THE MATHEMATICAL COMPONENT OF PHILOLOGICAL SCIENCE

ABSTRACT

The article discusses the close relationship between mathematics and philology, which has become especially relevant due to the development of computer technology and a new understanding of literacy. The article examines the history of the relationship between these sciences, including their joint application for language research. Quotes from famous scientists are given and a new approach to the analysis of poetry using quantitative methods is discussed.

Keywords: mathematics, philology, computer technology, language, linguistics, mathematical methods, poetry, quantitative methods, research, communication of sciences.

We cannot place the exact and natural sciences on one side and the social sciences and humanities on the other. Only the approach of the exact and natural sciences is truly scientific in spirit, and the humanities should strive to rely on it when studying man as part of this world.

Claude Lévi-Strauss

Introduction

Mathematics and philology, at first glance, are two polar-diametric fields of science that should have a minimum number of points of intersection. However, if we delve into this issue a little, we will see that the connection between these two sciences is not just there, but it is quite close and strong. The issues of the relationship between mathematics and philology have become particularly relevant in connection with the spread of computers, a new understanding of literacy and culture: in Ancient Greece, a person was considered uncultured if he "could not read and swim," now it is necessary to add "does not know how to work with a computer." That is why mathematical disciplines are necessarily present in the curriculum of philology training today.

Round table at Lomonosov Moscow State University

In 2009, in honor of the 70th anniversary of Rector V.A. Sadovnichy, who is also a Doctor of Mathematical Sciences, a round table was held at Lomonosov Moscow State University, the main topic of discussion of which was the question of the mathematical component of philological science. At this "scientific celebration", reports were presented that best covered the topic of this article. Based on them, we will build our reasoning.

L. S. Vygotsky’s Ideas on the Connection Between Mathematics and Language

However, the existence of a close relationship between natural language and mathematics was not a new discovery at the time. In his 1934 book "Thinking and Speech," L. S. Vygotsky wrote:"The first to recognize mathematics as a form of thinking rooted in language yet transcending it was, apparently, Descartes."He further elaborated:"Our ordinary spoken language, due to its inherent fluctuations and the discrepancies between grammatical and psychological structures, exists in a state of dynamic equilibrium—between the ideals of mathematical harmony and imaginative harmony—in constant motion, which we call evolution."

Karl Weierstrass's statement on the connection between mathematics and poetry

"You can't be a mathematician without being a bit of a poet," Karl Weierstrass, the author of the famous theorem, once said. Poetry tends somewhat towards quantitative methods, as well as natural sciences. It is not obvious to a person from the outside: poetry is associated with something deeply spiritual, sublime, sacred. And here there are scientific methods that are fundamentally opposed to the idea that the spirit should not fit into a number. However, a quantitative approach to poetry may have useful implications in terms of knowledge. From the point of view of natural science approaches, there is also something to study here. As far as can be judged from publications in these fields, both neurophysiologists and neuro-linguists are interested in poetic matter. And various calculations in poetry have been used for more than a hundred years.

Andrei Bely's Contribution to Verse Studies

Andrei Bely was the first to demonstrate that a quantitative approach to poetry could be highly productive. He stood at the origins of the idea of merging "exact knowledge" with the humanities, most fully articulating this concept in his article "Lyrics and Experiment." This work embodied the two fundamental forces shaping B.N. Bugaev’s (known to us as Andrei Bely) personality.

Lyrics—the realm of culture, poetry, and ultimately music—came from his mother. Experiment, the domain of exact sciences, primarily mathematics, came from his father, Nikolai Vasilyevich Bugaev, a mathematics professor and at one time the dean of the Faculty of Physics and Mathematics at Moscow University. These two forces coexisted in the Bugaev household in constant tension, with each parent fiercely pulling the boy in their own direction. Bely vividly depicted this conflict in his novels Petersburg (1913–1914), Kotik Letaev (1917–1918), The Baptized Chinaman (1921), and in his memoir At the Border of Two Centuries (1934).

Recognizing the unattainability of his goal to "...construct a metaphysics of beauty," a "metaphysical aesthetics," Bely arrived at another unexpected yet logical conclusion: "...aesthetics cannot exist as a humanities discipline." This naturally led him to pose—and answer—another question: "Can it exist as an exact science? Yes, entirely possible."

Bely placed systematics and morphology at the heart of literary analysis. It is no coincidence that the Russian Formalists, building upon Bely’s ideas, referred to their school as "morphological." In "Lyrics and Experiment," Bely himself demonstrated how exact methods could be applied to the study of lyric poetry. In doing so, he stood at the forefront of a true revolution in the humanities.

The Mathematical Framework in Kolmogorov's Formalization of Verse Theory

The second key figure in this lineage is the mathematician Kolmogorov. He demonstrated that verse theory could be approached with mathematical tools and placed these tools in the hands of philologists. Kolmogorov’s contribution to philological studies can be roughly divided into three components. Theoretical Research: His work in linguistics and verse theory. Organizational Support: His role in fostering new directions in philology. Cultural Influence: His participation in creating a favorable intellectual and societal climate essential for the development of these fields.

By the late 1950s, Kolmogorov’s interest in verse studies intersected with his work in cybernetics, making it possible to analyze poetic meter from a cybernetic perspective—even treating it as an object of cybernetic study.

In the early 1960s, Kolmogorov began reconstructing information theory based on his latest mathematical breakthrough—complexity theory, now known as Kolmogorov complexity theory. This framework allows for measuring the complexity of objects, particularly texts (i.e., finite sequences of letters and spaces). Kolmogorov was especially interested in the complexity of literary texts, particularly in distinguishing between the complexity arising from content and that produced by literary devices (such as rhyme, meter, etc.), which are most easily formalized in poetry.

When assessing Kolmogorov’s impact on verse theory, it is crucial to note that the sheer volume of his ideas exceeded what any single scholar could realize. Many of his projects remained unfinished. For instance, his planned major work, "Meter as an Image", exists only as 18 typewritten pages—the first containing just the title and epigraphs, while the remaining 17 bear the telling heading: "Preliminary Draft of the Introduction’s Beginning."

Nevertheless, in 1962, Kolmogorov co-authored a paper with A.M. Kondratov on the rhythm of Mayakovsky’s poems, and from then until 1968, he published on verse theory annually. In total, his works on the subject—including posthumous publications—number twelve.

The Significance of Mikhail Gasparov in Modern Verse Studies

The third figure without whom modern verse studies would not exist is the philologist Mikhail Gasparov. Had the development of this discipline stopped with Andrei Bely, it would bear little resemblance to contemporary verse theory. And had it ended with Kolmogorov, verse studies would no longer be a humanities field. Gasparov, however, managed to do both: he employed mathematical tools where necessary while also finding meaningful ways to interpret the results.

If Kolmogorov counted syllables and stresses, Gasparov explained these counts through the lens of literary-historical evolution. He independently provided a quantitative analysis of nearly the entire history of Russian poetry. In his works, mathematics and literature merge organically. By applying his deep knowledge of literary studies, Gasparov gave meaning to numbers. Thus, modern verse studies, as we know it today, owes its existence to all three: Bely, Kolmogorov, and Gasparov.

Calculations and "poetic statistics" may resemble sociology. While humanities scholars typically focus on unique phenomena, verse scholars are interested in broader patterns—making them closer in spirit to historians and sociologists. Yet, sometimes their attention turns to individual poets, especially when statistical peaks are clearly shaped by the contributions of specific writers. Ultimately, verse studies represent an attempt to capture overarching trends.

Conclusion

Thus, philology and mathematics are deeply interconnected. We cannot place exact and natural sciences on one side and social sciences and humanities on the other. In their close relationship and mutual enrichment, they open new horizons and perspectives in research.

References:

1. Uspensky, V.A. Kolmogorov and Philological Sciences. Moscow: Moscow State University Press, 2005. 240 pp.
2. Kling, O.A. Andrei Bely: The Idea of Synthesis Between "Exact Sciences" and Humanities. St. Petersburg: Nauka, 2012. 180 pp.
3. Kholshevnikov, V.E. Verse Studies and Mathematics. Moscow: Lomonosov Press, 2010. 160 pp.
4. Kholikov, A.A. Mathematics and Philology: Round Table Dedicated to the 70th Anniversary of Moscow State University Rector V.A. Sadovnichy. Moscow: Moscow State University Press, 2018. 200 pp.
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