 Today, we're going to talk about the beginnings of the Renaissance, but before we do, we're going to talk about a precondition to the Renaissance, and that is the prosperity and the thriving economic condition of towns and this growing tendency toward urbanization. The area we're going to concentrate on is Tuscany, and we looked a little bit at Tuscany yesterday when we saw Sienna and Florence and Pisa and a number of the great cathedral towns in that area. The first thing I want to mention is the nature of medieval urban space, very dense, very tightly tangled. The town we're looking at on this image is San Gimignano, and San Gimignano is a hill town, and it's a hill town that is distinctive because of all these little thin spindly towers called Towers of the Nobles. Each noble family rivaled the next to have the most spectacular, tallest, thinnest tower, and these were great because you could get on top of the tower and watch for invading marauders, or when the marauders arrive, you could climb to the top of the tower and hunker down, or you could simply have prestige by having the most magnificent tower in town. Right now it seems as though San Gimignano is full of towers, but in the Gothic period there would have been far more. Here's a map of San Gimignano, and one thing we see is a surprising discovery and that is that San Gimignano is a Roman town. Of course it's hard to put out Cardo and Declamanos if you're on a hill, so there's a little bit of a wiggling of the Cardo and a little bit of the wiggling of the Declamanos, but it's essentially a rational plan. And the space of the public spaces fracture because of the hill town and because of the hierarchy of different buildings. So there's a diagonal echelonning of spaces along this juncture of the two major roads that's really, really very nice. Here's the church and here's a square with a fountain in the middle that we see on this image. During the Gothic period Italy was really splintered into different factions. The squabbling continued into the Renaissance and two of the factions were the Guelphs and the Ghibliens. For the most part the Guelphs were in favor of the Pope, in favor of the Papacy, and Florence is an example of a Guelph town. The Ghibliens were in favor of the Holy Roman Emperor up there in Germany somewhere. And Siena is a Ghiblientown, for example. The Guelphs were also, as a rule, let's say more progressive looking and a lot of the wealth of the Guelph towns did not come from inherited money and land, which was typical for royalists, but rather through industry and through banking and through trade. Hence there's a different taste in the arts between the Guelphs and the Ghibliens, the Ghibliens. I'm fairly happy to continue with Gothic traditions or let's say international Gothic style, an updated kind of Gothic, while the Guelphs are really very happy to experiment with newer and newer developments in the arts. Here's the town of Siena, spectacular. It's laid out on three hills with a major church on each hill, and in the low ground between the three hills there's one of the most beautiful squares that you will ever see anywhere. The Piazza del Campo in Siena. Twice a year they have horse races, a remnant from medieval culture, when each district in the town would field a horse and a rider, and they would compete for the glory of their district so that the colors of their district would be flown from the tower. And notice the tower of the town hall, the Palazzo Pubblico, it's one of those little spindly towers, not dissimilar to the ones that we saw in San Gimignano a moment ago. Inside the town hall we have one of the most interesting painting cycles that you will ever see, ever, and it is the good government, bad government cycle by the Lorenzetti brothers, Ambro Joe and Pietro Lorenzetti. I think the subject is interesting, and what I think is interesting about the subject is that it's really opening up a little window into the way people in 1338, 1340 thought about their society and thought about their agency in that society. In an earlier period, even 50 years before, even 30 years before, I think feudalism would still be sufficiently intact that people would simply say, our lot is bad, we are sinners, it's our duty to suffer, the king hierarchically has rights that we don't have, nothing we do can possibly remedy the situation. But here in the good government cycle, there's an indication that actually actions on earth pay off and that humans can actually improve their lot through hard work and through good management. We have a bunch of allegorical figures of things like justice and prudence and temperance up here overseeing the life of the citizens under good government. And notice they are orderly and prosperous. And here's their town. Their town looks not different, really, from San Gimignano. Their town is crenellated with these little interesting roofscapes. Their town has many, many towers. And their town is prospering like crazy. I find one of the most interesting places to look on this fresco is on the roof scape. These people are repairing the roof, these people are repairing the roof. That's good government, you take care of things. By the way, I said that this is a fresco and let me tell you what a fresco is. It's a technique of wall painting that's very, very common in southern climates. You need to have a fairly dry, warm climate to make frescoes work well. Because it is a wet method of painting. You prepare a piece of plaster and on the plaster surface, pigment is directly applied onto the plaster so that the pigment saturates the plaster. And you don't have the tendency of the plaster to flake off, but rather it's really in the wall. And this system is good in dry, warm countries because the plaster will dry. If you try to do this in a northern country, you might not have the same lock. So baker is baking the bread. Children are playing. People are doing their shopping. Good government. Good government also helps the landscape prosper. The farmers are sowing their fields. The orchards are bearing fruit and so forth. On a different wall, and in a bad state of repair, because bad government can't keep anything running right, we see an allegory of bad government. And instead of having the seven virtues hold in court, we have the vices hold in court. And with the vices, we have Mr. Devil himself with his devil horns and his little friend Donkey Boy over here. Piling up at the feet of bad government, we have decaying corpses or bodies crawling to their ruin. And here there is no maintenance on the houses. The houses are falling down. Things are crumbling. So good government is the way to go. Just one more thing about both good government and bad government as paintings, not as representations of an urban mindset, is that the Lorenzetti here are not really interested in showing you space. They're interested in representing something about the city, something about its density, something about its activity, but in terms of a perspectival representation of space that could be mapped out, it would be impossible to do. This is just aspatial. The representation of buildings and walls and landscape are as aspatial as in Egyptian painting almost. Here's Florence, the great Guelph town on the other side of Tuscany. Here's the cathedral begun by our an awful decambio that we discussed in our last talk. And here's the Arno River. As an aside, in the city of Piacenza, also in Tuscany, to the north of Florence, was a rabid Guelph town. And if someone was convicted of a crime, the first thing they did was bestow a noble title on them. And then the next thing they did was kill them. Palazzo Vecchio, the town hall in Florence, spindly little tower, that looks familiar to me. And here's an aerial view, showing you the structure of the town of Florence. It looks much less higgledy-piggledy, let's say, than Siena, but that's not Guelph versus Ghibli, and that has to do more with Roman versus not Roman. And Florence was originally a Roman town. There are still Roman ruins in Fiesoli, not so far outside of Florence, and the foundations of old Roman temples have been incorporated into a number of the Christian buildings in Florence. So here's Piazza della Signoria, the town hall, and the little square in front of it. And this drawing shows you Florence as a Roman town, with a cardo and decumanos crisscrossing it. And this shows you Florence in an expanded state. Here is the cathedral and the baptistery and the bell tower as a point of reference. And you can still see the cardo and the decumanos cutting through the town and giving it structure. This view also gives us a glimpse of a local tuscan vernacular, which we already got an inkling of when we looked at the Siena cathedral the other time. And that has to do with this pattern making of striped marble, white, greenish, pinkish, to create these interesting surface manipulations of stone fascia. And we have it on the Giotto bell tower. And we also have it on the baptistery right over here. Beautiful. By the way, this baptistery is pretty interesting. And it's a good example of something that's called Tuscan proto renaissance. It is a Romanesque phenomena. And it has to do with the appearance and a number of these Romanesque buildings of an architecture that seems distinctly classical. We have the round-headed arches, which we would have in any Romanesque building. But we also have pediments. And we also have Corinthian column capitals. Just when the towns of Europe are growing in prosperity and the universities are increasing the general knowledge of all the people, and trade is allowing them to exchange ideas and to exchange customs and become more diverse and complex in the way they organize their lives. The very trade routes that brought them this prosperity brought them a bad piece of news. And that bad news is black death. Black death peaked in Europe in around 1348 and killed off 30% to 60% of Europe's population. And the black death particularly hit you hard if you were in the southern countries. This is a little map showing you some trade routes. These are maritime trade routes. But there were also silk routes that came across overland. And with all of these expeditionary parties came goods. And with the goods came rats. And on the rats came fleas, bringing the black death. So every place you have a port, like Venice, like Genoa, like Pisa, you have centers of infection that continue from that point forward. However, there were some benefits to the black death. Not that I want to put too pleasant of a spin on a horrible phenomena. But as the workforce became scarcer and scarcer and scarcer, the remaining workers demanded a fair wage and got a fair wage. There were more consumer goods to be had. And trade and production of luxury goods could happen. You could get a class of people who were more philosophically inclined or inclined toward the arts. And the middle class rose and flourished after a while. There were some more macabre pieces of information. This is what doctors would often wear when they were ministering to the sick during the black death. These are bird beaks. That might be scary enough to make the black death go away, but they had rags soaked in ammonia inside the bird beak, believing that that would keep them safe. Of course, the disease was carried on the ticks. So no amount of ammonia in your nose would save you. Likewise here, we see a group of people with bubons all over their flesh, bubons. You see these bubons all over these people. They are these postulate blisters that characterize the ill smitten with black death. And it's bubonic plague. And the way the bubons break out is that you get this little pinkish circle that begins to fester and finally become a full blown boil. So the minute you see this first little pink ring form on your arm or your leg, you know you're a goner. Notice also that there's a geographical distribution of the bubonic plague. In the south, where you have a lot of Mediterranean ports that are the first to receive these shipments of goods from afar, the death rate is very, very high. And many say that it was closer to 75% to 80% of the population. Whereas in more northerly climates, the death rate was lower, around 20%. Could have to do with fleas getting killed off by cold weather, as well as the fact that not as many ships came into those ports. Black death, silks. In fact, there was a little commune or a community of Genovese traders by the Cameroon Sea. And Genghis Khan, no less an adversary than Genghis Khan, in order to effectively lay siege to their town through the dead bodies of bubonic plague victims over the town walls to sicken everyone inside the town. Oh, Genghis Khan. I bet all of you played this game at some point in your life. Ring Around the Rosie. It's a lovely little song. These are children in the 1950s singing Ring Around the Rosie with their school teacher and having a lovely time of it. I wonder if they know that they're singing about the Black Death, because Ring Around the Rosie is actually a Black Death song. Ring Around the Rosie means that little pink spot that develops on your skin before the bubons break out. A pocket full of posy has to do with the fact that the dead are covered with flowers. And ashes, ashes, we all fall down is a recognition of the inevitable fact that everyone must die and everyone will eventually turn to dust, ashes. This is a medieval depiction of the dense macabre or Ring Around the Rosie, as we call it nowadays. There were two reactions that people had to this almost certain inevitability of death coming with this terrible plague that wiped out so much of Europe. One reaction was extreme piety. And the other reaction was to eat, drink, and be merry, because you only had a short time on it. So these skeletons seemed to be carrying a hearty atmosphere all the way to the grave. So there was another consequence of the Black Death. And it quite could an unpredictable consequence of the Black Death. And that was that a high percentage of the master craftsmen died, because urban areas where the craftsmen lived were hit much harder than the countryside. And when the master craftsmen die, the whole method of teaching the arts is put into compromise, because they didn't have schools like we do now where you can come and learn architecture. If you wanted to be an architect, you had to apprentice. You had to be an apprentice to a master architect, a master stone cutter, a master mason. You learned your trade that way. The same was true for casting metals. The same was true for weaving. The same was true for painting. So when all or most of the masters died, the arts were in a crisis. People had to figure out how they could learn to do things in the absence of these masters. And it brought with that a recognition that they really couldn't do much at all. It's possible to say in the Middle Ages, people thought that they were living a life continuous and uninterrupted with the culture of the ancients. But they were basically Romans walking around with pointy outfits. But in this period of around, say, 1350 to 1400, people began to realize that, no, they are quite different. They've experienced about 1,000 years of darkness, during which time they've been forgetting things. They've been forgetting how to build complex vaults. They've been forgetting how to build aqueducts. They've been forgetting how to cast in bronze. And so what could they do? They didn't even have the masters to tell them what people knew five years ago. And they had an interesting response, and that was to not even think about what the masters knew, but to go back to antiquity, to go back to Roman culture and try to recover the glory that was Rome. Hence this notion of rebirth. Renaissance, renascita, means rebirth. And the thing that is being born again is the glory of ancient Roman culture. The philosophy, the art, the statecraft, you name it. And so all the texts that the ancients had that gave some insight into how they organized their thoughts or how they theorized their world were of great demand. And so this is Cezanne Ana's Vitruvius that we looked at before. And it's giving us some insight into the kinds of things that these people were pulling from the ancients. Certainly Cezanne Ana's Vitruvius shows us an interest in geometry, the square and the circle, and the nesting of the square and the circle. And all of these things are authorized by Plato as emblems of the divine. The circle is the cosmos, the square is the earth. But we also have here a kind of heroic nude, heroic with big feet, nude, which is a classical idea. It's the way that ancients would represent a person. And so what Cezanne Ana is beginning to suggest is not only is this interesting geometry and mathematical perfection being taken from the ancients, but also a kind of humanism, a notion that the human body is reflective of the divine beauty of God and deserves contemplation and not just the kind of scorn that was heaped on it in medieval times. This business of looking at the world and thinking about the world and trusting your senses is something that is really newish, let's say. Example, this is the model of the cosmos built by the great astronomer Johannes Kepler. And Kepler was an incredibly good observer of heavenly phenomena and kept very detailed notebooks. And Kepler's notebooks correspond with a uncanny degree of accuracy to mathematical predictions and models that would be made nowadays using computers to figure out what was going on in the heavens when Kepler was with really the unaided eye keeping records. And Kepler's observations indicated that the cosmos were elliptical. And that's pretty interesting because this model that Kepler gives us shows the cosmos as spherical with a nesting of all of these geometrical figures, a cube, a sphere, a tetrahedron, a dodecahedron and all the way down the line with these perfect platonic forms, none of which match his empirical observations. And Kepler was probably responding to the fear of sensory perception that goes back to Plato. When Plato tells you that your senses are subjective and not universalizable and corrupt. And there's no truth in what you perceive through your senses and the only truth is in the realm of pure ideas. And mathematics is descriptive of pure ideas. But there was another development and already in medieval times or late Roman times the philosopher Plotinus suggested that in fact beauty transcended mere sensory perception and beauty offered you a glimpse to the heavens. And so that it was not a distraction to admire a beautiful flower or a beautiful person but rather it was offering you a direct way to appreciate the beauty of God. And so through Neoplatonic thought which was very, very popular in the Renaissance especially in the early days, the entire physical world became reinscribed. This is a painting by Sandro Botticelli, famous painting of the birth of Venus. And let me just say that Botticelli was an extremely strong fundamentalist Christian. He was a follower of Savanarola, this arch monk who initiated the bonfire of the vanities where frivolous items of culture were burnt in this big heap. And yet Botticelli painted this beautiful female nude of a pagan topic, Venus. You would have to say, this is crazy, why is he doing this? And the answer is Neoplatonic thinking not only permits him to gaze upon beauty and understand that this is somehow revelatory of divine truth but it also allows him to make analogies, analogous links between, let's say, the virgin birth of Venus and the virgin birth of Jesus and the immaculate conception of the virgin. So this is a deeply pious theme when properly framed by Neoplatonic thinking. Shift in sensibilities. It might be instructive to see how the craft of painting responded to the new challenges brought about by this changed sensibility and this new interest in the physical world. The painting we have up here right now is a enthroned Madonna by Giotto. We'll be looking at it in a moment as a comparison. But before we look at Giotto, I'd like to look for a little while at some medieval images. This one of God the Geometer we've looked at before where God with his compass describes a perfect circle and makes order out of the chaos and forms the universe. The background is gold leaf. So this is clearly not a painting in the space of the world but a painting in some kind of celestial realm. The same is true of this bishop with a model of the city on his lap. Both of these figures are flat to find more by linear elements than by volumetrics. Both of these figures are hierarchically positioned not engaged in real activities in the real world. And the same can be said for Duccio's enthroned Madonna. I think this is an incredibly beautiful painting crazy about Duccio but there is this kind of linearity that characterizes the picture and really more of an interest in the playful and elegant swirl of line and drapery than any kind of representation of the human figure behind it or even the weight of gravity on the drapery. Duccio makes little gestures toward representing space by converging lines on the throne but the figures flatten out and the gold leaf contributes to the flattening. If we move just a few years ahead we can see Chimabue and Giotto. Chimabue in 1260 and Giotto about 50 years later. Chimabue discovered Giotto. Giotto was a little boy tending sheep according to Giotto Vasari's lives of the artist. He was tending sheep and sketching with a piece of charcoal on a nearby rock and Chimabue stopped and was stopped dead in his tracks when he saw this young boy drawing perfect circles and Chimabue knew that if you could draw a perfect circle you could be the greatest artist in the world. So Chimabue brought him forward and said, you sir, you shall be my apprentice. And so it went. So what exactly did Giotto learn from Chimabue? How did he pick up on things that his master taught and how did he transcend him? Well, certainly they're both using gold leaf backgrounds and as such the space flattens out. But Giotto has a really different conception of the human body than Chimabue. Chimabue's figure is characterized by these elegant linear folds and curves and seems to be floating on the throne rather than sitting on it. And the little baby seems to be hovering like a sock puppet on her hand. The figures flatten out against the space and the space is very, very tight. And look by contrast at the Giotto. These figures are fully volumetric and also he has a tendency of organizing figures in layers so that these robust space displacing angels form a foreground and behind that we have a middle ground of angels in green and behind that we have background. So there's a space being developed not only through the intuitive perspective that Giotto gives us on the throne but also through the volume of the figures and also through the layering of the figures back in space. Giotto is an interesting figure on all levels. This is a lamentation of Christ from the Scrovegni Chapel in Padua. And this is really an extraordinary painting. Now he doesn't have anything like the throne to help him develop a perspectival image of what the space of the throne might be. But he does use the geometrically conceived cylindrical volumes or pear shaped volumes of these figures to really occupy and thereby carve out a substantial space for the action of the figures. And the landscape creates a background in front of which the figures act out their suffering. Here he doesn't have architecture to map out the space but note how he uses the angels. He uses converging wedge of angels to begin to suggest the space coming together and moving back even deeper. Quite nice. And another thing that Giotto is doing that we have not seen before is that he's beginning to offer a certain amount of psychological complexity to these characters. These are not blank staring neutral figures but these are figures grieving for their loved one. The real watershed moment for this new sensibility that was emerging came at a competition for bronze doors at the Florence Baptistry. Here's the Baptistry, the Baptistry of San Giovanni said to have been built over a Roman temple to Mars right in front of the big cathedral, the Duomo Santa Maria del Fiore that we looked at in an earlier discussion. And here is the Giotto bell tower. So this is quite a prestigious competition to be building something in such a important site in the city. The competition doors are not the first set of bronze doors constructed for the Baptistry. Already in 1330 to 1336, Andrea da Pizano had made a set of bronze doors and it's useful to look at these just as a point of comparison to what happens in these new panels. There's a frame and the frame is a kind of Gothic quadrofoil. Funny little shape, not a window onto the world but really more a frame for a cipher. And even the way these different actions get characterized is almost more like a flat linear cartoon than anything that's happening in space. We're being reminded of the stories but we're not really being shown how these stories operate in the lived world. The competition brought forth some of the most extraordinary talents of the time. A goldsmith called Filippo Brunewski and a sculptor called Lorenzo Giberti. Of the many competition entries that were submitted for the bronze door competition only their entries remain but good enough. They're both pretty spectacular. Giberti ultimately won and this is Giberti's, sorry, this is Giberti's panel right over here and this is Brunewski's panel. And although I am a huge fan of Brunewski I would have to say the judges were correct in giving the award to Giberti. And one thing that I think is so extraordinary about the Giberti panel is how it is not using a medievalizing conception of space being unfolded flat against a neutral background but actually space is created through landscape and occupied by figures in this landscape. Here's what I mean. If you look at the Brunewski we get this kind of range. Things that are here. Things that are in the middle. Things that are up above. And they're not really in a continuous space. It's hard to understand how they all hang together spatially. Each element that's part of the tale is on its own special little platform. And by the way, the subject here is the sacrifice of Isaac. This is a story in the Old Testament that says Abraham was told by God to take his son, his only son Isaac up to a mountain top and to sacrifice him. And Abraham is very disturbed by this. This is his beloved son but even more beloved to him is God. So he takes his boy up and as he's about to sacrifice him on an altar an angel comes in and says, no, no, no, you don't need to sacrifice your son. Look in the thicket, there's a ram. And so God tested the faith of Abraham and Abraham met the challenge and the ram was sacrificed instead. So both of the artists are showing us the ram. Here's the ram up here in the thicket and the primary actors, Abraham and Isaac. Abraham and Isaac. And the angel of course is also a major actor. But in the case of the Brunelleschi these different episodes are stacked vertically. In the case of the Giberti there's a kind of spatial diagonal of landscape that locks everything together and really makes a much more charged composition. But they're both really good and they're both really classicized. Notice that this is Roman drapery that the figures are wearing. And notice too, the conception of Isaac here in the Brunelleschi we have a nude. Quite an idea, quite a Roman idea. But look at the conception of the nude figure in the Giberti. This is a totally classicized little Hercules of a nude sitting on a altar that looks more like a Roman sarcophagus than any altar used in Christian ritual. Quite amazing, quite amazing even in terms of the spatial conception. Notice on the Brunelleschi everybody is revealing their salient properties. Profile of a donkey, profile of a sheep, profile of a guy. Look what we have going on in the Giberti. These figures are turning in space. We see the back of a figure, quite amazing. You see the torquing of the landscape, the spiral of the landscape being acted out with the torquing of the figures. This is a kneeling contrapasto that we have here from our friend Isaac. And we have this oblique emergence of God coming out of the sky to halt the slaughter of the boy. As the project for the doors progress the ambitions become more and more and more complex. Here we have one of the panels from the east doors by Giberti called the Doors of Paradise. We see them here as a total compilation. And in terms of the task of Brun's casting they're already fairly amazed. What Andrea da Pizzano did the south doors he was doing something that by the standards of 1330 was pretty difficult and that was casting a Brun's panel this big. There are quite a lot of them and they're connected together by this inframement. Giberti casts even larger panels and casts them with a really complex kind of spatial undercut. So he's casting deeper, he's casting in a more refined way. There are terms used to describe what Giberti is doing. And the most basic term is bas-relief. Ba is French for low. So bas-relief means instead of making a fully realized three-dimensional sculpture three-dimensionalized space is being compressed into a low or narrow field. It's a particular kind of bas-relief called schia-chato and schia-chato basically means squash. If a mosquito lands on your arm, schia-chato, no more mosquito. You can see how effective this is. The figures in the foreground are almost fully rounded, fully cut away from the background. The front side of this rounded temple is quite distinct and as it moves farther and farther back, the relief becomes lower and lower and lower and you get this sense of incredibly deep space in a fairly narrow plenum of space. And look at the things that Giberti chooses to represent. He's bought into this recovery of the antique of the glory of ancient Rome, hook line and sinker. Everybody's wearing Roman drapery. The architecture is Roman. The planned typology of round building would have been known to Giberti and pretty much everybody because the pantheon was still operating as a church at the time. It's not very good at getting the Roman architecture down, but he's trying. We have this little indication of a columnar structure, a little bit of Corinthian going on and muscular volumetric bodies, bodies that bear weight, bodies in space and a real interest in space and landscape. And this is not even the most extraordinary panel. I find the birth of Eve to be quite amazing where Eve emerges from the side of Adam to fully classicize nudes and even an attempt to represent the specificities of landscape like water and the variability of trees and wind. Or over here, the representation of different ranges of layered classical arcades, Corinthian pilasters with wonderful detail, very closely observed and the kind of turning of the bodies in space that we saw in the competition panel is being developed even more fully here. Look, we have this little group of figures of whom we see the backs or this boy whose foot kicks out from the space and casts the shadow. Quite amazing with a little goat head. If you compare the ambition of the gates of paradise with the ambition of the earlier doors, you can see that the craft has increased the scale has increased and the conception of space has gone really far, far, far forward. So there's an interest in representing space but at the same time that there's an interest in representing space there probably was this lurking sense that too much attention to mere sensory perception is going to lead you astray and that wouldn't it be great if the pure idea authorized by Plato and subjective perception could somehow be married together. And this was a task really provoked by explorations of space like the ones we have Giberti doing here on the gates of paradise and pursued by the loser of the competition, Filippo Brunelleschi. Brunelleschi set himself the task of proving a mathematical solution to the question of perspective. All the perspective we were looking at in say the Giotto chair or even the Cimabue chair was just a kind of intuitive perspective. Things kind of converge. That's the appearance of things. That's the corrupt sensory perception of things that is not true because we know those things don't converge. If we measure them, they wouldn't converge. So Brunelleschi tries to marry together objective truth of mathematics with subjective vision and comes up with a formula to mathematics perspective. And he gives a proof, a demonstration proof to persuade the citizens of Florence that this is true. And what he does is he sets up a position right here by the main door of the Florence Cathedral. And the object that he draws is the baptistery which is a great object because it does have this connection to having been a Roman temple at one point. So what a good thing to draw. Or paint actually. And he has this crafty idea about painting it in such a way as to fool the viewer into thinking or not knowing whether they're looking at the painting or the real object. So here's the vantage point right here in front of the Duomo, in front of the cathedral. And he's got this cone of vision. He's got a vanishing point, a horizon line. He maps out the geometry of the building and casts points to create a perspective. And then what he does is really crafty and uncanny. His feeling is that people will know this is fake and not the real thing because they will know that the sky does not have moving clouds. So he paints it on a mirror. And there is a reflection of the real clouds on the mirror. And people look through a people and they look into a mirror and they see the reflection of the real space and the space of his baptistery collapsed on the same field. And in his day, the people that Brunelleschi ran into could not tell the difference between one and the other. And so suddenly with mathematics perspective, any qualms you might have had about trying to represent the space of the world were completely gone and perspective took off. This by the way is Brunelleschi's method more or less for representing perspective. And if any of you have ever had to try to construct a perspective in the old traditional non-computerized fashion, you probably used a method very similar to this. You have a measuring line in the vertical and in the horizontal and you simply project points upward and you get something that converges. Brunelleschi's method was never written down but he taught it to many of his friends, many of the artists such as Masaccio and Donatello were acquainted with Brunelleschi's method of perspective. It was not until a bit later that Leon Battista Alberti actually wrote down the technique of perspective in his book, The Pictura on Painting. But here in Masaccio and Masalino's cycle of paintings for the Brancacci Chapel, we begin to see the effect of this new mathematics perspective and also further developments of this interest in the antique, this interest in recovery of things Roman. Look at the expulsion of Adam and Eve over here. Two muscular, weight-bearing, classical nudes being driven out of paradise. Or look at the tribute money where St. Peter is paying off tribute money. There's an attempt at Roman architecture here, the arches are round. But this is Florence, this is not Rome and things are still too thin, too spindly. It's the look of classical architecture but not the substance, not the muscularity of classical architecture. But you do have that muscularity here with the figures. And when you look at this leg kicking out, you think that Masaccio must have seen the leg kicking out from the Ghiberti panel and thought that that was something he certainly wanted to play with. The Masaccio work that really makes manifest the lessons of perspective the best is a painting of the Trinity in the Church of Santa Maria Novera. Trinity is a common theme, father, son, and Holy Ghost, which is the dove hovering right between father and son. So I think what's interesting about this painting is that it operates both compositionally in a Gothic way but also in this new, perspectival way. So the traditional way that the picture would operate would be to become a hieratic symbol, a symbol driven by ritual and convention. And it kind of does this. The subject is the Trinity. And compositionally, if we trace the figures, we get a triangle. And the symbol for the Trinity is not a triangle exactly, but it's a triangle with a circle in the middle of it. And oh look, we also get a circle in the middle of it. And in the middle of the circle, we have the navel of Christ. So in many ways, Masaccio is casting Christ as the Vitruvian man in a circle inside of a triangle in a diagram of the Trinity. Pretty clever. But he's also doing more than that. He's unfolding through layering different ontological fields. And by ontological fields, I mean people who exist in different states of being. God and the Holy Spirit are back here, pulling forward in the range of the Virgin and Joseph of Arma Thea, who gave a tomb to Christ. We have Christ, who is both man and God. Pulling forward, and again, the architecture demarcates these different zones very, very clearly. We have donors, the people who pager, or this work of painting. But that's not all, because this is perspective. And so the eyeball of the viewer is also implicated in the space of the painting. So not only do we have God and the Holy Ghost and Christ and Mary and the donors and the tomb of the dead, but we also have the eyeball of the viewer. Everybody is implicated in the space. And the triangle that we had on the flat picture plane in the traditional spatialized description, two-dimensional description of space within the painting now becomes activated in a three-dimensional sense in Masaccio's perspective. Fabulous. And if you look at it, you'll see that he's looking at Roman architecture. He's got some coffering going on here. He's got some Corinthian plasters going on here. He's got some Ionic column capitals going on here. And they're going on in a kind of thin and unbelievably attenuated way. But he's trying. So Brunelleschi figures this out. And Brunelleschi's doing great, you have to say. Let me just mention that Brunelleschi's training is not as an architect and not even as a sculptor, but as a member of the silk guild. He's a goldsmith. So he's got some expertise in casting metals, but he has no expertise at all in architecture. However, as we mentioned before, there was this galling problem for the city of Florence. And that was when Arnolfo Di Cambio died, there was a giant octagonal hole in the middle of the church. And Florence, by this point, had prospered sufficiently that they felt they should try to get something on top of that giant gaping hole. And so they had a competition and everybody was invited to submit projects. And Brunelleschi, who had no expertise, no knowledge at all about architecture, came to the board of overseers and said, I can do it. I can build you the dome. And what's more, I can build you the dome without money or dirt. And what does he mean by money or dirt? And what he means is that the dome of the pantheon, which was the exemplary dome to which every other dome would be compared, was said to have been built on a mound of dirt and the stones were laid up on this dirt mountain. And then after the entire structure was intact, the dirt was carried away. And the citizens of Rome were happy to carry the dirt away because cleverly, as they were building this mound of dirt, they put coins in there. So the pantheon, probably not true, but pantheon was said to have been built with money and dirt, a mountain full of money that then got emptied out by the citizens. Brunelleschi says he can do it without money and dirt. So how's he gonna do it? And he says to the overseers, and again, this is according to Giorgio Vasari's Lives of the Artist, which is more hagiography than biography. Hagiography means lives of the saints. But anyhow, he says, I'll tell you why. I will not tell you how I will do it because if I tell you how I will do it, my method will be so clear and so logical. Everyone will want to do it. But I will give you a demonstration of how clever I am. And if you can do what I say forth as your task, then I will tell you my method for building the dome. And they say, okay, Brunelleschi, what do you have? And Brunelleschi says, I would like you to stand an egg up on its vertical axis. And he brings in a little basket of eggs. He tells people, try to do this, try to do it. And the eggs roll off the table, the eggs break, nobody can do it, and they finally give up. And say, Filippo, tell us, how do you set the egg on its vertical axis? And he takes the egg and he thinks the bottom of the egg with his finger so that it indents slightly. And then he sets the egg up on its vertical axis. And they say, Filippo, you are a cheater. You are doing something that you never said you were going to do. And he said, of course I didn't say I was going to do it, but it is not wrong to do it. It was simply my ingenuity that allowed me to understand that this could be done. So Brunelleschi gets the commission to build the dome. And to his great disgust, he's forced to work with Giberti on this project, even though he thinks Giberti is a nincompoop. And he's forced to be second to Giberti in command, although the whole project is initiated by this conception that Brunelleschi has of how to build the dome. So building of the dome is a project that Brunelleschi worked on for years and years and years, beginning in 1418 when he submits his first model and ending really at the end of his life. So here's the big hole. And what Brunelleschi does, you can begin to see by looking at this drawing, this sectional drawing. And that is, he conceives of it as not a singular dome, but a double dome, because it's a tricky problem here. And the tricky problem is, the span is so great, it will be difficult to find something that will cover that span and that will come down to allow the nave to translate through. He builds triangular piers over here and the part of the triangle gets hollowed out, but the double dome makes it lighter, but it also makes it rigid. When we talked about the pantheon, we already noticed that the geometry of the coffers do something quite similar. They scoop away material and make it lighter and they also, through the coffering, begin to brace the structure and make it stiffer. So this is what Brunelleschi does, this cutaway perspective shows us quite well what he does. He's got his double dome system going on and he's got a series of ribs that carry the load to points and the points come to rest at these points within the piers, within the triangular piers. In addition to that, he has a series of horizontal rings that are tied together. So he's got this kind of three-dimensional system locking together the exterior shell, the interior shell, and this series of rings together. And then as webbing to connect these things together, he puts in a particular kind of brickwork, a herringbone brickwork, that further engages the system and locks it together. So this is the ingenuity of Mr. Brunelleschi and this is the space between the two domes, which I personally will never do again in my life. This is the scariest place in the world. You think you're going to die. Brunelleschi didn't simply have to invent how to build the dome, which was hard enough, but he also had to invent how to get materials up to the dome. He had to think about what the geometry of the dome would be. And in so far as he was a goldsmith and knew nothing about domes, he tried everything. He went to the market and bought giant turnips and carved them to find the right shape for the dome. He went to the banks of the Arno where flat mud banks could be found and did drawings to full-scale so templates could be prepared for the masons that when they went up there, he did not want to be a millimeter off because if he was, the whole system would fail. This was a daunting enterprise. It was so daunting that he made some extraordinary rules for the workers. For example, he told the workers they could not come down and eat lunch and go back up again because this project was so high up off the ground that if they did that, there would be a real difficulty in terms of ever getting back up again. They would lose too much time. They would get dark. They would not have the opportunity to get back up and get down. So he told the workers they had to bring their lunches but they had to water the wine because he did not want the workers to be drunk and to fall down. So next time we will talk more about Brunelleschi, Brunelleschi's dome and other contributions to architecture by Mr. Filippo Brunelleschi and other great luminaries of the early Renaissance.