Hinton - The Fourth Dimension.pdf

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262 THE FOURTH DIMENSION By using a more extended sequence of consonants and vowels a larger set of cubes can be named. To name a four-dimensional block of tesseracts it is simply necessary to prefix an “e,” an “a,” or an “i” to the cube names. Thus the tesseract blocks schematically represented on page 165, fig. 101 are named as follows:— elen elet elel alen alet alel ilen ilet ilel elan elat elal alan alat alal ilan ilat ilal elin elit elil alin alit alil ilin ilit ilil eten etet etel aten atet atel iten itet itel etan etat etal atan atat atal itan itat ital etin etit etil atin atit atil itin itit itil * enen enet enel anen anet anel inen inet inel enan enat enal anan anat anal inan inat inal enin enit enil anin anit anil inin init inil 1 2 3 2. DERIVATION OF POINT, LINE, FACE, ETC. NAMES. The principle of derivation can be shown as follows: Taking the square of squares * en et el an at al in it il
APPENDIX II: A LANGUAGE OF SPACE 263 the number of squares in it can be enlarged and the whole kept the same size. * en et et el an an at at at at al al in it it il Compare fig. 79, p. 138, for instance, or the bottom layer of fig. 84. Now use an initial “s” to denote the result of carrying this process on to a great extent, and we obtain the limit names, that is the point, line, area names for a square. “Sat” is the whole interior. The corners are “sen,” set sen sel san sin sat sal sit sil ”sel,” “sin,” “sil,” while the lines are “san,” “sal,” “set,” “sit.” I find that by the use of the initial “s” these names come to be practically entirely disconnected with the systematic names for the square from which they are derived. They are easy to learn, and when learned can be used readily with the axes running in any direction. To derive the limit names for a four-dimensional rectangular figure, like the tesseract, is a simple extension of this process. These point, line, etc., names include those which apply to a cube, as will be evident on inspection of the first cube of the diagrams which follow. All that is necessary is to place an “s” before each of the names given for a tesseract block. We then obtain apellatives which, like the colour names on page 174, fig. 103, apply to all the points, lines, faces, solids, and to
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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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NOMENCLATURE AND ANALOGIES 137 to a
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NOMENCLATURE AND ANALOGIES 139 null
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NOMENCLATURE AND ANALOGIES 141 laye
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NOMENCLATURE AND ANALOGIES 143 a li
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NOMENCLATURE AND ANALOGIES 145 oppo
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NOMENCLATURE AND ANALOGIES 147 the
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NOMENCLATURE AND ANALOGIES 149 dime
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NOMENCLATURE AND ANALOGIES 151 larg
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NOMENCLATURE AND ANALOGIES 153 axes
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NOMENCLATURE AND ANALOGIES 155 lie
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CHAPTER XII THE SIMPLEST FOUR-DIMEN
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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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Page 241 and 242: APPENDIX I THE MODELS IN Chapter XI
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Page 257 and 258: APPENDIX I: THE MODELS 247 sponding
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Page 275 and 276: Sil Sit Sin Sil Sit Sin Silan Sitan
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