Hinton - The Fourth Dimension.pdf

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138 THE FOURTH DIMENSION null beyond it, while the oranges increase in a double way. x Null Red Red Red Null Yellow Orange Orange Orange Yellow Yellow Orange Orange Orange Yellow Fig. 79. Yellow Orange Orange Orange Yellow Suppose this process of enlarging the number of the Null Yellow Null Red x Null Orange Red Yellow Fig. 80. Null Null Red Red Red Null squares to be indefinitely pursued and the total figure obtained to be reduced in size, we should obtain a square of which the interior was all orange, which the lines round it were red and yellow, and merely the points null colour, as in fig. 80. Thus all the points, lines, and the area would have a colour. We can consider this scheme to originate thus:--Let a small point move in a yellow direction and trace out a yellow line and end in a null point. Then let the whole line thus traced move in a red direction. The null points at the ends of the line will produced red lines, and end in
NOMENCLATURE AND ANALOGIES 139 null points. The yellow lines will trace out a yellow and red, or orange square. Now, turning back to fig. 78, we see that these two ways of naming, the one we started with and the one we arrived at, can be combined. By its position in the group of four squares, in fig. 77, the null square has a relation to the yellow and to the red directions. We can speak therefore of the red line of the null square without confusion, meaning thereby the line AB, fig. 81, which runs up from the initial null point A in the figure as B x A Red Null D C Fig. 81. Orange Yellow drawn. The yellow line of the null square is its lower horizontal line AC as it is situated in the figure. If we wish to denote the upper yellow line BD, fig. 81, we can speak of it as the yellow r line, meaning the yellow line which is separated from the primary yellow line by the red movement. In a similar way each of the other squares has null points, red and yellow lines. Although the yellow square is all yellow its line CD, for instance, can be referred to as its red line. This nomenclature can be extended. If the eight cubes drawn in fig. 82 are put close together, as on the right hand of the diagram, they form a cube, and in them, as thus arranged, a going up is represented by adding red to the zero, or null colour, a going away by adding yellow, a going to the right by adding white. White is used as a colour, as a pigment, which produces a colour change in the pigment with which it is mixed. From whatever cube of the lower set we start, a motion up brings us to a cube showing a change to red, thus light yellow becomes light yellow red, or light orange, which is called ochre. And going to 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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CHAPTER VIII THE USE OF FOUR DIMENS
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Page 117 and 118: CHAPTER IX APPLICATION TO KANT’S
Page 119 and 120: APPLICATION TO KANT’S THEORY OF E
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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
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 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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