A Connectionist Model of Poetic Meter

A Connectionist Model of Poetic Meter

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A Connectionist Model of Poetic Meter

Abstract. Traditional analyses of meter are hampered by their inability to image the interaction of various elements which affect the stress patterns of a line of poetry or provide a system of notation fully amenable to computational analysis. To solve these problems, the connectionist models of James McClelland and David Rumelhart in Explorations in Parallel Distributed Processing (1988) are applied to the analysis of English poetic meter. The model graphically illustrates the dynamics of a poetic line and incorporates a number of features associated with the actual oral performance of a poetic text, while providing a notational system that allows mathematical analyses of poetic meter.

One of the salient features of poetry is its metrical structure. Many poets use regular patterns of stress to achieve specific aesthetic effects; readers expect such patterns and foreground them in their oral interpretations of the poems, whether they be read aloud or subvocally. Consider the opening line to Wordsworth's "Tintern Abbey": "Five years have past; five summers, with the length . . ." According to traditional "rules" of scansion, this iambic pentameter line would receive a heightened stress on the alternate even numbered syllables years, past, sum-, with, and length. Yet the repetition of the adjective five calls for some degree of emphasis upon each occurrence of the word, even though it is found in an unstressed position. But how much emphasis? More than the "stressed" with? More than years? Is the stress equal in both uses of five? And where does the stress or emphasis come from--from our act of interpretation or from an intonation pattern generated by the syntax?

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From a lexical accent or from an attempt to emphasize a key element in the prosody of the poem? Such questions are legitimate, for poetry is a highly rehearsed speech act; the speaker has made interpretive decisions concerning the role of each word in its context, although the speaker may or may not embody all those decisions directly in a performance of the poem. Likewise, the poet has made decisions concerning the relative impact of each word on the total rhythm of the line and has structured the poem in accordance with intended and sometimes fortuitous effects. This single line indicates the problems facing an analysis of metrical patterns within a line of poetry. A full understanding its metrical rhythm--i.e., the stress pattern rendered in the performance of a poem that interacts with what Jacobson (1960) terms the "verse design" underlying the structure of a line--requires us to consider both a linguistic analysis of the line and the interpretations a reader might make of the line's meaning, the force of individual words within the line, the effect of various prosodic devices a poet might use.

The traditional or classical approach to metrical analysis has been by way of a notational system and a terminology borrowed from Latin quantitative verse. The system has been surprisingly resilient, primarily because of its simplicity and flexibility; traditional metrics is still widely taught in poetry classes. Dividing a line into units (feet) has allowed the creation of a vocabulary to describe some of the perceived effects of poetry. That poets themselves were aware of this system and consciously experimented with meter in its terms has helped justify it and has masked its shortcomings.

Chief among these shortcomings has been traditional metrics' inability to account for the interaction between all units in the line: to consider the line, that is, as a whole. Similarly, traditional metrics has no way to distinguish degrees of metricality or to decide if a line is metrical or not. Halle and Keyser (1971) provided an alternative mapping of poetic meter, devising a series of generative rules making use of syntactic boundaries to provide a measure of complexity and, ultimately, of metricality. Kiparsky (1975, 1977) incorporated the deep structure of words and phrases to account for certain ambiguities in Halle and Keyser's work. Among the more important innovations of Kiparsky's analysis was the distinction between metrical and prosodic rules; metrical rules generate from a set of basic patterns the abstract metrical patterns underlying the verse, while prosodic rules show how the metrical patterns may be linked to linguistic representations (Harvey, 1980). The ways these rules are phrased and the circumstances under which they are violated could be particularized to individual poets.

Since Kiparsky's articles, the most interesting work has been in grid based theories (Hayes, 1983; 1984; 1987; 1989), in Attridge's (1982; 1987; 1989) system of base rules and deviation rules, and in statistical analyses (Youmans, 1986; 1989a, b; Gasparov, 1987). These systems of analysis are strongest in their ability to describe both what is permissible in particular linguistic settings and ways in which individual poets have defined which rules must be adhered to and which may be violated in systematic ways.

There are, however, two areas which may have significance for an understanding of poetic meter which are not dealt with strongly by systems of generative metrics. First, as suggested above, a reader's interpretation of a poem will affect the production of a metrical pattern for a particular line. In the line from Wordsworth cited above, one reader might choose to emphasize the exact number of years, "five years" and "five summers." Another might focus on the time periods, "five years" and "five summers." According to generative metrics, and according to traditional metrics as well, both readings are allowable, though the first involves several permissable rule violations, creating a degree of complexity or tension in the line. Similarly, the repetition of sounds in a line of poetry, whether through assonance, alliteration, rhyme, or the repetition of an entire word, such as "five," might well be emphasized by a reader, again affecting the actual stress pattern which emerges in a performance. Which reading is chosen, and hence which metrical pattern appears in a performance, will depend not only upon the outcome of linguistic rules, but also upon the interaction of these rules with interpretive decisions made by the reader.

Another area of difficulty in both traditional and generative systems of metrical analysis is notation. Stress is most often listed as a binary value (strong or weak), a trinary value (as in grid based systems), or a quadrinary value (Harvey, 1980). Even when such values are understood as relational rather than as absolute values, there are difficulties in quantifying such values. Indeed, some systems of analysis are made even more difficult to quantify by the use of symbols, such as w S, +s -s, o B, ' ` , underlining, and, in grid theories, one or more x's above a word. Mathematical systems of analysis, however, such as Blain's (1987) model of alliteration, require a notational system that can be used computationally.

What connectionist model provides for metrical analysis is a system that, first, will account for the contribution of both linguistic elements, as in systems of generative metrics, and a reader's interpretions to the rhythm of the poetic line; second, will describe features in possible performances of the verse; and third, will provide a notational system useful for mathematical analysis. This model represents a way of looking at meter which complements that of generative metrics in that it considers the role of underlying lexical and syntactic structures in creating stress patterns. Yet it seeks to create not an fixed analysis of permissable structures and violations, but rather a model of performance which will be useful in understanding both the ways by which readers might arrive at the rendering of a line of poetry and the differences readers perceive between metrical regularity and metrical complexity. I will suggest as well that the model might be useful for quantifying distinctions between the works of individual poets.

The use of connectionist frameworks to model psychological processes has been detailed by McClelland (1988). Briefly, connectionist or parallel distributed processing models view cognitive processing not as as a strictly linear operation or sequential series of operations but as an active and simultaneous interplay between a number of individual but interconnected units. As Rumelhart and McClelland (1986) say, "These models assume that information processing takes place through the interactions of a large number of simple processing elements called units, each sending excitory and inhibitory signals to other units. In some cases, the units stand for possible hypotheses about such things as the letters in a particular display or the syntactic roles of the words in a particular sentence. In these cases, the activations stand roughly for the strengths associated with the different possible hypotheses, and the interconnections among the units stand for the constraints the system knows to exist between the hypotheses" (10). The activation of units spreads from one to the next, the amount of activation dependent on the strength or weight of the connection between the units, the initial input to the system, and the bias of the unit, or its inherent tendency towards activation. Because the units are interconnected, the activation of any one unit tends to affect the system as a whole, though because not all units are directly connected to one another or connected in the same ways, the system is neither simple nor linear. Measuring the activation of a particular unit takes place repeatedly--an updating--as the unit continues to be affected by, and to affect, changes in activation of the units surrounding it. The system is not strictly linear, for the updatings occur randomly; any two runs of the system will have different configurations, though they eventually tend toward similar patterns. Connectionist models have been used to examine a number of situations involving learning, language processing, perception, decision making, and other cognitive functions (see, for example, Dell, 1989; Elman, 1989; Kintsch 1988, 1990; Rumelhart & McClelland, 1988. For a critique of connectionist models see Fodor & Pylyshyn, 1988.)

The particular connectionist model I have chosen to apply to an analysis of poetic meter is a constraint satisfaction model. The model is useful for analyzing cases in which there are competing constraints or possible solutions to a problem which need to be reconciled or satisfied. McClelland and Rumelhart (1988) describe the constraint satisfaction model as a system comprised of units, wherein "each unit represents a hypothesis and each connection a constraint among hypotheses. Thus, for example, if whenever hypothesis A is true, hypothesis B is usually true, we would have a positive connection from unit A to unit B. If, other the other hand, hypothesis A provides evidence against hypthesis B, we would have a negative connection from unit A to B" (50). Some of the constraints may be seen as more important than others, reflected by a large weight in the connection strength of that constraint. There is also the possibility of a unit receiving external evidence, which McClelland and Rumelhart construe as "direct evidence for certain hypotheses" (50). Finally, there is the possibility for an a priori probability for a particular hypothesis, a bias which operates without additional evidence. In this model the system attempts to satisfy as many constraints as possible, balancing the number and strengths of the connections between the units, the initial inputs, and the initial bias. This model has been fruitful in analyzing events as simple as the perception of a Neckar Cube and as complex as the choice of scientific theories or juried legal decisions (Thagard 1989). A computer model is provided by McClelland and Rumelhart (1988).

In the case of poetry based upon an accentual-syllabic metrical system, such as English iambic pentameter verse, we might say that for each syllable in a line of poetry there is a unit representing a hypothetical amount of emphasis or stress for that syllable. The line--which I have termed the "metrical line," for it is here that the meter is finally realized--then consists of ten sequential units. In iambic poetry, the underlying pattern is of alternating weak and strong stresses; the model reflects this with a bias or a priori probability built in to the system that even numbered units will be stressed. Each unit in this metrical line is connected to other units in the system, which act as constraints on the amount of stress that each "metrical line" unit achieves. Into these other units inputs representing evidence favoring the possibility of stress might be placed. The probability that a particular syllable or unit in the metrical line will receive stress will be the result of all the constraints that act upon that unit which serve to encourage or suppress that probability. In this particular model, units in the metrical line are connected to five other types of units, representing intonation, lexical stress, prosodic features, propositional features, and interpretive decisions.

The first constraint to be considered is intonation. There is a positively weighted connection between the pitch of a syllable achieved by virtue of its intonation and the amount of stress the syllable receives when spoken. This is rendered as an input to each unit reflecting the intonation of each particular syllable in the line. The lexical features of individual words making up the line are the second constraint; each unit in the metrical line is connected to a unit representing lexical stress. The stress features of polysyllables are marked as inputs to the system. In addition, as these lexical features are related to intonation, there is a connection between lexical and intonational units as well. The prosodic features of the line (rhyme, assonance, alliteration, and so on), represent another set of possible constraints on the stress a syllable might achieve; a reader might accentuate alliteration through stress, for example. Thus each unit on the metrical line is connected to a unit representing a prosodic constraint, allowing a third set of inputs to the system. Stress might also be related to the significance of a word within the text base of the line. The main propositions within this text base receive an input. These units are also connected to those representing intonation and to those representing the fifth and last constraint, the reader's interpretation. Finally, words a reader deems important to the poem's interpretation may have an increased probability of being stressed and are given an input. The relative importance of each of these five constraints can be (and is) varied by the reader. Is alliteration emphasized? Should a play on words be foregrounded? Since intonation is affected by the meaning and each reader makes interpretative decisions about meaning, various renditions of the line are likely. However, within the range of possibilities, certain patterns emerge, as will be seen. The particular manner in which the stress is manifested may vary from reader to reader and from performance to performance.

In short, in this constraint satisfaction model of iambic pentameter verse, each unit representing the potential for being stressed is connected to five other units representing intonation, lexical stress, prosodic features, propositional features, and interpretative decisions. I have built into the system a bias towards stress in alternate, even-numbered positions. I have also built in negatively weighted connections between adjacent positions, with a greater negative weight to the following position, and a smaller negative weight to the preceding position. This bias and the negatively weighting of adjacent positions tend to force the line towards an iambic pattern, although not so strongly as to overcome high initial inputs in normally weak positions. In addition, some of the units are connected not only to units in the metrical line, but to each other as well. I have posited weak, positive connections between intonation and the lexical, propositional, and interpretative lines, and a weak positive connection between proposition and interpretation.

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