Lucidity and science I: Writing skills and the pattern perception hypothesis

Interdisciplinary Science Reviews

Volumn 22, Issue 3, 1997, Pages 199-216

  McIntyre, Michael E ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

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EID: 0346248852     PISSN: 03080188     EISSN: None     Source Type: Journal    
DOI: 10.1179/isr.1997.22.3.199     Document Type: Article

References (88)

1. 2-4
2. 71
3. J. MONOD: 'Chance and necessity', (transl. A. Wainhouse); 1971, Glasgow, Collins, 187pp. This classic gives a lucid and penetrating discussion of what was already known, in the 1960s, about molecular-scale cybernetics. That knowledge included details of the computational functionality of certain protein molecules, called allosteric enzymes, and, more importantly, a clear grasp of the general principles on which such functionality is based (Chap. 4). The far reaching implication, further discussed in Ref. 71, is that an arbitrarily specified logical or computational system can be realised as an interacting collection of protein molecules. Monod also offers, in the final chapter, some important, clear-headed insights into human nature and belief systems and their likely biological origins, a theme to be revisited in Part III.
4. D. BRAY: 'Protein molecules as computational elements in living cells', Nature, 1995, 376, 307-312. This review gives examples with up to eight inputs per molecule, more elaborate than the allosteric enzymes described in Ref. 3, and some simple 'circuits', i.e. computational subsystems, already known in detail. See also for instance N. BARKAI and S. LEIBLER: 'Robustness in simple biochemical networks', Nature, 1997, 387, 913-917 (commentary, p. 855), and R. M. DICKSON, A. E. CUBITT, R. Y. TSIEN, and W. E. MOERNER: 'On/off blinking and switching behaviour of single molecules of green fluorescent protein', Nature, 1997, 388, 355-358.
5. D. BRAY: 'Protein molecules as computational elements in living cells', Nature, 1995, 376, 307-312. This review gives examples with up to eight inputs per molecule, more elaborate than the allosteric enzymes described in Ref. 3, and some simple 'circuits', i.e. computational subsystems, already known in detail. See also for instance N. BARKAI and S. LEIBLER: 'Robustness in simple biochemical networks', Nature, 1997, 387, 913-917 (commentary, p. 855), and R. M. DICKSON, A. E. CUBITT, R. Y. TSIEN, and W. E. MOERNER: 'On/off blinking and switching behaviour of single molecules of green fluorescent protein', Nature, 1997, 388, 355-358.
6. D. BRAY: 'Protein molecules as computational elements in living cells', Nature, 1995, 376, 307-312. This review gives examples with up to eight inputs per molecule, more elaborate than the allosteric enzymes described in Ref. 3, and some simple 'circuits', i.e. computational subsystems, already known in detail. See also for instance N. BARKAI and S. LEIBLER: 'Robustness in simple biochemical networks', Nature, 1997, 387, 913-917 (commentary, p. 855), and R. M. DICKSON, A. E. CUBITT, R. Y. TSIEN, and W. E. MOERNER: 'On/off blinking and switching behaviour of single molecules of green fluorescent protein', Nature, 1997, 388, 355-358.
7. D. C. MARR: 'Vision: a computational investigation into the human representation and processing of visual information'; 1982, San Francisco, Freeman, 397 pp. On perceptual grouping, see for instance Figs. 2-5, 2-33 and surrounding discussion. 'Was the foundation of modern computational vision' (COLIN BLAKEMORE, personal communication). Very clear about the evidence pointing to the brain's multi-level internal models, or 'explicit internal symbolic representations'.
8. R. JACKENDOFF: 'Consciousness and the computational mind'; 1987, Cambridge, MA, MIT Press, 356 pp. Draws on analogies with vision, as well as linguistic studies, to argue cogently for the multi-level computational nature of language processing; see e.g. pp.101-104.
9. D. HOFSTADTER and co-workers: 'Fluid concepts and creative analogies: computer models of the fundamental mechanisms of thought'; 1995, New York, BasicBooks, 518 pp. See especially Chaps. 4 and 5, and the Epilogue, for a profoundly insightful perspective on real and artificial intelligence. The title could well have been extended to '...thought and perception'.
10. 31 for download in binary mode. All relevant file names begin with the eight characters lucidity.
11. -1.
12. W. STRUNK and E. B. WHITE: 'The elements of style', 3rd edn; 1979, New York, Macmillan, 92 pp. A miniature gem on writing technique - an elegant pocket book showing profound insight and compressing the essentials into a few dozen small pages.
13. 68 is a useful source of information on recent trends in vocabulary and usage. It features a good article on split infinitive, with many wonderful examples from the fourteenth century onward, though missing the rhythmic and emphatic significance as in 'to BOLDLY go'.
14. 68 is a useful source of information on recent trends in vocabulary and usage. It features a good article on split infinitive, with many wonderful examples from the fourteenth century onward, though missing the rhythmic and emphatic significance as in 'to BOLDLY go'.
15. 68 is a useful source of information on recent trends in vocabulary and usage. It features a good article on split infinitive, with many wonderful examples from the fourteenth century onward, though missing the rhythmic and emphatic significance as in 'to BOLDLY go'.
16. 38 also gives a telling but humane riposte to cultural relativism, dispelling the notion that the only alternative is 'brutal biological determinism'; see also:
17. 38 also gives a telling but humane riposte to cultural relativism, dispelling the notion that the only alternative is 'brutal biological determinism'; see also:
18. 12 as well as evolution in general. Here is abundant evidence - see for instance discussions of genotype-culture feedbacks and the 'Baldwin effect' -for a most intimate and subtle interplay between nature and nurture, between biological and cultural evolution.
19. This is a real example from Proc. R. Soc. (London), 1993, A 440, 530, 11th line from bottom. Also D. EDWARDS et al.: 'My pear tree has gone bananas: the collected philosophy of Don Edwards'; 1986, London, Reader's Digest Assoc. and Multiple Sclerosis Soc., 33 pp.
20. This is a real example from Proc. R. Soc. (London), 1993, A 440, 530, 11th line from bottom. Also D. EDWARDS et al.: 'My pear tree has gone bananas: the collected philosophy of Don Edwards'; 1986, London, Reader's Digest Assoc. and Multiple Sclerosis Soc., 33 pp.
21. M. W. GREGORY: 'The infectiousness of pompous prose', Nature, 1992, 360, 11-12. This 'Commentary' perpetuates the minor misconception that one should write with the 'fewest possible words', and the major misconception, far more serious - and dangerous because of its despairing cynicism - that writing is too difficult for most scientists and should be delegated to professional writers. Gregory rightly complains about what pretends to scientific professionalism, but amounts to tribalistic pressure to write in obscure and pompous ways - see also L. AVERY: 'Write to reply', Nature, 1996, 379, 293 - which pressure, in my opinion, should be stoutly resisted even when it comes from journal editors and referees. See also Ref. 66 for an example of obscure and pompous prose, from a published scientific paper, that outdoes even Example 1.
22. M. W. GREGORY: 'The infectiousness of pompous prose', Nature, 1992, 360, 11-12. This 'Commentary' perpetuates the minor misconception that one should write with the 'fewest possible words', and the major misconception, far more serious - and dangerous because of its despairing cynicism - that writing is too difficult for most scientists and should be delegated to professional writers. Gregory rightly complains about what pretends to scientific professionalism, but amounts to tribalistic pressure to write in obscure and pompous ways - see also L. AVERY: 'Write to reply', Nature, 1996, 379, 293 - which pressure, in my opinion, should be stoutly resisted even when it comes from journal editors and referees. See also Ref. 66 for an example of obscure and pompous prose, from a published scientific paper, that outdoes even Example 1.
23. 32
24. 32
25. M. HUNT: 'The story of psychology'; 1993, New York, Doubleday, 762 pp. The reference to the Three Mile Island nuclear accident, which began at 0400 hours on 28 March 1979, is in Chap. 18, p. 606. See also, for instance, C. CORDES: Amer. Psychol. Assoc. Monitor, May 1983, 14(5), pp. 1 and 13-14. Hunt also gives a convenient collection, with historical commentary, of standard examples of visual perceptual phenomena in Chaps. 10 and 14, e.g., grouping, pp. 287ff.
26. M. HUNT: 'The story of psychology'; 1993, New York, Doubleday, 762 pp. The reference to the Three Mile Island nuclear accident, which began at 0400 hours on 28 March 1979, is in Chap. 18, p. 606. See also, for instance, C. CORDES: Amer. Psychol. Assoc. Monitor, May 1983, 14(5), pp. 1 and 13-14. Hunt also gives a convenient collection, with historical commentary, of standard examples of visual perceptual phenomena in Chaps. 10 and 14, e.g., grouping, pp. 287ff.
27. See 'false scent' in Ref. 11 and 'garden path sentences' in Ref. 12.
28. 30
29. See Ref. 16, chapters on the discovery of Neptune and the 'Adams-Airy affair'. In this case the bright young man was the mathematician John Couch Adams, failing to persuade the Astronomer Royal, Sir George Biddell Airy, to be the first to point a large telescope toward the predicted position of Neptune. Adams' mistake was to think that a certain statement (about the smallness of changes in Uranus's angular momentum) was not only correct but also so obvious that it, and its consequences, were trivial matters that need not be explained to Airy, perhaps for fear of insulting the great man's intelligence. If Adams had attempted an explicit explanation, he might have persuaded Airy as well as seeing at once that the 'trivially obvious' statement was, in Littlewood's words, 'dead wrong'.
30. Minutes of the Sixth Annual General Meeting of the excellent Save British Science Society (Oxford, PO Box 241, OX1 3QQ, UK, http://www.dspace.dial.pipex. com/sbs/).
31. 30 (Essential reading, in my opinion, for anyone learning musical composition, more so than the average counterpoint text. I am grateful to Ian Cross for drawing my attention to this reference and the next.)
32. S. E. TREHUB and L. J. TRAINOR: 'Listening strategies in infancy: the roots of music and language development', in 'Thinking in sound: the cognitive psychology of human audition', (ed. S. McAdams and E. Bigand), 278-327; 1993, Oxford, Clarendon Press, 354 pp. This contains important recent evidence, and thoughtful discussion, bearing on the roles of genetic and individual memory in the development of perceptual processing.
33. R. L. GREGORY: 'The intelligent eye'; 1970, London, Weidenfeld and Nicolson, 191 pp. See especially p. 39 (Chap. 3).
34. J. P. FRISBY: 'Seeing'; 1979, Oxford, University Press, 160 pp. See especially pp. 110-111.
35. The relevant cortical processing timespans, though variable and not precisely known, are almost certainly of the order of tenths of a second (e.g. Ref. 32 p. 111-112); the subjective impression of still greater speed is likely to be an 'acausality illusion'. These points and the experimental evidence that bears on them will be discussed in Part II. What is important for the moment is that perceptual grouping takes place ahead of conscious thought.
36. J. MADDOX and D. C. MARR: Theorems of vision'; 1979, Radio interview in the series 'Mind, matter and mechanism' ('Scientifically Speaking', BBC Radio 3, 19 March 1979). See also Ref. 5.
37. J. MADDOX and D. C. MARR: Theorems of vision'; 1979, Radio interview in the series 'Mind, matter and mechanism' ('Scientifically Speaking', BBC Radio 3, 19 March 1979). See also Ref. 5.
38. R. N. SHEPARD: 'Mind sights'; 1990, New York, Freeman, 228 pp. 'Our perceptual experience of a stable, continuous, and enduring three dimensional surrounding retains no trace of the prodigiously complex neuronal machinery that so swiftly constructs that experience. Nor are we aware of the shifting, intermittent, pointillistic, upside down, curved, two dimensional patterns of retinal excitation from which the machinery of the brain constructs our visual world.' See also Sacks' description (Ref. 38, Chap. 1) of a case of brain damage that did, seemingly, allow some slight direct awareness of that same shifting, intermittent, pointillistic retinal imagery - enough to cause distress, disorientation, and inconvenience to the person concerned, the painter 'Jonathan I'.
39. G. L. BATESON: 'Style, grace and information in primitive art', in: 'Steps to an ecology of mind: collected essays on anthropology, psychiatry, evolution and epistemology', 101-125; 1972, San Francisco, CA, Chandler; Aylesbury, Intertext; Northvale, New Jersey, Jason Aronson. 510 pp. Gregory Bateson, son of the genetics and embryology pioneer William Bateson (1861-1926), began as an anthropologist working with, and marrying, Margaret Mead. His writings contain much wisdom.
40. There are philosophical traditions that use terms like 'sense data', 'sense perceptions', 'sense impressions', or 'Sinnesempfindungen' to mean not the raw sensory data but, rather, the percepts themselves, as apprehended subjectively. That, as Kant, Goethe, Popper, and other careful thinkers recognised long ago, begs all the questions about how perception works; indeed it begs just about every epistemological question there is. Parts II and III will give further discussion of this point, with reference to the cognate philosophical viewpoints called 'behaviourism', 'instrumentalism', and 'positivism'.
41. 5 and s. ULLMAN: 'The interpretation of visual motion'; 1979, Cambridge, MA, MIT Press, 229 pp.
42. 5 and s. ULLMAN: 'The interpretation of visual motion'; 1979, Cambridge, MA, MIT Press, 229 pp.
43. 2
44. 30 on conscious awareness, something that can occur whether or not it leads to perception, i.e., to awareness of something 'out there'. One can experience flashes of light without any sense of whence they come, as distinct from, for instance, being aware of a fire engine emitting flashes from a definite position 20 metres away.
45. 46 including the experiences famously reported by Poincaré and other great scientists.
46. 46 including the experiences famously reported by Poincaré and other great scientists.
47. M. PIATTELLI-PALMARINI: 'Inevitable illusions: how mistakes of reason rule our minds'; 1994, New York, Wiley, 242 pp. Mainly about the work of Amos Tversky and Daniel Kahneman on cognitive illusions and 'mind sets', or, as they call them, 'mental tunnels'. In the terminology used here, these can be understood as effects of prior-probability-driven combinatorial tree pruning. The book has a good collection of telling examples, including the famous 'three boxes' or 'three cards' trick. The trickster deals, face-down, three shuffled cards of which one is an ace. The victim chooses a card by putting a finger on its back. The trickster, who knows where the ace is, then removes another card that is not the ace and shows it to the victim. Most people, in the role of victim, intuitively feel - ahead of conscious thought - that given the new information their probability of having fingered the ace must now be 1/2. This is the brain's unconsious Occam's razor getting things wrong. It takes conscious mental effort to see that the probability is still 1/3 and that the probability of the remaining, unfingered card being the ace is now 2/3. See also Ref. 17, pp. 547, and Ref. 36. (Many sales pitches and incentives use exactly this kind of technique, as well as the more straightforward forms of camouflage and deception: Ref. 17, pp. 623-4, gives specific examples. See also M. Griffiths: 'Health and the National Lottery', Science and Public Affairs, Spring 1997, 5-7.).
48. M. PIATTELLI-PALMARINI: 'Inevitable illusions: how mistakes of reason rule our minds'; 1994, New York, Wiley, 242 pp. Mainly about the work of Amos Tversky and Daniel Kahneman on cognitive illusions and 'mind sets', or, as they call them, 'mental tunnels'. In the terminology used here, these can be understood as effects of prior-probability-driven combinatorial tree pruning. The book has a good collection of telling examples, including the famous 'three boxes' or 'three cards' trick. The trickster deals, face-down, three shuffled cards of which one is an ace. The victim chooses a card by putting a finger on its back. The trickster, who knows where the ace is, then removes another card that is not the ace and shows it to the victim. Most people, in the role of victim, intuitively feel - ahead of conscious thought - that given the new information their probability of having fingered the ace must now be 1/2. This is the brain's unconsious Occam's razor getting things wrong. It takes conscious mental effort to see that the probability is still 1/3 and that the probability of the remaining, unfingered card being the ace is now 2/3. See also Ref. 17, pp. 547, and Ref. 36. (Many sales pitches and incentives use exactly this kind of technique, as well as the more straightforward forms of camouflage and deception: Ref. 17, pp. 623-4, gives specific examples. See also M. Griffiths: 'Health and the National Lottery', Science and Public Affairs, Spring 1997, 5-7.).
49. E. DE BOND: 'Practical thinking'; 1971. Republished 1976, London and New York, Penguin, 189 pp. Discussion centres around a simple exercise in scientific model fitting, tried out on 1000 people, analysing 'why the black cylinder fell over', with insightful discussion of different kinds of mistakes and different kinds of correctness. 'The most important point is that mistakes arise directly from the way the mind handles information'; cf. Refs. 34, 35.
50. 70 artificial vision has even today come nowhere near rivalling human vision, despite the huge economic incentive and the decades of research effort.
51. O. SACKS: 'An anthropologist on Mars: seven paradoxical tales'; 1995. New York, Alfred Knopf, 330 pp. This is full of cogent lessons and wisdom about brain function, perception, and cognition drawn from clinical experience and shrewd observation. Of special interest here are the discussions of (i) colour vision, including Goethe's ideas and the Land effect (in the chapter on the colourblind painter 'Jonathan I.'), (ii) the work of the painter Franco Magnani, and (iii) the behaviour of the demonstrably blind, brain damaged, amnesic 'Greg F'. 'Greg' always insisted that he could see -and, for example, spent time 'watching' television -despite a total lack of visual data, implying, if taken at face value, the existence of a permanent adaptive visual hallucination. There is no mystery if we hypothesise the existence of an internal model having subjective visual force, for its own internal reasons, but being fitted to acoustic, tactile, and olefactory data alone.
52. 8 Again one sees the typical 'top down and bottom up' character.
53. 8 Again one sees the typical 'top down and bottom up' character.
54. 8 Again one sees the typical 'top down and bottom up' character.
55. 8
56. G. L. BATESON: 'Mind and nature: a necessary unity'; 1979, New York, Dutton; London, Wild wood then Fontana, 238 pp. This essay points out something that could hardly be more basic but is often overlooked, that juvenile play is essential for learning the difference between 'fact' and 'fiction', an abstract concept crucial to survival.
57. S. A. BARNETT: 'Of course, some of my best friends study Eng. Lit.', Interdisc. Sci. Rev., 1993, 18, 158-162. More remarks, from animal behaviourist, about the importance - the seriousness - of juvenile and adult play. Also a plea for universities 'to introduce courses orthogonal to the usual presentation of more and more about less and less.'
58. M. DAVIES-MITCHELL: 'Poetics now?', Europ. Rev., 1994, 2, 177-192. Professor Davies-Mitchell brings out the playfulness and elusiveness in poetry and introduces the reader to, among other delights, a marvellously musical riddle-poem by Seamus Heaney. She also delivers a splendid riposte to cultural nihilism: '...the demise of poetry... has frequently been predicted; but the patient, declared terminally ill one day, is reborn the next, proliferating like Proteus in new and surprising shapes - that capacity for self renewal offering proof, if proof were needed, that poetry, the writing and reading of it, is an intrinsic and essential aspect of human activity.' Like children's spontaneous storytelling, this is just what is to be expected on biological grounds - and it now seems likely that art forms that would today be called poetry must have been in existence for hundreds of thousands of years or more. I return to this in Part III.
59. H. MARKL: 'Language and the evolution of the human mind', Europ. Rev., 1997, 5, 1-19. A lively and perceptive survey by an animal behaviourist with a clear vision of the role of juvenile, and adult, play. There is also a useful bibliography of recent references, including many on primate behaviour and 'machiavellian intelligence'.
60. 30 The idea of ordinary perception as a model fitting process - as automatic, unconscious 'conjecture and refutation' - emerges clearly on p. 139. See also:
61. D. T. CAMPBELL: 'Evolutionary epistemology', in: 'The philosophy of Karl Popper'; Library of Living Philosophers, Vol. 14, (ed. P. A. Schilpp), 413-463; 1973, LaSalle, IL, USA, Open Court Press, 1323 pp. This surveys some relevant philosophical traditions from Kant onwards, expanding on Popper's aphorism that 'the growth of scientific knowledge may be said to be the growth of ordinary human knowledge writ large.' See also:
62. A. SHIMONY: 'Integral epistemology', in 'Search for a naturalistic world view', Vol. 1, 'Scientific methods and epistemology', 3-20; 1993, Cambridge, Cambridge University Press.
63. L. WOLPERT: 'The unnatural nature of science'; 1992, London, Faber, 191 pp. Gives much interesting history from the viewpoint not of a philosopher but of a leading scientist, and a very clear explanation of the difference between commonsense knowledge and scientific knowledge, with emphasis on the intellectual courage required to reach the latter, the courage required to take the scientific ideal seriously.
64. 35,36,62 The late John Bell ('Speakable and unspeakable in quantum mechanics', 166; 1987, Cambridge University Press, 212 pp.) has argued cogently to the effect that the term 'measurement', as often used in discussions of quantum mechanics, is likewise a self contradictory term.
65. 49 has been another notable contributor to this effort.
66. S. GOLDSTEIN: 'A theorist ignored: review of Infinite Potential: The Life and Times of David Bohm, by F. D. Peat', Science, 1997, 275, 1893-1894, and other papers at http://math.rutgers.edu/oldstein. See also reviews in Nature, 1997, 385, 592, by Chris Philippidis, and in Physics Today, 1997, 50, (3), 77-78, by James T. Cushing: '...this book does make a prima facie case for Bohm as a "fascinating and important scientist"... But it probably has not "given David Bohm his due".'
67. S. GOLDSTEIN: 'A theorist ignored: review of Infinite Potential: The Life and Times of David Bohm, by F. D. Peat', Science, 1997, 275, 1893-1894, and other papers at http://math.rutgers.edu/oldstein. See also reviews in Nature, 1997, 385, 592, by Chris Philippidis, and in Physics Today, 1997, 50, (3), 77-78, by James T. Cushing: '...this book does make a prima facie case for Bohm as a "fascinating and important scientist"... But it probably has not "given David Bohm his due".'
68. S. GOLDSTEIN: 'A theorist ignored: review of Infinite Potential: The Life and Times of David Bohm, by F. D. Peat', Science, 1997, 275, 1893-1894, and other papers at http://math.rutgers.edu/oldstein. See also reviews in Nature, 1997, 385, 592, by Chris Philippidis, and in Physics Today, 1997, 50, (3), 77-78, by James T. Cushing: '...this book does make a prima facie case for Bohm as a "fascinating and important scientist"... But it probably has not "given David Bohm his due".'
69. J. DERRIDA (transl. P.-A. Brault and M. B. Naas): 'The other heading: memories, responses and responsibilities', PMLA (Publ. Modern Lang. Assoc. Amer.), 1993, 108, 89-93. The phrase to which I refer comes from a sentence stated as an 'axiom' or 'law' on p. 90: 'What is proper to a culture is to not be identical to itself.' As with Fig. 4, this is designed to tickle our confusion-and-incoherence instinct. It is also a clever play on the words 'cultural identity'; the article is a kind of poetic meditation on what might be called cultural schizophrenia.
70. 8 The book is very clear on quantum mechanical fundamentals, and in this regard is an important reference for specialists and non-specialists alike.
71. I. STRAVINSKY: 'Poetics of music'; 1942, Cambridge, MA, Harvard University Press, 142 pp. A great composer presents, soberly yet passionately, a Platonic view of musical lucidity and of music as having 'a life of its own'.
72. I have discussed these matters with the composers Alexander Goehr, Robin Holloway, Virginia Seay Ploeser, Yuval Shay-El, Roderick Skeaping, and Hugh Wood, and heard corroborative remarks by Luciano Berio (BBC Radio 3, Promenade Concert interview, 29 July 1994), Julian Anderson (BBC Radio 3, Promenade Concert interview, 27 Aug 1994), and many others. Anderson's remarks, confirmed by Goehr (personal communication), were mainly about the composer Harrison Birtwistle and include a piece of history that seems to me artistically, psychologically, and biologically interesting, and relevant to my points about organic change and coherent ordering. It is also relevant to the crosscultural elements in music; see also Refs. 22 and 23 and Note 58. Anderson referred to a time in the middle of the twentieth century, the brief heyday of total serialism as embraced by the Darmstadt group, in which both Goehr and Birtwistle had been involved for reasons that included reaction against sterile academic musical conservatism. Total serialism, in some interpretations at least, had a taboo against repetition. It was held that, in Anderson's words, 'you couldn't repeat, and you certainly couldn't repeat rhythmically: it was regarded as passé.' Anderson continued, 'Sandy Goehr told me about a walk he took with Birtwistle, in about 1964 I think. And Birtwistle said quietly, 'You know, I do think it's time we started repeating things.' And then said nothing else. It wasn't until Tragoedia' came out the following year that Goehr realised exactly what he'd meant.' This was the first of a series of powerful, and now very influential, Birtwistle compositions that make extensive use of strongly rhythmic pattern-repetition.
73. A. PAY: 'Phrasing in contention', Early Music (Oxford University Press), 1996, 24, 291-321. A deeply perceptive essay by a world class musician, illuminating some of the profound connections between speech and music and noting some widely overlooked implications for musical performance. As Fowler's article on rhythm reminds us, speech for this purpose includes prose just as much as poetry. See also the remarks on perceptual grouping and perceptual units in Ref. 22.
74. Further examples of this type of pattern include Gershwin's 'I Got Rhythm', the 'Ode to Joy' from Beethoven's Ninth Symphony, Johann Strauss' 'Blue Danube' waltz, Leonard Bernstein's 'America' from 'West Side Story', Frederick Loewe's 'Wouldn't It Be Luverly' from 'My Fair Lady', Jeremiah Clarke's 'Trumpet Voluntary', the 'Goin' home' theme from Antonín Dvořák's 'New World' Symphony, and some of the themes from Igor Stravinsky's 'Rite of Spring'. Stravinsky's 'Rite', like much of his music, relies on patterns that are often rather irregular. (The composer Yuval Shay-El has pointed out to me that some of these patterns are like the elephant's feet in Fig. 4, playing on ambiguities between strong and weak beats.) Despite all this, however, the simple ABAC or 'surprising how often ... surprising how seldom ...' type of pattern is still conspicuous here and there. Examples are the principal melodic patterns at rehearsal numbers 91 and 94 and elsewhere in 'Mystic Circles of the Young Girls', (pp. 84-87 in the 1967 Boosey & Hawkes edition). Also essentially of the same type, despite subsidiary variations, are the opening of the second part, rehearsal number 79 (p. 76), and the theme of 'Glorification of the Chosen One', rehearsal number 104 (p. 91). In this last case one might quibble that the pattern is better described as ABA′B′, closer to 'surprising how often it happens that ..., and more surprising how often it happens, happens, happens again that ...'. Even the famous opening bassoon melody has a strong ABAC feeling, though broken up and interrupted - in detail, more like AA″AA′″, or, loosely, 'sur - prising how often it's surprising in some way, and surprising how seldom it isn't so surprise, well I mean, sur-'. This kind of variation, with interruption effects, is rather typical of the music of the 'Rite'.
75. 8 together with a few examples, including the so called 'Tristan chord', in an expanded version of this note in the file lucidity.ps.
76. A. GOEHR: 'Music as communication', in: 'Ways of communication', (ed. D. H. Mellor), 125-142; 1990, Cambridge, University Press. Alexander Goehr, one of our most respected masters of musical composition, has reminded me that in music and the other arts one has to include 'becoming coherent': there are many examples of musical 'shapes emerging from a... metaphorical mist'. His essay discusses this and other aspects of musical composition including aspects of the perception of music, and of the uses and associations of music in our own and other cultures.
77. W. A. MOZART: 'A Musical Joke'; 1787, K.522. Mozart's light-hearted dig at unskilful amateur composers and performers provides, among other things, examples of musical gratuitous (pseudoelegant) variation, such as the gratuitous modulation or key change at bars 37-38, and the gratuitous change in harmonic colour on the second beat of bar 38.
78. The basic techniques are care over first-occurrence signposting (see Appendix) and sufficient repetition of phrases that tie verbal to mathematical symbols (such as 'the potential energy P'). Such precautions - and generally being more explicit than the writer thinks necessary - can in turn reduce, even if not eliminate, the chances of the words and symbols being used inconsistently.
79. 12 but that is not fatal to the main message, which is that the artificial separation of numeracy and literacy is one of the ways in which nations damage themselves educationally, economically, and also politically through camouflage and deception by numbers - if you agree that the weakening of democracy counts as damage. The book points to known and tested educational countermeasures, referring especially to work by Constance Kazuko Kamii and collaborators. They have developed techniques that successfully use juvenile play to build numeroliteracy in young children.
80. S. WEINBERG: 'Dreams of a final theory - the search for the fundamental laws of nature'; 1993, Vintage Books, 260 pp. See especially pp. 64-66.
81. J. R. KLAUDER: 'Magic without magic' (John Archibald Wheeler Festschrift); 1972. San Francisco, CA, W. H. Freeman. See page 482; the quotation about 'genius' is attributed to Wheeler.
82. 10
83. 12 the biological reasons for which will be discussed in Part III. (A good illustration is the term 'symmetry breaking'. Nowadays this is often used in a trivial sense: becoming asymmetric because the externally imposed conditions are made asymmetric. The original, non-trivial sense is almost the opposite: becoming asymmetric despite the externally imposed conditions being symmetric. The original sense actually makes sense, literally, the externally imposed symmetry being the thing that is 'broken'. Symmetry breaking in this second, non-trivial sense now has to be called "spontaneous symmetry breaking" - at first occurrence at least - because of the trivialisation of the original, shorter term.)
84. 69
85. 7 of the word 'line'. There are 'nearly 150 predictable contexts..., which can be grouped into 30 or so senses', highlighting the ambiguity of the word 'line' when removed from the word pattern and context it is used in, e.g. 'high-voltage line', 'brought into line', 'what line to take', etc.
86. 67 which though mildly absurd does little harm. Careful choice of active or passive can be important for controlling rhythm and emphasis, e.g. to emphasise, or not to emphasise, the doer or the object of the doing. Such choice can also be important for controlling word order in the interests of lucidity. It is usually safest to put a pronoun close to its antecedent, the condition violated in Example 2′ above. Therefore the antecedent, the noun or other noun-like entity to which the pronoun refers, might need to occur late in the preceding clause or sentence whether or not it represents a doer. (I have sometimes thought that a significant aid to lucid writing might be a 'smart' word processor that could make the words 'this' and 'these' - the most dangerous pronouns because of their wide reach, hence scope for ambiguity - flash rapidly, or turn bright red, on the screen unless followed immediately by a noun or noun phrase that turns the pronoun into an adjective. Pronouns like 'it', 'they', 'them', 'their', 'none', etc., could perhaps flash a touch more slowly. This flashing of pronouns can usefully, in any case, take place in the writer's mind.)
87. 20 protein molecules in all, many of which are themselves logic gates.) See also Ref. 7 for an important independent critique of estimates of the kind in question, on purely computational and cognitive grounds.
88. 3