Mathematical evidences have been used in these discussions because they, of all lines of knowledge, afford a more just exemplification of intellectual evolution. The science of mathematics is the measure of the quality of intellectual growth and, therefore, its data, its postulates, hypotheses and advances clearly mark the stages of the intellectual movement.
Chapter X is the natural and logical sequence of the inquiry into the question of spatiality. The conclusions reached therein and the obvious inferences which should be drawn from the arguments presented flow inevitably not only from the evidences of mathematical data but of the common observations of life. And while we disclaim any intention of demanding acceptance of them as final, authoritative declarations, we shall be satisfied if the readers of this volume be incited to solve for themselves the problems which these queries naturally suggest. Happy indeed shall be the outcome if there be any who, following the path sketched herein, shall find the solution of the _Mystery of Space_ and apply its meanings to the enhancement of the values of the intuitive life.
In conclusion, the author esteems it a special obligation of gratitude that he should here acknowledge the debt which he owes to all of his friends who have in any way assisted or encouraged him in the completion of this work. Among those whom he is permitted to thank in this way is Mr. JAMES RINDFLEISCH who, having very kindly prepared the illustrations for the photo-engravers, is deserving of special mention.
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
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