My thanks are due to the friends who have assisted me in designing and preparing the modifications of my previous models, and in no small degree to the publisher of this volume, Mr. Sonnenschein, to whose unique appreciation of the line of thought of this, as of my former essays, their publication is owing. By the provision of a coloured plate, in addition to the other illustrations, he has added greatly to the convenience of the reader.
C. Howard Hinton.
CONTENTS
| CHAP. | PAGE | |
| [I.] | Four-Dimensional Space | 1 |
| [II.] | The Analogy of a Plane World | 6 |
| [III.] | The Significance of a Four-DimensionalExistence | 15 |
| [IV.] | The First Chapter in the History of FourSpace | 23 |
| [V.] | The Second Chapter in the History Of Four Space | 41 |
| Lobatchewsky, Bolyai, and Gauss Metageometry | ||
| [VI.] | The Higher World | 61 |
| [VII.] | The Evidence for a Fourth Dimension | 76 |
| [VIII.] | The Use of Four Dimensions in Thought | 85 |
| [IX.] | Application to Kant’s Theory of Experience | 107 |
| [X.] | A Four-Dimensional Figure | 122 |
| [XI.] | Nomenclature and Analogies | 136 |
| [XII.] | The Simplest Four-Dimensional Solid | 157 |
| [XIII.] | Remarks on the Figures | 178 |
| [XIV.] | A Recapitulation and Extension of thePhysical Argument | 203 |
| [APPENDIX I.]—The Models | 231 | |
| [APPENDIX II.]—A Language of Space | 248 | |
THE FOURTH DIMENSION
CHAPTER I
FOUR-DIMENSIONAL SPACE
There is nothing more indefinite, and at the same time more real, than that which we indicate when we speak of the “higher.” In our social life we see it evidenced in a greater complexity of relations. But this complexity is not all. There is, at the same time, a contact with, an apprehension of, something more fundamental, more real.
With the greater development of man there comes a consciousness of something more than all the forms in which it shows itself. There is a readiness to give up all the visible and tangible for the sake of those principles and values of which the visible and tangible are the representation. The physical life of civilised man and of a mere savage are practically the same, but the civilised man has discovered a depth in his existence, which makes him feel that that which appears all to the savage is a mere externality and appurtenage to his true being.
Now, this higher—how shall we apprehend it? It is generally embraced by our religious faculties, by our idealising tendency. But the higher existence has two sides. It has a being as well as qualities. And in trying to realise it through our emotions we are always taking the subjective view. Our attention is always fixed on what we feel, what we think. Is there any way of apprehending the higher after the purely objective method of a natural science? I think that there is.