Chapter II: Preface

I have endeavoured to present the subject of the higher dimensionality of space in a clear manner, devoid of mathematical subtleties and technicalities. In order to engage the interest of the reader, I have in the earlier chapters dwelt on the perspective the hypothesis of a fourth dimension opens, and have treated of the many connections there are between this hypothesis and the ordinary topics of our thoughts.

A lack of mathematical knowledge will prove of no disadvantage to the reader, for I have used no mathematical processes of reasoning. I have taken the view that the space which we ordinarily think of, the space of real things (which I would call permeable matter), is different from the space treated of by mathematics. Mathematics will tell us a great deal about space, just as the atomic theory will tell us a great deal about the chemical combinations of bodies. But after all, a theory is not precisely equivalent to the subject with regard to which it is held. There is an opening, therefore, from the side of our ordinary space perceptions for a simple, altogether rational, mechanical, and observational way of treating this subject of higher space, and of this opportunity I have availed myself.

The details introduced in the earlier chapters, especially in Chapters VIII., IX., X., may perhaps be found wearisome. They are of no essential importance in the main line of argument, and if left till Chapters XI. and XII. have been read, will be found to afford interesting and obvious illustrations of the properties discussed in the later chapters.

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-DIMENSIONAL
EXISTENCE 15

IV. THE FIRST CHAPTER IN THE HISTORY OF FOUR
SPACE 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 THE
PHYSICAL ARGUMENT 203

APPENDIX I.—THE MODELS 231

" II.—A LANGUAGE OF SPACE 248

THE FOURTH DIMENSION