 Last time we talked about Gothic, and not particularly these guys, but rather the kind of Gothic that had to do with the transformation really in culture from a monastic and insular sort of society that characterized the Middle Ages and even the beginning of the Romanesque period to a society that was much more urban, much more interested in trade, and much richer, quite frankly. And with those riches came an interest in expressing the power of the city-states, expressing the glory of the faith in God and building lots and lots of cathedrals. So the map we have here is fairly useless. It's just a map of France. So if you want to know where France is, there it is. Actually, the map shows us more or less what's left over in Europe in the 13th century, the beginning of the Gothic Age, after the partitioning of Charlemagne's empire. So over here the yellow stuff represents the Holy Roman Empire to the east, the Angevin kingdom to the west, and in the middle in the green we have France, where the area right around Paris and Île-de-France is the French royal domain, and the lighter green is the French vassals. So Europe has consolidated into several large chunks, and we also get a glimpse from this map of feudal land divisions. That is to say, all of the vassals of the king are the dukes, the lords, the minor landed gentry who pay homage and pay taxes to the king of France. And this division of land and the advent of feudalism, to a large extent, arose from the fact that Charlemagne didn't pay his troops that he used to mount his successful political campaigns, but in fact gave them land, gave him titles to land, hence the origins of the feudal society. The green stuff is where Gothic really took off, and interestingly enough this pink stuff down here is more or less where most of the Romanesque building campaigns were happening. This is centered around Clooney, the great monastic church that we looked at before. This is the road to Santiago de Compostela down there where all the monastic pilgrimage routes took place, and hence a burgeoning of Romanesque architecture when the pilgrimages to Santiago were important. Around the Île de France and around Normandy, where really Gothic emerged even a little bit earlier than around the Île de France, you have a different set of ambitions, and the ambitions have to do with these prospering cities and the cathedrals that make visible their success. We spoke last time about a couple of German words, and we're going to try to use German to the exclusion of English whenever we can. The words are Kunstvollen and Zeitgeist. Would anybody like to take a stab at defining them? I'm going to ask Danielle because I see her. Good, excellent answers. Zeitgeist means spirit of the time, and Kunstvollen means the will of art to find its form, and these are art historical terms used widely to talk about the similarity of cultural artifacts and artistic production from any given period. And Wolfland makes this magnificent argument that people in the Gothic period had this Kunstvollen, this will for artistic form to express itself as attenuated, as tapered, as pointy, as dematerialized, and that you find that not simply in the architecture but also in the representation of the body, in the patterning of textiles, and even in the pointy shoes. If you want things to be attenuated and dematerialized, and attenuated means stretched out, so think of something like taffy. You have this big goo ball of taffy or gum. You have this, let's say gum because you probably all have some gum in your mouth, and you can do an experiment right now. You have this goo ball of gum, and it's kind of a solid, it's kind of a haptic thing because you're eating seven sticks of gum right now, because the flavor is better that way. And you stretch it, and the condition of this solid lump transforms into something linear, something transparent, something spindly, and that is the ambition in Gothic architecture. This desire for lightness and verticality and dematerialization is made possible by the introduction of different structural systems that had been used during the Romanesque period and before. Specifically, it's a skeletal system, and here's our friend, Pardy Skeleton, to demonstrate that it's a skeletal system. It's a skeletal system that has to do with individuating loads to points rather than surfaces. We kind of saw something like that going on with the pendentives in the Agia Sophia, but instead of simply using this translation to point loads around a center, it becomes systematically developed along the line. So we have pier bundles here, these colonnets that are clustered together against a thicker mass that support ribs. And notice, in the case of this Gothic structure, it's a different shape of vault than the shape of vault that we saw in Romanesque architecture. And for your point of reference, this is the Church of Notre Dame Le Grand in Poitiers, France. It's got a good rounded barrel vault. The aisles also have rounded barrel vaults. And the walls are massive. The walls are thick, and they have to be thick because the geometry of the barrel vault is pushing loads out sideways. If we look at the pantheon, which has a round vault also, we see that you need these thick walls here to absorb all the lateral thrust. But in the condition of Gothic architecture, the walls can be much thinner because the loads are being translated sideways. There's also something about the shape of the vault that is, by its very nature, because it's pointed, it tends to go higher. So verticality is conferred to you by the geometry of the vault, and also dematerialization is conferred to you by the ribbing of the vault. So it's an excellent system. And it's also lighter. And so when things are lighter, you don't need as much heavy support beneath it to hold it all up. And so all these things are working together fabulously. We looked at some of these comparisons between different vaulting systems last time. But let's look at a comparison between walls. This is Durham Cathedral, which is really fairly late Romanesque and fairly highly developed Romanesque. And this is Saint Cathedral in France, south of Paris, which is a fairly early example of Gothic. Tell me some things that you see that mark these as different or same. Different and same are both acceptable. Yeah? Good. Excellent. In the Durham Cathedral, we have rounded Roman arches, which were popular in the Romanesque period. And in the Saint Cathedral, we have pointed arches. Good. What else? Yes. Yeah, yeah. And he's made the observation that from these photographs, you really can't tell anything. But the one on the right looks taller. And in fact, we see about this dimension before the springing of the vault. And we see a dimension that's much bigger than the springing of the vault. So yeah, the Saint Cathedral is much, much taller. Yes. Okay. It depends on what windows you're talking about. I think you're identifying something that we're going to talk about expansively as we go forward. The wall is not a simple thing. In both of these cases, the wall is perforated. And here we see a kind of gallery of perforations. And here we see a bigger gallery of perforations. So I think a big difference is that the place that's actually bringing light in, the clearer story, in the Romanesque Cathedral, is much smaller than the clearer story in the Gothic Cathedral that has expanded and brings more light in. So was that what you were saying? Okay. Yeah, yeah, yeah. No, I think that's absolutely right. That's, yes, sir. Good, good. He's observed that where the windows are actually introduced in the clearer story level, there's probably about twice as much structure at the Durham Cathedral as there is at Saint. And that at Saint, it's really just the space between structural elements that opens up. Yes? Excellent, excellent. He's looking at the columns. And if you look at the columns, in both of these churches, there's a rhythm where you have big things going all the way up to the vault and smaller things in between. And in the case of Durham here, we have this hulking big round column. And then we have fairly massive piers going up to support the vault. Everything that touches the ground is pretty massive and pretty thick. Forms like the cylindrical column we have here emphasize the massiveness. If we look over here at Saint Cathedral, the proportions of the column that we see here in Durham and that more or less pick up on the proportions of a classical column, although much bigger, but the proportions are the same, the width to height ratio are about the same. Here, that stuff has been blown away. The columns are colonettes, thin, narrow little tubes of columns. And even here in the intermediary bays, we have a much, much thinner, much more delicate structural element that's once again been represented as bundles of colonettes rather than a single mass of column. Good. Anything else? Yes. Right, right. On the Durham Cathedral, the ribs on the ribbed vaults are thicker. True. And I think that the ribbed vaults are there because it's a later addition also to the Durham Cathedral. Good observation. So you're beginning to see, although maybe at first glance, the Saint Cathedral and the Durham Cathedral look very, very similar. In actual fact, they're quite, quite different. There's a different attitude about the wall. There's a different attitude about the structure. There's a different attitude about surface between these. For the whole idea of wall thins out. The notion that the wall is plastic and caravable, which is conserved in Romanesque architecture and comes from Roman architecture, is thrown out in favor of this thin membrane that can simply disappear in between structural elements. Let's look at a church that actually made the transition. And that's the Church of Saint-Denis, just to the north of Paris. By the way, this is a drawing of Saint-Denis. He's a saint because he was decapitated. And the story of Saint-Denis is he was a Roman soldier who converted to Christianity and was asked to renounce his faith and would not do that. So they cut his head off. And he was such a good man that he picked up his head and walked for a while so that he wouldn't make a mess where he was he was killed. And the place that he ultimately expired was the site where the Church of Saint-Denis was built. So that is one tough cookie, Saint-Denis. Saint-Denis begins as a Romanesque church. But there was an abbot ruling the monastic complex at Saint-Denis called Abbot Sugey. Abbot Sugey. He's not a flying man, but this is a little bit of stained glass that represents Abbot Sugey. And what Abbot Sugey is trying to come to terms with is how God could be represented in an architectural form or even in painting. God is impossible to represent. In Islamic architecture, the whole emphasis on an iconic ornament, ornament that did not represent the body very much picked up on this idea that you cannot represent God. God is unknowable. God is impossible. God is all powerful. Sugey begins to think that light is the direct expression of the presence of God on earth. And an architecture that plays with light is an architecture that makes God visible, particularly if the light is a spiritual light, a light that is not the light of everyday activities, but say a colored pattern light coming in through stained glass windows. Sugey comes to become the head of a little church that looks something like this and begins an active campaign to expand it. You can see a kind of superposition of different conditions here. The Romanesque original church of Sandini is this simple Latin cross basilica with bearing walls and heavy piers. And as it expands, it not only gets bigger, but the envelope of the building gets more and more diaphanous. And this is such a smart idea, I have to say, that in the case of the Romanesque church, all the structural work is being done parallel to the longitudinal nave. And already here at Sandini, which is early, early, early, the structural work is being done by these buttresses that are perpendicular to the nave. So you have mass, you have material that holds the thrusts coming down from the ribs in check. But it's not blocking the space, but rather it's perpendicular to the space so that light can move through and you can have these large surfaces of stained glass windows. There's another thing that happens at Sandini advances. And that's the idea of the Chevet, or Chevet, or La La, or Chevet, if you really want to be cool about it. And the Chevet is this element, the ambulatory that we had seen before becomes more and more elaborated. You sometimes have double aisles going there. It becomes much more dematerialized. And also the transept frequently becomes incorporated into the body of the church and less of an expression of another volume criss-crossing through it. Sandini, the first Gothic church. And it's already got most of the pieces going on that we need to characterize it as Gothic. We saw the plan. And if we look at the exterior, we can see that this is a different sort of facade than the Romanesque facades we've been looking at. The Romanesque facades have been primarily an architecture of wall, massive walls with punches, maybe a little punch of a rose window, maybe a little punch of a portal. But this wall is conceptualized as a kind of plastic entity, almost like a weaving of these vertical bands and towers. By the way, this is a drawing of what Sandini is supposed to have looked like, but the second tower was never completed. So when you look at it, it's a little bit lopsided. But imagine that it had two towers. It's not a development of the West work that initiated in Romanesque architecture, but now understood in this plastic way, but also understood in another way, in a matrix-like way. And by that, I mean kind of like a grid that we have verticals and we have horizontals. And they begin to organize the information of the facade in a fairly orderly and also meaningful way. The development of Gothic architecture is certainly amplified by the thinking of Thomas Aquinas about the structure of heaven, that heaven is orderly. There is this hierarchy of elements moving down from man to the moon, to the planets, to the angels, to God. And the church facade can make those things visible and can make those things knowable. So a scholar called Evan Panofsky actually wrote a book called Gothic Architecture and Scholasticism. And it's a speculative book, but it tries to make an argument that some of the ambitions in articulating a facade in particular are driven by a strong desire to kind of make visible the map of the cosmos. You can kind of see this clear grid where we have typically a last judgment portal down here in the center. We have hope through Mary represented by the rose window and so forth. Here's the interior of Sandini looking good. And you can see that one of the things that's happening in Gothic architecture that didn't happen quite so successfully in Romanesque architecture is that there's a continuous wrapping of structure from the vertical supports that hit the ground to the ceiling. So you have the ribs almost like a tree taking a thick trunk and brachiating in a way that they become more and more slender and continuous. This is quite a different kind of space than say early Christian churches that we saw with big flat roofs and structure to the side. Quite different even from Romanesque churches that we saw where the superstructure of the roof and the wall articulation tended to be distinct. And this is just a detail of the Chevelle in Sandini. Let's compare it to a Romanesque church to see how far Sandini has developed this idea. This is Saint Foix in Conque, one of those pilgrimage churches that we looked at before. And the geometry is similar. But in the case of Saint Foix, these little chapels are little lumps like little potatoes stuck on the edge of the building or little eyes stuck on the big potato of Saint Foix. And there are tiny little punches. And here, the envelope of the building really is simply the disposition of structure. And in between structural elements, you get window. So this is what it would look like walking through that space. It's really quite beautiful. Here's the last judgment that we have in the central portal and that we find in many, many gothic churches and also Romanesque churches as the element that organizes the main door. In the Romanesque churches that we looked at before, we frequently saw the case that there might be two doors or one door. But by the gothic period, this trinity of doors becomes a standard feature that we find connecting to the notion of the trinity, the Father, Son, and Holy Ghost, that numbers matter. Different numerological ways of making repetitions or making formal organizations begin at a mathematical level to record the meanings of the church, just as at a symbolic level, the matrix-like structure of the façade is a model of the city of God. And just like on a sculptural way, the representations of things like the last judgment here are ways of reminding people to be good because people really don't know how to read. People are largely illiterate. Even royal lords rarely knew how to read because they didn't need to know how to read. They would have some mathematician who would help them out or some scribe who would help them out. The only people who needed to read really were the monks and the masons because they were the people who kept a kind of lore going that allowed the craft to develop and allowed the knowledge to become some base of information that had to be passed down to the next generation or to the next crew of workers. And because they were so successful and so well organized, it made it possible for the Gothic to spread across Europe. We already said that the Romanesque was a kind of international style and Gothic, likewise, even more so than Romanesque, was an international style. When I say international style, I mean you found it all over Europe. You found it in England and Spain and France and Germany and Poland. A little bit of it in Italy but not that much. We saw last time this image of God, the Geometer, that there's something about the making of geometrical figures here that controls chaos and creates a world. And this is a drawing of a medieval architect who holds as his tools the compass and the square the same tools that God used to create the universe. This is a carving of a very late master Mason, Peter Parler, about whom we'll talk later on. I simply have him here to represent master Mason. But the image on the left is a drawing that we have that actually comes down from a lodge book that was used in medieval Masonic lodges. The lodge would really be the place where they would get together and store these textbooks where these trade secrets would be taught, where building commissions would be organized and so forth. So this sketchbook was kept in the lodge as a resource that all the masons could look at. And the man who did this sketchbook was called Via del Nicole. And it's a funny little sketchbook. And I think the reason this first sketch that we're looking at is so strange is that paper was not easy to come by and paper frequently was parchment which was a kind of flattened animal skin. So if you had a piece of paper you were going to use it quite thoroughly. And Via is a free Mason he's traveling from town to town. Via's sketchbooks shows that he went to a lot of the major construction sites at the time like L'Anne where L'Anne Cathedral was being built and Amiens. We see drawings from those churches. And here he's comparing different ideas about apps. An idea about a extended series of round chapels coming off an app. And we'll see in a moment that this is in fact the apps of Amiens Cathedral or just different ideas about a structural base system that might result in a different kind of configuration. This to me looks English but I don't think that Via ever traveled to England to look at the works. But some other Mason might have. And that other Mason might have said Via they've got this perpendicular style going in England. Why don't you why don't you try some of that. Of course at the same time he's got these two guys wrestling and whether these were two Lodge brothers that were just fighting in the courtyard or if this was some kind of drawing for a sculptural program let's say Cain and Abel duking it out. Hard to say. But it's a nice mix of different things that are going on in the sketchbook. But some of the pages seem really aimed at instruction really aimed at teaching lessons. For example this page is pretty interesting. We see some things that are fairly straightforward like here's how you make an arch. You get a bunch of loose wars. You might make some formwork beneath it. Or here's how you make a kind of waterwheel if you're interested in that. Because remember Mason's don't just make buildings. They make clocks. They make armaments. They make machines. But when we get down in here there's something kind of enigmatic let's say going on or something that seems to be more about geometry than simply the fabrication of instruments of architecture or architectural devices. And I think this is a key drawing in VR's sketchbook. A square within a square. Frequently it is said that the Mason's had a secret, great dark secrets that were never revealed. And at least one scholar, a man called Paul Frankel, suggests that this is in fact the secret of the medieval Mason's. So now you know you don't have to join. But what does this represent? And what it represents is a system of proportioning. Think about it. We talked about Egypt. Like how can they build these big pyramids without drawings, without the kinds of tools that we have nowadays. And we said well they had certain techniques like the knotted rope that would give you the three, four, five triangle that would give you the right angle. If you compare a pyramid to a Gothic cathedral just in terms of the number of decisions that have to be made and the number of measurements that have to be taken and the number of pieces that have to be constructed, a giant pyramid seems pretty easy. Granted not easy, but it seems pretty easy. So this square represents this diagram of a square within a square where the central square gets rotated. And when the central square gets rotated, you now have a relationship between these two squares, which is based on the diagonal of the square, radical two. It's a geometrical proportion, proportioning system. But it's a proportioning system that could be done in the field. So you could tell your masons, get your three, four, five triangle out of a rope, mark the corners, and if you want to organize where the aisles go, you then hit the midpoints of all the things on the square, you rotate it, you know what that length is, and then you put that in there. And so you can use this diagram to understand a lot of the proportioning decisions that were done in Gothic cathedrals. Here's another page from VR's sketchbook, and it's really a fascinating thing, because he's talking at lots and lots of different levels. For example, here I think he's just teaching people how to draw. He's saying, well, frequently we need to draw an eagle. An eagle is an emblem of royal power. You need to know how to draw an eagle? I can't, it's too hard. Draw a star. Once you draw a star, put in the rest of the eagle. It's very easy. Eagle head, wings, tail, all you need is a star. You get the little feet coming out. It's a really good looking eagle. It's like a cartoon eagle falling from the sky. What if you have to draw a face? How are we going to manage to draw a face? Well, I believe you can draw a star. So why don't you just keep drawing a star? And you have that really gives you a handsome man, I have to say. If you have this star as your diagram, well, what if I have to draw a tower? Why don't you draw a star? So it's not only a star, you can also draw a triangle, right? You can get a horse out of a triangle. You can get a man out of a triangle. You can get a sheep out of a triangle. So geometry is being used in several ways by the one is that's a device to organize simple tasks for the carvers of decorative programs. But another is to organize really complex systems of laying out the plan without a scale. It's also probably true that they didn't simply have a knotted rope and the rotated square, but they also probably had templates. And they also have a measure that was specific to the height of the master mason. So they would have a long measure, which would be the mason kind of doing this. And they would have a short measure, which would be the arm of the mason, and they would have a shorter measure, which would be pretty much this. Then they would have the foot of the mason. And so dimensions that we use conventionally in the English system, like yard, a yard is your outstretched arm, a foot, your foot, an inch, an inch is your thumb. And so all of these kinds of measurements came into play. And they had templates, templates with carved patterns that would get positioned again and again. This is from a somewhat later lodge book from a German masonic lodge by master mason, Matthias Röhrichel. His drawings show you the same diagram that we saw in Villar, that you start with a square, you place a square within a square, and then you place a square within a square within a square, and then you straighten them all out. And that is how you proportion a finial. This is a drawing for a finial. And a finial is one of those little decorative towers that sits on top of a flying buttress. We'll see them later. So more great looking drawings by Villar. Villar is looking at the articulation of a cathedral wall. And the conversation we had earlier when we were looking at Saint Cathedral and Durham had us paying attention to similar things, that the wall is no longer just a surface with punches. The wall is this complex weaving with horizontal bands that have different articulation and vertical bands that have really complex rhythm. Let's look at an early Gothic church, particularly let's look at the cathedral in Laon, because it's one of my favorites. I'm always intrigued by these transitional moments in architecture where people don't know what to do and they're just kind of inventing the craft as they go along. There are moments of awkwardness, but in that awkwardness there's also real poetry and real truth. So this is the Laon Cathedral and it seems to do many of the things that we saw Saint Denis doing. For example, you tell me, what's it doing that we saw Saint Denis doing? How does this look like a Gothic facade and not a Romanesque facade? Yes, go ahead. It has the three doors, exactly right. Lisa, add to that. It has a rose window and notice how this rose window is a much, much bigger rose window than the kind of rose window we saw in Romanesque churches. This rose window is a rose window that extends from structural pier to structural pier. Max, add to that. It has pointed arches. Excellent. So we're no longer using rounded arches to organize things. We have pointed arches. Good. Andrew, add to that. Yeah, it's horizontally and vertically organized. It's that kind of matrix-like thing that we had observed before. Good. It also has something that I find to be really great and VR thought it was really great too. This is a sketch from VR's sketchbook and that is it has the most bizarre decorative program that you're ever going to see in a Gothic church ever. It has, well, I'll give you a better view of it. It has cows. It's full of cows. It's just a world of cows. So it's a little bit alarming. Later on, they figure out maybe we could put saints there. Maybe a devil. Maybe a gargoyle. But this is so early that they're just pretty much running with cows. So here's Laon Cathedral. And as I said before, Laon is early and it still has a fairly emphatically expressed transept. Although we'll see in some later churches that the transept gets smaller. And this is the section through Laon Cathedral. And we see a couple of things here. One, we see that the wall is articulated into four parts. We have all these different little bits of stuff. And we'll see it here. We have the arcade down below, which is this. We have a tribune, which is up here where you can walk. We even have a triforium, which is this little thing that you can walk on. And then we have clear story windows. I think it's beautiful. I think it's great. And one reason I love the Laon Cathedral is that I was once there in the winter time when it's dark anyhow and suddenly a storm came. It was maybe about four o'clock in the afternoon and suddenly the storm came and it became incredibly dark. And so I bought a candle for five francs because that's what we used in those days. And I walked around the church with a candle smelling, burning wax, looking at how the candle light reflected off of things. And I saw this church at a different scale than you usually see churches. Things like the quality of the stone or the little devil carving became very important. And this weird storm light washing across the vaults became very important. It's beautiful. And it's really simple and it's really nicely articulated. Notice here we still have columns that look a lot like the columns we saw at Durham. But the wall has become incredibly elaborated. And one of the prices you pay for this elaborate four-part division of the nave wall is that the amount of space you have left over for the clearer story is kind of reduced because you need the arcade, you need the tribune or gallery, you could also call this, you need the triforium and uh-oh not so much space for the clearer story. So one thing that happens as we move from early Gothic into high Gothic is that the nave wall gets played around with to figure out ways to bring more light in. And ultimately the triforium goes away and the clearer story just gets much, much, much bigger. There's also an idea here about the vaulting, which is six-part vaulting. You can kind of see it here. The method of connecting the vaults to the structure here. You have one, two, three coming in on each side. And so it's a complex pattern of criss- crossing. Kind of nice, kind of hard to do. Here's another early Gothic church that you probably know quite well because it's famous. And that's Notre-Dame of Paris. Notre-Dame de Paris. This is a really good example of the clarity of this kind of scholastic matrix-making of organization on the facade wall. Doing a lot of the things we saw in long. We have the three portals with the pointed windows. We have a rose window extending from structural bay to structural bay. We have these kind of wonderful arcades. Further dematerializing the surface of the wall while still behaving in an incredibly simple planar fashion. This is a really useful slide. I know you don't think it's a useful slide. But at a certain point, you're going to be looking at Gothic cathedral plans. And you're going to want to scream. And you're going to say, but they all look alike. How can I tell one from the other? And I'm giving you a tip right now. This is the plan of Notre-Dame. And this is your thumb. So look at your thumb. Remember what your thumb looks like. And when you see a plan that looks like your thumb, it will be Notre-Dame. That's extremely helpful. And it looks that way because it's so compact. Honestly, that's what your thumb looks like, right? And when I say it looks like your thumb, I mean, there are no projecting chapels off the chevet. The transept is subsumed within the body of the building. And it's got no elements projecting off the facade either. So in terms of organizing a Gothic cathedral in a compact volume, nobody does it better than Notre-Dame. Magnificent and magnificent. You can see it when you get the aerial expression of this. It's not quite so simple as the plan would indicate. There is a transept, but the transept ends where the aisles end. And there is a facade that pops up. But our only information about that in plan is the thickening of these masses here that begin to suggest that something heavy is being supported. Here's our section. And notice that we're already here at Notre-Dame, or at least in this section of Notre-Dame, getting rid of the triforium. We have the aisles down here. We have the gallery or the tribune here. And now we have clear a story. And so we get a lot more light coming in. We get a lot more dematerialization of the surface. And that's what you want because Abbe Suge tells us that making light visible is a physical expression of the presence of God in church architecture. So you get these larger expanses of stained glass and so more dappled polychromatic light coming in to create these really strong effects. So what we're seeing here in the section of Notre-Dame is a flying buttress. This bridge-like element transfers the load from the vault and takes it to this heavy mass displaced from the volume of the building with a finial on top of it. We also see here a little something that has to do with kind of numerological games that are going on because these monks have nothing to do with their time other than just figure things out in a minute way and then make these things become part of the iconological program of the building. Iconology, by the way, means a system of symbols, a kind of coding of symbols. So iconological and numerological, numerological, a system of coding numbers. Some of the proportions in the Notre-Dame, for example, are derived from literary descriptions of the proportions of the Temple of Solomon. So it's being built using these technical geometrical devices that we see in VR Don Corz sketchbook but the technical geometrical devices are being organized by a kind of higher numerological coding of meaning within the building. We saw the section of the flying buttresses of Notre-Dame but perhaps you'd like to see what they look like. They look great is the answer to that question because it makes the exterior skin of the building as lacy and diaphanous as the wall. So when you look at this the effect is totally different than the effect of looking at a Romanesque building where you see a strong difference between inside and outside. This is this kind of cage of wonderful interlacing things. And on the top of the roof you have these elements. Let me see if I see one here. Now maybe there's one here. I'll show you a detail. You have these elements like this guy. Anybody a Walt Disney fan? Anybody know what that is? It's a gargoyle, right? And the purpose of a gargoyle is to make you not sin because you don't want to be eaten by gargoyles when you die but it's also a way of getting water off the roof. So if you ever go past a Gothic cathedral when it's raining it's really quite spectacular because the gutters grain water into the gargoyles and they either spit at you or they pee at you all the water from the roof. So the whole church becomes alive with this operation. Anyhow, we're done for today. We'll see you again next time.