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( 2006 Massachusetts Institute of T
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Contents Acknowledgments ix INTRODU
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INTRODUCTION: TELL ME ALL ABOUT IT
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3 Answer Number One—What Do You S
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5 Answer Number One—What Do You S
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7 Answer Number One—What Do You S
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- 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 50 and 51: 39 Trying to Be Clear on correspond
- 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 72 and 73: I WHAT MAKES IT VISUAL? To a large
- Page 74 and 75: 63 Does Reasoning Include Calculati
- Page 76 and 77: 65 A First Look at Calculating he p
- Page 78 and 79: 67 A First Look at Calculating This
- Page 80 and 81: 69 A First Look at Calculating happ
- Page 82 and 83: 71 A First Look at Calculating with
- Page 84 and 85: 73 A First Look at Calculating so t
- Page 86 and 87: 75 A First Look at Calculating thin
- Page 88 and 89: 77 What Makes Calculating Visual? w
- Page 90 and 91: 79 What Makes Calculating Visual? w
- Page 92 and 93: 81 What Makes Calculating Visual? S
- Page 94 and 95: 83 What Makes Calculating Visual? b
- Page 96 and 97: 85 What Makes Calculating Visual? I
- Page 98 and 99: 87 What Makes Calculating Visual? t
- Page 100 and 101: 89 There Is No Vocabulary—Well, A
- Page 102 and 103: 91 There Is No Vocabulary—Well, A
- Page 104 and 105: 93 There Is No Vocabulary—Well, A
- Page 106 and 107: 95 There Is No Vocabulary—Well, A
- Page 108 and 109: 97 There Is No Vocabulary—Well, A
- Page 110 and 111: 99 A Second Look at Calculating A S
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- Page 116 and 117: 105 A Second Look at Calculating do
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109 A Second Look at Calculating an
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111 A Second Look at Calculating is
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113 A Second Look at Calculating A
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115 A Second Look at Calculating ha
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117 A Second Look at Calculating an
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119 A Second Look at Calculating is
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121 A Second Look at Calculating Fo
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123 A Second Look at Calculating An
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125 A Second Look at Calculating on
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127 What Schemas Show early stuff,
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129 What Schemas Show For example,
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131 What’s That or How Many? open
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133 What’s That or How Many? gone
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135 What’s That or How Many? sing
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137 What’s That or How Many? figu
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139 What’s That or How Many? Prim
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141 What’s That or How Many? long
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143 What’s That or How Many? The
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145 What’s That or How Many? The
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147 What’s That or How Many? it
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149 What’s That or How Many? them
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151 What’s That or How Many? and
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153 What’s That or How Many? shou
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155 Background again. My eyes are s
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157 Background you think you’re n
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II SEEING HOW IT WORKS An interesti
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161 Starting Over appear. In fact,
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163 Starting Over shape when I calc
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165 Back to Basics—Elements and E
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167 Back to Basics—Elements and E
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169 Back to Basics—Elements and E
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171 Back to Basics—Elements and E
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173 Back to Basics—Elements and E
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175 Back to Basics—Elements and E
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177 Counting Points and Seeing Part
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179 Counting Points and Seeing Part
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181 Shapes in Algebras and Algebras
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183 Shapes in Algebras and Algebras
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185 Shapes in Algebras and Algebras
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187 Shapes in Algebras and Algebras
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189 Shapes in Algebras and Algebras
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191 Shapes in Algebras and Algebras
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193 Shapes in Algebras and Algebras
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195 Shapes in Algebras and Algebras
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197 Boundaries of Shapes Are Shapes
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199 Boundaries of Shapes Are Shapes
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201 Boundaries of Shapes Are Shapes
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203 Boundaries of Shapes Are Shapes
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205 Boolean Divisions shape, and su
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207 Boolean Divisions parts of a sh
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209 Boolean Divisions doesn’t hav
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211 Boolean Divisions don’t have
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213 Euclidean Embeddings The algebr
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215 ‘‘Nor Do Lineaments Have An
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217 ‘‘Nor Do Lineaments Have An
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219 ‘‘Nor Do Lineaments Have An
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221 ‘‘Nor Do Lineaments Have An
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223 ‘‘Nor Do Lineaments Have An
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225 ‘‘Nor Do Lineaments Have An
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227 Solids, Fractals, and Other Zer
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229 How Rules Work When I Calculate
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231 How Rules Work When I Calculate
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233 How Rules Work When I Calculate
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235 Trying It Out The rule finds sq
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237 Trying It Out with a point on a
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239 Trying It Out In fact, my rule
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241 Trying It Out bðxÞ fi x þ b
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243 Trying It Out Fractals are zero
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245 Spatial Relations and Rules Mod
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247 Spatial Relations and Rules tha
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249 Spatial Relations and Rules and
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251 Spatial Relations and Rules Or
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253 Spatial Relations and Rules tha
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255 Spatial Relations and Rules wit
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257 Spatial Relations and Rules the
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259 Spatial Relations and Rules log
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261 Classifying Rules with Transfor
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263 Classifying Rules with Transfor
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265 Classifying Rules with Transfor
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267 Classifying Rules with Transfor
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269 Classifying Rules with Parts sq
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271 Classifying Rules with Parts or
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273 Classifying Rules with Parts wh
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275 How Computers Do It go beyond p
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277 I Don’t Like Rules—They’r
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279 I Don’t Like Rules—They’r
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281 I Don’t Like Rules—They’r
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283 Parts Are Evanescent—They Cha
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285 Parts Are Evanescent—They Cha
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287 Erasing and Identity and every
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289 Erasing and Identity are planes
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291 Erasing and Identity to produce
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293 Erasing and Identity and an ide
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295 Erasing and Identity four mediu
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297 Calculating and Continuity This
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299 Calculating and Continuity Tabl
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301 Design without Thought using on
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303 Background seeing isn’t lost
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305 Background in everyday design p
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307 Background segments of strings.
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309 Background To be sure, Mill wou
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III USING IT TO DESIGN We began utt
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313 Design Is Calculating rules, or
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315 Design Is Calculating gðxÞ fi
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317 Design Is Calculating but reall
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319 Tell Me What Schema to Use Tell
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321 Tell Me What Schema to Use defi
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323 What the Thinking Eye Sees What
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325 What the Thinking Eye Sees is d
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327 What the Thinking Eye Sees Figu
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329 What the Thinking Eye Sees But
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331 Chinese Lattice Designs—Seein
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333 Chinese Lattice Designs—Seein
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335 Chinese Lattice Designs—Seein
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337 Chinese Lattice Designs—Seein
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339 Chinese Lattice Designs—Seein
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341 They’re Shapes before They’
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343 They’re Shapes before They’
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345 They’re Shapes before They’
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347 They’re Shapes before They’
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349 They’re Shapes before They’
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351 They’re Shapes before They’
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353 They’re Shapes before They’
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355 Seeing Won’t Do—Design Need
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357 Seeing Won’t Do—Design Need
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359 Seeing Won’t Do—Design Need
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361 Seeing Won’t Do—Design Need
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363 Seeing Won’t Do—Design Need
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365 Seeing Won’t Do—Design Need
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367 Seeing Won’t Do—Design Need
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369 Getting in the Right Frame of M
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371 Getting in the Right Frame of M
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373 Getting in the Right Frame of M
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375 Getting in the Right Frame of M
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377 Getting in the Right Frame of M
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379 Getting in the Right Frame of M
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381 Latin and Greek, and Mathematic
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383 Latin and Greek, and Mathematic
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385 Latin and Greek, and Mathematic
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387 Background codes, student and f
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389 Background and his current foll
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392 Notes to pp. 47-48 1994), 221-2
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394 Notes to pp. 50-51 same—try p
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396 Notes to pp. 56-156 39. W. Jame
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398 Notes to pp. 156-304 20. M. Mer
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400 Notes to pp. 304-305 13. T. W.
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402 Notes to pp. 305-306 the world
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404 Notes to p. 388 reasonably stra
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406 Notes to p. 389 artist’s hand
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Index A þ E ¼ AE, 93 ababaababa,
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411 Index classifying plans, 361-36
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413 Index entropy, 50 erasing and c
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415 Index Kirsch R. A., 392n4 Klee,
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417 Index ‘‘palm-leaf umbrella,
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419 Index equivalence, 230-232 gene
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421 Index symmetry in lattice desig