CONTENTS 1. Early Stirrings 1 Perception torn from thinking, 2. The senses mistrusted, 4. Plato of two minds, 6. Aristotle from below and from above, 8. 2. The Intelligence of Perception (i) 13 Perception as cognition, 13. Perception circumscribed, 15. Exploring the remote, 17. The senses vary, 17. Vision is selective, 19. Fixation solves a problem, 23. Discernment in depth, 26. Shapes are concepts, 27. Perception takes time, 29. How machines read shape, 31. Completing the incomplete, 33. 3. The Intelligence of Perception (ii) 37 Subtracting the context, 37. Brightness and shape as such, 40. Three attitudes, 43. Keeping the context, 46. The abstraction of shape, 47. Distortion calls for abstraction, 51. Permanence and change, 52. 4. Two and Two Together 54 Relations depend on structure, 54. Pairing affects the partners, 60. Perception discriminates, 65. Perception compares, 66. What looks alike? 69. Mind versus computer, 72. 5. The Past in the Present 80 Forces acting on memory, 81. Percepts supplemented, 84. To see the inside, 87. Visible gaps, 89. Recognition, 90. 6. The Images of Thought 97 What are mental images like? 98. Can one think without images? 100. Particular and generic images, 102. Visual hints and flashes, 107. How abstract can an image be? 109. 7. Concepts Take Shape 116 Abstract gestures, 117. A pictorial example, 118. Experiments with drawings, 120. Thought in visible action, 129. 8. Pictures, Symbols, and Signs 135 Three functions of images, 135. Images to suit their functions, 140. What trademarks can tell, 144. Experience interacting with ideas, 148. Two scales of abstraction, 150. 9. What Abstraction Is Not 153 A harmful dichotomy, 154. Abstraction based on generalization? 157. Generality comes first, 163. Sampling versus abstraction, 169. 10. What Abstraction Is 173 Types and containers, 174. Static and dynamic concepts, 178. Concepts as highspots, 182. On generalization, 186. 11. With Feet on the Ground 188 Abstraction as withdrawal, 188. The extraction of principle, 191. Against the grain, 194. In love with classification, 199. In touch with experience, 202. 72. Thinking With Pure Shapes 208 Numbers reflect life, 208. Quantities perceived, 211. Numbers as visible shapes, 213. Meaningless shapes make trouble, 217. Self-evident geometry, 222. 13. Words in Their Place 226 Can one think in words? 227. Words as images, 229. Words point to percepts, 232. Intuitive and intellectual cognition, 233. What words do for images, 238. The imagery of logical links, 240. Language overrated, 242. The effect of linearity, 246. Verbal versus pictorial concepts, 251. 14. Art and Thought 254 Thinking in children's drawings, 255. Personal problems worked out, 260. Cognitive operations, 263. Abstract patterns in visual art, 269. 15. Models for Theory 274 Cosmological shapes, 274. The nonvisual made visible, 280. Models have limits, 282. Figure and ground and beyond, 283. Infinity and the sphere, 287. The stretch of imagination, 290. 16. Vision in Education 294 What is art for? 295. Pictures as propositions, 296. Standard images and art, 299. Looking and understanding, 301. How illustrations teach, 305. Problems of visual aid, 308. Focus on function, 313. The burden of it all, 315. Notes 317 Bibliography 325 Index 339