Chapter III: Preface: vii

INTRODUCTION: Explanatory Notes x

_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

CONSCIOUSNESS 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 FACULTIES

The Spiritualization of Matter Is the End of Evolution--Sequence
and Design in the Evolution of Human Faculties--The
Upspringing Intuition--Evidences of Supernormal Powers
of Perception and the Possibility of Attainment--The
Influence and Place of the Pituitary Body and the Pineal
Gland in the Evolution of Additional Faculties--The
Skeptical Attitude of Empirical Science and the Need
for a More Liberal Posture--The General Results of
Pituitarial Awakening Upon Man and the Theory of
Knowledge 327

BIBLIOGRAPHY 359

INDEX 367

THE MYSTERY OF SPACE