Hinton - The Fourth Dimension.pdf

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CHAPTER XI NOMENCLATURE AND ANALOGIES PRELIM- INARY TO THE STUDY OF FOUR-DIMEN- SIONAL FIGURES IN the following pages a method of designating different regions of space by a systematic colour scheme has been adopted. The explanations have been given in such a manner as to involve no reference to models, the diagrams will be found sufficient. But to facilitate the study a description of a set of models is given in an appendix which the reader can either make for himself or obtain. If models are used the diagrams in Chapters XI. and XII. will form a guide sufficient to indicate their use. Cubes of the colours designated by the diagrams should be picked out and used to reinforce the diagrams. The reader, in the following description, should suppose that a board or wall stretches away from him, against which the figures are placed. Take a square, one of those x shown in Fig. 77 and give it a neutral colour, let this colour be called “null,” and be such that it Fig. 77. makes no appreciable difference Red Null Orange Yellow 136
NOMENCLATURE AND ANALOGIES 137 to any colour with which it is mixed. If there is no such real colour let us imagine such a colour, and assign to it the properties of the number zero, which makes no difference in any number to which it is added. Above this square place a red square. Thus we symbolise the going up by adding red to null. Away from this null square place a yellow square, and represent going away by adding yellow to null. To complete the figure we need a fourth square. Colour this orange, which is a mixture of red and yellow, and so appropriately represents a going in a direction compounded of up and away. We have thus a colour scheme which will serve to name the set of squares drawn. We have two axes of colours—red and yellow—and they may occupy as in the figure the x Null Red Null Yellow Orange Yellow Fig. 78. Null Red Null direction up and away, or they may be turned about; in any case they enable us to name the four squares drawn in their relation to one another. Now take, in Fig. 78, nine squares, and suppose that at the end of the going in any direction the colour started with repeats itself. We obtain a square named as shown. Let us now, in fig. 79, suppose the number of squares to be increased, keeping still to the principle of colouring already used. Here the nulls remain four in number. There are three reds between the first null and the null above it, three yellows between the first null and the
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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
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THE EVIDENCES FOR A FOURTH DIMENSIO
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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
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Page 143 and 144: A FOUR-DIMENSIONAL FIGURE 133 note
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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
Page 189 and 190: REMARKS ON THE FIGURES 179 ochre cu
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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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