaw cathedral. And one thing that makes rhin, I think, so effective, is the wall is almost completely gone. In Shaw, we saw the rose window at Rhin. The rose window completely fills up the space between two structural elements. And it gets situated inside of a pointed arch. So you have this kind of double system of super dematerialization going on here. Big arch, big rose window. And another thing is going on, too, in terms of the plasticity of the wall. Quite different from, say, Notre Dame, which got its effect through subtraction of material. Rhin is additive. You get this big porch. And this big porch pulls away from the body of the church and becomes a kind of freestanding screen. Not freestanding, but, let's say, it is pulled out and becomes autonomous. And even the portals become like little towers and begin to invade the space of the upper range of the building. This aerial perspective begins to show you the degree to which the building envelope of Rhin is dematerialized. I don't know how well you can remember these plans from one to the other, but the amount of wall in between the piers is becoming greater and greater and greater as it becomes more cage-like and more lacy. Fabulous drawing by Vialet-le-Duc of Rhin Cathedral. And notice that Vial, don Cor, had been to Rhin and he did some sketches there, just as he did sketches of Laurent. And we can see that he's here interested in this complex rhythm of the nave wall, of the multiple scales of elements. Probably with Amiens Cathedral, High Gothic reaches its apotheosis. It reaches its high point. And part of that is that this is the tallest Gothic cathedral that managed to stand up. Some got higher for a little while, but Amiens still stands to this day. So we have to give lots of credit to the architects of Amiens Cathedral. And we even know the name of the architect of Amiens Cathedral, at least one of them, because this was an ongoing building campaign that lasted quite a long time, but Robert de Lousage. So here's Amiens Cathedral. And in many ways, it's playing a lot of the same games that I was in terms of the facade. And these are hard, right? You look at Amiens and you look at La and you think these things are incredibly similar. One of my colleagues, Professor Doug Graff, claims that when he was an architectural student, the only way he could tell them apart was to remember what car was parked in front of each one. So I don't know, I don't know what that car is, so you better learn the facade. And I would say certainly one thing to notice in the case of Amiens is that there is a round window and the round window is not inside of the pointed arch window. Otherwise, the two facades are incredibly similar because both of them have this autonomous screen. Both of them are really, really cagey and really dematerialized, but the condition of the rose window is quite different in Amiens. Also, the plans are different, as we'll see quite soon. As an aside, when you have the test, I won't just give you one incredibly obscure image and say, I hope you can figure out what this is. Here's a picture of a nave, go for it, what is that? But rather, I'll probably give you something like a plan, a facade, and something else so that there'll be a lot of different kinds of images that you can use to help you understand what's going on. So here's the plan and the nave. And I think the plan of Amiens is a distinctive plan. You should be able to remember this one. It's distinctive in the same way that Notre Dame is distinctive. That is to say, you can remember the shape as the one that has the like, you know, who's number one? Amiens is number one. Because it's got this little terminal chapel that extends beyond the rest of the volume of the building. And here in Amiens, we saw, when we looked at those comparative sections, that the clear story gets to be really, really huge. And in fact, it is a miracle that Amiens didn't fall down because throughout its career, even in the early days, Amiens was always falling down. It was an ambitious project. The villagers wanted to construct a church that could accommodate the entire population of 20,000 people. So it had to be large and it had to be tall. It also had to be thin because there was a rivalry among the different towns to get the tallest, thinnest, most spectacular cathedral. And so these thin, clear story elements began to buckle. And in fact, professors from Columbia University do laser scans and have discovered that it's in perilous shape even now. But in the medieval period, an astonishing technique was introduced to keep this thing or at least to try to keep this from collapsing. And that was to move away from the stone technology of the skeleton and to actually introduce a material that had not been used in building. And that was metal. They reinvented a ancient Greek tool called a hydraulic hammer and deployed it at a metal shop in the little town of Fontenheim. And they made this metal chain and wrapped the stressed elements in a metal tensile chain and they installed it hot, red hot, so that when the chain cooled, it would contract and become even tighter. We looked at VR D'Encore's sketchbook last time and we saw a number of different kinds of sketches. Sketches of cows at Laurent, sketches of stars beginning to generate everything from a person's face to an eagle to a tower. But we also saw these funny little diagrams and we had some conversations about what those diagrams could mean. And the diagram that we looked at was the rotated square. What is the rotated square? So it's interesting to look at something like, say, Amiens Cathedral with the idea of how the masons would have laid this thing out on the site, given that they didn't have any architectural drawings, given that they didn't have any, you know, standardized measuring systems. And you can look at the disposition of, say, the space of the nave to the extension of the transept to the location of the aisles. And a lot of it can be derived from this rotated square, which would be a way that masons could lay out the plan of a building in the field. You know, you don't have drawings, you don't have measuring tools, but you have ropes and you can use these things to lay out the plan of the building. So it seems to work pretty well with Amiens that this whole system is governed by this system of squares. And this system of squares is called quadrature, like quad, quadrangle, and square. So the architectural proportioning system, based on a system of nested squares, is called quadrature. And it's considered to be something that Gothic architects probably did again and again and again, because they didn't have any other way to transfer an architectural idea to the scale of a real building. So we see it works not only on the plan, but it also works on the elevation. There's a secondary system on this drawing showing you another ordering system being used to figure out exactly where everything hits on the facade of Amiens Cathedral, and that's nested triangles. And that proportioning system is called triangulation. And so these geometrical systems are good because the masons can do it, it's a way to organize things, but they're also good because they carry meaning. The triangle is a symbol of the trinity. So if you can superimpose the triangulation on top of the quadrature, it's another kind of marrying together heaven and earth. A lot of the proportions in Amiens are governed by sacred numbers. For example, the number 50 begins to inform the general square that organizes this proportional bay. And if you read biblical descriptions of Noah's Ark, it's described as 50 by 50 qubits. So just as Notre Dame was somehow finding the geometry God used to construct the Temple of Solomon, here at Amiens, the sacred proportions of the Noah's Ark are being used and encoded into this building. But that's not all because the height of the building measured in the same feat that gave us the 50 by 50 unit is 144. And 144 is the height of the city of God, according to revelations. So Amiens Cathedral is as reliant on sacred proportions and the embedding of the sacred meanings through numerology as Notre Dame, as probably are all the cathedrals. The fabulousness of Amiens. And now the tragedy of Beauvais. I said that Amiens was the tallest cathedral. It's the one that managed to stand up while being tall. But for a brief moment, Beauvais Cathedral just to the north of Paris was even taller than Amiens. And you wonder, well, too bad they gave up on the sacred proportions just to make the church taller and to best their rival village only 35 kilometers away. That's not actually the case. The people in Beauvais use the same number of 144 to get the vertical height. The unit that the masons used in Beauvais was a slightly larger unit than the unit that they used in Amiens. And since the masons at Beauvais have larger feet than the masons in Amiens, the cathedral reached higher. So I don't even know how any of these things got built because if you think about it, these Gothic cathedrals are almost like a house of cards that if you get both pieces in at the same time, they kind of balance each other. If you just have one piece in, it's kind of lopsided. So the task in building these cathedrals is not simply the idea or the engineering or the stone cutting, but it's also the staging of the construction so that you can get the pieces coming in together to help balance this intricate cage work. And in the case of Beauvais, they were sort of doing that. And then they had terrible rains and there was a spell of really, really bad rain. And the really bad rain made everything way more than it was supposed to weigh. And if everything weighed more, the loads just couldn't be supported. So for Beauvais, we only have this little chunk of Beauvais left, but the original idea of Beauvais was that it would have been a Gothic cathedral like the other Gothic cathedrals with this extensive nave. So all we have is the little choir in the crossing part. And it's kind of tragic. And if you look at this thing here, you would be struck with how thin it is. And in fact, what we see here represents a doubling of the structure from the original Gothic moment. That once it fell down, they added intermediary peers. But there was such a bold idea about what architecture could do and maybe also a belief that the affectual sense of miracle, God must be holding this up, really meant God was holding it up and you could use less and less and less material. So Beauvais is spectacular because Beauvais is so vertical and because it is so small, you sense it maybe even more palpably than in a church like Amiens, which is also vast and also linear. And one piece of Beauvais that you can occupy is the crossing, which is the tallest part. The crossing is where the transept and the nave come together. This is a structural diagram. Professor at Princeton called Robert Mark did a book of these things in the 1980s. So this is a pre-digital structural analysis model and they're really kind of cool and so labor-intensive it would just break your heart because you know you could just do this really easily nowadays. So this is like a little, I don't know, you know those kind of popsicles that you buy and you freeze yourself that are in little plastic bags? It's basically that, shaped like a cathedral. So there's some kind of, I don't know, some kind of matter inside that's heat-sensitive or stress-sensitive and you build the cathedral out of plastic and then you photograph it to see what parts of this model are experiencing different kinds of stresses. So the book is a kind of virtuoso thing and you can see these moments where stresses are becoming extreme and the idea of the cathedral standing up becomes less and less believable. But this is what the nave wall of Beauvais would have looked like if Beauvais had not been such a loser and had fallen down. And who knows, Beauvais might not have fallen down if the staging of the construction had been different and if there had not been the rain and if they had been able to get all the pieces in place quickly enough to assure the structural stability of this thing. And notice here this little partial plan shows you the rotated piers just like we saw the rotated piers in Sunday night. So that's sad. That's the last of the great Ildefrance big Gothic churches. But it's not the last of the Ildefrance Gothic. Gothic keeps going, but Gothic gets more and more and more, let's say flamboyant. And when I say flamboyant, I'm not just using the word flamboyant because I feel like saying it, but we call it flamboyant Gothic. And that means its ambitions shift a little bit. If one of the ambitions of high Gothic, let's say, is the expression of this Thomas clarity. Thomas means like Thomas Aquinas, the scholastic clarity of relationships between parts and the whole. By the time you get into the flamboyant or Reynette Gothic, the ornament becomes autonomous. The ornament begins to take over. Saint-Chapelle is a little bit of both, let's say. It's still pretty clear. It's quite small. You could probably fit, if we had a room twice this size and a lot taller, you could fit Saint-Chapelle inside of it. It's quite a small church. But look at the plan and look at the section. And the plan is dazzling. And this is a funny plan, by the way, because we're seeing two different conditions. The lower part of the plan is the plan through the crypt. So we're cutting through the buttresses and we're cutting through supporting walls down here. And the right-hand side of the plan is cutting through the upper part, where we see these thin perpendicular walls and this glassy surface. Because Saint-Chapelle is so small, it's easier to build than something as big as Amiens or Beauvais. And it's easier to support the vault because the vault is not so big, the vault is not so heavy. Saint-Chapelle is like a little lantern. You walk inside of Saint-Chapelle and the primary feeling you have is that you're inside some kind of, I don't know, glowing pavilion. And this was originally a royal chapel. So functionally, it's quite different than the churches that we were looking at before, which had to accommodate processions and liturgical rites. This is what the interior of Saint-Chapelle would look like. And that is to say, almost no wall whatsoever. Just glass, glass, glass, glass, glass, glass, glass. But you also might notice this painted polychromatic tracery. Tracery, by the way, is the word for the structural elements that go through the windows. So all of this decorative stuff that we see over here we could call tracery. It holds the glass in place, but it also casts shadows and becomes another element in the ornamental program. A lot of this stuff is painted gold. The tracery is painted gold. And the vaults are painted royal blue with little gold stars on them, which is crazy because that was all done in the 19th century by a restorer called Eugen Emmanuel Violet Leduc. You don't need his name right now, but when we talk about the 19th century, we're gonna talk about him a lot because he was really an important theorist for 19th century architectural thinking but made his money by restoring Gothic architecture. And it has been said by scholars of Gothic architecture that two world wars did not do as much damage to the patrimony of Gothic architecture as Violet Leduc did in his lifetime. When we talk next time, we'll look at Gothic architecture outside of France and right now I would urge you to hand your papers in if they're ready and if they're not ready, be ready to hand them in by the end of the day.