Representations of space in seventeenth century physics

255 Pages·2006·1.744 MB·English

by  Miller, David Marshall

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
UMI Number: 3224008
UMI Microform3224008
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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
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Copyright © by David Marshall Miller
2006
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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.

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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
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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
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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 SPATIAL ORIENTATION...................................................205
6.9 CONCLUSION................................................................................................207
7.0 CONCLUSION AND PROSPECTUS ...................................................................209
7.1 THE CONCEPTUAL, DESCRIPTIVE, AND EXPLANATORY
PROBLEMS......................................................................................................................209
7.2 THE CELESTIAL SOLUTIONS: GILBERT AND KEPLER..................211
7.3 THE TERRESTRIAL SOLUTIONS: GALILEO AND DESCARTES....213
7.4 THE CONTINUATION: HUYGENS, NEWTON, AND BEYOND..........215
7.5 CONCLUSION................................................................................................222
APPENDIX. EXCERPTS OF LETTER FROM JOHANNES KEPLER TO DAVID
FABRICIUS, 11 OCTOBER 1605..........................................................................................224
BIBLIOGRAPHY.....................................................................................................................236
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LIST OF FIGURES
Figure 1. Ptolemy’s Model for a Superior Planet........................................................................59
Figure 2. Copernicus’s Model for a Superior Planet..................................................................60
Figure 3. The Earth’s Axis...........................................................................................................60
Figure 4. The Third Motion..........................................................................................................61
Figure 5. Basic Epicycle/Deferent Model..................................................................................134
Figure 6. Circular Epicyclic Orbit.............................................................................................134
Figure 7. Elliptical Epicyclic Orbit............................................................................................135
Figure 8. Kepler’s 1602 and 1603 Models.................................................................................135
Figure 9. Bisected Eccentricity..................................................................................................136
Figure 10. Elongations on Epicycle...........................................................................................136
Figure 11. Secant Model............................................................................................................136
Figure 12. Libration Model........................................................................................................137
Figure 13. Descents Along the Radii..........................................................................................137
Figure 14. Descents Along Perpendiculars...............................................................................138
Figure 15. Measure of Attractive Force in the Planetary Body.................................................138
Figure 16. Derivation of Lever Law...........................................................................................139
Figure 17. Optical Percussion...................................................................................................139
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PREFACE
“He remarked to me then,” said that mildest of men,
“‘If your Snark be a Snark that is right:
Fetch it home by all means – you may serve it with greens,
And it’s handy for striking a light.’” (Lewis Carroll, The Hunting of the Snark)
I would be remiss and ashamed if I failed to acknowledge the support and guidance of the many
who contributed to this project. Their collective help carried me through the cycles of frustration
and inspiration that produced this dissertation.
First, I owe the deepest gratitude to the faculty and students of the Department of History
and Philosophy of Science at the University of Pittsburgh. Much of the ideas presented here
were developed in discussions with them, whether in seminars, in the hallways and offices of the
Cathedral of Learning, or over beers at the Holiday Inn and elsewhere. I profited immensely
from the collegiality, openness, and intelligence of every member of the department. Their
ideas, encouragement, and advice was and will always be welcome.
My advisors, Peter Machamer and Ted McGuire, merit the highest praise and
appreciation for their firm yet restrained supervision. This dissertation bears the marks of their
alternating approval and criticism, which cajoled me through its writing. I could not have
wished for a better pair of teachers, scholars, and friends to guide me. Jonathan Scott (of the
History Department) and Paolo Palmieri were also especially important resources upon whom I
had the pleasure to call.
Amongst my peers, I gained untold benefit from the friendship and conversation of Zvi
Biener, and, especially, Greg Frost-Arnold. Greg, along with Karen Frost-Arnold, must be
thanked for so many particular acts of insight, friendship, and tolerance I cannot begin to list
them here.
I could not have completed this project without the support of my parents, grandparents,
and brother. My family’s sympathy with my scholarly aspirations is remarkable and
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