A Statistical Theory of Language Translation Based on Communication Theory

Abstract

We propose the first statistical theory of language translation based on communication theory. The theory is based on New Testament translations from Greek to Latin and to other 35 modern languages. In a text translated into another language, all linguistic variables do numerically change. To study the chaotic data that emerge, we model any translation as a complex communication channel affected by "noise", studied according to Communication Theory applied for the first time to this channel. This theory deals with aspects of languages more complex than those currently considered in machine translations. The input language is the "signal", the output language is a "replica" of the input language, but largely perturbed by noise, indispensable, however, for conveying the meaning of the input language to its readers. We have defined a noise-to-signal power ratio and found that channels are differently affected by translation noise. Communication channels are also characterized by channel capacity. The translation of novels has more constraints than the New Testament translations. We propose a global readability formula for alphabetical languages, not available for most of them, and conclude with a general theory of language translation which shows that direct and reverse channels are not symmetric. The general theory can also be applied to channels of texts belonging to the same language both to study how texts of the same author may have changed over time, or to compare texts of different authors. In conclusion, a common underlying mathematical structure governing human textual/verbal communication channels seems to emerge. Language does not play the only role in translation; this role is shared with reader's reading ability and short-term memory capacity. Different versions of New Testament within the same language can even seem, mathematically, to belong to different languages. These conclusions are everlasting because valid also for ancient Roman and Greek readers. How to cite this paper: Matricciani, E.

Multiple Communication Channels in Literary Texts

“…This is a general feature of texts. For example, if we consider the regression line linking n S to n W in a reference text and that found in another text (e.g., written in the same language), it is possible to link n S of the first text to n S of the second text with another regression line without explicitly calculating its parameters (slope and correlation coefficient) from the samples, because the mathematical problem has the same structure of the theory developed in Section 11 of [2]. The theory, of course, does not consider the meaning of texts.…”

“…We can compare two texts by eliminating x, in other words, we compare the output variable y for the same number of the input variable x. In the example just mentioned, we can compare the number of sentences in two texts-for an equal number of words-by considering not only the average relationship Equation (1), but also the scattering of the data, measured by their correlation, Equation (2). We refer to this communication channel as the "sentences channel".…”

“…Regression lines, however, take care and describe only one aspect of the relationship, namely the average values-recall that average values, as those shown in Table 1, belong to the regression line-and do not show the other aspect of the relationship, namely the scattering of data, which may not be the same when two regression lines almost coincide. The theory of linguistic channels recalled in Section 2, on the contrary, by considering both slopes and correlation coefficients, provides a reliable tool for comparing two sets of data, each described by the linear relationship Equation ( 2), according, for example, to the signal-to-noise recalled in Section 2 or to Shannon channel capacity [2].…”

“…Because the two noise sources are disjoint and additive, the total noise-to-signal ratio of the channel connecting text k Y to text j Y , for a given stochastic variable, is given by [2]:…”

“…Notice that Equation ( 9) can be represented graphically [2]. Finally, the total signal-to-noise ratio is given by:…”