CONTENTS
| PAGE | ||
| [Preface] | vii | |
| [Introduction]: Explanatory Notes | 1 | |
| PART ONE | ||
| [CHAPTER I] | ||
| The Prologue | ||
| On the Variability of Psychic Powers—The Discovery ofthe Fourth Dimension Marks a Distinct Stage inPsychogenesis—The non-Methodical Character ofDiscoveries—The Three Periods of PsychogeneticDevelopment—The Scope and Permissibility ofMathetic License—Kosmic Unitariness UnderlyingDiversity | 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 ParallelPostulate the Root and Substance of the Non-EuclideanGeometry—The Three Great Periods: The Formative,Determinative and Elaborative—Riemann and the Propertiesof Analytic Spaces | 44 | |
| [CHAPTER III] | ||
| Essentials of the Non-Euclidean Geometry | ||
| The Non-Euclidean Geometry Concerned with ConceptualSpace Entirely—Outcome of Failures at Solvingthe Parallel-Postulate—The Basis of the Non-EuclideanGeometry—Space Curvature and Manifoldness—SomeElements of the Non-Euclidean Geometry—Certainty,Necessity and Universality as Bulwarks ofGeometry—Some Consequences of Efforts at Solvingthe Parallel-Postulate—The Final Issue of theNon-Euclidean Geometry—Extended Consciousness | 69 | |
| [CHAPTER IV] | ||
| Dimensionality | ||
| Arbitrary Character of Dimensionality—Various Definitionsof Dimension—Real Space and Geometric SpaceDifferentiated—The Finity of Space—Difference Betweenthe Purely Formal and the Actual—Space as DynamicAppearance—The A Priori and the A Posteriori asDefined by Paul Carus | 92 | |
| [CHAPTER V] | ||
| The Fourth Dimension | ||
| The Ideal and the Representative Nature of Objects inthe Sensible World—The Fluxional, the Basis ofMental Differences—Natural Symbols and ArtificialSymbols—Use of Analogies to Prove the Existence ofa Fourth Dimension—The Generation of a Hypercubeor Tesseract—Possibilities in the World of theFourth Dimension—Some Logical Difficulties Inheringin the Four-Space Conception—The Fallacy of thePlane-Rotation Hypothesis—C. H. Hinton andMajor 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 Degreesof Realism—Sufficiency of Tridimensionality—TheInsufficiency of Self-consistency as a Norm ofTruth—General Forward Movement in the Evolutionof Consciousness Implied in the Hyperspace Concept—TheHypothetical Nature of Our Knowledge—Hyperspacethe Symbol of a More Extensive Realm ofAwareness—Variations in the Methods of InterpretingIntellectual Notions—The Tuitional and theIntuitional Faculties—The Illusionary Character ofthe Phenomenal—Consciousness and the Degrees ofRealism | 161 | |
| [CHAPTER VII] | ||
| The Genesis and Nature of Space | ||
| Symbology of Mathematical Knowledge—Manifestationand Non-manifestation Defined—The Pyknon andPyknosis—The Kosmic Engenderment of Space—Onthe Consubstantiality of Spatiality, Intellectuality,Materiality, Vitality and KosmicGeometrism—Chaos-Theos-Kosmos—Chaogeny andChaomorphogeny—N. Malebranche on God and theWorld—The Space-Mind—Space and Mind AreOne—The Kosmic Pentoglyph | 203 | |
| [CHAPTER VIII] | ||
| The Mystery of Space | ||
| The Thinker and the Ego—Increscent Automatism ofthe Intellect—The Egopsyche and the Omnipsyche—KosmicOrder or Geometrism—Life as EngenderingElement—The Mystery of Space Stated—Kathekosand Kathekotic Consciousness—Function of the Ideal—ThePath of Search for an Understanding of the Nature andExtent of Space Must Proceed in an Inverse Direction | 242 | |
| [CHAPTER IX] | ||
| Metageometrical Near-truths | ||
| Realism Is Psychological and Vital—The Impermanence ofFacts—On the Tendency of the Intellect to Fragmentate—TheIntellect and Logic—The Passage of Space—Kosmometerand Zoometer, Instruments for the Measurement of thePassage of Space and the Flow of Life—The Disposal ofLife and the Power to Create—Space, a Dynamic, CreativeProcess—Numbers and Kosmogony—Kosmic Significance ofthe Circle and the Pi-proportion—Mechanical Tendenceof the Intellect and Its Inaptitude for the Understandingof Life—The Criterion of Truth | 284 | |
| [CHAPTER X] | ||
| Media of New Perceptive Faculties | ||
| The Spiritualization of Matter Is the End of Evolution—Sequenceand Design in the Evolution of Human Faculties—TheUpspringing Intuition—Evidences of Supernormal Powersof Perception and the Possibility of Attainment—TheInfluence and Place of the Pituitary Body and the PinealGland in the Evolution of Additional Faculties—TheSkeptical Attitude of Empirical Science and the Needfor a More Liberal Posture—The General Results ofPituitarial Awakening Upon Man and the Theory ofKnowledge | 327 | |
| [Bibliography] | 359 | |
| [Index] | 367 | |
THE MYSTERY OF SPACE