Hinton - The Fourth Dimension.pdf

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120 THE FOURTH DIMENSION If the order and the law we see is due to the conditions of conscious experience, we must conceive nature as spontaneous, free, subject to no predication that we can devise, but, however apprehended, subject to our logic. And our logic is simply spatiality in the general sense —that resultant of a selection of the permanent from the unpermanent, the ordered from the unordered, by the means of the group and its underlying duality. We can predicate nothing about nature, only about the way in which we can apprehend nature. All that we can say is that all that which experience gives us will be considered as spatial, subject to our logic. Thus, in exploring the facts of geometry from the simplest logical relations to the properties of space of any number of dimensions, we are merely observing ourselves, becoming aware of the conditions under which we must perceive. Do any phenomena present themselves incapable of explanation under the assumption of the space we are dealing with, then we must habituate ourselves to the conception of a higher space, in order that our logic may be equal to the task before us. We gain a repetition of the thought that came before, experimentally suggested. If the laws of the intellectual comprehension of nature are those derived from considering her as absolute chance, subject to no law save that derived from a process of selection, then, perhaps, the order of nature requires different faculties from the intellectual to apprehend it. The source and origin of ideas may have to be sought elsewhere than in reasoning. The total outcome of the critique is to leave the ordinary man just where he is, justified in his practical attitude towards nature, liberated from the fetters of his own mental representations. The truth of a picture lies in its total effect. It is vain to seek information about the landscape from an examina-
APPLICATION TO KANT’S THEORY OF EXPERIENCE 121 tion of the pigments. And in any method of thought it is the complexity of the whole that brings us to a knowledge of nature. Dimensions are artificial enough, but in the multiplicity of them we catch some breath of nature. We must therefore, and this seems to me the practical conclusion of the whole matter, proceed to form means of intellectual apprehension of a greater and greater degree of complexity, both dimensionally and in extent in any dimension. Such means of representation must always be artificial, but in the multiplicity of the elements with which we deal, however incipiently arbitrary, lies our chance of apprehending nature. And as a concluding chapter to this part of the book, I will extend the figures, which have been used to represent Kant’s theory, two steps, so that the reader may have the opportunity of looking at a four-dimensional figure which can be delineated without any of the special apparatus, to the consideration of which I shall subsequently pass on.
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THE FOURTH DIMENSION
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THE FOURTH DIMENSION BY C. HOWARD H
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PREFACE I HAVE endeavoured to prese
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CONTENTS CHAP. PAGE. I. FOUR-DIMENS
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THE FOURTH DIMENSION ————
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FOUR-DIMENSIONAL SPACE 3 existence
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FOUR-DIMENSIONAL SPACE 5 Bringing i
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THE ANALOGY OF A PLANE WORLD 7 him.
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THE ANALOGY OF A PLANE WORLD 9 to a
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THE ANALOGY OF A PLANE WORLD 11 Aga
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THE ANALOGY OF A PLANE WORLD 13 sec
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CHAPTER III THE SIGNIFICANCE OF A F
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SIGNIFICANCE OF A FOUR-DIMENSIONAL
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CHAPTER IV THE FIRST CHAPTER IN THE
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THE FIRST CHAPTER IN THE HISTORY OF
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CHAPTER V THE SECOND CHAPTER IN THE
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SECOND CHAPTER IN THE HISTORY OF FO
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CHAPTER VI THE HIGHER WORLD IT is i
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THE HIGHER WORLD 63 dimensions. His
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THE HIGHER WORLD 65 If now he turns
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THE HIGHER WORLD 67 to him that, by
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Page 87 and 88: THE EVIDENCES FOR A FOURTH DIMENSIO
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Page 133 and 134: A FOUR-DIMENSIONAL FIGURE 123 The r
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Page 167 and 168: CHAPTER XII THE SIMPLEST FOUR-DIMEN
Page 169 and 170: THE SIMPLEST FOUR-DIMENSIONAL SOLID
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THE SIMPLEST FOUR-DIMENSIONAL SOLID
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THE SIMPLEST FOUR-DIMENSIONAL SOLID
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Purple Red THE SIMPLEST FOUR-DIMENS
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Light blue Gren Light purple THE SI
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REMARKS ON THE FIGURES 179 ochre cu
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REMARKS ON THE FIGURES 181 for it i
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REMARKS ON THE FIGURES 183 that is
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REMARKS ON THE FIGURES 185 yellow l
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REMARKS ON THE FIGURES 187 As the r
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REMARKS ON THE FIGURES 189 cubes, w
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4 4 REMARKS ON THE FIGURES 191 The
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REMARKS ON THE FIGURES 193 face or
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REMARKS ON THE FIGURES 195 face in
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REMARKS ON THE FIGURES 197 space, a
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REMARKS ON THE FIGURES 199 Hence wh
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REMARKS ON THE FIGURES 201 sections
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CHAPTER XIV * A RECAPITULATION AND
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RECAPITULATION AND EXTENSION 205 ou
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RECAPITULATION AND EXTENSION 207 ha
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RECAPITULATION AND EXTENSION 209 Bu
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RECAPITULATION AND EXTENSION 211 We
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RECAPITULATION AND EXTENSION 213 Th
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RECAPITULATION AND EXTENSION 215 th
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RECAPITULATION AND EXTENSION 217 In
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RECAPITULATION AND EXTENSION 221 ta
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RECAPITULATION AND EXTENSION 223 If
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RECAPITULATION AND EXTENSION 227 di
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RECAPITULATION AND EXTENSION 229 If
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APPENDIX I THE MODELS IN Chapter XI
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APPENDIX I: THE MODELS 233 in an op
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APPENDIX I: THE MODELS 235 would be
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APPENDIX I: THE MODELS 237 have to
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APPENDIX I: THE MODELS 239 can be u
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APPENDIX I: THE MODELS 241 The four
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APPENDIX I: THE MODELS 243 orange f
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APPENDIX I: THE MODELS 245 we make
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APPENDIX I: THE MODELS 247 sponding
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APPENDIX II: A LANGUAGE OF SPACE 24
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Sil Sit Sin Sil Sit Sin Silan Sitan
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TRANSCRIBER’S NOTE. Do what thou
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