Hinton - The Fourth Dimension.pdf

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188 THE FOURTH DIMENSION whatever cubic view we take of them we can say exactly what sides of the tesseracts we are handling, and how they touch each other.* Thus, for instance, if we have the sixteen tesseracts shown below, we can ask how does null touch blue. In the arrangement given in fig. 111 we have the axes white, red, yellow, in space, blue running in the fourth dimension. Hence we have the ochre cubes as bases. Imagine now the tesseractic group to pass transverse to our space—we have first of all null ochre cube, white Yellow axis Red axis x Light yellow hidden A.b0 Yellow direction White axis Fig. 111. Red direction White direction Light green hidden B.b1 ochre cube, etc.; these instantly vanish, and we get the section shown in the middle cube in fig. 103, and finally, just when the tesseract block has moved one inch transverse to our space, we have null ochre cube, and then immediately afterwards the ochre cube of blue comes in. Hence the tesseract null touches the tesseract blue by its ochre cube, which is in contact, each and every point of it, with the ochre cube of blue. How does null touch white, we may ask? Looking at the beginning A, fig. 111, where we have the ochre * At this point the reader will find it advantageous, if he has the models, to go through the manipulations described in Appendix I.
REMARKS ON THE FIGURES 189 cubes, we see that null ochre touches white ochre by an orange face. Now let us generate the null and white tesseracts by a motion in the blue direction of each of these cubes. Each of them generates the corresponding tesseract, and the plane of contact of the cubes generates the cube by which the tesseracts are in contact. Now an orange plane carried along a blue axis generates a brown cube. Hence null touches white by a brown cube. Red axis x C.y 0 Blue axis White hidden White axis Red direction C.y 1 Fig. 112. Blue direction White direction Light yellow hidden If we ask again how red touches light blue tesseract, let us rearrange our group, fig. 112, or rather turn it about so that we have a different space view of it; let the red axis and the white axis run up and right, and let the blue axis come in space towards us, then the yellow axis runs in the fourth dimension. We have then two blocks in which the bounding cubes of the tesseracts are given, differently arranged with regard to us—the arrangement is really the same, but it appears different to us. Starting from the plane of the red and white axes we have the four squares of the null, white, red, pink tesseracts as shown in A, on the red, white plane, unaltered, only from them now comes out towards us the blue axis.
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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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5 THE USE OF FOUR DIMENSIONS IN THO
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THE USE OF FOUR DIMENSIONS IN THOUG
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CHAPTER IX APPLICATION TO KANT’S
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APPLICATION TO KANT’S THEORY OF E
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3 APPLICATION TO KANT’S THEORY OF
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A FOUR-DIMENSIONAL FIGURE 123 The r
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A FOUR-DIMENSIONAL FIGURE 125 new d
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A FOUR-DIMENSIONAL FIGURE 127 pick
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A FOUR-DIMENSIONAL FIGURE 129 Now s
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A FOUR-DIMENSIONAL FIGURE 131 of me
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A FOUR-DIMENSIONAL FIGURE 133 note
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A FOUR-DIMENSIONAL FIGURE 135 These
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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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Page 189 and 190: REMARKS ON THE FIGURES 179 ochre cu
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Page 215 and 216: RECAPITULATION AND EXTENSION 205 ou
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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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