The Legacy of Tatjana Afanassjewa: Philosophical Insights from the Work of an Original Physicist and Mathematician (Women in the History of Philosophy and Sciences Book 7)

This book presents a collection of essays that explore the life and works of Tatjana Afanassjewa (1876-1964), a Russian-Dutch physicist-mathematician. Readers will discover a scientist whose work on the foundations of thermodynamics significantly influenced the field itself as well as the philosophy of physics. This book highlights the philosophical consequences of her work in physics and mathematics and discusses historical aspects of her writings on the foundations of physics. In addition, it features English translations and critical reviews of key selections from her texts. First and foremost, the book highlights the numerous contributions that Afanassjewa made to the field. In particular, the authors examine her work on the foundations of thermodynamics and statistical physics, starting in the 1920s and extending to 1956, well after the untimely death of her husband in 1933. They also explore her almost entirely forgotten work on the didactics of mathematics. In addition, they discuss her influential collaboration with her husband, the Austrian physicist Paul Ehrenfest (18801933). The portrait that emerges is that of a highly original physicist and mathematician, whose legacy continues to influence scientists and philosophers today and whose lesser-known works deserve more attention than they have received. Readers will find a rich body of work that continues to this day to yield insights into the foundations of physics and mathematics.--Back cover Series Foreword 6 Preface 7 Introduction 9 Part I: Tatiana Afanassjewa’s Life and Forgotten Legacy 10 Part II: The Ehrenfests’ Work on the Foundations of Statistical Mechanics 11 Part III: Translations from German and Dutch 12 Contents 14 Part ITatiana Afanassjewa’s Life and Forgotten Legacy 15 1 Tatiana Ehrenfest-Afanassjewa: No Talent for Subservience 16 1.1 The Alarming Rectilinearity of Her World line 18 1.2 Higher Women Courses for the Weaker Sex 19 1.3 Afanassjewa’s Analytical Mind and Ehrenfest’s Physics Intuition 23 1.4 Undervalued: Kruzhoks and Odd Jobs 24 1.5 A Vibrant Household in Traditional Leiden 26 1.6 The First Cracks in the Relationship 28 1.7 Novel Ideas, not Always Appreciated 29 1.8 Drifting Apart, the Downhill Slope 31 1.9 Hardship with Integrity 33 1.10 Final Years in Her Own Sphere 37 References 39 2 Intuition, Understanding, and Proof: Tatiana Afanassjewa on Teaching and Learning Geometry 42 2.1 Introduction 42 2.2 Göttingen 44 2.3 The Value of Geometry Education 48 2.4 Intuition, Understanding, and Logical Thinking 51 2.4.1 The Role of Intuition 51 2.4.2 Understanding and Logical Thinking 53 2.5 The Study of Space and the Axiomatics of Geometry 55 2.5.1 The Systematic Approach 57 2.5.2 The Experimental Approach 58 2.5.3 The Propaedeutic Course and the Systematic Courses 60 2.6 The Reception of Afanassjewa's Approach to Teaching Geometry 62 References 65 3 Afanassjewa and the Foundations of Thermodynamics 68 3.1 Introduction 68 3.2 The Axiomatic Approach to Thermodynamics: From Carathéodory to Afanassjewa 71 3.3 Reversible Processes Versus Quasi-Processes 74 3.4 The Distinction Between Heat and Work 80 3.5 Afanassjewa on Negative Absolute Temperatures 84 3.6 Conclusion 89 References 90 Part IIThe Ehrenfests’ Work on the Foundations of Statistical Mechanics 96 4 Ehrenfest and Ehrenfest-Afanassjewa on Why Boltzmannian and Gibbsian Calculations Agree 97 4.1 Introduction 97 4.2 Boltzmannian and Gibbsian Statistical Mechanics 98 4.3 Ehrenfest and Ehrenfest-Afanassjewa on Gibbs Versus Boltzmann 101 4.4 Assessment of Ehrenfest and Ehrenfest-Afanassjewa's Argument 102 4.5 Beyond Dilute Gases 106 4.6 An Example Where Boltzmannian Equilibrium Values and Gibbsian Phase Averages Differ 107 4.7 When Boltzmann and Gibbs Agree 109 4.8 Conclusion 110 References 111 5 Ehrenfest and Ehrenfest-Afanassjewa on the Ergodic Hypothesis 112 5.1 Introduction 112 5.2 The Origin of the Ergodic Hypothesis 113 5.3 Ehrenfest and Ehrenfest-Afanassjewa's Critique of the Ergodic Hypothesis 116 5.4 Proof of the Impossibility of Ergodic Systems 121 5.5 The Ergodic Theorems and the Notion of Metric Transitivity 123 5.6 The Problem of Metric Transitivity 126 5.7 Conclusion 128 References 129 6 The Ehrenfests' Use of Toy Models to Explore Irreversibility in Statistical Mechanics 132 6.1 Introduction 132 6.2 Toy Models and Their Functions 133 6.3 The Ehrenfests' Toy-Models 135 6.3.1 The Urn Model 135 6.3.2 The P–Q model 138 6.4 Why These Toy Models Work 142 6.5 Complementary Use of Toy Models 145 6.6 Conclusion 147 References 148 Part IIITranslations From German and Dutch 149 7 Translation from German: Foundations of Thermodynamics 1925 and 1956 150 8 Translation from Dutch: Papers on the Pedagogy of Mathematics 189 8.1 Which Use Can Geometry Education Have for Students that Do not Continue with Mathematics? 189 8.2 What Is Being Logical? 191 8.3 Can Geometry Education Promote the Development of Logic? 195 8.4 The Introductory Geometry Course 199 8.5 Some Examples of Questions that Would Be Suitable for an Introductory Course 202 Front Matter ....Pages i-xv Front Matter ....Pages 1-1 Tatiana Ehrenfest-Afanassjewa: No Talent for Subservience (Margriet van der Heijden)....Pages 3-28 Intuition, Understanding, and Proof: Tatiana Afanassjewa on Teaching and Learning Geometry (Marianna Antonutti Marfori)....Pages 29-54 Afanassjewa and the Foundations of Thermodynamics (Jos Uffink, Giovanni Valente)....Pages 55-82 Front Matter ....Pages 83-83 Ehrenfest and Ehrenfest-Afanassjewa on Why Boltzmannian and Gibbsian Calculations Agree (Charlotte Werndl, Roman Frigg)....Pages 85-99 Ehrenfest and Ehrenfest-Afanassjewa on the Ergodic Hypothesis (Patricia Palacios)....Pages 101-120 The Ehrenfests’ Use of Toy Models to Explore Irreversibility in Statistical Mechanics (Joshua Luczak, Lena Zuchowski)....Pages 121-137 Front Matter ....Pages 139-139 Translation from German: Foundations of Thermodynamics 1925 and 1956 (Marina Baldissera Pacchetti)....Pages 141-179 Translation from Dutch: Papers on the Pedagogy of Mathematics (Pauline van Wierst)....Pages 181-198