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415 Index Kirsch R. A., 392n4 Klee, P., 10, 45, 50, 241, 251–252, 303, 323– 329, 340, 341, 372, 383, 388, 393–394n12, 398n3, 403–404n1, 405n9 Knight, T. W., 304, 375–376, 388, 389, 393– 394n12, 398n8, 398–399n9, 400n13, n18, 407n21 Krishnamurti, R., 305, 400n17, n19 Krstic, D., 305, 400n20 Kuhn, T., 144 labels and layers, 217, 219, 289 sets, 219–220, 222 shapes, 216–219 symbols, 219 transformations, 219 weights, 222 Lagrange’s theorem, 266–267, 304 Langer, E. J., 56, 396n44, 403–404n1, 405– 407n20 Langer, S. K., 18–19, 27, 51, 53, 54, 65, 180, 392–393n6, 395n28, 401–402n25 language and drawing, 18–19, 385 of sentences, 18 of shapes (designs), 18 Latin, 311, 381, 385 lattice for calculating with shapes, 108 lines, 168 parts of shapes, 207 schemas, 378 topology of shapes, 293 lattice operations (meet and join), 168–170, 184–185 Lavoisier, A. L., 151 layers, 217, 219, 289 learning and cheating, 380–381 and copying, 381, 385–387, 388 and creativity, 64–65, 157, 274, 321, 342, 381, 386–387, 398–399n9 and experience, 274 mindful, 56, 396n44, 398n28, 405–407n20 and reasoning, 64, 116, 130 situated, 133, 157, 396n44, 398n28 and tests, 42, 56, 132, 309, 380–381 least upper bound lines, planes, and solids, 168–169 weights, 224 Lego, 41, 75, 399 Lentin, A., 403n36 Leonard, H., 210, 211, 402n27 Lesneiwski, S., 305 ‘‘less is more,’’ 55 Levine, M., 41, 56, 396n43 Li, A., 388, 405n16 Lindenmayer system, 51, 65, 275, 307 line weights, 223–224 linear equations, 14, 164 lines and angles, 214 material (weights), 214, 216, 219–224 recursion, 251–252 symbols (labels), 215, 216–219 lines (basic element), 2, 164–165 linguistics, 20, 52, 81, 137, 194, 310, 392– 393n6, 394n16, 398–399n9, 404n3 Lissitzky, E., 393–394n12 lists, 1, 10, 21, 36, 52, 69–70, 71, 125, 137, 150, 155, 157, 183, 184, 226, 304, 310, 379 ‘‘little minds,’’ 76, 157 logic and algebra, 306 and architecture, 392–393n6 and drawings (shapes), 65 of inquiry, 49, 125, 157, 393n11 logical analysis, 125 logicians and meaning theorists, 145 Los Angeles, 152, 158 Lotze, R. H., 155 lowest-level constituents, 65, 155–156 136 mappings and rule application, 286–287, 298, 306 for sets and shapes, 285 March, L., 153, 158, 305, 347, 388–389, 391– 392n2, 392–393n6 mathematics for design, 11, 12, 13–14 of design, 11, 12, 14–16 and seeing, 159 and teaching, 321, 385, 387–388
416 Index maximal elements and basic elements, 181 definition, 181–182, 183 lines, 186–188 and parts, 184 and set equivalence, 182–183 McCarthy, J., 139–140, 141, 143, 148, 156, 397n12 meanders, 375–376 meaning, 27–28, 75, 179–180, 208, 228, 310, 357, 401n24 means and ends, 153, 157 measurement and counting, 57, 161, 179, 271, 307, 398– 399n9 of complexity, 227, 271, 307 of information, 57, 161 medial lines, 10, 50, 241, 393–394n12 membership relation, 53, 81, 159, 167, 177, 210, 226, 271, 275, 285, 310, 393–394n12 memory, 5, 40, 49, 53, 61, 71, 129, 133–136, 144, 159, 228, 233–234, 368, 405–406n20 Menand, L., 405–406n20 mereology, 305 Merleau-Ponty, M., 143, 156, 398n20 metaphors and equivalencies calculating is counting, 141, 179, 268 calculating is painting, 54, 138–139 calculating is seeing, 179 design is calculating, 14, 311, 329, 389 design is copying, 386, 405n20 design is drawing, 312, 318, 354, 387–388 drawing is calculating, 311 drawing is language, 385 inventing is observing, 234, 309, 368 invention is thought, 301, 309 metaphysics, 37, 40, 44, 47 Mill, J. S., 234, 308–309, 357, 368–369 Miller, G. A., 159, 161, 163, 305, 308, 400n23 Minsky, M. L., 16, 17, 51, 139, 140, 143–144, 148, 156, 394n18, 397n14 Miss H——, 9–11, 14, 17, 32, 36, 41, 50, 53, 125, 241, 380, 381, 430–404n1 missionaries and cannibals puzzle, parable, and aboriginal tale, 139–140, 143, 156 MIT, 16, 17, 139, 398–399n9, 401n24 Mitchell, W. J., 392–393n6, 393n7 monoid, 194, 306 morality and rationality, 160, 368 Morris, C., 392–393n6 Mutt, R. (see Duchamp, M.) ‘‘myriad myriads,’’ 162 Narasimhan, R., 155, 396n8 narrative, 50 Necker cube (see tetrahedron) networks, 71, 225 Neurath, O., 13, 50, 394n16 Newell, A., 51, 139, 395n21 Newton, I., 33, 55 AMBIGUITY 305, 318 noise, 56, 159, 161, 163, 305, 308, 334 nominalistic syntax, 210, 305 nonstandard praxis, 392n3 norms for calculating, 131–133, 179–180 notation, 219 novelty, 2, 21, 41, 44, 56, 64–65, 131, 151– 152, 405–407n20, and wherever there’s ambiguity Nude Descending a Staircase (No. 2), 430–404n1 observation and invention, 234, 302, 308–309, 310, 368– 369 rules, 85, 233, 283 old fogyism, 149, 155, 397n14 ordering plans, 361–363 overlap relation, 169–170 Ozkar, M., 385, 389, 405n19, n20 paint by number, 11 painting, 18, 21, 27, 54, 138–139, 156, 319– 322, 340, 341, 374–375, 385, 387–388, 403– 404n1 painting rules, 303, 304 palindromes, 11, 17, 26–28, 269, 391n2, 405– 406n20 Palladian villa plans Angarano, 346–347 Barbaro, 347, 351–354 Foscari, 341–349 new plans (copies, fakes, and forgeries), 346– 347, 350 Rotonda, 349 Palladio, A., 48, 341–342, 349, 388, 405n11
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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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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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106 I What Makes It Visual? Table 2
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110 I What Makes It Visual? artifac
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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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148 I What Makes It Visual? and six
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150 I What Makes It Visual? and its
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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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170 II Seeing How It Works while th
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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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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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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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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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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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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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284 II Seeing How It Works applies
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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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322 III Using It to Design Figure 1
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324 III Using It to Design —divid
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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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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 425: 414 Index greatest lower bound, 224
Page 429 and 430: 418 Index Quine, W. V., 57, 58, 210
Page 431 and 432: 420 Index shape grammars (cont.) an
Page 433: 422 Index Van Gogh, V., 403n1 Vanto
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