galileo galilei’s location, shape and size of dante’s...
TRANSCRIPT
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
GALILEO GALILEI’S LOCATION, SHAPE AND SIZE OF DANTE’S INFERNO
AN ARTISTIC AND EDUCATIONAL PROJECT
Aplimat -Bratislava February 4 – 6 , 2014 1
http://fds.mate.polimi.it
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Text Presentation QR code
The lectures on Dante’s Inferno
Autograph manuscript of Galileo’s lectures
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The Artistic and Educational Project
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Martina RIZZATI Rubinia DI STEFANO 6
Marta FONTANA 7
Poster of the project 8
Dante’s Memorial
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Bergamo’s Science Festival
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1586 The Little Balance
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Guidobaldo Del Monte
Università degli Studi di Pisa
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1540 Cosimo I de’ Medici
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1633 Two New Sciences
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The structure of the Inferno by Antonio di Tuccio Manetti
Filippo Brunelleschi
1377 - 1446
GEOMETRY
ARITHMETIC
COSMOGRAPHY
ASTRONOMY
Antonio di Tuccio
Manetti Florence 1423 -1497
PERSPECTIVE
VITA DI FILIPPO BRUNELLESCHI
DIALOGO CIRCA IL SITO, FORMA ET MISURA DELLO INFERNO
Paolo dal Pozzo Toscanelli
1397 -1482
Leon Battista Alberti
1404 -1472
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Alternative structures of the Inferno
Commedia’s
Florentine Editions
Antonio di Tuccio Manetti
Commedia’s Venetian
Editions
Alessandro Vellutello
1544
Accademia Fiorentina
Galileo Galilei’s lectures
1587 -1588
Cristoforo Landino
1481
Girolamo Benivieni
1506
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Map ( XII century)
Map T - O (1472)
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Cape of Ptolemy
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The shape of the Inferno
Jerusalem is in the middle of the arc.
The angle at the center is 60 degrees.
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The funnel of the Inferno
Giovanni Stradano (Jan van der Straet) Bruges 1523-Florence 1605
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Traditional pattern of the Inferno
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• 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.
The First Six Levels
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
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Antonio Manetti’s plan
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Grand Old Man of Crete
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Grand Old Man
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Dante’s path
Inferno XIV , 121 - 129
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».
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Dante’s path
Inferno XIV , 121 - 129
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."
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Dante’s path
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Thales’ Similarity Theorem
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• 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
Inferno XXIX , 7 - 9
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.
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Malebolge
Inferno XXX , 85 - 87
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.
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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
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2/8 (3245 5/11) - 81 3/22 = 730 5/22
The depht of Geryon’s ravine
(17 1/2 : 700) (3245 5/11) = 81 3/22
Distance of Malebolge from the center of the Earth
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The Well of Giants
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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
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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).
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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
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The size of Lucifer and the spheres of ice
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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
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Pinecone is bronze artefact of Roman origin, which is now in the Belvedere’s Garden (Città del Vaticano, Rome)
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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
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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
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We can assess the huge size of Lucifer if we compare his height with that
of the tallest buildings in the world
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Students
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FEDERICA AMORUSO
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FEDERICA AMORUSO
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CARLO BARONI
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CARLO BARONI
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ANNA BASSI
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ANNA BASSI
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ANDREA BERTOLETTI
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ANDREA BERTOLETTI
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CLAUDIA CARIGLIA
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CLAUDIA CARIGLIA
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RUBINIA DI STEFANO
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BIANCA FASIOLO
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BIANCA FASIOLO
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MARTA FONTANA
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CAMILLA GUERRA
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CAMILLA GUERRA
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ELENA MAFFIOLI
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ELENA MAFFIOLI
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MARTINA RIZZATI
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But you have disposed all things by measure and number and weight.
Holy Bible, The Book of Wisdom, 11 - 20
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Alessandra Angelini
Artist and Graphic Art professor
Accademia di Belle Arti di Brera www.alessandraangelini.org
Paola Magnaghi-Delfino Tullia Norando
Department of Mathematics
FDS Laboratory
Politecnico di Milano www.mate.polimi.it
Thank you for your attention
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Social Network
MostraGalileoPolimi MostraGalileoPolimi MostraGalileoPolimi
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Manutius edition-1515
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Alessandro Vellutello’s Inferno Galileo Galilei’s Life Magnaghi & Norando – FDS Main Projects
Stradano 1523 - 1605 Vellutello 1544
Alternative funnels of the Inferno
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Alessandro Vellutello’s plan
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Alessandro Vellutello versus Antonio Manetti
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Galileo Galilei’s life
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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.
Galileo Galilei’s life
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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)
Galileo Galilei’s life
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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 on
the List of Prohibited Books
1616 – Private letter Discourse on the Tides
1617 – Moves into Bellosguardo, west of Florence, near his daughters'
convent; observes double star Mizar in Ursa Major
1630 – Completes Dialogue Concerning the Two Chief World Systems and
subsequently receives approval of Church censor
1632 – Publishes Dialogue Concerning the Two Chief World Systems
Galileo Galilei’s life
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1633 – sentenced by the Inquisition to imprisonment, commuted to house
arrest, for vehement suspicion of heresy
1633 – Catholic Church places Dialogue Concerning the Two Chief World Systems on the List of Prohibited Books
1638 – Publishes Dialogues Concerning Two New Sciences
1642 – death in Arcetri, Italy
FDS - Magnaghi & Norando - Main Projects
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Dante’s Commedia
Luca Pacioli’s Capital Letters in progress
Jonathan Swift’ Laputa Island Alessandro Mazzucotelli, the iron and fire of Art Through the looking-glass in progress
Stage 2009-2010
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Our project’s aim is the study of the structure of Laputa Island, the floating island which
appears in the third chapter of Jonathan Swift’s novel “Gulliver’s Travels”. The students
conjecture that this island can really float thanks to the magnetic field, created by the
material which constitutes magnetic field, created by the material which constitutes the
core.
Analisi della struttura dell’Isola di Laputa Jonathan Swift’ Laputa Island
Stage 2010-2011
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Alessandro Mazzucotelli was born in Lodi not far from Milan, his family were dealers in
iron and he worked as blacksmith. He also designed jewellery and fabrics for the weaving
factory at Brembate. He is best-known for his wrought ironwork, in a vigorous Art
Nouveau, the style he not only followed but which he managed to exceed thanks to his
thorough studies from life of nature inspiration to the artistic movement, from which he
discovered also geometric -mathematical formulas.
The students , inspired by his works , decided to create a frieze.
Il sacro fuoco ( e il ferro ) dell'arte Alessandro Mazzucotelli, the iron and fire of Art
TeatroInMatematica
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I Numeri Primi e la Crittografia Prime Numbers and the Cryptography
Topics: Prime Numbers, Cryptography
Parallelismi: Geometrie Euclidee e Non Straight Line and Geometry that it describes
Topics: Euclidean a
Non-Euclidean Geometry
Il Caso Probabilmente: la partita a dadi The chance: a game of dice
Topics: The roots of the Probability’s Theory
I 7 ponti e il mistero dei Grafi The seven bridges and the mystery
of Graph Theory
Topics: Graph Theory
Il Dilemma del Prigioniero Prisoner’s Dilemma
Topics: Games Theory
L’Irrazionale leggerezza dei Numeri The Irrational Number Lightness
Topic: Irrational numbers
Metti, una serie a cena One night, a series at dinner
Topics: Fibonacci’s series, Golden Ratio
Appuntamento al limite Appointment to the Limit
Topics: Function, Limit, Derivatives
Stage 2007-2008
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In this project, the students apply the properties of the cycloid to the study
of special and giants slalom.
La cicloide: nuovi orizzonti per lo sci The Cycloid: a new way of skiing
Stage 2008-2009
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Marptolemaeus, an hypothetical Mercian astronomer, has defined the mathematic model
of the cosmologic system. This is the aim of these research: building the Mercian system,
supposing Mars to be at the centre of the universe. The choice of an astronomic theme
has been influenced by the fact that 2009 has been proclaimed the year of astronomy
because for the first time four thousand years ago Galileo observed the sky with the
telescope. Besides the Sun moves around Mars following an ellipse. The other planets,
Earth, Mercury and Venus, instead, describe orbits which don’t appear in our earthly
geometric books and that we have imaginatively called “epiclissoidi”.
La teoria martolemaica The Marptolemaeus’ solar system theory
Stage 2009-2010
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This paper deals with a research carried out in Monza to analyse the efficiency of the
network of chemists through the study of minimum paths and Voronoi tessellation of the
city map. In the first part, we give an in-depth explanation of the nature and purpose of
Voronoi diagrams and we briefly discuss Fortune’s algorithm for computational
construction of V.d. and how they can be applied to our study case. The second part of
the paper relates how we enforced our mathematical model by means of a statistical
inquiry and how we came to set up a working simulation.
Analisi della rete delle farmacie di Monza Analysis of the chemists network in Monza
Stage 2010-2011
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This project was finalized at calculating the mass
of Jupiter through observing the same four
satellites (Io, Europa, Ganymede and Callisto)
which both Galileo and Kepler used to follow
with their means almost 400 years ago. This
project implied several on-the-ground
experiences at the Astronomical Observatory of
Merate (AOM) which greatly enriched our
knowledge about some astronomical related
subjects that had been studied at school only
under their theoretical aspect.
Sulle orme di Keplero A study about Jupiter’s mass
Stage 2011-2012
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Operazione meridiana Sundial
The main aim of this project is to complete the
mathematical and geometrical planning as well as
the construction of a fully working sundial, equipped
with a solar calendar The position of the hour-lines
and date-lines has been calculated and laid out
through the application of some theorems about
spherical trigonometry in order to sort out a spatial
geometry problem. An important part of the project
consists in planning a spreadsheet which calculates
the equations of hour-lines and date-lines for a
sundial working in Central Europe.
Stage 2012-2013
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Il suono delle campane The song of bells
A systematic study regarding bells sound
requires the knowledge of three
important features: the theoretical model
about sound characteristics, the technical
aspect of the instrument and the
historical-artistic one. The students
contacted the Italian Campanology
Association, then, they applied the
Fourier analysis to examine the sound
produced by two different bell concerts:
Lodi Cathedral and Wilten Abbey in
Innsbruck.
Stage 2012-2013
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Sunshine project: let’s roll!
The purposes of this project are the following: studying the differential rotation of
the Sun and making three-dimensional images of the star. This project allowed the
students to develop abilities in taking pictures of the Sun through a solar dedicated
telescope and to improve their knowledge about the Sun. It was carried out on two
complementary sides: the direct observations of the Sun were made in the Brera
Astronomic Observatory in Merate (LC) and a study about the differential rotation of
the Sun conducted, following the motion of solar spots, analyzed using our
knowledge of Kinematiks and pictures of the satellite (SOHO).
Learning Week
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In Action with Math
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