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To Mario Geymonat Michele Emmer Editor Imagine Math Between Culture and Mathematics Michele Emmer Department of Mathematics Sapienza University of Rome ISBN 978-88-470-2426-7 ISBN 978-88-470-2427-4 (eBook) DOI 10.1007/978-88–470-2427-4 Library of Congress Control Number: 2011944690 Springer Milan Dordrecht Heidelberg London New York c Springer-Verlag Italia 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broa- dcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the Italian Copyright Law in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the Italian Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Translation: Kim Williams for the contributions by E. Fabbri, E. Gamba, M. Costamagna, S. Caran- dini, C. Viviani and M. Emmer (“Visual Harmonies: an Exhibition on Art and Math” and “The Fantastic World of Tor Bled-Nam”) Cover-Design: deblik, Berlin Cover-Image: Lucio Saffaro, “Il piano di Orfeo” (particular). Courtesy of Fondazione Lucio Saf- faro, Bologna; Springer thanks Gisella Vismara Typesetting with LaTeX: CompoMat S.r.l., Configni (RI) Printing and Binding: GECA Industrie Grafiche, Cesano Boscone (MI) Printed in Italy Springer-Verlag Italia S.r.l., Via Decembrio 28, I-20137 Milano Springer fa parte di Springer Science + Business Media (www.springer.com) Contents Introduction ................................................... 1 Homage to Benoˆıt Mandelbrot The Fantastic World of Tor’ Bled-Nam Michele Emmer ................................................. 5 Venice and “La Fenice” The Reconstruction of the Teatro La Fenice: “splendidezze” and “dorature” (Gleam and Gilding) Elisabetta Fabbri ............................................... 15 Homage to Andrea Pozzo Exactitude and Extravagance: Andrea Pozzo’s “Viewpoint” Filippo Camerota ............................................... 23 The Apse Scenes in the Prospective Inventions of Andrea Pozzo Silvia Carandini ................................................ 43 Andrea Pozzo: Art, Culture and Mathematics Marco Costamagna ............................................. 57 Homage to Hypatia Hypatia as Polymath Michael A. B. Deakin ............................................ 73 Women’s Contributions to the Progress of Mathematics: Lights and Shadows Elisabetta Strickland ............................................ 83 vi Contents Hypatia’s Dream Massimo Vincenzi ............................................... 91 Mathematics and Art Modern Geometry versus Modern Architecture Isabeau Birindelli and Renata Cedrone .............................105 Visual Harmonies: an Exhibition on Art and Math Michele Emmer .................................................117 Emilio Prini, Alison Knowles, and Art’s Logic Cornelia Lauf ..................................................123 All the Numbers End in Numbers. On a Work by Alighiero Boetti Andrea Valle ...................................................127 Mathematics and Literature The Unreasonable Effectiveness of Mathematics in Human Sciences: the Attribution of Texts to Antonio Gramsci Dario Benedetto, Emanuele Caglioti and Mirko degli Espositi ..........143 Lost in a Good Book: Jorge Borges’ Inescapable Labyrinth William Goldbloom Bloch ........................................155 Mathematics and Applications The Many Faces of Lorenz Knots Marco Abate ...................................................169 Waiting for ABRACADABRA. Occurrences of Words and Leading Numbers Emilio De Santis and Fabio Spizzichino .............................175 E Pluribus Unum Marco Li Calzi .................................................187 Aperiodic Tiling Gian Marco Todesco .............................................197 Contents vii Mathematics and Medicine Connecting Ventricular Assist Devices to the Aorta: a Numerical Model Jean Bonnemain, Simone Deparis and Alfio Quarteroni ...............211 Mathematics Elsewhere Numeracy, Metrology and Mathematics in Mesopotamia: Social and Cultural Practices Gregory´ Chambon ..............................................227 Origami and Partial Differential Equations Paolo Marcellini and Emanuele Paolini .............................241 Mathematics and Film The Mobius¨ Strip Edouard Blondeau ..............................................253 From Brigitte Bardot to Angelina Jolie Michele Emmer .................................................259 Homage to Luca Pacioli The Mathematical Ideas of Luca Pacioli Depicted by Iacopo de’ Barbari in the Doppio ritratto Enrico Gamba ..................................................267 De divina proportione: from a Renaissance Treatise to a Multimedia Work for Theatre Simone Sorini ..................................................273 Mathematics and Music Towards a Rational Practice of Arithmetic. A Model for the Musical (and Multimedia) Composition Francesco Scagliola .............................................283 Introduction Imagine all the people Sharing all the world ... John Lennon Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine solving great problems, imagine new problems never before thought of, imagine music, art, poetry, literature, architecture, theatre and cinema with mathematics. Imagine the unpredictable and sometimes irrational applications of mathematics in all areas of human endeavour. Imagination and mathematics, imagination and culture, culture and mathematics. For some years now the world of mathematics has penetrated deeply into human cul- ture, perhaps more deeply than ever before, even more than in the Renaissance. In theatre, stories of mathematicians are staged; in cinema Oscars are won by films about mathematicians; all over the world museums and science centres dedicated to mathematics are multiplying. Journals have been founded for relationships be- tween mathematics and contemporary art and architecture. Exhibitions are mounted to present mathematics, art and mathematics, and images related to the world of mathematics. “Imagine Math” is intended to contribute to grasping how much that is interesting and new is happening in the relationships between mathematics, imagination and culture. A look at the past, at figures and events that made history, can also help to under- stand the phenomena of today. It is no coincidence that this volume contains an homage to the great Italian artist of the 1700s, Andrea Pozzo, and his perspective views. It also has a particular focus on Luca Pacioli, who remains today a source of inspiration not only for art, but for theatre. Here theatre, art and architecture are the topics of choice, along with music, literature and cinema. No less important are applications of mathematics to medicine and economics. Nor does this particular focus neglect the universality of mathematics, from its ori- gins in Mesopotamia up to the geometry of Japanese origami. The topics are treated in a way that is rigorous but captivating, detailed but full of evocations. An all-embracing look at the world of mathematics and culture. Michele Emmer Emmer M. (Ed.): Imagine Math. Between Culture and Mathematics DOI 10.1007/978-88-470-2427-4 1, c Springer-Verlag Italia 2012 Homage to Benoˆıt Mandelbrot The Fantastic World of Tor’ Bled-Nam Michele Emmer Let us imagine that we have been travelling on a great journey to some far-off world. We shall call this world Tor’ Bled-Nam. Our remote sensing device has picked up a signal which is now displayed on a screen in front of us. The image comes into focus and we see. [...] What can it be? Can it be some strange looking insect? Or could it be some vast and oddly shaped alien city, with roads going off in various directions to small towns and villages nearby? Maybe it is an island – and then let us try to find whether there is a nearby continent with which it is associated. This we can do by ‘backing away’, reducing the magnification of our sensing device by a linear factor of about fifteen. Lo and behold, the entire world springs into view. [...] Wemayexplore this extraordinary world of Tor’ Bled-Nam as long as we wish, tuning our sensing device to higher and higher degrees of magnification. We find an endless variety: no two regions are precisely alike – yet there is a general flavour that we soon become accustomed to. [...] What is this strange, varied and most wonderfully intricate land that we have stumbled upon? No doubt many readers will already know. But some will not. This world is nothing but a piece of abstract mathematics – the set known as the Mandelbrot set [1, p. 74-79]. The journey into the land of Tor’ Bled-Nam begins the chapter that Roger Pen- rose dedicates to the relationship between mathematics and reality in the book The Emperor’s New Mind. It may seem paradoxical that the Mandelbrot set is the first example that Penrose uses to confirm the Platonic reality of mathematical concepts, objects that can only be seen on the monitor of a computer! But for Penrose
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