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Lezione Di Galileo Galilei Sull'inferno Di Dante

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Lezione Di Galileo Galilei Sull'inferno Di Dante GALILEO GALILEI’S LOCATION, SHAPE AND SIZE OF DANTE’S INFERNO AN ARTISTIC AND EDUCATIONAL PROJECT Alessandra Angelini Corso di Grafica d’Arte dell’Accademia di Belle Arti di Brera Paola Magnaghi- Delfino Tullia Norando Laboratorio Didattico FDS -Politecnico di Milano Aplimat -Bratislava February 4 – 6 , 2014 1 http://fds.mate.polimi.it 2 Text Presentation QR code 3 The lectures on Dante’s Inferno Autograph manuscript of Galileo’s lectures 4 The Artistic and Educational Project 5 Martina RIZZATI Rubinia DI STEFANO 6 Marta FONTANA 7 Poster of the project 8 Dante’s Memorial 9 Bergamo’s Science Festival 10 1586 The Little Balance 11 Università degli Studi di Pisa Guidobaldo Del Monte 12 1540 Cosimo I de’ Medici 13 1633 Two New Sciences 14 The structure of the Inferno by Antonio di Tuccio Manetti Paolo dal Pozzo Toscanelli 1397 -1482 PERSPECTIVE GEOMETRY ARITHMETIC Filippo Brunelleschi 1377 - 1446 COSMOGRAPHY Antonio di Tuccio Manetti Florence 1423 -1497 ASTRONOMY Leon Battista Alberti 1404 -1472 VITA DI FILIPPO BRUNELLESCHI DIALOGO CIRCA IL SITO, FORMA ET MISURA DELLO INFERNO 15 Alternative structures of the Inferno Cristoforo Landino 1481 Antonio di Tuccio Manetti Girolamo Benivieni Accademia 1506 Fiorentina Commedia’s Florentine Editions Galileo Galilei’s lectures Alessandro Vellutello Commedia’s Venetian 1544 Editions 1587 -1588 16 17 Map ( XII century) Map T - O (1472) 18 Cape of Ptolemy 19 The shape of the Inferno Jerusalem is in the middle of the arc. The angle at the center is 60 degrees. 20 The funnel of the Inferno Giovanni Stradano (Jan van der Straet) Bruges 1523-Florence 1605 21 Traditional pattern of the Inferno 22 The First Six Levels • Distance from the Earth’s center The various levels of Manetti’s Inferno are regularly spaced, in fact the first six levels are equidistant with 1/8 the radius of the Earth between each level and the next. Level Distance from the Earth’s center Limbus 2839 17/22 Level 2 2434 1/11 Level 3 2028 9/22 Level 4 1622 8/11 Level 5 1217 1/22 Level 6 811 4/11 23 Antonio Manetti’s plan 24 Grand Old Man of Crete 25 Grand Old Man 26 Dante’s path E io a lui: «Se 'l presente rigagno si diriva così dal nostro mondo, perché ci appar pur a questo vivagno?». Ed elli a me: «Tu sai che 'l loco è tondo; e tutto che tu sie venuto molto, pur a sinistra, giù calando al fondo, non se' ancor per tutto il cerchio vòlto: per che, se cosa n'apparisce nova, non de' addur maraviglia al tuo volto». Inferno XIV , 121 - 129 27 Dante’s path And I to him: "If so the present runnel Doth take its rise in this way from our world, Why only on this verge appears it to us?“ And he to me: "Thou knowest the place is round, And notwithstanding thou hast journeyed far, Still to the left descending to the bottom, Thou hast not yet through all the circle turned. Therefore if something new appear to us, It should not bring amazement to thy face." Inferno XIV , 121 - 129 28 Dante’s path 29 Thales’ Similarity Theorem 30 • Widths of the first six levels Manetti divided the length of the arc on the surface from Cuma to Jerusalem into two parts: 1000 miles + 700 miles In the first 1000 miles he marked 10 spaces, each one of 100 miles, beginning from the mouth; from these he deduced the widths of the first six levels widths on the surface Limbus 87 1/2 100 Level 2 75 100 Level 3 62 12 100 Level 4 50 100 Ring 1 37 1/2 Level 5 112 1/2 300 Ring 2 37 1/2 Ring 3 37 1/2 Ring 1 25 Level 6 75 300 Ring 2 25 Ring 3 25 31 Malebolge Tu non hai fatto sì a l’altre bolge; pensa, se tu annoverar le credi, che miglia 22 la valle volge. Thou hast not done so at the other Bolge; consider, if to count them thou believes, that two – and – twenty miles the valley winds. Inferno XXIX , 7 - 9 32 Malebolge Cercando lui tra questa gente sconcia, con tutto ch’ella volge 11 miglia, e men d’un mezzo di traverso non ci ha. Seeking him out among this squalid folk, although the circuit be eleven miles, and be not less than half a mile across. Inferno XXX , 85 - 87 33 Malebolge Dante says that the ninth bolgia turns through 22 miles, and, in consequence, the diameter must be 7 miles. Then Dante also says (Inferno, XXX, 82-87) that the tenth bolgia turns through 11 miles, and, in consequence, the diameter must be 3 1/2 miles. Manetti thus supposed that the radii of the bolge were in arithmetic progression and obtained Bolgia Arc lenght Diameter Radius 10 11 3 1/2 1 3/4 9 22 7 3 1/2 8 33 10 1/2 5 1/4 7 44 14 7 6 55 17 1/2 8 3/4 5 66 21 10 1/2 4 77 24 ½ 12 1/4 3 88 28 14 2 99 31 ½ 15 3/4 1 110 35 17 1/2 34 (17 1/2 : 700) (3245 5/11) = 81 3/22 Distance of Malebolge from the center of the Earth 2/8 (3245 5/11) - 81 3/22 = 730 5/22 The depht of Geryon’s ravine 35 The Well of Giants 36 The width of Malebolge and Well width on the Earth’s surface Bolgia 1 1 3/4 70 Bolgia 2 1 3/4 70 Bolgia 3 1 3/4 70 Bolgia 4 1 3/4 70 Bolgia 5 1 3/4 70 Bolgia 6 1 3/4 70 Bolgia 7 1 3/4 70 Bolgia 8 1 3/4 70 Bolgia 9 1 3/4 70 Bolgia 10 1/2 20 Land Malebolge-Well 1/4 10 Well 1 40 37 In the Divina Commedia from these verses Facemmo adunque più lungo viaggio, Volti a sinistra; e al trar d’un balestro Trovammo l’altro assai più fiero e maggio. Therefore a longer journey did we make, Turned to the left, and a crossbow-shot oft We found another far more fierce and large. Inferno, XXXI, 82 -84 We can argue that “Dante and Virgilius turn around the well” and so the well must have a circular or polygonal shape, and that the distance from one Giant to the other is about 300 braccia (a crossbow-shot). 38 The size of Lucifer and the spheres of ice Lo ‘mperador del doloroso regno da mezzo ‘l petto uscia fuor de la ghiaccia; e più con un gigante io mi convegno, che i giganti non fan con le sue braccia The Emperor of the kingdom dolorous from his mid-breast forth issued from the ice, and better with a giant I compare than do the giants with those arms of his Inferno , XXXIV, 28 - 31 39 The size of Lucifer and the spheres of ice 40 The size of Lucifer and the spheres of ice La faccia sua mi parea lunga e grossa come la pina di San Pietro a Roma, e a sua proporzione eran l’altre ossa His face appeared to me as long and large As is at Rome the pine-cone of Saint Peter's, And in proportion were the other bones Inferno , XXXI, 58 - 60 41 Pinecone is bronze artefact of Roman origin, which is now in the Belvedere’s Garden (Città del Vaticano, Rome) 42 Height of a man = 8 times the face Height of a man = 3 times the arm Height of a man = 4 distance from the navel to the middle of the chest 43 braccia Pinecone 5 ½ Nembrot 44 Dante 3 Arm of Lucifer 645 1/3 Lucifer 1936 Navel- middle of the breast 484 braccia Fourth sphere 500 Third sphere 1000 Second sphere 1500 First sphere 2000 44 We can assess the huge size of Lucifer if we compare his height with that of the tallest buildings in the world 45 Students 46 FEDERICA AMORUSO 47 FEDERICA AMORUSO 48 CARLO BARONI 49 CARLO BARONI 50 ANNA BASSI 51 ANNA BASSI 52 ANDREA BERTOLETTI 53 ANDREA BERTOLETTI 54 CLAUDIA CARIGLIA 55 CLAUDIA CARIGLIA 56 RUBINIA DI STEFANO 57 BIANCA FASIOLO 58 BIANCA FASIOLO 59 MARTA FONTANA 60 CAMILLA GUERRA 61 CAMILLA GUERRA 62 ELENA MAFFIOLI 63 ELENA MAFFIOLI 64 MARTINA RIZZATI 65 But you have disposed all things by measure and number and weight. Holy Bible, The Book of Wisdom, 11 - 20 66 Alessandra Angelini Artist and Graphic Art professor Accademia di Belle Arti di Brera www.alessandraangelini.org Thank you for your attention Paola Magnaghi-Delfino Tullia Norando Department of Mathematics FDS Laboratory Politecnico di Milano www.mate.polimi.it 67 Social Network MostraGalileoPolimi MostraGalileoPolimi MostraGalileoPolimi 68 Manutius edition-1515 69 Alessandro Vellutello’s Inferno Galileo Galilei’s Life Magnaghi & Norando – FDS Main Projects 70 Alternative funnels of the Inferno Stradano 1523 - 1605 Vellutello 1544 71 Alessandro Vellutello’s plan 72 Alessandro Vellutello versus Antonio Manetti 73 Galileo Galilei’s life Galileo Galilei was born on February 15, 1564, in Pisa in the Duchy of Florence, Italy. He was the first of six children born to Vincenzo Galilei, a well- known musician and music theorist, and Giulia Ammannati. In 1574, the family moved to Florence, where Galileo started his formal education at the Camaldolese monastery in Vallombrosa. 74 Galileo Galilei’s life 1581 – Enrols as medical student at University of Pisa 1582 – Attends mathematics lecture by Ostilio Ricci and decides to study math and science 1585 – Leaves University of Pisa without degree and works as tutor 1586 – Invents hydrostatic balance; wrote La Balancitta (The little balance) 1589 – Appointed to Mathematics Chair, University of Pisa 1590 – Partially completes De Motu (On Motion), which is never published 1591 – Death of his father, Vicenzo Galilei 1592 – Appointed professor of mathematics at University of Padua, remains 18 years ~1593 – Invents early thermometer that unfortunately depended on both temperature and pressure ~1595 – Invents improved ballistics calculation geometric and military compass, which he later improves for surveying and general calculations and earns income from tutoring on its use 1600 – First child, Virginia is born; ~1600 Le Meccaniche (Mechanics) 75 Galileo Galilei’s life 1610 – Publishes Siderius Nuncius(Starry Messenger); views our moon's mountains and craters and brightest 4 of Jupiter's moons 1611 – Discovers phases of Venus; granted audience with Pope; made member of Lincean Academy 1616 – Officially warned by the Church not to hold or defend the Copernican System 1616 – The Catholic Church places De revolutionibus orbium coelestium
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