Produced by Robert Cicconetti, Les Galloway and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)
_The domain of the senses, in nature, is almost infinitely small in comparison with the vast region accessible to thought which lies beyond them._--TYNDALL, "On Radiant Heat."
_A Study of the Hyperspace Movement in the Light of the Evolution of New Psychic Faculties and An Inquiry into the Genesis and Essential Nature of Space_
NEW YORK E. P. DUTTON & COMPANY 681 FIFTH AVENUE
COPYRIGHT 1919, BY E. P. DUTTON & COMPANY
_Printed in the United States of America_
WHOSE WIFELY DEVOTION, SYMPATHETIC ASSISTANCE AND ENCOURAGEMENT DURING THE EARLY LABORS ON THE TEXT WERE A CONSTANT SOURCE OF INSPIRATION AND FORTITUDE TO THE AUTHOR, THIS BOOK IS DEDICATED AFFECTIONATELY
Mathematics is the biometer of intellectual evolution. Hence, the determination of the _status quo_ of the intellect at any time can be accomplished most satisfactorily by applying to it the rigorous measure of the mathematical method. The intellect has but one true divining rod and that is mathematics. By day and by night it points the way unerringly, so long as it leads through materiality; but, falteringly, blindly, fatally, when that way veers into the territory of vitality and spirituality.
Wherefore, when we have wished to ascertain the real status of the intellect, as well as its limitations, tendencies, possibilities, we have turned to its conduct in the field of mathesis where it is least trammeled in its ingressive and egressive motivations because of the natural and easy accommodation which is offered for intellectual movement. Whether there are signs of moribundity or symptomatic evidences of marked growth or of a termination of intellectual regnancy, or whatever may be the occasion for the examination, no surer index than the mathematical may be found for the purpose. Full logical justification is, therefore, claimed for the choice of mathematical evidences to test the assumption that a new era of conscious mental conquest is opening for the vanguard of humanity and sequently for the human family.
The treatment of these evidences has fallen logically into two divisions, namely, the first, a brief and elementary review of the principles of the non-Euclidean geometry and their bearings upon the question of space as the subject of mathematical study; and second, the consideration of space as a psychological, vital and dynamic or creative phenomenon.