Linguistic Mathematical Relationships Saved or Lost in Translating Texts: Extension of the Statistical Theory of Translation and Its Application to the New Testament

Abstract

The purpose of the paper is to extend the general theory of translation to texts written in the same language and show some possible applications. The main result shows that the mutual mathematical relationships of texts in a language have been saved or lost in translating them into another language and consequently texts have been mathematically distorted. To make objective comparisons, we have defined a “likeness index”—based on probability and communication theory of noisy binary digital channels-and have shown that it can reveal similarities and differences of texts. We have applied the extended theory to the New Testament translations and have assessed how much the mutual mathematical relationships present in the original Greek texts have been saved or lost in 36 languages. To avoid the inaccuracy, due to the small sample size from which the input data (regression lines) are calculated, we have adopted a “renormalization” based on Monte Carlo simulations whose results we consider as “experimental”. In general, we have found that in many languages/translations the original linguistic relationships have been lost and texts mathematically distorted. The theory can be applied to texts translated by machines. Because the theory deals with linear regression lines, the concepts of signal-to-noise-ratio and likenss index can be applied any time a scientific/technical problem involves two or more linear regression lines, therefore it is not limited to linguistic variables but it is universal.

Multiple Communication Channels in Literary Texts

“…In recent papers [1] [2] [3], we have developed a general statistical theory on translation of literary texts, based on communication theory, which involves linguistic stochastic variables and communication channels suitable defined. For "translation" we mean not only the conversion of a text from one language to another-what is properly understood, of course, as translation-but also how some linguistic parameters of a text are related to those of another text in the same language.…”

“…Over time the interdisciplinary and specialization of the subject increased and theories and models have been imported from other disciplines [4] [5]. References [6]- [12] report results not based on mathematical analysis of texts, as we have done [1] [2] [3]. When a mathematical approach is used, as in References [13]- [25], most of these studies neither concern the aspects of Shannon's communication theory [26], nor the fundamental connection that some linguistic variables have with reader's reading ability and short-term memory capacity [1] [2] [3].…”

“…References [6]- [12] report results not based on mathematical analysis of texts, as we have done [1] [2] [3]. When a mathematical approach is used, as in References [13]- [25], most of these studies neither concern the aspects of Shannon's communication theory [26], nor the fundamental connection that some linguistic variables have with reader's reading ability and short-term memory capacity [1] [2] [3]. In fact, these studies are mainly concerned with automatic translations, not with a response of human readers.…”

“…To avoid this cost, it is necessary to develop mathematical algorithms which approximate human judgment [27]. The theory developed in [1] [2] [3] and the advances presented in the present paper can set some benchmarks for assessing translation quality. The variables considered in the theory are: Total number of words W, sentences S, interpunctions I; readability index for any alphabetical language G; number of words n W , sentences n S , and interpunctions n I per chapter (or any chosen subdivision of a literary text, large enough to provide reliable statistics, e.g.…”

“…The variables considered in the theory are: Total number of words W, sentences S, interpunctions I; readability index for any alphabetical language G; number of words n W , sentences n S , and interpunctions n I per chapter (or any chosen subdivision of a literary text, large enough to provide reliable statistics, e.g. few hundreds of words); number of characters per word C P , words per sentence P F , words per interpunctions I P (this parameter, called also "words interval", is linked to the short-term memory capacity of readers [1] [2] [3]), interpunctions per sentence M F (this parameter gives also the number of I P contained in a sentence).…”