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317 Design Is Calculating but really anything will do. All rectangles may be alike or quadrilaterals or polygons In fact, I can make the predicate that defines the assignment g as wild as I please. Maybe x in the schema x fi y is a blob of some special kind or any simple closed curve—whatever makes sense when you look is OK as long as there’s a general transformation t g for it. It’s also worth repeating that the predicates I use to define rules needn’t be preserved as I calculate. I can put two quadrilaterals together not unlike adding polygons and their transformations in the schema x fi x þ tðxÞ, and then move triangles according to the schema x fi tðxÞ. Predicates are simply a convenient way of describing rules—a way that doesn’t carry over to calculating. Then descriptions
318 III Using It to Design don’t count. There’s no reason for me to be consistent about the things I see. Consistency is at root conservative—insisting that the language I’ve used in the past is kept as I see and do more makes calculating much too rigid. Certainly, it’s logical—words make sense, so that things stay the way you say they are, and behave properly in the way you expect them to—but it isn’t necessary. Why should words trump shapes when their parts can change freely in an open-ended, creative process? There’s plenty of ambiguity and the paradigm (gestalt) switches that go along with it—what you see is what you get, any time you try another rule. And you can go on from whatever it is you see without ever thinking about it. There’s always more to do. Ambiguity is to use. There’s no reason to hesitate— AMBIGUITY No one ever says ‘‘Stop!’’ Nothing blocks my way. Whatever I see is OK. Neither descriptions nor representations of shapes are needed to calculate—they don’t intrude when rules are used to see and do. So far, so good, but what about design?—that’s what I want to use rules and schemas for. The problem here is to convince you that design is calculating. This is harder than it looks—not because it’s difficult to produce designs by calculating, but because whatever I do may not be what you call design. Design varies so widely and unpredictably from person to person and from time to time that any calculating I do isn’t likely to cover very much of it. Calculating to make designs will just have to do, with the promise that if you want to do it in another way, then shapes and rules are up to the task. And this doesn’t mean starting over from scratch every time you have another idea or want to try something new, but rather adding rules or relaxing the ones you’ve already got to allow for more, so that designing, like seeing, is an open-ended process. This seems OK, but maybe I should look for a way to prove my claim that design is calculating. Well, this probably won’t work—it’s more a question of confirming a thesis in ongoing practice, and, in fact, there’s a strong precedent for this in the argument that algorithms are Turing machines. I like to think that there’s plenty of solid evidence in my examples. I’ll trace these in a kind of personal history that shows some of the things I’ve tried to design by calculating. Most of what I say is pretty impressionistic, although not because I have to be so. The details are given elsewhere, so they needn’t be a distraction here. It’s more important now to emphasize key ideas that run through what I try and how they’re expressed in rules and schemas. There’s a lot to see that shows what rules can do, and most of it is just like drawing—but surely, this is already evident from statement 3 design is drawing and what follows in statement 4 for shapes of all kinds.
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SHAPE
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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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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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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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