Dino Boccaletti The Shape and Size of the Earth A Historical Journey from Homer to Artificial Satellites The Shape and Size of the Earth Dino Boccaletti The Shape and Size of the Earth A Historical Journey from Homer to Artificial Satellites 123 Dino Boccaletti Rome Italy ISBN 978-3-319-90592-1 ISBN 978-3-319-90593-8 (eBook) https://doi.org/10.1007/978-3-319-90593-8 Library of Congress Control Number: 2018941978 © Springer International Publishing AG, part of Springer Nature 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. 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Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland To Ruben and Matilde Preface How an Interest was Born, Developed, and Produced a Book The reader may be intrigued by the genesis of a book such as this. Actually, what stimulated me to think about this subject was another interesting reading. Many years ago, in the first phase of my teaching in the University of Rome “La Sapienza”, I was charged with teaching a course on Institutions of Mathematics to students pursuing a degree in Chemistry. In that occasion, I happened to read a very beautiful book: Mathematical Methods in Science of George Pólya, in which I found this passage: That Eratosthenes’ result is inaccurate does not really detract from the greatness of his achievement. It is his method that excites our admiration. Would not a giant measure the Earth by encircling it with his arms to compare its circumference with his span? And what did our little pygmy Eratosthenes do? At Alexandria at noon on a certain midsummer’s day long ago, he observed the shadow cast by a little stick and used his protractor. A mere shadow and the pygmy a giant who spanned the Earth.1 The reading of this passage, addressed to the measurement of the terrestrial meridian executed by Eratosthenes (in the third century BC), of which until then I had a superficial knowledge, and the appreciation—enthusiastic to say the least— that Pólya attributed to that event, inspired my interest in expanding on the subject, and I started a series of considerations. First of all, I began to think that, through the centuries, the great significance attributed to the Copernican Revolution ended up obscuring another great conquest of the human thought: the sphericity of the Earth. The idea and personal conviction, contrary to the immediate evidence, that the ground on which one was walking was not a roughly flat surface (apart from the mountains!), but was rather the surface of a sphere whose boundaries could not be discerned, was undoubtedly a great con- quest (even if it could not be defined as a revolution). Earlier on, one confused the sphere with the tangent plane! 1 G. Pólya: Mathematical Methods in Science (Washington, 1977). vii viii Preface Pólya’s admiration for Eratosthenes was based on the method he had used: Eratosthenes had, so to speak, measured the terrestrial meridian while seated in his room and using mathematics. From this, the power of mathematics is evident, as was underlined by Eugene Wigner some years before in his celebrated paper “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”2 At the beginning of the paper, Wigner used the rhetorical expedient of narrating the conversation between two old high school classmates, one of whom had become a statistician working in population trends. This one showed to the other a reprint of a publication of his where a Gaussian distribution and also the symbol p appeared. The friend asked: “And what is this symbol here?”“Oh”, said the statistician, “This is pi”. “What is that?” “The ratio of the circumference of the circle to its diameter.”“Well, now you are pushing your joke too far,” said the classmate, “surely the population has nothing to do with the circumference of the circle.” Here, we are at the root of the problem of interpreting nature with the tool of mathematics and of the dual nature of mathematics as both a tool and an inde- pendent science: a problem that is up to us to deal with. We only want to emphasize the maieutic role that some problems presented by nature have had in giving birth to branches of mathematics during history. Of course, as all know, three centuries before Wigner, Galileo (in the Assayer, 1623) had upheld the indispensability of mathematics for interpreting nature. If we want go back further, even Robert Grosseteste (see Sect. 3.5.2) had upheld the same. The second consideration is this: once established that it had been demonstrated that the Earth had a spherical shape since the middle of the third century BC, and that an evaluation of its size had also been proposed, how did the thought on this question evolve in the following centuries? Had the fact that an adequately rigorous answer to such an important question had been given since the third century been sufficient to convince the general opinion? Actually, quoting the result of a dis- covery (or of a theory), such as that of Eratosthenes (as well as those of the philosophers who preceded him), means establishing only its chronological priority, but not the moment when this discovery (or theory) has become part of the cultural heritage of humanity. An investigation of the problem leads to the discovery that the notion of the Earth’s sphericity, which nowadays the children learn since the primary school, took centuries to be universally accepted. As happened with other questions, the Catholic Church also took part in the discussion, which lasted for centuries, together with all the philosophers of the Middle Ages. The debate arose from the conflict between what was written in the Bible and the results of the natural sciences. 2E. Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, in Communications in Pure and Applied Mathematics 13(1) 1960: 1–14. Preface ix Obviously, during the centuries, the scientific research evolved, even arriving to the point of stating that the reference figure is no longer a sphere (it has been called a “geoid”) and that, due to its rotation, the shape is oblate (through the disputations and the measurements occurred in the eighteenth century). Through the work of Newton, Clairaut, Maupertuis, Delambre, and others, and through the progress of technology, we have arrived to satellite geodesy. Every stage of these both theo- retical and experimental advancements has constantly involved the development of new mathematical techniques, always reinforcing Wigner’s assertion. Narrating this fascinating story from the beginning reveals more about the evolution of the human thought than only about the evolution of the specific concept of Earth’s sphericity, and is certainly worth the effort. In fact, there are many works which deal with the subject, many of which mainly concern the controversies on the Earth’s ellipsoid shape,3 but the ambition of this present book is that of pointing out how from the very beginning the speculations about the shape and the size of the Earth were not confined to the technology but traversed the evolution of human thought itself. Notice to the Reader Subjects The reader may wonder at not finding certain subjects dealt with when particular authors or particular periods are mentioned. We have set ourselves to cover exclusively what concerns the theories and the experiments on the shape and the size of the Earth and, as said above, their impact on secular society. Thus, for instance, when we dealt with Ptolemy’s Geography and projections therein, we did not seize the opportunity to talk about cartography despite the fact that it was an appealing subject given its relationship with mathematics. Excerpts Except for the Greek philosophers, we have always preferred to supply the text with English translations of works being discussed and report in footnotes the quoted excerpts in their original language. This is done to avoid arbitrary interpretations and variants of tradition in subsequent quotations. We have not always found the chosen Latin excerpts translated into English by competent scholars. In those cases, we have compensated for lack with a translation of our own. Let us hope we have obtained a passable result. Bibliography Every single chapter is equipped with footnotes referencing papers and books quoted. We considered them exhaustive and decided not to weight each chapter down with the usual ad hoc bibliography. We have rather preferred to include a list of suggested readings, often classical textbooks, for a prospective widening of the context.