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I WHAT MAKES IT VISUAL? To a large extent it has turned out that the usefulness of computer drawings is precisely their structured nature and that this structured nature is precisely the difficulty in making them. . . . An ordinary draftsman is unconcerned with the structure of his drawing material. Pen and ink or pencil and paper have no inherent structure. They only make dirty marks on paper. The draftsman is concerned principally with the drawings as a representation of the evolving design. The behavior of the computer-produced drawing, on the other hand, is critically dependent upon the topological and geometric structure built up in the computer memory as a result of drawing operations. The drawing itself has properties quite independent of the properties of the object it is describing. —Ivan Sutherland Use Your Eyes to Decide Visual reasoning means using your eyes to decide what to do next. This formula looks just about right—it puts seeing and doing together in the way I like. But there’s more to say about what makes visual reasoning useful in design. Just what makes reasoning visual anyway? How does calculating fit into this? And why are seeing and drawing an effective way of thinking? That’s the nub of what I’m trying to do. In fact, I’m going to adopt the point of view of someone who thinks about design and how seeing and drawing help to make it work. This turns into a practical concern for shapes and rules, and their value in the design process. So there are some parallel questions that also require answers as I go on. How can I make anything that’s really new when I calculate with shapes? How creative can I possibly be if I only use rules? Can I find another way to design? Am I any more creative if I don’t use rules? Does this make sense? What’s at stake? A good way to see how all of this lines up is to try my first question, (1) What makes reasoning visual? I’m not going to answer question 1 directly. Instead, I’m going to pose two ancillary questions that seem easier, probably because I have something to say about them. Here they are:
62 I What Makes It Visual? (2) What makes calculating visual? (3) Does reasoning include calculating? I’ll take a meandering route through their answers that digresses now and then to explore other questions like the unnumbered ones in the previous paragraph. This isn’t exactly what Plato recommends in the quote that heads the introduction, but wandering around aimlessly to see what’s what—changing your mind freely—is a useful way to get new results. It’s a nice way to see what calculating with shapes and rules is all about. It feels right, and there’s some logic to it. If my answer to question 3 is yes, then I can argue by analogy that visual reasoning includes visual calculating. And if I can answer question 2, then I can use visual calculating to understand visual reasoning. It’s reasoning by inference—from the properties of a part to the properties of the whole. Of course, this assumes that parts and wholes are alike. I’ve already said so for shapes and embedding. This makes calculating with shapes and reasoning (inference) the same in at least one respect. Plus, I’m more confident about the mechanics of calculating than I ever will be about reasoning generally. I’ve always liked engineering, with its sensible outlook and palpable results. It’s the same when I calculate. I can point to examples—some of my own invention— and go through them step by step. But it’s hard to know about reasoning. My own reasoning when it goes beyond calculating is as suspect as any. Whenever I think I have a good argument, someone soon comes along and proves the opposite. And it’s just the same if I try to follow the reasoning of others. I go from thinking I’m thinking to thinking I’m not. I’d rather stick with engineering and show how things work out sensibly. It’s easy to do applying rules to calculate with shapes. I can’t be sure until I show you, but I’m almost positive—you’re going to be surprised at how much more there is to visual reasoning than you imagine, if it’s anything at all like visual calculating. The kinds of things I have in mind don’t come from complicated ways of counting or clever coding tricks that take real brainpower—from what’s customarily valued and encouraged in calculating. They come straight from seeing. It’s all there whenever you look. I’ve framed my questions with respect to the following diagram that shows how everything is supposed to fit together. This extends counting to calculating in what I said in the final pages of the introduction about reasoning at its best and why its visual counterpart is something to explain. Diagrams are meant to see.
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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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Page 20 and 21: 9 Answer Number Two—Three More Wa
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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
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Page 75 and 76: 64 I What Makes It Visual? Whenever
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110 I What Makes It Visual? artifac
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116 I What Makes It Visual? looks l
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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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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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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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200 II Seeing How It Works maximal
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206 II Seeing How It Works made up
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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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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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