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Galileo Galilei's Location,Shape and Size Of GALILEO GALILEI’S LOCATION,SHAPE AND SIZE OF DANTE’S INFERNO: AN ARTISTIC AND EDUCATIONAL PROJECT MAGNAGHI-DELFINO Paola - NORANDO Tullia Paola Magnaghi and Tullia Norando are members of the School of Engineering of the Politecnico di Milano and, in particular, of the FDS Laboratory. The FDS laboratory (Formation, Science Communication, Didactics and Experimental Teaching) operates in Mathematics' teaching and in science communication. Teaching activities are developed in co-operation with the world of primary and high school, for the training of teachers and students and the experimentation of non-traditional forms of learning. In this context, FDS promotes large-scale initiatives for the dissemination and the "demystification" of the difficulties of mathematics . If you are interested in more information about our activities, we are at your disposal. You can visit this website. Now we start our presentation. We can see the text using this QR code. Introduction There is a close relation between Mathematics and Fine Arts during the Renaissance: mathematical knowledge is applied in drawings and paintings with the use of symmetry, producing ratios and proportions. Within the study of such a context arises our artistic and educational project as a collaboration between the FDS Laboratory and Accademia di Belle Arti di Brera. The project is inspired by the first of two lectures held by Galileo Galilei at the Accademia Fiorentina in 1588. These lectures were commissioned by the Accademia to solve a literary controversy concerning the interpretation of Dante’s Inferno. In these lessons Galileo took the opportunity to show his mathematical abilities combined with his strong background in Humanities. When giving his lectures Galileo probably used drawings to explain how to map Dante’s Inferno, because the difficulty of the subject which does not admit of easy explication in writing. Galileo’s manuscript survives and is catalogued in the Filza Rinucciniana 21 of the Biblioteca Nazionale di Firenze, but the drawings are lost. The artistic and educational project The artistic and educational project “Galileo Galilei’s location, shape and size of Dante’s Inferno” was proposed to a group of students of Graphic Art course in the Accademia di Belle Arti di Brera. Students were the actors in the project, the first addressees of all communication; each of them was the creator of his artwork. The project here presented was meant as an opportunity for the students of Graphic Art to investigate the relationship between geometric representation and artistic interpretation. The work plan was divided in two parts: the mathematical laboratory and the artistic work. In the second part the students were followed by their teacher and artist Alessandra Angelini. The mathematical laboratory The students followed lessons about the cultural environment and the mathematical aspects of the topic and then they went into the concept of mathematical perspective and the use of proportion and similarity in order to render mathematically the precise positions of Inferno’s rings. They studied the Inferno’s architecture, the Manetti’s plan and estimated the sizes, the widths, the lengths of the eight levels and finally the height of Lucifer. 1 The artistic work: technical drawing and free creative artwork First, each student created a “technical drawing” that is a scaled drawing of Dante’s Inferno, based on Galileo’s calculations, using different types of paper and free-chosen drawing techniques. The choice of different colouring techniques and papers made possible that every drawing could give emotions strongly different, despite being equal ratio and proportion. Therefore there was the same Inferno, in shape and measure, but much different in impressions and feelings. After, each student created a “creative artwork” aroused from his artistic vision and inspired to the Commedia’s verses. They were free to choose the artistic techniques, supports and dimensions of them works, so all students created very different works. They realized drawings, paintings, original engravings and various dimensions woodcuts, rich in colour and sign and all tightly related to the author’s reflections. At the end of our presentation, you will see a selection of the technical drawings and the free creative artworks and can help to understand the thinking and the creative force that characterized this project and the students’ different solutions. The students’ works were displayed on the exhibition that was held at Politecnico di Milano (May 2012). After the works were exhibited at the Museo Dantesco of Ravenna (September 2013) and at the Bergamo Science Festival (XI Edition, October 2013). Some sketch from Mathematical Laboratory Galileo Galilei. In 1586, the young Galileo Galilei wrote his first scientific book La Bilancetta (The little balance). He sent his work to many Italian mathematicians and he got a favorable reply from Guidobaldo Del Monte, Inspector of Fortifications of the Granduca of Tuscany, Ferdinando I de’ Medici. When the chair of Mathematics at Pisa became open, Guidobaldo arranged an invitation for Galileo to address to the Accademia Fiorentina two lectures on mathematical topics. The Accademia Fiorentina was founded in Florence in 1540 in accordance with the wishes of Cosimo I de' Medici. Cosimo instituted the Fiorentina’s public lectures to supplement its private meetings, allotted stipends to members and encouraged the Accademia to render “every science from every other language into our own”. The principal topic of discussion of the Accademia was the question of what should constitute the basis for Italian language. Indeed at those times it was referred to as volgare, roughly "the common tongue", and not yet organized into a framework of rules. The Accademia Fiorentina believed it should be based on contemporary Florentine usage and on the language of Dante. Galileo’s audience at the Accademia Fiorentina was not a mathematical one: it was a lecture on Literature that would turn Galileo's fortunes. In 1589 indeed, he was appointed to the chair of Mathematics in Pisa. For a long time the manuscript of the two lectures was forgotten, perhaps hidden by Galileo himself, because it contains a mistake about the question of the scale invariance. The last book of Galileo “Two New Sciences” (1633) begins with the subject of scaling and the observations on scaling in general are ingenious and deserving of the prominent place he gives them. It is clear that Galileo assign enormous importance to the problem. The beginning of his interest in this issue is certainly to be found in these two lectures. In the lectures, Galileo examines the opposing views concerning the structure of the Inferno proposed by Antonio di Tuccio Manetti and Alessandro Vellutello. The two arguments are identical as regards the general appearance of the Inferno, but are considerably different regarding the shape and the size. 2 Antonio Manetti Antonio di Tuccio Manetti (1423–1497) was a Florentine mathematician and architect, member of Accademia Fiorentina, and biographer of the architect Filippo Brunelleschi. Manetti thus wanted to show that Architecture is not only a useful technique, but has a role comparable to that of the Humanities. For this reason Manetti attempted to map out the realm Dante described, based on the textual evidence and using scientific methods. Although Manetti never himself published his research regarding Dante's Inferno, the earliest Renaissance Florentine editors of the poem, Cristoforo Landino and Girolamo Benivieni, reported the results of his research in their respective editions of the Divina Commedia. Dante’s geography Manetti’s plan is based on Dante’s geographical knowledge and the religious beliefs. The sphericity of the Earth was of course well known in the Middle Ages: the Earth was represented in maps called Mappae Orbis Terrae, or T-O maps, where a T-shaped Mediterranean sea divided the three continents known at the time (Asia, Africa and Europe), surrounded by the Great Ocean. The reason is that during the Middle Ages, it was believed that land occupied half of the Earth’s surface, while the other hemisphere was occupied by the Ocean; maps were thus related only to land. Maps also had a symbolic meaning: Jerusalem was always at the center and Asia was always in the upper section. In the maps the regions North of the Arctic Circle and the part that lies South of the Tropic of Cancer (Hic sunt leones) were missing, what remains was an area called Spherical Trapezium and had a shape similar to a cloak (cape of Ptolemy). The land, called the Oecumene, ranged from the Pillars of Hercules (Cadiz) to the mouth of Ganges, whose distance for Dante was 180°, while in reality it is 120°, so it seems that the Earth was “stretched” from East to West. Jerusalem, the center of Mankind, was exactly at the center of Oecumene. In the Middle Ages, people believed that the terrestrial radius was about 3250 Florentine miles (1 Florentine mile is about 1,74 Km), so the measure is about the 88% of the terrestrial radius. Manetti’s Inferno Manetti’s Inferno is a cone-shaped region in the Earth, with the vertex in the center of the Earth and the base on the surface, centered on Jerusalem. The cone is generated by rotation of the circular sector which has radius identical to the terrestrial radius. Because the distance from Jerusalem to Cuma was believed to be 1700 miles, the arc which is drawn from Jerusalem to the edge of the mouth of the Inferno is of 1700 miles. Therefore the circular sector has the angle at the vertex of 60°. The Inferno does not occupy the whole spherical sector but only the part of the cone which is, under Jerusalem, at the depth of 1/8 of the terrestrial radius. The funnel is made of nine circles. The first circle is the widest; progressively, the ninth circle is the smallest.
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