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y^^f Digitized by tine Internet Arciiive in 2010 with funding from Boston Library Consortium IVIember Libraries http://www.archive.org/details/fourthdimensionbOOgran THE FOURTH DIMENSION AND THE BIBLE ^ BY WILLIAM ANTHONY GRANVILLE, Ph.D., LL.D> PRESIDENT OF GETTYSBURG COLLEGE. Formerly Instructor of Mathematics in Yale University; Author of Granville's Differential and Integral Calculus, Granville's Plane Trigonometry, Granville's Spherical Trigonometry, and Gran- ville'sLogarithmic Tables;loint Author ofSmith and Gran- ville's Elements of Analysis; Inventor of Polar Co- ordinate Plotting Paper, Yale System of Mathemat- ical Note Books, and Granville's Transparent Combined Ruler and Protractor. BOSTON RICHARD BADGER G. THE GORHAM PRESS Copyright, 1922, by William A. Granville All Rights Reserved .^7 Made in the United States of America The Gorham Press, Boston, U. S. A. J30STON mUM^E MBRARl 11 r1AY 1972 477046 PREFACE That philosophy and the physical sciences, when called to the defence of Christianity, have so often proven to be broken reeds has been a keen disappointment to many sincere seekers after the truth. A little reflection, however, will make clear that in the very nature of things such fail- ures must inevitably result, because structures resting on shifting sand can never serve as strong buttresses. No two systems of philosophy agree and every philosopher is continually tinkering with his own system. There is no final authority in philosophy to which an appeal can be made. Such being the case it is obviously not to be ex- pected that philosophy can furnish us with proofs of the truths of Christianity whose validity will be generally recognized. And the sciences have also fallen short for similar reasons. The foundations of our physical sciences are far from stable. To doubtthe principles of the conservation of energy, the conservation of matter, or the Indivisibility of the atom, would have been considered as rank scientific heresy a few years ago; today all physi- cists are familiarwith phenomena which contradict iv Preface one or more of them. The Einstein Theory of Relativity is now opening up new fields for scientific investigation which promises results that will practically revolutionize many current fundamen- tal scientific concepts. In fact, the foundation principles on which the physical sciences rest have been changing so rapidly of late that practically all the science text-books now used in our schools are more or less obsolete. The physical sciences as well as philosophy are in a constant state of flux and flow as well as of growth, and this must necessarily continue to be the situation until the ultimate truth is reached, If it is ever attained, in these domains of knowledge. As all will readily agree that the limits of these regions have not yet been reached and, what is more, that these limits are not even measurably in sight, it is evident that we cannot reasonably expect that much con- structive light will be thrown on Christianity now or in the near future by either philosophy or the physical sciences. To satisfy completely human reason any confir- mation of our Christian beliefs must come from a source whose authority no one can question. Is there then any department of human knowledge whose foundations rest, not on shifting sand, but on the bed rock of absolute truth? Pure mathematics satisfies this condition it is the only exact ; science that God has revealed to man and the