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The "Golden Section" and the Metaphysics of Pushkin's Verse

            I would like to explore the question of how the reader perceives particular elements of this process—elements such as harmony, expression, and heightened emotion. More specifically, I will be asking how rhythm, which "directly accompanies meaning,"[2] involves the reader in the poetic text, and I will try to identify the ways in which rhythm contributes to this involvement. These sensations are, indeed, always spontaneous and unmediated. They arise during the actual utterance of the text and shape the artistic image of the content, in constant interaction with the consciousness and the subconscious (with a slight temporal delay in the shaping of that image). In accordance with Belyj's views on the question of the unity of the rhythm and content of verse, and conceiving of the role of rhythm as a "particularly artistic rhythmic responsiveness,"[3] I intend to address another crucial question, heretofore unanswered, in the study of prosody. Тhis is the question of whether there are ways of revealing and formally establishing this particular rhythmic responsiveness or agitation, and if so, exploring the degree to which it corresponds to the emotional and thematic aspects of concrete excerpts of a poetic text. Such issues are among the most complex and delicate in humanistic scholarship, and the sophistication of the methods used to examine them, and, in the final analysis, the actual approach to the problem of correspondence between the forms of the poetic text and its esthetic content, leaves much to be desired.


Prosody, Mathematics, and the "Golden Section"


            The necessity of resorting to the term "subjective time" becomes more intelligible if one recalls a fact that has been established in experimental psychology, that fact being that "for a person experiencing positive emotions, the subjective flow of time speeds up; in the presence of negative emotional experiences, a subjective retardation of time may be observed."[4] The words of Stefan Zweig are particularly apt in this regard: "In the life of a human being, external and internal time coincide only partially; only the fullness of experience may serve as the measure of the soul; the soul counts the internal passage of hours in its own way—not as the indifferent calendar does."[5]

            In order to answer these questions, I will begin by examining the notions of "subjective time" and the "rhythm" of verse, as well as the applicability of well-known prosodic concepts to the questions I have articulated. I wish to point out that due to their basic premises, neither the methodology of structural prosody, nor the framework of that approach that has come to be known most widely as "meter and meaning," promise the scholar the slightest chance of success in his endeavors.[6]  The matter is further complicated by the fact that we are concerned here with artistic time and space, that is, with that which arises in the reader not during the process of perception of objective reality (nature, one's external environment, or other people), but during the process of undergoing the actual effects produced by the reading of literary (esthetically significant) texts.

            The essence of the problem consists in the fact that the study of the form and content of verse is much more complex, not so much due to the absence of other—not static, but dynamic—procedures for the analysis of rhythm in verse, but because the rhythm of Russian verse as a division of contemporary prosody rests on the notion of rhythm as alternation of stressed and unstressed syllables (elements of the motion of articulatory force with contrasting significance).[7] Indeed, any movement (from the periodic, and even strictly ordered, to the chaotic) alwaysinvolves an alternation of contrasting states of a certain object. Rhythm, however, is something different, though it involves the same alternating and contrasting states.

            In order to create the conditions for studying such elusive and equivocal material as the experiential and sensory aspects of the poetic text, one must acknowledge, first, that rhythm is a relationship,[8] and not an alternation of stressed and unstressed syllables (in Russian verse), and, second, one must abandon the flawed theory that rhythm may be posited as some sort of average in a predictable (according to the statistical mean) poetic line. This is tantamount to measuring the average temperature of all the patients in a hospital, and has nothing to do with the actual perception of a poetic text.

            In my work, I assume the rhythm of verse to mean the measure of the harmonious ordering of movement of poetic thought, determined by the mutual relationship of stressed and unstressed syllables in a Russian poetic text. This mutual relationship is not absolute, but relative; it is measured as the deviation of the real rhythm from the harmonic rhythm.[9] The harmonic rhythm, in its turn, is defined as the proportion of the "golden section" at the key (rhymed) points in a verse. The dynamic principle of the "golden section" enables one to unite three characteristics of a poetic text—rhythm, rhyme, and stanzaic structure—under a single criterion. Note that none of the prominent scholarly methods for studying poetic texts is able to achieve this. Moreover, the importance of a systematic approach in analyzing the architectonics of the poetic text was stressed by V.M Zhirmunsky more than 80 years ago, when he cited the words of Hugo, saying "rhyme is the measure of verse that has become perceptible to the ear," as well as the words of B. de Fouquier: "As soon as we cease to perceive rhyme, rhythm is immediately disrupted."[10]

            Another more general aspect of the problem concerns the question of the use in literary scholarship of mathematical methods, and even the expediency of such practices. On the one hand, classical literary scholarship avoids mathematical research as applied to the analysis of prosody, and there are grounds for avoiding it.  One of the primary reasons for this is that the method that has reigned in prosody for nearly one hundred years is the statistical method, and even probability theory—that "mistaken" method (S. M. Bondi) that militates against even the hope of studying the artistic expressiveness of poetic texts. On the other hand, the methods based on "divine" proportions of rhythm (the "golden section"), were never applied in prosody until the very end of the 20th century. For this reason, the deeply rooted skepticism of literary scholars was perfectly logical and understandable. In order to explain why I hold fast to another point of view, it is sufficient to recall the words of two great thinkers. The first is Kant, who wrote:  "In every science, there is as much truth as there is mathematics." The second is Stendhal: "Of all the sciences, I love mathematics most, as it admits of absolutely no hypocrisy."[11]


Poetic Material and Prosodic Concepts


            To illustrate my claims I have chosen two excerpts from Pushkin's novel in verse, Eugene Onegin. In Pushkin's work, "road" verses are most immediately represented in "Excerpts from ‘Onegin's Journey'," but they are not confined to these passages. I was drawn to two shorter, but no less compelling, parts of the work: stanzas from the third and fifth chapters, in which Tatiana "flees." In the first example, Tatiana flees while "wide-awake" from the inexorable approach of the meeting with Onegin (which we are led to understand takes place in the fourth chapter). Then, in the fifth chapter, Tatiana flees in her "dream" from the "unbearable" bear (cf. Table). These very closely related motifs of "flight" have, in both cases, the "semantic aureole" (borrowing the terminology of M.L. Gasparov) of the road.

            However, it is not the semantic aureole in and of itself that interests me, that "aggregate of all the semantic nuances of a given example"[12], but the particular and concrete "expressive aura" (V.V. Vinogradov's term[13]). To be even more specific, what interests me is the rhythmic and expressive aura that emerges in reading the disparate passages of Eugene Onegin that express with the greatest emotional and semantic urgency the actions of the novel's heroine. There is no doubt that in the two passages I have cited, which occur in close proximity in the narrative, the emotional states of Tatiana are distinctly different. In the third chapter, her emotional state could be described as confusion, alarm (albeit a romantically colored alarm), while in the episode from Tatiana's "dream," she is in a state of deep-seated fear or dread, which turns into resigned hopelessness.

            It is important here to recall the concept of associative semantic fields, well known in linguistics. The associative field for "rhythm" is formed from the following attributes or modifiers: "precise, ragged, strict, slow, quick, headlong or impetuous, mad" («четкий, рваный, жесткий, медленный, быстрый, стремительный, бешенный»), and others.  For "breathing" or "breath" the field is quite different: "fresh, heavy, even, frequent, free, hot, uneven, intermittent, timid, labored, calm, quickened, difficult" («свежее, тяжелое, ровное, частое, свободное, горячее, неровное, прерывистое, робкое, сдавленное, спокойное, учащенное, трудное»), and others.[14] The attempt to align such associative fields with the possibilities of the central device of the Structuralists, i.e. with the "rhythmic profiles" of verse, is doomed to failure. The axiomatic position of the structuralist critics, who claim that an "organic connection between the rhythm and the theme is usually absent,"[15] is logically presupposed by the very means of analysis of rhythm in verse, which only allows for establishing "rhythmic profiles," and has its origins in the notion of the "early" Belyj that "rhythm is symmetry in deviation from meter."[16] S.M. Bondi considered this theory to be "mistaken.".[17] According to M.L. Gasparov, Bondi's "attitude toward these calculations and graphs was one of restrained hostility: why spend so much time counting, when it is audible without it?"[18]

            I will begin my examination of the fundamental traits of poetic material by looking at a number of important and well-known compositional and architectonic features of the two episodes in Pushkin's novel.

            First, the passages presenting Tatiana's "flight" to the reader are distributed differently in their respective chapters. The "flight wide-awake" is found at the very end of the third chapter (stanza XXXVIII), and the "dream flight" is presented in the first third of the fifth chapter (stanzas XIII and XIV).

            Second, in both passages Tatiana's "flight" ends in the same way: the heroine falls. In the first case, she falls on a bench, and in the second, in the snow. In the first case, however, both the nature of the flight, and the rhythmic, and overall stylistic, means that Pushkin employs are distinct from those he uses in the fifth chapter.

            In contrast to the "dream flight," during the "flight wide-awake" everything is more emotionally urgent and dynamic, and one can speak of headlong, rushing movement. When she is awake, the heroine not only runs, she "flies, flies…" (летит, летит…») (line 8a). Toward the end of the episode this impression is amplified still more by the use of the gerundial form "…flying toward the stream" («…летякручью») (line 13a). There is other, equally compelling, evidence of the intense expressiveness of this episode. The entire length of the excerpt (11 lines, from 5a to 15a) is two and a half times shorter than the contrasting episode in the fifth chapter (29 lines, from 1b to 29 b), and the non-coincidence of the metrical, syntactic, and stanzaic boundaries of the narrative in the "flight wide-awake" episode acquire "an intense dramatic expressiveness."[19] In fact, the text of stanza XXXVIII ends with a classic example of stanzaic enjambment (the split-level line 15a). Earlier in the stanza, the reader encounters a line enjambment: «Летит, летит; взглянутьназад/ Несмеет» ("She flies, she flies; to look back / She does not dare") (lines 8a-9a).


Fragments of the Text from Pushkin's Novel

a) Chapter 3, Tatiana's "flight wide-awake"

b) Chapter 5, Tatinana's "dream flight"






Но день протек, и нет ответа.


Как на досадную разлуку,


Другой настал: все нет, как нет.


Татьяна ропщет на ручей;


Бледна как тень, с утра одета,


Не видит никого, кто руку


Татьяна ждет: когда ж ответ?


С той стороны подал бы ей;


Приехал Ольгин обожатель.


Но вдруг сугроб зашевелился,


"Скажите: где же ваш приятель?–


И кто ж из-под него явился?


Ему вопрос хозяйки был.–


Большой, взъерошенный медведь;


Он что-то нас совсем забыл".


Татьяна ах! а он реветь,


Татьяна, вспыхнув, задрожала.


И лапу с острыми когтями


– Сегодня быть он обещал,–


Ей протянул; она скрепясь


Старушке Ленский отвечал,–


Дрожащей ручкой оперлась


Да, видно, почта задержала.


И боязливыми шагами


Татьяна потупила взор,


Перебралась через ручей;


Как будто слыша злой укор.


Пошла - и что ж? медведь за ней!






Смеркалось; на столе блистая

1 b

Она, взглянуть назад не смея,


Шипел вечерний самовар.


Поспешный ускоряет шаг;


Китайский чайник нагревая,


Но от косматого лакея


Под ним клубился легкий пар.


Не может убежать никак;


Разлитый Ольгиной рукою,


Кряхтя, валит медведь несносный;


По чашкам темною струею


Пред ними лес; недвижны сосны


Уже душистый чай бежал,


В своей нахмуренной красе;


И сливки мальчик подавал;


Отягчены их ветви все


Татьяна пред окном стояла,


Клоками снега; сквозь вершины


На стекла хладные дыша,


Осин, берез и лип нагих


Задумавшись, моя душа,


Сияет луч светил ночных;


Прелестным пальчиком писала


Дороги нет; кусты, стремнины


На отуманенном стекле


Метелью все занесены,


Заветный вензель 0 да Е.


Глубоко в снег погружены.



1 а

И между тем, душа в ней ныла,


Татьяна в лес; медведь за нею;

2 а

И слез был полон томный взор.


Снег рыхлый по колено ей;

3 а

Вдруг топот!.. кровь ее застыла.


То длинный сук ее за шею

4 а

Вот ближе! скачут... и на двор


Зацепит вдруг, то из ушей

5 а

Евгений! "Ах!" - и легче тени


Златые серьги вырвет силой;

6 а

Татьяна прыг в другие сени,


То в хрупком снеге с ножки милой

7 а

С крыльца на двор, и прямо в сад,


Увязнет мокрый башмачок;

8 а

Летит, летит; взглянуть назад


То выронит она платок;

9 а

Не смеет; мигом обежала


Поднять ей некогда; боится,

10 а

Куртины, мостики, лужок,


Медведя слышит за собой,

11 а

Аллею к озеру, лесок,


И даже трепетной рукой

12 а

Кусты сирен переломала,


Одежды край поднять стыдится;

13 а

По цветникам летя к ручью,


Она бежит, он всё вослед:

14 а

И задыхаясь, на скамью


И сил уже бежать ей нет.



15 а



Упала в снег; медведь проворно…

«Здесь он! здесь Евгений!


            In contrast to this unaccountable impetuousness, the movements of the heroine in the passage from Tatiana's "dream" begins with only an "acceleration" of her steps, which are no more than "hurried," and between the two lines with the word «бежит» ("runs") (4b and 27b), significant space is devoted to a description of nature in winter (lines 6b to 14b). The general dynamic of the narrative is thus checked, and there is a pause in the development of the motif of "flight."

            This impeded action is reflected by the very verbal lexicon and syntax of stanza XIV: «снегрыхлыйпоколеноей», «сук…зацепит», «увязнетмокрыйбашмачок», «выронитонаплаток» ("the loose snow is up to her knees," "a branch…snags," "her wet shoe gets stuck," "she drops her shawl"). There are no line enjambments in the either stanza XIII or XIV of the fifth chapter, nor is there any stanzaic enjambment. The narrative here is on the whole more equable and calm. As regards the extra-schematic stress (spondee) in the second line of stanza XIV («Снегрыхлый», line 16b), it no doubt disrupts the smoothness of speech, but in its alternation with fully stressed lines it is not very conspicuous. In the third chapter, a marker nearly identical in strength («Вдругтопот!…» in line 3a) portends the beginning of Tatiana's "flight"; it is precisely here that a new thematic turn arises, and in this brief exclamation of surprise the spondee is significantly more emotional and expressive.

            In principle, I could end this short critical analysis of some features of the rhythm of the two episodes of Tatiana's "flight" here; but only in the case that one considers no mathematics to be necessary, since it is audible without it.

            I hold another view, and the fact that the formal apparatus of my study is based on a kind of mathematics, which, I repeat, was simply not utilized during Bondi's time, is particularly germane to my argument. This is the mathematics of harmony.[20]

            To continue this discussion, it is important to recall that "short phrases and sentences in Pushkin's style are not only dynamic, but also expressively diverse"[21]; "stanzaic enjambment… is a result of a delicate and difficult rhythmic and compositional device that amplifies and deepens the tone of a story by means of intentionally transgressing the break between stanzas"[22]; that in Pushkin these rhythmical effects "always harmonize with the content of the story"[23]; and that in the third chapter "this device expresses perfectly Tatiana's agitated state."[24]

            I would like to point out several facts that are related to the traditional prosodic parameters of the poetic text and are connected, in the first place, with an analysis of the mean of the number of stressed syllables in lines and stanzas (Tстркand Tстрф, respectively).

            The mean of the tonic volume of the stanzas (Тср) overall for the third and fifth chapters of the novel are closely comparable (44.95 and 44.89 stressed syllables). Against this background, Tatiana's "flight" episodes are clearly demarcated statistically: 47,30 stressed syllables in the "flight wide-awake" and 46.25 for the "dream flight." Furthermore, while in the beginning of stanza XXXVIII ("flight wide-awake") the retardation of speech is clearly felt (all eight of the first lines of stanza XXXVIII are fully stressed), a certain acceleration begins in line 9 with the line enjambment «несмеет…»: five lines have three stresses each, and the last line has only two. This kind of consistent reduction of the mean number of stressed syllables in a line (Tстрк)is present neither in stanza XIII, nor in stanza XIV of the fifth chapter ("dream flight"). Furthermore, it is evident that line 13a is the only line in the stanza which omits a stress on the first metric foot («Поцветникамлетякручью»); it is then followed by the only line containing just two stresses, which ends syntactically in the first line of the next stanza with the word «Упала…», constituting an internal rhyme with lines from the previous stanza: «обежала—переломала—упала» (9a—12a—15a).

            Thus, the reduced number of stressed syllables toward the end of the "flight wide-awake," the Tстркmean, attests to an acceleration of movement, or (amounting to the same thing) an increasing tempo in the reading of the text. At the same time, the number of rhythmically conditioned events (semantically differentiating tensions of vocal participation) toward the end of the stanza decreases. If one defines time in the usual way as the number of significant events in an entity of objective time-space, the reader's subjective experience of time is amplified (i.e., time moves more slowly) from the beginning of the stanza to its close. In this case, the given entity is the fixed volume of stressed syllables in the Onegin stanza, which equals 118.

            This conclusion, however, contradicts what I claimed above, namely that Tatiana's "flight wide-awake" is characterized by a positive emotional state. After long expecting a response from Onegin, and on the threshold of a meeting with him, a strongly desired meeting that has just become inevitable, we might assume that Tatiana could have no other possible feelings. In that case, however, according to psychological findings, Tatiana's subjective experience of time (and that of the reader who experiences it sympathetically with her) should speed up (as the number of events increases), and not slow down, as my analysis of the text above suggests is the case. This leads us to conclude that the psychological effect of acceleration (or deceleration) of the subjective experience of time is not determined by a simple alteration in the number of events in an entity of objective time, but, as I will demonstrate below, the rate of the change in rhythm of the poetic text. More specifically, it is not only the speed, but the vector of change, rising in the presence of positive emotions and falling in the presence of negative ones, that is significant (cf. graphs 2 and 3).

            I should add that the empirical data do not support the more superficial conclusion that there is a clear relationship between the positive emotional state of Tatiana and the increase in the tempo of speech in stanza XXXVIII of the third chapter. I will explain why. First, the acceleration of the tempo of speech is clearly felt only in the last line of the stanza, while a substantively new action (the "flight" of Tatiana) begins in the sixth line («Татьянапрыгвдругиесени»). In other words, Tatiana is already running, and even "flying" («летит, летит…»), and Pushkin renders the description of this headlong displacement in the form of "slow," four-foot iambic lines in which every stress is realized. Recall that the fully stressed lines in stanza XXXVIII begin with the first and extend to the 8th line (1a—8a). Second, in the full text of the novel Eugene Onegin such"sharpening" of a stanza[25] occurs in 14 instances, and although one would have to be careful about making such a claim for stanza XXIV («ЗачтожвиновнееТатьяна?») in the third chapter, it would be completely inappropriate for stanza XII of the same chapter («Анынчевсеумывтумане»).  As regards the "dream flight" episode, only at the very beginning of stanza XIII is an acceleration in the tempo of speech evident: lines 1b—3b have a Tстркof four, three, and two stressed syllables, respectively (Tстрк=2 in line 3b: «Нооткосматоголакея»). One encounters no more lines with two stresses throughout the whole "dream flight" episode, and the ordinary alternation of lines in the novel having Tстрк=4 and Tстрк=3 offer no grounds for such a conclusion about the connection of this parameter with the emotional and thematic aspect of poetic narrative.


The Metaphysics of Space-Time in the Poetic Text


            The question of time (physical and psychological) is one of the philosophical concepts about which scholars and scientists have argued for many centuries, and which they continue to dispute to this day. An analysis of the various approaches to the notion of time as a philosophical concept does not fall within the purview of this study. A number of well-known claims, however, support my views on the matter of subjective time in the poetic text, and these are relevant to my argument in this paper.

            "If one studies time simultaneously with space," V.I. Vernadskij wrote, "the passage of time will inevitably be expressed in terms of vectors. This will not be a linear expression of time, as people sometimes say, but a vectoral expression of time. On a given line, between two and the same points, several vectors may be marked in directions that are analogous to them in their position in space-time."[26]  Time, as studied by physicists, and the subjective time of a human being, the scientist emphasized, differ from one another, insofar as "the transitory nature of life is experienced by us as duration, connected not only to intellectual processes, but to the fundamental life processes." If the measurement of time in physics is connected to motion and "based ultimately on the well-known idea of periodicity—the return of an object to its former state" (for example, astronomical time and the time on our watches), then "in this approach the direction of time is lost from view."[27] Thus, in contrast to physical time, subjective time is real and unambiguous, its perception is based on duration, and it is precisely this subjective time that has direction and is inevitably expressed in vectors.

            The words of P. Florensky encourage the application of these views to the study of the literary text: "When I approach a work of literature, unconsciously following its governing scheme, I project it as though according to an internal rhythm. A work is constructed in such a way that this transformation of the scheme into a rhythm occurs spontaneously. If it does not transpire, or until it transpires, the work remains incomprehensible. For the work, until it has been read and realized in time, is not a literary work for us."[28]

            The "scheme" of a poetic text, "projected" by the internal rhythm of the reader, is in my view analogous to the objective (objectified) psychological time within the framework of which the linear subjective time of every reader emerges, experienced by him as duration, which must therefore be characterized inevitably by different vectors. This difference in the perception of verse, or more specifically, this difference in addition to others, has long been known to literary scholars: "each person reads a poem in one's own way,"[29] but the "uniqueness of rhythm is much easier to catch than it is to explain, because esthetic perception is more intuitive than creativity is."[30]

            The obvious manifestation of objective space-time in the poetic text is the stanza—a localized, periodically recurring systemic or structural entity in a text, which imposes certain limitations on the very movement of poetic thought by means of a framework of fixed space-time. Needless to say, the stanza as an esthetic form is an analogue to physical time, enacted in art as "objectified" artistic or literary time, i.e. the kind of time that in Husserl's view "must necessarily…be experienced and grasped."[31]

            Subjective time is generated by rhythm as a relationship between elements in the progressive movement of a stream of speech: "Time determines the relationship of conceptions within our interiority, our inner state…it is a form of contemplation, and does not contain anything but relationships."[32] Nature (the biological system) did not provide living beings with any other means of perceiving and evaluating actual time, and for the human being this means is in no sense an exclusive invention insofar as it was passed down to him from his "animal ancestors" and is based on "mechanisms of so-called ‘anticipatory reflection'."[33]

            In examining two aspects of poetic speech—the aspect of generation and the aspect of perception of a work of art—we encounter in both of them two types of subjective time: that of the poet and that of the reader. If we endorse Belyj's contention that poetry is a "juncture linking time and space," and, at the same time, that it is a "bridge thrown across from space to time,"[34] the psychological picture becomes a great deal clearer. The artist's own subjective time is reflected through the prism of a particular artistic form and is fixed in a concrete literary fulfillment of this form. For the reader, this form appears as an external spatial-temporal scheme, projected by him during the act of reading, and allowing him through this activity, and only through it, to experience his own subjective time as duration.[35] "Movement that takes the form of the comprehension of time reigns in the world, and a notion or conception is a momentary photograph of this unbroken sequence of phenomena, this eternal motion.[36]

            A stanza of a poetic text is a measure of objective space-time of poetic speech; it is a form of limited and periodically renewed structural and systematic space-time, a form that provides the poet with the possibility of using one or another means of literary realization of esthetic thought. The stanza as a measure of objective artistic time establishes various, but always specific, spatial-temporal limitations for the development of poetic thought. In order to confirm this thesis, it is sufficient to recall the words of G.O. Vinokur, who wrote that Pushkin "thought in the stanzas"[37] of his novel, or to cite N. Gumilev: "After choosing an image, the poet is immediately faced with the question of its development and its proportions. Both of these determine the choice of the number of lines and stanzas…One stanza or another exerts greater influence on the poet's train of thought…even such simple stanzas as the quatrain or the couplet have their peculiarities, which the poet takes into account, albeit subconsciously."[38]

            Moreover, the stanza as a measure of objective time not only imposes certain limitations on the literary realization of the poet's thought, but also permits different variations on the structuring of its artistic space, i.e. it permits a varying architectonic organization of the text. Three variations of the stanzas of the Russian classical line with an identical number of syllables (42), but different poetic meter and a different number of lines to a stanza (four-line five-foot iamb with paired feminine-masculine rhyme; five-line four-foot iamb with aBaaB-rhyme; four-line asymmetrical meter 6464-iamb with paired masculine-feminine rhyme[39]). It is relevant to recall here that in poetry, according to Joseph Brodsky, "poetic meters are in and of themselves spiritual entities, and they have no equivalents. They cannot be substituted, even by one another, all the more by a line written in free verse. Non-correspondence of meters is non-coincidence in breathing and in the contracting of the heart muscle. Non-correspondence in the rhyme scheme is the non-coincidence of brain functions."[40]

            I repeat, for the reader periodic objective time is determined by the external architectonic parameters of the stanza: meter, number of lines, rhyme. Through its architectonic specificity, the stanza as the measure of movement of poetic thought has the unique capacity to translate the subjective space of the poet into the subjective space-time of the reader. This translation or transmission does not point to the literal coincidence of these kinds of time, but condition the maximum degree of proximity, imparted both as syllabic and as the metrical-structural specificity of the stanza. Possible objections, connected for example with various tempos of reading architectonically identical stanzas, are dispelled by the fact that in the reality of our perception, neither the subjective time of the poet, imparted to the reader in concrete material substance as objective time, nor the actual subjective time of the reader, both without each other, or one without the other, do not exist, and their distinction is only the means of scholarly analysis of the problem of artistic space-time. The goal of such analysis is to examine the distinctiveness (particularity) of objective and subjective artistic time and to establish the essence of their natural unity as a dynamic relationship, formally expressed as the "divine" proportion of rhythm. Recall that the latter operates with the same interdependent values as those that are also correlates of objective (the total number of syllables) and subjective (the number of stressed syllables) of time in the poem.

            I will formulate both general and practical conclusions in the following way.

            Subjective time (duration) with rich emotional content is based on rhythm, which is immanent and, at the same time, the latent qualitative and quantitative foundation of the verse. It is this foundation that, on the one hand, is discovered by the poet and conditionally fixed by him in the text, and on the other hand, it is the essential quality of the line that is revealed (or not revealed) by the reader during the process of his collaborative interpretation of the author's poetic world. It is this rhythm that must be found by the reader, which is "not given but guessed," for, according to A. Belyj, rhythm is that which "must be found."[41]

            The rhythm of the line, understood as the relationship between essential elements of poetic speech, forms in the reader an alternation of experiences or feelings that lies at the base of subjective time of the life virtually lived by him. If it is true that on the basis of what we read "we recreate images and their alternation,"[42] the rhythm of the text that is being read manifests itself by means of an anticipatory effect as an emotionally expressive portent of future events in the virtual temporal space of the poetic text.[43] It is precisely this quality of rhythm that may also serve as the foundation for recognizing the triadic formula "rhythm-form-content" as the central axiom of scholarship on verse.


Expression, Emotion, and Rhythm in Verse


In order to return to an analysis of concrete excerpts from Pushkin's novel, I will refer to Heidegger's notion that "the experience of ‘time' is the closest phenomenal aspect of ephemerality," the ephemerality of presence that creates "timing" or the "measurement of time" and engenders the "everyday, ordinary notion of time."[44] Mathematical analysis is capable exclusively of calculating moments of time, but the calculation itself, considered outside the esthetic essence of rhythm as relationship, is not productive for this study.

I will return to our original argument and examine the behavior of two parameters: indices of rhythmical and harmonic precision (RHP—РГТ) tand the coefficient of expressivity of the sense of rhythm (CE—Кэ), calculated as the rate of change of the value t(cf. Graphs 1-3, Dynamic Models of the Rhythm of Pushkin's Verse).

The behavior of parameter CE is particularly deserving of attention, in my view. The beginning of movement in the episode "flight wide-awake" (graph 2) is presented as a "positive" vector, establishing the amplifying tendency toward an increase in the rate of change of the value RHP. This positive tendency is revealed already before the appearance of Onegin on the porch of the Larin's home (which occurs in the beginning of stanza XXXVIII) and even earlier, in the fifth line of the previous stanza (XXXVII). At this key juncture of the narrative the negative tendency (cf. parameter CE in graph 2.) changes to a positive one.

The principle of this graph and the point of departure of the "negative" vector CE corresponds to the fourth line of the first quatrain of stanza XXXVI («Татьянаждет: когдажответ?»), and the next quatrain ends with the line «Ончто-тонассовсемзабыл» (second point of measurement). Here the sharp decline on the CE curve gives way to a small rise, a clear accompaniment of a burst of hope in the third quatrain («—Сегоднябытьонобещал…Давиднопочтазадержала»), and then the decline reasserts itself («Какбудтослышазлойукор») and is consummated at the end of the first quatrain of stanza XXXVII. The eight following lines of this stanza seem to give no reason for positive emotion (tea-drinking, Tatiana's thoughtfulness), but the vector of the CE curve, changing the sign to a positive one, demonstrating to us the growth, albeit not yet very noticeable, of the emotional component of the narrative. Rhythm, as I have already pointed out, is capable of anticipating emotion—this becomes amply apparent a bit later in the opening scene of Tatiana's "flight." The first eight lines of stanza XXXVIII indicate a sharp and prolonged rise of CE, reaching its maximum in line 8a «Летит, летит…»

            We observe another picture in the beginning of the "dream flight" (graph 3). The decline begins here still later, at the end of stanza XII, and ends in line 8b (cf. Table). This is followed by a sharp, brief incline (line 12b «Дорогинет; кусты, стремины»), and again a prolonged, gently sloping decline asserts itself, until line 26b («Одеждыкрайподнятьстыдится»). I would like to point out that the first "negative" vector begins in the text even earlier,[45] with the first line of stanza XII, «Какнадосаднуюразлуку», and extends for 22 lines altogether. The second negative vector extends for fourteen lines, which (with an extremely short four-line positive jump) is very expressive. It is just this short jump that increases the effect of extension of the emotionally fading activity that makes it possible, I reiterate, not only simply to extend the given episode, as such, but also to impart to it a minor expressive and semantic tone.

            Thus, long before the beginning of Tatiana's "dream flight" the expressiveness in verse falls—until it becomes clear that «Дорогинет.» At this crucial juncture of the verse a short, sharp jump is registered, and then the curve again descends, and only with the words «Онабежит…» does the vector of movement change direction and rise. Here, however, the deviation of the CE value is not as great as it was formerly, and it is significantly less than the analogous expressive jumps in the episode "flight wide-awake." Juxtaposing the CE graph to the text, it is possible to see the anticipatory effect of rhythm, insofar as the basis for the change in emotion and the glimpse of hope for a fortuitous ending of the meeting between Tatiana and the bear appear in the text only starting with the third quatrain of stanza XV: «ияркосветитсяокошко…Здесьмойкум, Погрейся  унегонемножко». But the negative vector of movement changed its sign into a positive one as many as twelve lines before, at the end of the previous stanza (graph 3), proving thereby what to the reader has become not so very "terrifying" long before he reads these words in the text itself of the fifth chapter.

            Thus, the CE curve in stanza XXXVIII of the third chapter is for the most part not a falling one, as in stanzas XIII and XIV of the fifth chapter, but a rising one, with one short, negative deviation in the third quatrain of this stanza (cf. graph 2). The same difference is evident in the CE average of 0.93 for the "flight" of Tatiana in the fifth chapter, and 1.62 for the "flight" episode in the third chapter of the novel. All of this provides some basis for generalization.


In Lieu of a Conclusion


The clear, graphic picture of the acceleration of subjective time in the episode "flight wide-awake," in contrast to the deceleration in the "dream flight" episode, confirms my assumption that the first excerpt engenders in the reader (or more specifically, is capable of engendering) a positive emotional attitude, and in the second, a negative one. This conclusion completely accords with the results of the literary analysis of the emotionally charged content of Pushkin's excerpts, as well as with scholarly findings in psychology.

Subjective time, perceived by the reader as duration, is represented in the form of vectors of parameter CE substituting one another—the rate of change of the value of the rhythmic and harmonic precision of verse. The general orientation of these vectors in the episodes of Tatiana's "flight wide-awake" and "dream flight" are clearly opposed to one another. In the first case, we observe a more and more headlong growth in the positive vector of change of the CE parameter against the background of a high level of rhythmic and harmonic precision of the verse (RHP). The second excerpt is formally presented as two long negative CE vectors, interrupted by just one short splash that serves to strengthen the general expression of continually fading expressiveness of movement. The very lowest level of rhythmic and harmonic precision of the verse from the beginning of the fifth chapter corresponds to this feeling. However, as becomes clear further in the text, the rhythmically emphasized hopelessness of what has occurred is not hopeless at all, and the rhythmic impulses later begin to give rise to hope for a better outcome of the "flight wide awake" episode.

The fact of the anticipatory effect of the rhythm as an emotional and expressive portent of future events is analogous to phenomena that are well established in nature, in which the preemptive, and therefore protective, actions of animals is a response to the anomalous rhythmic impulses that portend catastrophe.[46] Drawing such parallels is by no means so precipitate and unfounded as might first appear, for, as Kant wrote, nature dictates rules to art by means of genius,and, according to Marina Tsvetaeva, "art is the same thing as nature."[47]

Thus, the excerpts of Pushkin's novel, identical in their "semantic aureole," are actually very distant from one another in their "expressive aureole," and justifying this critical conclusion from the position of a unified rhythmo-semantics was possible only on the basis of the methodology and method of formalist esthetic prosody. I hope to lend this conclusion a more weighty axiomatic character in forthcoming studies. Here ends my attempt to "verify by the algebra of harmony" a poetic text. 






[1]Бонди С.М. О ритме // КОНТЕКСТ 1976: Литературно-теоретич. исследования. М. 1977. С. 122, 124.  Here аnd henceforth quotations are mine, unless otherwise indicated.

[2]"Content and rhythm," Andrej Belyj wrote, "coincide in the majority of cases. Rhythm breaks out spontaneously: it is a direct accompaniment to meaning."—See Белый А. О ритмическом жесте // Структура и семиотика художественного текста / Учен. записки Тартусского ун-та. Вып. 515. Тарту. 1981.  С. 139.

[3]БондиС. М.Оритме. С. 116.

[4]ЛеоновА.А.., ЛебедевВ.ИПсихологическиеособенностидеятельностикосмонавтов. М., 1971. С. 76.

[5]Цвейг С. Мария Стюарт. М., 1959. С. 20.

[6]The notion of "meter and meaning" is not applicable in the study of verse that is written in the most productive of Russian poetic meters, the four-foot iamb; on the statistical method, see below.

[7]For example: "Rhythm is the real alternation of stresses in verse…"—See ЖирмунскийВ.М. Теориястиха. М., 1975. С. 7.

[8]"Rhythm is the harmony of relationships" wrote A. Belyj in 1917. SeeБелыйА. Оритмическомжесте. С. 132. No less significant is the fact that in biomechanics "rhythm is the temporal  measure of relationship between segments of movement. It is determined by the comparative relationship of duration of segments of movement: ∆t1:∆t2:∆t3…"—See ДонскойД.Д., ЗациорскийВМ. Биомеханика. М., 1979. С. 25.

[9]The same holds true in medicine (the rhythm of the heart, the rhythm of the brain waves) and in biomechanics, in which the notion of "optimal" rhythm has been introduced, which allows for the achievement of the best results with the minimum expenditure of energy.—See КоробкоВ.И., КоробкоГ.Н.Золотаяпропорцияичеловек. М., 2002. С. 132-143; Донской Д.Д. Зациорский В.М. Биомеханика. С. 25.

[10]Жирмунский В. М. Теория стиха. С. 611.

[11]As quoted in: Арнольд В. И. Что такое математика? М., 2002. С. 7.

[12]Гаспаров М. Л. Метр и смысл. М., 1999. С.88.

[13]Виноградов В. В. О языке художественной литературы. М., 1959. С. 28.

[14]Русский ассоциативный словарь. Ред. Ю.Н. Караулов. Т. I., С. 186; Т. II.,  С. 732.

[15]Тарлинская М. Синтаксис строфы в «Евгении Онегине» (анализ по главам) // Philologica, T. 6, No. 14/16. М., 2001. С. 341. For the Structuralists to accept the fallacy of this claim would be to subject their own convictionсto devastating criticism, insofar as the postulate about the "independence" of rhythm in a line of verse validates, whatever the nature of the poetic text, the operation of the statistically average line of verse and the computation for that line of the average (of all the lines taken together) meaning of the syllable stresses.

[16]Belyj's fundamental conceptions are laid out in the works "An Attempt to Characterize the Russian Four-foot Iamb" and "Comparative Morphology of the Rhythm of Russian Lyric Verse in Iambic Dimeter," which together with the work "A.S. Pushkin's ‘Непойкрасавицапримне…': An Attempt at a Description" are included in Belyj's book Symbolism—SeeБелыйА. Символизм. М., 1910. С. 286-330; 331-395; 396-428.

[17]In the words of S.M. Bondi, "A. Belyj distinguishes in verse, on the one hand, poetic meter, and on the other, "symmetry in deviation from ‘meter,' which he calls ‘rhythm'…This ‘rhythm', i.e. regularity (‘symmetry,' ‘uniformity,' ‘unity') in deviation from ‘meter' A. Belyj and his disciples tried to establish with the help of mathematical calculations, graphs and statistical tables. As we see, the broad definition of the notion of ‘rhythm' becomes here extremely narrow and turns into a specific term, closely linked to a concrete prosodic (mistaken) theory."—See БондиС.М. Оритме. С. 113. It is significant that in his later works, Belyj rejected this position; his disciples, however, did not.

[18]Гаспаров М. Л. Записки и выписки. М., 2000. С. 315.

[19]Винокур Г. О. Филологические исследования. М., 1990. С. 163-164.

[20]Стахов А. П. Новая математика для живой природы: Гиперболические функции Фибоначчи и Люка.  Винница, 2003.

[21]Виноградов В. В. Стиль Пушкина. М., 1999. С. 424.

[22]Гроссман Л. П. Онегинская строфа // Гроссман Л. П. Собр. соч. В 4-х т. Т.I., М., 1928. С. 148.

[23]Томашевский Б. В. Пушкин. Работы разных лет. С. 365.

[24]Набоков В. В. Комментарий к роману А. С. Пушкина «Евгений Онегин». СПб., 1998. С. 339.

[25]"Sharpening" (заострение) of a stanza refers to the reduction in tonic length of the last two lines of a stanza: in this case the 13th line (Tстрк=3) and in the 14th line (Tстрк=2).—See ГринбаумО. Н. Гармониястрофическогоритмавэстетико-формальномизмерении. СПб., 2000. С. 92-93.

[26]Вернадский В. И. О жизненном (биологическом) времени // философские мысли натуралиста. М., 1988. С. 298. (Italics Vernadskij's.)

[27]Вернадский В. И. Проблема времени в современнй науке // философские мысли натуралиста. М., 1988. С. 296.

[28]Флоренский П. А. Анализ пространственности и времени в художественно-изобразительных произведениях. М., 1973. С. 117.

[29]Холшевников В. Е. Основы стиховедения. СПб., 1996. С. 149.

[30]Холшевников В. Е. Стиховедение и поэзии. Л., 1991. С. 147.

[31]Гуссерль Э. Феноменология внутреннего сознания времени. М., 1994. С. 76.

32Кант И. Сочинения в шести томах. Том 3. М., 1964. С. 136

[33]Анохин П. К. Опережающее отражение действительности// Вопросы философии. 1962. С. 87.

[34]Белый А. Формы искусства // А. Белый. Символизм как миропонимание. М., 1994. С. 91.

[35]For the sake of simplicity and specificity, we will use the terms "objective" and "subjective" time henceforth in the text.

[36]Белый А. Формы искусства. С. 93.

[37]Винокур Г. О. Слово и стих в «Евгении Онегине» // Винокур Г. О. Пушкин. М., 1941. С. 176.

[38]Гумилев Н. С. Письма о русской поэзии. М., 1990. С. 70, 72.

[39]Forexample, inPushkin'spoems«Там у леска, за ближнею долиной…», «П. А. Осиповой» и «На холмах Грузии…»,  respectively.

[40]Бродский И. А. Сын цивилизации // Сочинения Иосифа Бродского. Т. V. СПб., 1999. С. 104.

[41]Белый А. Ритм как диалектика и «Медный Всадник». М., 1929. С. 60.

[42]Белый Формы искусства. С. 92. КурсивА. Белого.

[43]"…prose sometimes emerges from the anticipated intonations and rhythms of future phrases; poetry almost always emerges in this way…"—See ВейдлеВ. В. Эмбриологияпоэзии. М., 2002.С. 84.

[44]Хайдеггер М. Бытие и время. М., 1997. С. 234-235.

[45]On the graph this point is not indicated; in comparison with the value CE=0.29 for the fourth line in stanza XII, the value of the same parameter in the last line of stanza XI is 12 times greater (CE=3.52).

[46]For example, witnesses recall that in 1960, on the eve of an earthquake in Agadir (Morocco), all the stray dogs fled the city (not only rats run from danger). Three years later the same thing happened in the city of Skopje (Yugoslavia)—fleeing dogs as harbingers of underground quakes of destructive orders of magnitude. History contains numerous examples of other such incidents, the most recent of which was the devastating tsunami in Southeast Asia. In ancient China, dogs were kept as heralds of natural disasters.

[47]Цветаева М. И. Искусство при свете совести // А.С. Пушкин: proetcontra. T. II. СПб., 2000. С. 89.




O. N. Grinbaum


Translated by Polly Gannon