| | PAGE |
| Preface | vii |
| Introduction: Explanatory Notes | 1 |
| | |
| PART ONE | |
| | |
| CHAPTER I | |
| The Prologue | |
| On the Variability of Psychic Powers—The Discovery of the Fourth Dimension Marks a Distinct Stage in Psychogenesis—The non-Methodical Character of Discoveries—The Three Periods of Psychogenetic Development—The Scope and Permissibility of Mathetic License—Kosmic Unitariness Underlying Diversity | 23 |
| | |
| CHAPTER II | |
| Historical Sketch of the Hyperspace Movement | |
| Egypt the Birthplace of Geometry—Precursors: Nasir-Eddin, Christoph Clavius, Saccheri, Lambert, La Grange, Kant—Influence of the Mecanique Analytique—The Parallel Postulate the Root and Substance of the Non-Euclidean Geometry—The Three Great Periods: The Formative, Determinative and Elaborative—Riemann and the Properties of Analytic Spaces | 44 |
| | |
| CHAPTER III | |
| Essentials of the Non-Euclidean Geometry | |
| The Non-Euclidean Geometry Concerned with Conceptual Space Entirely—Outcome of Failures at Solving the Parallel-Postulate—The Basis of the Non-Euclidean Geometry—Space Curvature and Manifoldness—Some Elements of the Non-Euclidean Geometry—Certainty, Necessity and Universality as Bulwarks of Geometry—Some Consequences of Efforts at Solving the Parallel-Postulate—The Final Issue of the Non-Euclidean Geometry—Extended Consciousness | 69 |
| | |
| CHAPTER IV | |
| Dimensionality | |
| Arbitrary Character of Dimensionality—Various Definitions of Dimension—Real Space and Geometric Space Differentiated—The Finity of Space—Difference Between the Purely Formal and the Actual—Space as Dynamic Appearance—The A Priori and the A Posteriori as Defined by Paul Carus | 92 |
| | |
| CHAPTER V | |
| The Fourth Dimension | |
| The Ideal and the Representative Nature of Objects in the Sensible World—The Fluxional, the Basis of Mental Differences—Natural Symbols and Artificial Symbols—Use of Analogies to Prove the Existence of a Fourth Dimension—The Generation of a Hypercube or Tesseract—Possibilities in the World of the Fourth Dimension—Some Logical Difficulties Inhering in the Four-Space Conception—The Fallacy of the Plane-Rotation Hypothesis—C. H. Hinton and Major Ellis on the Fourth Dimension | 118 |
| | |
| PART TWO | |
| SPATIALITY: AN INQUIRY INTO THE ESSENTIAL NATURE OF SPACE AS DISTINGUISHED FROM THE MATHEMATICAL INTERPRETATION | |
| | |
| CHAPTER VI | |
| Conciousness the Norm of Space Determinations | |
| Realism Is Determined by Awareness—Succession of Degrees of Realism—Sufficiency of Tridimensionality—The Insufficiency of Self-consistency as a Norm of Truth—General Forward Movement in the Evolution of Consciousness Implied in the Hyperspace Concept—The Hypothetical Nature of Our Knowledge—Hyperspace the Symbol of a More Extensive Realm of Awareness—Variations in the Methods of Interpreting Intellectual Notions—The Tuitional and the Intuitional Faculties—The Illusionary Character of the Phenomenal—Consciousness and the Degrees of Realism | 161 |
| | |
| CHAPTER VII | |
| The Genesis and Nature of Space | |
| Symbology of Mathematical Knowledge—Manifestation and Non-manifestation Defined—The Pyknon and Pyknosis—The Kosmic Engenderment of Space—On the Consubstantiality of Spatiality, Intellectuality, Materiality, Vitality and Kosmic Geometrism—Chaos-Theos-Kosmos—Chaogeny and Chaomorphogeny—N. Malebranche on God and the World—The Space-Mind—Space and Mind Are One—The Kosmic Pentoglyph | 203 |
| | |
| CHAPTER VIII | |
| The Mystery of Space | |
| The Thinker and the Ego—Increscent Automatism of the Intellect—The Egopsyche and the Omnipsyche—Kosmic Order or Geometrism—Life as Engendering Element—The Mystery of Space Stated—Kathekos and Kathekotic Consciousness—Function of the Ideal—The Path of Search for an Understanding of the Nature and Extent of Space Must Proceed in an Inverse Direction | 242 |
| | |
| CHAPTER IX | |
| Metageometrical Near-truths | |
| Realism Is Psychological and Vital—The Impermanence of Facts—On the Tendency of the Intellect to Fragmentate—The Intellect and Logic—The Passage of Space—Kosmometer and Zoometer, Instruments for the Measurement of the Passage of Space and the Flow of Life—The Disposal of Life and the Power to Create—Space, a Dynamic, Creative Process—Numbers and Kosmogony—Kosmic Significance of the Circle and the Pi-proportion—Mechanical Tendence of the Intellect and Its Inaptitude for the Understanding of Life—The Criterion of Truth | 284 |
| | |
| CHAPTER X | |
| Media of New Perceptive Fa
THE MYSTERY OF SPACE
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