Hinton - The Fourth Dimension.pdf

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128 THE FOURTH DIMENSION are at a distance 0 from our space in the fourth dimension, the second showing all those that are at a distance 1, and so on. These figures will each be cubes. The first two are drawn showing the front faces, the second two the rear faces. We will mark the points 0, 1, 2, 3, putting points at those distances along each of these axes, and suppose i k D B C 3210 j 0h 1h E2 E 2h 3h Fig. 71. all the points thus determined to be contained in solid models of which our drawings in fig. 71 are representations. Here we notice that as on the plane 0i meant the whole line from which the distance in the i direction was measured, and as in space 0i means the whole plane from which distances in the i direction are measured, so now 0h means the whole space in which the first cube stands—measuring away from that space by a distance of one we come to the second cube represented.
A FOUR-DIMENSIONAL FIGURE 129 Now selecting according to the rule every one of one kind with every other of every other kind, we must take, for instance, 3i, 2j, 1k, 0h. This point is marked 3210 at the lower star in the figure. It is 3 in the i direction, 2 in the j direction, 1 in the k direction, 0 in the h direction. With 3i we must also take 1j, 2k, 0h. This point is shown by the second star in the cube 0h. 2130 3120 3210 i 3021 3102 1032 k 1230 1320 2310 2031 j 3201 0h 1h 0132 1302 0312 3021 2h 3h Fig. 72. 2301 0231 0321 1023 0123 2013 2103 0213 1203 In the first cube, since all the points are 0h points, we can only have varieties in which i, j, k, are accompanied by 3, 2, 1. The points determined are marked off in the diagram fig. 72, and lines are drawn joining the adjacent pairs in each figure, the lines being dotted when they pass within the substance of the cube in the first two diagrams. Opposite each point, on one side or the other of each
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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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THE HIGHER WORLD 69 simply the plan
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THE HIGHER WORLD 71 turn these rods
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THE HIGHER WORLD 73 revolution, the
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THE HIGHER WORLD 75 the mode of act
Page 87 and 88: THE EVIDENCES FOR A FOURTH DIMENSIO
Page 95 and 96: CHAPTER VIII THE USE OF FOUR DIMENS
Page 97 and 98: 5 THE USE OF FOUR DIMENSIONS IN THO
Page 99 and 100: THE USE OF FOUR DIMENSIONS IN THOUG
Page 117 and 118: CHAPTER IX APPLICATION TO KANT’S
Page 119 and 120: APPLICATION TO KANT’S THEORY OF E
Page 123 and 124: 3 APPLICATION TO KANT’S THEORY OF
Page 133 and 134: A FOUR-DIMENSIONAL FIGURE 123 The r
Page 135 and 136: A FOUR-DIMENSIONAL FIGURE 125 new d
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Page 141 and 142: A FOUR-DIMENSIONAL FIGURE 131 of me
Page 143 and 144: A FOUR-DIMENSIONAL FIGURE 133 note
Page 145 and 146: A FOUR-DIMENSIONAL FIGURE 135 These
Page 147 and 148: NOMENCLATURE AND ANALOGIES 137 to a
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Page 165 and 166: NOMENCLATURE AND ANALOGIES 155 lie
Page 167 and 168: CHAPTER XII THE SIMPLEST FOUR-DIMEN
Page 169 and 170: THE SIMPLEST FOUR-DIMENSIONAL SOLID
Page 185 and 186: Purple Red THE SIMPLEST FOUR-DIMENS
Page 187 and 188: 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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