View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by D-Scholarship@Pitt REPRESENTATIONS OF SPACE IN SEVENTEENTH CENTURY PHYSICS by David Marshall Miller Bachelor of Arts, Yale University, 1999 Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2006 UNIVERSITY OF PITTSBURGH FACULTY OF ARTS AND SCIENCES This dissertation was presented by David Marshall Miller It was defended on April 10, 2006 and approved by John Earman, University Professor, Department of History and Philosophy of Science Paolo Palmieri, Assistant Professor, Department of History and Philosophy of Science Jonathan Scott, Carroll Amundson Professor of British History, Department of History Dissertation Co-Director: Peter K. Machamer, Professor, Department of History and Philosophy of Science Dissertation Co-Director: James E. McGuire, Professor, Department of History and Philosophy of Science ii Copyright © by David Marshall Miller 2006 iii REPRESENTATIONS OF SPACE IN SEVENTEENTH CENTURY PHYSICS David Marshall Miller, PhD University of Pittsburgh, 2006 The changing understanding of the universe that characterized the birth of modern science included a fundamental shift in the prevailing representation of space – the presupposed conceptual structure that allows one to intelligibly describe the spatial properties of physical phenomena. At the beginning of the seventeenth century, the prevailing representation of space was spherical. Natural philosophers first assumed a spatial center, then specified meanings with reference to that center. Directions, for example, were described in relation to the center, and locations were specified by distance from the center. Through a series of attempts to solve problems first raised by the work of Copernicus, this Aristotelian, spherical framework was replaced by a rectilinear representation of space. By the end of the seventeenth century, descriptions were understood by reference to linear orientations, as parallel or oblique to a presupposed line, and locations were identified without reference to a privileged central point. This move to rectilinear representations of space enabled Gilbert, Kepler, Galileo, Descartes, and Newton to describe and explain the behavior of the physical world in the novel ways for which these men are justly famous, including their theories of gravitational attraction and inertia. In other words, the shift towards a rectilinear representation of space was essential to the fundamental reconception of the universe that gave rise to both modern physical theory and, at the same time, the linear way of experiencing the world that characterizes modern science. iv TABLE OF CONTENTS PREFACE....................................................................................................................................IX 1.0 INTRODUCTION: PHYSICAL UNDERSTANDING AND REPRESENTATIONS OF SPACE............................................................................................. 1 1.1 THREE LEVELS OF UNDERSTANDING...................................................... 2 1.1.1 Explanations and Descriptions .................................................................... 2 1.1.2 Descriptions and Concepts........................................................................... 9 1.1.3 Representations of Space............................................................................ 14 1.1.4 Reciprocal Iteration.................................................................................... 20 1.2 METHOD OF INVESTIGATION................................................................... 25 1.2.1 Historical Description................................................................................. 25 1.2.2 Historical Explanation................................................................................ 27 1.3 DISTINCTION FROM THE LITERATURE: JAMMER AND KOYRÉ.. 31 1.4 PLAN OF CHAPTERS ..................................................................................... 37 2.0 PLURIBUS ERGO EXISTENTIBUS CENTRIS: COPERNICUS, ASTRONOMICAL DESCRIPTIONS, AND THE “THIRD MOTION”.............................. 39 2.1 SPHERICAL UNIVERSE ................................................................................ 41 2.2 SCHOLASTIC PHYSICS................................................................................. 44 2.3 PTOLEMY’S DESCRIPTIVE AIMS.............................................................. 46 2.4 COPERNICUS’S REDESCRIPTION............................................................. 48 2.5 DIFFICULTIES RAISED................................................................................. 51 2.6 THE “THIRD MOTION”................................................................................. 55 2.7 CONCLUSION .................................................................................................. 57 3.0 GILBERT’S “VERTICITY” AND THE “LAW OF THE WHOLE” .................. 62 3.1 GILBERT’S RESPONSE TO COPERNICUS ............................................... 62 v 3.2 THE DE MAGNETE.......................................................................................... 65 3.2.1 Book I ........................................................................................................... 65 3.2.2 Book II.......................................................................................................... 67 3.2.3 The Instantiation of the Geographical Representation of Space............ 71 3.2.4 Books III-IV: Magnetic Motions .............................................................. 73 3.2.5 Book VI: The Earth’s Motions ................................................................. 76 3.2.6 A Blind Alley ............................................................................................... 79 3.3 GILBERT’S TREATMENT OF THE “THIRD MOTION”: VERTICITY AND THE LAW OF THE WHOLE................................................................................. 82 3.4 CONCLUSION .................................................................................................. 86 4.0 KEPLER AND THE DISCOVERY OF COSMIC LINEARITY ......................... 88 4.1 PROLOGUE: O MALE FACTUM!................................................................. 88 4.2 INTRODUCTION: SOURCES AND AIMS.................................................. 89 4.3 BACKGROUND: RELIGIOUS EPISTEMOLOGY .................................... 91 4.4 SETTING UP ..................................................................................................... 95 4.5 THE PROBLEM OF SHAPE: THE ELLIPSE ............................................. 97 4.6 THE PROBLEM OF DISTANCE: THE SECANT MODEL ...................... 99 4.7 THE PROBLEM OF LONGITUDE: THE ELLIPSE................................ 105 4.8 THE PROBLEM OF EXPLANATION: CONSIDERATION OF CAUSES.. ........................................................................................................................... 112 4.9 THE PROBLEM OF DIRECTION: GILBERT’S LAW OF THE WHOLE AND THE MAGNETIC BALANCE .............................................................................. 114 4.10 THE PROBLEM OF SINES AND COSINES: SUMS OF FORCE .......... 124 4.11 CONCLUSION: THE STATUS OF LINES IN GILBERT AND KEPLER... ........................................................................................................................... 130 5.0 INERTIAL DEFLECTIONS, REPRESENTATIONS OF SPACE, AND GALILEAN INERTIA ............................................................................................................. 140 5.1 THE PROBLEM OF FREE FALL................................................................ 141 5.2 HUNTERS AND CANNONS.......................................................................... 145 5.3 RECTILINEAR AND SPHERICAL SPACE............................................... 151 5.3.1 Large-Scale Space ..................................................................................... 151 vi 5.3.2 Small-Scale Space...................................................................................... 157 5.4 LINEAR AND CIRCULAR INERTIA ......................................................... 160 5.5 CONCEPT OF INERTIA ............................................................................... 166 5.6 THE ARCHIMEDEAN APPROXIMATION............................................... 170 5.7 CONCLUSION ................................................................................................ 173 6.0 PROMOTION TO THE FOUNDATIONS: CARTESIAN SPACE .................. 176 6.1 DESCARTES’ CONCEPTUAL FRAMEWORK ........................................ 177 6.2 DESCARTES’ REPRESENTATION OF SPACE ....................................... 181 6.3 THE ORIGINS OF CARTESIAN SPACE ................................................... 184 6.3.1 Optics ......................................................................................................... 185 6.3.2 Geometry ................................................................................................... 188 6.4 PLACE AND MOTION IN THE RULES ..................................................... 191 6.5 THE WORLD ................................................................................................... 193 6.6 COSMIC VORTICES..................................................................................... 196 6.7 PLACE AND MOTION IN THE PRINCIPLES OF PHILOSOPHY ......... 199 6.8 ARBITRARY