Besides the temporal linking of elements (including their more or less overt causal linking), which is constitutive of narrativity, there is also non-temporal linking, which is an important constructive device of narrative accounting for its semantic density. A linking is regarded as non-temporal if segments of the story or of the text, regardless of their position in time and irrespective of their causal embedding, are associated on the basis of properties they are perceived to share. The foremost manifestation of non-temporal linking, which is based on the paradigmatic structure of the text, is equivalence (Jakobson 1960), comprising both similarity and contrast. The dual nature of equivalence is expressed by Lotman’s ( 1977) synonymous term “co-opposition” (so-protivopostavlenie).
Equivalence means equality of two elements with regard to a certain value, i.e. identity of the elements in a particular feature and non-identity in others. In verbal texts, equivalence refers to features either of the text itself (formal equivalence) or of what is depicted in it (thematic equivalence). Thematic equivalence can refer to situations, characters, and actions. Situational and actional equivalence refers either to one and the same character (isofigural equivalence) or to different characters (heterofigural equivalence). Whereas in poetry, formal equivalence is based mainly on sound instrumentation and rhythm dominates, in classical prose narration it is thematic equivalence that takes the lead.
Equivalence has been promoted by Jakobson (1960) to a constitutive device of verbal art, i.e. of texts dominated by the poetic function. Although Jakobson does not restrict the sphere of poetic function to poetry, in his examples he concentrates on genres with a high degree of sound repetitions such as lyric verse, political slogans or common sayings. Twenty years later Jakobson expands the range of equivalence or, as he says now, of parallelism. According to him, parallelism is constitutive of poetry, but also occurs in narrative prose, for while parallelism is not so dominant in the areas of prosody, metrics, grammar and lexis, it can be found in larger thematic structures: “the composition of the plot, the characterization of the subjects and objects of the action, and the sequence of themes in the narrative” (Jakobson & Pomorska  1983: 107).
Equivalence produces, against the sequentiality of the story (Grabes → Sequentiality), a simultaneity (Margolin → Simultaneity in Narrative) of elements which are often distant from one another not only on the syntagmatic axis of the text, but also on the time axis of the story. As equivalences form non-temporal links between elements scattered across the text, the result could be called the work’s “spatial form,” to use Joseph Frank’s ( 1963) mistakable and often misunderstood term. In any case, equivalence competes with temporal links such as sequentiality and causality. These cannot be transformed into equivalences. Being before or after, being cause or effect are ontological designations of a completely different nature to being equivalent. The categorical difference between temporal and non-temporal linking cannot be dissolved.
Similarity and contrast, the manifestations of equivalence, can be represented as bundles of identities and non-identities concerning those features actualized by the story. Whether an equivalence appears as similarity or contrast is not decided by the number of identities and non-identities, but solely by the position that the corresponding features take in the story’s hierarchy. The process of hierarchization undergone by the features in a story can be very dynamic. When the story emphasizes a feature x in which two elements A and B are identical, the equivalence of A and B appears as a similarity. In another phase of the story, a feature y can be highlighted. If the elements A and B are non-identical in y, the equivalence appears as a contrast, regardless of in how many other, non-actualized features A and B coincide.
An equivalence, in particular a thematic equivalence, must be actualized in order for it to be noticed. The safest way to actualize an equivalence and to ensure its noticeability is its intersection with other equivalences, either on the same structural level or on another level.
The highlighting of specific features and the assignment of equivalences is a matter of interpretation. Although the equivalences do characterize and reciprocally determine one another, their identification and integration into a semantic thread remains an action to be performed by the reader. The actualization of potential equivalences contained in the work will always be only partial. This partialness is not only based on the number of equivalences, but also on their multiple relatability, which produces new results from each different analytical perspective. Of all the equivalences and equivalence relations available in a text, the reader will always select only the ones that correspond to the meaning s/he expects or wishes. Reception reduces the complexity of the work in that it selects those relations that become identifiable as meaningful within its particular horizon. In reading and interpreting, we therefore draw a thread through the thematic and formal equivalences and the thematic features that can be actualized in them, and we necessarily disregard an abundance of other features and equivalences (Schmid 1984).
Once euphonic and rhythmical repetitions enter into the formal equivalence, the narrative text approaches a prose type which is widespread in the literatures of post-realist modernism. That type is called “poetic” or, in Russian philology, “ornamental” prose (Schmid → Poetic or Ornamental Prose). Ornamentalism, however, is not merely a stylistic, but also a structural phenomenon which manifests itself as fully in the narrated story as in the texture. The formal equivalences overlay the linguistic syntagma of the narrative text, resulting in rhythmic patterns and sound repetition. The thematic equivalences project a network of non-temporal concatenation onto the temporal sequence of the story. In extreme ornamental prose, narrativity can be weakened to such a degree that no story whatsoever is told any more. The temporal links are then merely embryonic and no longer align the happenings with the continuity of a story. The unity of the work is provided instead by, as it were, simultaneously given equivalences. An example is the “Symphonies” by the Russian symbolist Andrej Belyj, which strive to implement musical composition in verbal art.
Equivalence plays an essential role not only in ornamental, but also in ‘normal’, action-oriented classical narrative prose without a peculiar sound elaboration of the texture, as in the novels of Tolstoj or Dostoevskij. These novels are by no means ornamental, yet they do contain a more or less overt paradigmatic design, as in the oppositions found in Tolstoj’s War and Peace (1868–69), for example. The situations denoted in the work’s title form an opposition that organizes the whole work, as do the juxtapositions of town and country, Petersburg and Moscow, French and Russian, Napoleon and Kutuzov. Not by chance, in a letter, Tolstoj (1936–64: LXII, 269) mentions the “labyrinth of linkages” that determines the message of his novel Anna Karenina (1875–77). In Dostoevskij’s Brothers Karamazov (1879–80) there is a superficial similarity between Ivan Karamazov and his followers such as Smerdjakov, Rakitin and Kolja Krasotkin. But on closer examination it appears that all of Ivan’s adepts realize only one of his different positions, whereas Ivan himself keeps changing his positions with each of the many treatises he writes. So instead of a similarity of views, we get a contrast of the adherents’ highly selective and fixed, if not to say petrified, worldviews on the one hand, and an ever-changing one of their idol on the other. In both cases, equivalence, whether in the form of dominating similarity or of contrast, plays a seminal role in the works’ signifying structures.
Among the functions of equivalence in narrative, at least five can be distinguished.
The first function is shared by narrative with persuasive texts, characterized by advertising and rhetoric. Such texts tend to use equivalence abundantly, either in the form of leitmotifs, where similarity clearly dominates, or in the form of equivalences proper, where the relationship between similarity and contrast is balanced. In both cases, parallelism serves the purpose of persuasion, as in Marc Antony’s “But Brutus is an honorable man.” An intermediate means to this aim is increased memorability and heightening of the power of suggestion.
Increased memorability and heightening of the power of suggestion are effective in narrative prose, as well. It is not seldom that leitmotifs contribute to these effects. For example, leitmotifs function as carriers of connotations. Tolstoj’s novels provide numerous cases of connotative leitmotifs: in War and Peace, to mention just one example, the “shortened upper lip of the little princess Bolkonskaja,” Andrej Bolkonkij’s wife, who is doomed to die during her first childbirth.
Another device that rhetoric and narrative have in common is shaping an equivalence between the beginning and the end of the text. However irrelevant the similar and dissimilar passages may be for the core of the message, the listener will get the impression that the speech is well structured. The effect of a well-wrought construction gives not only a certain aesthetic satisfaction, but will also be interpreted by the listener in the sense that the speech is well-thought-out and that its arguments are well-founded. This, of course, enhances the persuasiveness of the orator’s theses. Comparable effects can be observed in narrative where the ending, for the sake of an effect of well-structuredness, density, and closeness, is constructed equivalent to the beginning, sometimes leading authors to implement a “false ending” (Šklovskij [1921c] 1991: 56) consisting, say, of a description of nature which compensates for a lack of a real conclusion.
Equivalence of situations in a narrative can be compared to rhyme in verse. This is known as “situation rhyme” (Meijer 1958). According to Jakobson (1960: 372), “in poetry, any conspicuous similarity in sound is evaluated in respect to similarity and/or dissimilarity in meaning.” The linkage of two words by the similarity of their sounds produces hybrid semantic associations that Lotman ( 1977: 146) calls archisemes. It would be more correct to say “archisememes.”
An archisememe is an intersection or set union of sememes, or meanings of words. An archisememe can unite contrasting but compatible sememes such as “north” and “south” or “birth” and “death,” containing semantic features common to both sememes. In poetry an archisememe can unite sememes that may be completely incompatible. From a poem “I am Goya” by Andrej Voznesenskij, Lotman cites the sememes Goya (the name of the painter), gore (“grief”), golos (“voice”) and golod (“hunger”), all united into an archisememe. This archisememe exists solely on the basis of the sound similarity of the signifiers, is found only in this poem, is completely bound to its structure and is hard to explain in words.
A comparable semantic process can be observed in situation rhymes of narrative prose. We can thus speak of archisituations based on the equivalence of two or more situations.
In Anna Karenina, we have a striking resemblance of dream motifs that are shared by both Anna and Vronsky. It is the vision of a little and dreadful-looking peasant with a disheveled beard, working on something made of iron and murmuring some incomprehensible words in French. This vision enters Anna’s mind after her first encounter with Vronsky when a railway worker was run over by the train. After several occurrences, it reappears at her suicide under the wheels of the train. In this way, the nightmare contributes to the fatal end of Anna’s story.
Another example of Tolstoy’s art of shaping significant and psychologically motivated chains of equivalences is the motif of cutting a body into pieces. This motif establishes a tripartite chain that stretches across the whole part of the novel devoted to Anna. The motif occurs for the first time when Anna’s acquaintance with Vronsky is overshadowed by the accident in which the rail worker’s body is cut in two. The second occurrence is after the lovers’ consummation of their love. Vronsky is compared, evidently from Anna’s point of view, to a murderer, who “with fury, as it were with passion, […] falls on the body [he has robbed of life] and drags it and cuts it; so he covered her face and shoulders with kisses” (Part II, Chapter 11). Anna carries this image within herself until her destiny has been fulfilled under the slicing wheels of the train. With this concatenation of motifs, Anna’s death under the wheels of the train appears as the fulfillment of a schema of her fate which was sealed as early as her first encounter with Vronsky.
Thematic equivalences contribute to the semantic framework of a story in that they do not only shape a bridge between more or less remote passages of the text, but can convey certain connotations. Features foregrounded in them determine the categorical frames of the storyworld functioning as carriers of symbolic or symptomatic meanings.
In Anna Karenina, there is a set of physical details characterizing the heroine: “the little willful tendrils of her curly hair that would always break free about her neck and temples”; her “small, skillful, magic hands”; her “easy, resolute steps”—everything metonymically representing her liveliness and life force, and above all her often mentioned “narrowed eyes,” symbolizing her narrow perception of reality. During Anna’s lifetime, Vronsky’s even strong teeth are mentioned several times, but after her death he goes to the Serbian war with toothache. Anna’s hair and Vronsky’s teeth forming chains of leitmotifs, on the one hand, and contributing to a series of similarities and dissimilarities, on the other, become indicators of the characters’ inner situations.
To be narrative implies 1) a temporal structure with two states, the initial state and the final state, and 2) an equivalence of the initial and final states. With every story, the reader will concentrate primarily on the temporal links and their logic. In the interpretation of a narrative text, the first question to be asked is in what way initial and final states of the storyworld differ (cf. Stierle 1977: 217). The ascription of meaning in the reading of narrative texts aims to identify changes to the initial situation as well as the logic that underpins these changes. Not only the determining causes, but even the changes themselves are only rarely described explicitly and reliably and must therefore usually be reconstructed. In their reconstruction, the reader is called on to draw on equivalences. In many cases, it is only non-temporal linking that brings temporal changes and their logic to the surface.
It is not seldom that a change of state underlying a whole novel can be tracked only in many small and inconspicuous steps. An example is Thomas Mann’s novel Buddenbrooks, depicting the “decline of a family,” as stated in the subtitle of the German original. The changes between the many steps, however inconsiderable they may seem, manifest themselves in symptoms appearing not only in the characters and their behavior but also in small details of the setting. In Mann’s Buddenbrooks such symptomatic details form pairs of similarity and contrast that make the changes observable.
As in poetry, so in prose: equivalence generates structures which can be described in terms of gestalt psychology (Schmid 1977). But whereas in poetry the gestalt emerges from sound and rhythm, in prose it is mainly thematic units that form the material of the gestalten. Equivalences, together with their configurations and concatenations, project their patterns onto the storyworlds, giving them a specific character of structuredness. The effect is that Tolstoy’s worlds, for example, evoke an impression very different from Dostoevskij’s or Puškin’s.
The study of equivalence or parallelism in narrative was developed primarily by Russian formalists and scholars close to them. The essays by Šklovskij gathered in his collections (1921a, [1921b] 1991, [1921c] 1991,  1991) drew attention to the fundamental devices of sjužet construction such as parallelism, stepped construction, and the opposition of action and counter-action (cf. Hansen-Löve 1978). The representatives of the Russian theory of composition (esp. Petrovskij  1987, 1925, 1927; cf. Aumüller 2009) concentrated on functional aspects of novella composition. In postformalist times, Vinogradov (1934, 1941), inspired by sjužet and composition theory, made extensive observations on the paradigmatic construction of Puškin’s narrative prose. Jakobson, who as early as 1921 ( 1979) had studied varying forms of parallelism in poetry, including the “realization of an inverse parallelism” as a sjužet construction, introduced in 1935 the dichotomy of the paradigmatic chains—metaphor/similarity/poetry vs. metonymy/contiguity/prose—and he demonstrated their hybridization with the example of the poet Pasternak’s prose (1935).
Due to the fact that the theory of equivalence and parallelism had been formulated in Russia and that those phenomena took a significant position in Russian literature from Puškin to Tolstoj and to postrealist prose (Čexov, symbolism, avant-garde of the 1920s), further theoretical development of the concept in the West and its practical application to texts took place predominantly in the context of Russian philology.
A prominent part was played by Dutch Slavists. As early as 1958, Meijer examined “situation rhyme” in a novel by Dostoevskij (1958). Van Holk examined Puškin’s Coffin-maker, demonstrating that the tale is a “typical specimen of a poet’s prose in that its composition turns out to be extremely rigorous, while on the other hand the relationships between the personages remain elementary” (1968: 109). Van der Eng dealt theoretically with juxtapositions of motifs and chains of oppositions in narrative prose (1973, 1978a, 1993) and also analyzed different forms of paradigmatization in the prose of Puškin (1968) and Čexov (1978b, 1981), examining in particular progressive and regressive semantic accumulation.
In the vein of the Dutch research and referring to the Slavic tradition, Schmid formulated a theory of equivalence in prose narrative (1984), analyzed the semantic effects of intratextual motif paradigms in Puškin’s Tales of Belkin ( 2013), and provided interpretations of ornamental narrative in Čexov and Russian writers of the 1920s (1992, 1998).
The question that needs to be addressed most urgently is the sensual aspects of non-temporal linking. Formalist and structuralist interpretations are mostly satisfied with exploring the semantic results of the paradigmatic arrangement, but at the same time neglecting the non-cognitive side of the sjužet construction. This aspect is difficult to describe, but it exists nonetheless and plays a not insignificant role in our perception of narratives.