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413 Index entropy, 50 erasing and counting, 147–148 erasing rules, 79, 83, 247, 288, 354–355, 357– 358, 369, 384 ‘‘. . . Eros is Eros . . . ,’’ 52, 145, 403–404n1 Euclidean embedding for i ¼ j, 213–214 properties and the index j, 181, 195 space, 306 transformations, 194–195, 228 Euler, L., 32, 54–55, 395n32 Evans, T. G., 65, 144 Evans’s grammar, 65–66, 155–156 problem, 66, 84, 155–156 shape, 66, 155–156 evolutionary algorithms, 51 existentialism, 143 experiments, 6, 25, 41, 44, 56, 69, 112, 160, 215, 216, 223, 227, 252, 307, 311, 321, 323, 330, 381, 385, 389 experts, 69, 227, 307 expert systems, 275 explicit pictures, 307–308 expression constitutive, 47, 71, 149, 392n3 poetic, 13, 45, 51, 137, 162, 392n3 variational, 392n3 visual and verbal, 7–8, 21, 33, 45, 46, 47, 50, 53, 63, 139, 180, 204, 277, 282, 394n16 extension, 32–33, 54, 165, 305 extensive abstraction, 394 connection, 174, 211, 305 E Z , 50, 384, 389, 394n15 fakes, 48, 349 fathers and daughters, 42 Federico, J., 395n33 Fenollosa, E., 13 Fibonacci numbers, 291–292, 301 ‘‘figures on paper,’’ 132, 134, 137, 372, 389 figure-ground relationship, 205–206, 209, 306 finite elements, 76, 392n3 firmness, 341 Flemming, U., 389, 407n21 Flores, F., 140–141, 143, 156, 397n16 forensic rule application, 351 forgery, 334, 350 forgetting, 5–6, 134, 364 ‘‘form follows function,’’ 226, 308 forof 11–12 Fountain, 403–404n1 Fowler, D. H., 391–392n2 fractal cities, 58, 125, 396n51 fractal geometry rules, 242–244, 274, 277 self-similar patterns, 274 symmetry, 242 units and dimension, 76, 226–227 freedom, 56, 287, 309, 324, 329, 337, 353– 354, 361, 383 Frege, G., 388 Froebel, F., 9, 18, 250, 304, 392n6 functional ambiguity, 394 Fundierung relations, 142 fusing lines, 5 Gadamer, H.-G., 141, 156, 397n17 Gaitskell, C. D., 403n1 Galison, P., 392–393n6, 394n11, n16, 400n18 Galton, F., 57, 396n49 generalists, 354 generalized Boolean algebra, 206, 208, 226, 306 generative grammar, 17–18, 20, 52, 194, 268– 269, 271, 291, 307, 308 genius, 144, 155 geographical information systems, 125 gestalt switch (see paradigm switch) gestalt/paradigm, 1, 47, 105, 144, 153, 156, 318, 376 Gips, J., 47–48, 50, 303, 304, 392n4, n5, 394n15, 403n37, 405n5, n17 Glarner, F., 374, 379, 388 Goethe, J. W. von, 54 going on, 153, 387 Goldring, E., 50 good and evil, 33 Goodman, N., 92–94, 98, 148, 157, 210, 211, 304, 305, 398n23, 400n13, 402n27, n30 graduate/doctoral students, 58, 85, 140, 144, 148–149, 305, 320–321, 401n24 graphs, 71, 184, 225–226, 275
414 Index greatest lower bound, 224 Greek geometry and design, 391–392n2 language, 311, 381, 385 meander designs, 375–377, 388 Green, H., 403n1 grids, 42, 44, 96–97, 249–250, 273, 332, 343, 379 Gross, M., 403n36 group of transformations, 37, 162, 195, 231– 232, 237–238, 244, 253, 262, 266–267, 304, 373 habit, 55–56, 144, 233, 304–305, 401–402n25 Hammond, T., 401n24 Hanks, W. F., 157, 398n28 hard problems, 357, 389 Hegel, G. W. F., 153 Heidegger, M., 141 hermeneutics, 75, 141–142 heuristic search, 144, 156, 163, 401–402n25 hierarchically organized list structures, 21, 52, 137, 310 hierarchy, 54, 108, 135–136, 138, 139, 206, 342, 347, 397n14 Hilbert, D., 320 history of shapes, 6, 105, 273, 287, 368, 405– 407n20 Hillier, B., 58, 396n51 Hobbes, T., 63 Holland, J., 395n22 honor codes, 386–387 how to be clear, 37–41, 55, 148 how to calculate, 16, 20, 44, 123, 141, 149, 214, 342, 387 Hurwitz, A., 403n1 Heyting algebra, 306 ice-rays, 334–341 identity relation, 7–8, 53, 58, 63, 164, 215 rule, 29, 85, 160, 333–334, 381–382 transformation, 37, 214, 219, 224 impenetrability, 145 inclusion lattice for schemas, 378 indices i and j, 181, 195–196 individuals and basic elements, 211 regions, 211, 305 shapes, 210–211, 305 nominalistic syntax, 210, 305 induction, 389 ineffable experience, 28, 355, 403n1 inference and calculating, 25–28, 112, 249 circumscriptive, 139, 156 and redescription, 153, 233 and reasoning, 62 types of, 389 information theory, 19, 50 intelligence, 57, 226, 388, 401–402n25 intersection for lines, 3, 23–24, 89, 121–122, 236, 260–263, 265 sets, 226 invention and observation, 234, 368–369 thought, 301–302, 309–310 inverse rules, 28–29, 99, 111, 117–118, 128, 230– 232, 238–239, 245, 328–329, 344, 369–372, 378, 384 transformations (t 1 ), 231–232, 405– 406n20 irony, 6, 20, 153, 158, 163, 277, 337, 386, 394n16 irregularity, 324, 329, 388 it, 44 James, W., 41, 56, 64–65, 77, 82, 107, 130– 131, 143, 144, 149, 151–153, 154, 155, 157, 193, 233–234, 308, 368, 389, 398–399n9, 405–407n20 Jones, G., 48 Jowers, I., 400n17 Kandinsky, W., 50, 393–394n12 Kierkegaard, S., 17, 19, 49, 51, 76, 107, 148, 155, 158, 380–381, 389, 393n9 kindergarten grammars, 252–260, 304 kindergarten method building gifts, 18, 304 categories, 252, 304 occupations, 9 tablets, 252 kinematic chains, 309–310
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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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9 Answer Number Two—Three More Wa
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11 Answer Number Two—Three More W
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33 Trying to Be Clear Points aren
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35 Trying to Be Clear and twenty-fo
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37 Trying to Be Clear things look.
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39 Trying to Be Clear on correspond
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41 Tables, Teacher’s Desks, and R
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43 Tables, Teacher’s Desks, and R
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45 It Always Pays to Look Again In
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47 Background always more when you
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49 Background Getting it first and
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51 Background and not These are the
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53 Background and count as I please
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55 Background and time. The way Eul
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57 Background them apart—a triang
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59 Background without ‘‘agreeme
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62 I What Makes It Visual? (2) What
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64 I What Makes It Visual? Whenever
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66 I What Makes It Visual? calculat
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68 I What Makes It Visual? And my r
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70 I What Makes It Visual? more tha
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72 I What Makes It Visual? Table 1
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74 I What Makes It Visual? but neve
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76 I What Makes It Visual? may be f
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78 I What Makes It Visual? formula
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80 I What Makes It Visual? But what
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82 I What Makes It Visual? they pro
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84 I What Makes It Visual? The one
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86 I What Makes It Visual? I see a
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88 I What Makes It Visual? But this
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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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100 I What Makes It Visual? and the
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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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128 I What Makes It Visual? Here, g
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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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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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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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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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280 II Seeing How It Works Indeterm
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288 II Seeing How It Works in terms
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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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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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316 III Using It to Design that I d
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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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360 III Using It to Design with the
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Page 402 and 403: Notes Introduction 1. S. Pinker, Th
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Page 421 and 422: 410 Index Aristotle, 81, 167, 337 A
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Page 429 and 430: 418 Index Quine, W. V., 57, 58, 210
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Page 433: 422 Index Van Gogh, V., 403n1 Vanto
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