Surfaces and Essences

by Douglas Hofstadter

  literal encoding as inadequate, 174–175; see also abstraction

  literal-mindedness in the Copycat domain, 348–349, 351, 355, 357–360, 363–364

  Locke, John, 22

  logic: influence on psychologists’ theories of categories, 55, 436; the small role of, in thinking, 258, 288, 392; versus psychologic, 410; see also analogic versus logic

  loot carried off by thief, 472

  “lovely spots” on city streets, as influencing perception, 296–297

  lowercasing of categories, 34–35, 44

  “lustre”, as possible French analogue to English word “score” in Gettysburg-address translation challenge, 372

  —M—

  Macbeth effect, 289–290

  Mach, Ernst, 487

  machine translation, see translation

  Madonna, 223; syllogistic proof of mortality of, 193

  magical angel stung by randomly buzzing interplanetary bumblebee, 493

  magnet in motion, giving rise to electric field, 493

  making distinctions and seeing commonalities, 189, 198

  Malevich, Kazimir, 296

  “man”, ambiguity of, 193–195

  Mandarin, see Chinese

  Mandelbrot, Benoît, 444

  manipulations, routine, in math, 449–450

  manipulators versus manipulatees, 382–383

  Marceau, Marcel, 322

  marking, 186–187, 193–204, 217–218; applied to proper nouns, 227; and category extension, 254; helping to reveal a concept’s essence, 255; list of examples of, 195; in mathematics, 228–232, 419; in metaphor understanding, 229–232; origin of the term, 218

  marriage, concept of, in constant evolution, 53

  Martin, Mr.: as dog fancier, 238–239; as multi-categorizer, 189–190, 197, 248, 435

  Mary, mother of Jesus, 38

  Maslow, Abraham, 301

  mass: barrier between two varieties of, 476, 478, 484; belonging to immaterial phenomena, 475; conservation of, 472, 475; interconvertibility between two varieties of, 480, 484; loss of, as result of radiation, 470–471, 475; normal versus strange, 476–485; poofing out of existence, 472, 475, 477–479, 481, 482, 484; possessed by energy, 471–478; possessed by heat, 475, 476; possesses energy, 482; two types of, 476, 477–478, 485

  mass/energy analogy in Einstein’s mind, 472, 479–481, 482, 484; running aground on a fatal snag, 480, 484

  mathematical formulas, mistaken views of, 391–394

  mathematicians: arguing over category membership, 392; reluctant to extend categories, 440–444; seeing analogies between analogies, 502; “sniffing” the crux of a problem, 451; thinking by analogy, 439–451; toolkit of, 450

  mathematics: ambiguity in, 237; analogy with Monopoly, 450–451; causality in, 411; imagined as lacking blurriness, 233, 392, 439; intuition in, 451; marking in, 228–232; naïve analogies in, 407–434, 439; rooted in everyday experiences, 393, 427; routine situations in, crying out for specific routine techniques, 449–450; spectrum of subtlety of analogy-making in, 451; unusual categorizations of, 510; use of analogy in, 439–451

  matter as imbued with energy, 481

  Maxwell, James Clerk, 130, 212, 213, 275, 361, 453, 459, 502

  Maxwell–Boltzmann distribution, 457, 458; see also ideal gas

  Maxwell’s equations of electromagnetism, 361, 410–411, 456, 459, 489; both confirmed and undermined by one and the same experiment by Hertz, 460

  measurement: contrasted with sharing, 420, 422–426; of energy E in units of size hν, 459; as key concept in division, 420

  “Mecca” pluralized to “mecca”, 220

  meccas, list of, 220; of wind-surfing, 229

  mechanical translation, see translation

  mechanics: defined, 466; generalized to all of physics, 466–467, 494–495, 499

  medium: in producing shadows, 207–208; of waves, 210–214

  “melting” of components in compound words, 87, 111

  membership in categories: non-black-and-white nature of, 14, 55–57; transitory nature of, 225

  memo to office assistant, ambiguity of many words in, 395

  memories of the past, as allegedly shackling people, 313–315

  memory retrieval: alleged uselessness of, 338, 341; allegedly triggered by irrelevant features, 341; salient features’ dominance in, 342; surface-level features’ alleged dominance in, 337–346; virtuosity in, 110; see also remindings

  menace, as typical example of a verb naming a category, 66–67

  mental blocks, recipes for escape from, 248–249

  mental bridges, 183–184; see also analogy-making

  mental lexicon, 137

  mental simulation in math word-problems, 421–425, 427–429

  mental spaces, 365; see also Fauconnier

  mess, as example of a highly protean concept, 5, 127, 510

  meta-analogies: in doing theoretical physics, 212; in evolution of wave concept, 211–212; in ordinary conversation, 27

  metallurgists appreciating the blurriness of the category metal, 60

  metaphorical versus literal meanings, 37–38

  “metaphorical” usages: not always metaphorical, 229–230; three types of, 230–232

  metaphors: conventional, 229–232; creativity in many, 510; embodiment and, 286–289; families of, 63; as flapdoodle, 22; Glucksberg–Keysar theory of, 228–229; going dead over time, 64; list of common words used as, 62; list of sentences using stock, 232; mixture of abstract and concrete in, 286–290; “mobile army of” (Nietzsche), 21; process of understanding of, 228–232; scorned by Hobbes, 22; used to criticize metaphors, 22

  “me too”, unclear halo implicit in the phrase, 145, 150–153

  me-too analogies, 143–153; in Copycat’s microdomain, 346–358; marginal members of the category, 147; phrases that often are giveaways of, 143, 152, 507; the ubiquity of, 507–508

  métro in Paris, 215; American transculturation of, 377–379

  microworlds, 305

  “Mighty oaks from little acorns grow”, 109

  military-budget arguments mobilizing flow of ideas, 26

  military versus non-military analogies in times of war, 333–335

  milk carton too heavy for bag, 133

  Millikan, Robert, 461

  Minkowski, Hermann, 453, 498–499

  mistaken-identity scenes, 291–292

  “mobile army of metaphors” (Nietzsche), 21, 509

  Molière, 186, 248

  Mommy as core of concept mother, 34–37

  Mona Lisa with mustache, 351

  monolithicness of categories, illusory, 3–5, 9–13, 71, 81–83, 241

  Monopoly, 11, 450–451

  Moon, analogical extension of, leading to the concept moon, 43–45, 64, 147, 210, 217

  moonlets in Saturn’s rings, waves in medium of, 21

  “morsel of shame”, 140

  Moser, David, 89, 150–151, 259, 291–292

  mosquito: in nudist colony, 320; perspective on Albert Einstein of, 163, 164–165

  mother: abstract extensions of the category, 37–38, 53; development of the category, 34–38, 48, 53; marginal cases of, 37–38; as opposed to the concept mommy, 36

  motion, children’s naïve view of, 294–295

  Mount Analogy: scaling hardest slopes with and without pitons, 131; trekking on, 126, 131–132

  mouse, as tangible gateway to intangible world, 252–253, 509

  mouse/limb analogy, 252–253

  Mozart, Wolfgang Amadeus, 223; of mushrooms, the, 222, 229

  “much”: syntactic slots for, as a category, 68–70

  much-situations: nature of, 67–68; role of expectations in, 68

  multi-categorizability: of objects, 59, 189–192; of situations, 117–118, 188, 248

  multiplication: apparent asymmetry of, 413, 415, 428; commutativity of, 413–416; generalized to abstract objects, 446–447; mental simulation used to solve, 424–425, 427–429; naïve analogies for, 411–416; as necessarily making larger,
413–414, 416; as repeated addition, 412–416, 427–429; tables, patterns in, 446–447

  multitasking: concept borrowed without awareness from computer world, 402–403; passage of the concept into the everyday world, 404

  Munich conference, 332, 334; pluralization of, 335

  Murphy, Gregory, 60, 436

  Mussolini, Benito, of mulligatawny, the, 222, 360

  music keyboards, electronic, and musicianship, 131

  musical instruments and zeugmas, 11–12

  mystical characterization of genius, 501

  —N—

  naïve analogies, 31–32; as bases for effective interfaces, 400; coexisting with other views, 389, 409; concerning analogy-making, 451; concerning categorization, 435–436; concerning cicadas, 388; concerning disk ejection, 401; concerning division, 416–421, 425–426; concerning email addresses, 385–387; concerning the equals sign, 407–411; concerning icons, 402; concerning motion, 294–295; concerning multiplication, 411–416; concerning shaving, 385–387; concerning size changes, 295; concerning titmice, 385–387; concerning virtual desktops, 401; deep entrenchedness of, 394, 409; defined, 386; education and, 389–394, 409, 411–434; like groomed-slope skiers, 389; linking cleanliness to morality, 289–290; made by analogy experts, 436–437; in mathematics, 407–434, 439; in mathematicians’ minds, 439, 441; misleading nature of, 400–401; not eliminated by scientific training, 389, 394; permeating today’s computer technology, 400; rooted in everyday experience, 386, 389, 391, 393–394; stemming from the computer world, 402–407; unconscious character of, 386, 389, 512; underlying jargon-creation, 399–400; utility of, 389

  naïve equations, 407–411

  names: conflated with items they name, 227; retrieved by analogy, 224–225

  Napoleon: of fossil bones, the, 222; frame-blended with emperor penguins, 380

  nature, cut at the joints by categories, 14, 77, 522–523

  N-dimensional spaces, 443–444

  nebula, as image for a language’s filling of a conceptul space, 119

  necessary and sufficient criteria for category membership, 55, 436

  negative numbers: fear of, 439–442; square roots of, 442–443

  Neruda, Pablo, 522

  nested radicals in polynomial solution-formulas, 445

  Newman, Paul, 318

  Newton, Isaac, 130, 210, 443, 471, 490, 491, 500; law of gravitation of, 389, 489; second law of motion of, 410, 491; of terrorism, the, 222

  New York subway, as translation of Paris métro, 378

  Nick’s me-too quip to the Nubian taxi driver, 151–152

  Nixon, Richard: of superheroes, the, 222; yearining to be known as “RMN”, 90

  Nietzsche, Friedrich, 21, 509

  9/11, see September 11th

  Nobel Prize: citation for Einstein, extreme caution of, 461–462; for creative extensions of categories, 464–465

  non-Euclidean geometry, 16, 498–499

  non-lexicalized concepts, 30, 137, 139–140, 176–180

  normalement, as monolithic concept in French, 82

  normal mass/potential energy analogy, 480–481

  normal mass/strange mass membrane, broken, 480–481, 482, 484

  Norman, Donald, 259, 400

  norms as directing word choices, 73

  novices: inability to spot depth, 341; versus experts, 236–246, 255, 392–394

  Nubians harmed by dam, me-too analogy centered on, 151–152

  number : blurriness of the category, 392; relentless conceptual broadening of, 439–443, 447–448

  numerical comparisons as analogies, 153–154, 281–282, 285, 331

  —O—

  oars replaced by javelins, 317, 322

  object recognition, mediated by analogy, 19, 184

  objectivity: of analogies, 522–526; of categorization, 522–526

  obsessions engendering analogies galore, 258, 299–305, 524

  October 11th crash, 31, 297

  “Ode to Constraints” (James Falen), 315

  “office” versus “study”, 47–49, 74, 76

  office visit as an example of a schema, 336–337

  “official” boundaries of categories, 64–65

  old town, as metaphor for a category’s core, 61–62, 65

  Once bitten, twice shy: as an abstract category, 100, 103–106, 516; as a proverb incarnated in various languages, 105; as analogical pressure in column-translation dilemma, 306–307

  “one”, as the name of a category, 75

  one-dollar bill, as minimal banknote, 280

  one-line analogies, list of, 135

  one-member categories, see single-member categories

  “one smart dude”, as indicative of category of speaker, 75

  opacity: of acronyms, 91–93; of compound words, 86–87; of idiomatic phrases, 97–98

  operation–result naïve analogy for equations, 407–411; see also cause–effect