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39 Trying to Be Clear on corresponding points in figure 2. Even Birkhoff’s aesthetic measure distinguishes the figures—without really looking! In particular, Peirce’s figure 1 taken as a square in this orientation has a higher value than figure 2 as the rotation The score is 1.50 to 1.25. Does this miss the mark? What are the objects (parts) in Peirce’s two figures anyway? Are they so obviously individual points, permanently fixed before I have a chance to look? Maybe they’re different in each figure and vary unpredictably. Suppose they’re horizontals or likewise verticals. Things don’t have to touch to hang together. Stars don’t in constellations. How does this change the arrangements the figures show? What happens to the identity between them now, when they aren’t even numerically the same? Is any relationship ever going to be guaranteed? What if figure 1 is something else, perhaps the sum of four squares that touch at their corners and figure 2 is five squares with common sides Is this really a false distinction? Perhaps it misses what’s actually there—both of my figures contain sixteen lines
40 Introduction: Tell Me All About It that depend on the same twelve points Or is it four points and five Are boundary elements more meaningful than centers? Who’s to say? Do I have to decide once and for all? I can change my mind about what I see anytime I want. Is this automatically an error? Where’s the pitfall? Seeing isn’t stuck—it has no roots in metaphysical ground. Nothing is certain. It’s merely a convenience to assume that the things in the world are so forever, and keep all of their original parts. It facilitates taking roll. But if I only count, I’m going to miss a whole lot. Once I begin, I lose my chance to change. There aren’t any surprises with symbols. Parts don’t fuse as long as I remember what they are. Everything divides in the same old way with the same old constituents. Combinatorial play makes perfect sense for games like checkers and chess, or for construction sets like
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Page 5 and 6: ( 2006 Massachusetts Institute of T
Page 8: Contents Acknowledgments ix INTRODU
Page 12 and 13: INTRODUCTION: TELL ME ALL ABOUT IT
Page 14 and 15: 3 Answer Number One—What Do You S
Page 20 and 21: 9 Answer Number Two—Three More Wa
Page 22 and 23: 11 Answer Number Two—Three More W
Page 44 and 45: 33 Trying to Be Clear Points aren
Page 46 and 47: 35 Trying to Be Clear and twenty-fo
Page 48 and 49: 37 Trying to Be Clear things look.
Page 52 and 53: 41 Tables, Teacher’s Desks, and R
Page 54 and 55: 43 Tables, Teacher’s Desks, and R
Page 56 and 57: 45 It Always Pays to Look Again In
Page 58 and 59: 47 Background always more when you
Page 60 and 61: 49 Background Getting it first and
Page 62 and 63: 51 Background and not These are the
Page 64 and 65: 53 Background and count as I please
Page 66 and 67: 55 Background and time. The way Eul
Page 68 and 69: 57 Background them apart—a triang
Page 70: 59 Background without ‘‘agreeme
Page 73 and 74: 62 I What Makes It Visual? (2) What
Page 75 and 76: 64 I What Makes It Visual? Whenever
Page 77 and 78: 66 I What Makes It Visual? calculat
Page 79 and 80: 68 I What Makes It Visual? And my r
Page 81 and 82: 70 I What Makes It Visual? more tha
Page 83 and 84: 72 I What Makes It Visual? Table 1
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Page 89 and 90: 78 I What Makes It Visual? formula
Page 91 and 92: 80 I What Makes It Visual? But what
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90 I What Makes It Visual? contains
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92 I What Makes It Visual? and othe
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94 I What Makes It Visual? The lett
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96 I What Makes It Visual? and corr
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98 I What Makes It Visual? (Is hh i
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100 I What Makes It Visual? and the
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102 I What Makes It Visual? There
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104 I What Makes It Visual? to the
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106 I What Makes It Visual? Table 2
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108 I What Makes It Visual? is trie
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110 I What Makes It Visual? artifac
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112 I What Makes It Visual? and thi
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116 I What Makes It Visual? looks l
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120 I What Makes It Visual? when th
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122 I What Makes It Visual? until t
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124 I What Makes It Visual? The fir
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126 I What Makes It Visual? What Sc
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128 I What Makes It Visual? Here, g
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130 I What Makes It Visual? be desc
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132 I What Makes It Visual? An addi
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134 I What Makes It Visual? forget
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136 I What Makes It Visual? that bl
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138 I What Makes It Visual? Why is
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140 I What Makes It Visual? see wha
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142 I What Makes It Visual? to calc
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144 I What Makes It Visual? How cav
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146 I What Makes It Visual? togethe
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148 I What Makes It Visual? and six
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150 I What Makes It Visual? and its
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152 I What Makes It Visual? these h
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154 I What Makes It Visual? So how
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156 I What Makes It Visual? (TRI(XY
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158 I What Makes It Visual? The fir
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160 II Seeing How It Works was thre
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162 II Seeing How It Works and lowe
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164 II Seeing How It Works Back to
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166 II Seeing How It Works Divide e
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168 II Seeing How It Works There ar
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170 II Seeing How It Works while th
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172 II Seeing How It Works there ar
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174 II Seeing How It Works This has
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176 II Seeing How It Works And noti
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178 II Seeing How It Works looks ex
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180 II Seeing How It Works meaning.
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182 II Seeing How It Works and the
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184 II Seeing How It Works Embeddin
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186 II Seeing How It Works both of
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188 II Seeing How It Works but in a
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190 II Seeing How It Works It’s e
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192 II Seeing How It Works of one i
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194 II Seeing How It Works how it w
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196 II Seeing How It Works Table 7
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198 II Seeing How It Works of these
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200 II Seeing How It Works maximal
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202 II Seeing How It Works They’r
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204 II Seeing How It Works So, bðA
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206 II Seeing How It Works made up
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208 II Seeing How It Works boundary
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210 II Seeing How It Works First, t
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212 II Seeing How It Works topology
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214 II Seeing How It Works This has
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216 II Seeing How It Works where po
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218 II Seeing How It Works Operatio
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220 II Seeing How It Works is part
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222 II Seeing How It Works In parti
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224 II Seeing How It Works suggest
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226 II Seeing How It Works intricat
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228 II Seeing How It Works see what
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230 II Seeing How It Works to show
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232 II Seeing How It Works It’s a
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234 II Seeing How It Works that can
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236 II Seeing How It Works But supp
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238 II Seeing How It Works And toge
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240 II Seeing How It Works with poi
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242 II Seeing How It Works It’s f
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244 II Seeing How It Works to limit
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246 II Seeing How It Works and two
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248 II Seeing How It Works And the
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250 II Seeing How It Works (inducti
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252 II Seeing How It Works Two seco
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254 II Seeing How It Works Or I can
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256 II Seeing How It Works I can’
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258 II Seeing How It Works —and s
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260 II Seeing How It Works Now, no
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262 II Seeing How It Works up of se
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264 II Seeing How It Works These co
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266 II Seeing How It Works Why? The
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268 II Seeing How It Works and its
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270 II Seeing How It Works square f
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272 II Seeing How It Works descript
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274 II Seeing How It Works produce
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276 II Seeing How It Works points.
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278 II Seeing How It Works x fi y t
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280 II Seeing How It Works Indeterm
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282 II Seeing How It Works Or I can
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284 II Seeing How It Works applies
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286 II Seeing How It Works the same
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288 II Seeing How It Works in terms
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290 II Seeing How It Works It’s e
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292 II Seeing How It Works If a rul
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294 II Seeing How It Works But then
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296 II Seeing How It Works And, cer
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298 II Seeing How It Works are all
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300 II Seeing How It Works combine
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302 II Seeing How It Works In fact,
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304 II Seeing How It Works next pap
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306 II Seeing How It Works Table 12
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308 II Seeing How It Works initial
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310 II Seeing How It Works Kinemati
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312 III Using It to Design (3) desi
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314 III Using It to Design does mor
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316 III Using It to Design that I d
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318 III Using It to Design don’t
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320 III Using It to Design fix the
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322 III Using It to Design Figure 1
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324 III Using It to Design —divid
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326 III Using It to Design Perhaps
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328 III Using It to Design I seem t
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332 III Using It to Design Then the
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334 III Using It to Design and ‘
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338 III Using It to Design But this
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340 III Using It to Design but occa
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342 III Using It to Design numbers
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344 III Using It to Design to start
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346 III Using It to Design The rule
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348 III Using It to Design Everythi
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352 III Using It to Design Let’s
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354 III Using It to Design ever hav
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356 III Using It to Design (2) Furt
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358 III Using It to Design that wor
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360 III Using It to Design with the
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362 III Using It to Design are equi
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364 III Using It to Design and in f
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366 III Using It to Design to the p
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368 III Using It to Design rules th
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370 III Using It to Design x fi bð
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372 III Using It to Design These we
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374 III Using It to Design easy to
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376 III Using It to Design and spir
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378 III Using It to Design I said I
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380 III Using It to Design include
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382 III Using It to Design x fi x i
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384 III Using It to Design It’s g
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386 III Using It to Design take car
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388 III Using It to Design wealth o
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Notes Introduction 1. S. Pinker, Th
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393 Notes to pp. 48-50 Langer’s d
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395 Notes to pp. 51-55 19. H. L. Dr
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397 Notes to p. 156 9. C. Alexander
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399 Notes to p. 304 of lowest-level
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401 Notes to p. 305 24. The ‘‘n
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403 Notes to pp. 306-387 35. G. Sti
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405 Notes to pp. 388-389 M. A. Bode
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407 Notes to p. 389 The essence in
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410 Index Aristotle, 81, 167, 337 A
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412 Index creativity and (cont.) re
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414 Index greatest lower bound, 224
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416 Index maximal elements and basi
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418 Index Quine, W. V., 57, 58, 210
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420 Index shape grammars (cont.) an
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422 Index Van Gogh, V., 403n1 Vanto
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