Studies on Binocular Vision: Optics, Vision and Perspective from the Thirteenth to the Seventeenth Centuries (Archimedes Book 47)

This Book Clarifies The Interrelationship Between Optics, Vision And Perspective Before The Classical Age, Examining Binocularity In Particular. The Author Shows How Binocular Vision Was One Of The Key Juncture Points Between The Three Concepts And Readers Will See How Important It Is To Understand The Approach That Scholars Once Took. In The Middle Ages And The Renaissance, The Concept Of Perspectiva -- The Latin Word For Optics -- Encompassed Many Areas Of Enquiry That Had Been Viewed Since Antiquity As Interconnected, But Which Afterwards Were Separated: Optics Was Incorporated Into The Field Of Physics (i.e., Physical And Geometrical Optics), Vision Came To Be Regarded As The Sum Of Various Psycho-physiological Mechanisms Involved In The Way The Eye Operates (i.e., Physiological Optics And Psychology Of Vision) And The Word 'perspective' Was Reserved For The Mathematical Representation Of The External World (i.e., Linear Perspective). The Author Shows How This Division, Which Emerged As A Result Of The Spread Of The Sciences In Classical Europe, Turns Out To Be An Anachronism If We Confront Certain Facts From The Immediately Preceding Periods. It Is Essential To Take Into Account The Way Medieval Scholars Posed The Problem -- Which Included All Facets Of The Latin Word Perspectiva -- When Exploring The Events Of This Period. This Book Will Appeal To A Broad Readership, From Philosophers And Historians Of Science, To Those Working In Geometry, Optics, Ophthalmology And Architecture. -- Publisher's Description Perspectiva Naturalis/artificialis -- Knowledge And Beliefs Regarding Linear Perspective -- Understanding Errors In Perspective -- Fact And Fiction Regarding Masaccio?s Trinity Fresco -- Ibn Al-haytham On Binocular Vision -- The Legacy Of Ibn Al-haytham -- The Rejection Of The Two-point Perspective System -- The Properties Of Two-point Perspective -- The Hauck?panofsky Conjecture Regarding Curvilinear Perspective -- The White?carter Conjecture On Synthetic Perspective -- De Mesa?s Hypothesis Regarding The Arithmetic Construction Of Perspective. Dominique Raynaud. Includes Bibliographical References (pages 267-281) And Indexes. Preface 6 Contents 10 1 Perspectiva Naturalis/Artificialis 13 Abstract 13 1.1 Perspective in the Classification of the Sciences 14 1.2 The Phases in the Development of Optics 16 1.3 The Similarities Between Perspectiva and Perspective 17 1.4 The Differences Between Perspectiva and Perspective 21 Errors 25 2 Knowledge and Beliefs Regarding Linear Perspective 26 Abstract 26 2.1 The Myth of Perspective 27 2.1.1 Filippo Brunelleschi 27 2.1.1.1 Leon Battista Alberti 30 2.1.1.2 Masaccio 32 2.2 Perspective and Knowledge 34 2.2.1 Geometry and the Perspective of the Circle 34 2.2.2 Optics and Binocular Vision 41 2.3 Conclusion 44 3 Understanding Errors in Perspective 47 Abstract 47 3.1 The Classification of Errors 48 3.2 Methods of Foreshortening 49 3.2.1 Correct Foreshortening 51 3.2.2 Under-Foreshortening 51 3.2.3 Over-Foreshortening 54 3.3 Some Examples of Erroneous Foreshortening in Renaissance Painting 55 3.4 Conclusion 61 4 Fact and Fiction Regarding Masaccio’s Trinity Fresco 63 Abstract 63 4.1 Recent Research 64 4.2 The Construction of the Vault Ribs 68 4.3 Masaccio’s Use of the So-Called Costruzione Legittima 71 4.4 The Determination of the Viewing Distance 75 4.5 Conclusion 77 Theory 78 5 Ibn al-Haytham on Binocular Vision 79 Abstract 79 5.1 The Cases of Homonymous and Heteronymous Diplopia 83 5.2 The Notion of Corresponding Points in Binocular Vision 85 5.3 The Study of Physiological Diplopia (Experiments 1 and 2) 87 5.4 The Determination of the Horopter (Experiments 3 and 4) 88 5.4.1 The Theoretical Horopter 89 5.4.2 The Experimental Horopter 94 5.5 Panum’s Fusional Area (Experiment 5) 97 6 The Legacy of Ibn al-Haytham 102 Abstract 102 6.1 The Availability of the Texts of Ibn al-Haytham in the West 102 6.2 Obstacles to the Binocular Theory of Vision 108 6.2.1 Physiological and Pathological Diplopia 109 6.2.2 Diplopia Is not an Unusual Phenomenon 110 6.2.3 Images Are not Blurred in Diplopia 111 6.2.4 Different Theories Regarding the Unification of Binocular Images 112 6.2.5 Neutralization Is not Constant 118 6.3 Conclusion 121 7 The Rejection of the Two-Point Perspective System 122 Abstract 122 7.1 In the Earliest Italian Art Academies 123 7.1.1 Vignola and Danti (1559–1583) 123 7.1.2 Martino Bassi (1572) 128 7.2 In the Circles of the Académie Royale de Peinture 129 7.2.1 Grégoire Huret (1670) 129 7.2.2 Sébastien Le Clerc (1679) 131 7.3 Conclusion 136 Sifting the Hypotheses 137 8 The Properties of Two-Point Perspective 138 Abstract 138 8.1 Typical Constructions 140 8.2 Perspectives in Which the Spectator Is not Placed at Infinity 141 8.3 Perspectives that Differ from Linear Perspective 142 8.3.1 Central Perspective 142 8.3.2 Bifocal Perspective 145 8.3.3 Trifocal Perspective 151 8.4 The Principles of Binocular Perspective 151 8.4.1 The Vantage Point and the Vanishing Point 151 8.4.2 Depth Gives Rise to Disparate Images 152 8.4.3 The Determination of the Fixation Point 154 8.4.4 The Crossing of the Orthogonals on the Axis Communis 156 8.4.5 Examination of the Plans and Elevations 160 8.4.6 An Exploration of the Relationship FF′ ∝ XP/HX 160 8.5 Conclusion 163 9 The Hauck–Panofsky Conjecture Regarding Curvilinear Perspective 165 Abstract 165 9.1 Compositions Based on a Vanishing Axis 168 9.1.1 The Basis of Panofsky’s Interpretation 169 9.1.2 The Limitations of Panofsky’s Interpretation 171 9.2 Our Methodological Approach 171 9.2.1 Errors in Panofsky’s Reconstruction 171 9.2.2 The Criteria Used to Test Panofsky’s Hypothesis 172 9.3 Analysis of a Corpus of Works 175 9.4 Conclusion 178 10 The White–Carter Conjecture on Synthetic Perspective 180 Abstract 180 10.1 The Mathematical Properties of Synthetic Perspective 184 10.1.1 The Case of Linear Perspective 185 10.1.2 The Case of Synthetic Perspective 187 10.2 Conclusion 189 11 De Mesa’s Hypothesis Regarding the Arithmetic Construction of Perspective 193 Abstract 193 11.1 The Arithmetic Construction Hypothesis 196 11.2 The Absence of Multiples or Submultiples of the Measurement Units 198 11.3 The Absence of Simple Proportional Ratios 205 11.4 The Length of the Operating Series 210 11.5 The Coincidence of Points at Infinity with Visible Loci 213 11.6 Reinterpreting Perspective Anomalies 214 Conclusion 216 Appendix A: Error Analysis and Perspective Reconstruction 225 Appendix B: Catalogue of the Works 244 Appendix C: Errors of Reconstruction 246 Appendix D: Distance Between the Vanishing Points 248 Appendix E: Plates 250 Bibliography 265 Index Nominum 280 Index Rerum 286 This book clarifies the interrelationship between optics, vision and perspective before the Classical Age, examining binocularity in particular. The author shows how binocular vision was one of the key juncture points between the three concepts and readers will see how important it is to understand the approach that scholars once took. In the Middle Ages and the Renaissance, the concept of Perspectiva - the Latin word for optics - encompassed many areas of enquiry that had been viewed since antiquity as interconnected, but which afterwards were separated: optics was incorporated into the field of physics (i.e., physical and geometrical optics), vision came to be regarded as the sum of various psycho-physiological mechanisms involved in the way the eye operates (i.e., physiological optics and psychology of vision) and the word 'perspective' was reserved for the mathematical representation of the external world (i.e., linear perspective). The author shows how this division, which emerged as a result of the spread of the sciences in classical Europe, turns out to be an anachronism if we confront certain facts from the immediately preceding periods. It is essential to take into account the way medieval scholars posed the problem - which included all facets of the Latin word perspectiva - when exploring the events of this period. This book will appeal to a broad readership, from philosophers and historians of science, to those working in geometry, optics, ophthalmology and architecture.-- Provided by publisher This book clarifies the interrelationship between optics, vision and perspective before the Classical Age, examining binocularity in particular. The author shows how binocular vision was one of the key juncture points between the three concepts and readers will see how important it is to understand the approach that scholars once took. In the Middle Ages and the Renaissance, the concept of Perspectiva? the Latin word for optics? encompassed many areas of enquiry that had been viewed since antiquity as interconnected, but which afterwards were separated: optics was incorporated into the field of physics (i.e., physical and geometrical optics), vision came to be regarded as the sum of various psycho-physiological mechanisms involved in the way the eye operates (i.e., physiological optics and psychology of vision) and the word?perspective? was reserved for the mathematical representation of the external world (i.e., linear perspective). 0 Front Matter....Pages i-xi Perspectiva Naturalis/Artificialis....Pages 1-12 Front Matter....Pages 13-13 Knowledge and Beliefs Regarding Linear Perspective....Pages 15-35 Understanding Errors in Perspective....Pages 37-52 Fact and Fiction Regarding Masaccio’s Trinity Fresco....Pages 53-67 Front Matter....Pages 69-69 Ibn al-Haytham on Binocular Vision....Pages 71-93 The Legacy of Ibn al-Haytham....Pages 95-114 The Rejection of the Two-Point Perspective System....Pages 115-129 Front Matter....Pages 131-131 The Properties of Two-Point Perspective....Pages 133-159 The Hauck–Panofsky Conjecture Regarding Curvilinear Perspective....Pages 161-175 The White–Carter Conjecture on Synthetic Perspective....Pages 177-189 De Mesa’s Hypothesis Regarding the Arithmetic Construction of Perspective....Pages 191-213 Back Matter....Pages 215-297