Surfaces and Essences

by Douglas Hofstadter

  INDEX

  —A—

  “A”, diversity of members of the category, 4–5, 57; picture, 5

  “a”: as naming a category, 76; as vowel recognized in speech without one’s knowing how, 511, 512

  “A rolling stone gathers no moss”, opposite interpretations of, 102

  Aaron, Henry, 325–326

  abc ⇒ abd, see Copycat analogies

  Abel, Niels Henrik, 446

  abstract dog and abstract bite, 104

  abstract, grounded in the concrete, 28–29, 286–289, 333–337

  abstraction: absurd levels of, 107–108, 166, 354, 448–449; as central to expertise, 245–246; by children, 38, 42–43; defined, 187; drive towards, 288; going hand-in-hand with generalization in math, 449; hierarchies of, 235–246; as impoverishing and enriching, 250; as key to encoding, 172, 174–176; legitimized by physics, 448; as luxury add-on to embodied cognition, 288–289; moving between levels of, 30–31; nature of, 107; opaque legalese as bad form of, see legalese; optimal level of, 108; relentless push towards, in mathematics, 448; streamlined by preplaced pitons, 131; techniques for, in mathematics, 449; unconscious acts of, 150–152, 165–166; in word problems in math, 428; see also category extension

  accelerating frames of reference, 486, 488

  acceleration: as indistinguishable from gravity, 491–492, 493–494, 496; linear versus circular, 497

  acronyms, 89–93; catchiness of, 90; early examples of, 89–90; efficiency of, 92; list of, 90–91

  actable-upon objects, category of, 253

  action errors, caused by analogies, 279–280, 404–407

  activated categories seeking instances of themselves, 299

  adaptation of word meanings to contexts, 196–198

  address, generalization to virtual world, 385–386, 395, 398

  ad-hoc categories, 137–138; in metaphor understanding, 228–229, 232

  adjectives: as labels for the two types of mass, 485; as names of categories, 272

  Æsop, 112, 115, 388

  affordances, perceptual, 278, 345, 450

  airlines and airports as parts of hub concept, 52

  airplanes, undetectabilityof motion of, 466–467

  airport scenes: evoking words left and right, 33–34; evoking memories of analogous scenes, 157–158; as transculturation of métro scene, 377–379

  Alberic of Monte Cassino, 22

  Albert Einstein, Creator and Rebel, 473; see also Banesh Hoffmann

  Albert’s Auberge, excellent coffee of, 462

  algebra of classical categories, 56

  Alice in Many Tongues (Weaver), 369–370, 372

  alignment of two lives on time axis, 433–434

  allegory for strange versus normal mass, 476

  ambiguous category-membership, 59, 189–192

  America/China frame blend, 367–368

  amplification, proverbs about, 109

  analogic versus logic, 258, 307–310, 311–312, 338, 393, 410, 439, 452, 453, 474, 499–500, 501; see also esthetics

  analogical fabric of thought, 127

  analogical reasoning, mistaken for analogy’s essence, 16–17, 283

  analogies: between analogies, 27, 211–212, 502; between random things, 302; as bridges between mental entities, 181–184; coercing one’s flow of thought, 257, 258, 310–313, 444; as cognitive luxuries, 506; in competition, 260–278, 333; conveying truth despite falsity, 366; to counterfactual situations, 362; deep versus shallow, 337–346, 351–357, 375–376, 454–455, 517; as discardable crutches, 392, 421; down-to-earth, great utility of, 23, 507, 509, 516; by Einstein turning out to be eternal truths, 453–454, 486; engendered by obsessions, 258, 299–305, 524; extremely bland cases of, 155–156, 281–284, 507–509; failure of one as stepping stone en route to a deeper one, 356–357, 481, 490–491; as fallible and misleading, 22–24, 435; formal versus physical, 458; as frilly baubles and bangles, 506; functional and visual, coordinated, 277–278; as gems, 16, 506; high frequency of, 18, 507–510; as icing on cognition’s cake, 506, 508; imposing themselves, 29, 31, 289–307, 310–314; inspired by previous analogies, 211–212; invading minds willy-nilly, 257; involving frame-blending, 359–367; involving grammar patterns, 69–70; irrepressibility of, 104, 155, 157, 297, 305–313, 513–514; jumping unbidden to mind, 513–514; latent in semantic halos, 49, 271; like asparagus tips, 135; at the low end of the creativity spectrum, 450; manipulated by us, 331, 382–383, 513; manipulating our thoughts, 29, 31, 315, 331, 382–383, 501, 514; as mere sparkle and pizzazz, 506; as misleading, 21–23; mundane, by Albert Einstein, 454–455; nonstop deluge of, 155; not necessarily a source of pride, 517; objectivity of, 181–183; partially correct and partially wrong, 361; power of, 331–332, 444; pressures pushing for, 300–301, 355–356, 458; purposeless, 258, 281–286; rarity of, 506; seen as analogous to wild horses, 392; as sources of speech and action errors, 259–280; spicy one-line examples, list of, 136; stereotypes of, 135–136, 392, 486; strength of, as reflecting number of resemblances, 516; as strokes of genius, 16–17; superficial, in machine translation, 373, 375; taboo cases of, 104; as training wheels, 392; trivial and meaningless, ceaseless production of, 282, 284–286; unconscious, 259–281, 282, 285–286, 383, 386, 390, 403–407, 514; as uninvited guests, 31, 257; used in thermodynamics but not in electrodynamics, 337; versus frame blends, 363–364, 366–367; visual and sensory, 277–278, 286–289; wild and implausible, as hypothetical crux of creativity, 452

  analogues versus schemas, 336–337

  analogy: as analogous to asparagus tips, 135; as analogous to siren songs, 23; as analogous to wild horses, 392

  analogy leapfrog, 211–212

  analogy-making: addictive nature of, 155; as applying to entities versus applying to relations, 517–519; automaticity of, 513–514; as bridge-building between two items on the same level, 519–522; as a cognitive luxury, 506; as compatible with very few disparities, 515–517; as a conscious process, 510–513; as contrasted with assignment to a schema, 336; as the core of cognition, 3, 18, 25–26, 383, 505, 530; as creative, 508–510; as the crux of intelligence, 127; in decision-making, 330–337; as the Delaware of cognition, 17; delight provided by, 506; dependence on familiarity of source domain, 339–340; described by experts exactly as categorization is described, 436, 506; driven by surface-level cues, 337–346; efficiency of, 346; embodiment and, 287–289; in everyday life versus in wartime, 333–335; evoking symbol-manipulation recipes in mathematics, 450–451; as fallible and misleading, 22–24, 435, 527–529; as formal reasoning, 16; frame-blending and, 357–367; as the fuel and fire of thinking, 3; in getting used to new mathematical concepts, 442–444; going as deep as one can go in, 360; as the heartbeat of thought, 15, 17; identity with categorization, 503–530; illusion of necessary seriousness of, 282; incessant avalanche of, 18, 24, 28; as jumping between two levels of abstraction, 519–522; lack of right answers in, 16, 350, 352; as lacking in computers, 25; as the machinery of categorization, 15, 17, 39–49, 183–184, 309, 336, 399; as making the novel familiar, 436, 506; as making the world predictable, 436; by mathematicians, 439–451; as mediating object recognition, 19; misleading stereotypes of, 15–17; in mundane mathematical manipulations, 449–450; naïve analogy concerning, 451; as noble, 508; not used in domestic politics, 337; as objective, 522–526; opacity of the mechanisms of, 511; at the origin of metaphors, 63–64; in poetry translation, 380–381; as prerequisite to survival, 155, 157; as primarily done in intelligence tests, 16; as a rare luxury, 505–508; in real life as opposed to the lab, 339; as reliable, 527–529; as risky, 527; as routine, 508–510; in scientific discovery, 32, 210–214, 361; as subjective, 522–526; supposedly driven by superficial features only, 337–340; supposedly strengthened by disparities, 515–517; as suspect, 527–529; in translation of this book, 377–382; ubiquity of, 506–508; as an unconscious process, 510–513; underlying all word choices, see word choices; utility of, 135; versus categorization, 434–437; as a voluntary process, 513–514; in wartime de
cision-making, 17, 331–337; wide range of, 19; wide spectrum of abstraction of, in mathematics, 451

  “analogy”, rarity of the word, 135

  and-situations as a category, 55, 70–75; contrasted with but-situations, 72–75

  Anderson, John, 436

  angel stung by bumblebee, see interplanetary bumblebee

  animal, as highly variegated category, 516

  animal words as metaphors, 228–232

  animals: conceptual repertoires of, 54; as Platonic categories, 56

  Ann, as member of many categories, 59, 190, 191

  Anna, as spokesperson for the centrality of analogy-making, 503–529; poofing into thin air, 529; see also Katy, Katyanna

  annihilating nano-boulders, 482

  annus minimus of Ellen Ellenbogen, 463–464

  annus mirabilis of Albert Einstein, 453, 467, 468–469

  “Ant and the Grasshopper” (Æsop), 388

  anti-economy, principle of, as a consequence of the dominance of the superficial in reminding, 341

  ants: near Grand Canyon, see Danny at Grand Canyon; on orange, watching eclipse, 204–205, 367

  appearances, as deceptive versus revelatory, 345

  Arabic language, proverb in, 106

  Archimedes, 130, 250–252, 300–301, 509; of minigolf, the, 222

  Argentina, role of, in Falkland Islands War, 332

  Aristotle, 15–16, 21, 437; of the airwaves, the, 222

  arithmetical operations, relative difficulty of, 425

  “Arizona Ants” (Kellie Gutman), 160, 380–381

  army/thought analogy, 26, 27

  Arnaud, Pierre, 259

  Ars Magna (Cardano), 438–439

  articles (“a” and “the”), as names of categories, 76

  artificial intelligence, 20, 25

  artistic unity, as goal of Einstein, 477, 495; see also esthetics

  “as deep as one can go”, in analogy-making, 360

  asparagus tip analogies, 19

  “atmospheric harbor” as incomprehensible phrase, 86

  “atom” as an unsplittable etym in English, 89 atom/solar system analogy, 142–143, 510, 513, 515, 518

  atoms: lingering doubts about existence of, 459, 475, 487; vibrating in solids to make heat, 461, 475; vibrating in wall of black body, 456

  attic, concept of 48–49, 278

  avoidance maneuvers while walking, analogy-making in, 285

  —B—

  Babbage, Charles, 369

  Bach, Johann Sebastian, 312; of the vibraphone, the, 222; rapid essence-spotting by, 501;

  Bachelard, Gaston, 22

  bagels belonging to a single batch, 309–310, 529

  bait-and-switch as a concept available to anglophones, 123–124

  balls, bells, and bowls, 488

  Banach, Stefan, 502

  banalogies (banal analogies), 143–156, 281–286; certainty of, 529; by Einstein, 454–455; elusiveness of, due to blandness, 152, 282, 285–286; great utility of, 23, 507, 509, 516, 529

  bananalogy, of use when seeking bananas, 156

  “band”, diverse meanings of, 3–4

  Bar-Hillel, Yehoshua, 370

  bark worse than bite category, 96

  Barsalou, Lawrence, 137–138

  baseball-based caricature analogies, 325–326, 383

  base-level categories, 190

  basketballs as members of the category floating objects, 58

  Bassok, Myriam, 345

  bassoonist falling off roof as source of me-too analogy, 150–151

  “Bayh”/”bye” analogy, 27

  “beaucoup”, as compound word in French, broken into two concepts in English, 83

  bending over backwards to accommodate contrary evidence, 291–292

  Bengali poetry, as perceived by non-speakers, 343

  Benserade, Isaac de, 112

  betting one’s life at all moments on a myriad of trivial and unconscious analogies, 156

  Bezout, Étienne, 413, 415, 420

  bibles, category of 220, 229

  bike-rental anomaly, explained by analogy, 328–330

  bilingual data bases in machine translation, 369, 372–373

  biplans: involving actions, 279; linguistic, 268–270

  bird: as an example of an imprecise category, 55–56, 58, 59–60; as a platform for making inferences, 102

  birds in airport/accordionist in métro analogy, 378, 380

  black body: defined, 455; Max Planck and, 456–457; spectrum of, 455–459

  black body/ideal gas analogy: as found by Einstein, 457–459, 463; as found by Wilhelm Wien, 458

  black body/swimming pool explanatory analogy, 455, 456, 458

  blended scenario, see frame blends

  blending, see frame blends, lexical blending

  blinders, categorical, 58, 290–296

  blindness as result of an inability to categorize, 21

  blobs, colored, in conceptual spaces, 78–81

  boat in amusement park as member of category trolleycar, 521

  boat on tracks as category, 521–522

  body-to-body analogies, 155–156

  Bohr, Niels, 143; pooh-poohing Einstein’s light quanta, 462

  Bolt, Usain, 75; of cognitive science, the, 222

  Boltzmann, Ludwig, 457

  Bombelli, Raffaello, 440, 442

  bongos on savannah in museum, 364–366

  books: as abstract, immaterial entities, 7; strange types of, 83

  Borges, Jorge Luis, 38, 188

  “bosse” (French word), 198–200

  bottle, evolution of the concept in a child’s mind, 198–200

  bottlecaps on ground, see Dick at Karnak

  bottles thrown overboard, 284

  box canyon, see impasse

  boxes, as misleading model of categories, 13–14, 20, 52, 54–57, 60–61, 435

  brainbows, 182–184

  brain tumors, analogy between two, 312–313

  “brand”, evolution of meanings of, 202

  brand names, genericized, 217–218

  Brazilian street vendors’ arithmetic, 414–415, 422

  breaking, marginal examples of the category, 41–42

  bridge, as surprisingly elusive category, 67

  bridges everywhere lighting up when button is pushed, 67

  bridges, mental, 183–184, 336; see also analogy-making Brissiaud, Rémi, 424

  Brownian motion, 458

  “browse”, old-fashioned definition of, 397

  “brush”, used zeugmatically, 8

  “Brustwarze”, unheard parts inside, 87

  bubbling-up of concepts from dormancy, 67, 170–171, 489, 491, 492, 498, 511, 513–514, 525; see also remindings, memory retrieval

  Buffett, Warren, 320

  bumblebee, see angel stung by bumblebee

  bureaucratic use of acronyms, 92

  Buresh, Ellie, 364–366

  Buridan’s ass, 454

  Bush/Schwarzenegger analogical conflation, 275

  but as a category, 55, 70–75; contrasted with and, 72–75; in Russian, 74

  “butter for lobster tails” joke, 358

  “butterfingers”, as isolated metaphorical usage, 63–64

  button #1/button #2 analogy by Monica, 169–170

  buzzing interplanetary bumblebee, see randomly buzzing interplanetary bumblebee

  —C—

  c, the: in string abc, 349, 355; in string xyz, 354, 356

  c2, enormous size of, 471, 482

  Cairo, 75, 151, 162, 192

  “camel”, marked and unmarked senses of, 199–200

  Camille (who undressed the banana), 39, 41, 126

  candle problem, Duncker’s, 250, 256

  canine concepts, 178–181

  canonization of individuals, 221–222

  can-opener, universal, 439

  Cantor, George, 444

  “car”, marked versus unmarked senses of, 197, 230, 232

  Cardano, Gerolamo, 438–440, 441, 445, 449

/>   caricature analogies: analyzed, 320–330; blurted out, 323–324, 382–383; cascade of, 323–324; clarity as goal of, 317–318, 326–330; concreteness as force in, 329; creativity of, 324–326; diverse forms of, 320; drastic simplification in, 326; essence-spotting in, 321–322, 324–330; exaggeration as inadequate for, 321; for explaining subtle ideas to others or oneself, 326–330; feeble example of, 320; humorous baseball examples of, 325–326, 383; involving French number-words “cinq” and “six”, 380; list of, 318–320; involving Jan’s liquid and frozen assets, 476, 481, 485; mini-scenarios imagined in creation of, 323–324; mocking the timidity of Einstein’s Nobel Prize citation, 462; non-uniqueness of, 323, 325; rapidity of, 321, 323–324; reasons for concocting, 31, 317–318, 322, 324–328; search processes in, 321–322, 324–325; translation of, 380; used by the authors, 13, 18, 22, 25, 65, 108, 281, 320, 321, 337, 340, 366, 370–371, 411, 454, 462, 468, 476, 485, 497, 527

  Carol signing with maiden name, 148–149

  cars, blue, analogy between, 283

  carving up the world in “the right way”, 14, 77, 522–523

  casting pearls before swine, as category, 165

  categorical blinders, 290–296, 400

  categories: absurdly fine-grained, 83; ad-hoc, 137–138; base-level, 190; as blinders, 290–293, 313; blurriness in, 60, 61, 214–216, 244, 523; as boxes, 13–14, 435–436, 520, 522; of children, 39–43, 45; classical approach to, 13–14, 54–57, 435; competition between, 260–278, 281; defined by fables, 29–30, 113–118; as defining identity, 190; degree of centrality of members of, 57; development over time, 34–38, 43–45, 198–204; in discourse space, 69–76; of dogs, 178–181; dominant, 191; as drawers in a dresser, 13; extended by analogy-making, 34–38, 46, 62, 115–116, 246–248; with extremely intangible flavors, 75; as filters on perception, 292, 298–299; handed out on the silver platter of one’s language and culture, 123–124, 128–131; ideal degree of refinement of, 83–84, 108; imprecision of boundaries of, 55–61; instantly forgotten, 284; jumping unbidden to mind, 513; levels of abstraction of, 188; as the motor and fuel of cognition, 506; natural grain size of, 84; nested in the manner of Russian dolls, 520; non-lexicalized, 137, 139–140, 166–167, 176–180; organization of, as critical for expertise, 187, 237–246, 393; as organs of perception, 257, 299, 314; outnumbering words by far, 85; overly subdivided, 83; people’s frequent conflation with sets of visible objects, 54–55; private repertoire of, 166–168, 283–284; as relational, 517–519; seeming to be objectively there, 110, 111, 132–133; suburbs of, 65, 202, 213; unnoticed at their birth, 167; whose members exhibit great variety, 516; see also concepts categorization: as allowing prediction, 14–15; as applying to entities versus applying to relations, 517–519; as assignment to a schema, 336; automaticity of, 513–514; as bridge-building between two items on the same level, 519–522; carried out by analogy-making, 18–19, 179, 183–184, 309, 336, 399; as compatible with many disparities, 515–517; competition during, 261; as a conscious process, 510–513; as a constant necessity, 505; as the core of cognition, 505, 530; as creative, 508–510; described by experts exactly as analogy-making is described, 436, 506; errors in, 102–103, 527; by experts versus by novices, 342–344, 346; as fallible and misleading, 527–529; growing smoothly out of a single first instance, 182–184, 336, 520, 522; as humdrum, 508–510; identity with analogy-making, 503–530; illusion of automaticity of, 450, 513–514; as a judgment call, 117–118, 126; as jumping between two levels of abstraction, 519–522; as making the novel familiar, 436, 506; as making the world predictable, 436; as the meat and potatoes of cognition, 506; nature of, 13–15; not taught in schools, 60, 65, 126, 127; as objective, 522–526; as often being erroneous, 102–103, 527; opacity of its mechanisms, 511; “pure”, 65; rapid, as crucial for survival, 79, 83, 505–506; as rapid simplification, 505–506; reflecting one’s current perspective, 526; as reliable, 527–529; as risk-free, 527; as routine, 508–510; shades of gray in, 14; as subjective, 522–526; as suspect, 527–529; as an unconscious process, 510–513; as uncreative, 509; versus analogy-making, 434–437; as a voluntary process, 513–514; as weakened by disparities, 515–517