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Critical Calculations: Measure and Symmetry in Literature

Published online by Cambridge University Press:  01 December 2020

R. G. Peterson
R. G. Peterson*
Affiliation:
St. Olaf College, Northfield, Minnesota
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Abstract

Since 1937, critics have been discovering integrated into the structure of literary works various numerological and symmetrical patterns. Lines, chapters, books, episodes, characters, images, etc. are found in symbolic numbers like 3, 4, 10, 33, etc. and in symmetrical arrangements (concentric, triadic, or parallel). Both were known in classical times, but nowhere in surviving classical theory is there explicit recognition of any large-scale use of number or pattern in literature; nor are there important references in modern critical writing before this century. Nevertheless, even though the esthetic relevance of highly complicated or esoteric number systems is doubtful, many symmetrical (often concentric) and numerological patterns have been convincingly demonstrated in works from the Iliad to the Divine Comedy and Paradise Lost, as well as in other poems and novels from the Renaissance to the present. But problems remain as to what can properly be measured and what validates the patterns detected.

Type
Research Article
Information
PMLA , Volume 91 , Issue 3 , May 1976 , pp. 367 - 375
Copyright
Copyright © Modern Language Association of America, 1976

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References

Notes

1 Hieatt, Short Time's Endless Monument: The Symbolism of the Numbers in Edmund Spenser's Epithalamion (New York : Columbia Univ. Press, 1960).

2 Not quite, because David M Vieth discussed concentric structure at an MLA Seminar in.1969. This prompted more comments on the use of concentric structure by Dryden and other writers from the 17th and 18th centuries. See Vieth's own account, “Concept as Metaphor: Dryden's Attempted Stylistic Revolution,” in Language and Style, 3 (Summer 1970), 197—204. Some of the history of critical attention to this matter is evident in the many references in his addenda and notes. Vieth himself, in 1949, described the concentric structure of Pope's Windsor Forest (n. 10); and he recalls Frederick W. Hilles analyzing Tom Jones in this way in 1947 (n. 11). I am indebted to Roy Arthur Swanson who in 1960 introduced me to concentric structure in the Latin lyric poets and to David Vieth, with whom I have often discussed the subject over the last few years and who was kind enough to offer suggestions for the present essay.

3 Ernst Robert Curtius, European Literature in the Latin Middle Ages, trans. Willard R. Trask (1953; rpt. New York: Harper, 1963), p. 502. See also Murley, “The Structure and Proportion of Catullus LXIV,” Transactions of the American Philological Association, 68 (1937), 305–17, and Hopper, Medieval Number Symbolism: Its Sources, Meaning, and Influence on Thought and Expression (1938; rpt. New York: Cooper Square, 1969), pp. 136–201.

4 Whitman, Homer and the Heroic Tradition (1958; rpt. New York: Norton, 1965), pp. 257, 253.

5 The pattern is ABCDEEDCBA; of the 408-line poem, the 2 central sections (Ariadne's curse and Theseus' fate) take up 11. 124–248.

6 Duckworth, Structural Patterns in Vergil's Aeneid: A Study in Mathematical Composition (Ann Arbor: Univ. of Michigan Press, 1963), pp. 37–38. There are numerous references to works on the Golden Section and the Fibonacci series, but no ancients describe them in precise terms.

7 Scaglione, The Classical Theory of Composition from Its Origins to the Present: A Historical Study (Chapel Hill: Univ. of North Carolina Press, 1972), pp. 1–2.

8 Spitzer, Classical and Christian Ideas of World Harmony-Prolegomena to an Interpretation of the Word “Stimmung,” ed. Anna Granville Hatcher (Baltimore: Johns Hopkins Press, 1963), p. 67. For a recent and very complete account, see S. K. Heninger, Jr., Touches of Sweet Harmony: Pythagorean Cosmology and Renaissance Poetics (San Marino: The Hunt i 374 ington Library, 1974), esp. the section on “Doctrine,” pp. 71–284.

9 Butler, Number Symbolism (London: Routledge, 1970), pp. 2–4, 41, 55–56.

10 Heninger, chapter on “Poem as Literary Microcosm,” pp. 364–93.

11 “E.g., in the index to Ancient Literary Criticism, ed. D. A. Russell and M. Winterbottom (Oxford: Clarendon, 1972), there are listed 22 obvious uses, from the earliest fragments to Longinus.

12 For the analogy concentric squares would do as well, but 1 follow Butler following the ancients, Jung, and many others in regarding the circle as of primary importance as an “uncon scious and purely natural unity” (Butler, p. 164).

13 See David H. Porter, “Ring-Composition in Classical Literature and Contemporary Music,” Classical World, 65 (Sept. 1971), 1–8.

14 This is the implication of some of the diagrams (3–5) in Constantinos A. Doxiadis' 1937 study, Architectural Space in Ancient Greece, ed. & trans. Jaqueline Tyrwhitt (Cambridge, Mass.: MIT Press, 1972); for additional evidence of wide-spread concentricity and numerical patterning, see the text and illustrations of Joseph Campbell's The Mythic Image (Princeton: Princeton Univ. Press, 1974), esp. the sections entitled “The Calendric Round,” “The Revolving Sphere of Space-Time,” and “The Center of Transformation,” pp. 141–207.

15 With minor differences, the concentric structure was described in the headnote to Paradise Lost in the first edition of The Norton Anthology (New York: Norton, 1962), i, 912; John A. Shawcross discussed “The Balanced Structure of Paradise Lost” in Studies in Philology, 62 (1965), 697–718; Vieth put it on the list of concentric works at the end of “Concept as Metaphor,” p. 201; William B. Hunter in “The Center of Paradise Lost,” English Language Notes, 7 (1969), 32–34, pointed out that in the first edition the word “ascended” is “both preceded and followed by 5, 275 lines” and argued that Milton, in his additions to the 1674 version of the poem, tried to keep this word at the center.

16 Swing, The Fragile Leaves of the Sibyl: Dante's Master Plan (Westminster, Md.: Newman, 1962), pp. 75, 130–31.

17 Butler refers frequently to Pietro Bongo's Mystieae Numerontm Significationis Liber (Bergamo, 1585).

18 For studies of other works, see Alastair Fowler, Spenserand the Numbers of Time (London: Routledge, 1964) and the essays in Silent Poetry, ed. Fowler (London: Routledge, 1970).

19 As quoted by Bernard Weinberg in his History of Literary Criticism in the Italian Renaissance, 2 vols. (Chicago: Univ. of Chicago Press, 1961), ii, 716–19.

20 Discourses on the Heroic Poem, ed. & trans. Mariella Cavalchini and Irene Samuel (Oxford: Clarendon, 1973), pp. 60–61.

21 Notice, e.g., the satisfaction with which Douglas Brooks in Number and Pattern in the Eighteenth-Century Novel (London: Routledge, 1973), pp. 12, 17, n., comments on the way Alastair Fowler and J. C. Eade have added to the complexity of Hiealt's analysis of Epithalanuon; note also Brooks characterization (p. 26) of George A. Starr's numerological interpretation of Gray's Elegy as “elementary.”

22 Rose, Shakespearean Design (Cambridge, Mass.: Harvard Univ. Press, 1972), pp. 7–9.

23 Visible Words: A Study of Inscriptions in and as Books and Works of Art (Cambridge, Eng.: Cambridge Univ. Press, 1969), p. 51.

24 In making an exclusively formal analysis of a Poussin. Maurice de Sausmarez, in On Poussins “Orpheus and Eurydice,” Painters on Painting, ed. Carel Weight (London: Cassell, 1969), pp. 25–26, demonstrates the importance of geometrical substructures based on the Albertian Ratios, the Golden Section, and concentric circles but avoids claiming that Poussin worked consciously on the basis of these structures.

25 Battestin, The Providence of Wit: Aspects of Form in Augustan Literature and the Arts (Oxford: Clarendon, 1974), p. 149.

26 See Brooks, pp. 14–15 and Chs. i and v. To Shaftesbury, Battestin adds Francis Hutcheson (p. 15) and quotes from Isaac Hawkins Browne's poetical Essay on Design and Beauty (1739) lines to the effect that parts of a work of art though “wide dispers'd” should “harmoniously agree” and “in Proportion fall, / Till the Relation centers in a Whole” (p. 53).

27 See also Frederick W. Hilles, “The Plan of Clarissa,” Philological Quarterly, 45 (Jan. 1966), 236–8.

28 See, e.g., Hieatt, p. 81, Battestin, pp. vii, 270–71, and Heninger, p. 15; and, in contrast, Butler, pp. 159–78, for remarks on the possibility of an “aesthetic of proportion” in the 20th century.

29 For account and diagram, see Peter Salm, The Poem as Plant: A Biological View (Cleveland: Case Western Univ. Press, 1971), pp. 71–74.

30 Harry Levin described A Portrait as “symmetrically constructed,” in James Joyce: A Critical Introduction (Norfolk, Conn.: New Directions, 1941), p. 53.

31 Stuart Gilbert, James Joyce's Ulysses, 2nd ed., rev. (1952; rpt. New York: Random, 1955), pp. 212, 226; the “symmetry” is said to involve a prelude of 3 episodes, a central section of 12, and a finale (or nostos) of 3 (p. 31).

32 Seidlin, “The Lofty Game of Numbers: The Mynheer Peeperkorn Episode in Thomas Mann's Der Zauberberg,” ?MLA, 86 (1971), 924–39.