So in the last lesson we left off with intuition 18, we said that the Middle Ages were not fundamentally interested in a realistic rendering of space. Giotto instead recovered a sense of realism that ranges from the carnality of the figures, let's say, to the realism of the truth of the things of the narrative. He has above all a spatial realism. There is the desire to place his figures within credible spatial environments to give body, volume, plasticity to his figures. He does this through spatial boxes. We have seen not only through spatial boxes, but the spatial box is a mechanism, an idea that greatly helps the composition of space, but he always does it in an empirical way. What does it mean? It means that Giotto has an idea of spatiality and of the progression of the figures that, going towards the horizon, become smaller and smaller, but he scales them in an intuitive way, that is, he does not follow a mathematical rule. The first to follow a mathematical rule and, let's say, codify this mathematical rule will be Filippo Brunelleschi, with whom the Renaissance is traditionally considered to begin, at least with this triad. The very important artists are Brunelleschi as regards sculpture, Donatello for that, who remained, used architecture, Donatello for that. which concerns Masaccio's sculpture and which concerns us painting, what does Bonelli do, that in reality nothing remains written of what he codified? We know that he betrayed 1.414 and 1400 16 euros in what he builds, he creates two small panels, two tables with two perspective views, one of Piazza della Signoria with, let's say, the Palazzo Vecchio framed in a certain sense and the other with the Baptistery of Florence. The panels have a function and are built according to a grid of lines that converge in a central vanishing point on the horizon, therefore everything from all the instrumentation, everything that is created follows this trend of these lines. The panel in particular had a sort of hole at the height of the vanishing point and therefore you looked from behind this little tale, you looked into the hole and with a mirror placed frontally if you had the image reflected perfectly in perspective, a linear perspective I remember, has something to do with what interests us, even this central perspective tries to create a credible environment, tries to give the sense of the perspective escape of the buildings or of the characters and figures. which however reduce in size going towards the horizon but it is absolutely not the most realistic way of seeing in the sense that the human being does not see according to the central perspective to begin with we do not have a point of view because we have two eyes and therefore it is evident that the human vision is a different vision this perspective grid is rigid but it is also true however that this was a mathematical method that gives a very strong sense of depth and of a regulated regular depth how it works you see an ideal city by Leon Battista Alberti it is evident that the buildings that surround so to speak the temple he cried control units we find precisely at the center of the images on which the vanishing point is set are instead placed according to a grid you see a grid that is built divides the space and allows us to understand many there are also within a delimited space many safe ones that precisely descend let's say towards the horizon you see that the buildings follow in a millimetric way those are the perspective grids created starting from the vanishing point on the other hand all of us in middle school played the game they made us play the game of cypresses 9 vanishing point on the horizon a construction and then the setting of these of these times that should represent them cps that follow these lines that start precisely from the vanishing point after he says obviously removing the lines I this avenue let's say so the safe ones that narrow and therefore move away from my point of view towards the horizon so let's say it is an attempt to search in the number that is in the regularity of nature a possibility of creating a complete space that is an ideal space in this sense there is the immediate absolute total recovery at least from a conceptual point of view of the activity we know that ancient art focuses fundamentally on the proportions that is on the dimensional relationships between the parts between the objects between the parts for example of a body we also know that Greek art places man and the beauty of man at the center of the universe we know that man is perfect as he evidently made in the image of the divinity and of the Greek and Roman lymph are anthropomorphic so it is evident if the god is beautiful and perfect the man is equally and the proportions of the place must be sought within a dog and so we look for an old mathematics to establish what the dimensions of the various parts of the human body should be and descending from these dimensions we do the same in architecture where for example the diameter of the column taken at the base values the same does in Amatrice for all the other dimensional and proportional ratios so it is evident just as I will have a man who is made is eight times the length of a column that is 10 times the height of the diameter of the base that is a series of established proportional ratios of rules that give me the opportunity to build perfect safes that are connected to mathematics and mathematical laws that are directly taken from nature we talked this morning in classes on the golden section and therefore we saw how the golden section is a rule let's say that gives us the possibility of building perfection if not of the Greeks and also according to those who recover the golden section in the Renaissance but that the Greeks discovered the golden section the ratios that link the proportions of the golden section of nature we said that we find them for example in the structuring of the galaxy in the way in which if you position them in the center of the sunflower then We have a series of mathematical geometric rules that are directly drawn from nature. Now the problem of the Renaissance is that the Renaissance programmatically chooses to recover the classical world but knows almost nothing about the classical world. It does not know the canon, for example, it knows that the canon of Polifin Eto'o exists but it does not know what the established proportions canonized by Policleto are. It has a very vague idea of what the average rates are. What is not, a few examples of the classical world are buildings. The people in Rome remain and they are ruins. It is unable to make a clear difference between the first classicism and the second, a drought or everything. I see that the Roman between what is imperial and what is instead late antique and late Roman and therefore you see well that by class we mean a bit of everything. The recomposition of this classical world is something very complex. These artists, but above all these humanists, will have to start rediscovering by digging into classical literature that what can be found in the libraries of the scriptoria of the letter on the classical and through literature reconstruct a series of rules of doing. For example, we know that the first chair of Greek language well let's say a stability and elected in an Italian university in Florence in the fifteenth century and therefore you will see that this interest in the world also for the classicism evident won in Florence a push apart from flying but we also know for example that in this period the treatise of Vitruvius, the de architectura, was rediscovered that he was an architect of this incredible importance has become an absolute point of reference for the artists and architects of the Renaissance because precisely this manual of architecture deals with protections, a manual where it is explained how the orders, the proportions, the various buildings, the parts in the c. is a manna and a blessing for the artists and architects of the Renaissance because finally a text that in the quota how the Romans built buildings and on this text they can base their research the image that you see on your right is precisely of interpretation in the man gist ruviano which is given precisely by Leonardo 12 who builds this perfect man who is perfectly inscribable in a circle in a program that are two perfect figures par excellence because the square all in four equal installments for where it is evident how it is a central figure like the circle man who knows and let's say the center the navel and the center precisely of the circle and and this does not compose let's say a figure that is perfect not so much in size as in proportions image you see instead above is taken from the treatise and excuse the repetition by Francesco di Giorgio Martini Francesco di Giorgio Martini a bit like it is done in the classical world tries to reconstruct the perfection the regularity of the layout of a basilica you see with which the transept is also due your mind one on the proportion of the human being nor the man therefore it is evident of this connection between man and the nature of architecture and art an evidently immediate connection clear and which is taken directly from the classical world this frame goodbye to an infinity of studies and to a treatise also rather stringent so we will try to talk about painting of architecture of sculpture and perspective we were also thinking of perspective Pingelli by Piero della Francesca trying to establish rules simply to give a series of canonizing of codifying rules to give a series of indications as precise as possible often with mathematical directions to construct certain objects whether painted, sculpted or constructed figures. Consider that the Renaissance will have a very large literature dedicated to the theme of the ideal city, that is, how a perfect city can be built from scratch from scratch. This ideal city will be looked at by Francesco di Giorgio Martini, for example, there is the network that his Sforzanda hypothesizes. There is the ideal city of Sforza, therefore in the due of Milan and which obviously will have very regular proportions of dimensions, therefore a square shape. If you remember the functioning of the Roman city, you will not find the castrum with the decumanus cardo with the four doors, that is, a series of indications of irregularity and of structured established dimensions that gave harmony to the figures. It is therefore evident that the Renaissance searches for this sense of harmony in the classical world and the linear perspective centers in which we have spoken is nothing but one of the many attempts to reconnect to the classical world in the sense that what is sought is precisely a golden iron mathematical rule that can direct in some way guide the artist and the realization of his works. We will see that the artist is precisely central who From the beginning of this whole story it will be Filippo Brunelleschi who will meet his contemporaries, his greatest contemporaries in 1400. In the competition for the second door of the Baptistery of Florence he will not win the competition and this theme is fortunate because it is not the es that will not take this defeat well, it is probably precisely thanks to this defeat that he will decide to abandon at least in part the sculpture and from metalwork techniques in general to dedicate himself to architecture. Brunelleschi will go to Rome where he will really study what remains of Rome, therefore not only on some texts and on some finds that had remained in Florence from the source to Rome, therefore the actual finds, he will measure, make sketches, choose which parts are to be recovered and then he will build an entire language that does not invite the classical world but reconstructs in some way a new classicism and this is the strength of the Renaissance. It is not a simple imitation, therefore it is not a question of copying the burn of the sure hands, the exteriority of the sure hands of recreating a classical environment that ideally philosophically the classical. The will is to take an example in order to build a new classicism there is a world where man is once again at the center of the universe man with all his characteristics and in all his aspects therefore not only in art therefore in sculpture of painting with architecture but in literature of philosophy of politics therefore man as the new center of the universe next time we will talk precisely about the competition of 1401 and the beginnings let's say if we finally look at the Renaissance also looking at some works of art finally making some comparisons