 We're going to talk today about the organization of cities in Quattrocento, Italy because we've been discussing a lot about certain ideas about ideal geometry, ideal proportion, formal organization that has to do with individual buildings. But a lot of those theories also pertain to cities. We'll come back to this image in a little while, but I just want to show you somebody who you know very well by now, the Vitruvian man and the whole Albertian discussion of the circle as an ideal geometry that we went over briefly last time. The ideality of the circle or the centralized organization goes beyond mathematics, but is also found in other authorities that people would have paid attention to in those days, the authority of nature. You look at nature, you see circles everywhere, the sun, the moon, cut through a tree, make a snowball. Everything is a circle. You also look to antique precedent. You look to the Romans, and they were making circular buildings, the Pantheon, Santa Costanza, Santo Stefano Rotondo, and so why not try to get this ideal form, not simply to organize individual buildings, but also to become an organizing strategy for urban structures. Well, this is certainly not hitting that mark, is it? This is the painting of good government from the Polazzo Comunale in Siena that we looked at earlier in this class when we were talking about gothic space. In the painting of good government, if you had the task of drawing a plan of that city, you would have absolutely no clue what to do. There doesn't seem to be anything going on except a kind of general sense that people are busy and the city is dense. By the time we move into the Quatrocento, space is becoming carved out in representations of towns. This is a proof of the true cross in Arezzo by Piero della Francesca, one of my favorites. This is a Quatrocento artist who was totally out of favor for a long part of history, and he was rediscovered again by the Cubists as somebody from the renaissance that they could really look up to and things that people admired about Piero was his interest in abstracting away the idiosyncrasies of individual form and finding a way that geometry could control the whole thing. But if I had asked you to draw a plan of the space in the Piero fresco, I think you could probably do it. Well, others could do it. Kidding. You could do it. You see here quite clearly that there's an edge of buildings. You see quite clearly here that there's a kind of object and far into the distance we see another little town. Notice also that the architecture is quite different than the architecture in the good government. In good government, this is a real Gothic architecture. It is a wall architecture with these crenellated structures and towers of the nobles popping up everywhere. Here we have quite a nice little temple and we have fairly orderly buildings without all of the fussiness that that we associate with Gothic architecture. Look, here's even a little temple up here on top. And you see again and again in the work of Renaissance artists this attempt not simply to carve out a space, a plausible space that people are acting in, but to understand it as a space fleshed out by lots and lots of nice classicized buildings. This is Andrea Mantegna's St. James cycle. This is one of the great tragedies of art history. This was a incredibly important cycle of frescoes that got bombed to smithereens in World War II and no longer exists. It only exists in in images like black and white images. And this is Donatello's Feast of Herod. Nice techniques. Radical Worms Eye View. Worms Eye View is a vantage point in perspective where you imagine you're a worm. So you're low to the ground and you're looking up at the figures and this Worms Eye View vantage point that Mantegna gives you enforces a kind of nobility or a kind of heroicism on the characters that are being admired. So that's one idea about the city. The city has space. The city is filled with classical buildings. But another idea about the city goes back to the notion of the Vitruvian man and the notion of geometry. And so that idea of the city is a centralized idea of the city. This is a drawing for an ideal town by a lumbard architect called Filarete. And it really is all about geometry. It's all about the circle. It's all about this stellar fortification that's situated inside the circle and then the palace. And down here are a collection of ideal town plans by a number of Quatrocento and Cinquecento architects all about the center. And very few of these towns ever got built by the way. Because unlike, say, Ohio, Europe is already full. There really aren't that many open sites where you could plan an ideal town. There are existing settlements. There are existing villages. There are existing churches. And so for the most part these ideal towns have to be dreamt and maybe little pieces of them can get constructed, but not a whole cloth. This is from the Cinquecento. It's the town of Palma Nova. And this is what you would expect the organization of an ideal centralized town planned to be. That is to say, radio. You put the castle in the middle. You have a radio organization of streets. This is actually quite lovely. You have all these little plazas in here. And these are the fortified walls that keep lions outside. There are some other ones like this one in here that are gridded. And I once went on a tour of this little town outside of Mantua and the tour guide said it is a very clever defensive strategy. And I said, well, what is it? And they said, we have a grid. They said, well, how's that going to help you? They said, well, you know, you get on a road and you take the road and you find the palace and you, you know, you kill the Duke, but we have a grid. So where are you going to go? And I thought that was amazing. You know, like, well, take a left, take a right. You get there. But I'm from Ohio. I'm used to grids. But I guess all of the marauders were just stumped. They just didn't know whether to go left or right. And in fact, on one occasion, I was with a group of Ohio State students and we shared a bus with a bunch of Clemson students who had this old Italian professor with them. And the Italian professor was trying to give the bus driver directions to get to these Palladian villas in a part of Veneto that was gridded. It was an old Roman establishment. It had this very clear grid. And the Italian professor was giving instructions to the driver saying left. Left. Left. Left. Left. And we could never get there. It took, it took us like four hours to go 20 miles. And this guy was just so insistent that, you know, I am the Italian. I know what I'm doing. Left. Eventually the bus driver just mutinied and took us there. There's just one more idea about an ideal town plan, which I think is incredibly sweet. This is by Francesco di Giorgio. And Francesco di Giorgio here is in a sense extrapolating on the idea of the Vitruvian man. The Vitruvian man as a generator of geometry and a container of geometry. And so instead of using geometry per se to organize the town plan, he uses this anthropomorphic metaphor where the piazza is in the stomach, which I think is nice. And the castle is in the head and the arms and the feet are all fortified towers protecting the piazza. And where is the heart? Or where is the church? The church is the heart on the piazza. And Francesco di Giorgio also used the same kind of anthropomorphic diagram to give structure to a church plan that he drew. So these are ideas floating around. And the third idea that I wish to introduce is the notion of perspective, which Alberti codified and published. And there's another aspect to Alberti's theory of perspective. It wasn't simply vanishing points and horizon lines, but he also had this idea that a picture is like a window. As if looking through a window, you see a painting and even had this device, which was a gridded screen that you could put up in front of the thing you're trying to draw. And the thing you're drawing on has a similar kind of grid. And so you look at this gridded thing and you simply connect the dots more or less to get the perspective down. So this would be a way of constructing a perspective without actually doing all the math to make a perspective, but to get it right. And so you get these paintings that begin to deal with the theme of ideal centralized town. This is the one that we had on our introductory slide, and it shows you more or less two things that are highly valued in the Renaissance, especially in the Quattrocento. The temple, the centralized ideal church, fabulous. This is another thing that people in the Renaissance had hard time building. You desperately want the centralized church. You desperately want the centralized town plan. Can't quite pull it off. But here in the panel, we have a plaza organized to receive perspectively in a really clear way. Even the paving is gridded to help your eye understand that. And in the middle, we have this round church. And a similar idea is going down here in Perugino's consignment of the keys to St. Peter. It's an incredibly fabulous, perspectival plaza. Really deep space, but crazy at the same time. This doesn't look like the world. Here's an art history term that you can forget immediately. It's isocephaly. You find this a lot in Quattrocento paintings where everybody's head lines up. That's isocephaly. Everybody's head lines up and that makes a plane. And in that way, even if you're not dealing with something like the layered arches that create space in Donatello's Feast of Herod, you can still get that kind of layering to organize the space for you. Fabulous. This is really great. I love the trees that Perugino put in here. And what I like about them is that they're not symmetrical. It's like he's cataloging nature. He's saying nature is, in fact, variable and foolproof. And so let's just register some of the kinds of trees we could get. It's funny, given how symmetrical the painting is and given how there really is this equation of sameness on both sides, that he just has to sneak in a little bit of hypernaturalism. This is just one more idealized temple in a gridded landscape. Raphael's Marriage of the Virgin. So what did towns look like in the Quattrocento? We know what people wanted them to look like. We know what painters and architectural theorists wanted them to look like. And the answer is, well, they probably looked more like the Lorenzetti image of the good government than like these ideal schemes. These are two Cinquecento images of the city, but I think it's worth looking at them and looking at them critically as a way to begin to understand attitudes toward classical architecture. And attitudes toward Gothic architecture in the early Cinquecento. This is from Salio's treat as it was published in the 1540s, but it was written before that. And these are not real cities, by the way. These are stage sets. On the left, we have the comic stage set, Sheina Comica, and on the right, we have the tragic stage set, Sheina Trajica. And look at the architecture. The comic stage set is Gothic. These people are funny. They have pointed arches, lots of pointed arches, funny little spindly towers of the nobles, the Altana that we saw in the Palazzo d'Avanzati, and the space of the square is irregular. Things don't line up, things poke out. There's a grid. OK, we can kind of read the space perspectivally, but the space is incredibly irregular and incredibly diverse. There is not a single language organizing all the pieces. If we go over here to the Sheina Trajica, the tragic scene, and in tragedy, of course, you have the heroes and in comedy, you have the buffoons. Here we see a perfectly fleshed out classical space with some kind of triumphal arch opening up vistas beyond. And instead of the old fashioned little noble towers that we see here in the Sheina Comica, we have an obelisk. We have something pointy, but it's something pointy and antique. Nice round headed arches, nicely delineated cone of space, nice trapezoid of space. This is a 12th century Palazzo in Florence. Palazzo is a building type. I don't know if I've introduced it before, but you're going to be hearing a lot about Palazzo because it's really one of the defining types. An easy way to do it is to have a building type. An easy way to describe Palazzo is square doughnut. Mmm, sounds good. And when I say square doughnut, what I mean is it has a courtyard. It is a perimeter organized around a courtyard. And the courtyard is the giver of form. The courtyard is the figural space around which a perimeter of varying dimensions and varying amounts of irregularity can be organized. These two little drawings show you a plan diagram of Palazzo as square doughnut and an elevation diagram. Palazzo has a series of stacked stories, particularly emphasizing the idea of base, middle and top. This tripartite organization that becomes specific about meeting the ground and meeting the sky and doing something in the middle. You can see those ideas rehearsed here in Palazzo da Vanzatti. For example, it's a square doughnut, but it's a square doughnut that's been beat up a little bit. It's somebody sat on it on the bus or something like that. But the important thing is that there's a clearly defined courtyard that organizes the perimeter. In the case of Palazzo da Vanzatti, the perimeter is quite irregular. The little yellow thing here means courtyard and the irregular sprawl of rooms means rooms. So you enter in through the oblique side and you find yourself in the courtyard. And up you go, the courtyard cuts through the entire length of the building and gives you a piece of space that you can call your own and provides ventilation and light for the interior of the building. It's a typical typology that you have in dense urban towns. It's not so different from the Roman atrium house that we looked at before. We also had to negotiate the density of the urban fabric with houses packed next to each other. And that also had to deal with the fact that there's a climate here that's not so favorable. And that if you can provide a way of organizing buildings together so that they cast shadows on themselves, it will be a nicer microclimate than if you allow them to get baked in the sun. If you look at the site plan of this area around Santa Croce in Florence, where we saw the Roman amphitheater stuck in the fabric of Florence, you can begin to see how these palazzi make possible domestic arrangements in this very, very dense fabric. There are little courtyards tucked in all over the place and you're probably thinking that you can't see them very well. The reason you can't see them very well is that this plan just shows you walls and property lines and streets and squares in a way that doesn't differentiate in a very emphatic way. And there's a much better way to represent urban space. And of course, this is a much later drawing than the period we're talking about in the Quattrocento. But in 1748, an engraver named Noly gave us a really kind of spectacular, multi-panel figure ground plan of the city of Rome. If you look at this, you can probably identify some buildings you're familiar with, like, for example, the Pantheon right over here, or like, for example, this large square called Piazza Navona, built around the hippodrome of Domitian, an old Roman relic. Other buildings that you'll eventually become familiar with, a little church by Boromini, San Evo. But it's not all about monuments. It's also about palazzi. And when we look at this plan, we see all of these little white marks here, all of these little white marks. I once showed this plan to a group of freshmen, and I asked them, what do you think we're looking at? And they said, these are probably houses with driveways. And of course, that's what you'd think if you're from Ohio. But in fact, these are the courtyards of the palazzi, and they're all packed in tightly together. And the black means uninterrupted packing in of urban fabric, like this area in Florence that we're looking at. But now, in the Roman example, we can read it quite clearly, because the figure ground diagram has made visible the difference between private space, black, and public space. And in the Noli map, there's a very interesting construction of what constitutes public space. Public space isn't simply the Piazza or the street, but public space is also the interior of a church, or the interior of a major public building. So if you look at the façade of Palazzo d'Avanzatti, you see a couple of things. One, boy, would this be a nice place. This area, Altana, is what it's called, where you're up getting the breezes, looking around, and then big old wall with punched windows. If you had to say, how is this thing articulated? And by articulate, I mean, how does it begin to clarify the relationships of parts to the whole? You might say, well, there are some horizontal string courses in here that begin to give it some structure, but for the most part, it is just a big, hulking, sprawling thing. So one of the tasks that the architects in the Quattrocento, the architects who embrace this new interest in Roman-ness, this new interest in finding an architecture that moves away from this thin, Gothic quality to something more robust and gutsy and Roman. What would they do? And they had all kinds of ideas. This is an early one. This is by the architect Michalotso. It's the Palazzo Medici, now called Palazzo Medici Ricardi, because other people came into possession of it, but it was originally one of the Medici palaces. And a technique that Michalotso is using here has to do with materiality. Anybody remember what materiality is? I'll tell you what materiality is. Materiality has to do with the qualities of material, but not simply in a constructional sense. Like, we're going to use some of that concrete because it's a good material, it's going to do the job, it's going to get it done, but we're going to use this material because of its color, because of its texture, because of the way light hits it. The qualities of the material become a kind of giver of meaning to the architecture. So here Michalotso uses rustication. And rustication is the deliberate use of rough-looking stone, almost boulders here at the base level. And he articulates the building by transforming the condition of the materiality of the wall from really crazy rustication, to this more finely-dressed ashlar, square-cut panels of stone facing. And then when he gets to the very top story, it's the smoothest yet. So it's as if there's some kind of idea here of horizontal stacking that's a lot more emphatically developed than it was in the Palazzo davansati. But this idea about rustication that's worth mentioning, it's also making an argument, let's say, about what it is to be near the ground and what it is to be near the sky. And that is consistent with all of these notions that things on earth are corrupt and contaminated, things in the heavens are divine and pure. So as the material, the Palazzo medici ricardi, goes higher and higher and higher, it becomes more and more refined. There's a negotiation going on here between two different tastes, this carryover of a medievalizing sensibility, because this is quite early, this is 1430, this is really the first of the great renaissance palaces. So notice this window, and one thing you would notice is, well, it's a nice round-headed window, I'm incredibly enthusiastic about that, but it does break up into something that is almost akin to Gothic tracery. This is a device called Bifora, and it's also used to describe Gothic tracery, but here it's done in a round-headed way. And probably a lot of that had to do with the fact that you wanted to have a dimension that you could control. A dimension this big would not be something that you could enclose very well, but it also adds this more delicate scale to a building that for the most part is pretty gutsy and pretty robust. Here's a plan of the Palazzo medici ricardi. And you can see this notion of Palazzo, I think well-developed in the plan. Courtyard, fabulous. In fact, the courtyard is so fabulous that it's even square. So, you would say, but everything's square, and I would answer to that, these people are the medici. If they want a square palace, they can just kill everybody and get a square palace. Let's say the organizing feature is this courtyard, and around the courtyard you have wrapping rooms. Now, this seems like a trivial question, like how do you put a courtyard in a palace? You want to have a colonnade around the edge, but already here in the Palazzo medici ricardi, a big problem emerges about what do you do with a corner? And this is a problem that bothered people during classical antiquity and bothered people like crazy throughout the Renaissance. What do you do in the corner? Easy, easy, easy to do the middle. Like, here's a column, here's an arch. Here's a column, here's an arch. I slam, I hit the corner. So, there's a battle between where you want to have the column logically and what you want to see visually. And visually, when you're standing in the courtyard, you would actually like to see the corner column. But in fact, you can't because it also belongs to the edge of columns. It's not an ideal solution. It doesn't create enough difference within the system to solve the problem of being on the corner. Here's another Palazzo. This one is the Palazzo ruccelli by no less an architect than Leon Batista Alberti. This is a bit later than the Palazzo medici. And Alberti is, of course, the smartest guy around at the time. So, it's not going to be sufficient for Alberti to say, I'm going to deal with rustication and I'm going to deal with stacking. And I'm going to let material carry the brunt of my argument. Instead, Alberti has to be archaeological. Alberti has to go back to Roman precedent and try to figure out what to do. And that's a hard problem because if you're thinking about something like, oh, I'm going to make a church facade. A church facade is a singular thing. And so maybe a triumphal arch works. Maybe a temple works. Maybe you can super position a temple and a triumphal arch and you get something that is compatible with the new building type of this the Silicon section church that you're organizing. But that also makes reference to antique precedent. So what do you do here? Of course, Alberti does not pause for long. He looks at the Colosseum. And he realizes that although the Colosseum is entirely different in its scale and in its function than a domestic space like a Palazzo, it nonetheless gives us an ancient model of what it is to stack stories. Alberti adds more to the whole conversation than Michalotso did because Michalotso was interested in organizing the horizontal bands in a clear way. And from the model of the Colosseum, Alberti adds vertical base structure. We have the vertical base structure. And in the Colosseum, we have this double system, right? We have the arcuated system that organizes the wall and superimposed over that we have a traviated system that organizes the levels. And the same kind of thing is going on here too. We have an arcuated system that organizes the windows and a traviated system that organizes the levels of the building. I just wonder if anybody can guess. I doubt that you can see well enough to know what the orders are in the Alberti building. But does anybody have an idea about how they might work based on classical precedent? Does anybody remember how they work in the Colosseum? Can anybody read? Thank you. Exactly right. In the Colosseum, the system of organizing the orders is to take Doric, Ionic, Corinthian and stack them up that way with Doric being the masculine order, Ionic being the matronly order, Corinthian being the maidenly order. And Alberti takes that also. Now, in the case of the Colosseum, this is a much more plastic wall. These are engaged columns and there's a lot of depth and plasticity to the surface. Here, Alberti flattens it out. And he flattens it out because he has a completely different site condition. But he also flattens it out because of decorum, right? He does not want to make a monument. He wants to make a dwell-in. And there are different ways of responding to these different kinds of tasks. And to be too pretentious or too monumental in your conception of a domestic space would be breaking the rules of decorum. This has lots of nice gravitas. It's an urban building, nicely articulated, and it adheres well to ancient models. You see the plasticity of a piece of the Colosseum versus the planarity of the Alberti building. If you were to go to Florence and look for the Palazzo Ruccelli, you would only find about three bays of it built. But Alberti had originally conceived of it as this much more symmetrical organization. Let's look at one of the rare examples in the Quattrocento when someone had an opportunity actually to configure and to conceptualize an urban space. This was the restructuring of the town of Pienza. The architect is Bernardo Rosalino, and the client is the Pope. That's a good client. If you can't work for the Medici, work for the Pope. And the Pope is Aeneas Silvio Piccolomini, and he was a humanist. He was a really renaissance man, let's say, in that he was a great scholar of the classics. He was a great lover of music. He was a great collector of ancient art. And so his hometown is this little hill town in Tuscany called Pienza. And he wants to restructure his hometown with this notion that it will become a showpiece of the Renaissance. So this is his hometown. It's actually a great little town. This is a ridge, and it's more or less a really steep cliff over here. But what makes this town so nice is that there's a parking lot right over here. Unlike so many hill towns where you have to walk up, there's a parking lot right over here. If you look at this town, you see a couple of things right away. One, Piazza II did not completely restructure the town, but he only emphasized this one space. Piazza Piazza II, we call it because Piazza II is the Pope. It's an interesting question, and probably he didn't want to displace all of his neighbors and flatten the hill and make a nice radial town plan. But given that he's only doing one moment within the fabric of the city, what strategies are available to him? You might quibble and say, given the fact that you're doing one thing, why can't you at least do that right? The space here is not ideal. The space here is trapezoidal, which is a surprise. Because you would think that he would want one of those super clear geometries that we saw in the paintings of the ideal city by the unknown artist, or super clear geometries that we saw in paintings like The Consignment of the Keys by Perugino. But instead he goes for this trapezoidal space, and you have to say, why? And one reason he may have gone for the trapezoidal space is that there is a Roman precedent. There is an antique precedent for trapezoidal spaces, and it's a very honorable antique precedent. And that is the space of the Roman Forum, not to be confused with the Imperial Fora. The Imperial Fora are orthogonal, they're bounded, they're self-contained. And the Roman Forum, by contrast, is trapezoidal. The Basilica Amelia and the Basilica Julia crank out at canted angles and begin to crack open the space. It's a leaky space, offering views up to the Capitoline Hill over here, offering views across to other monuments within the city. And therefore the space becomes enlivened and enriched because of the very breach in geometry. It also is a kind of perspectival cone of vision. This is Alberti's diagram for setting up a perspective. There's this notion of vanishing point and things receding to the vanishing point. And probably these architects who went to the Roman Forum and studied things saw the power of these canted edges. And thought that that would be a way to build in the physical world the kind of space that the painters were able to capture in the pictorial world of their canvases. And so this cone of vision, this forced perspective, is built into the space by Rossellino. So you get a lot of things happening, you get a lot of benefits. One, the relationship between the façade of the building and the viewer. Let's say the viewer is over here, coming down the street, becomes more immediate. And two, you get a relationship between the façade of the building and the distant landscape, really colliding together. And that's something you see again and again and again in Renaissance painting. This is a really sweet painting by Gierlandi of an old man and his grandson. One thing I find so sweet about this painting is how disturbing it is to see this bulbous nose on the old man and the tenderness in his expression. And to look at this pattern that is so sort of hideous and disfiguring in the old man and see that it's sort of matched by the delicate, charming curls on the child's hair. And the gaze between the two of them that transcends the physical deformities of one and the extreme beauty of the other. But that's beside the point. The point I'm making is smash the figures against the picture plane and whoosh the space back. And if you think Gierlandi is a minor figure, it happens again and again. For example, Leonardo da Vinci, very important man. The Mona Lisa, no less, slammed against the picture plane with the landscape rushing back. In exactly the same way that the façade of the church in Pienza is slammed against the picture plane and the rest of the space whooshes back. This is the view into the deep landscape that you get from up here because the space cracks apart. You see all these contingent things happening, but notice that we're setting up the ideal view. As the town hall slips to one side, people move through there and this is the vantage point from which everything makes sense. This is the vantage point that collects together the flatness of the façade and the depth of the landscape beyond. It's like Alberti's window. The city is not being imagined as a fully three-dimensional centralized radial construct like Palmanova or Sforzinda. But it's being understood as a picture. It's being understood more like the Urbino panels of a picture of an ideal town plan. The church is situated at the edge of the cliff, which is really a radical move to make. But it's a radical move that produces two very different results. One result is extreme planarity in the front. The building establishes edge, helps configure the space and really renounces its ability to operate as ideal object. It is not the little temple where the marriage of the Virgin is taking place on that side. However, as it extends over the cliff, and you can see that in this image over here, it changes its figure. It becomes suddenly ideal centralized object. Longitudinal, authorized by the anthropomorphism of the Latin cross plan, and centralized. Centralized as a circle, but let's say centralized as an octagon. And you almost see this battle between building as center and building as Latin cross as these things play out for dominance. And it's almost like cell division where centralized building goes over the cliff and longitudinal building, Latin cross building comes forward. And in coming forward, there is a really strange hyperplanarity to the building. So that everything that is figural and everything that is decorative seems to be subtracted or rather sucked in. As if the ability to be figural in this building is thrust through the facade and only can fully materials back out as the objects liberate themselves into the landscape. If you look at it from the back, you see this kind of ideal centralized object like the church in the marriage of the Virgin by Raphael. Perfect. So it's a real kind of double game that is being played here. Nor did Rosalina completely give up on ideal geometry. In fact, if you look at this thing, you would have to say that this is some kind of reverie to the square. Or some kind of marching through permutations of how can you present variations on the theme of the square variations on the theme of the nine square grid, variations on the theme of the four square grid. If you look at all these places, there's that kind of game going on. Like look at the well right over here by the Palazzo Piccolomini. It's like a hinge point really. You look at this thing and it seems as though this gridded pavement in front of the church in the square rotates this whole half of the organization off in that direction. If we look at the facade of the church, there's a little circle here that's kind of making some kind of argument about orthographic projection as if the ideal structure of the church is being mapped in plan here and being revealed in elevation here. Totally clever stuff. In fact, this is a very funny church facade, given church facades that we've seen before. We haven't seen that many. But we've seen two kinds. We've seen flat as a pancake and we've seen plastic. And flat as a pancake would be something like Sant'Avriano Vella by Alberti, where it's all about making the surface and articulating the surface. And hyper articulated would also be an Alberti church, let's say the Tempio Malatestiano, which tries to become a big triumphal arch. And all of those do things through pulling out material. And this articulates itself by sucking material in, as though the figureality of this church is being thrust to the back so it can be as emphatically planar as possible. Clever. If we look at the Palazzo Piccolomini over here, we also see another kind of riff on the square. It's another one of these early Quattrocento courtyards that have not quite yet solved the corner. But you have a really narrow dimension here. So if you're standing inside the courtyard and you look up the sky, the cornice of the courtyard frames the sky. And you see this, within your cone of vision, you see the sky, this kind of ideal square, uncluttered, the heavenly square. And then you come out here and you get a kind of real paradise garden, a four square garden. By the way, this is something that should give you pause. I know it always shocks me. If you look at the Palazzo Piccolomini over here, the palace for Pius II, it looks almost exactly like the Palazzo Ruccelli by Alberti. You would have to say, well, that seems wrong. That seems like cheating a little bit. Here we have the Palazzo Piccolomini and here we have the Palazzo Ruccelli. How is that possible? Well, one way that it's possible is that Alberti was a man of theory. He didn't really know how to build things. And so it's thought that he probably had Rosalino actually execute the Palazzo Ruccelli on his behalf. But it's also true that I think intellectual property was not held as tightly as it is nowadays. And so people work within a tradition. People work with precedent. I mean, otherwise you'd have to say every Greek temple is a plagiarized attempt to rebuild the last Greek temple that people ever saw. You can also see the radical juxtaposition of figure in the foreground and landscape in the background. And these portraits by Piero della Francesca, a Federico da Monte Feltro, and his dead wife. Batista Sforza. It's a nice painting. You know how we know it's his dead wife? Well, historical records tell us that she was dead. But Piero also paints her with this kind of real power. He drains the color from her skin. She's white. So it's his beautiful dead wife. And this is the same Piero I said that was admired by the Cubists because of his willingness to go beyond appearance and to abstract the geometric essence from people. Federico is another one of these condotieri like Sigismundo Malatesta that we looked at last time. Incredibly successful warlord, incredibly brutal man. You might be wondering why he's so unattractive and why he's portrayed in profile. And the answer is he lost one eye in battle. So this is his good side. And he lost part of his nose in battle also. But this is still his good side. So God help you if you have to look at the other side of Porold Federico. But at the same time he was a humanist. He was a great patron of the arts. He was a patron of Alberti. He was a patron of Luciano Lorano. He was a patron of the young Bramante. Here's another painting by Piero showing you the extreme attention to perspective. In fact, there's a historian called Martin Kemp who says of all the constructions of perspective put forward in the Renaissance, only Piero got it right. And Piero's method of constructing perspective was crazy. It required the plotting of many, many, many points. For example, he's looking at the structure of a head here. This is how Piero gets these perfect egg-shaped oval heads for people like Battista Sforza. And speaking of perfect oval egg-shaped heads, just want to show you one more painting by Piero. Because it's a pretty interesting one. It's the Brera Madonna, called the Brera Madonna because it's in the Brera Museum in Milan. The subject matter seems fairly conventional. That is to say, unenthroned Madonna surrounded by saints. There's a name for this kind of painting. It's called the Sacred Conversation, Sacra Conversazione. As though the Virgin is talking to all of these saints like John the Baptist, who she could have known, and St. Francis and St. Jerome, who are very removed from her in time. But this is happening on a different ontological plane than ordinary life. We do have someone here representing the lived world, and that's the donor. And the donor here again is Federico da Montefeltro. By now we would know that little notch in his nose anywhere. Gotta love Piero. Look at the isocephaly going on. Wham! The entire canvas gets divided in half between world of people and world of architecture. There's such tough geometry going on here. Like the head of the Virgin becomes this perfect oval. He's really locking the vertical line, going through the middle of the vault, going through the Virgin, going through the child's navel. And there you have it. Not much you can do with Federico, I have to admit. He's still a bit rough around the edges. But he's the donor. And because he's the donor, he's included in the portrait. The thing that is always enigmatic, and I don't know if you guys have a solution, because nobody has known yet what the answer to this is, is why is an egg hanging in the space? Anybody have an idea about an egg hanging in the space? There are some theories going around, but nobody's quite sure. There are scholars, such as Millard Mies and Marilyn Lavin, who have done studies about this painting, reconstructing the perspective of Piero. Because Piero is accurate. With Piero gives you a perspective, you know how deep that space is. The mathematics of the space are not just visual hints at what it might be, but it can be unraveled. And according to the scholars, the egg is about 8 inches high, and it is about 45 feet behind the Virgin. That probably doesn't matter. Because I think the question that's more interesting is, what's the egg? What's going on with the egg? Especially if you think about the notion that things down here belong to one kind of world, and things up here are in another world. So what's the thing in the egg? Yes. Is it like the ringing of a bell? Like if the Madonna would like a cup of tea, she pulls the egg, and Mary Magdalene comes rushing out? No. That is not what's going on. It is not how she calls the butler. Yes? Well, that's interesting. I think that's a possible reading. It's usually talked about as an egg, but it could be understood as a pearl. That you have this protected thing, the shell, with something precious inside, which is one way that the Virgin is thought of. We spoke when we were talking about the rose window, about the cult of Mary, and the idea of the rose, that the rose is a beautiful thing, but it's protected by the thorns. So I think that's a nice idea, that it could be understood to be a pearl protected by the shell. And so here we're seeing the beauty of the Virgin, and we're seeing that which protects her. That's nice. Any other readings? It matches the shape of the Virgin's head exactly. And so some kind of equation is being made between the Virgin and this perfect thing. Or it could be talking about the birth of Christ, the kind of Virgin birth of Christ, like an egg cracks open. But I like your reading a lot. I like the pearl reading a lot. I recently read a really interesting discussion about this painting, that talks about it in terms of what's missing, as well as what's present. And based on other paintings we've seen, say for example, Masaccio's Trinità, when we look for what's there, we see two donors. And we see this beautiful triangle created by a plane of donors, several saints, and then the holy figures in an arch. Not such a different construction from the one that Piero is using here. And we get the triangle through the egg, or even through the Virgin, and someone's missing. And you might be inclined to say, perhaps Batista Sforza is missing. We know that she's dead. We knew that from our previous set of paintings, and so we have the widower, Federico da Montefel, through there, mourning alone. But it could also possibly be argued that there is something about this perfect oval, this perfect whiteness, this perfect white oval egg hanging in space, that is to remind Federico of Batista. And that this is about him looking toward her absence, and the egg representing her presence in this sphere up above. Federico, patron of the arts, had a palace built for him. And this is an example of a fairly complex program. And it's also considered to be one of the first instances where the question of what do you do at the corner gets tackled in a fairly serious way. Not tackled in Palazzo Medici, not tackled in Palazzo Piccolomini. But sort of tackled here. From the exterior, it doesn't look particularly renaissance-y, but you do have to remember that Federico is a crazy warlord, and he kind of needs a fortification in order to keep other armies from trying to take him over. The decorous urbane elegance that we saw in Medici palaces in Florence, or Ruccelli palaces in Florence, just wouldn't work if you're on this ragged outcropping of a hill like Urbino. And the palace itself negotiates the irregularities of the topography and organizes itself around several courtyards. The main courtyard, the courtyard associated with the architect Luciano Laureano, is this beautiful square courtyard. And it's famous because it's really the first example of an architect tackling the question of the interior corner in a serious way. So Laureano is trying to figure out how do you end the system? Middle, middle, middle, easiest pie, and difficult. You can't see it very well in this image, but his method of ending it is not to try to put something in the corner, but to double it, and to leave a slight void in the corner. So he has this kind of double-pollaster system, little column system with a void in the corner. And that way the visual weight on both sides is equal. And that he gets something that addresses the layer of the first level, as well as the arcuated system around the courtyard. Clever man. Probably the most interesting space in the palace of Federico da Monte Feltro in Urbino is a little space called the studiolo. And the studiolo means little study. And of course, if you're a great Renaissance humanist, where are you going to put your loot? Where are you going to put your books? Where are you going to put your stuffed owl? Where are you going to put your harpsichord? Maybe you didn't have a harpsichord. Where are you going to put your stuff? Your swords, even. And the answer is in your little study. And here it is. I made it a little kind of greenish square, tucked in between these two fortified towers, right over the entry to the palace, is Federico studiolo. With a very specific light source coming into it. And it's decked out with these elaborate representations of scenes that might be seen through a window, if there had been a window there. So it's perspectively very exact and very complex. Complex because it anticipates this limited light source, so all the light in the illusionistic panels are as if they came from the window in the space. And it's also complex because it's not painted, all of these images are constructed with inlaid wood of different colors. So here we see inlaid wood paneling, showing us something similar to those ideal towns that we saw before, with the gridded pavement and the nice palazzi lining up and giving us a nice trapezoidal space. And these are some of the attributes of a Renaissance humanist. You want to have your lutes, you want to have your perspectively complex objects, you want to have little mechanical clocks and so forth. The technique that's being used here to represent illusionistic things that continue the perspective of the room onto the pictorial space is called trompe l'oeil. Trompe l'oeil means trick your eye. So if you see something and it's perspectival and it looks like it's continuing the space that you're in, that's a trompe l'oeil. It's tricking your eye into thinking that the pictorial space depicted on the wall is the real space of the world. There's this very complex trompe l'oeil stuff going on here. And the construction on the Ducal Palace in Urbino was such a vast task that everybody was brought in to work on it. And by everybody I mean there was a little shepherd boy, a little farmer boy, let's say, who lived down the lane, the young Bramante, who would have under normal circumstances continued to be a little farmer boy, was brought in and was an apprentice to the painting workshop in the Palace of Federico. And it is thought that the perspective of the Stuyolo may have been laid out by the young Bramante. And Bramante is a really famous Renaissance architect whom we'll talk about quite soon.